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Development of tools and techniques for non-invasive microwave-induced hyperthermia treatment of breast and brain tumors

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DEVELOPMENT OF TOOLS A N D TECHNIQUES FOR NON-INVASIVE
MICROWAVE-INDUCED HYPERTHERMIA T R E A T M E N T OF B R E A S T
A N D BRAIN TUMORS
by
Earl Zastrow
A dissertation submitted in partial fulnllment of
the requirements for the degree of
Doctor of Philosophy
(Electrical Engineering)
at the
UNIVERSITY OF WISCONSIN-MADISON
2010
UMI Number: 3471127
All rights reserved
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UMI 3471127
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Development of tools and techniques for non-invasive
microwave-induced hyperthermia treatment of breast
and brain tumors
submitted to the Graduate School of the
University of Wisconsin-Madison
in partial fulfillment of the requirements for the
degree of Doctor of Philosophy
By
Earl Zastrow
Date of final oral examination:
August 24, 2010
Month and year degree to be awarded: December 2010
The dissertation is approved by the following members of the Final Oral Committee:
Susan C. Hagness, Professor, Electrical and Computer Engineering
Barry D. Van Veen, Professor, Electrical and Computer Engineering
Joshua E. Medow, Assistant Professor, Neurological Surgery
Daniel W. van der Weide, Professor, Electrical and Computer Engineering
John H. Booske, Professor, Electrical and Computer Engineering
1
ACKNOWLEDGMENTS
First and foremost, I would like to express my sincere gratitude to my research advisors,
Profs. Susan Hagness and Barry Van Veen for their extraordinary support and guidance
through out the course of this research. Their vision, consistently high standards, and their
meticulous attention to detail will stay with me through out my professional career.
Footnotes are included at the start of each chapter to acknowledge the collaborative
effort and the source of funding. In addition to the acknowledgement in the footnotes, I
gratefully acknowledge Dr. Joshua Medow for his insightful suggestions towards the clinical
directions and his endless passion for this research. Drs. Essex Bond and Shakti Davis
for graciously sharing their expertise and their extensive involvement that help move this
research forward. It was my pleasure to have also collaborated with: Matthew Burfeindt, Dr.
Panogiotis Kosmas, Dr. Mariya Lazebnik, Al Mashal, and Henri Tandradinata in several
research projects. I look forward to future collaboration with any of them.
I am incredibly grateful to my graduate student peers for their friendship and their compassion during trying times, especially Keely Willis for also enduring hours of brainstorming
with me. Also, I acknowledge Tony Hammond for keeping our computer cluster up and running making this computational research possible. I am grateful to my mother, Wilai, for
her unconditional support and belief in me, as well as my brother and sister, Arty and Anne,
for their love and encouragement. And last but certainly not least, I am forever grateful to
my friend and husband, Elliott, for his love, encouragement, and infinite patience through
the years of my graduate study.
11
TABLE OF C O N T E N T S
Page
LIST OF TABLES
vi
LIST OF FIGURES
vii
ABSTRACT
xvi
1
Introduction
1.1
1.2
1.3
2
1
Hyperthermia in oncology
1
1.1.1 Cell death by hyperthermia
1
1.1.2 Adjuvant hyperthermia therapy
3
Existing non-invasive technologies for inducing local, deep-seated hyperthermia 6
Overview of contributions
7
1.3.1 Computational tools for simulating microwave-induced hyperthermia
treatments
7
1.3.2 Computational study of non-invasive focused microwave hyperthermia
treatment of localized breast tumors
9
1.3.3 Computational study of non-invasive microwave-induced hyperthermia
treatment of localized brain tumors
10
1.3.4 Time-multiplexed beamforming for non-invasive microwave hyperthermia treatment
12
Computational codes for simulating multi-physics interactions in hyperthermia treatments
14
2.1 Electromagnetic (EM) simulations
2.1.1 Dielectric properties of biological tissue
2.1.2 Heating potential calculation
2.2 Thermal simulations
2.3 Parallel computing
15
15
16
18
19
Ill
Page
3
Development of anatomically realistic numerical breast phantoms with
accurate dielectric properties for modeling microwave interactions with
the human breast
3.1
3.2
3.3
3.4
4
2-D computational study of time reversal techniques for ultra-wideband
microwave hyperthermia treatment of breast cancer
4.1
4.2
4.3
4.4
4.5
5
Introduction
Methodology
4.2.1 TR hyperthermia in dispersive media
4.2.2 Relation to beamforming
Numerical testbeds
Results
Conclusions
3-D computational study of non-invasive patient-specific microwave hyperthermia treatment of breast cancer
5.1
5.2
22
24
24
28
36
38
43
44
45
45
46
47
48
51
56
Introduction
Models and methods
5.2.1 Numerical testbeds
5.2.2 Beamformer design
5.2.3 Performance evaluation methods
Results
5.3.1 Performance as a function of operating frequency
5.3.2 Performance as a function of propagation model complexity
Discussion
Summary and conclusions
Enhanced microwave hyperthermia treatment via CNT contrast agent . . . .
57
59
59
63
64
67
68
71
80
81
82
Preliminary computational study of non-invasive microwave hyperthermia treatment of brain tumors via transmit beamforming array
85
5.3
5.4
5.5
5.6
6
Introduction
Method for developing a numerical breast phantom
3.2.1 MRI processing and structural development
3.2.2 Dielectric properties mapping
Examples
Summary
21
IV
Page
6.1
7
Non-invasive microwave hyperthermia using canonical head phantoms . . . .
6.1.1 Continuous current distribution
6.1.2 Discrete current sources distribution
6.1.3 Conclusions
85
86
88
94
3-D computational study of non-invasive patient-specific microwave hyperthermia treatment of brain cancer
95
7.1
7.2
7.3
7.4
8
Time-multiplexed beamforming for non-invasive microwave hyperthermia treatment
8.1
8.2
8.3
8.4
8.5
9
Introduction
Models and methods
7.2.1 Numerical testbeds
7.2.2 Beamformer design
7.2.3 Performance evaluation
Results and Discussion
Conclusion and future work
Introduction
Modeling and design tools
8.2.1 Testbed
8.2.2 Electromagnetic and thermal simulation tools
8.2.3 Focused transmit beamforming
Time-multiplexing design procedure
8.3.1 Identify at-risk regions associated with target location
8.3.2 Assign spherical suppression volumes to cover the at-risk regions in
the head
8.3.3 Design beamformers
8.3.4 Calculate time duration of each beamformer to form a sequence . . .
Results and discussion
8.4.1 Time-multiplexing design example
8.4.2 Time-multiplexed beamforming performance
Summary
Summary and future directions
LIST OF REFERENCES
APPENDICES
95
97
97
98
99
100
101
106
107
109
109
110
Ill
112
113
113
114
115
116
117
118
125
128
132
V
Page
Appendix A: Safety assessment of breast cancer detection via ultrawideband microwave radar
Appendix B: Implementation of a 3D microwave imaging system for granular materials research
143
153
VI
LIST OF TABLES
Table
2.1
Page
Summary of the parameters associated with single-pole Debye dispersion of the
dispersive dielectric properties of tissues in the head
17
2.2
Summary of the thermal properties of the tissues in the head
20
3.1
Single-pole Cole-Cole parameters for the eight wideband dielectric properties
curves
36
Single-pole Debye parameters (3-10 GHz) for the eight wideband dielectric properties curves
39
Microwave power deposition metrics for the Q distributions of Figures 4.2, 4.3
and 4.4. (S: area outside focal region with Q > ?3 dB, as a percentage of the
total breast area. Pf power absorbed inside focal region as a percentage of the
total power absorbed in the breast.)
50
Percentage of breast area above 42癈, 41癈 and 40 癈 for the profiles of Figure
4.5
51
5.1
Thermal properties used in the FDTD-thermal model
67
5.2
Selective heating efficacy quantified in terms of four thermal metrics evaluated
for a numerical phantom with homogeneous breast tissue. Homogeneous propagation models are used in the wideband beamformer design. The performance
is evaluated as a function of dielectric properties mismatch with respect to the
true properties of the breast. A negative (positive) percentage mismatch refers
to the case in which the propagation model underestimates (overestimates) the
dielectric properties
78
3.2
4.1
4.2
8.1
Hyperthermia performance metrics (defined in Section 8.4) for the conventional
beamforming with no-suppression beamformer and the proposed time-multiplexed
beamforming for targets in the thalamus, parietal lobe, and frontal lobe
126
Vll
LIST OF FIGURES
Figure
1.1
Page
(a) Survival rate of Chinese hamster ovary cells (CHO-lOB cell) heated over a
range of temperatures, (b) Survival rate of human melanoma cells (HTB-66)
heated over similar range of temperatures (Reprinted from Figure 1 of [1] with
permission from Elsevier. �91 Elsevier.)
2
Arrhenius plots for a series of rodent and human cell lines derived from Figure 1.1.
(Reprinted from Figure 2 of [1] with permission from Elsevier. �91 Elsevier.)
3
Hyperthermia treatment overview. (Reprinted from Figure 1 of [2] with permission from Informa Healthcare. �05 Informa healthcare.)
5
Implementation work flow for simulating the performance of non-invasive microwave hyperthermia techniques
14
Location of Q at each spatial location (i,j, k) with respect to the six electric field
vector components
18
2.3
(a) Original computational grid (b) Sub-domains for parallel computing
19
3.1
A coronal slice from a 3D MRI of the breast (a) before, and (b) after homomorphic
filtering is applied to reduce the slowly varying gradient artifact. The color bars
represent MRI voxel intensity before and after
filtering
25
Breast segmentation masks which result from traversing the coronal slice shown
in Figure 3.1(b) from (a) left to right, (b) right to left, (c) top to bottom and,
(d) bottom to top. (e) The resulting coronal composite mask and its best-fit
ellipse. White and gray areas represent matrix elements that are set to 0 and 1,
respectively
27
1.2
1.3
2.1
2.2
3.2
3.3
Illustration of a 3D anatomical breast model created from a 3D MRI. (a) Smooth
3D surface of the breast formed by stacking the best-fit ellipses from each coronal
slice, (b) Coronal view of the 3D anatomical model, (c) Sagittal view of the 3D
anatomical model. In (b) and (c) the skin layer is identified by the black contour. 28
Vlll
Figure
Page
3.4
A representative piecewise-linear map illustrating the linear mapping between
seven intervals along the MRI voxel intensity axis (Igi, Ig2, hrans, Ifi, If 2, If 3)
and seven intervals along the dielectric properties axis (Pgi, Pg2, Ptrans, Pfi, Pf2,
P / 3 ) . The MRI in this example is of a patient with extremely dense breast tissue. 30
3.5
(a) Histogram of MRI voxel intensities for a patient with extremely dense breast
tissue, and the composite two-component GMM of the histogram, (b) The two
individual components of the GMM corresponding to fatty tissue (dashed) and
glandular/fibroconnective tissue (solid). Each component is labeled with its
GMM parameters. The eight piecewise-linear mapping parameters are indicated
along the MRI voxel intensity axis (top edge)
31
(a) Histogram of MRI voxel intensities for a patient with almost entirely fat
breast tissue, and the composite two-component GMM of the histogram, (b)
The two individual components of the GMM are shown with dashed and solid
lines. Each component is labeled with its GMM parameters. The eight piecewiselinear mapping parameters are indicated along the MRI voxel intensity axis (top
edge)
32
(a) Wideband dielectric constant and (b) effective conductivity curves that define
the bounds on seven ranges of dielectric properties. The range labels (Pgi, P92,
Pg3, Ptrans, Pfii Pf2i a n d Pfz) correspond to seven tissue categories. The two dotted curves represent the maximum and minimum tissue properties. The two solid
curves represent the median properties of predominantly glandular/fibroconnective
tissue and predominantly fatty tissue. The two pairs of dashed curves represent
the 25 t h and 75 t h percentile properties for predominantly glandular/fibroconnective
tissue and predominantly fatty tissue. The Cole-Cole parameters for these eight
curves are given in Table 3.1
35
Sagittal cross-sections showing MRI voxel intensity for patients with (a) almost
entirely fat breast tissue (ACR I) and (b) scattered fibroglandular breast tissue (ACR II), with the corresponding cross-sections of the 3D numerical breast
phantoms showing the dielectric constant at 6 GHz. The two phantoms in (c)
and (d) (shown in color) were derived from (a) and (b) respectively, using the
GMM-based piecewise-linear mapping scheme proposed in this paper. The two
phantoms in (e) and (f) (shown in color) were derived from (a) and (b) using a
uniform mapping scheme
40
3.6
3.7
3.8
IX
Figure
3.9
4.1
4.2
4.3
4.4
4.5
Page
Sagittal cross-sections showing MRI voxel intensity for patients with (a) heterogeneously dense breast tissue (ACR III), and (b) extremely dense breast tissue
(ACR IV), with the corresponding cross-sections of the 3D numerical breast
phantoms showing the dielectric constant at 6 GHz. The phantoms in (c) and
(d) (shown in color) were derived from (a) and (b), respectively, using the GMMbased piecewise-linear mapping scheme proposed in this paper
41
Dielectric constants at 6 GHz for the two numerical breast phantoms considered
in this study. The antenna array elements and tumor locations (stated in Section
3) are marked with crosses (original figure in color)
47
Effect of applying dispersive loss compensation to the T R inputs of the hyperthermia experiment involving (a),(b) homogeneous and (c),(d) heterogeneous
versions of the second breast phantom. All four images show power density
distributions (Q) in dB. On the left (right), Q is calculated without (with) compensation applied to signals computed from a propagation model matched to the
homogeneous phantom. -3 dB contour plots are shown with black lines (original
figure in color)
53
T R (left) and STTB (right) power density distributions (Q) in dB for the scattered fibroglandular phantom. The T R and STTB weights are designed using
(a),(b) the exact propagation model, and (c),(d) a homogeneous propagation
model. -3 dB contour plots are shown with black lines (original figure in color).
54
T R (left) and STTB (right) power density distributions (Q) in dB for the heterogeneously dense phantom. The T R and STTB weights are designed using (a),(b)
the exact propagation model, and (c),(d) a homogeneous propagation model. -3
dB contour plots are shown with black lines (original figure in color)
54
Temperature profiles resulting from the T R power deposition patterns for: (a)
the scattered fibroglandular phantom and an exact propagation model, (b) the
heterogeneously dense phantom and a exact propagation model, (c) the scattered
fibroglandular phantom and a homogeneous propagation model, and (d) the heterogeneously dense phantom and a homogeneous propagation model (original
figure in color)
55
X
Figure
5.1
5.2
5.3
5.4
5.5
5.6
Page
Cutaway view showing the relative permittivity distribution at 5 GHz in each of
four 3-D numerical breast phantoms used as performance testbeds. The desired
focus is indicated by a cross-hair and the 24 antenna locations are marked by
small circles. The phantoms are representative of all four categories of breast
tissue density, (a) Fatty, (b) Scattered fibroglandular. (c) Heterogeneously
dense, (d) Extremely dense. (Original figures in colour)
61
Relative permittivity distribution in the coronal cross-section containing the desired focus (indicated by a cross-hair) in each of the phantoms of Figure 5.1. The
antenna locations at elevation x = xj (noted in the upper right corner of each
image) are indicated by 'o' markers, (a) Fatty, (b) Scattered fibroglandular. (c)
Heterogeneously dense, (d) Extremely dense
62
(a) Relative permittivity as a function of frequency for representative voxels in
the heterogeneous propagation model, (b) Effective conductivity as a function
of frequency corresponding to the data shown in (a), (c) Relative permittivity as a function of requency in the homogeneous-low, homogeneous-high, and
homogeneous-average propagation models, (d) Effective conductivity as a function of frequency corresponding to the data shown in (c). (Original figures in
colour)
65
Selective heating efficacy quantified in terms of four thermal metrics for the four
virtual patients, as a function of frequency. Results are shown for the case where
a heterogeneous propagation model is used to design the transmit signal set. (a)
Volume of breast tissue with temperature greater than 43癈. (b) Distance from
the desired focus to peak breast interior temperature, (c) Peak skin temperature
(癈). (d) Peak breast interior temperature (癈)
70
Normalized EM heating potential (coronal cross-section) resulting from narrowband focusing at different operating frequencies, for a patient with fatty breast
composition (see Figures 5.1(a) and 5.2(a)). Results are shown for the case
where a heterogeneous (exact) propagation model is used in the beamformer design. The contour lines indicate -10 dB contours, (a) 1 GHz. (b) 2 GHz. (c) 3
GHz. (d) 4 GHz
72
Steady-state temperature distribution (coronal cross-section) corresponding to
the heating potential of the fatty breast shown in Figure 5.5. (a) 1 GHz. (b) 2
GHz. (c) 3 GHz. (d) 4 GHz
73
XI
Figure
57
Page
Normalized EM heating potential (coronal cross-section) resulting from narrowband focusing at different opeiatmg frequencies, for a patient with exticmely
dense breast composition (see Figures 5 1(d) and 5 2(d)) Results are shown for
the case where a heterogeneous (exact) propagation model is used m the beamformer design The contour lines indicate -10 dB contours (a) 1 GHz (b) 2
GHz (c) 3 GHz (d) 4 GHz
74
Steady-state temperature distribution (coronal cross-section) corresponding to
the heating potential of the extremely dense breast shown m Figure 5 7 (a) 1
GHz (b) 2 GHz (c) 3 GHz (d) 4 GHz
75
Comparison of steady-state temperature distributions (coronal cross-section) resulting from wideband focusing and narrowband focusing at the optimum frequency Results are shown for the case where the heterogeneous (exact) propagation model is used m the beamformer design (a) wideband (fatty)
(b)
optimum narrowband (fatty, 3 0 GHz) (c) wideband (extremely dense) (d)
optimum narrowband (extremely dense, 1 5 GHz)
76
5 10 The best achievable selective heating efficacy of narrowband operation quantified
m terms of four thermal metrics for the four patients (fatty, scattered fibroglandular, heterogeneously dense, extremely dense), as a function of propagation
model complexity used m the beamformer design (heterogeneous, homogeneousaverage, homogeneous-low, homogeneous-high) The results are shown at the
optimal narrowband frequency of each paring of patient and propagation model
(a) Volume of breast tissue with temperature greater than 43癈 (b) Distance
from the desired focus to peak breast interior temperature (c) Peak skm temperature (癈) (d) Peak breast interior temperature (癈)
77
5 11 Selective heating efficacy of wideband operation quantified in terms of four thermal metrics for the four patients (fatty, scattered fibroglandular, heterogeneously
dense, extremely dense), as a function of propagation model complexity used m
the beamformer design (heterogeneous, homogeneous-average, homogeneous-low,
homogeneous-high) The results are shown for each paring of patient and propagation model (a) Volume of breast tissue with temperature greater than 43癈
(b) Distance from the desired focus to peak breast interior temperature (c) Peak
skm temperature (癈) (d) Peak breast interior temperature (癈)
79
58
59
Xll
Figure
Page
5.12 Sagittal view through the target location of the heating potential [W/m3] for
an extremely dense numerical breast phantom. Two treatment scenarios are
compared, (a) The tumor is targeted with CNTs. (b) The tumor is not targeted
with CNTs
84
5.13 Differential steady-state temperature distribution resulting from the difference in
heating potentials obtained from hyperthermia treatment with and without the
use of CNTs. The steady-state temperature distributions for the two scenarios
are calculated assuming the same input power coupled into the breast volume
(9.6 Watts). Heating enhancement within the tumor is achieved with the use of
CNTs
84
6.1
6.2
6.3
6.4
6.5
6.6
z-directed current on the surface of a sphere. (Reprinted from Figure 1 of [3]
with kind permission from IEEE. �87 IEEE.)
86
Dissipated power in a volume of grey matter as a function of distance from the
center of the volume for operating frequencies of 100 MHz, 433 MHz, 915 MHz,
2 GHz, 2.45 GHz, and 5 GHz
88
Construction of spherical geodesic grids. Examples of source locations are indicated by red circle markers, (a) Icosahedron. (b) New vertices obtained by
bisecting the edges of the icosahedron. (c) The new vertices projected out onto
the sphere
90
Spherical geodesic grid of different resolutions S. N source locations are colocated with the N vertices of the grid where z > 0. The iV source locations are
indicated by red "o" markers, (a) S = 12 (N = 6), (b) S = 42 (N = 26), and
(c) S = 162 (N = 91)
90
Dissipated power inside a volume of grey matter on the z = 0 plane at the
operating frequency of 915 MHz for N source locations co-located with the N
vertices of the geodesic grid where z > 0. The grid is circumscribed inside a 12
cm sphere indicated by the dash-dotted line. The average head radius of 8 cm is
indicated by the dashed line, (a) TV = 6, (b) N = 26, and (c) N = 91
91
Dissipated power inside a volume of grey matter on the z = 0 plane at the
operating frequency of 2.45 GHz for N source locations co-located with the iV
vertices of the geodesic grid where z > 0. The grid is circumscribed inside a 12
cm sphere indicated by the dash-dotted line. The average head radius of 8 cm is
indicated by the dashed line, (a) N = 6, (b) iV = 26, and (c) N = 91
92
Xlll
Figure
6.7
6.8
7.1
7.2
7.3
7.4
7.5
8.1
Page
Source configurations. The source locations are on the surface of a 12 cm-radius
sphere, (a) Sources are placed on three concentric rings (N ? 24). (b) Sources
are placed on the vertices of a geodesic grid (N = 26)
92
Dissipated power inside a volume of grey matter on the xy-pla,ne (top) xz-pla,ne
(middle), and yz-plane (bottom), at the operating frequency of 915 MHz. The
source locations follow the cases illustrated in Figure 6.7(a) (left) and Figure
6.7(b) (right). The dash-dotted line indicates the 12 cm-radius spherical surface
where the source locations are. The dashed line indicates the average head radius
of 8 cm
93
Computational domain containing each virtual patient and the associated antenna array considered in the study. The array elements are represented by red
triangle markers, (a) Adult male patient, (b) 6-year-old male patient
98
Steady-state temperature distribution for the target location in the thalamus
through the three principle planes. 40癈 contours are indicated by dash lines
and 42癈 contours by solid lines. (a),(c),(e) Adult male patient (left column).
(b),(d),(f) 6-year-old male patient (right column)
102
Steady-state temperature distribution for the target location in the parietal lobe
through the three principle planes. 40癈 contours are indicated by dash lines
and 42癈 contours by solid lines. (a),(c),(e) Adult male patient (left column).
(b),(d),(f) 6-year-old male patient (right column)
103
Steady-state temperature distribution for the target location in the frontal lobe
through the three principle planes. 40癈 contours are indicated by dash lines
and 42癈 contours by solid lines. (a),(c),(e) Adult male patient (left column).
(b),(d),(f) 6-year-old male patient (right column)
104
Steady-state temperature distribution for the target location in the frontal lobe
through the axial plane of the adult male patient before and after channel weights
adjustment. 40癈 contours are indicated by dash lines and 42癈 contours by solid
lines
105
Numerical model of an adult female head (Ella model, Virtual Family, IT'IS
Foundation) surrounded by an array of 134 small current sources. The locations
of the sources are marked by the white circles. The orthogonal cuts show the
interior dielectric properties at 1 GHz. (a) Relative permittivity, (b) Effective
conductivity (S/m)
110
XIV
Figure
8.2
8.3
8.4
8.5
8.6
8.7
Page
Illustration of the recursive spherical suppression volume assignment process.
Rectangles depict at-risk regions, shaded circles depict suppression volumes, and
'x' denotes the location of the peak temperature within each at-risk region, (a)
Three suppression volumes are centered on the locations of peak temperature
in each at-risk region, (b) Two at-risk regions remain after removing portions
covered by suppression volumes identified in (a). Two additional suppression
volumes are centered at the peak temperature location in each residual at-risk
region. All at-risk regions are now covered by suppression volumes
114
At-risk regions and spherical local suppression volumes associated with the first
target location, (a) Steady-state temperature profile that is used to identify atrisk regions in the head volume, in an axial cut through the target location (z
= 170 mm). The temperature at 17 (marked by crosshairs) is driven to 43.5癈.
The at-risk regions (> 41癈) are enclosed by black solid lines. The boundaries
of spherical local suppression volumes are shown as black dashed lines. Black
dotted lines depict the treatment and brain volume contours, (b) 3-D view of
spherical local suppression volumes (red) and at-risk region volumes (green). . .
119
Effective conductivity at 1 GHz in an axial cut through the first target location
in the thalamus at 17 = (150,175,170) mm (marked by crosshairs). The second
target location in the parietal lobe at 17 = (170,170,170) mm is also shown
(marked by 'o' marker)
119
Example heating potentials for the first target location. The heating potentials are shown for axial cuts through the target location (z = 170 mm). The
boundary of the local suppression volume is shown as a dashed line in (a) (c). (a) Local-suppression beamformer 1. (b) Local-suppression beamformer 4.
(c) Local-suppression beamformer 11. (d) Combined-suppression beamformer
(beamformer 13)
120
Heating potentials obtained with whole-head-suppression and no-suppression design criteria for the first target location, shown for axial cuts through the target
location (z = 170 mm), (a) Whole-head-suppression beamformer (beamformer
14). (b) No-suppression beamformer (beamformer 15)
121
Beamformer sequence for the first target location. The shaded bars indicate the
duration of the corresponding beamformers. Note that beamformers 2, 5, 6, 8,
10, 12, 14, and 15 are not used
121
XV
Figure
88
Page
Steady-state temperature profile m the orthogonal cuts through the location of
the peak temperature m Vt (maiked by ciosshaus) for the first target location in
the thalamus at 17 = (150,175,170) mm The peak temperature m Vt is driven to
43�1癈 (a) Temperature profile (axial cut) obtained from conventional beamformmg with the no-suppression beamformer
(b) Temperature profile (axial
cut) obtained from conventional beamformmg with the whole-head-suppression
beamformer (c) Tempeiature profile (axial cut) obtained via time-multiplexing
of all candidate beamformers with equal duration (d)-(f) Temperature piofiles
obtained via the proposed time-multiplexed beamformmg method The sequence
illustrated m Figure 8 7 is used m time multiplexing (d) Axial cut (e) Sagittal
cut (f) Coronal cut
123
Steady-state temperature profile m the axial cut through the location of the peak
temperature m Vt (marked by crosshairs) for the second target location m the
parietal lobe at 17 = (170,170,170) m m The peak temperature m Vt is driven
to 43�1癈 (a) Temperature profile obtained from conventional beamformmg
with no-suppression beamformer (b) Temperature profile obtained from timemultiplexed beamformmg, using the designed sequence for this target location
124
8 10 Effective conductivity at 1 GHz m an axial cut through the location of the peak
temperature m Vt (marked by crosshairs) for the third target located m the
frontal lobe at 17 (150,125,180) mm
125
8 11 Steady-state temperature profile m the axial cut through the location of the
peak temperature m Vt (marked by crosshairs) for the third target location m
the frontal lobe at 17 (150,125,180) mm The peak temperature m Vt is driven
to 43�1癈 (a) Temperatuie profile obtamed fiom conventional beamfoimmg
with no-suppression beamformer (b) Temperature profile obtained from timemultiplexed beamformmg, using the designed sequence for this target location
127
89
XVI
ABSTRACT
Microwave-induced hyperthermia treatment is a suitable modality for the treatment of localized breast tumors due to the breast's limited vasculature and the centimeter-size treatment
resolution achievable by microwave techniques. We establish the sensitivity and robustness
of microwave beamforming for non-invasive breast hyperthermia treatment. Patient-specific
microwave propagation characteristics are used in the beamfoimer design. We develop highfidelity MRI-derived numerical breast phantoms as our virtual patients and numerically
simulate hyperthermia treatments. We demonstrate the capability of non-invasively treating
a centimeter-size region in breasts of varying density. Moreover, the method is demonstrated
to be robust to mismatch between the actual and assumed patient-specific information.
The feasibility of microwave-induced hyperthermia for non-invasive treatment of brain cancer is evaluated in a computational study using numerical simulations based on MRI-derived
numerical head phantoms of virtual patients. The human head presents greater challenges
than the breast and the conventional beamforming method is shown to have limitations for
brain cancer treatment. Unintended hot spots occur in some virtual patients because the
cerebrospinal fluid (CSF) exhibits an effective conductivity that greatly exceeds that of any
other tissue in the brain. We address this challenge by implementing a time-multiplexed
beamforming strategy t h a t is based on sequential applications of multiple beamformer designs. Each design emphasizes the reduction of microwave absorption in a different region of
the head. We hypothesize that switching through beamformers with different beam patterns
XVII
over time will reduce or eliminate auxiliary hot spots. The proposed technique is tested in a
computational study using an adult head phantom with a large volume of CSF as a test bed.
We show that this technique results in fewer unintended hot spots compared to conventional
beamforming.
1
Chapter 1
Introduction
1.1
Hyperthermia in oncology
The clinical application of hyperthermia in oncology involves elevating the temperature at the
tumor location to 39-45癈 for a certain amount of time. For low-temperature hyperthermia,
the treatment region is elevated up to a temperature of 39-41癈 for durations of up to 72
hours. For moderate-temperature hyperthermia, the treatment region is elevated to 41-45癈,
typically for 30-60 minutes [2]. Hyperthermia causes cytotoxicity due to many factors such
as the increase in the rate of metabolic reactions, protein denaturation , and direct heat
damage, (see, for example, [4,5]). Clinical studies also found hyperthermia to increase the
sensitivity of cancer cells to radiation therapy and chemotherapy (see, for example, [5-9]).
An overview of the cellular effects of hyperthermia is given below.
1.1.1
Cell death by hyperthermia
The rate of cell death during hyperthermic exposure is dependent on the time and temperature of exposure. Figure 1.1 illustrates the time-temperature relationship to the rate of cell
death for two families of cells. It describes the following important characteristics of thermal
therapy:
1. The rate of killing depends on the temperature of exposure. For example, there is very
little killing of the CHO-10B cell when heated at 42� C for 5 hours whereas the amount
of killing increases by three orders of magnitude when heated at 42.5癈 for the same
duration.
2
(a)
(b)
Figure 1.1 (a) Survival rate of Chinese hamster ovary cells (CHO-10B cell) heated over a
range of temperatures, (b) Survival rate of human melanoma cells (HTB-66) heated over
similar range of temperatures (Reprinted from Figure 1 of [1] with permission from
Elsevier. �91 Elsevier.)
2. Each cell type develops resistance to heating after a certain period of heating. The
thermal resistance is indicated by the change in the slope of the curves. The CHO-10B
cell shows the reduction in the slope after 4 hours of heating at 42.5癈 and the HTB-66
cell shows the reduction in the slope after 3 hours of heating at either 42.5 and 43癈.
3. The thermosensitivity varies between cell type. It can be observed that CHO-10B cell
is more sensitive to heat than HTB-66. For 5 hours of heating at 42.5癈, the surviving
fraction of CHO-10B cell is 0.001 while for the HTB-66 cell, the surviving fraction is
around 0.03.
The temperature of 43癈 has been widely used as a therapeutic temperature at which thermal
damage starts to occur (break temperature). This reference temperature has been arbitrarily
chosen as a good estimate of a typical break temperature of several cell types [10]. However,
the break temperature is cell dependent and is generally determined by analyzing the rate of
cell death vs 1/temperature (癒). The rate of cell death is defined as 1/D0; where D 0 is the
3
number of minutes required to reduce survival by 63%. Figure 1.2 illustrates the Arrhenius
plots used in determining the break temperature of rodent and human cell lines. The slope
of the Arrhenius plot is biphasic and by definition, the break temperature is a temperature of
which the change in the slope of the Arrhenius plot occurs. The curve typically has steeper
slope below than above the break temperature.
癱
41.5
42.5
43.5
44.5
45.5
317
316
315
314
1
0.1
0.01
0.001
318
5
1/Tx10 (癒)
Figure 1.2 Arrhenius plots for a series of rodent and human cell lines derived from
Figure 1.1. (Reprinted from Figure 2 of [1] with permission from Elsevier. �91 Elsevier.)
1.1.2
Adjuvant hyperthermia therapy
As summarized in Section 1.1.1, direct cell death by hyperthermia is more likely at moderate hyperthermia temperatures (44-45癈). However, subtle effects of hyperthermia, such
as chemo-sensitization and radio-sensitization, can be achieved even at mild hyperthermia
temperature (39-41癈). The efficacy of hyperthermia alone is low in comparison to existing
standard cancer therapy such as radiation therapy, chemotherapy, and radio-chemo therapy. However, multiple clinical studies have demonstrated improvements in the efficacy of
the standard therapy when delivered in conjunction with hyperthermia. Hyperthermia has
4
been demonstrated to be correlated with increased perfusion rate and metabolic activity,
induced hypoxia in high vasculature regions (such as solid tumors), and cellular protein
denaturation. Such mechanisms enhance drug and molecular uptake, radio-sensitivity, and
chemo-sensitivity [11-14]. The effects of hyperthermia is highlighted in Figure 1.3.
Hyperthermia combined with radiation therapy is the most common dual-modality treatment
involving hyperthermia [7]. Clinical studies have shown that hyperthermia does increase the
efficacy of radiation therapy. An example of such studies is a multi-institution randomized
trial for the treatment of advanced melanoma by Overgaard et al. (1995) [12]. Complete
response (CR) rates of 70% for the combined treatment whereas CR rates achieved by hyperthermia and radiation therapy alone are 15% and 35%, respectively, have been reported
for local superficial malignancy. An excellent review that summarizes the numerous clinical
trials is given by [7]. A more recent review by Horsman and Overgaard (2007) [15] compiles
the clinical randomized trials for different treatment locations. The benefits of combining
hyperthermia with radiation therapy are elaborately discussed in these review articles.
Hyperthermia is found to modify the cytotoxicity of some chemotherapeutic drugs (see,
for example, [14,16-20]). Each therapeutic agent seems to posses its own unique threshold temperature of which thermal enhancement is observed (i.e. converting drug-induced
sub-lethal damage to lethal damage) [14]. The threshold temperature lies within the mild
hyperthermia regime (40-43癈). This mild hyperthermia temperature not only enhances the
cytotoxicity of chemotherapeutic drugs, it also causes increased tumor blood supply which
enhances the drug uptake in the tumor. Tri-modal therapy that incorporates hyperthermia,
radiation, and chemotherapy is also of interest in oncology. Several clinical trials of tri-modal
therapy have shown positive outcomes (see, for example, [21-23]).
In summary, hyperthermia is a promising modality for cancer treatment.
Mild temper-
ature hyperthermia (39-41癈), when applied for many hours, can enhance the efficacy of
Thermal Therapy Treatment Options
Cr^ofJierag^L
T<-5f 'C *or ?> 10 ii it
AT = -90 C
scnamstns
|
Freeze Thaw transition
i
D srupts cell membrane
I Complete ceiUa- ceslrjct'or
Low Temp Hyperthermia
T = 39-41 癈 for 1-72 hrs
AT = 2-4癈
Moderate Temp Hyperthermia
T = 41-45癈 for 30-60 mm
AT = 4-8癈
techanisrrss
Decease blcoe perus on DO
Decease perncaoil ty
SAlisufasator
Decrease cellar netabos ST
Mechanisms
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permeability, pH, pCfc
Increases metabolic activity,
drug uptake
Radiosensitization,
Chemosensitization
Mechanisms
Increases perfusion,
permeability, pH, pC>2
Increases metabolic activity,
drug uptake
Radiosensitization,
Chemosensitization
Some cell kill at higher
temperatures/doses
Potential HT Techniques
Whole Body
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RF, MW,US <
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RF, MW, US
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RF, MW, US <?
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Ferroseeds, Thermorods
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Figure 1 3 Hyperthermia treatment overview. (Reprinted from Figure 1 of [2] with permission from Informa
Healthcare. �05 Informa healthcare.)
Oi
6
radiation therapy and chemotherapy However, it is unlikely to cause direct cell damaging
effects when used solely
Moderate temperature hyperthermia (41-45癈) can be used to
achieve the same enhancing effects for standard therapy and it decreases the treatment time
considerably (30-90 minutes)
Moderate temperature hyperthermia can also cause direct
cell-killing at the higher end of the hyperthermia temperature spectrum (44-45癈)
1.2
Existing non-invasive technologies for inducing local, deepseated hyperthermia
In this dissertation, we are interested m non-mvasive means of inducing local hyperthermia
Figure 1 3 highlights the existing external technologies under research and development
There are numerous devices, both commercial and under academic development, for inducing local hyperthermia inside the human body They all derive from either electromagnetic
(EM) or ultrasound (US) technologies Stauffer et al (2005) [2] gives an extensive survey of
the existing devices used m local hyperthermia The mechanisms of heating based on EM
and US technologies are summarized m this section
EM technologies
Heating via EM wave is directly proportional to the field strength and the total induced currents Depending on the frequency of the wave, conduction current or displacement current
can dominate At lower EM frequencies (e g RF), the conduction current dominates and
heating is generated by the ohmic loss m the tissue
At higher EM frequencies (e g mi-
crowave), the displacement current dominates and heating is induced by the friction between
oscillating polai molecules m lcsponse to the time-vaiymg EM field The field strength decays exponentially with the distance traveled m tissue and the attenuation in tissue increases
with the frequency of operation The treatment resolution (size of the therapeutic region)
is approximated by half of the wavelength m tissue Therefore, there is a trade-off between
deep tissue penetration at lower frequency and low treatment resolution (large therapeutic
region) Contrary, at higher frequencies, higher treatment resolution can be achieved at the
7
expense of penetration depth.
US technologies
US is a pressure wave, and heating is induced by mechanical losses in tissue. Similar to
EM irradiation, US strength decays exponentially with the distance traveled in tissue and
similar trade-offs between penetration depth and resolution exist. Treatment resolution of
US-induced hyperthermia is on the order of millimeters while EM-induced hyperthermia
provides centimeter-size treatment resolution.
1.3
Overview of contributions
This dissertation contributes to the studies of microwave-induced hyperthermia treatment
of breast and brain tumors via transmit beamforming. We conduct numerical simulations
to design and evaluate the efficacy of microwave beamforming arrays using high fidelity
numerical phantoms of the human breasts and heads as our testbeds. We report the findings
regarding the feasibility of hyperthermia treatment for breast and brain tumors via transmit
beamforming technique. The remainder of this thesis consists of eight main chapters and
a conclusion.
This section provides an overview of the motivation for each chapter and
its contribution towards current progress in microwave-induced hyperthermia treatment of
breast and brain tumors.
1.3.1
Computational tools for simulating microwave-induced hyperthermia treatments
Recent advances in computational power has enabled computer simulations to become a
complementary method of investigating interactions of electromagnetic waves and the hum a n body. Chapters 2 and 3 of this thesis are dedicated to the development of computational
tools which can be utilized in numerical studies of microwave-induced hyperthermia treatment.
8
The numerical investigation of microwave-induced hyperthermia treatment requires the modeling of microwave interactions with the human body as well as the thermal response within
the body induced by the microwave interactions.
Finite-difference time-domain (FDTD)
method is a well-accepted tool for modeling microwave interactions and thermal responses.
Furthermore, the F D T D simulation domain can be divided into sections which are then computed simultaneously. Using parallel computing, simulation time can be reduced to make
modeling of large-scale problems feasible.
In Chapter 2, we summarize the development
of three dimensional F D T D computer codes that simulate these multi-physics interactions.
The codes were parallelized using Message Passing Interface (MPI). The computer codes can
be applied to the study of microwave-induced hyperthermia treatment of breast and brain
tumors.
Numerical phantoms are widely used in the investigation of treatment techniques.
They
arc less costly and easily modified in compaiison to physical phantoms. They can be utilized
in feasibility or proof of concept studies prior to physical system implementation without
risking possible health-related complications in the human subjects. Chapter 3 reports of
the development of anatomically realistic numerical breast phantoms. The phantoms capture the complex network of glandular, adipose, and fibroconnective tissue within the breast.
They also capture the significant heterogeneity of dielectric properties of normal breast tissue, as revealed by a comprehensive characterization study of normal breast tissue dielectric
properties conducted recently by University of Wisconsin and University of Calgary [24,25].
The phantoms will support further development of novel therapeutic microwave techniques
for breast cancer treatment, and provide common grounds for comparison among methods.
They can also be utilized for diagnostic microwave techniques for breast cancer detection.
9
1.3.2
Computational study of non-invasive focused microwave hyperthermia treatment of localized breast tumors
The breast is a natural candidate for heat treatment as it has limited vasculature (in comparison to the liver, for example) and blood perfusion. Volumes from 3 cm up to 9 cm in the
largest dimension are commonly targeted for treatment [26]. Focused microwave technology
is suitable for this application as it offers promise for creating a centimeter-size heating zone
(dictated by the wavelength in glandular breast tissue at microwave frequencies) from a single intended focal point.
Progress towards non-invasive microwave-induced thermal therapy of breast cancer has been
made over the past decade. Fenn et al. [27], Gardner et al. [28], and Vargas et al. [29] conducted clinical studies of an adaptive microwave phased array with an invasive electric-field
feedback probe. The breast was compressed in order to immobilize the tissue and improve the
coupling of microwave energy into the breast. The electric-field probe was used to adjust the
phased array to achieve a focus at the treatment site. A more comprehensive review of these
and other clinical studies was recently reported by Dooley et al. [26]. Theoretical studies of
other focusing methods, such as time reversal [30,31], use of a deformable mirror [32], and
transmit beamforming [33,34], were conducted using computational electromagnetic (EM)
and thermal simulations with two-dimensional (2-D) numerical breast phantoms of varying realism. While these techniques are intended to achieve focusing of microwave energy
non-invasively, the theoretical performance demonstrations were successful in part because
some degree of knowledge about the breast tissue configuration and dielectric properties was
assumed to be available.
Chapter 4 and 5 are two self-contained reports concerning the feasibility of non-invasive
focused microwave hyperthermia treatment of breast tumors. In Chapter 4, we utilize the
numerical breast phantoms described in Chapter 3, and conduct a two-dimensional feasibility study of breast hyperthermia treatment. We consider the feasibility of two wideband
10
focusing methods: wideband microwave beamforming [33,34] and time-reversal [30,31]. The
relationship of the two methods are also discussed.
In Chapter 5, we rigorously establish the sensitivity and robustness of transmit beamforming
for future clinical implementation. We investigate the use of patient-specific information in
the beamformer design under the assumption that a perfect knowledge of the patient's breast
may not be available. Performance of the beamforming method is assessed for microwave
within the frequency range of 1 - 5 GHz, where the resulting resolution is appropriate for the
treatment of cm-size lesions while deep penetration through the breast tissue is feasible. The
performance of beamforming method is investigated for patients with widely varying breast
tissue density. Smallest treatment regions of 1-2 cm in size are achieved within the breasts
considered in the study. This dimension is suitable for achieving target treatment volume
associated with stage I and II localized breast tumors which range from 2 to 7 cm. We
have explored the use of patient-specific propagation models of varying complexity. Use of
propagation models with patient-specific dielectric properties improves the focusing efficacy
of beamforming ? particularly in dense breasts. The study also illustrates that a complete
patient-specific knowledge such as interior tissue structure, and the dielectric properties of
breast tissue, is not needed to obtain selective heating for effective hyperthermia treatment as
long as the appropriate homogeneous properties of the breast are assumed in the propagation
model.
1.3.3
Computational study of non-invasive microwave-induced hyperthermia treatment of localized brain tumors
Primary brain malignancy occurs statistically more frequent in children younger than 15
years of age and in older adults. Brain tumors are the second leading cause of deaths in
children under the age of 20 [35]. It accounts for high cancer-related death rates in every
age groups and patients have poor prognosis. The standard treatments for brain tumors are
surgery, radiation therapy, and chemotherapy. Surgery is the primary form of treatment for
11
brain tumors that lie within the membranes covering the brain or in parts of the brain that
can be removed without damaging critical neurological functions. Because a tumor is likely
to recur if any tumor cells are left behind, the goal of surgery is to remove the entire tumor
whenever possible. Radiation therapy and chemotherapy are generally also administered to
reduced recurrence rate. Radiation and/or chemotherapy are used without surgery when the
tumor is inoperable.
Children undergoing radiation therapy have a consistent 5-year-survival without recurrence
rate. However, radiation therapy causes neurotoxicity and affects brain growth and development in pediatric patients. If the tumor cannot be removed by surgery, chemotherapy is
usually administered to delay radiation therapy until the patient has achieved full growth
(see, for example, [36-38]). Several studies concluded a correlation between high radiation
doses and severe cognitive impairment (see, for example, [39,40]). Researchers are attempting to lower radiation doses in pediatric patients with the hopes of lowering post-treatment
cognitive impairment while maintaining a high survival rate (see, for example, [41,42]).
Unfortunately, the reduction in radiation dose has been associated with an increased risk
of recurrence and a lower survival rate than the standard radiation dose [42]. In a limited number of test cases, fewer cognitive impairments were found in younger children who
had received the lower radiation dose [41]. Combined chemo-radiation therapy with several
chemotherapeutic agents was also considered in an attempt to reduce the dose of radiation. The studies concluded an encouraging recurrence-free 5-year survival rate, however,
the neurotoxicity was significant. In addition, many of the children also developed hearing
impairments and many developed second malignancies [43,44].
The brain is not such a natural candidate for non-invasive heat treatment. Brain matter is
high in perfusion, superficial cooling is limited by the skull, and there is very little room for
mistakes. However, multiple clinical studies have demonstrated improvements in the efficacy
of chemotherapy and radiation therapy when delivered in conjunction with hyperthermia.
12
Consequently, researchers are investigating the increase in efficacy of chemotherapy and radiation therapy by hyperthermia for the treatment of brain tumors (see, for example, [45,46]).
The use of hyperthermia to lower the dose of radiation may alleviate the neurotoxicity in
children undergoing brain cancer treatments.
In Chapters 6 and 7, we explore the use of non-invasive microwave transmit beamforming
to induce local moderate temperature hyperthermia inside the brain volume. The method
is non-ionizing, and therefore does not increase the neurotoxicity. The beamformer is designed using patient-specific information and the efficacy of microwave beamforming method
is evaluated using F D T D and realistic numerical head phantoms available from third party
vendors. We demonstrate that microwave transmit beamforming could induce local hyperthermia non-invasively with centimeter treatment resolution. However, heat damage within
the normal brain tissue and/or the scalp are quite considerable in some phantoms and could
not be overcome.
1.3.4
Time-multiplexed beamforming for non-invasive microwave
hyperthermia treatment
Given the brain's critical role in human function, any hyperthermia system must confine the
thermal damage to the cancerous tissue and avoid harming the healthy brain tissue. This remains one of the challenges of non-invasive microwave hyperthermia treatment for the brain.
With the use of patient-specific, location-specific propagation data, we have demonstrated
t h a t microwave beamforming technique is able to focus microwave energy within the brain
volume. However, the thermal damage induced in healthy brain tissue cannot be avoided
with conventional beamforming alone.
In Chapter 8, we propose a new microwave hyperthermia approach that uses time-multiplexing
of multiple beamformers to address this challenge. Each patient-specific beamformer is designed to focus microwave energy at a target location while suppressing energy deposition
13
in a normal-tissue region that has the potential for absorbing a large amount of microwave
energy. The location of the suppression is unique to each beamformer. We hypothesize that
switching through these different beamformers over time will reduce or eliminate auxiliary
hot spots. We test this hypothesis using a high-fidelity numerical model of the head of
an adult female. Our performance evaluations involve electromagnetic and thermal simulations of the proposed time-multiplexing strategy, as well as the conventional beamforming
approach for comparison. The design procedure we have proposed for the technique is appointed ad hoc to serve as a proof of concept. The time-multiplexed beamforming technique
is shown to reduce the amount of damaged healthy tissue inside the head without affecting
the treatment resolution.
14
Chapter 2
Computational codes for simulating multi-physics interactions in hyperthermia treatments
There are two types of numerical simulations being utilized in the study of non-invasive
microwave-induced hyperthermia treatment:
1. Electromagnetic simulation for evaluating the interactions between microwaves and the
body (inside the breast or the head).
2. Thermal simulation for evaluating the thermal response inside the body.
The block diagram in Figure 2.1 illustrates the implementation and evaluation steps of noninvasive microwave-induced hyperthermia techniques for the treatment of breast and brain
tumors.
Microwave Transmit
Signal Set Design
Propagation Model
w
r
Evaluate Power
Deposition Pattern
Inside the Body
EM Simulation
w
r
Evaluate the Resulting
Temperature Profile
Inside the Body
Thermal Simulation
Figure 2.1 Implementation work flow for simulating the performance of non-invasive
microwave hyperthermia techniques.
The electromagnetics computational code was modified from original contribution by Henri Tandradinata.
15
2.1
Electromagnetic (EM) simulations
F D T D method [47] is used to solve Maxwell's equations and simulate EM interactions with
biological tissue. Efficient F D T D algorithm are available for simulating media described by
single-pole Debye dispersion [47]. The Uniaxial perfectly matched layer (UPML) boundary
conditions are used to terminate the grid [47].
2.1.1
Dielectric properties of biological tissue
Single-pole Debye dispersion model
The frequency-dependent dielectric properties of biological tissues at microwave frequencies
can be efficiently incorporated into F D T D codes using a single-pole Debye dispersion model.
In a single-pole Debye medium, the complex relative permittivity, e, is expressed in the
frequency domain as
. ,
a
e(u) = e00 + +
jue0
Ae
,
.
(2.1)
1+JUJT
where j = A/?I, e^ is the permittivity at very high frequencies, es is the static relative
permittivity, UJ is the angular frequency (rad/s), and r is the relaxation time constant of the
material. Ae = es ? e^ describes the magnitude of the dispersion.
Dielectric properties of breast tissues
For the numerical study of non-invasive microwave breast hyperthermia techniques, the dielectric properties of normal breast tissue incorporated into the numerical simulation are
derived from a large-scale study of dielectric properties [24,25]. In [24,25] the normal tissue
samples are divided into three adipose-defined groups and the single-pole Cole-Cole parameters for the dielectric properties of the three adipose-defined groups are reported. Single-pole
Debye dispersion model is used to incorporate the reported dielectric properties from the
large-scale study in the FDTD-EM simulations. The Debye parameters for the dielectric
properties are reported in Chapter 3.
16
Dielectric properties of biological tissues in the human head
The numerical study of non-invasive microwave brain hyperthermia techniques requires a
computational electromagnetics model of the human head with appropriate dielectric properties assigned to each tissue type in the model. The high fidelity head phantoms from the
Virtual Family [48] provided by IT'IS Foundation (Zurich, Switzerland) and the adult male
head phantom, based on the data set of the Visible Human Project, provided by Remcom
Inc. were used as our numerical testbeds. Once again, single-pole Debye dispersion model is
used to incorporate the dielectric properties of biological tissues exist in the numerical head
phantoms in FDTD-EM modeling. The Debye parameters were derived from the four-pole
Cole-Cole dispersion model for the normal tissue provided by Gabriel et al. [49]. Table 2.1
summarizes the single-pole Debye parameters for the tissue in the numerical head phantoms.
2.1.2
Heating potential calculation
The heating potential, Q [W/m3], is defined as power dissipated per unit volume. The
distribution of the heating potential is evaluated for wideband operation using the FDTDcomputed time-domain field quantities as follows:
Qv,k = RJ2 fe ? fZ,k)At
[W/m]
(2.2)
n=0
Here i,j, k are the computational grid indices, R is the assumed pulse repetition rate, At is
?*
?
*
the FDTD timestep, E and J are the time-domain electric field and total current density
vectors, respectively, and n max is the maximum timestep in the simulation. Similarly, Q is
evaluated for narrowband operation using the following expression:
Qv,k =
f
E
(K^-J^k)At
[W/m3]
(2.3)
^ ? ^ m a x ~~ ^ p e r i o d
where T is the period of the continuous wave illumination and nperiod is the number of time
steps in one period. The simulations are executed until steady-state field interactions are
established. In the FDTD implementation, the electric field vector components are staggered
17
Table 2 1 Summary of the parameters associated with smgle-pole Debye dispersion of the
dispersive dielectric properties of tissues m the head
Tissue
o
Air (internal)
Ae
TS
(S/m)
T
(PS)
Tissue
Coc
Ae
a, (S/m)
Mucosa
32 02
15 05
0 66
41 62
19 54
13 01
0 47
27 41
T
(ps)
1 00
0 00
0 00
7 00
Greymatter
30 17
22 56
0 76
25 97
Nerve
Artery
29 55
31 80
1 36
19 32
Pharynx
1 00
0 00
0 00
7 00
Commissura
22 63
16 26
0 46
25 87
Skin
26 97
14 44
0 73
31 08
Skull
6 65
5 88
0 09
29 92
posterior
Whitematter
22 63
16 26
0 46
25 87
Spmal cord
21 00
25 33
0 54
24 87
Cartilage
18 87
24 03
0 59
27 48
SAT
3 99
148
0 04
22 87
Cerebellum
30 07
19 56
1 07
32 93
Teeth
6 65
5 88
0 09
29 92
Cerebrospinal
29 30
39 39
2 24
15 52
Tendon
16 68
29 31
0 55
20 17
fluid (CSF)
Connective
hga
ment
16 68
29 31
0 55
20 17
tissue
Ear cartilage
18 87
Ear skin
Thalamus
36 68
17 26
0 73
42 78
Tongue
34 52
21 32
0 76
27 65
29 55
31 80
1 36
19 32
24 03
0 59
27 48
Vein
26 97
14 44
0 73
31 08
Vertebrae
4 19
64 82
1 50
7 26
28 05
18 91
0 66
25 54
3 99
1 48
0 04
22 87
oblongata
Hippocampus
30 17
22 56
0 76
25 97
Cornea
37 49
Hypophysis
34 91
25 25
0 86
23 82
Sclera
34 52
Hypothalamus
34 91
25 25
0 86
23 82
Commisura
22 63
Intervertebral
18 87
24 03
0 59
27 48
anterior
Esophagus
Vitreous
hu
mor
Lens
Fat
disc
Larynx
6 65
5 88
0 09
29 92
Pmealbody
34 91
25 25
0 86
23 82
Pons
30 17
22 56
0 76
25 97
Medulla
30 17
22 56
0 76
25 97
18 76
1 19
38 06
21 32
0 76
27 65
16 26
0 46
25 87
30 97
34 09
1 01
18 02
32 02
15 05
0 66
41 62
34 91
25 25
0 86
23 82
18 87
24 03
0 59
27 48
18 87
24 03
0 59
27 48
Esophagus lu
Mandible
6 65
5 88
0 09
29 92
men
Midbrain
30 17
22 56
0 76
25 97
Thyroid
Muscle
28 28
26 72
0 80
17 85
gland
6 65
5 88
0 09
29 92
Trachea
Bone
'"';< >
*�..*.
Figure 2.2 Location of Q at each spatial location (i,j, k) with respect to the six electric
field vector components
in space. Figure 2.2 illustrates the spatial averaging of electric field vector components used
in the Q calculations. The heating potential is calculated using the six-field-component
approach [50]. Furthermore, since a time derivative of the electric flux density is required,
the Q calculations are staggered in time with lespect to the electric field updates.
2.2
Thermal simulations
A 3-D FDTD-thermal model based on the Pennes bio-heat equation [51] is used to obtain
the steady temperature profile in the numerical phantoms (breast or head).
Cp{v)p{v)^-
= V - ( ^ ( r ) V T ( r ) ) + A,(r) + Q(r)
-B(r)(T(r)-TB)
(2.4)
[W/m3]
Here, Cp, p, K, AQ, B, are the specific heat, tissue density, thermal conductivity, metabolic
heat generation, and capillary blood perfusion coefficient, respectively. The blood perfusion
coefficient for each tissue is assumed to be time-independent and at its basal value. Tg is the
blood temperature which is assumed to be constant and equal the body core temperature
of 37癈 and Q is the heating potential computed by the FDTD-EM model. A convective
heat boundary condition is employed at the interfaces between the body and the immersion
media. The FDTD implementation of (5.5) and the convective heat boundary condition
19
follows the method described in [52]. The FDTD-Thermal simulations are executed until
steady-state temperature is reached. The thermal properties of biological tissues existed
in the numerical head phantoms recommended for the Virtual Family by IT'IS Foundation
(Zurich, Switzerland) are utilized in our thermal simulations. The properties are summarized
in Table 2.2. For the breast phantoms, we assign the thermal properties of fat and muscle
to the fatty and glandular breast tissues, respectively.
2.3
Parallel computing
Both EM and thermal computer models can be parallelized using Message Passing Interface (MPI). By utilizing parallel computing, the models are capable of simulating problems
requiring a large computational grid. First the computational grid is divided into many
sub-domains and the field quantity in each sub-domain is computed in parallel. To update
the variable located at the boundary of each sub-domain, communication between processors
must be initiated. The computational space is divided along one axis, creating "bread slices"
as illustrated in Figure 2.3, to minimize the communication between processors. With this
kind of division each processor has to communicate with at most two processors.
(a)
(b)
Figure 2.3 (a) Original computational grid (b) Sub-domains for parallel computing.
20
Table 2.2 Summary of the thermal properties of the tissues in the head.
Tissue
P kg/m
3
W/m3
C? [ J / k g / � C ]
K [W/m/癈]
B [ml/min/kg]
Air (internal)
0
1006
0 03
0
0
Greymatter
1039
3675
1 13
671
7100
Artery
1060
3824
0 51
N/A
0
Commissura posterior
1043
3621
0 50
237
7100
Whitematter
1043
3621
0 50
237
7100
Cartilage
1100
3664
0 47
50
1600
Cerebellum
1040
3640
0 53
560
7100
Cerebrospinal fluid (CSF)
1007
4191
0 60
0
0
Connective tissue
1013
3035
0 37
39
300
Ear cartilage
1100
3664
0 47
50
1600
Ear skin
1100
3437
0 35
97
1620
Vitreous humor
1009
3932
0 59
0
0
Lens
1090
3664
0 40
38
0
Fat
916
2524
0 25
27
300
Hippocampus
1039
3675
1 13
549
7100
Hypophysis
1066
3761
0 53
1697
64000
A0
Hypot halamus
1050
3761
0 53
1697
7100
Intervertebral disc
1100
3664
0 47
50
1600
Larynx
1082
3664
0 47
50
1600
Mandible
1990
1289
0 40
22
610
Midbrain
1039
3675
1 13
549
7100
Muscle
1041
3546
0 53
28
480
Bone
1990
1289
0 40
22
610
Mucosa
1050
3150
0 34
120
1600
7100
Nerve
1038
3664
0 46
549
Pharynx
0
1006
0 03
0
0
Skin
1100
3437
0 35
97
1620
Skull
1990
1289
0 40
22
610
Spinal cord
1038
3664
0 46
549
7100
300
SAT
916
2524
0 24
27
Teeth
2160
1340
0 40
0
0
Tendon ligament
1110
3500
0 50
50
1600
Thalamus
1039
3675
1 13
671
7100
Tongue
1041
3546
0 53
28
2704
Vein
1060
3824
0 51
N/A
0
Vertebrae
1990
1289
0 40
22
590
Pinealbody
1050
3600
0 53
3059
64000
Pons
1039
3675
1 13
549
7100
Medulla oblongata
1039
3675
1 13
549
7100
Cornea
1076
3793
0 52
38
0
Sclera
1032
3000
0 40
38
0
Commisura anterior
1043
3621
0 50
237
7100
480
Esophagus
1040
3500
0 53
383
Esophagus lumen
1050
1006
0 03
0
480
Thyroid gland
1050
3553
0 53
9938
7100
Trachea
1100
3664
0 47
50
0
21
Chapter 3
Development of anatomically realistic numerical breast
phantoms with accurate dielectric properties for modeling microwave interactions with the human breast
Computational electromagnetics models of microwave interactions with the human breast
serve as an invaluable tool for exploring the feasibility of new technologies and improving
design concepts related to microwave breast cancer detection and treatment. In this paper
we report the development of a collection of anatomically realistic 3D numerical breast
phantoms of varying shape, size, and radiographic density which can be readily used in
FDTD computational electromagnetics models. The phantoms are derived from Tl-weighted
magnetic resonance images (MRIs) of prone patients.
Each MRI is transformed into a
uniform grid of dielectric properties using several steps. First, the structure of each phantom
is identified by applying image processing techniques to the MRI. Next, the voxel intensities
of the MRI are converted to frequency-dependent and tissue-dependent dielectric properties
of normal breast tissues via a piecewise-linear map. The dielectric properties of normal breast
tissue are taken from the recently completed large-scale experimental study of normal breast
tissue dielectric properties conducted by the Universities of Wisconsin and Calgary. The
� 2008 IEEE. Reprinted, with permission, from E. Zastrow, S. K. Davis, M. Lazebnik, F. Kelcz, B. D.
Van Veen and S. C. Hagness, "Development of anatomically realistic numerical breast phantoms with accurate dielectric properties for modeling microwave interactions with the human breast," IEEE Transactions
on Biomedical Engineering, vol. 55, no. 12, pp. 2792-2800, Dec. 2008.
The work presented in this chapter was supported by the National Science Foundation under grant
CBET 0201880, the National Science Foundation under a Graduate Research Fellowship, and the National
Institutes of Health under grant R01 CA112398 awarded by the National Cancer Institute.
22
comprehensive collection of numerical phantoms is made available to the scientific community
through an online repository.
3.1
Introduction
Many candidate microwave techniques for breast cancer detection and treatment applications have been proposed in recent years. The growing interest in microwave breast imaging
is evidenced by the increasing number of publications on the topic. In the 1990's, there were
approximately a dozen journal papers related to microwave breast imaging (see, for example, [53-56]), whereas between 2000 and the present nearly 100 journal papers have appeared
(see, for example, [57] and references therein) with over a quarter of those published last year.
The body of work on microwave breast cancer detection is quite diverse, and includes narrowband and wideband inverse scattering or tomographic techniques [58-62]; ultrawideband
radar and other time-domain techniques such as time reversal [63-67]; microwave-induced
thermo-acoustic tomography [68,69]; microwave radiometry [70-72]; and microwave holography [73].
There is also continuing interest in research and development of microwave therapeutic
techniques for the breast, such as microwave-induced hyperthermia and microwave ablation.
Numerous technological advancements for treatment and temperature monitoring techniques
have been reported recently (see, for example, [27-30,33,34,74]).
Research on both diagnostic and therapeutic microwave techniques benefits from anatomically realistic numerical breast phantoms that model structural complexities, tissue heterogeneity, and dispersive dielectric properties. One well-accepted tool used in the investigation
of these microwave techniques is a finite-difference time-domain (FDTD) [47] computational
electromagnetics model of the breast (referred to here as a numerical breast phantom).
To date, most numerical breast phantoms have been limited to anatomically realistic 2D
23
phantoms [59,65] or relatively simple 3D phantoms [65,75]. In all of these cases, as well as
the few examples of anatomically realistic 3D phantoms [66,76], the accuracy of the assumed
dielectric properties of the various tissues in the breast has been limited by gaps and discrepancies in previously published small-scale experimental dielectric spectroscopy studies. None
of these previous phantoms are consistent with the comprehensive findings on normal breast
tissue dielectric properties reported recently in the large-scale Wisconsin-Calgary dielectric
characterization study [25,77].
FDTD models of other parts of the human body - namely those that are comprised of
well delineated tissue types, each with spatially invariant dielectric properties - are derived
from magnetic resonance images (MRIs) with relative ease and are arguably commonplace
these days. In contrast, the accurate derivation of numerical breast phantoms from MRIs
is a non-trivial and in fact quite involved process due to the complex network of glandular,
adipose, and fibroconnective tissue in the breast and the significant heterogeneity of dielectric properties of normal breast tissue, as revealed by the Wisconsin-Calgary study.
In this paper we report for the first time the development of a collection of anatomically and
dielectrically realistic 3D numerical breast phantoms of varying shape, size, and radiographic
density. The structural heterogeneity of the breast is derived from 3D MRIs of patients with
normal breast tissue (no malignancy or other abnormality) while the frequency-dependent
and tissue-dependent dielectric properties are derived from the Wisconsin-Calgary study.
The primary novel contribution is the introduction of a physiologically realistic method for
mapping breast MRI voxel intensity to accurate dielectric properties of normal breast tissue.
Our mapping is based on a two-component Gaussian Mixture Model (GMM) [78] and is
motivated by the fact that normal breast tissue is composed of two tissue types that are distinctly different in terms of both physiology and dielectric properties. The numerical breast
phantoms presented in this paper are not intended to exactly mimic any specific patient's
24
breast, but rather to serve as representative models of the human breast for use in computational studies. The phantoms will support further development of novel diagnostic and
therapeutic microwave techniques for breast cancer detection and treatment, and provide
common grounds for comparison among methods.
The rest of the paper is organized as follows. Section 3.2 is divided into two parts. Section
3.2.1 describes in detail the image processing steps used to construct anatomical models from
MRIs. Section 3.2.2 discusses the mapping between the voxel intensity of the anatomical
models and the dielectric properties of normal breast tissue. Examples of 3D anatomically
realistic numerical breast phantoms are illustrated in Section 3.3 and are followed by concluding remarks in Section 6.1.3.
3.2
Method for developing a numerical breast phantom
The goal is to create a collection of realistic numerical breast phantoms where the breast
tissue is modeled as a uniform grid of spatially dependent dielectric properties. We seek to
capture in a representative sense both the structural heterogeneity of normal tissue and the
dispersive dielectric properties of normal breast tissue. Structural realism is achieved in the
proposed phantoms through the use of 3D breast MRIs while dielectric properties realism is
achieved through the use of data from the Wisconsin-Calgary study [25,77]. The key steps
are described below.
3.2.1
M R I processing and structural development
The numerical phantoms are derived from Tl-weighted MRIs of prone patients. The anonymous breast MRI datasets are obtained from the University of Wisconsin Hospital and Clinics. Each breast MRI is assigned a classification based on the standard tissue composition
descriptors used by radiologists to classify X-ray mammograms. The American College of
Radiology (ACR) defines four categories of breast composition according to the radiographic
25
density of the breast: (I) almost entirely fat, (II) scattered
fibroglandular,
(III) heteroge-
neously dense, and (IV) extremely dense [79]. A series of sagittal slices comprises each 3D
MRI. The spacing between slices is typically 1.5 mm but varies from patient to patient.
Each sagittal slice contains 256 x 256 pixels. The field-of-view for a sagittal slice varies from
patient to patient depending on breast size, but for a typical field-of-view of 16 cm x 16
cm, the MRI voxel size is 0.625 mm x 0.625 mm x 1.5 mm. Several image processing steps
are applied to the original MRIs to remove image artifacts and to automate the structural
development of the numerical phantoms.
The first step in the structural development of the phantoms is to reduce the dominant
artifact in the breast MRI. Non-uniformity of the magnetic fields leads to slowly varying
intensity gradients in the image, particularly in the tissue region near the coils. This image artifact is illustrated in Figure 3.1(a) for a coronal slice through the 3D image.
A
homomorphic filter [80] is applied to the MRI to mitigate these effects by filtering out the
low-frequency spatial variations in the image. Figure 3.1(b) shows the same coronal slice
after homomorphic filtering.
2
4 6 8 10 12
span in cm
(a)
2
4 6 8 10 12
span in cm
(b)
Figure 3.1 A coronal slice from a 3D MRI of the breast (a) before, and (b) after
homomorphic filtering is applied to reduce the slowly varying gradient artifact. The color
bars represent MRI voxel intensity before and after filtering.
26
Next, the MRI is linearly interpolated to achieve a 3D grid of 0.5-mm cubic voxels while
preserving the physical dimensions of all structures in the MRI. The grid cell size of 0.5
mm x 0.5 mm x 0.5 mm is chosen to satisfy the grid resolution requirements for F D T D
computational electromagnetics modeling in the microwave frequency range. For example,
at 10 GHz, this grid cell size corresponds to a sampling density of approximately 10 points
per wavelength in those grid cells containing the densest tissue properties (which, for the
phantoms discussed in this paper, correspond to glandular/fibroconnective tissue, with peak
values of er = 52.64, a = 14.97, A = 4 mm).
T h e breast volume is then segmented from the background by applying an edge finding
algorithm to each coronal slice of the interpolated 3D image. Each coronal slice is treated
as a 2D matrix where the matrix elements are the MRI voxel intensities. We traverse each
line in the matrix (either a row or column) in four directions: left to right, right to left, top
to bottom, and bottom to top. For each direction of traversal, we create a logical mask - a
matrix containing l's and 0's. For example, while traversing each row of the coronal slice
shown in Figure 3.1(b) from left to right, each matrix element in the logical mask is set to
zero until a voxel intensity in the coronal slice is found to exceed a specified threshold; the
threshold value is usually chosen to be the voxel intensity close to that of the skin or the
subcutaneous fat layer near the skin contour. The remaining matrix entries along that row
are set to one. The resulting logical mask is shown in Figure 3.2(a). An analogous procedure
is used to create the three other logical masks shown in Figures 3.2(b), 3.2(c), and 3.2(d).
The four masks are combined using element-by-element matrix multiplication to produce a
coronal composite mask t h a t is used to segment the breast interior from the background.
T h e coronal composite mask of the coronal slice shown in Figure 3.1(b) is shown as the
shaded area in Figure 3.2(e).
T h e segmentation works particularly well on coronal slices where there is a well-defined
contrast between the MRI voxel intensity of the tissue and the background region. However
27
(a)
(b)
2
(c)
(d)
4 6 8 10 12
span in cm
^
Figure 3.2 Breast segmentation masks which result from traversing the coronal slice shown
in Figure 3.1(b) from (a) left to right, (b) right to left, (c) top to bottom and, (d) bottom
to top. (e) The resulting coronal composite mask and its best-fit ellipse. White and gray
areas represent matrix elements that are set to 0 and 1, respectively.
imperfections still arise in the coronal composite masks. For example, the coronal composite
mask in Figure 3.2(e) does not have a smooth edge. Such roughness, which is non-physical
and may lead to unrealistic scattering, is eliminated by fitting each coronal composite mask
with an ellipse to ensure smooth contours on the 3D phantom. An example of a best-fit
ellipse for a coronal composite mask is plotted in Figure 3.2(e) as a dashed-dotted line.
The ellipse is fit to boundary points of the previously identified coronal composite mask
using a penalized least-squares criterion to select the coordinates of the center of the ellipse
and the major and minor axes that minimize the penalized error. The penalty function is
chosen to give preference to ellipses whose contours fall on or inside the segmented tissue
region and to discourage those extending beyond the segmented tissue region and into the
background region. The selected ellipses, one from each coronal slice, are stacked to form a
smooth 3D breast surface as illustrated in Figure 3.3(a). The breast interior is now defined
by the volume enclosed by the smooth breast surface.
28
The skin is usually not imaged with high fidelity and is mostly eliminated during segmentation. Hence, a 1.5-mm-thick skin layer is artificially introduced into the model by performing
image erosion [81] on the previously obtained smooth breast surface. The thickness of the
skin layer is chosen to be the average value of breast skin thickness reported in [82]. Finally,
the breast interior region comprises all voxels contained within the 3D breast surface after
image erosion is performed. The skin region comprises all the voxels contained between the
surfaces before and after erosion. A 1.5-cm-thick subcutaneous fat layer and a 0.5-cm-thick
muscle chest wall are introduced at the base of the breast to complete the structural development of the model. The chosen thickness of the subcutaneous fat layer represents the
average thickness from 35 MRI datasets; this parameter can be easily adjusted to account
for more or less fat on the chest wall. Figures 3.3(b) and 3.3(c) show coronal and sagittal
slices of the resulting 3D anatomical model.
^玈"iSiS�换Kfc **� if m-.s.J t r a :
1'
12,
E
S
10,
12
8
1 1(
a
c 8
a)
Q. ?
w 6
6
4
2
4
;
1
\
\
\\
**t
<籮far-�.
9 ??*
4 r
15 *
Sk "'?"
;
^fi*'
w
\
\
*?
'/
J
,
> /
/
,
f /
/
2
(cm) 8
12
\1
2
4
(a)
"6
8
(cm)
10 12 14
4
6 8 10 12 14
span in cm
(b)
5
10
span in cm
15
(c)
Figure 3.3 Illustration of a 3D anatomical breast model created from a 3D MRI. (a)
Smooth 3D surface of the breast formed by stacking the best-fit ellipses from each coronal
slice, (b) Coronal view of the 3D anatomical model, (c) Sagittal view of the 3D anatomical
model. In (b) and (c) the skin layer is identified by the black contour.
3.2.2
Dielectric properties mapping
The voxel intensities within the 3D anatomical model are transformed into dielectric properties via a piecewise-linear map. An example of a piecewise-linear mapping between MRI
29
voxel intensity and dielectric properties is illustrated in Figure 3.4. The piecewise-linear map
provides the necessary flexibility to account for the facts that a) the MRI voxel intensities
of fatty and
fibroconnective/glandular
tissue tend to exhibit bimodal distributions, and b)
while the the dielectric properties of normal breast tissue in the microwave regime span a
wide and continuous range of values, they too are clustered based on tissue type.
Our mapping between MRI voxel intensity and dielectric properties consists of seven linear segments, each corresponding to a specific tissue category. We define the seven tissue
categories as follows: glandular-1, glandular-2, glandular-3, transitional, fatty-1, fatty-2, and
fatty-3. Our decision to use seven categories was motivated by the format of the dielectric
properties data reported in the Wisconsin-Calgary study. A minimum of three categories is
needed to account for physiological heterogeneity in the breast. The use of seven linear segments, instead of three, provides greater flexibility in capturing the dielectric heterogeneity
reported in [25,77]. The corresponding voxel intensity intervals are denoted as Igi, Ig2, Ig3,
Itrans, Ifi, If2, and If3. Similarly, the dielectric properties intervals are denoted as Pgl,
Pg2,
Pg3, Ptrans, Pfi, Pf2, and Pf3. The range of intensity values for each I is linearly mapped to
the corresponding properties range for each P, as illustrated in Figure 3.4.
The next subsection describes our procedure for identifying the intensity intervals for each
tissue category. The second subsection describes the procedure for assigning ranges of dielectric properties to each properties interval.
3.2.2.1
The seven intervals of M R I voxel intensity
The upper- and lower-bounds of the seven intervals of MRI voxel intensity are given by the
eight piecewise-linear mapping parameters labeled in Figure 3.4 (mg, mag, fig, Mg,m,f, /if,
and Mf).
maf,
These parameters are found by first fitting the histogram of MRI voxel intensi-
ties from the breast interior with a two-component Gaussian mixture model (GMM) [78].
Higher voxel intensities in the Tl-weighted MRI correspond to fatty tissue while lower voxel
30
VV*83
trans
fl' f2' B
X
>
,
H,
m
of
M,
0
&
OH
1
2
3
4
MRI voxel intensity
6 a-
Figure 3.4 A representative piecewise-linear map illustrating the linear mapping between
seven intervals along the MRI voxel intensity axis (Igi, Ig2, hrans, Ifi, If 2, If 3) and seven
intervals along the dielectric properties axis (Pgi, Pg2, Ptrans, Pfi, Pf2, Pfz)- The MRI in
this example is of a patient with extremely dense breast tissue.
intensities correspond to glandular/fibroconnective tissue. Each component of the GMM
represents an MRI intensity region corresponding to either glandular/fibroconnective or
fatty tissue [83]. The probability density function (pdf) for the two-component GMM is
represented as g(x; aii, a2, /ii, \i2, af, a | ) = aifi(x;
Hi, a\) + a2f2(x; fi2, &2)-> where ft(x; a, b),
i = 1, 2 is the Gaussian pdf of the ith GMM component with mean a and variance b. The six
distribution parameters aXl a2, fi\, /i2, af, and o\ are estimated using the method proposed
in [78]. Examples of normalized histograms and their two-component GMM are shown in
Figures 3.5(a) and 3.6(a) for patients with extremely dense breast tissue and almost entirely
fat breast tissue, respectively. Figures 3.5(b) and 3.6(b) each show the two individual Gaussian components of the GMM and their mean {ji) and standard deviation (a).
W i t h the exception of breast compositions that are almost entirely fat, we have found the
two Gaussians to be well separated, as illustrated in Figure 3.5. When the breast is almost
31
0.08
Tl
I T
FT
m
ii M m, a, m ,
og g g
f n
of
1-'
M,
f
0.06
"g.0.04
0.02
2
3
4
MRI voxel intensity
5
(a)
0.
0
2
3
4
MRI voxel intensity
5
(b)
Figure 3.5 (a) Histogram of MRI voxel intensities for a patient with extremely dense
breast tissue, and the composite two-component GMM of the histogram, (b) The two
individual components of the GMM corresponding to fatty tissue (dashed) and
glandular/fibroconnective tissue (solid). Each component is labeled with its GMM
parameters. The eight piecewise-linear mapping parameters are indicated along the MRI
voxel intensity axis (top edge).
entirely fat, there are very few voxels with low intensities (glandular/fibroconnective tissue
voxels) and the two Gaussian components are both fit to the dominant peak in the fatty
tissue region, as illustrated in Figure 3.6.
The eight piecewise-linear mapping parameters are defined from the distribution parameters
of the GMM. We define the minimum, intermediate, mean, and maximum voxel intensities
as mg, mag, /j,g, and Mg, respectively, for glandular/fibroconnective tissue and rrif,
maf,
Hf, and Mf, respectively, for fatty tissue. The eight piecewise-linear mapping parameters
are indicated along the MRI voxel intensity axis in Figures 3.5(b) and 3.6(b) for patients
with extremely dense breast tissue and almost entirely fat breast tissue, respectively. We
summarize the relationship between the piecewise-linear mapping parameters and the GMM
distribution parameters (shown in Figures 3.5(b) and 3.6(b)) below.
For the case where the two Gaussians are well separated, as in the extremely dense case of
Figure 3.5, the upper bound of the glandular/fibroconnective region (Mg) is defined as an
intensity value that is one standard deviation above the mean // 1; while the lower bound of
32
0.08
.
.
? histogram
?
?
?
>
0.06- " " G M M
h' \
0.02
t
1
0.08
II
I
m pLI M m, Li,
og g g f n
m
9
2
3
4
5
MRI voxel intensity
1.0.04
\
n
0.02
6
�
(a)
i
m ,
1
2
3
4 �MRI voxel intensity
1
1
of
f\1
0.06
1.0.04-
�
1
-
V
5
6
(b)
Figure 3.6 (a) Histogram of MRI voxel intensities for a patient with almost entirely fat
breast tissue, and the composite two-component GMM of the histogram, (b) The two
individual components of the GMM are shown with dashed and solid lines. Each
component is labeled with its GMM parameters. The eight piecewise-linear mapping
parameters are indicated along the MRI voxel intensity axis (top edge).
the same region (mg) is the lowest voxel intensity value in the image. Conversely, the lower
bound of the fatty region (rrif) is defined as an intensity that is one standard deviation below
/j,2, while the upper bound of the region (Mf) is defined as the highest voxel intensity value
in the image. For both the glandular/fibroconnective and fatty regions, the mean (fj,g or fif)
is calculated as the expected value of the voxel intensity using the GMM for that region. We
define the intermediate voxel intensity as an intensity that is one standard deviation above
H2 for the fatty region (maf)
and as an intensity that is one standard deviation below JJLI for
the glandular/fibroconnective region
(mag).
For the case where the two Gaussians are not well separated, as in the almost entirely
fat case of Figure 3.6, the upper bound of the glandular/fibroconnective region (Mg) is
separated from the fatty region by a user-defined positive scalar, 5.The intermediate voxel
intensity for the glandular/fibroconnective region (mag)
is defined as an intensity that is
Mg ? fj,g below the mean voxel intensity of the glandular/fibroconnective region (fj,g). The
other piecewise-linear mapping parameters (mg, /xg, rrif, Mf, and tif) are defined as in the
preceding case. Hence, the eight piecewise-linear mapping parameters are selected as follows.
33
Let X be the set of voxel intensities in the breast interior; then
mg = inf(x : x G X)
{
(3.1)
/ii + o"i, if (/i2 - <J2) - (/ii - oi) > 5
(3.2)
1^2 ? &2 ? $, otherwise
Vg =
xg(x;ai,a2,/J>i^2,(?i,crl)dx
(3.3)
JX<Mg
{
flt - CTi, if (/i 2 " CT2) - (/ii - CTi) > 5
(3.4)
2/i 5 ? M g , otherwise
mf
= fj,2-
(3.5)
<?2
M / = sup(x : x G X )
Hf =
(3.6)
xg[x\ax,Oi2,\i\,ii2,(y\,ol)dx
(3.7)
" V = A*2 + o"2
(3.8)
The eight piecewise-linear mapping parameters are used to specify the voxel intensity intervals corresponding to the seven tissue categories as Igl = (mg,mag),
Ig3 = (fig,Mg),
3.2.2.2
hrans = (Mg,mf),
In
= (mf,/jf),
If2 = (nf,maf),
Ig2 =
and If3 =
(mag,/jg),
(maf,Mf).
Dielectric properties assignment
Each of the seven MRI voxel intensity intervals is linearly mapped to an appropriate range
of normal breast tissue dielectric properties. The seven ranges of dielectric properties are
denned by the eight wideband dielectric properties curves shown in Figure 3.7. An example
of the eight bounding dielectric constant values evaluated at 6 GHz is illustrated in the
graph in Figure 3.4, wherein the bounding values are labeled as maximum, glandular-high,
glandular-median, glandular-low, fat-high, fat-median, fat-low, and minimum. The curves
in Figure 3.7 are derived from the 0.5-20 GHz results reported in [25,77] as follows:
34
? The maximum and minimum curves (dotted) are the upper and lower bounds, respectively, of the frequency-dependent dielectric properties data presented m [77]
The
lower dotted curve corresponds to the dielectric properties of lipids measured m our
laboratory, while the upper dotted curve corresponds to the frequency-by-frequency
maximum dielectric properties (envelope) of all the curves shown m Figure 8 of [77]
? The solid curves are the median dielectric properties curves associated with the adiposedefined tissue gioup 1 and 3 lepoited m [25, 77]
We icfei to these two cuives as
"glandular-median" and "fat-median" curves
? The two pairs of dashed curves are the 25 t h and 75 t h percentile dielectric properties
curves for tissue groups 1 and 3 reported m [25, 77]
We refer to these curves as
"glandular-low" (25th percentile, group 1), "glandular-high" (75 t h percentile, group 1),
"fat-low" (25 t/l percentile, group 3), and "fat-high" (7bth percentile, group 3)
The eight wideband dielectric properties curves are used to specify the dielectric properties
intervals as P/3 = (minimum,fat-low), P/2 = (fat-low,fat-median), Pf\ =
(fat-median,fat-
high), Ptrans = (fat-high,glandular-low), Pg3 = (glandular-low,glandular-median), Pg2
=
(glandular-median,glandular-high), and Pg\ = (glandular-high,maximum)
Smgle-pole Cole-Cole parameters for the eight curves in Figure 3 7 are summarized in Table
3 1
While these Cole-Cole models provide a compact, general representation of the dis-
persive dielectric properties of breast tissue, they are not easily incorporated into wideband
F D T D simulations The Cole-Cole models can be replaced by other dispersion models suitable for use m F D T D computations
For example, a simple Debye model has been shown
to accurately capture the frequency dependence of these properties m the microwave frequency range [84] As dictated by the piecewise-lmear map, the dielectric properties values
themselves (m the case of a single-frequency simulation) or the appropriate dispersion model
parameters (m the case of a wideband simulation) for a specific voxel in the breast interior are computed as a weighted average of the upper- and lower-bound dielectric properties
35
80
1
'
1
o0
70
6
60 -
4
c
B 50
CO
c
o 40 O
o
o 30
P~ - - .
??玙 ---..
P , ^ ~ - ~ ~ - ^ *" ~ g3
^ - \ ~ ~ , _
2
""---玙__
p
t,
^ ^ Tf37 7 ^
4
6
-
8
03
b 20
p
""?--?7~~~
trans
10 -
-
0
10
Frequency (GHz)
15
20
(a)
5
10
Frequency (GHz)
15
(b)
Figure 3.7 (a) Wideband dielectric constant and (b) effective conductivity curves that
define the bounds on seven ranges of dielectric properties The range labels (Pg\, Pg2, Pg3,
Ptrans, Pfii Pf2, a n d P/3) correspond to seven tissue categories. The two dotted curves
represent the maximum and minimum tissue properties. The two solid curves represent the
median properties of piedominantly glandular/fibroconncctive tissue and piedominantly
fatty tissue. The two pairs of dashed curves represent the 25 t h and 75th percentile
properties for predominantly glandular/fibroconnective tissue and predominantly fatty
tissue. The Cole-Cole parameters for these eight curves are given in Table 3 1.
36
Table 3.1 Single-pole Cole-Cole parameters for the eight wideband dielectric properties
curves.
f oo
Af
T (ps)
a
as (S/m)
maximum
1.000
66.31
7.585
0.063
1.370
glandular-high
6.151
48.26
10.26
0.049
0.809
glandular-median 7.821
41.48
10.66
0.047
0.713
glandular-low
9.941
26.60
10.90
0.003
0.462
fat-high
4.031
3.654
14.12
0.055
0.083
fat-median
3.140
1.708
14.65
0.061
0.036
fat-low
2.908
1.200
16.88
0.069
0.020
minimum
2.293
0.141
16.40
0.251
0.002
curves for the tissue category into which the MRI voxel intensity falls. In summary, the voxel
intensities within the glandular/fibroconnective region, Igi, Ig2, and Ig3, are mapped to dielectric properties Pgi, Pg2, Pg^ voxel intensities within the fatty region, 1^, If2, and 7/ 3 , are
mapped to dielectric properties Pfi, Pf2, -P/3; and voxel intensities within the transitional
region, Itrans, are mapped to dielectric properties Ptrans-
3.3
Examples
We provide examples of four anatomically realistic numerical breast phantoms with realistic wideband dielectric properties of normal breast tissue. Each phantom is derived from a
representative MRI from each of the four ACR classifications. Since there exists no standard procedure for classifying MR images into the four categories, for the purpose of our
research we adopt a procedure to classify a numerical phantom according to its relative
tissue composition based on the parameters of the GMM. We classify a phantom into one
of the four categories based on the probability of a voxel being assigned to fatty tissue,
37
Pr(x > rrif) = Jx>m g(x; oti, a^-, /ii, ^2, cr?, c l ) ^ x - Phantoms with a relatively large proportion of fatty tissue (smaller proportion of glandular/fibroconnective and transitional tissues)
are assigned to ACR categories I or II, while phantoms with a smaller proportion of fatty
tissue (larger proportion of glandular/fibroconnective and transitional tissues) are assigned
to ACR categories III or IV. We use the following rules to classify a phantom into a tissue
composition category C:
I, Pr(x > rrif) > 0.95
11,0.9 < Prix
C=(
> mf)
< 0.95
111,0.8 < Pr{x > mf)
(3.9)
< 0.9
IV, Pr(x > mf) < 0.8
T h e four examples are illustrated in Figures 3.8 and 3.9. Figures 3.8(a),3.8(b) and 3.9(a),3.9(b)
show sagittal cross-sections of MRIs classified as ACR I, II, III, and IV, respectively. Figures
3.8(c),3.8(d) and 3.9(c),3.9(d) show the correspondingcross-sections of the phantoms derived
using the GMM-based piecewise-linear mapping scheme proposed in this paper. The dielectric constant at 6 GHz is displayed in all phantom images. To illustrate the importance of
the piecewise-linear map, we include in Figure 3.8 two phantoms derived with an alternative mapping scheme applied to the latest dielectric properties data - namely the uniform
mapping between MRI voxel intensities and dielectric properties that has been adopted previously (see, for example, [65,66]).
A comparison between Figures 3.8(c),3.8(d) with Figures 3.8(e),3.8(f) indicates that uniform
mapping scheme introduces artificially high dielectric properties in the fatty tissue region of
the breast while the piecewise-linear mapping avoids this error and preserves breast physiology. The erroneously high dielectric properties values assigned to fat in Figures 3.8(e),3.8(f)
increase the microwave attenuation throughout the breast and decrease the effective heterogeneity of the phantom by reducing the electromagnetic contrast between glandular and
fatty tissue types.
38
The phantoms can be readily used in FDTD simulations conducted at microwave frequencies.
We fit the Cole-Cole models described in Section 3.2.2.2 with single-pole Debye dispersion
models over the 3 to 10 GHz frequency band. The frequency range chosen for this example is of specific interest because it coincides with FCC band allocated for ultrawideband
applications. The MRI voxel intensities are then mapped to the Debye parameters using
the procedure described in Section 3.2.2. A set of Debye parameters appropriate for the
illustrative frequency range of 3-10 GHz is listed in Table 3.2.
This paper has focused on the treatment of the dielectric properties of normal breast tissue
inside the breast phantom. The dielectric properties of skin and muscle are well known in
the microwave frequency range, and can be selected from reliable databases such as that provided by Gabriel et al [49] and assigned to the skin and chest wall regions of the phantoms in
a straightforward manner. Synthetic lesions, such as the malignant and benign lesion models
reported in [85], can be superimposed onto the normal breast phantoms reported here. ColeCole models representing the frequency-dependent dielectric properties of malignant breast
tissue are reported in [25].
3.4
Summary
We have developed anatomically realistic numerical breast phantoms based on Tl-weighted
MRIs of prone patients. The 3D MRIs are transformed into high-resolution dielectric grids
using a piecewise-linear mapping approach between MRI voxel intensity and dielectric properties. Recently reported dielectric properties of normal breast tissues in the microwave
frequency range are incorporated into the numerical breast phantoms. The result is a set
of phantoms that captures the heterogeneity and range of microwave dielectric properties
expected in women. We have also introduced a breast composition classification scheme
based on the tissue composition of each phantom. An online repository containing a comprehensive collection of anatomically realistic numerical breast phantoms as well as detailed
39
Table 3.2 Single-pole Debye parameters (3-10 GHz) for the eight wideband dielectric
properties curves.
^00
Ae
T (PS)
as (S/m)
maximum
23.2008
46.0517
13.0000
1.3057
glandular-high
14.2770
40.5152
13.0000
0.6381
glandular-median 13.8053
35.5457
13.0000
0.7384
glandular-low
12.8485
24.6430
13.0000
0.2514
fat-high
3.9870
3.5448
13.0000
0.0803
fat-median
3.1161
1.5916
13.0000
0.0496
fat-low
2.8480
1.1041
13.0000
0.2514
minimum
2.3086
0.0918
13.0000
0.0048
40
10
(cm)
(c)
(d)
10
(cm)
(e)
(f)
Figure 3.8 Sagittal cross-sections showing MRI voxel intensity for patients with (a) almost
entirely fat breast tissue (ACR I) and (b) scattered fibroglandular breast tissue (ACR II),
with the corresponding cross-sections of the 3D numerical breast phantoms showing the
dielectric constant at 6 GHz. The two phantoms in (c) and (d) (shown in color) were
derived from (a) and (b) respectively, using the GMM-based piece wise-linear mapping
scheme proposed in this paper. The two phantoms in (e) and (f) (shown in color) were
derived from (a) and (b) using a uniform mapping scheme.
41
1D
(cm) '
(a)
10
5
(cm)
(c)
tL
t
6
(b)
(cm)
(d)
Figure 3.9 Sagittal cross-sections showing MRI voxel intensity for patients with (a)
heterogeneously dense breast tissue (ACR III), and (b) extremely dense breast tissue (ACR
IV), with the corresponding cross-sections of the 3D numerical breast phantoms showing
the dielectric constant at 6 GHz. The phantoms in (c) and (d) (shown in color) were
derived from (a) and (b), respectively, using the GMM-based piecewise-linear mapping
scheme proposed in this paper.
42
instructions is accessible through our research group website: http://uwcem.ece.wisc.edu/.
The authors would like to acknowledge the technical assistance of the University of Wisconsin Hospital and Clinics radiology staff in acquiring the MRIs and Henri Tandradinata
for his contributions in the early-stage development of the numerical breast phantoms.
43
Chapter 4
2-D computational study of time reversal techniques for
ultra-wideband microwave hyperthermia treatment of
breast cancer
We present a computational study of the application of time reversal (TR) principles to
microwave hyperthermia treatment of breast cancer. A wideband source is excited at the
tumor location (the desired focus) in an electromagnetic (EM) simulation based on the finitedifference time-domain (FDTD) method and the transmitted wave is recorded at multiple
antenna locations. The FDTD-computed signals are time reversed for transmission into the
breast. The same set of FDTD-computed signals is also used in a comparative investigation
of a space-time beamforming technique, which has been previously studied for microwave
hyperthermia. We discuss the relation between these two approaches, and compare the focusing efficacy and heating selectivity of the T R and beamforming approaches using F D T D EM
and thermal simulations with anatomically realistic numerical breast phantoms. Promising
results from both methods are obtained.
� 2007 IEEE. Reprinted, with permission, from P. Kosmas, E. Zastrow, S. C. Hagness and B. D.
Van Veen, "A computational study of time reversal techniques for ultra-wideband microwave hyperthermia
treatment of breast cancer", in Proc. IEEE/SP 14th Workshop on Statistical Signal Processing, pp. 312-316,
Aug. 2007.
The work presented in this chapter was supported by the National Science Foundation under grant
CBET 0201880, and the National Institutes of Health under grant R01 CA112398 awarded by the National
Cancer Institute.
44
4.1
Introduction
Microwave hyperthermia treatment of breast cancer aims to raise the temperature in the
tumor volume to about 43� C while preserving normal physiological temperatures in the
surrounding tissue. Since there is little contrast in the dielectric properties of normal and
malignant glandular tissue in the breast [77], [25], highly effective focusing schemes are required in order to achieve selective absorption of microwave energy in the tumor volume.
Most of the investigations to date have involved narrowband phased arrays (see, for example, [27], which uses feedback from an invasive electric-field probe to achieve adaptive
focusing). More recently, the feasibility of using wideband microwave signals in conjunction
with non-invasive beamforming techniques has been demonstrated [33], [34]. In this paper,
principles from time reversal (TR) theory [86], which has been previously considered for the
tumor detection problem [87], are adapted for the breast cancer hyperthermia treatment
application.
T h e paper is structured as follows. In Section 4.2, the proposed approach to T R microwave
hyperthermia is described. The effect of loss and dispersion, which breaks time reversal invariance, and the relation between beamforming and time reversal are also discussed. Section
4.3 presents the numerical breast phantoms used in this study, and introduces metrics for
evaluating the performance of the T R approach and comparing it with that of beamforming.
Results of this performance evaluation are reported in Section 4.4, which presents calculated electromagnetic (EM) power density deposition distributions and temperature profiles
obtained from both methods. To calculate these quantities, finite-difference time-domain
(FDTD) EM and thermal simulations of the hyperthermia experiment are performed, using
realistic breast phantoms based on magnetic resonance images (MRIs). The microwave-frequency dielectric properties of the various tissues of interest are based on a recently completed
large-scale wideband dielectric spectroscopy study [77], [25]. Promising results for different
45
breast phantoms and tumor locations are presented. A summary with conclusions is given
in Section 4.5.
4.2
Methodology
A virtual experiment is simulated with the FDTD to generate the signal set for the microwave
hyperthermia antenna array. In this experiment, a source is placed inside a numerical breast
model at the known tumor location. The recorded signals are then time reversed and used
as the input signals for the hyperthermia system. We refer to the breast model used to
generate these signals as the propagation model. The complexity of this propagation model
can be adjusted according to the assumed knowledge of the breast heterogeneity. This is
a fundamental difference from the study of TR hyperthermia presented in [30], where time
reversal was applied to signals generated from a simulated experiment that involved sources
external to the breast. In contrast to [30], our proposed approach does not require estimation
of the tumor response from the clutter-dominated signals.
Two important issues are considered in the following two subsections. The effect of loss
and dispersion to the application of time reversal for the hyperthermia problem is discussed
in Section 4.2.1. In Section 4.2.2, the beamforming formulation of [34] is related to the TR
approach considered here.
4.2.1
T R hyperthermia in dispersive media
As discussed in [86], application of time reversal in a dissipative medium is not optimal, since
TR invariance of the wave equation is no longer valid. Amplitude correction techniques to
partially account for dissipation effects have been proposed for ultrasound waves [86], as
well as for EM dispersion effects in homogeneous media [88]. A simple method for loss
compensation is considered here: a lossless homogeneous breast model with an average
dielectric constant is used as a reference to which the signals from the dispersive propagation
46
breast model are compared. The propagation model signals are then amplified by the scaling
factors obtained from this comparison with the reference lossless model.
4.2.2
Relation to beamforming
The T R process is equivalent to a frequency-domain phase conjugation of the signals received
due to the wave generated by the source at the desired focal point. This T R operation can
be cast as a beamformer, with a weight vector h^/j equal to the steering or "Green function"
vector [89], describing one-way propagation from the focal point Yf to each element of the
antenna array,
h T fl = g ( r / )
(4.1)
where frequency dependence is suppressed in the notation.
The weight vector YITR of Eq.
(4.1) can be related in a straightforward manner to the
single frequency space-time transmit beamforming (STTB) solution of [34], which is given
by,
h6 = a(Q + eiiv)-1d(r/)
(4.2)
In Eq. (4.2), a is a scaling factor, and d ( r j ) = g ( r / ) when the exact propagation model assumed in the T R process is available. The matrix Q is used in [34] to preferentially decrease
the power deposited in specified breast regions. We ignore this design option for comparison
with T R by setting Q = 0. In this case hfe (Eq. (4.2)) differs from hTR
(Eq. (4.1)) by
a scaling factor. This scaling factor has no impact on the spatial distribution of deposited
energy.
Note that T R and STTB will differ for wideband excitations, in general, due to the manner
in which STTB incorporates temporal filtering. This is the primary reason for discrepancies between the T R and STTB results presented in Section 4.4. STTB and T R will also
differ if dispersion compensation is used in T R as suggested in Subsection 4.2.1, or if Q is
incorporated to customize the STTB beampattern.
47
4.3
Numerical testbeds
As in [33], [34], we perform two-dimensional (2-D) simulations to calculate absorbed power
density deposition and temperature profiles inside the breast. A detailed description of the
EM and thermal F D T D models can be found in [33], [34]. For this 2-D study, we assume
t h a t the patient lies on a prone position, and an ellipsoidal array comprised of 16 antenna
elements surrounds the breast.
"Phantom 1"
"Phantom 2"
Figure 4.1 Dielectric constants at 6 GHz for the two numerical breast phantoms
considered in this study. The antenna array elements and tumor locations (stated in
Section 3) are marked with crosses (original figure in color).
We simulate this configuration using coronal slices taken from two distinct MRI-dcrivcd
three-dimensional (3-D) numerical phantoms [90]. The spatial profile of the dielectric constant at 6 GHz in each phantom is shown in Figure 4.3; the effective conductivity profile is
identical except for the range of values which spans 0.017 to 6.4 S/m at 6 GHz. "Phantom
1" is derived from a patient with a larger total breast tissue volume and breast density classified by the American College of Radiology (ACR) [79] as "scattered fibroglandular," while
"Phantom 2" corresponds to a patient with an ACR classification of "heterogeneously dense"
and an overall smaller tissue volume. The slices were taken at 5.9 cm and 3 cm from the chest
48
wall for the first and second phantoms, respectively A 5-mm-diameter tumor inclusion is introduced m the dense tissue region at (x=5 70 cm ,y=5 95 cm) for "Phantom 1" and (x=7 90
cm ,y=5 95 cm) for "Phantom 2" The EM properties assigned to the tumor are similar to
those of muscle and fall withm the lange of properties of flbroconnective/glandular tissue
This is an important difference from the study in [33], [34], which assumed a high contrast
between the tumor and surrounding tissue All phantoms include a 2-mm-thick skin layer,
and are immersed m DI water
As in [34], one of the figures of merit used to evaluate the focusing efficacy of the hyperthermia approach is the spatial distribution of the heating potential, or power dissipated per
unit volume (Q), which is calculated via F D T D EM simulations
Ultimately, the quantity
of interest m hyperthermia applications is the temperature distribution within the breast,
which may be insensitive to small differences m the power density profiles achieved with different methods These temperature profiles are calculated using an F D T D thermal model
We also calculate several metrics which facilitate a quantitative comparison of the different
cases considered m this study We define the focal region as a circle with a diameter twice
t h a t of the tumor and calculate the power inside this region (denoted as Pf) as a percentage
of the total power absorbed in the breast We also calculate the area of all regions that exhibit Q > ? 3 dB outside of the focal region (denoted as S), as a percentage of the total area
of t h e breast
Finally we calculate the percentage of breast area that exhibit tempeiatures
above certain thresholds using the d a t a computed from the thermal model
4.4
Results
The impact of dispersion is studied m the first set of simulations We consider the more dense,
second phantom to better demonstrate the effect of applying dispersive loss compensation
to the hyperthermia system input signals We initially consider a tumor-free homogeneous
version of the second breast phantom with dielectric properties equal to the spatial average
49
of the heterogeneous phantom, and a propagation model that is matched to the homogeneous
phantom. The deposited power densities without and with compensation for loss are shown
in Figures 4.2 (a) and (b), respectively. These results demonstrate that focusing near the
tumor is improved somewhat by dispersive loss compensation at the expense of increased
absorbed power throughout the breast. The results of repeating this experiment with the
heterogeneous breast phantom but the same homogeneous propagation model are shown in
Figures 4.2 (c) and (d). As in the homogeneous case, dispersive loss compensation achieves
slightly better focusing in the neighborhood of the tumor at the expense of increased power
deposition throughout the remainder of the breast. These observations are supported by the
quantitative data presented in Table 4.1. These results suggest that it is preferable to use
the signals generated directly from the dispersive propagation model without compensating
for loss. We adopt this strategy of avoiding compensation for the remaining investigations
reported in this paper.
Mismatch between the propagation model and the actual breast will result in suboptimal
focusing performance. Since exact structure and dielectric properties are generally not available in practice, we compare the robustness of TR and STTB focusing performance to
mismatch for the first and second phantoms in Figures 4.3 and 4.4, respectively. The top
row of each figure depicts power deposition when the exact propagation model is used to
design the TR and STTB weights, while the bottom row depicts power deposition when a
homogeneous dispersive propagation model is used to design the TR and STTB weights.
The dielectric properties in the homogeneous model are set equal to the spatial average of
the phantom properties. All power density distributions are normalized to the power at the
central tumor location. Focusing metrics for these examples are given in Table 4.1.
Figure 4.3 illustrates that use of the homogeneous model results in slightly higher power deposition away from the focus location. This effect is more pronounced for the heterogeneously
dense phantom as shown in Figure 4.4. The STTB approach is slightly more sensitive to
50
1 Microwave power deposition metrics for the Q distributions of Figures 4.2, 4.3
(S: area outside focal region with Q > ?3 dB, as a percentage of the total breast
power absorbed inside focal region as a percentage of the total power absorbed in
the breast.)
Figure 4.2(a)
Figure 4.2(b)
Figure 4.2(c)
Figure 4.2(d)
S{%)
2.5
0.8
1.7
3.3
Pf(%)
7.5
7.0
8.2
5.8
Figure 4.3(a)
Figure 4.3(b)
Figure 4.3(c)
Figure 4.3(d)
S{%)
0.0
0.1
0.4
1.2
Pf(%)
14.5
13.0
12.0
11.7
Figure 4.4(a)
Figure 4.4(b)
Figure 4.4(c)
Figure 4.4(d)
S(%)
0.7
1.0
1.7
4.2
pf(%)
12.5
12.0
8.2
4.7
deviations between the true and assumed models than T R in both phantoms. These results
suggest that use of detailed information is beneficial. Note also that the differences between
T R and STTB are relatively small as expected in light of the analysis in Section 4.2.2. T R
seems to perform slightly better in both phantoms, which may be a consequence of the frequency filtering performed by the wideband implementation of STTB.
T h e temperature profiles corresponding to the T R power density distributions of Figures
4.3 and 4.4 are shown in Figure 4.5. Temperature profiles for the S T T B power densities of
Figures 4.3 and 4.4 are very similar and are not shown. Figure 4.5 shows that the desired
increased temperature at the tumor is achieved for both exact and homogeneous propagation
models. A slight increase in the overall temperature of the breast is observed for the profiles
corresponding to the approximate propagation models (Figures 4.5 (b) and (d)), especially
for the more challenging heterogeneously dense breast phantom. This is confirmed by calculating the percentage areas above specified temperatures given in Table 4.2. The relatively
51
small differences in the temperature profiles between the exact and homogeneous propagation models suggests that some of the most visually apparent differences in the distribution
of Q may not have a significant impact on the resulting temperature distributions.
Table 4.2 Percentage of breast area above 42癈, 41癈 and 40 癈 for the profiles of Figure
4.5.
4.5
Figure
<ST>42癈*(%)
5x>4i癱(/o)
<5T>40癈*(%)
4.5(a)
0.52
1.40
2.90
4.5(c)
0.57
1.70
3.27
4.5(b)
0.80
2.11
4.06
4.5(d)
1.17
2.82
5.12
Conclusions
We presented a computational study for the application of a TR approach to microwave
hyperthermia. The proposed method is based on constructing a propagation model which
generates the signals to be used in the TR hyperthermia system. For exact TR focusing,
this propagation model requires a fully known breast phantom, with accurate EM properties
of the various tissues. The same model can be used in the context of STTB, which has been
previously studied for hyperthermia. The relationship between TR and STTB was discussed.
The impact of dispersion on TR was also briefly examined, and it was shown that accounting
for loss by pre-compensation can cause an increase in the power dissipated in breast regions
other than the tumor. This leads to the conclusion that a dispersive propagation model is
preferable, as it "favors" input signals from those antennas that can contribute the most in
focusing the energy back onto the tumor.
Results for breast phantoms with different anatomical characteristics show that good focusing can be achieved even when an approximate propagation model is used for generating the
input signals of the hyperthermia system. Very similar results were obtained from TR and
52
STTB methods. Temperature profiles throughout the breast resulting from the calculated
power densities indicate that the proposed methods can achieve the desired hyperthermia
treatment objective without damaging surrounding tissues.
53
5 y(cm)
10
5
y (cm)
10
Figure 4.2 Effect of applying dispersive loss compensation to the TR inputs of the
hyperthermia experiment involving (a),(b) homogeneous and (c),(d) heterogeneous versions
of the second breast phantom. All four images show power density distributions (Q) in dB.
On the left (right), Q is calculated without (with) compensation applied to signals
computed from a propagation model matched to the homogeneous phantom. -3 dB contour
plots are shown with black lines (original figure in color).
54
y(cm)
12
2
y(cm)
Figure 4.3 TR (left) and STTB (right) power density distributions (Q) in dB for the
scattered fibroglandular phantom. The TR and STTB weights are designed using (a),(b)
the exact propagation model, and (c),(d) a homogeneous propagation model. -3 dB
contour plots are shown with black lines (original figure in color).
Figure 4.4 TR (left) and STTB (right) power density distributions (Q) in dB for the
heterogeneously dense phantom. The TR and STTB weights are designed using (a),(b) the
exact propagation model, and (c),(d) a homogeneous propagation model. -3 dB contour
plots are shown with black lines (original figure in color).
55
Figure 4.5 Temperature profiles resulting from the TR power deposition patterns for: (a)
the scattered fibroglandular phantom and an exact propagation model, (b) the
heterogeneously dense phantom and a exact propagation model, (c) the scattered
fibroglandular phantom and a homogeneous propagation model, and (d) the
heterogeneously dense phantom and a homogeneous propagation model (original figure in
color).
56
Chapter 5
3-D computational study of non-invasive patient-specific
microwave hyperthermia treatment of breast cancer
Non-invasive microwave hyperthermia treatment of breast cancer is investigated using threedimensional (3-D) numerical breast phantoms with anatomical and dielectric-properties realism. 3-D electromagnetic and thermal finite-difference time-domain simulations are used
to evaluate the focusing and selective heating efficacy in four numerical breast phantoms
with different breast tissue densities. Beamforming is used to design and focus the signals
transmitted by an antenna array into the breast. We investigate the use of propagation
models of varying fidelity and complexity in the design of the transmitted signals. An ideal
propagation model that is exactly matched to the actual patient's breast is used to establish a best-performance baseline. Simpler patient-specific propagation models based on a
homogeneous breast interior are also explored to evaluate the robustness of beamforming
in practical clinical settings in which an ideal propagation model is not available. We also
investigate the performance of the beamformer as a function of operating frequency and compare single-frequency and multiple-frequency focusing strategies. Our study suggests that
� 2010 IOP Publishing. Sections 5.1 - 5.5 is reprinted, with permission, from E. Zastrow, S. C. Hagness
and B. D. Van Veen, "3D computational study of non-invasive patient-specific microwave hyperthermia
treatment of breast cacer", Physics in Medicine and Biology, vol. 55, pp. 3611-3629, 2010. Section 5.6 is
not part of the copyrighted material.
Section 5.6 is the results of a collaboration with A. Mashal, P. Avti, B. Sitharaman, J. H. Booske, and
S. C. Hagness
The work presented in this chapter was supported by the National Science Foundation under grant
CMMI 0625054, and the National Institutes of Health under grant R01 CA112398 awarded by the National
Cancer Institute.
57
beamforming is a robust method of non-invasively focusing microwave energy at a tumor
site in breasts of varying volumes and breast tissue density.
5.1
Introduction
Numerous studies have shown that hyperthermia (40-45癈, for 60-90 minutes duration)
causes direct cytotoxicity due to heat damage (see, for example, [4,5]) and increases sensitivity of cancer cells to radiation therapy and chemotherapy (see, for example, [5-9]).
The goal of hyperthermia cancer treatment is to achieve a temperature of approximately
40-45� C in a region which includes the tumor and a margin of healthy tissue while maintaining normal temperatures in surrounding tissue. The negative margin targeted by thermal
therapy [91,92] is on the order of 1 cm. This practice is consistent with surgical resection
protocols which typically involve the removal of a 1-cm negative margin in an attempt to
reduce local recurrence rates [93-96]. According to the American Cancer Society [97], the
most common stages of diagnosis of breast cancer are stages I and II, which include localized
tumors from 1 mm to 5 cm in their largest dimensions. Volumes from 3 cm up to 9 cm in
the largest dimension are commonly targeted for treatment [26]. High-frequency (1-4 MHz)
focused ultrasound hyperthermia creates a millimeter-size heating zone, thereby requiring
multiple sonications in order to treat centimeter-size tumors [98-100]. Lower-frequency (1
kHz) ultrasound-based therapy has been explored recently [101] as a means to achieve a
larger heating zone with a single sonication. Focused microwave hyperthermia also offers
promise for creating a centimeter-size heating zone from a single intended focal point.
Progress towards non-invasive microwave-induced thermal therapy of breast cancer has been
made over the past decade. Fenn et al. [27], Gardner et al. [28], and Vargas et al. [29] conducted clinical studies of an adaptive microwave phased array with an invasive electric-field
feedback probe. The breast was compressed in order to immobilize the tissue and improve
the coupling of microwave energy into the breast. The electric-field probe was used to adjust
the phased array to achieve a focus at the treatment site. A more comprehensive review of
58
these and other clinical studies was recently reported in Dooley et al. [26]. Theoretical studies
of other focusing methods, such as time reversal [30,31], use of a deformable mirror [32], and
transmit beamforming [33,34], were conducted using computational electromagnetic (EM)
and thermal simulations with two-dimensional (2-D) numerical breast phantoms of varying realism. While these techniques are intended to achieve focusing of microwave energy
non-invasively, the theoretical performance demonstrations were successful in part because
some degree of knowledge about the breast tissue configuration and dielectric properties was
assumed to be available.
The objective of this 3-D numerical study is to evaluate the sensitivity and robustness of
non-invasive transmit beamforming for hyperthermia treatment of localized breast tumors
for future clinical implementation. Transmit beamforming involves passing microwave signals through a set of filters which are designed to compensate for dispersive propagation
effects in the interior of the breast so that, ideally, the transmitted signal from each antenna adds coherently at the treatment location and incoherently elsewhere. The efficacy
of transmit beamforming depends on the quality of the assumed propagation model used in
the design of the filters. The propagation model describes the one-way propagation effects
from each antenna to the target location. In this numerical study, we investigate the use of
propagation models of varying complexity and fidelity in the design of the beamformer; that
is we investigate the use of patient-specific information under the assumption that the exact
knowledge about the patient's breast may not be available.
The performance of microwave beamforming is assessed within the frequency range of 1
- 5 GHz.
This frequency range is higher than the operating frequencies of most clinical
applicators, which generally operate at a frequency within the 100 - 1000 MHz band (see,
for example, [6,102]). We are interested in higher frequencies because they offer better resolution for the treatment of cm-size lesions (A ~ 4.3 cm at 1 GHz and A ~ 0.90 cm at 5 GHz,
where A is the wavelength in glandular tissue) and adequate penetration through breast
59
tissue (5 fat ~ 20.2 cm, <5gianduiar ~ 4.2 cm at 1 GHz and 5 fat ~ 5.5 cm, d g i andular ~ 0.85 cm
at 5 GHz, where S is the depth at which the amplitude of an electromagnetic plane wave is
attenuated by 1/e).
This numerical study represents significant advances over past studies [33, 34] in terms of
the realism of the testbeds used. The 2-D phantoms used in past studies underestimated the
degree of dielectric heterogeneity of breast tissue and overestimated the dielectric contrast
between normal and malignant breast tissue ? both of which overly simplified the challenge
of selectively heating the tumor. In this study, we use three-dimensional (3-D) anatomically
realistic numerical breast phantoms as our numerical testbeds. The dielectric properties of
the phantoms are obtained from the Wisconsin-Calgary large-scale dielectric spectroscopy
study [24]. We assume no contrast between normal fibroglandular and malignant tissue, instead of the ~ 1 0 % contrast reported by Lazebnik et al. [25]. This assumption eliminates the
role of differential microwave power absorption in the selective heating of tumors, thereby
creating a more challenging testbed wherein selective heating must be achieved solely by
focusing.
5.2
Models and methods
Beamforming hyperthermia performance is evaluated in four virtual patients represented by
numerical breast phantoms having different breast compositions. A patient-specific propagation model is constructed from 3-D finite-difference time-domain (FDTD) EM simulations
of the numerical phantom and is used to design the beamformer signal set that is transmitted into the breast. Next, the hyperthermia performance of the beamformer signal set is
evaluated by calculating heating potential and steady-state temperature distributions inside
the breast using 3-D FDTD-EM and FDTD-thermal models.
5.2.1
Numerical testbeds
We utilize four anatomically realistic numerical breast phantoms derived from MRIs of patients with varying breast compositions [103] as our virtual patients. The phantoms are
60
digitized to 0.5 mm x 0.5 mm x 0.5 mm resolution.
The specific numerical phantoms
chosen for this study include one example of each of the following four American College of
Radiology (ACR) categories of breast tissue density [79]: fatty, scattered fibroglandular, heterogeneously dense, and extremely dense. No tumors are present in the numerical phantoms
used in this study. The absence of tumors provides a worst-case selective heating scenario by
eliminating the benefit of any conductivity contrast between the tumor and the surrounding breast tissue. This is a significant difference from the previous studies of Converse et
al. [33,34], which assumed a high conductivity contrast between the desired focus (tumor)
and the surrounding tissue.
Figure 5.1 depicts the four virtual patients used in this study. The patient is assumed to be
in a prone position with three 8-element conformal arrays surrounding the breast as shown
in Figure 5.1 by the circles. The arrays are placed at elevations x ? Xf and x ? x / � 1 . 5
cm, where Xf represents the x-coordinate of the desired focus. Figure 5.2 illustrates coronal
cuts at x = Xj through the four phantoms. The focus location for each patient is marked
with a cross-hair. The desired focus is chosen to be located in fibroglandular tissue in each
phantom at a depth at least 2 cm from the skin and not near the chestwall. The array
elements are vertically directed electric current sources. Each element is excited with the
corresponding beamformer output signal. Forced-air cooling of 20癈 is assumed in the environment surrounding the breast. The optimal antennas, array configuration, and coupling
medium for clinical hyperthermia experiments may differ from those employed in this study.
For example, these omnidirectional antennas are too inefficient for a clinical hyperthermia
system, but suffice to evaluate focusing performance. Also, hyperthermia performance may
be further improved with the use of an optimized array configuration and an optimal choice
of coupling medium between the antennas and the breast.
61
10 20
30
40 50 60
15
^,
10 20
30
40 50 60
50 60
108
^
(a)
10 20
30 40
^
(b)
10 20
30 40
50 60
J ,810~
2 (cm)
(c)
(d)
Figure 5.1 Cutaway view showing the relative permittivity distribution at 5 GHz in each
of four 3-D numerical breast phantoms used as performance testbeds. The desired focus is
indicated by a cross-hair and the 24 antenna locations are marked by small circles. The
phantoms are representative of all four categories of breast tissue density, (a) Fatty, (b)
Scattered fibroglandular. (c) Heterogeneously dense, (d) Extremely dense. (Original
figures in coloui)
62
10
20
30
40
o
0
o
50
60
10 20 30 40 50 60
x=7 7cm
/
X
\
r
J
/ �
1.
o
2
o
4
6
8 10 12 14 16
z (cm)
2
4
6 8
z (cm)
10 12
(b)
(a)
10 20 30 40 50 60
12
o
10
o
�"
x=5 5cm
10
20
30
40
50
60
* *
8
6
4
2
o
2
o
4
6 8
z (cm)
(c)
10 12
2
4
6 8 10 12 14
z (cm)
(d)
Figure 5.2 Relative permittivity distribution in the coronal cross-section containing the
desired focus (indicated by a cross-hair) in each of the phantoms of Figure 5.1. The
antenna locations at elevation x = Xf (noted in the upper right corner of each image) are
indicated by V markers, (a) Fatty, (b) Scattered fibroglandular. (c) Heterogeneously
dense, (d) Extremely dense.
63
5.2.2
Beamformer design
The beamformer consists of a finite-impulse response (FIR) filter m each antenna channel
The filters are designed to focus microwave energy at the target region by adjusting the
frequency-dependent amplitude and phase of transmitted signals Let Hn(u),n
= 1,
,N
be the frequency response of the FIR filter for the n t h channel, and let T n (cu,r f ) represent
the frequency-dependent one-way propagation from the nth source to the target location rf
The beamformer design objective is to maximize the fraction of the total transmitted power
delivered to the target location rf This is expressed mathematically as
2
/ E^=i#nHT n (u;,r f )
dui
?
max
We solve (5 1) by writing Hn(u)
= Y,k=i hn[k]e-^kT%
(5 1)
where hn[k],k
= 0,1,
,M - 1
are the FIR filter coefficients in the nth channel and Ts is the sampling interval
The FIR
filter coefhcients are then obtained by solving an eigenproblem as m [104]
After the FIR
filter coefficients are determined the transmitted signal at each channel is then obtained by
passing a desired input signal through the filter,
Yn(u)
where I(to) is the input signal spectrum
= Hn(u)I(u)
(5 2)
Previous studies used a simple analytical prop-
agation model to obtain T n (a;, rf) (see, for example, [33])
In this study we use F D T D
simulations to accurately identify T n (o;,r f ) for each propagation model
Four types of propagation models ? one heterogeneous and three homogeneous ? are constructed for each patient
The heterogeneous model assumes that full knowledge of the
patient's breast is available, including not only the breast shape and interior tissue structure, but also the spatially varying tissue dielectric properties
This knowledge permits us
to construct a propagation model that corresponds to the true propagation characteristics of
the patient's breast Thus, Figure 5 1 depicts not only the numerical phantoms but also the
64
heterogeneous propagation models for the four patients
The range of dielectric properties
for heterogeneous propagation models is illustrated in Figures 5 3(a) and 5 3(b)
Each of
the three homogeneous propagation models is constructed under the assumption that the
knowledge of the breast shape and the skm thickness is available The interior properties are
either patient-specific average pioperties or one of two different patient-independent propeities
The patient-specific average properties are obtained by spatially averaging the true
properties of each patient, we denote this propagation model as "homogeneous-average "
Since we consider four specific patients m this study, one from each of four classes of breast
density, we have four examples of homogeneous-average models
The "homogeneous-low"
propagation model consists of patient-independent median adipose properties reported m
the Wisconsin-Calgary study [24] while the "homogeneous-high" propagation model consists
of patient-independent properties that are equal to 3 5 times the median adipose properties
Figures 5 3(c) and 5 3(d) illustrate the wideband dielectric properties of the interior breast
tissue for the three homogeneous propagation models
5.2.3
Performance evaluation methods
The four distinct propagation models described in Section 5 2 2 are used to design the beamformer for each of the four virtual patients
This results in a total of 16 different pairings
between patients and propagation models A transmit signal set is calculated for each case
and hyperthermia performance is evaluated for both wideband operation (1-5 GHz, 10%
powei bandwidth) and narrowband operation at seven different frequencies evenly spaced
between 1 and 4 GHz This results m 128 simulated hypertheimia experiments
T h e computational domain of the FDTD-EM model comprises a uniform spatial grid of
cubic Yee cells
The grid cell size of Ax = Ay = Az = 0 5 mm provides a grid sampling
density of N\ ~ 18 m glandular tissue at 5 GHz Uniaxial perfectly matched layer (UPML)
absorbing boundary conditions are used to terminate the computational domain
Materi-
als dispersion is incorporated into the F D T D model via the auxiliary differential equation
65
2
3
frequency (GHz)
4
frequency (GHz)
(a)
30
20
- - ? homog -high (patient-independent)
? homog -low (patient-independent)
*? extremely dense
%
e? heterogeneously dense I homog -average
B - scattered fibroglandular? (patient-specific)
9? fatty
J
(b)
4
3.5
3
25
- - homog -high (patient-independent)
? homog -low (patient-independent)
*? extremely dense
^
e? heterogeneously densel homog -average
B- scattered fibroglandulair (patient-specific)
v? fatty
J
2
15
10
frequency (GHz)
(c)
frequency (GHz)
(d)
Figure 5.3 (a) Relative permittivity as a function of frequency for representative voxels in
the heterogeneous propagation model, (b) Effective conductivity as a function of frequency
corresponding to the data shown in (a), (c) Relative permittivity as a function of requency
in the homogeneous-low, homogeneous-high, and homogeneous-average propagation
models, (d) Effective conductivity as a function of frequency corresponding to the data
shown in (c). (Original figures in colour)
method [47]. A Courant factor of S = 0.5 is chosen to ensure stability. The distribution
of the heating potential, Q [W/m3], inside the numerical breast phantoms is evaluated for
66
wideband operation using the FDTD-computecl time-domain field quantities as follows:
^max
71 = 0
Here i,j, k are the computational grid indices, R is the assumed pulse repetition rate, At is
the FDTD timestep, E and J are the time-domain electric field and total current density
vectors, respectively, and n max is the maximum timestep in the simulation. Similarly, Q is
evaluated for narrowband operation using the following expression:
QiJ,k = T
E
Tl-?fimax
(^k.Jf^k)At
[W/m3]
(5.4)
^period
where T is the period of the transmitted signal and nperi0d is the number of time steps in one
period. The simulations are executed until steady-state field interactions are established. In
both Eq. 5.3 and Eq. 5.4, we use the six-field-component averaging approach described in [50].
A 3-D FDTD-thermal model based on the Pennes bio-heat equation [51] is used to obtain
the steady temperature profile in the numerical breast phantoms.
Cp(r)p(r)^
=
V - ( A - ( r ) V T ( r ) ) + 4 ) ( r ) + g(r)
-B(v)(T(v)-TB)
(5.5)
[W/m3]
The tissue-dependent thermal parameters, Cp, p, K, A0, B, are the specific heat, density,
thermal conductivity, metabolic heat generation, and capillary blood perfusion coefficient, respectively. The blood perfusion coefficient for each tissue is assumed to be time-independent
and is assigned its basal value. We assume that Tg, the blood temperature, is constant and
equal to the body's core temperature of 37癈. Q is the heating potential computed by the
FDTD-EM model. We assign the thermal properties of fat and muscle to the parameters for
fatty and fibroglandular breast tissue, respectively. The thermal properties of fatty breast
tissue and skin used in the thermal model are the same values found in [34]. The thermal
properties of fibroglandular breast tissue and muscle chest wall are the same as the thermal
properties of muscle listed in [105]. The thermal properties are summarized in Table 5.1. A
67
Tissue
Table 5.1 Thermal properties used in the FDTD-thermal model
Cp [J/kg/癈] p [kg/m3] K [W/m/癈] A0 [W/m3] B [W/m3/癈]
skin
3765
1085
0.397
fatty tissue
2279
1069
0.306
fibroglandular
3600
1050
0.5
1620
5929
. 350
2229
690
2700
tissue and muscle (chestwall)
convective heat boundary condition is employed at the skin-air interface with a convection
coefficient of h = 5 [W/m 2 /癈] ? a value appropriate for natural convection or low-flow
forced convection of air [106]. The F D T D implementation of Eq. 5.5 and the convective
heat boundary condition follows the method described in [52]. The grid resolution of the
FDTD-thermal model is identical to that used in the FDTD-EM model. The FDTD-thermal
simulations are executed until the steady-state temperature is reached.
T h e relative amplitude and phase of each signal to be transmitted into the breast is obtained from Eq. 5.2. However, the absolute amplitude across the array ? that is, the input
power required to achieve the desired temperature ? is not determined by the beamformer
design process. Therefore, our strategy is to conduct an FDTD-EM simulation using the
beamformer signal set obtained from Eq. 5.2 and compute the heating potential. Then we
conduct several F D T D thermal simulations using scaled versions of the heating potential as
the source to determine the amplitude factor that achieves a steady-state temperature at
the desired focus, rf, of 45 �15癈. Finally the steady-state temperature distribution is
reported for the appropriately scaled transmitted signal set.
5.3
Results
We quantify the selective heating efficacy of transmit beamforming using several thermal
metrics defined as follows:
68
1. V43 (cm 3 ): the volume of breast tissue with temperature greater than 43癈.
2. r (mm): the radial distance from rf to the location of peak breast interior temperature.
3- �&kin (癈): peak skin temperature.
4- ^breast (癈): peak breast interior temperature.
Our goal is to induce therapeutic heating in a volume of tissue roughly on the order of 1 cm 3 .
This is considered to be a small volume in the context of microwave hyperthermia. In addition to a small V43, we consider accurate focusing (small r ) , a low peak skin temperature (low
*skin),
an
d a peak breast interior temperature close to the temperature at rf (ibreast ? 45癈)
to be desirable. For each patient, the hyperthermia experiments are evaluated for four distinct propagation models used in beamformer design: heterogeneous, homogeneous-average,
homogeneous-low, and homogeneous-high. For each propagation model, we consider beamforming performance under seven different cases of narrowband operation and under wideband operation. Beamforming performance for the 32 experiments performed on each of the
four patients is reported in two stages to streamline the presentation. In Section 5.3.1, we
consider performance as a function of operating frequency, while in Section 5.3.2 we consider
performance as a function of the propagation model used in beamformer design.
5.3.1
Performance as a function of operating frequency
Figure 5.4 illustrates the narrowband performance trends for the four patients as a function
of operating frequency, in terms of the thermal metrics defined above. Results are shown
for the case where a heterogeneous propagation model is used to design the transmit signal
set. The trends indicate that for each patient, there exists an operating frequency at which
the narrowband beamformer achieves a desirable outcome. This optimal frequency depends
upon the physical structure and tissue composition of the breast.
T h e results in Figure 5.4 indicate that in the fatty breast, the smallest Vi3 (~1.6 cm 3 ),
and the smallest r (~1.4 mm) are achieved at the operating frequency of 3.0 GHz.
The
69
peak temperatures in the skin and the breast interior increase slightly at operating frequencies greater than 3.0 GHz. The operating frequency for the scattered fibroglandular
breast with minimum V43 (~0.4 cm 3 ) is 4.0 GHz while minimum r (~1.0 mm) occurs at
1.0 GHz. However, the peak skin temperature reaches an unsafe value (kin ~ 45癈) at
1.0 GHz. Therefore, the optimal operating frequency for the scattered fibroglandular breast
is 4.0 GHz. For these two low density breasts (fatty and scattered fibroglandular), the results
presented in Figure 5.4 show small variations in the heating zone size and focusing accuracy
over the frequency range of interest.
In contrast, the performance trends presented in Figure 5.4 for the heterogeneously dense
breast and extremely dense breast show significant variations in the heating efficacy over the
frequency range of interest. The narrowband frequency for the heterogeneously dense breast
with minimum V43 (~1.4 cm 3 ) and r (~2.1 mm) is 1.5 GHz. For the extremely dense breast,
the best performance is also observed at an operating frequency of 1.5 GHz, which yields the
smallest V43 (~1.6 cm 3 ) and the smallest r (~1.2 mm). For these two high density breasts
(heterogeneously dense and extremely dense), the results presented in Figure 5.4 show the
peak skin and the peak breast interior temperatures increasing rapidly for operating frequencies greater than 2.0 GHz. Poor focusing accuracy, indicated by r >10 mm, occurs at
operating frequencies greater than 3.0 GHz.
Figures 5.5-5.8 present the normalized EM heating potential and steady-state temperature distributions as a function of operating frequency for patients with fatty and extremely
dense breasts. Figures 5.5 and 5.6 depict Q(r) normalized to Q(v{), and the corresponding
steady-state temperature distribution, respectively, in the coronal plane containing rf for the
fatty breast. The normalized Q of 0 dB corresponds to a specific absorption rate of 181, 305,
340, and 348 W / k g in Figures 5.5(a), 5.5(b), 5.5(c), and 5.5(d), respectively. Figures 5.7
and 5.8 depict similar information for the extremely dense breast. The specific absorption
rates corresponding to a normalized Q of 0 dB in Figures 5.7(a), 5.7(b), 5.7(c), and 5.7(d) are
70
20
30
-fatty
-scattered fibroglandular
- heterogeneously dense
-extremely dense
25
15
-fatty
-scattered fibroglandular
- heterogeneously dense
-extremely dense
20
15
E 10
10
2
2.5
3
Frequency (GHz)
2
2.5
3
Frequency (GHz)
(a)
(b)
57
55
-fatty
-scattered fibroglandular
- heterogeneously dense
-extremely dense
53
O
S 51
49
25
1.5
2
2.5
3
Frequency (GHz)
(c)
3.5
2
2.5
3
Frequency (GHz)
(d)
Figure 5.4 Selective heating efficacy quantified in terms of four thermal metrics for the
four virtual patients, as a function of frequency. Results are shown for the case where a
heterogeneous propagation model is used to design the transmit signal set. (a) Volume of
breast tissue with temperature greater than 43� C. (b) Distance from the desired focus to
peak breast interior temperature, (c) Peak skin temperature (癈). (d) Peak breast interior
temperature (癈).
71
141, 218, 215, and 118 W/kg, respectively. Detailed discussion of these results is provided
in Section 5.4.
The results presented in Figure 5.9 compare steady-state temperature distributions for
wideband excitation and the optimal narrowband frequency in fatty and extremely dense
breasts. We observe that narrowband excitation at the optimal frequency results in slightly
better selective heating performance in the extremely dense breast and comparable performance in the fatty breast. The similarity between wideband and optimal narrowband
performance in the fatty breast is evident by comparing the steady-state temperature distributions shown in Figures 5.9(a) and 5.9(b). For the extremely dense breast, the performance
with wideband excitation (Figure 5.9(c)) is poorer than that with the optimum narrowband
excitation of 1.5 GHz (Figure 5.9(d)); namely, the treatment region obtained with wideband
excitation is skewed from rf. The skin temperature remains below 30癈 for both excitations.
5.3.2
Performance as a function of propagation model complexity
In this section, we report the selective heating performance as a function of propagation
model assumed in the design of the beamformer. We begin by reporting the performance
of the narrowband beamformer at the optimal operating frequency. The optimal operating
frequency varies within a given patient, depending on the propagation model used in the
beamformer design. The bar graphs in Figure 5.10 illustrate the best achievable performance
in each pairing of patient and propagation model. The heterogeneous model generally provides the best overall performance. The metrics V43 and r are more sensitive to propagation
model choice than tsk;n and tbreast-
Figure 5.11 illustrates the performance of the wideband beamformer in each pairing of
patient and propagation model. The performance trends of the wideband beamformer for
the four patients follow the narrowband performance trends. For the fatty and scattered
72
2
4
6
8 10 12 14 16
z (cm)
2
4
6
(b)
(a)
2
4
6
8 10 12 14 16
z (cm)
(c)
8 10 12 14 16
z (cm)
5
10
z (cm)
(d)
Figure 5.5 Normalized EM heating potential (coronal cross-section) resulting from
narrowband focusing at different operating frequencies, for a patient with fatty breast
composition (see Figures 5.1(a) and 5.2(a)). Results are shown for the case where a
heterogeneous (exact) propagation model is used in the beamformer design. The contour
lines indicate -10 dB contours, (a) 1 GHz. (b) 2 GHz. (c) 3 GHz. (d) 4 GHz.
73
2
4
6
8 10
z (cm)
12
14 16
2
4
6
4
6
8 10
z (cm)
(c)
12
14 16
12
14 16
(b)
(a)
2
8 10
z (cm)
12
14
16
2
4
6
8 10
z (cm)
(d)
Figure 5.6 Steady-state temperature distribution (coronal cross-section) corresponding to
the heating potential of the fatty breast shown in Figure 5.5. (a) 1 GHz. (b) 2 GHz. (c) 3
GHz. (d) 4 GHz.
74
2
4
6 8 10 12 14
z (cm)
2
4
6 8 10 12 14
z (cm)
(b)
2
4
6 8 10 12 14
z (cm)
(c)
2
4
6 8 10 12 14
z (cm)
(d)
Figure 5.7 Normalized EM heating potential (coronal cross-section) resulting from
narrowband focusing at different operating frequencies, for a patient with extremely dense
breast composition (see Figures 5.1(d) and 5.2(d)). Results are shown for the case where a
heterogeneous (exact) propagation model is used in the beamformer design. The contour
lines indicate -10 dB contours, (a) 1 GHz. (b) 2 GHz. (c) 3 GHz. (d) 4 GHz.
75
20
25
2
30
4
35
40
45
20
25
30
35
40
45
35
40
45
6 8 10 12 14
z (cm)
(b)
20
2
4
6 8 10 12 14
z (cm)
(c)
25
2
30
4
6 8 10 12 14
z (cm)
(d)
Figure 5.8 Steady-state temperature distribution (coronal cross-section) corresponding to
the heating potential of the extremely dense breast shown in Figure 5.7. (a) 1 GHz. (b) 2
GHz. (c) 3 GHz. (d) 4 GHz.
76
2
2
4
4
6
6
8 10 12 14 16
z (cm)
6 8 10 12 14
z (cm)
(c)
2
4
8 10 12 14 16
z (cm)
6 8 10 12 14
z (cm)
(d)
Figure 5.9 Comparison of steady-state temperature distributions (coronal cross-section)
resulting from wideband focusing and narrowband focusing at the optimum frequency.
Results are shown for the case where the heterogeneous (exact) propagation model is used
in the beamformer design, (a) wideband (fatty), (b) optimum narrowband (fatty, 3.0 GHz).
(c) wideband (extremely dense), (d) optimum narrowband (extremely dense, 1.5 GHz).
77
14
14
^ 1 heterogeneous
12 I I homogeneous-average
I I homogeneous-low
I .1 homogeneous-high
10
E
?
heterogeneous
homogeneous-average
12 . ?
I I homogeneous-low
. C 3 homogeneous-high
10
-
8
J? 6
in
fatty
ttt\t\
scattered
heterog.
fibroglandular dense
i
^r
fatty
extremely
dense
(a)
,?| -
^
r
scattered
heterog.
fibroglandular dense
extremely
dense
(b)
50
40
?
heterogeneous
I I homogeneous-average
48 I I homogeneous-low
\Z3 homogeneous-high
?
heterogeneous
I I homogeneous-average
I 1 homogeneous-low
35 SB homogeneous-high
o
O
46
30
??= 44
25
20
42
fatty
scattered
heterog.
fibroglandular dense
extremely
dense
40
fatty
scattered
heterog.
fibroglandular dense
extremely
dense
(d)
(c)
Figure 5.10 The best achievable selective heating efficacy of narrowband operation
quantified in terms of four thermal metrics for the four patients (fatty, scattered
fibroglandular, heterogeneously dense, extremely dense), as a function of propagation
model complexity used in the beamformer design (heterogeneous, homogeneous-average,
homogeneous-low, homogeneous-high). The results are shown at the optimal narrowband
frequency of each paring of patient and propagation model, (a) Volume of breast tissue
with temperature greater than 43� C. (b) Distance from the desired focus to peak breast
interior temperature, (c) Peak skin temperature (癈). (d) Peak breast interior temperature
(癱).
78
Table 5.2 Selective heating efficacy quantified in terms of four thermal metrics evaluated
for a numerical phantom with homogeneous breast tissue. Homogeneous propagation
models are used in the wideband beamformer design. The performance is evaluated as a
function of dielectric properties mismatch with respect to the true properties of the breast.
A negative (positive) percentage mismatch refers to the case in which the propagation
model underestimates (overestimates) the dielectric properties.
% mismatch
V43 (cm 3 )
r (mm)
tfekin (癈)
t b r e a s t (癈)
-75%
6.89
2.01
32.40
46.54
-50%
5.00
1.66
32.38
46.36
-25%
3.87
1.37
32.24
46.09
0%
3.47
1.35
32.29
45.96
+25%
3.41
1.39
32.66
45.92
+50%
3.46
1.43
33.27
45.87
+75%
3.67
1.49
33.94
45.92
fibroglandular breasts, the performance is comparable across the four propagation models while for the patients with more heterogeneous breast tissue (heterogeneously dense
and extremely dense), the use of patient-specific propagation models (heterogeneous or
homogeneous-average) generally provides better selective heating in the breast.
In order to separate the effects of heterogeneity and misestimation of tissue properties,
we consider a virtual patient with homogeneous breast tissue. We assume wideband operation and construct seven homogeneous propagation models: correct properties and � 2 5 % ,
�%, and � 7 5 % misestimation of properties. The results are summarized in Table 5.2.
T h e performance is found to degrade more rapidly with underestimation of properties than
with overestimation.
79
14
14
?
heterogeneous
12 I I homogeneous-average
I I homogeneous-low
^_j n0m0geneous_|1|g|-|
10
^ 1 heterogeneous
12 I I homogeneous-average
I I homogeneous-low
10 J j ~ 3 homogeneous-high
8
6
?n-n
fatty
r
rf
MMA
M
scattered
heterog.
fibroglandular dense
bi Iextremely
I IJ
extremely
dense
fatty
scattered
heterog.
fibroglandular
scattered
hidense
dense
(b)
50
40
?
heterogeneous
1 1 homogeneous-average
1 i homogeneous-low
35 C 3 homogeneous-high
^ 1 heterogeneous
I I homogeneous-average
48 I I homogeneous-low
UZI homogeneous-high
r?
It
P
o
30
25
20
I JJ[ J
fatty
1
scattered
heterog.
fibroglandular dense
(c)
extremely
dense
46
to
nj
Q)
42
40
fatty
scattered
heterog.
fibroglandular dense
extremely
dense
(d)
Figure 5.11 Selective heating efficacy of wideband operation quantified in terms of four
thermal metrics for the four patients (fatty, scattered fibroglandular, heterogeneously
dense, extremely dense), as a function of propagation model complexity used in the
beamformer design (heterogeneous, homogeneous-aver age, homogeneous-low,
homogeneous-high). The results are shown for each paring of patient and propagation
model, (a) Volume of breast tissue with temperature greater than 43� C. (b) Distance from
the desired focus to peak breast interior temperature, (c) Peak skin temperature (癈). (d)
Peak breast interior temperature (癈).
80
5.4
Discussion
We first consider the performance of transmit beamforming as a function of narrowband
operating frequency for fatty and extremely dense breasts. The EM heating potential in the
interior of the fatty breast shown in Figure 5.5 is highest in the fibroconnective/glandular
tissue region (see Figure 5.2(a) for tissue distribution), while absorption in the fatty region
is minimal. These results arc consistent with the differences in effective conductivity between fat and fibroglandular tissue. Absorption in the fatty region is only slightly elevated
at higher frequencies. The elevated absorption in the fatty region at 4.0 GHz, illustrated in
Figure 5.5(d), leads to a skewed treatment region in the direction of the elevated absorption
region, as shown in Figure 5.6(d). The skin remains cool due to the 20癈 forced air cooling
over the range of frequencies considered. The treatment volume size (V43) spans the range
of 1.6-5.5 cm3.
In contrast, the heating zone size varies considerably with excitation frequency for the extremely dense breast as shown in Figures 5.7 and 5.8. The treatment region is skewed and
grossly enlarged at the higher operating frequencies. Note that V43 spans a wider range (1.625.7 cm3) in extremely dense breast tissue than in fatty tissue. This is a direct consequence
of the presence of a greater amount of fibroconnective/glandular tissue (see Figure 5.2(d) for
tissue distribution).
Next we consider the selective heating performance as a function of the propagation model
assumed in the design of the beamformer for the fatty and extremely dense breasts. We
limit the discussion to these two patients as they represent the least and most challenging testbeds, respectively, for selective heating. For both patients, we observe a slight decrease in the heating zone volume when patient-specific propagation models (heterogeneous
or homogeneous-average) are used in the beamformer design. The performance in the fatty
breast is comparable for the three homogeneous propagation models as shown in Figures 5.10
81
and 5.11. The best achievable V43 in the fatty breast ranges from 1.6 cm3 to 3.1 cm3 in the
narrowband case and 1.9 cm3 to 3.1 cm3 in the wideband case, in spite of the fact that
the homogeneous-high er (dashed line in Figure 5.3(c)) overestimates the average er of the
patient by a large margin. Therefore, the results indicate that transmit beamforming is able
to accommodate the overestimation of the average er introduced in the homogeneous-high
propagation model for this patient.
In contrast, the average er of the extremely dense breast is close to the homogeneous-high
er (dashed line in Figure 5.3(c)) while the homogeous-low er (solid line in Figure 5.3(c))
significantly underestimates the average er. Figures 5.10 and 5.11 show that the best achievable V43 ranges from 1.5 cm3 to 2.2 cm3 in the narrowband case and 3.0 cm3 to 4.6 cm3
in the wideband case for the heterogeneous, homogeneous-average and homogeneous-high
propagation models. However, the use of homogeneous-low propagation model in the beamformer design leads to a larger heating zone, causing the best achievable V43 to increase
to 4.3 cm3 and 13.8 cm3 in the narrowband and wideband cases, respectively. Therefore,
transmit beamforming is relatively sensitive to underestimation of average er in this patient.
The results in Table 5.2 show that selective heating efficacy in a homogeneous phantom
is also much more sensitive to underestimation of er than to overestimation. Hence, we
conclude that the sensitivity of transmit beamforming to underestimation of the average er
is not limited to scenarios with a high degree of heterogeneity, as in the extremely dense
breast. These results indicate that overestimation of the average er used in the beamformer
design is preferable to underestimation.
5.5
Summary and conclusions
This study illustrates the potential of non-invasive patient-specific microwave hyperthermia
treatment via transmit beamforming with assumed knowledge of the breast shape. 3-D
82
anatomically realistic numerical breast phantoms with accurate dielectric properties of normal breast tissue were used as our testbeds. We have assumed that there is no conductivity
contrast between malignant and normal fibroglandular tissue in order to create the most
challenging selective focusing scenarios. Focus locations were chosen to be in
fibroglandular
tissue, at least 2 cm from the skin surface, and away from the chestwaU. We have investigated
the performance of transmit beamforming for patients with widely varying breast tissue density. Treatment regions as small as 1-2 cm in size were achieved within the breasts considered
in the study. We have explored the use of patient-specific propagation models of varying
complexity. Use of propagation models with patient-specific dielectric properties improves
the focusing efficacy of beamforming ? particularly in dense breasts. Complete patientspecific knowledge such as interior tissue structure, and the dielectric properties of breast
tissue, is not needed to obtain selective heating for effective hyperthermia treatment as long
as appropriate homogeneous properties of the breast are chosen for the propagation model.
In general, the performance of microwave hyperthermia via transmit beamforming is more
sensitive to underestimation of properties in the propagation model than overestimation.
Lastly, the study also indicates t h a t for each patient, there exists a narrowband frequency at
which focusing is optimum and slightly better than that obtained with wideband focusing.
The promising results obtained here suggest that future work involving experiments with
physical phantoms is warranted.
5.6
Enhanced microwave hyperthermia treatment via C N T contrast agent
T h e presence of CNT in or near a malignant lesion will result in changes to the dielectric
properties of malignant tissue. If these changes are significant, they can be used to enhance
the selectivity of higher power microwave thermal therapy. The enhanced dielectric properties and heating response, reported in [107], suggest that CNTs are promising theranostic
agents for microwave detection and thermal treatment of breast cancer. Here, we present
83
their impact on hyperthermia performance using computational electromagnetic and thermal simulations of a numerical breast phantom containing tumor targeted with CNTs. We
simulate two the hyperthermia treatment scenarios achieved in an extremely dense numerical
breast phantom with assumed inclusion of lcm-diameter in size. First, we simulate a scenario of which no CNT is used in the treatment. The dielectric properties of the inclusion is
assumed to be the properties of malignant breast tissue reported in [25]. Second, we simulate
a scenario of which CNTs are used to enhance the dielectric properties contrast between the
tumor and the surrounding glandular tissue. The dielectric properties of the tumor targeted
with CNTs are adjusted to account for the increase reported in [107]. Narrowband transmit
beamforming operating at 1 GHz is utilized as a method of focusing microwave power at the
tumor location.
Figures 5.12(a) and 5.12(b) show the sagittal view of the heating potentials obtained from
treatment scenarios with and without the use of CNTs, respectively. The results show an
increase in power dissipation of greater than 40% in the contrast enhanced tumor. In order to evaluate the heating enhancement provided by CNTs, we calculate the steady-state
temperature distributions resulting from the heating potentials illustrated in Figure 5.12
using the same scaling factor to ensure equal input power for the two treatment scenarios.
The total power dissipated within the breast for each case is calculated to be 9.6 Watts.
Figure 5.13 shows the difference in the steady-state temperature distributions. It indicates
that for 9 Watts of power dissipated within the breast volume, the use of CNTs can provide
heating enhancement of up to 1.5癈 within the tumor.
84
5
10
5
10
z(cm)
z(cm)
(a)
(b)
Figure 5.12 Sagittal view through the target location of the heating potential [W/m3] for
an extremely dense numerical breast phantom. Two treatment scenarios are compared, (a)
The tumor is targeted with CNTs. (b) The tumor is not targeted with CNTs.
1.5
1
. ? *.
*
0.5
#4
5
10
i
15
0
-0.5
z(cm)
Figure 5.13 Differential steady-state temperature distribution resulting from the difference
in heating potentials obtained from hyperthermia treatment with and without the use of
CNTs. The steady-state temperature distributions for the two scenarios are calculated
assuming the same input power coupled into the breast volume (9.6 Watts). Heating
enhancement within the tumor is achieved with the use of CNTs.
85
Chapter 6
Preliminary computational study of non-invasive microwave hyperthermia treatment of brain tumors via
transmit beamforming array
This chapter reports the results from a preliminary study of non-invasive microwave hyperthermia treatment of brain tumors via beamforming array. We have identified narrowband
beamforming technique to be an appropriate method of inducing local hyperthermia. This is
motivated by findings in our previous study for the breast reported in Chapter 5 that comparable performance between narrowband and wideband focusing methods can be achieved
at appropriate narrowband frequencies.
In this chapter, a theoretical study is conducted
to identify the effects of some system parameters for non-invasive hyperthermia (e.g. number of sources in the beamforming array, frequency of operation, and array configuration)
in the development of narrowband microwave hyperthermia technique using canonical and
anatomical head phantoms.
6.1
Non-invasive microwave hyperthermia using canonical head
phantoms
Rappaport et al. [3] illustrated the concept of non-invasive microwave hyperthermia treatment of brain tumors using a homogeneous volume of muscle surrounded by a continuous
spherical current sheet. The study reported that selective focusing of microwave at the center of the numerical phantom can be achieved non-invasively. Frequency of around 915 MHz
was identified by the study to be optimal for non-invasive brain hyperthermia application.
In this chapter, theoretical and computational studies are conducted in order to evaluate the
effects of several system parameters for non-invasive microwave hyperthermia treatment for
the brain.
In Section 6.1.1, the theoretical study [3] is revisited and focusing at the center of a homogeneous volume of grey matter is evaluated at different microwave frequencies. A continuous spherical current sheet is used as the energy source. As continuous source distribution
cannot be utilized in practice, it is appropriate to consider antenna arrays with discrete
source distributions. In Section 6.1.2, similar study is conducted for a discrete array based
on a spherical geodesic grid [108]. Selective focusing efficacy is determined as a function of
source density. We also compare the performances of two distinct array configurations in
Section 6.1.2.2.
6.1.1
Continuous current distribution
Following the study in [3], a continuous current distribution (with z-directed current) is
assumed as the energy source. The current distribution is illustrated in Figure 6.1. The
Figure 6.1 z-directed current on the surface of a sphere. (Reprinted from Figure 1 of [3]
with kind permission from IEEE. �87 IEEE.)
expression for E-field can be found by starting with the vector potential:
E {f) = -ju>A{f) - j^V
(V ? A(r})
(6.1)
87
ik \T?i
p
dV'e^
A(r) = ^v
'
4TT JV,
..?(?)
(6.2)
47r|r-r 1 , |
v
The current density J^) is assumed to be z-directed with unit amplitude and only exists
on the surface of the sphere. Therefore, J(r') = 5(r ? R)z and (6.2) becomes:
.. c>2
rlix
A(r) = ^L- /
PTT
2
p-jkVR
+r2-2rRcos9'
d(/>' / s i n 6 ' d 6 ' - y = = = z
(6.3)
where r is assumed to lie on the z-axis. Integrating (6.3) yields:
A(f) = z ^ ^ (e-MR+r\ - e-^R-r\)
jkr to be:
Finally the electric field expression is2 found
(6.4)
EM = - , . ? � , - (i [(�)' (*<*,) - *�) + (�)' (2 kr
(6.5)
>.7'l(fcr)
-jo(kr) + 3-
The dissipated power in a medium of conductivity a is calculated by:
P(rl = ^\E\2
(6.6)
The power deposition in a volume of grey matter normalized to the power at the origin,
is plotted as a function of radius at z = 0 in Figure 6.2 for several microwave frequencies.
The intersection of each curve with unity determines the maximum allowable sphere radius.
As expected, the lower operating frequencies provide greater penetration depths, whereas
the higher operating frequencies provide narrower focal width.
It is interesting to note
that at 433 MHz and 915 MHz the penetration depths are actually greater than at 100
MHz. At 2.45 GHz, 2 GHz, and 915 MHz, the patterns provide adequate resolutions at
the center of the sphere as well as large penetration depths. The full-width half-maximum
(FWHM) of the focal width at those frequencies are 3.5 mm, 4.3 mm and 9 mm respectively
and the maximum allowable sphere radii at those frequencies are 8.3 cm, 10 cm, and 13.9
cm respectively. According to the average values of male and female data for head width
measurements [109], the average width of children and adult heads ranges from 14 - 16 cm.
I
i
1\
0.8
1
�6
A
1
\_
1
S
N
100MHz
???433MHz
?e? 915MHz
2GHz
2 45GHz
?M?5GHz
*
1
1
/1
1
J
T
9
* p T
* m 9
* * X 9 9e
*
J
I
'
Jr 9
I
I
-?**
1
?
*J A
* r r
' A I
1
(
I
i
*1 v
1
\
1
I
I
/ --'"' /
/
i
-o
<u
*i
/**
/
N
I 0.4
?| A
1 /
/J
// /
/ jr
J
o
z
jr
*
Jr / *
Jr
0.2 i l l JOTM
^
y/
/
*
__-*ri^
*^y^
i * / *^^LrfPC^tC�','"^1,^^
r (cm)^ 8
6
10
12
14
Figure 6.2 Dissipated power in a volume of grey matter as a function of distance from the
center of the volume for operating frequencies of 100 MHz, 433 MHz, 915 MHz, 2 GHz,
2.45 GHz, and 5 GHz
The frequency range of 1 - 2.5 GHz provides sufficient maximum allowable sphere radius
of around 8 - 1 4 cm and focusing resolution of 3.5 mm to 9 mm. This frequency range
is identified as an appropriate frequency range for non-invasive microwave hyperthermia.
These performance figures should be interpreted as the theoretical best performance as no
clinical realism are taken into account.
6.1.2
Discrete current sources distribution
Discrete distributions of Hertzian dipoles are assumed as energy source instead of a continuous current sheet. A geodesic array configuration is considered for operating frequencies
of 915 GHz and 2.45 GHz. These frequencies are considered as they are the lower- and
upper- bounds of the appropriate frequency range for the application. The array geometry
is described in Section 6.1.2.1. We derive the analytical solution for an array of Hertzian
dipole as follows. The vector potential for a z-oriented Hertzian dipole is given by [110]:
A(f)
-jk\r?r
Aix\r ? f1
|
(6.7)
where r and f are the position vectors of the observation point and the source point respectively. I is the length of the Hertzian dipole and Ie is the amplitude of the electric current
of the Hertzian dipole. Using (6.1), the electric field expression in rectangular co-ordinates
is found to be:
E(x,y,z)
x
+y
+z
{x-x)(z-z)
(y-yi)(z-z>)
uifie 4TTRZ
-j
fiIele~ikR
uj/ie
ATIR2
-j
(z-z')(z-z>)
ijjjie
fiIele~jkR
1
2
Jjk
4yri?
\ " ' R/
where R = \f ? r*\. (x',y',z')
and (x,y,z)
!iIeleAnR2
3kR
R
3jk
3
R
2
&
3jk
3
2
'R '
R
e
3jk
R2
R
+
'
+
R3
(6.
3
R3
are the Hertzian dipole and the observation
co-ordinates respectively. u> = 2nf, where / is the frequency of excitation.
6.1.2.1
Spherical geodesic array configuration
We consider an array geometry which follows a spherical geodesic grid [108]. Examples of
source locations on the geodesic grids are indicated by red circle markers in Figure 6.3.
T h e grid is constructed from an icosahedron which has 20 triangular faces and 12 vertices
illustrated in Figure 6.3(a). The twelve vertices of the icosahedron on the unit sphere centered
at the origin are as follows: ( � r , � 0 , 0),(盺>, 0, � r ) , ( 0 , � r , �/>). r = -?==
a is the golden ratio (a =
1
~Y5).
y/Wc
and
Bisecting the edges divides a triangular face into four
smaller triangles and increases the number of faces by a factor of four. The bisection points
become new vertices, so the number of double vertices increases by the number of edges as
illustrated in Figure 6.3(b). The new vertices are projected out onto the sphere as illustrated
in Figure 6.3(c). The bisection process is repeated to generate finer grids. The geodesic
grid's most obvious advantage is that distance between any adjacent vertices is nearly the
same [108]. This enable us to increase the number of sources in a systematic manner while
fixing the inter-element spacing of the sources. The current sources are placed on the vertices
of spherical geodesic grid circumscribed by a 12-cm-radius sphere of which z > 0.
The
90
selected grid resolutions ? denoted by the number of the vertices of the polyhedron ? are
S = 12, S = 42 and 5* = 162. The three source distributions are illustrated m Figure 6.4.
(a)
(b)
(c)
Figure 6.3 Construction of spherical geodesic grids. Examples of source locations are
indicated by red circle markers, (a) Icosahedron. (b) New vertices obtained by bisecting
the edges of the icosahedron. (c) The new vertices projected out onto the sphere.
(a)
(b)
(c)
Figure 6.4 Spherical geodesic grid of different resolutions S. N source locations are
co-located with the N vertices of the grid where z > 0. The N source locations are
indicated by red "o" markers, (a) S = 12 (N = 6), (b) S = 42 (N = 26), and (c) S = 162
(TV = 91).
Figures 6.5 and 6.6 show the dissipated power patterns inside a homogeneous grey matter
evaluated for operating frequency of 915 MHz and 2.45 GHz. They show a general trend
that the power deposition pattern is more desirable as the number of sources increases (e.g.
larger maximum safe radius m the xy-plane). Note that the maximum safe radius on the
91
y (cm)
(a)
y (cm)
(b)
y (cm)
(c)
Figure 6.5 Dissipated power inside a volume of grey matter on the z = 0 plane at the
operating frequency of 915 MHz for N source locations co-located with the N vertices of
the geodesic grid where z > 0. The grid is circumscribed inside a 12 cm sphere indicated
by the dash-dotted line. The average head radius of 8 cm is indicated by the dashed line.
(a) N = 6, (b) N = 26, and (c) N = 91.
xy-plane extends beyond the average head radius for the operating frequency of 915 MHz
in Figure 6.5(c). Figure 6.6 indicates that the maximum safe radius inside a volume of grey
matter for the operating frequency of 2.45 GHz on the xy-plane is in between 3 - 5 cm.
This safe radius is smaller than the average head size of any child or adult. Therefore this
operating frequency does not appear to provide adequate penetration depth without risk of
overheating the surface of the head for the considered source densities.
In the next section, we compare the performance of two array configurations.
6.1.2.2
Performance comparison of two array configurations: cylindrical vs. spherical geodesic
Figure 6.7(a) shows a source configuration where 3 concentric rings of sources are centered
around the z-axis at height z = 0, z = 6 cm, and z ? 9 cm. Each ring comprises eight sources.
Again, the source locations are on the surface of a 12 cm-radius sphere. Figure 6.7(b) shows
a source configuration where 26 sources are placed on the vertices where z > 0 of a geodesic
grid with resolution S = 42. The deposition patterns in the major planes (xy, xz, and yz
planes) for the two source distributions are compared in Figure 6.8.
92
?5dB
-3dB
OdB
10
5
5
-5dB
1 o
1
x
u
1
0
^
*-%
-5dB
-3dB
OdB
-5dB
10
--^
X
-5
-10
> t
-10
-5
0
5
y(cm)
-10
10
--^
< 7
v ->
*-i"A
/iV-
w ~"-~' >^
-5
^%.
r.--
\ '"^nr^f"
-10
(a)
-5
0
5
y(cm)
U
-10
10
(b)
*-.
-5
..-''
0
y(cm)
>7
\
\
-5dB
-3dB
OdB
-5dB
'
t
>,
10
(c)
Figure 6.6 Dissipated power inside a volume of grey matter on the z = 0 plane at the
operating frequency of 2.45 GHz for N source locations co-located with the N vertices of
the geodesic grid where z > 0. The grid is circumscribed inside a 12 cm sphere indicated
by the dash-dotted line. The average head radius of 8 cm is indicated by the dashed line.
(a) N = 6, (b) N = 26, and (c) N = 91.
y(cm)
-10
-10
(a)
x(cm)
(b)
Figure 6.7 Source configurations. The source locations are on the surface of a 12 cm-radius
sphere, (a) Sources are placed on three concentric rings (N = 24). (b) Sources are placed
on the vertices of a geodesic grid (TV = 26).
For the two cases, the power deposition patterns in the sy-plane are quite similar. However,
the power deposition patterns in the xz- and yz- planes show smaller deposition at the top of
the head and higher deposited power at the focal point for the cylindrical array configuration
while the spherical geodesic array configuration provides more desirable deposition pattern
aiound the sides of the head The results indicate that different array configurations provide
93
-~
10
*-
/ i
J>* ^
.^
5
5
E
o
-5dB
-3dB
OdB
-5dB
10
X'
o
0
0
y
X
-5
-10
\
r )
v
y
r~^
;
/
X
I
-10
* -
0
5
y(cm)
'XT'
-5
>0P
>'
/- "S. M '
.-
-5
-10
K
Ci - X '
10
?IK0
5
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Figure 6 8 Dissipated power inside a volume of grey matter on the rry-plane (top) xz-plane
(middle), and yz-plane (bottom), at the operating frequency of 915 MHz The source
locations follow the cases illustrated in Figure 6 7(a) (left) and Figure 6 7(b) (right) The
dash-dotted line indicates the 12 cm-radius spherical surface where the source locations
are The dashed line indicates the average head radius of 8 cm
94
different desirable qualities. Therefore, the design of array configuration plays an important
role in non-invasive hyperthermia treatment and further research and development in this
area is needed.
6.1.3
Conclusions
In this chapter, we identified the effects of some system parameters to hyperthermia performance. Operating frequency of 2.45 GHz is determined to be inadequate for the application
at a fairly high source density (N = 91). A more promising results were reported for operating frequency of 1 GHz for an idealized scenario (e.g. at-center focusing in a homogeneous
greymatter environment). We also considered two array configurations with roughly the
same number of sources and both cylindrical and spherical geodesic array configurations
appear to possess different desirable attributes.
95
Chapter 7
3-D computational study of non-invasive patient-specific
microwave hyperthermia treatment of brain cancer
Hyperthermia has been shown to be effective in the treatment of cancerous tumois
Use
of antenna arrays and microwave beamformmg to induce localized hyperthermia may be
advantageous relative to current bram tumor treatments Microwave beamformmg is noninvasive, unlike surgical excision and radio-frequency ablation Microwave beamformmg is also
non-iomzmg, unlike radio-surgery Recent advances in computational power and numerical
tools open up the possibility of using simulation software to design a microwave beamformer
based on accurate microwave-tissue interaction
Moreover, the availability of realistic nu-
mcucal head phantoms allows the effectiveness of oui design to be evaluated under realistic
conditions
7.1
Introduction
Inducing localized hyperthermia in the bram via a microwave transmit beamformmg array may have advantages relative to current treatment methods
Microwave beamformmg
would be a non-mvasive process Therefore, it might allow the treatment of deep-set tumors
The work presented in this chapter is adapted from a conference presentation M Burfemdt, E Za
strow, S C Hagness, B D Van Veen, and J E Medow, "Non-invasive Microwave induced Therapeutic
Focused Bram Hyperthermia via Space time Transmit Beamformmg A numerical study", presented at the
USNC/URSI Meeting, Boulder, CO (Jan 2010)
The work presented in this chapter was supported by the SEMCAD for Science program, DoD SMART
Scholarship for Service, and the University of Wisconsin Comprehensive Cancer Center
96
t h a t cant be treated safely by surgical excision. Microwave radiation is also non-ionizing,
unlike the gamma radiation often employed in radiation therapy. Ionizing radiation cannot
be used to treat brain tumors in children, as it can lead to developmental defects later in life.
Numerical studies of noninvasive focused microwave systems for the brain have been conducted in the past. Dunn et al. [ I l l ] used a spherical array of sources and analytical methods to focus electromagnetic energy at the center of a human head phantom. Karanasiou et
al. [112] focused microwave energy into a human head phantom using an ellipsoidal reflecting
dish. Recent years have seen advancements in numerical simulation tools and computational
power. MRI-derived, anatomically realistic human phantoms have also become available.
Thus, the possibility of designing microwave beamforming arrays based on focus locationspecific propagation data has opened up. Numerical studies of such arrays for focusing in
the breast have recently been performed [33,34,113]. Using such a system for the brain
presents different challenges, as most matter in the brain is lossy high water content tissue.
In contrast, the breast is largely dominated by lower loss adipose tissue.
In this chapter, we conduct a 3D computational study of non-invasive patient-specific microwave hyperthermia treatment of brain cancer via microwave beamforming.
Operating
frequency of 1GHz is considered in order to achieve cm-size focus inside the brain volume and
adequate penetration through brain. EM and thermal simulations based on F D T D method
described in Chapter 5 are used in the beamformer design and the evaluation of performance.
High fidelity head phantoms of a 6-year-old boy and an adult male are used as our numerical
testbeds. Focus locations are chosen in the frontal lobe, parietal lobe, and the thalamus.
In each case, we obtained heating volumes surrounding the focus locations with diameters
below 2 cm where the temperature ranged between 42癈 and 45� C. Locations exterior to
these heating volumes are kept below 42� C.
97
7.2
Models and methods
Performance of the beamforming method is evaluated for the two virtual patients. In this
study, we design microwave beamforming arrays using electromagnetic finite-difference timedomain (FDTD) software. First, we obtain a patient-specific propagation data needed to
design the beamformer by running a simulation with a vertically polarized source at the
desired focus location and recording the electric field at all antenna locations in the array.
Using these data, we choose the channel weights to maximize the fraction of the total delivered power at the focus while maintaining equal transmit power at all antennas.
We run two simulations in order to evaluate the performance of the beamformer. We first
run an electromagnetic F D T D simulation using the beamformer weights to determine the
microwave interactions with the body and the dissipated power distribution resulted from the
beamforming arrays. We then run a thermal F D T D simulation using the power dissipation
distribution from the electromagnetic simulation.
7.2.1
Numerical testbeds
We utilize two anatomically realistic head phantoms of a 6-year-old boy available through
the Virtual Family [48], provided by IT'IS Foundation (Switzerland) and an adult male head
phantom based on the data set of the Visible Human Project, provided by Remcom Inc.
(USA) as our virtual patients. No tumors are assumed in the numerical phantoms to model
a worst-case selective heating scenario by assuming no dielectric contrast between the target
location and the surrounding tissue.
A de-ionized water half space is assumed to be surrounding the head and act as a cooling medium for the two patients. Array of voltage sources with 1 GHz operating frequency
are used as microwave energy sources for both patients. The element spacing of the array is 2 cm and the number of elements are 144 and 188 for the 6-year-old and the adult
patients, respectively. The number of elements in the arrays are chosen to provide similar
98
(a)
(b)
Figure 7.1 Computational domain containing each virtual patient and the associated
antenna array considered in the study. The array elements are represented by red triangle
markers, (a) Adult male patient, (b) 6-year-old male patient.
brain coverage in the two patients. Each element is excited independently with the waveform determined by the beamformer design describes in Section 7.2.2. Figure 7.1 illustrates
the computational domains of the patients. The antenna array configuration and coupling
medium chosen in this study may not be the optimal choice for clinical hyperthermia experiments. They are chosen to provide adequate EM energy delivery and adequate cooling
within the testbeds considered in this study. The hyperthermia performance may be further
improved with the use of an optimized array configuration and an optimal choice of coupling
medium between the antennas and the patients.
7.2.2
Beamformer design
For each virtual patient, we construct a heterogeneous propagation model. The model assumes that full knowledge of the patient's head is available, as well as the full registration of
the entire treatment domain. This includes the head shape, interior tissue structure, and also
the tissue dielectric properties present in the head. This knowledge permits us to construct
a propagation model that corresponds to the true propagation characteristics of the patient.
T h e process is described in our similar study for the breast in Chapter 5. The beamformer
99
design strategy also follows closely to the strategy described in Section 5.2.2 in Chapter 5.
The beamformer design is formulated as follows. Let the N x 1 vector, h = [hi, h2, ? ? ? , /IAT]H
be the complex weight vector where hn is the complex weight for the n t h channel. Let the
JV x 1 vector, p = [pi(rf),p 2 (rf), ? ? ? ,pN(rf)]T
where pn(rf)
is the one-way propagation for
a specific operating frequency from the n t h channel to the target location rf. The energy
delivered to r f can be approximated by:
Ef = h ^ Q f h
where Qf = p p ^ .
(7.1)
The beamformer design objective is to maximize the fraction of the
total transmitted power delivered to the target location rf while maintaining equal transmit
power at all antennas to prevent excessive heating at any specific regions. The optimization
problem can be expressed mathematically as:
hHQfh
argn
ri^Qh
(7 2)
-
where Q is a diagonal matrix with Qnn represent penalty for the n t h channel and when
Qnn ?Pn(rf),
7.2.3
the transmit signal amplitude across all channels are equal.
Performance evaluation
T h e set of complex weights, h, obtained from (7.2) is transmitted into the head and hyperthermia performance is evaluated for the two virtual patients at operating frequency of
1 GHz. For each patient, we consider three target locations in the following regions of the
brain: frontal lobe, parietal lobe, and the thalamus.
The computational domain of the electromagnetic F D T D model comprises uniform cubic Yee
cells with A x = Ay = Az = 1 mm providing grid sampling density of N\ ~ 40 in the brain
greymatter at 1 GHz and N\ ~ 30 in de-ionized water. The uniaxial perfectly matched layer
(UPML) absorbing boundary conditions are used to terminate the computation domain.
The materials dispersion are incorporated into the F D T D model using single-pole Debye
100
dispersion described in Chapter 2. Although the study is carried out with narrowband operation, the sourcing function in the computational domain is a raise cosine and therefore
possesses spectral content other than the operating frequency of 1 GHz. The Courant factor
of S = 0.5 is utilized to ensure stability. The distribution of the heating potential is evaluated for narrowband operation using the expression in (2.3) of Chapter 2.
The dielectric and thermal properties are summarized in Tables 2.1 and 2.2 of Chapter 2.
A convective heat boundary condition is employed at the skin-air, and skin-water interfaces
with convection coefficients of 10, and 200 [W/m 2 /癈], respectively. These values are appropriate for natural convection or low-flow forced convection of air and forced convection
of water [106]. The same grid resolution as the electromagnetic FDTD model is used. The
Thermal FDTD simulations are executed until steady-state temperature is reached.
7.3
Results and Discussion
Figures 7.4 - 7.2 illustrate the steady-state temperature distribution for the three target
locations for the two patients.
We first define a treatment zone to be a volume containing tissue with temperature of 42癈
or greater in the vicinity of the target location. Temperature lower than or equal to 40� C
in the normal brain tissue is considered safe. We also define an intermediate zone to be the
normal brain tissue with temperature greater than 40癈 and less than 42癈. It is desirable
to create a treatment zone without inducing any intermediate zones or regions of higher
temperature away from the target location inside the brain.
For both patients, non-invasive microwave hyperthermia treatment via beamforming array yields a treatment zone of 2.5 - 3 cm in brain tissue. The steady-state temperature
distributions of both patients for similar target location have similar heating characteristics.
Figures 7.2(e) and 7.4(e) show significant scalp heating in the temporal muscle region in the
101
adult phantom. This is due to the significant difference of the temporal muscle thickness
between the child and adult phantoms.
The undesirable scalp heating can be mitigated
by lowering the transmitted power in the channels closer to the location of excessive heating ? this can be done by adjusting the values for Qnn in those channels. We investigate
this hypothesis by considering the adult phantom with target location in the frontal lobe.
Figures 7.5(a) and 7.5(b) show the steady-state temperature distributions before and after
the channel weights adjustment, respectively. The results indicate t h a t hot spots can be
mitigated with an appropriate choice of channel penalty weights.
7.4
Conclusion and future work
In this study we report the performance of non-invasive microwave hyperthermia treatment
of brain tumors via microwave transmit beamforming. The study is the first demonstration
of array-based microwave hyperthermia where the transmit signal amplitude of the channels
arc chosen according to patient-specific, location-specific propagation data.
A treatment
resolution of 2.5 - 3 cm is achieved with the method and undesired hot spots can be mitigated
by lowering the transmitted power in some channels. We are unable to establish successful
hyperthermia treatment for all considered cases in this study.
Significant heating in the
temporal muscle and brain tissue in the vicinity is evident in the adult patient.
Further
research and development is needed in order to ensure the safety of brain tissue outside of
the treatment region.
-5
0
Span (cm)
5
-5
(a)
-5
0
Span (cm)
0
Span (cm)
(e)
5
(b)
5
-5
0
Span (cm)
5
(d)
(c)
-5
0
Span (cm)
5
-5
0
Span (cm)
5
(f)
Figure 7.2 Steady-state temperature distribution for the target location in the thalamus
through the three principle planes. 40癈 contours are indicated by dash lines and 42癈
contours by solid lines. (a),(c),(e) Adult male patient (left column). (b),(d),(f) 6-year-old
male patient (right column).
103
-5
0
Span (cm)
5
-5
(a)
-5
0
Span (cm)
0
Span (cm)
(e)
5
(b)
5
(d)
(c)
-5
0
Span (cm)
5
-5
0
Span (cm)
5
(f)
Figure 7.3 Steady-state temperature distribution for the target location in the parietal
lobe through the three principle planes. 40癈 contours are indicated by dash lines and 42癈
contours by solid lines. (a),(c),(e) Adult male patient (left column). (b),(d),(f) 6-year-old
male patient (right column).
104
-5
0
Span (cm)
5
-5
(a)
-5
0
Span (cm)
0
Span (cm)
(e)
5
(b)
5
- 1 0 - 5
0
Span (cm)
5
(d)
(c)
-5
0
Span (cm)
5
-5
0
Span (cm)
5
(f)
Figure 7.4 Steady-state temperature distribution for the target location in the frontal lobe
through the three principle planes. 40癈 contours are indicated by dash lines and 42癈
contours by solid lines. (a),(c),(e) Adult male patient (left column). (b),(d),(f) 6-year-old
male patient (right column).
105
(a)
(b)
Figure 7.5 Steady-state temperature distribution for the target location in the frontal lobe
through the axial plane of the adult male patient before and after channel weights
adjustment. 40癈 contours are indicated by dash lines and 42癈 contours by solid lines.
106
Chapter 8
Time-multiplexed beamforming for non-invasive microwave
hyperthermia treatment
A non-invasive microwave beamforming strategy is proposed for selective, localized heating
of biological tissue. The proposed technique is based on time-multiplexing of multiple beamformers. We investigate the effectiveness of the time-multiplexed beamforming in the context
of brain hyperthermia treatment using a high-fidelity numerical head phantom of an adult
female from the Virtual Family (IT'IS Foundation) as our testbed. An operating frequency of
1 GHz is considered to balance the improved treatment resolution afforded by higher frequencies against the increased penetration through the brain afforded by lower frequencies. The
exact head geometry and dielectric properties of biological tissues in the head are assumed
to be available for the creation of patient-specific propagation models used in beamformer
design. Electromagnetic and thermal simulations based on the finite-difference time-domain
method are used to evaluate the hyperthermia performance of time-multiplexed beamforming and conventional beamforming strategies. The proposed time-multiplexing technique is
shown to reduce unintended heating of healthy tissue without affecting the treatment temperature or volume. The efficacy of the method is demonstrated for target locations in three
different regions of the brain. This approach has the potential to improve microwave-induced
localized heating for cancer treatment via hyperthermia or heat-activated chemotherapeutic
drug release.
The material in this chapter is submitted for publication consideration with the IEEE Transactions on
Biomedical Engineering. Personal use of this material is permitted. If accepted for publication, permission
to use this material for any other purposes must be obtained from the publisher. The work presented in this
chapter was supported by the National Science Foundation under grant CMMI 0625054.
107
8.1
Introduction
The clinical application of hyperthermia in oncology involves elevating the temperature of
cancerous tissue to induce cell death or make the cells more susceptible to radiation therapy
or chemotherapy [4-9]. For low-temperature hyperthermia, the treatment region is elevated
to a temperature of 39-41癈 for up to 72 hours [2]. For moderate-temperature hyperthermia,
the treatment region is elevated to 41-45癈, typically for 30-60 minutes [2]. One method for
inducing hyperthermia non-invasively is to focus microwave energy at the tumor site using transmitters external to the body. Examples include adaptive microwave phased-array
techniques that use feedback probes [27] and microwave beamforming techniques that use
patient-specific propagation models [113]. These and other strategies for microwave-induced
hyperthermia have been investigated extensively in the context of breast tumor treatment
(e.g., [30-32,34]). In the breast cancer application, the avoidance of unintended hot spots is
facilitated not only through focusing strategics but also by the fact that the effective conductivity of malignant tissue is not exceeded by that of any other tissue in the breast [24].
The development of a non-invasive microwave hyperthermia technique for the treatment
of brain tumors is also of great interest (e.g., [Ill, 112]). This clinical application presents
formidable challenges that arguably exceed those present in the breast cancer application.
We have recently reported simulation results that demonstrate the theoretical feasibility of
focusing microwave energy at a brain tumor site within a child's head using a narrowband
microwave transmit-beamforming technique [114]. However, our prior work also shows that
brains with large volumes of cerebrospinal fluid (CSF) are highly susceptible to auxiliary hot
spots because the microwave-frequency effective conductivity of CSF [115] greatly exceeds
that of any other tissue in the brain. Given the brain's critical role in human function, any
viable hyperthermia system must confine the thermal damage to the cancerous tissue and
avoid harming the healthy brain tissue. The conventional microwave beamforming approach
that transmits a single set of signals that are variable in amplitude and phase across the
108
array but constant over time for the duration of the treatment period does not meet this
requirement.
In this paper, we propose a new microwave hyperthermia approach that uses time-multiplexing
of multiple beamformers. Each patient-specific beamformer is designed to focus microwave
energy at a target location while minimizing energy deposition in a normal-tissue region that
has the potential for absorbing a large amount of microwave energy. The location of the minimum is unique to each beamformer. We hypothesize that switching through these different
beamformers over time will reduce or eliminate auxiliary hot spots. We test this hypothesis
in the challenging context of brain hyperthermia treatment. Our performance evaluations
involve electromagnetic and thermal simulations of the proposed time-multiplexing strategy, as well as the conventional beamforming approach for comparison, using a high-fidelity
numerical model of the head of an adult female. We demonstrate the efficacy of the timemultiplexing approach for selectively heating three different regions of the brain.
The rest of the paper is organized as follows. Section 8.2 describes the computational testbed
and tools used in our study. The procedure for designing our time-multiplexed beamformers
is presented in Section 8.3. The beginning of Section 8.4 describes our performance evaluation metrics, while the remainder of Section 8.4 presents results that illustrate the design
procedure and demonstrate the performance of our proposed technique compared to conventional beamforming.
Lower and upper case boldface type is used to denote vector and matrix quantities, respectively. Superscripts T, H, and ?1 represent matrix transpose, complex conjugate transpose,
and inverse, respectively.
109
8.2
8.2.1
Modeling and design tools
Testbed
Figure 8.1 illustrates the computational testbed for this study. The testbed includes a numerical head phantom and microwave source array. The head of the "Ella" model from the
Virtual Family (IT'IS Foundation, Zurich, Switzerland) [48] is chosen as the numerical head
phantom. The model is based on high resolution magnetic resonance images of a healthy
26-year-old female volunteer. The cutaway views in Figures 8.1(a) and 8.1(b) illustrate the
relative permittivity and effective conductivity, respectively, at 1 GHz in the head interior.
This particular phantom has a large volume of CSF distributed throughout the brain. Specifically, the volume of CSF in the Ella model is 271 mL, whereas the volume of grey and white
matter is 1100 mL. This large amount of CSF introduces challenges for selectively focusing
microwave energy as CSF exhibits a much higher effective conductivity (CTCSF = 2.4 S/m at
1 GHz) than grey matter (o"grey matter = 0.9 S/m at 1 GHz).
The microwave source array consists of 134 small z- directed current sources surrounding
the head, each operating at 1 GHz. The sources are distributed evenly across five full elliptical rings and three partial elliptical rings separated by a 2-cm elevation spacing. The
element-to-element spacing within each ring is 4 cm. The source locations are indicated
by white circles in Figure 8.1. Deionized (DI) water and air are assumed to be in contact
with the surface of the head and neck. The water-air interface is located at z ? 100 mm,
with DI water filling the upper region (z > 100 mm). These cooling media are assumed
to be at a constant temperature of 15癈. The optimal antennas, array configuration, and
coupling medium for clinical hyperthermia experiments may differ from those employed in
this study. For example, the omnidirectional, electrically small sources used in this study
are too inefficient for a clinical hyperthermia system, but suffice to evaluate the performance
of the proposed time-multiplexing strategy. Also, hyperthermia performance may be further
110
improved with the use of an optimized array configuration and an optimal choice of coupling
medium between the antennas and the head.
(a)
(b)
Figure 8.1 Numerical model of an adult female head (Ella model, Virtual Family, IT'IS
Foundation) surrounded by an array of 134 small current sources. The locations of the
sources are marked by the white circles. The orthogonal cuts show the interior dielectric
properties at 1 GHz. (a) Relative permittivity, (b) Effective conductivity (S/m).
8.2.2
Electromagnetic and thermal simulation tools
Time-domain computational electromagnetic and thermal simulations are conducted in both
the beamformer design and performance evaluation phases of this study. Note that in the
clinical application, simulations would similarly be used in the treatment planning phase to
design the beamformers, while the performance evaluation phase would involve applying the
treatment protocol to actual patients. Here we provide a brief overview of the finite-difference
time-domain (FDTD) electromagnetic (EM) and thermal solvers. The 3-D computational
domain of the FDTD-EM model comprises a uniform spatial grid of cubic Yee cells with
dimensions of Ax = Ay = Az = 1 mm. This grid resolution corresponds to a grid sampling density of Nx ~ 40 in grey matter and Nx ~ 30 in DI water at 1 GHz. A Courant
factor of S = 0.5 is chosen to ensure stability. Uniaxial perfectly matched layer absorbing
boundary conditions are used to terminate the grid. The dielectric properties at 1 GHz
Ill
compiled in [115] are assigned to the various tissue types in the head phantom. The array of
current sources shown in Figure 8.1 is excited by the transmit signal set obtained from the
beamformer design process (Section 8.2.3). Jz components in the F D T D grid are used as
the current sources. The steady-state heating potential inside the head is computed using
the approach described in [113].
The steady-state temperature profile in the head is evaluated using a 3-D F D T D thermal
model based on the Pennes bio-heat equation [51]. The grid resolution of the FDTD-thermal
model is identical to that used in the FDTD-EM model. The blood perfusion coefficient for
each tissue is assumed to be time-independent and is assigned its basal value. The blood
temperature is assumed to be constant and equal to the body's core temperature of 37癈.
The thermal properties of the various tissue types are assigned the values provided with the
Virtual Family software. A convective boundary condition is employed at the skin-water
and skin-air interfaces with convection coefficients of 200 and 10 W/m 2 /癈, respectively.
These values are appropriate for forced convection of water and natural or low-flow forced
convection of air [106]. The F D T D implementation of the Pennes bio-heat equation and the
convective boundary condition follow that reported in [52].
8.2.3
Focused transmit beamforming
A microwave transmit beamformer for a A'-channel array is described by a set of K complex
weights. The weights represent the phase shifts and amplitude factors required to focus
microwave power at the target location while minimizing power deposition elsewhere. We
design the beamformer using a heterogeneous propagation model that incorporates exact
knowledge of the patient's head and treatment domain, including the head shape, interior
tissue structure and dielectric properties, and the current source locations with respect to the
head. This exact model is available in our study because we are working with numerical head
phantoms as our virtual patients. In the clinical application, the structural information for
the propagation model would be obtained from a patient-specific MRI; dielectric properties
112
estimates would be obtained from existing data in the literature. The complex valued oneway propagation coefficient from each source to all voxels of interest in the head is required
in the beamformer design process. A set of FDTD-EM simulations is used to measure the
propagation effects from each source to points in the head distributed over a 1-cm spaced grid.
Let the K x 1 vector, h = [hi, h2, ?.., hx]H, be the beamformer weight vector where hk is the
complex weight for the kth channel. Let the K x 1 vector, p ( r ) = [pi(r), p2(r),...
,p^(r)]r,
be the propagation vector where Pk(r) is the one-way propagation transfer function from the
kth channel to a location r for a specific operating frequency, obtained from the FDTD-EM
simulation. The power dissipation per unit volume at a target location, 17, is then expressed
as:
Ej = h ^ h
(8.1)
where R / = a ( r j ) p ( r / ) p ( r / ) i f and (7(17) is the effective conductivity at 17 for the operating
frequency. We seek to maximize Ef while minimizing factors such as total transmit power,
power dissipation in healthy tissue, etc. We express the dependence of these other factors on
the weights as the quadratic h ^ R h where R is a positive definite matrix chosen to represent
undesired effects. Examples for R are given in the following section. Our beamformer design
objective is expressed as the following optimization:
hHRfh
argm aX
h h^Rh
.
,
(8 2)
'
This design goal maximizes the ratio of desired to undesired effects. The solution for h can
be shown to be the eigenvector corresponding to the largest eigenvalue of R ~ 1 R / .
8.3
Time-multiplexing design procedure
Our time-multiplexing hyperthermia approach makes use of a sequence of beamformers designed to control undesired heating of healthy tissue. Our examples assume that the sequence
duration is Ts = 5 seconds and that the sequence is repeated until a steady-state temperature distribution is obtained with the FDTD-thermal simulation. In general, the length of
113
time each beamformer is applied within the sequence is unequal. The treatment volume is
the region intended for therapeutic heating. In our examples, we assume that the treatment
volume is a 2-cm radius spherical volume centered on a target location ry. The maximum
safe temperature for brain matter outside the treatment volume is assumed here to be 41癈.
At-risk regions are healthy tissue volumes that are more susceptible to unintended and unsafe
heating than others. The details involved in identifying at-risk regions, designing beamformers with low power deposition in those regions, and determining the time duration allocated
to each beamformer during one sequence are described in the following subsections.
8.3.1
Identify at-risk regions associated with target location
We begin by designing a beamformer to maximize the total transmitted power absorbed
at Yj using (8.2) while constraining each antenna to deliver equal power. The equal power
constraint is enforced by setting R = R p , where R p is a diagonal matrix with [Rp]
|pj(r/-)|.
The heating potential is calculated using an FDTD-EM simulation.
=
Next, an
FDTD-thermal simulation is performed using an input power level that results in a steadystate temperature at r^ between 43癈 and 44癈. This temperature profile is representative
of a hyperthermia treatment achieved via conventional beamforming and is used solely for
the purpose of identifying the at-risk regions specific to each patient. At-risk regions are
identified as all voxels in the head and outside the treatment volume with temperatures
exceeding 41� C.
8.3.2
Assign spherical suppression volumes to cover the at-risk
regions in the head
In general, the at-risk regions are comprised of multiple discrete volumes. Moreover, the
number, size, and spatial location of those regions vary considerably and are dependent
on the location of the target and the dielectric properties distribution. In order to obtain
approximately equal level of suppression for all beamformers, we cover the at-risk regions
with multiple spherical suppression volumes, each fixed at 10% of the brain volume. More
114
Iteration 2
(a)
(b)
Figure 8.2 Illustration of the recursive spherical suppression volume assignment process.
Rectangles depict at-risk regions, shaded circles depict suppression volumes, and 'x' denotes
the location of the peak temperature within each at-risk region, (a) Three suppression
volumes are centered on the locations of peak temperature in each at-risk region, (b) Two
at-risk regions remain after removing portions covered by suppression volumes identified in
(a). Two additional suppression volumes are centered at the peak temperature location in
each residual at-risk region. All at-risk regions are now covered by suppression volumes.
than one spherical suppression volume may be required to cover an at-risk region. We begin
the assignment process by locating the peak temperature of each distinct at-risk region and
center a suppression volume at each peak location. Portions of the at-risk regions covered
by these suppression volumes are removed and peak temperatures of the residual at-risk
regions are used to identify new suppression volumes. This recursive process is repeated
until all at-risk regions are covered by N local suppression volumes. Figure 8.2 illustrates
the identification of suppression volumes.
8.3.3
Design beamformers
The suppression volumes are now used to design beamformers according to (8.2) by setting
R = R p + ah~Rh + a s R s where Rp is as denned in Section 8.3.1, R^ = J #
a(r)p(r)p(r)Hdr,
and R s = J $ cr(r)p(r)p(r) i i dr. Here &h is the volume of the head phantom with z > 130
mm, while $ s is the suppression volume. Note that h ^ R ^ h and h ^ R s h are the total dissipated power per unit volume in <f?h and <E>S, respectively, an and as are positive scalars,
chosen to balance the dynamic range of power across the source array against the power
absorbed to $^ and $ s . Balancing these effects is necessary to avoid an impractical beamformer ? that is, a beamformer with excellent suppression in $ s but large power dissipation
115
elsewhere in the head. Multiple factors, such as the target location and the location of the
suppression volumes with respect to the target location, affect beamformer and hyperthermia performance for a given ah and as. In this study, we assume a^ and as are constant for
all local suppression regions associated with a target location and choose appropriate values
empirically by evaluating hyperthermia performance for several different sets of values.
We obtain four different categories of candidate beamformers for multiplexing by varying
ah, as, and $ s as defined below. Let $ n , n = 1, 2 , . . . , N, be the local suppression volumes
resulting from the step described in Section 8.3.2.
1. Local suppression: We design iV beamformers each emphasizing its own local suppression by choosing 0 < a^ < as and setting $ s = <&n, n = 1, 2 , . . . , N.
2. Combined suppression: We design the (N + l)st beamformer emphasizing combined
local suppression using $ s = $ i U $2 ? ? ? U $JV, 0 < a^ < as.
3. Whole-head suppression: We design the (N + 2)nd beamformer that minimizes power
deposition in $/j by choosing ah = 1 and as = 0.
4. No suppression: We design the (N + 3)rd beamformer without any suppression by
setting ah ? as = 0.
These four design strategies result in N + 3 candidate beamformers for multiplexing for a
target location.
8.3.4
Calculate time duration of each beamformer to form a sequence
After the TV + 3 beamformers for the target location are designed, we form a sequence by
assigning a duration, r m , to each beamformer. We have adopted an ad hoc design guideline
t h a t uses the steady-state heating potential distribution resulting from time multiplexing as
a surrogate for temperature. Let the L x 1 vector, q m , m = 1, 2 , . . . , N + 3, be the heating
116
potential of the m t h beamformer at L spatial locations in the head volume, excluding the
treatment volume. The net heating potential over the sequence is
,
N+3
QnetO) = ^^2
where rm
> 0 and ) ] m ^ r m
= Ts.
qm7m
We choose r
(8-3)
= [TI, T 2 , . . . , TN+3]
to minimize the
squared error between q n e t ( r ) and the uniform heating potential q 0 = q0[l, 1 , . . . , 1] T where
^�
=
(N+3)L
E m = i ^2i=i [<im]t
an
d [q m ], denotes the lih element of q m .
This is a linear
programming problem which we solve in MATLAB using the built-in function fminsearch.
Note that if r m = 0, then the corresponding m t h beamformer is not used in the multiplexing
sequence.
8.4
Results and discussion
Three target locations in different regions of the brain are considered. The first target location is in the thalamus with 17 = (150,175,170) mm, the second target location is in the
parietal lobe with r^ = (170,170,170) mm, and the third target location is in the frontal lobe
with rf = (150,125,180) mm. For each target location considered in this study, we compare
the performance of our proposed time-multiplexed beamforming strategy with the performance of conventional beamforming. The hyperthermia result from conventional beamforming is obtained from the thermal simulation with a single heating potential, Q(r), used as
the source. The hyperthermia result for time-multiplexed beamforming is obtained from the
thermal simulation with a time-varying heating potential, Q(r,t),
used as the source. Each
steady-state temperature distribution is obtained from an FDTD-thermal simulation configured to achieve a peak temperature of 43�1癈 in the treatment volume. The following
thermal metrics are defined to quantify performance:
1. Vt (mm 3 ), the volume of brain tissue within the treatment volume with temperature
> 41癈.
117
2. Vd (mm 3 ), the volume of brain tissue outside Vt (e.g., healthy tissue) with temperature
> 41癈.
3. Tpeak (癈), the peak temperature within Vd.
4. r (mm), the radial distance between the location of peak temperature in Vt and rj.
In Section 8.4.1 below, we demonstrate the time-multiplexing design procedure presented
in Section 8.3 for one target location. The results for all target locations are presented in
Section 8.4.2.
8.4.1
Time-multiplexing design example
This example uses the first target location. The heating potential and steady-state temperature profile are computed to identify the at-risk regions, according to the criteria given
in Section 8.3.1. Figure 8.3(a) shows the steady-state temperature profile that is used to
identify the at-risk regions in an axial cut through 17 = (150,175,170) mm. The steady-state
temperature at the target location, marked by crosshairs, is driven to reach 43.5癈 in the
FDTD-thermal simulation. At-risk regions are enclosed by 41癈 contours and are shown
as black solid lines. The treatment and brain volume contours are shown as black dotted
lines. The procedure described in Section 8.3.2 is used to identify N = 12 spherical local
suppression volumes for this target location. The boundaries of these volumes are marked
with black dashed lines in Figure 8.3(a). The numeric labels indicate the order in which
local suppression volumes are identified. Figure 8.3(b) provides a 3D view of the spherical
local suppression (red) and at-risk (green) volumes.
Figure 8.4 shows the effective conductivity distribution at 1 GHz for an axial cut through the
first target location. There are large CSF volumes, identified by regions of highest effective
conductivity (brown) in Figure 8.4, distributed throughout the brain volume. Regions containing CSF are more susceptible to high microwave absorption. Examples of these regions
118
are identified by the at-risk regions covered by local suppression volumes 8, 9, and 10 in Figure 8.3(a). The brain-bone-scalp interfaces are also susceptible to unintended heating due to
the contrast in dielectric properties and the low thermal conduction and perfusion through
the bone layer. Examples of these regions are identified by the at-risk regions covered by
local suppression volumes 1, 2, and 4 in Figure 8.3(a).
Next, we follow the design procedure described in Section 8.3.3 to obtain N + 3 = 15
candidate beamformers for the target location.
We choose a^ = 5 and as = 5 in the
local-suppression and combined-suppression designs to balance the transmit power across
the source array against undesirable absorption within the head. Figures 8.5(a), 8.5(b), and
8.5(c) illustrate the heating potential for local suppression volumes 1, 4, and 11, respectively.
Figure 8.5(d) illustrates the heating potential obtained with the combined-suppression design criterion, labeled as beamformer 13. Figure 8.6 depicts the heating potentials obtained
with the whole-head-suppression and no-suppression design criteria, labeled as beamformers
14 and 15, respectively.
The duration of each beamformer is determined as described in Section 8.3.4. The resulting
five-second sequence is illustrated in Figure 8.7. For this particular target location, only
6 out of 15 beamformers have non-zero durations. The duration of beamformer 13 (see
Figure 8.5(d) for corresponding heating potential) accounts for more than half of a cycle.
8.4.2
Time-multiplexed beamforming performance
Figure 8.8(a) and (b) show the steady-state temperature profile resulting from conventional
beamforming (e.g., without time multiplexing) for the first target location. The profile in
Figure 8.8(a) illustrates the performance of the no-suppression beamformer (Section 8.3.3,
Category 1) when used for conventional beamforming. Two hot spots in healthy tissue regions near the brain-bone-scalp interfaces are visible in the profile. Figure 8.8(b) shows the
performance of the whole-head-suppression beamformer (Section 8.3.3, Category 3) when
119
; 170 mm
250
r ? 20
� r ~ 25r
:
\
--"
200
' ? 45?
40
3 0 - - ^35-
^ -,
C)
^\
Jtr\
200 J
? 150
? 11 � :
V"'"'
100
^*SL
<&y^';
6 iv
^:;:%h^l
1
| 150100
3
^^3 \_^^tri
\ J^
50
LO ^ i s l ^ " ' '
^
300 "
50
100
150
200
y (mm)
300
100
<(mmj
250
(a)
100
/(mm)
(b)
Figure 8.3 At-risk regions and spherical local suppression volumes associated with the first
target location, (a) Steady-state temperature profile that is used to identify at-risk regions
in the head volume, in an axial cut through the target location (z = 170 mm). The
temperature at 17 (marked by crosshairs) is driven to 43.5癈. The at-risk regions (> 41癈)
are enclosed by black solid lines. The boundaries of spherical local suppression volumes are
shown as black dashed lines. Black dotted lines depict the treatment and brain volume
contours, (b) 3-D view of spherical local suppression volumes (red) and at-risk region
volumes (green).
z = 170 mm
250
?150
100
Figure 8.4 Effective conductivity at 1 GHz in an axial cut through the first target location
in the thalamus at 17 = (150,175,170) mm (marked by crosshairs). The second target
location in the parietal lobe at 17 = (170,170,170) mm is also shown (marked by 'o'
marker).
120
z = 170 mm
z = 170 m m
mI K ;
250
250
0.2
0.4 ,---0.6
0.8
ill*
0.4
0.2
1
- 0.6:
0.8
: -?-1
'-*-? .&'
' '
0
^__�*
200
200
? 150
150
IB
50
150
y (mm)
100
200
250
j * ^ ,
200
150
y (mm)
200
250
0.6-- .
Kill1
0.8
*>>? ^ ^ ^ H j
jyjfeN)- r�
" ^ W i; ?
iff -^raWT--* j E
150
100
z = 170 m m
'
:
0.4
0.2
Mf
(b)
z = 170 m m
msmut.
K9|
EJ4|
50
(a)
0
^^^^5Sp
^85
100
100
250
.*** , < * ' '
? lB Ji^s.
X I
w
100
50
100
150
y (mm)
(c)
200
250
150
y (mm)
200
(d)
Figure 8.5 Example heating potentials for the first target location. The heating potentials
are shown for axial cuts through the target location (z = 170 mm). The boundary of the
local suppression volume is shown as a dashed line in (a) - (c). (a) Local-suppression
beamformer 1. (b) Local-suppression beamformer 4. (c) Local-suppression beamformer 11.
(d) Combined-suppression beamformer (beamformer 13).
121
z = 170 m m
z = 170 m m
250
200
150
100-
150
y (mm)
200
150
y (mm)
(a)
200
250
(b)
Figure 8.6 Heating potentials obtained with whole-head-suppression and no-suppression
design criteria for the first target location, shown for axial cuts through the target location
(z = 170 mm), (a) Whole-head-suppression beamformer (beamformer 14). (b)
No-suppression beamformer (beamformer 15).
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
2
3
time (s)
Figure 8.7 Beamformer sequence for the first target location. The shaded bars indicate the
duration of the corresponding beamformers. Note that beamformers 2, 5, 6, 8, 10, 12, 14,
and 15 are not used.
122
used for conventional beamforming. This profile illustrates the hyperthermia performance
when we introduce global suppression throughout the head in the beamformer design. In
comparison with the no-suppression beamformer, the whole-head-suppression beamformer
reduces unintended heating in certain regions of the head while increasing unintended heating in other regions of the head. For example, the temperature in the vicinity of CSF in the
front of the head (around x = 150 mm, y = 100 mm), near the treatment volume (around
x = 170 mm, y = 200 mm), and near the brain-bone-scalp interfaces on the left side of the
head (around x = 80 mm, y = 175 mm) is decreased. However, the temperature near the
brain-bone-scalp interfaces on the right side of the head (around x = 210 mm, y = 175 mm)
is increased. Figure 8.8(c) shows the temperature profile resulting from time multiplexing
using a sequence formed by all of the 15 candidate beamformers.
equal duration.
Each beamformer has
This profile illustrates the hyperthermia performance when we use time
multiplexing, but do not optimize the duration of each beamformer within the sequence.
Hyperthermia performance similar to that obtained with the whole-head-suppression beamformer is achieved.
Figures 8.8(d)-(f) show the hyperthermia results obtained with the
time-multiplexing design presented in Section 8.4.1. Table 8.1 summarizes the hyperthermia
performance results using the metrics described at the beginning of this section. The results
in Figure 8.8 and Table 8.1 indicate that the proposed time-multiplexed beamforming strategy successfully avoids overheating healthy tissue regions without affecting the treatment
resolution in the thalamus region. Namely, Vd ? 0 with time-multiplexed beamforming and
Vt obtained with the time-multiplexed beamformers is comparable to Vt obtained with the
no-suppression beamformer.
Next, we compare the performance of conventional beamforming with no-suppression beamformer (Section 8.3.3, Category 4) and time-multiplexed beamforming for the second target
location (parietal lobe, 17 = (170,170,170) mm). As a reference, Figure 8.4 shows the effective conductivity at 1 GHz for an axial cut through the second target location (marked by
'o' marker). The results in Figure 8.9 illustrate that time-multiplexed beamforming reduces,
123
50
(a)
(d)
(b)
(e)
100
150
y(mm)
200
250
(c)
(f)
Figure 8.8 Steady-state temperature profile in the orthogonal cuts through the location of
the peak temperature in Vt (marked by crosshairs) for the first target location in the
thalamus at 17 = (150,175,170) mm. The peak temperature in Vt is driven to 43�1癈.
(a) Temperature profile (axial cut) obtained from conventional beamforming with the
no-suppression beamformer. (b) Temperature profile (axial cut) obtained from
conventional beamforming with the whole-head-suppression beamformer. (c) Temperature
profile (axial cut) obtained via time-multiplexing of all candidate beamformers with equal
duration, (d)-(f) Temperature profiles obtained via the proposed time-multiplexed
beamforming method. The sequence illustrated in Figure 8.7 is used in time multiplexing.
(d) Axial cut. (e) Sagittal cut. (f) Coronal cut.
124
but does not eliminate, unintended heating in the region on the right side of the head. In
particular, we observe a significantly lower peak temperature outside of Vt (e.g., Tpeak) in
Figure 8.9(b). Figure 8.9(b) shows that this reduction is accompanied by the introduction
of a few small hot spots elsewhere in the head. These new hot spots occur in CSF regions.
The summary of performance metrics in Table 8.1 for this target location indicates that the
peak temperature of the overheated healthy brain tissue is reduced from 48癈 to 45� C and
Vd is reduced by 23%.
z = 170 m m
50
100
150
y (mm)
(a)
z = 171 m m
200
250
50
100
150
y (mm)
200
250
(b)
Figure 8.9 Steady-state temperature profile in the axial cut through the location of the
peak temperature in Vt (marked by crosshairs) for the second target location in the parietal
lobe at Tf = (170,170,170) mm. The peak temperature in Vt is driven to 43�1癈. (a)
Temperature profile obtained from conventional beamforming with no-suppression
beamformer. (b) Temperature profile obtained from time-multiplexed beamforming. using
the designed sequence for this target location.
The last target location considered in this study is in the frontal lobe, at 17 = (150,125,180)
mm. The effective conductivity at 1 GHz for an axial cut through the location of the peak
temperature in Vt is shown in Figure 8.10. Figure 8.11(a) shows one hot spot that occurs from
conventional beamforming with no-suppression beamformer (Section 8.3.3, Category 4) in a
125
region of high effective conductivity near the front of the head. Figure 8.11(b) and Table 8.1
report the improvement in hyperthermia performance achieved with the time-multiplexed
beamforming technique. The peak temperature of overheated healthy brain tissue (Tpeak) is
decreased by 2癈 and Vd is reduced by 90% for this target location.
50
100
150
y (mm)
200
250
Figure 8.10 Effective conductivity at 1 GHz in an axial cut through the location of the
peak temperature in Vt (marked by crosshairs) for the third target located in the frontal
lobe at Tf (150,125,180) mm.
8.5
Summary
We have proposed and demonstrated a time-multiplexed beamforming technique for noninvasive localized heating. We test the proposed strategy in the context of non-invasive
microwave brain hyperthermia therapy using a high fidelity head phantom of an adult female as a testbed. Three target locations in different regions of the brain volume are chosen to test the robustness of the proposed technique. The proposed technique is based on
patient-specific transmit beamforming and time-multiplexing design. The time-multiplexed
beamforming technique reduces the amount of overheated healthy tissue inside the head and
the peak temperature in healthy tissue for all cases considered in the study, without affecting the treatment temperature or volume. While we have conducted our investigation in the
hyperthermia context, we note that the time-multiplexing strategy for localized heating is
Target location
Vd (mm3)
Vt (mm3)
?L peak ( C )
r (mm)
555
2427
41.8
6.5
0
2509
40.3
5.9
Conventional
28232
6258
48.0
3.2
Time-multiplexed
21733
4797
44.9
2.5
3386
3644
43.8
3.5
316
3356
41.5
3.5
Beamforming
strategy
Thalamus
Parietal lobe
Conventional
Time-multiplexed
Conventional
Frontal lobe
Time-multiplexed
Table 8.1 Hyperthermia performance metrics (defined in Section 8.4) for the conventional
beamforming with no-suppression beamformer and the proposed time-multiplexed
beamforming for targets in the thalamus, parietal lobe, and frontal lobe.
127
z = 182mm
50
100
150
200
y (mm)
z = 182mm
250
50
100
(a)
150
200
y (mm)
250
(b)
Figure 8.11 Steady-state temperature profile in the axial cut through the location of the
peak temperature in Vt (marked by crosshairs) for the third target location in the frontal
lobe at 17 (150,125,180) mm. The peak temperature in Vt is driven to 43�1癈. (a)
Temperature profile obtained from conventional beamforming with no-suppression
beamformer. (b) Temperature profile obtained from time-multiplexed beamforming, using
the designed sequence for this target location.
also relevant to heat-activated chemotherapeutic drug release.
The design procedure we have proposed is intuitive, yet ad hoc, and clearly demonstrates the
potential of a time-multiplexed beamforming strategy for enhancing the performance of hyperthermia treatment. The challenge with obtaining more optimal time-multiplexing design
procedures is the non-linear and time-varying dependence of temperature on beamforming
weights.
128
Chapter 9
Summary and future directions
This thesis contributes to the development of numerical tools and techniques for non-invasive
microwave-induced hyperthermia treatment of cancer. We limit' our investigation to the applications of breast and brain tumors treatment. However, the numerical tools and techniques
presented in this thesis are applicable to other applications. In this chapter, we summarize
the contributions of this thesis and suggest future research directions for the topics within
this dissertation.
The first contribution towards breast cancer treatment is the development of anatomically
realistic numerical breast phantoms (Chapter 3). This collection of anatomically realistic 3D
numerical breast phantoms of varying shape, size, and radiographic density can be readily
used in FDTD computational electromagnetics models and is made available to the scientific
community through an online repository. The phantoms are derived from Tl-weighted magnetic resonance images (MRIs) of prone patients. Each MRI is transformed into a uniform
grid of dielectric properties using a piecewise-linear mapping scheme. The dielectric properties of normal breast tissue are taken from the recently completed large-scale experimental
study of normal breast tissue dielectric properties conducted by the Universities of Wisconsin and Calgary. As for future research directions, these phantoms can be further developed
to incorporate irregular shaped inclusions that represent tumors. Also, the development
of physical phantoms will be useful for research towards establishing clinical feasibility of
non-invasive microwave hyperthermia treatment.
129
Secondly, we demonstrate the feasibility of non-invasive microwave hyperthermia treatment
of breast cancer via transmit beamforming through F D T D simulations (Chapter 4-5). We
have rigorously established the focusing capability of the method using sophisticated 3-D
numerical breast phantoms.
Beamforming is used to design and focus the signals trans-
mitted by an antenna array into the breast. We have investigated the use of propagation
models of varying fidelity and complexity in the design of the transmitted signals.
An
ideal propagation model that is exactly matched to the actual patient's breast is used to
establish a best-performance baseline. Simpler patient-specific propagation models based
on a homogeneous breast interior are also explored to evaluate the robustness of microwave
transmit beamforming in practical clinical settings in which an ideal propagation model is
not available. We also investigate the performance of the beamformer as a function of operating frequency and compare narrowband and wideband focusing strategies. Our study
suggests that patient-specific microwave beamforming is a robust method of non-invasively
focusing microwave energy at a tumor site in breasts of varying volumes and breast tissue
density. Towards the clinical feasibility of non-invasive microwave hyperthermia treatment
of breast cancer, several areas of research may be explored: (1) An optimal configuration
of 3-D antenna array should be investigated; the elliptical arrays used in the study are selected primarily to ease the numerical implementation. (2) Appropriate microwave antenna
design is also an important feature of the hyperthermia system; the single-component current sources used in the study are too inefficient to be clinically feasible. (3) The coupling
medium between the antennas and the breast should be optimized foi efficient power delivery and adequate superficial cooling. (4) We have demonstrated the feasibility of transmit
beamforming as a focusing method of microwave power through intact breast; a comparison
of performance among other focusing methods using common testbeds is warranted.
For the contribution towards brain cancer treatment, we conduct computational studies of
patient-specific, non-invasive microwave hyperthermia treatment of brain cancer. Focusing
capability of narrowband transmit beamforming method (Chapter 6-7) has been evaluated.
130
The study revealed some clinical challenges of the application that were not apparent in the
breast cancer application, such as unavoidable unintended hot spots in healthy brain region
induced during the treatment and inadequate cooling of the scalp. Similarly to the breast
cancer application, areas of exploration such as optimal array configuration, microwave antenna design, and coupling medium, should be further investigated.
One of the challenges in non-invasive hyperthermia treatments is limiting the thermal dose
to be completely confined within the treatment region while maintaining safe temperature
in healthy tissue. We addressed this challenge in the context of brain cancer treatment in
the attempt to overcome the limitations of conventional beamforming method evident in our
previous studies reported in Chapter 7. We propose a new microwave hyperthermia approach
that uses time-multiplexing of multiple beamformers and conduct a proof-of-concept study
(Chapter 8). Each patient-specific beamformer is designed to focus microwave energy at a
target location while minimizing energy deposition in a normal-tissue region that has the
potential for absorbing a large amount of microwave energy. The location of the minimum
is unique to each beamformer. We hypothesize that switching through these different beamformers over time will reduce or eliminate auxiliary hot spots. We test this hypothesis in the
challenging context of brain hyperthermia treatment. Our performance evaluations involve
electromagnetic and thermal simulations of the proposed time-multiplexing strategy, as well
as the conventional beamforming approach for comparison, using a high-fidelity numerical
model of the head of an adult female. The proposed method is shown to reduce the amount
of damaged healthy tissue inside the head without affecting the treatment resolution. The
design procedure we have proposed was appointed ad hoc to serve as a proof of concept, and
was by no means optimal. Further algorithm development and design optimization of this
promising method is needed. The areas of further exploration may include : (1) Incorporating multi-sequence design. Our current design assumes a single unique sequence that is
repeated throughout the entire treatment duration. Future studies may choose to investigate a multi-sequence scheme; real-time temperature profile may be incorporated to provide
131
feedback for an iterative solution method. (2) Optimizing the order of the beamformers in a
sequence. In our study, the order of which the beamformers are sequenced through was not
chosen by design; we assumed that the ordering of the beamformer in the sequence does not
affect the final hyperthermia performance. This assumption simplifies the design procedure
and exempts us from solving the Traveling Salesman Problem. Future studies may choose
to incorporate this combinatorial optimization problem. (3) Optimizing the duration of a
sequence. Currently, we require a sequence duration t h a t is much shorter than the steadystate thermal response time and assume a sequence duration of 5 seconds. The sequence
duration may have significant impact on the final hyperthermia performance.
In summary, we find patient-specific microwave beamforming to be a feasible method of
inducing local hyperthermia for breast cancer treatment through rigorous numerical simulations. Hardware implementations and experimental studies are warranted to establish future
clinical feasibility. We find similar conventional beamforming method to have limitations
when applied to the brain, due to the heterogeneity of tissue and the dielectric distribution
in the brain volume. Evident by our work, these limitations may yet be overcome with
further investigation and development.
132
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Appendix A: Safety assessment of breast cancer detection via ultrawideband microwave radar
Included in this appendix:
E. Zastrow, S. K. Davis, and S. C. Hagness, "Safety assessment of breast cancer detection
via ultrawideband microwave radar operating in pulsed-radiation mode," Microwave and
Optical Technology Letters, vol. 49, no. 1, pp. 221-225, Jan. 2007. doi: 10.1002/mop.22089
E. Zastrow, S. K. Davis, and S. C Hagness, "Safety assessment of breast cancer detection via ultrawideband microwave radar operating in swept-frequency mode," Antennas and
Propagation Society International Symposium 2006, IEEE, pp. 721-724, Jul. 2006. doi:
10.1109/APS.2006.1710627
144
a g a i n s t the Rcfs 7 8 and 9 r e s p e c t i v U v
In iddition the p r o p o s e d
filtci can be i m p l e m e n t e d b \ u s i n g a P C B t e e h n o l o g v to a c h i e v e
low cost easily integrated design and fabrication
RLfLRkNCbb
Figure 5
(29 7 3 j i
Photo L riph of the pn.pt set! JiSlei
0 1 m m and c
0 4 6 m m i s s h o w n in H e u r c 3 and
its Simulated and m e i s u r c d i t s p o n s e s a i c s h o w n in F i g u r e 4 T h e
simulated and m e a s u r e d insertion l o s s e s ( S 2 1 ) a i c ?2 > and
3 2
dB return losses ("?,,) arc - I s a n d - 1 2 d B a t 2 4 5 G H z respectively T h e s i m u l a t e d a n d m e a s u r e d i 2 , a i e ?1 4 a n d ?3 4 d B
5
n
ire - 2 0 and
results
10 d B at 5 2 G H z
respectively
anil
From these
it t a n b e seen thai a little f r e q u e n e y shift b e t w e e n the
aiTiml ttion and mciMiitnic.nl t a n be o b s t i v e d
I h c slight differ
e n c e b a w t t n the s i m u l a t e d and m e a s u r e d results m i g h t b e b e c a u s e
of fabrication crroi a n d this c o u l d b e c o n t r o l l e d bv the i m p i o v c
m e n t of fabrication t e e h n o l o g v T h e p i o p o s e d filter w a s built with
R o g e r s R O 3 0 0 3 s u b s t i a t e with a r e l a t i v e dielectric c o n s t a n t o t 3 a
loss t m g e n t ot 0 0 0 2 7
and a t h i c k n e s s ot 0 76 m m b v u s i n g a
standaid P C B process
F i g u i e S s h o w s p h o l o g i a p h of the p r o p o s e d filter and the total
size of the filtci is less than 14 m m X 14 m m
Moicovcr
the
p r o p o s e d filter h a s smallci 玦ze as c o m p a r e d with the basse t o p o l
o c y of s t o p b a n d filters [3 4J ind SIR niters [5 6] as listed in f a b l e
1 il Miyake S Kila/au玦 T Ishi/aki T Y intdda and Y Na^alom \
m r n n l u n / e d nionolithic d m l band filter using ceiamic lammiuon
technique lor dull mode portable telephones IFFF MTT S Ini Dig
Denier CO (1997) 7 8 9 - 7 9
2 S Wu and B Ra? a vi A. 900 MHz/1 b GHz CMOS receiver loi
d u a l l i n d IF-Ffc J So] d Scale Circuits H)(!99K) 217S 2185
1 J S Hong dn 1 M J 1 jnc aster Microstnp filter for RF/nucrowave
applications Wde> New York 2001 Ch 8
4 S B Colin Parallel coi pled transmiss o i lint reson lor filters IRT
T n n Micrc wave Theory Tech MTT 6(19:>8j 22^-231
5 E G Cnslid and S Frankel Hairpin line and h j b u d hairpin line/
l n l h v a \ e panllel coupled line filters IFEE T i m s M i u o \ \ a \ e Theorv
lech M i l 20 (1972) 7 1 9 - 7 2 8
6 C Quendo F Rius and C Person An original lopolocy of diul band
liitei with transmission zeros IEEE MTT S Int M i u o w a x e Svmp Dig
W E 1 D 7 f 2 0 0 ^ 109* 1096
7 I C Tsii and C W Hsuc Dual band bandpi s filters u ing equil
length coupled seriu! shunted hues and Z iransl urn technique 1CEC
Tians Miciuwave Tiieory fech s 2 (2004) 1111 1117
8 S F Clntij, Y H Jenc and J I Chen Dual band step impedance
bandpass filter for muRunode wireless LANs Electron Lett 40 (2004j
b-39
9 S Sun and L Zhu Compact dun] band mtcrosuip bandpass h l k r
withoil external feeds 1FFF Micjmwve Wireless Cornpon I ell 15
C00*) 6 4 4 - 6 4 6
10 ! Wnllf Microstnp bandpass nltu usnie degenenle modes ol a
m i u o s m p ring resonator Flection L a t & (1972) 163-164
LI VI Makimoto and S Yanicishua Bandpass Idlers usin^ parallel coct
pled sinphne stepped impedance resonators IEEE Trans Microwave
theory lech 2* U980) 1413-1417
12 J S Honj, and M J 1 ancisiei Microstnp bandpiss filler u ing decen
erate modes ot a novel meander loop resonator IEEE Microwave
Guided Wave Lett 5 (1995) 371 372
13 I H Hsieh and K Chang Dull mode quasi elliptic function bandpiss
hirers usint, ring resonators with enhanced coupling lunmg stubs
IEEE Tians M i u o w a c e Theory Tech - 0 (2002) n ^ 0 - H 4 5
1 I h e p r o p o s e d filter also p r o v i d e s the size r e d u c t i o n of a b o u t 9 8
77
and I5c/t
a g a i n s t the Rcfs
filter has attractive features
7 9 respectively
including dual band
The proposed
� 2006 Wilev Periodicals Inc
applications
s m a l l e r size with r e s p e c t t o the o t h e r m i c i o s t n p ring b a n d p a s s
h l t e i s is v e r \ suitable for m o b i l e c e l l p h o n e and I F F E 8 0 2 I ! a/b/g
4
CONCLUSION
In this letter
a m i n i m i z e d c l o s e d L o o p d u a l b a n d filters
b i s e c t i o n S I R s t u i c t u r c is c o n s t r u c t e d a n d i m p l e m e n t e d
usins
A tnsce
tion SIR is d e r i v e d and d e s i g n e d t o h a v e identical f u n d a m e n t a l and
the first h i g h e r order r e s o n a n t f r e q u e n c i e s M o r e o v c i the p r o p o s e d
filtei also p r o v i d e s the size r e d u c t i o n of a b o u t 9 8
77 a n d 1 3 %
TABLE 1 The Size of the Proposed Filter Compared with
Those in Other References
This work
3
0 76
14 X 14
2 4/5 2
]4 X 14
196
F
/; (mm)
Size
f (GHz)
Converter
Aieadnm )
x*[
Comerler
,
t
|71
|S|
!9|
615
0 63
140 X 3 0
2 4/5 2
200 X 71
12900
325
0 7:>
S5 X 15
2 4/5 7
57 2 X l a 6
858
I07
0 b35
10 2 X 12 i
2 4/S 2
IS 8 \ 22 68
231
r e f O mm)
?r
?
?r relative x mm)
ref (v mm)
;???reldtive(v mm)
DOI 10 1002 mop
MICROWAVE AND
SAFETY ASSESSMENT OF BREAST
CANCER DETECTION VIA
ULTRAWIDEBAND MICROWAVE RADAR
OPERATING IN PULSED-RADIATION
MODE
Earl Zastrow, Shakti K Davis, and Susan C Hagness
Department of Electrics ind Cornp jter Eng neet ng
Un varsity of W scorsin Madison
Madison Wl
Retened
H May
^006
\ B S T R A C T We conduct an finite difference time domain eonipitta
tional elt clromannetic ai alysis oj the safelv of ullrawdehand
micro
wave bttast earner deteitwn teihmques Pulses aie transmuted into
anatomicalh nafiitn
\1R! ictned numeiicul bieast phantom? with dif
jtient le\eh )f tissue hi terigtneit\
at well as-foreign entities such as
implants and s-urgual ihf s- and the spuific absorption is computed
0 2 0 0 6 Wilev FenodicaK Int Microwave Opt Technol Lett 49 221-22^
2007 Published online m Wilev InterSciencc ( u w w rnkrscrenct wrley
com) DOI 10 1002/mop 22089
TECHNOLOGY LETTERS / Vol 49 No 1 January 2007
221
145
Ki\ wen its idtrawuliband r> ia\ a e radii breast cane > (hi
sptufu ab\( ipiton
applicable to scvci il picclmical embodiments of UWB microwave
bicast cancel detection technology
1 INTRODUCTION
2 MODELS AND METHODS
Dosimetric studies ot human exposure to ultr iwldcband (UWB)
election! ignctic wa\t<. are of inu easing import incc because of the
growing interest over the pa&t dec ide in the use of LWB electro
magnetic radiation in medicine For example UWB m i c r o n a u
radai has received much attention recently as a promising modality
forcarlv stage breast cancer detection [1 5] Thisapproachinidj.es
tumor signiturcs m backscrtter received by in antenna anav in
response lo the tiansimssion of low power UWB microwave sig
nils into the breast While u his been assumed thu low power
UW B technology pose- no health risk to the patent it is important
to formally verify that elcctiomagnctic energy absorption in the
breast tails within accepted s itcty guielelmes prioi to clinical
implementation of UWB initio wave breast cancel detection tech
nology
In this article we report the results of a hmtc difference time
domain (FDTD) anal) sis [61 of electromagnetic energy absorption
in the bicast due to microwave radiation m the 1-11 OH7 band
We issiiinc diaf the LWB signals aic gcnerited physically as
t mc domain impulses lather than synthetically using a swept
frequency input (The latlei scenario is considered in [7J) We
compute the specific absorption (SA) m anatomically realistic 3D
numeucal bicast phantoms containing ditfetent levels of tissue
heterogeneity as well as foreign entities such as surgical marking
dips and saline bieast implants I his safetv assessment is bioadlv
We consider the microwa\c imaging scenario wherein a patient
lies prone with an antenna an ay cncucling the breast Wc leprcscnt
this scenuio numeucalh bv modeling an anatomically realistic
breast immersed in a low loss coupling medium A single UWB
pvramidal horn antenna [8J is placed near the bieast Wc position
the intenna with the iperture ?2 5 cm lway from the bicast
centered in the t} plane as ilkisti itcd in Figuie 1
The shape and the intenoi tissue stiucturc of the anatomically
realistic breast phantoms are denved fiom 3D MRI data sets The
MRI voxel intensity in the bicast interior is mapped to a diclectnc
model via a pieccwise lin^ai map [9J for which we spceifv the
mcdun diclectnc propeities 101 lat and hbio玪andular tissues and
assume + 1 0 % variation about each median Although fattv ind
fibiogjandulai tissues are considered to be distinct types of normal
bicast tissue with distinct dielectnc chaiactciistics the bulk of the
current literiturc on diclcdiK characterization of breast tissue at
microwave frequencies docs not make this distinction [10-12J
We expect bbroslandular tissue to exhibit highci diclectnc prop
emes than fat For this safety assessment study wc considci the
worst case seenano b\ assuming thai the dielectnc properties data
in the liter iture represents predominantly lattv breast tissue In lieu
of an established range of values for hbioganduhr tissue we
consider two estimates ol the, dicleetnc properties of fibroghndular
tissue T\pe A is a moderate estimate (also used in Rcf 9}
whereas type B is an extreme estimate with dielectric propeities
that aic significantlv higher than tho^c teported to date in the
literature
Wc describe all of the dispersive media piopertics in our
models using \ single pole Debye expression lor the complex
permittivity
z(<�)
2 4 6 8 10 1214 165
z err)
c^
lb)
Figure 1 3D FDTD model computed ot an VJRI denved numeucal
Imasi phantom (Phantom II) and an UWB amenm fa) Full \uw showing
the hieasi surface (b) Cross secliond! view showing (he breast interior
?Q\ e
JU)?
1 +
}OiTi
(l)
I able 1 summarizes the Dcbse paiameteis toi the dispersive
dielectric media in the models The Debvc parameters for muscle
(the 1 5 em thick chestv*all) and skin (a 2 mm thick laver) were
chosen to mimic the properties reported in Rcf 13 over the
frequency tange of interest
The degree of heterogeneity of bieast tissue \anes from patient
to patient bar completeness we investigate energy depositions m
tour numerical phantoms based on patients with the iollowing
bicast composition (i) almost entirely fat (11) scattered hbioglan
dului tissue (in) hetcroecncously dense and (iv) extremely dense
A cross sectional view of Phantom II is shown in Figure 1(b) Foi
each of the four phantoms v\e consider both type A and type B
dielectric propeities to repiesent the fibroglandular tissue In ad
dmon to the four numerical breast phantoms with \ uying tissue
TABLE 1 Debye Parameters Used in the FDTD Models
(Si)
Vltdia
Coupling medium [41
Breasl f u [31
FiLsioglandulai tissue t\pe \ |9[
hbroghndnlar tissue type B
Skin[9]
Muscular chestwall
Ph) lolngicil Naline (0 15 M) 141
2�
9 00-11 00
20 11-24 8"
42 94-52 48
57 00
'4 00
77 9
2 54
610 7 70
5 51-6 7*
1 98^4 8b
4 00
4 00
4 15
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 'Vol 49 No 1 January 2007
0 05
0 133-0 165
0 279-0 341
0 558-0 682
1 10
0 70
1 7'
DOI 10 1002/mop
N/A
7 00
7 00
7 00
7 23
7 00
8 97
146
I
i.b>
(b)
i j)
*
if
(u
<il)
Id!
Figure 3 Pe ik Ltna\eras,ed S\ in ea h coronal shee (corresponding to
depth A) tor nch tissue type lor Phantom I (type A) ihiough IV (type A)
Figure 2 Una\ ei at,ed SA diitnbution of the cor nal slice com lining, the
ploba! peak absorption (mJ/kj,) for Phantrm 1 (i\pe A) ihiough IV (type A)
compositions we consider thiee scenarios where foreign materials
are present in the breast phantoms Foi the fust scenano wc obtain
an MRI of a patient with bicast implants and assign the dielectric
properties, of physiologic d saline (0 15 M) [14] to the region of the
implani Wc use the t>p^ B properties to represent the hbroglan
dular tissue in this phantom In the second and thud sccnanos
titanium suigiL.il marking clips commonly deploved in cxcisional
biopsy procedures are ainficially inserted m Phantom III We
assign the type S properties to the hbioghnduiar tissue in the
phantom for both of these scemrios Ihe two suigicai clips wc
consider die a 2 y 2 mm 2 horseshoe shaped clip [IS] and a 5 x
1 mm 2 line shaped clip The clips arc centered at A 5 0 em > ~
5 0 cm and
6 1 cm ( OS cm beneath the skin lavet and on the
axis of the antenna)
An PDTD simulation is conducted for each of the 11 breast
phantoms described abo\c The excitation waveform applied at the
feedpoint of the UWB hoin intenna is a modulated Gaussian pulse
with a temporal full width at half-maximum of 120 ps and a
spectral peak at 6 GHz The unavcraged SA during single pulse
cxposme is computed at everv voxel in the breast phantom as
follows
SA
E(r) J(f)dt
(2)
peak unavcraked SA in a coronal slice at depth x tor I specihed
tissue type These figiucs show that the spatial distribution of
una\cidged SA vanes with the distance from the antenna as well
as the tissue type As expected the absorption in the interior
tissues (fat and fibroglandular) is le^s than the absorption in the
sktn Vamtions in the absorption in the breast interim for different
phantoms aic relatively small Ihe peak undveraged SA consis
tently occurs m the skin liver and has simil u makniludc lor all
tour phantoms
Wc further investigate the absorption in fibioglandular tissue a->
a function of its diclcctnc properties Figuie 4 shows the peak
unaveraged SA value for the fibioglandular tissue in each coronal
slice of Phantom 111 with tvpe A and type B tissue properties The
energy absorbed in type B fibroglandular tissue is approximately
twice the encigy absorbed in type A but icmains significantly
lower than the absorption in the skm and fat
Next we evaluate absorption when foreign objects arc picsent
in the bicast In our first seen ino we consider the absoiption in the
brc is,t phantom eonl unmg a saline implant as depicted by Figuie
5 Figuie 6 u ) shows the unavciaged SA of the eoional slice
containing the peak absorption for this phantom The absorption
level at the tissue implant interface is elevated abov e othci interior
legions inside the breast Figure 6(b) shows the peak unavcraged
SA in each coronal slice for each tissue type and tor saline I h e
saline implant alteis the breast shapv. and distribution of the fi
broglandular tissue thereby modifying the interior scattering and
using the six field component approach [161 The tissue densitv p
is assumed to be 1 g/cm' L and J are the electric field and total
cuirent density vectors respectively and 1 is the duration ot the
simulation We also compute the peak 1 g SA for each ph-tntom
All absorption values aie normalized to I mj of radiated encrsv
3 RESULTS
Figuie 2 shows the spatial distribution ot unaveraged SA ovci the
eoional shee containing the global peak absoiption in mJ/kg lot
Phantoms 1 thiough IV with tvpc A fibroglandular tissue propei
tics The energy deposition as a function of tissue tvpe within each
phantom is shown in Figure 3 where each cuive leprcscnts the
DO 10 1002 mop
Figure 4 Peak una\eraj_ed SA in the fibroglandular tissue in eai.h
coronal 玥ce {corresponding to depth x) of Phantom 111 for lv\o types of
libroglandular tissue properties (tvpe A and B)
MICROWAVE AND OPTICAL TECHNOI OGY LETTERS
Vol 49 No 1 January "007
147
10u
? *r
<
AQ
A)
6
B
10 12
14
l (an;
ISI'S
>j ^
0
Figure 5 Cioss s u una! view of the ^D FDTD mode! comprised ol an
MRI demed mime L J breast pinnlorn 0>Pe &J Lfnfdimm, a saline im
plant
absorption piopcrtics As a result the SA lc\cls in fibroglandular
tissue (type B) in this phantom aic higher than those obseived in
Figme 4 tor Phantom HI ftjpe B)
In our second scenario \vc evaluate the situ ition where metallic
suigical clips arc tntioduccd ai i sh illou location in the subculi
ncous fat lajcr of Phantom III (t>pc B) Wc considered several
orientations ot the two clips described in the picvious section and
found that the absorption is highest when the clips are oncntcd in
the x direction Wc report the results tor this orientation Hgurc 7
shows that the piesence of these clips iaiScs Ihe level of unaver
aged SA in ihe \itmity of the clips Clculy the ib&orption ehar
actcristics depend on the specific shape of the clip The line chp
induce1; two localized absorption peaks at the ends of the clip Ihe
horseshoe clip induces a single localized absorption peak between
the two prongs Ihe v ilues of the peik absorption arc eompaiable
for both clips These sharp increases in absorption aic highly
s
G
TTjimMfQ
a
10
z cm)
\2
(a)
to
40
?0
(b)
Figure 7 Peak uni\eiaged S \ m each coronal slice foi each tissue tvpe
of Phiniom III (tvpe B) with a fa) line shaped clip nd (b) hnst^hoe
shaped chp centeied at K 50cm s ? s 0 cm and
6 t cm
localized and therefore h ive little impact on the 1 g SA around the
chp region The peak 1 g SA remains in the skin region
Tabic 2 summarizes the peak una\eragcd and peak 1 g SA
noimahzcd to I ml of ladiatcd energy fiom a s i n j c UWB pulse
for all numerical phantoms The variation in the shape si?e and
tissue composition of the phantoms results in onh minor variation
in the peak absorption values and the foreign objects have no
noticeable impact on the peak 1 g SA
The results of Table 2 along with the exposure limits established bv IFFF standard C9:> 1 [17] make it possible to assess the
safety of futuic clinical systems The 1FFF peak 1 g SA limit foi
a 6 min exposure is 576 J/kg [17] This hmit is ~ 2 8 000 times
highci than the peak 1 L SA fiom i single 1 mJ UWB pulse in
Ttble 2 With these numbers wc can predict limits on die approx
imate amount of energy radiated in each pulse the numbci of
TABLE 2
80
c
a)
SA in mJ/kg for 1 mJ of Radiated Energy
Computed During Single-pulse Exposure
4(l
EM Model
Peak
l ! iiaveraj,ed
SA
Pe_k
lgSA
68 �
68 17
80 i9
80 " 0
7.06
71 (P
84 47
84 48
63 46
108 6
92->2
1810
18 .0
' 1 75
2171
18 12
1811
20 81
20 81
17 72
18 11
J819
tr
20
:
?
%
(b)
Figure 6 (a) Lnaveraged SA di tnbuuon of die coronal slice containine.
ihe global peak absorption (mJ/kg) for the phantom (tvpe B) containing the
salme implant (b) Peak unavuaged SA in eiih coronal slue fee rrcspond
ine lo depth x) for each tissue tvpe and the implant
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
I ttype A)
I (type B)
il (type A)
i[ (type B)
[[I (lype A)
III (tvpe B)
i\ (type Al
IV (tvpe B)
(tvpe B) unit breast impl ml
ill (type B) with horseshoe shaped clip
III (ty ie B) with line shaped clip
MICROWAVE AND OPTICAL TCCHNOl OGY LETTERS / Vol 49 No 1 January 2007
DOM 0 1002 mop
148
putsch ladiarcd p e r a n t e n n a
ana>
a n d the n u m b c i of a n t e n n a s in an
Fot e x a m p l e if each p u l s e c a i n e s 1 m j o f e n e r g v
it w o u l d
he p e r m i s s i b l e t o c o u p l e u p to 28 0 0 0 p u l s e s into the b r e a s t o v e r a
6 m m peiiod
sccmno
In a pi ac t i e d U W B
i n u r o w a v e radar
9
imaging
an array of u n l c n n a s s u n o u n d s the b i c i s t v o l u m e and
e a c h c l e m e n t sequentially i l l u m i n a t e s the b r e a s t
A typical a n ay
may c o n t a i n on the ordci of 50 a n t e n n a s s u g g e s t i n g that up to 5 6 0
10
p u l s e s c o u l d be Transmitted by e a e h a n t e n n a w i t h o u t e x c e e d i n g the
p e a k 1 g S A l i m i t s u c g t sted in the J b b b e x p o s u i e g u i d e l i n e
Note
l i n t the level of c x p o s u u of 5 6 0 pul&cs p e r a n t e n n a is m u c h h i g h e r
11
than w e a n t i c i p a t e n e e d i n g for this a p p l i c a t i o n
12
4 CONCLUSIONS
W c have i n v e s t i g a t e d the a b s o r p t i o n of short ( 1 2 0 ps
earner)
miciowavc
pulses
in a n a t o m i c a l l y
b i e a s t p h a n t o m s in a n effoit t o f o r m a l K
realistic
6GH/
n
numerical
e \ a l u a t c the safety of
U W B m i c r o w a v e breast e n i c e r d e r a t i o n teehnolog> o p e r a t i n g in
14
the 1 11 G H z rariL.e W e h a v e found t h a t the S A d o e s n o t \ a r y
greatly with p a t i e n t t o p i t i e n t variations in b r e a s t s h a p e
composition
or fibroglandular
diclcetne properties
tissue
While
15
the
specific c h a r a c t c n s n c s ( a n t e n n a latitat ion patterns c o u p l i n g m e d i a
properties
etc ) of future clinical s\ s t e m s m a y differ from t h o s e
a s s u m e d t o r this c o m p u t a t i o n a l sttid\
the S A values are n o t
16
e x p e c t e d to vary s i g n i f k a n t K as i function of t h o s e e h a r a e t e n sties
The n o r m a l i z e d S A values l c p o r t c d in this p a p e r c a n b e scaled to
a c e o u n t for the total n u m b e r of p u l s e s l a d i a t c d a n d d i t f e i c n r p u l s e
energies
p r o v i d i n g v a l u a b l e g u i d a n c e in the d e s i g n of
futuie
clinical s v s t e m s that arc in c o m p l i a n c e with safety s t a n d a r d s
Foi
a n t i c i p a t e d e m b o d i m e n t s of s u c h a s y s t e m w e c o n c l u d e that U W B
m i c r o w a v e breast c a n c e r detection m o d a l i t i e s p o s e n o health n s k
17
horn inlenna with curved hunching plane for pulse radiation IFFF
Antennas W i r e l e ^ Propig I ett v 200^1 2">9-262
VI Converse h i Bond B D Van Veen m d S L Harness \ com
puialional study of tiltiawideband veisus nanowband microwave hy
pcrtliemin for bieast cancel treatment IEEE Tians Microwave Theorv
Tech M (200b) 2169-^lSO
\ \ T Jomes ^ Zhang C Li and R L Jirile The measured electrical
properties of normil ind malignant human tissues from ^0 lo 900
MH? Mtd Phys (1994) 5 4 7 - " 0
A J Surowiec S S Stuchly J R Barr and A Swamp Dielectiu
propeities oi breast carcinoma m d die surrounding tissues IEEE Fi ns
Biomed Eng l a ("1988) 257-263
S Chaudh^ry R Mishia A Swamp and J T h o r n s Dielectric
pioperlies of n o t m J md malignant human brea I tissue at radiowave
m d microwave frequencies Ind T Riochem Biophys 21 (1984) 7 6 - 7 9
S Gibnel R W I an m d C Gabriel The dielectric properties oi
bioloeuil tissues UI Parametric models for the dicleclnc spectrum of
tissues Phys Med Biol 41 (1996) 2271-229-.
J HiUnnd Simple sensoi system for measuring the dielectric pioper
ties of s d m e solutions Mtas Set Tcchnol (L997) 901 910
D M Lanners K k Amrami R S Jonsgaaid J J Gisvold and J P
Felmlee Safety and MRI artifict evaluation at 1 D T of metallic
mount inu she uh of a m irking clip madvcrlentH deployed it sleieo
tactic biopsy Am J Roentgenol (200^) 8 2 5 - 8 2 9
K Caputa M Okomewski and M A Stuchly An aleonthm for
compulsions of the power deposition in human tissue IEEE Antennas
Piopag Mag 41 (1999) 102-107
IEEE Standaid for safety levels widi respect lo human exposure to
radio frequency electromagnetic fields 3 kHz to 00 G H / IEEE
SLmchrdC95 I 1999
<Q 2006 Wilev Periodicals Inc
t o the p a t i e n t
ACKNOWLEDGMENTS
1 his w o r k w a s s u p p o r t e d b \ the N a t i o n a l Institutes of H e a l t h u n d e i
g i a n t H ! C A 1 1 0 9 1 2 a w a i d e d b y the N a t i o n a l C n i c e r Institute and
the N i t i o n - d Science F o u n d a t i o n u n d e r g r a n t B E S 0 2 0 1 8 8 0
RFFFRFNCFS
1 S C H i g m s s A laflove jiid J E Bridges 1 wo dimensional F D I D
analysis of a pulsed rwuowave conlocal svsiem lor bieasl cancer
detection Fixed locus and antenna array --ensorv IECE Trans Biomed
hn fo (1998! 1470-147b
2 F C Fear md M A Sluchly Microwive system lor breisl tumor
detection ICEC Microwave Guided Waxe Lett 9 (1999) 4 7 0 - 4 7 2
"i E J Bond \ Li S C Hagness and B D Van Veen Microwave
imaging v n space time bcamforming lor eirlv detection ot breisi
cancer IEEE Trans Antennas Propag (2001) 1690 1705
4 X Li S K Davis S C Hagness D W v a n d e r W e i d e and B D Van
Veen Microwave imiging v n space lime beamforitung Experimental
investigation of fumoi detection m mull layei breast phantoms IFFF
Trans Microwave Theorv Tech {20041 1856 186a
5 J M Sill and E C Fear Tissue sensing adaptive ladai lor breast cancer
detection?F^penmenlal investigation of simple lumoi models IFFF
Tians Microwave Theoiv Tech 53 (200^) 1 3 1 2 - ^ 1 9
6 A Taflove and S C Hagness Computational electrodynamics The
finite difference time domiin method 3id ed Artech House N r r
wood MA 200^
7 C Zasliow S K Davis and S C Magnets Safety assessment ol breast
cancel detection via i] lira wideband m i u o w a v e ridar opoeraung in
swept frequency mode in Proceedings o1 I F F F Inlemilional Sympo
sium on Antennas md Propagation Albuquerque N M Jul\ 2006 in
press
8 X Li S C Hagness M K Choi and D W v a n d e r W e i d e Numeric i]
and experimental investigation of an ultravvideband ridged pynmidal
DOM 0 1002 mop
MICROWAVE AND OF
APPLICATION OF THE FOLDY-LAX
MULTIPLE SCATTERING METHOD TO
THE ANALYSIS OF VIAS IN BALL GRID
ARRAYS AND INTERIOR LAYERS OF
PRINTED CIRCUIT BOARDS
C-J Ong,1 D Miller,2 L Tsang,1 B Wu,1 and C -C Huang2
1
Department ot Electrical Engineering
Un versity of Washington
Paul Allen Center PoomAblOOR
C a n p u s Box 3 5 2 5 0 0
Seattle WA98195 2500
* Intel Ooiporation
Jones Farm o 2111 N E 25th Avenue
Hillsboro OR 97124 D961
Received 12 Mav 2006
ABSTRACT The authors apfhed iht method of Tolds?Lax multiple
scattering equations to multiple ius in hall i,ud ana) s and the interior
lasers of printed aicmt boards The method gives the Mattering pat am
elets of the atra\ The result1; ate w lifted with Ansoft s NFS') with \en
little difference between the Fold) Lax approach and the HF&& results
The CPL required for the method is only a small fraction of tht time
that HFb& tequila
For a 16 X 16 arias- ot itus the method calculates
all the $ pa/ametei s of tht 512 potts m 4 mm for 10 frequencies on u
Pentium 3 2 Gfh PC O 2006 Wiley Periodicals Inc Microwave Opt
Technol Lett 49 225-211 2007 Published online in Wiley fnlerScience
(www inierscience vviley com) DOI 10 1002/mop 22091
Key words \ia\ multiple scattermf,
punted an uit hoards
signal mtei,iit)
ball },tid
TfCHNOLOGY LETTERS / Vol 49 No 1 January 2007
attuys
225
Safety A s s e s s m e n t of B r e a s t C a n c e r D e t e c t i o n v i a
U l t r a w i d e b a n d M i c r o w a v e R a d a r O p e r a t i n g in
Swept-Prequency M o d e
Eail Zastrow*, Shakti K Davis and Susan C Hagncss
Department of Elccti ical and Computer Engineering
University of Wisconsin Madison W I 53706
Email cpratoomQcae wise edu
Introduction
Ultrawideband (UWB) nnciowave radar is a promising modality for detecting cailystagc breast cancer [1] In our current prototype [1], we synthesize an antenna array
by scanning a single antenna to each array position and sequentially transmitting
a swept-fiequency signal and receiving the backscattcr Our U W B tadar operates
m the 1-11 GHz frequency band Whrle it has been assumed t h a t low-power U W B
microwave bieast cancer detection technology poses no health risk, it is important to
formally evaluate the absorption of electromagnetic energy in the breast to establrsh
t h e safety of such exposure prior to clinical implementation In this paper, wc report
the results of hmte-diffcrcnce trmc-domain (FDTD) [2] rnvestigations of the specific
absorption l a t e (SAR) in 3-D numerical breast models due to microwave radiation
m the 1-11 GHz frequency band
Models and Methods
In our d a t a acquisition scenario a patient lies prone with an antenna array surrounding the breast We represent this scerrarro numcrrcally by modeling an anatomrcally
realrstic breast with 2-mm-thick skm and a 1 5-cm-thick muscular chestwall T h e
breast is immersed m a low-loss couphng medium and a numerical representation of
our U W B pyramidal horn antenna [3] is placed near the bieast T h e antenna feed
is exerted with a resistive voltage source [2] For our safety assessment we position
the antenna with t h e a p e i t u r e approxrmately 2 5 cm away from the breast centered
on the xy-plane as lllustiated in Figure 1(a)
Normal breast tissue is a highly heterogeneous mrxture of fatty and frbroglandular
trssues Wc derrve an anatomrcally realrstrc breast model by basing the interior
on a 3-D MRI of an actual patient Breast tissue composition varies from patient
to patient and to some extent wc expect the powci deposition to depend on the
composition To investigate this hypothesis, we constiuct four numencal phantoms
based on patients with the following categories of breast composition (I) almost
entuely fat (II) scattered fibroglandular trssue (III) heterogeneously dense, and
(IV) extremely dense A cut-away view of the Category III model is shown in Figure
1(b) T h e MRI voxel intensity is m a p p e d to a dielectric model via a piecewise linear
map [4] wheie we specify the median dielectric piopertics foi fat and fibroglandulai
tissue and assume a � 1 0 % variation about each median Since out radar system
operates at multiple frequencies we describe the dispersive media properties using
a smgle-pole Debye expression Table 1 summarizes the Debye parameters for t h e
150
dispcisive dielectnc media in the models
An F D T D simulation is conducted for each discrete frequency of nitcicst withm the
U W B lange of opeiation Once the simulation has reached the sinusoidal steady
state tho SAR is computed Following the six-held-component approach [5], we
calculate both peak 1-g and unaveiaged SAR values thioughout the numerical breast
p h a n t o m lepiesentmg each of the four breast compositions All absoiption values
arc noimahzed to 1 m W of radiated powci
Results and Conclusion
Figures 2(a) (c) (e) show the spatial distribution of unavcraged SAR over t h e coronal slice containing t h e global peak absorption of the Categoiy III breast p h a n t o m
for operating frequencies of 1, 6 and 11 GHz, respectively These SAR distributions
demonstrate how absoiption mcieases with frequency while penctiation depth decreases with ftequency Each curve in Figures 2(b) (d),(f) represents t h e peak SAR
m a coronal slice at depth x foi a specified tissue type T h e absoiption is greatest
m the skm layer at all depths Figuie 3 compares the spatial distribution of unavcraged SAR foi diffucnt bicast compositions These i t s u l t s suggest t h a t t h e breast
composition does not significantly affect the amount of powci deposition withm the
breast interior Table 2 summarizes the peak 1-g SAR for all breast models It
is interesting to note t h a t the laigest SAR values occur m the Category II breast
phantom
T h e SAR values leported in Table 2 can be leadily scaled to generate results for an
experimental setup with known radiated power As an illustration we determine
the peak 1-g SAR value for t h e Category III breast example under radiation at 6
GHz in a breast cancel detection scenario t h a t makes use of a network analyzer with
a p o i t powci setting of -17 d B m as the swept-frequency source Assuming perfect
power transfer we scale the values in Table 2 by 1/50 to obtain estimates of SAR
due to 0 02 m W of radiated powei This results in a peak 1-g SAR of 0 385 m W / k g
at 6 GHz
We conclude t h a t the absorption due to miciowave radiation in the 1-11 GHz b a n d
m t h e application of low-power U W B microwave breast cancer detection is well
below the suggested I E E E exposure limit of 1 6 W / k g [6]
References
[1] X Li, S K Davis, S C Hagncss, D W van der Weide and B D Van Veen,
"Microwave imaging via space-time bcamfornnng Experimental investigation
of tumoi detection in multi-layer breast phantoms,' IEEE Trans
Microwave
Theory Tech , vol 52, pp 1856-65 August 2004
[2] A Taflove and S C Hagness Computational
Electrodynamics
The FiniteDifference Time Domain Method, 3rd ed , Norwood MA Artcch House, 2005
[3] X Li, S C Hagness, M K Choi, and D W van der Weide, 'Numerical and
experimental investigation of an ultrawideband ndged pyramidal-horn antenna
151
with cm ved launching plane foi pulse radiation,' IEEE Antennas Wireless Propaqat Lett , vol 2, pp 259-62, 2003
[4] M Conveise, E I Bond B D Van Veen, and S C Hagncss, 'A computational
study of ultrawidcband versus narrowband microwave hyperthermia for breast
cancer treatment' IEEE Trans Microwave Theory Tech , submitted
[5] K Caputa, M Okomcwski, and M A Stuchly, 'An algorithm foi computations of the power deposition m human tissue ' IEEE Antennas Propagat Mag ,
vol 41, pp 102-7, August 1999
[0] 'IEEE Standard for Safety Levels with Respect to Human Exposure to Radio
Fiequency Electromagnetic Fields, 3 kHz to 300 GHz ' IEEE Std C95 1, 1999
Media
Coupling medium [1]
Fat [4]
Fibroglandular tissue [4]
Skm [4]
Chcstwall*
c9
2 54
10 00 �%
21 57 +10%
37 00
54 00
too
&s
T (ps)
2 54
7 00 �%
6 14 �%
4 00
4 00
0 05
0 15 �%
0 31 �%
1 10
0 70
7
7
7
7
7
00
00
00
23
00
"The Debyc parameters for the chestwall arc based on the tumor propeities in [4] since muscle
and malignant breast tissue aie electromagnetically similar
Table 1 Dcbyc parameters used in FDTD models
Breast model
Category I
Category II
Category III
Category IV
1GHz
6 38
1108
8 27
9 91
2GHz
8 08
10 68
9 39
9 50
6GHz
vin
20 89
19 25
19 42
10GHz
35 49
42 76
34 52
40 75
11 GHz
44 62
47 71
44 32
44 07
Table 2 Peak 1-g SAR m mW/kg as a function of frequency for 1 mW of radiated
power
(a)
(b)
Figure 1 3-D FDTD model comprised of an MRI-derivod miiiiei ical bi east phantom
(Category III) and an UWB antenna
152
Skin
? Fat
? Fibroglandular
.!';
^Sv^
10 12
z (cm)
14
4
x (cm)
(a)
(b)
-
Skin
oi60 ? Fat
.M
Fibroglandular
1 40
"V
a:
^20
10 12
z (cm)
4
x (cm)
14
(c)
(d)
10'
''
Skin
? 2 0 0 ? Fat
en
10� | 150
E
? 100
10 <
� 50
10 12
z (cm)
6
Fibroglandular
/\->
4
x (cm)
14
(e)
(f)
Figure 2: Unaveraged SAR for the Category III breast phantom at operating frequencies (a)-(b) 1 GHz, (c)-(d) 6 GHz, (e)-(f) 11 GHz. (a),(c),(e) Spatial distribution of SAR in mW/kg of the coronal slice containing the global peak absorption.
(b).(d),(f) Peak unaveraged SAR value in each coronal slice (corresponding to depth
x) for each tissue type.
12
10
x = 4 75 err
"6
| p f '/
4
4
6
8 10 12 14
z (cm)
(a)
L
10
z (cm)
(b)
1
Ikh !\ 1
8
5
10
z (cm)
15
(c)
Figuie 3 Unaveraged SAR distribution in mW/kg of the coronal slice containing
the global peak absorption at 6 GHz operating frequency in the (a) Category I (b)
Category II and (c) Category IV breast phantoms
153
Appendix B: Implementation of a 3D microwave imaging system for granular materials research
Included in this appendix:
C. Van Niekerk, E. Zastrow, S. C. Hagness, and J. T. Bernhard, "UWB radar target sensing
and imaging for granular materials research applications," to appear in Antennas and Propagation Society International Symposium 2010, IEEE.
K. M. Hill, Y. Fan, J. Zhang, C. Van Niekerk, E. Zastrow, S. C. Hagness, and J. T. Bernhard,
"Granular segregation studies for the development of a radar-based three-dimensional sensing
system," Granular Matter, vol. 12, no. 2, pp. 201-207, Apr. 2010. doi: 10.1007/sl0035-0100167-x
154
U W B R a d a r T a r g e t S e n s i n g a n d I m a g i n g for G r a n u l a r
Materials Research Applications
C Van Niekcrk* 1 , E Zastiow 2 S C Hagncss 2 , and 7 T
1
Bernhaid1
University of Illinois at U i b a n a - C h a m p a i g n , U r b a n a IL 61801
2
University of Wisconsin at Madison Madison, WI 53706
E-mail cvanmc2@illmois cdu
Introduction
Granular materials research involves the study of dynamic movement of objects with
gianulai shape and chaiacteirstics Researchers in this held of study tely on accurate
experiments to validate theoietical models or solve problems empirically Current
expciimcnts aie either expensive (e g , MRI or X-ray technologies), limited in scope
(e g High-Speed High-Resolution Photography which is limited to 2D experiments
due to granular material opacity) or extremely tedious and time-consuming
In
this papci we investigate a fiist-gcneiation p i o t o t y p e o( a ladai system t h a t will
provide a minimally invasive fully automated mcasuiement of individual and bulk
particle movement in a 3D volume T h e radai system [1] comprises inexpensive
tracer particles as targets a test signal geneiation and measurement unit and a
post-piocessing unit for imaging T h e proposed target is a square rctrorcfiector
which is made up of three oithogonal square metal plates (sec Figure 1) An array
of wideband antennas surrounding the testbed is operated in monostatic mode using
swept-frcquency VNA measurements t h a t arc processed to mimic an ultrawideband
(UWB) bandpass pulse In oui fust-generation prototype we synthesize a linear
array by moving the testbed relative to a single antenna The testbed contains one
or moic targets deployed m a free-space (rather t h a n granular material) volume
Wc perform delay-and-surn beamforrmng to reconstruct an image of the testbed
Images aie geneiatcd foi the rctioieflcctoi at two distinct onentations - (normal
and oblique) relative to the array
T h e retroreflector
T h e simplf- geometry of the ietioipflre toi with its ught-anglcd trihedral coiners is
known to positively lemforcc a strong monostatic radar cross section (RCS) from
almost all incident angles [2] Numerous papers have shown t h a t any deviation from
t h e classic geometry (l e orthogonal plates) results in a decrease in RCS [3] While
its operation is well understood and known exactly when it is several wavelengths
in size, its performance is less familiar when t h e dimensions of the refiorefiertoi
are sub-wavelength, as is the case m this application [4] For use as a radar target
in granular materials experiments, the target has to be encased in spherical shell
to facilitate case of motion during t h e experiment
T h e size of letioreflcctor is
ultmutely limited by the size of granular materials under test If t h e retioflectoi
is significantly larger t h a n a gianular m a t e n a l particle its movement will not be
representative of that of the granular material Plastic refroieftcctor elements were
manufactured using a rapid prototyping process T h e retrorefiectoi targets were
manufactured to have a square plate length of 12 7 m m (or plate diagonal of 18
155
m m ) T h e taigets were then coated with several layeis of silver paint this coating
ensures a good mctalizcd target (1 e the target wall produces stiong inflection and
minimal transmission chaiacterrstics)
When analyzing the target s RCS performance we are primarily concerned with only
monostatic r c t u i n since the letioieflectoi s structuic is biased to stiong backscatter
returns Here we limit our comrncntaiy to the monostatic RCS frequency response
(5 to 15 GHz) at normal incidence and then the monostatic RCS spatial response
foi one q u a d i a n t (oi t i i h e d i a l c o m a ) of the letioieflectoi at fixed hcqucncics of
5 10 and 15 GHz T h e backscattei i c t u i n fiom the retioicflcctor increases with
frequency in a monotomc fashion There is howcvci, a large null at the ft equency
t h a t c o n e s p o n d s to a edge length of loughly a half wavelength At this frequency the
letioieflectoi expciionccs maximum diffiaction at edges paiallcl to t h e polarization
direction of the incident wave Since diffiaction is a phenomenon where encigy is
ladiated in all directions equally (I e , similar to a isotropic ladiator) the amount of
scattered energy is substantially reduced in t h e backscatter direction Meanwhile,
t h e angular monostatic R C S lesponse shows a deciease in vailability as t h e electrical
size of t h e letioieflectoi is shiunk m clcctiical size In other words, toward the lowei
end of the hequency langt the letioieflectoi looks like a small metal sphere (l c , no
angle dependency)
Delay-and-sum beamforming
T h e frequency-domain Sii d a t a recorded at all N antenna locations is fust transformed into time-domain A modulated Gaussian pulse (center frequency = 10 GHz,
full-width half-maximum = 8 GHz) is assumed to be the desired incident waveform
T h e synthesized discrete time-domain wavefoim at each channel includes the incident wave the leflection fiom the expoiimcntal fixtuie and the backscatter from
the target We isolate the target backscattei by subtracting a reference waveform
collected at each channel in the absence of the testbed This yields a calibrated
dataset containing only t h e backscatter from the target collected fiom N channels,
A\,Ai
,AJV as illustrated m Figure 2(a) Each time-domam signal contains M
time samples At each scan location, r, in the imaging region, the discrete-tune delay
needed to achieve a synthetic focus at r is T?(r) = 2d?(r)/(vAt),
where dn = |r?r?|
is the distance between r and t h e transmit/receive nth antenna located at r ? v
is the propagation speed in the background medium (I e free space) and At is
the time-sampling interval T h e calibrated wavefornrs Ai,
,AN are time-shifted
to time-align all N signals and scaled to compensate for the radial spreading of
the wave traveling fiom r ? to r T h e time-aligned and scaled waveforms A\
A'N
(illustrated in Figure 2(b)) are then summed to obtain the beamformer waveform,
z m
\ ] = E n = i ^ n ( m ) (illustrated m Figure 2(c)) Finally the energy in the bcamforrnei o u t p u t calculated as p(r) = ~^z{m]2, where t h e summation is performed
over an appropriate time window
156
Experimental implementation using a linear array configuration
The goal of this experiment is accurate localization and imaging of the rotioieficctoi
taigct in the experimental volume For thrs experiment the target is m a static
position and placed with specific orientation relative to the sensing linear array Two
distinct orientations are analyzed and are desrgnatcd normal (one of the vertical
plates arc parallel to plane of the antenna array) and oblique (which is normal
orientation shifted by 45�) A distance of 20 cm exists between the plane of the
airay and the target Presently, the linear array rs implemented synthetically by
using one stationary antenna and moving a single target to eight seperate positions
in the measurement space This implementation not only produces a cost saving
for the prototype system but also eliminates potential array coupling issues The
major disadvantage is that there are unavoidable placement errors due to the manual
movement of the target Also, the experiment takes much longer to complete than
if it were automated
The specific arrangement of the experiment is depicted m Figure 3, which shows the
measurement space wrth grid foi both orientations The target position is shown
by cross hairs (at -10 cm on y-axrs and 20 cm on x-axis) and the eight synthesized
antennas are shown by x markers on y-axis Figure 4 shows resulting radar images
for both orientations The cross hairs indicate the exact position and onentatron
of the target while the experimental result is shown by a deep red spot For the
normally oriented rotioieflector the image shows a localization error of less than
1 cm with the image target center is further back and slightly to the right than the
true situation Meanwhile for the oblique case the result is much more accurate
wrth error less than 0 5 enr Both orientations also show a fair amount of image
ghosting but the target is clearly discernible from the ghost image
Conclusion
A prototype system has been shown to work using a hncar array and single target,
albeit with sonic localization error This error can be accounted for by the inherent
inaccuracy of placing the target at the correct position and face angle with manual
means Thrs error wrll be eliminated by implementing the actual array
References
[1] K M Hill, Y Fan, J Zhang, C Van Niekerk, E Zastrow S C Hagncss J T
Bernhard, 'Granular Segregation Studies for the Development of a Radar-Based
Three-Dmicnsional Sensing System,' Granular Matter, 2010 (in press)
[2] G T Ruck, D E Barrick, W D Stuart and C K Krrchbaum, Radar Cross
Section Handbook, vol 2 New York, NY Plenum 1970
(3] W C Anderson, 'Consequences of nonorthogonahty on the scattering properties of dihedral reflectors IEEE Transactions on Antennas and Propagation,
vol 35, no 10, pp 1154-1159, 1987
157
[4] R Green 'The echo area of small icctangular plates with linear slots,' IEEE
Ttaasactions on Antennas and Piopagatton vol 12, no 1 pp 101-104 1964
5
%-
(a)
Figure 1 (a) Squaic ictioieflcctoi
(b)
(b) Silvci spiay-pamtcd utioicflcttoi
Figure 2 (a) Time-doniam signals (b) Time-aligned signals for scanned location r
(c) Bcamfoimer output for scanned location r
I T TTT I I T
1
2
3
4
5
(a)
6
7
8
TI I I TTI T
1
2
3
4
S
6
7
8
(b)
Figuif 3 Experimental setup with rctioioflectoi of different orientation (a) Normal
orientation (b) Oblique orientation
Figure 4 Beamformer image for the two experiments with retrotoflcctoi of different
orientation (a) Normal orientation (b) Oblique orientation
Granular M a t t e r manuscript N o
(will be inserted by the editor)
Granular Segregation Studies for the Development of a
Radar-Based Three-Dimensional Sensing System
K M . Hill*, Y Fan*, J. Z h a n g j , C Van
N i e k e r k | , E . ZastrowJ, S. C. HagnessJ, and J
T. B e r n h a r d t
Received date / Accepted date
A b s t r a c t The behavior of dense granular materials is difficult to measure in threedimensions due to the opacity of the materials \ \ c present a new radar-based sensing system that has the capability of measuring three-dimensional particle movement
throughout the bulk of high solids fraction granular s> steins A key component of the
new system involves letroreficctors imbedded in objects resembling the particles in the
bulk granular systems These embedded rctroreficctors may be used as tracers in systems comprised of relatively large particles However in systems of smaller particles
the most versatile use of this new sensing system requires an understanding of the details of relative particle movement based on particle size and other particle properties
Towards this, we present new ongoing experimental and computational results toward
building a versatile sensing system foi high solids fraction granular systems We then
comment on additional research needed on the behavior of the components in granular
mixtures for a fully versatile sensing system
K e y w o r d s Remote sensing, dense granular materials, segregation
P A C S 42 68 Wt 47 57 Gc
81 05 Rin
1 Introduction
Over a centurv of research has provided a wealth of insight on the behavior of granular
materials Constitutive laws based on kinetic theory have been relatively successful at
modeling the behavior of collisional particulate flows [1] Constitutive laws based on
plasticity theory have been relatively successful at modeling small deformations [2]
However, an appropriate framework for modeling the intermediate regime of sheared
flows at relatively high solids fractions remains a matter of debate [3j-[5] Theoretical
discrepancies are hard to resolve because of the paucity of data it is difficult to measure
the kinematics of granular materials m three-dimensions due to their opacity
*University of Minnesota Minneapolis MN 55414
"("University of Illinois Urbana IL 61801
tUniversity of Wisconsin Madison, WI 53706
Fig 1 Schematic of one embodiment of the new three dimensional sensing system Ihe image
at the right is a sketch of the tr icer particle consisting of an embedded ret rentier tor described
in the text As shown the basir design consists of three orthogonal intersecting plates
Experimental techniques designed to provide further insight and computational
model validation of granular flow come m many forms For example magnetic resonance imaging (MRI) [6] positron emission tracking studies [7], and x-ra>s [8] have
been used to measure granular flow m three dimensions However, these techniques
arc restrictive in terms of system si^c and/or particle t j p e and can be prohibitively
expensive Recently particle tracking from two-dimensional images taken using digital
cameras have repealed much of the structure and kinematics of granular flow [9] the
method is less restnetn e m terms of particle properties, but due to the opacity of granular materials it cannot be used for tlircc-dimcnsional studies The behavior of granular
systems has been shown to be influenced by their boundaries [10], which restricts this
technique to two-dimensional behavior and the behavior of three-dimensional flow near
boundaries Finally, confocal microscopy in conjunction with index-matched particles
and fluids has recently shown some promise [11] Howevei due again to the opacity of
the granular materials this technique can only be used li the particles arc cmerscd in
an index-matched fluid so it is restricted to wet granular flows
To address the evident need for a robust method to collect three-dimensional experimental data on dry dense granular materials, we introduce a new sensing system
currently under development The sensing system depicted m Fig 1 is based on an
ultrawideband (UWB) radar imaging technique for localizing and tracking deployed
targets and is comprised of three components (1) passive radar targets that serve as
tracer particles interspersed throughout the volume of interest (2) an array of wideband antennas that are positioned outside the volume, and (3) a signal generation and
processing system that sequentially excites the wideband antennas and then records
and processes the returned signals
In this paper, we present the new radar system and design requirements of the
passive radar targets / tracer particles The issues are two-fold and specifically involve
the electromagnetic and material properties of the granular system Section 2 concerns
some of the most critical electromagnetic design issues surrounding the radar targets
As will be described to address these requirements in a relatively cost-effective manner
these tracer particles need to be relatively large (on the order of 1 cm) and the most
direct use of this sensing system is in systems of coinparably-sized particles (approximately 1 cm in diameter) However, for many applications where tins sensing system
would be useful, the particles of interest are significantly smaller For quasi-static systems where the primary interest involves whether or not there is local translational or
rotational movement, the tracer particles may still be used For continuously deforming
3
systems where the details of the displacements are of interest, the use of larger tracer
particles in a matrix of smaller particles may piescnt some problems
Section 3 addresses some of the material design issues related to tins issue Specifically, particles of dispaiatc properties move differently from their neighbors Thus
m these cases, the radar targets would not necessarily act as pure tracer particles
that move with the material of interest Giavity, velocity giadients, poiosity gradients
and associated granular temperature gradients, as well as simple geometric details of
the particle displacements all appear to affect the kinematics of components in dense
sheared granular mixtures Many of these factors are only margin ally-well understood
In section 3, we investigate rather naive solutions to this design issue for free surface
gravity-driven granular flow This is very much a work m progress and requires additional work m the relative behavior of mixture components within dense sheared
granular mixtures for a fully versatile sensing system for dense sheared granular flows
We conclude the paper with a description of additional research needed
2 E l e c t r o m a g n e t i c I s s u e s R e g a r d i n g T r a c e r Particle D e s i g n
A key component of the radar-based sensing system involves radar targets consisting of
rctroreflcctors embedded in particles Standard retrorcflcctors arc comprised of three
orthogonal intersecting metal planes (see Fig 1) and are known to strongly reflect
incident radar signals Such retioreflcctors were deposited on the surface of the moon
by Apollo missions 11, 14, and 15 to enable precise distance measurements using lasers,
and they arc also commonly used for nautical safety, mounted to masts or cabins of
small sea craft [12] For rctrorcflcctois to be adapted for granular material studies
several critical parameters must be considered
The size of the retroreflector compared with the operating wavelength A = vj f, is an
important determinant of the system's sensing capabilities Here, v is the propagation
velocity of the signal from the radar antenna through the bulk granular material to
the retroreflector, and f is the operating frequency of the radar The effective relative
permittivity of the bulk material, n, decreases the propagation velocity relative to
c the velocity in free space (e g v = c/y^eft) a " d therefore decreases the operating
wavelength relative to the free-space wavelength, Ao = c/f The relative permittivity
of air is very close to unity The relative permittivity of some materials used m granular
experiments range from 2 - 4 for plastic, 5 5 - 7 for glass and 10 5 - 15 for zirconium
silicate [13] The effective permittivity of bulk granular materials is a weighted average
of that of the solid and that of air depending on the size and composition of the
beads We found that for 2 5 mm diameter beads, the bulk effective permittivity for
plastic glass, and zirconium silicate beads are 2 4 3 0, and 3 4, respectively [14] This
causes the retroreflector to appear electrically larger (I c resulting in a larger radar
return signal) when embedded m the bulk medium than if it were m air for a given
signal frequency The larger the retroreflector is compared to A, the larger its radar
cross section an indicator of the radar return signal Reasonable detection results are
produced when the lateral dimension of the retroreflector is > A/2
For a fixed retroreflector size, these relationships largely determine the minimum
operating frequency of the system radar (and the cost of the system) For example
a retroieflector with a lateral dimension of 10 mm corresponds to a minimum radar
operating frequency of ~ 1 5 GHz in air, a relatively accessible radar system While the
requirements are not quite as restrictive m bulk granular materials the principle is the
4
same A smaller ret r ore fleet or provides a smaller return signal and requires a higher
frequency ladar system typically more expensi\c Hence to some extent minimizing
costs associated with maximum signal strength means lnaximi/mg tracer particle size
Tor many basic granular materials studies there is little restriction on particle size
except for practical limits on the system size However for certain applications the
si/e of the particles of interest is small enough (such as sind < 0 5 rnm) that matching
the retrorcfltctor particle size to the bulk particle si/e would require an unpractically
high frequency radar signal Tor these cases retrorcflcctor tracer particles would ha\c
to be larger than those m the bulk so that they are detectable with less expensive radar
equipment There arc several apphc itions where the details of the movement is less
important than the detection of any increment at all such as slope failure or adjacent
excavation m dense construction zones Tor these cases no special interpretation of
the tracer particle is needed However m certain powder processing applications one
may want more details of the movement of particles m the bulk As mentioned larger
retrorcnector particles would not m general act as pure tracer particles that move with
the material of interest If the movement of larger tracer particles were considered
identical to the mo\emcnt of the background particles of concern one would be misled
as to the overall beha\ lor of the system In the next section we present granular
materials studies performed to nnestigate a potential simple solution to this problem
3 Retroreflector Tracer Particle D e s i g n size and density
It is well known that the lelatrvc size and density of a particle affects the movement
of that pirticlc relative to others of disparate properties Most studies on the relative
movement of disparate particles concern their mean relative mo\emcnt
large parti
clcs tend to rise lelative to smaller particles [15] and denser particles tend to sink
relative to their les-s dense counterparts [16] Velocity variances also vary with particle
property Recent experimental and computational results suggest there is a simple geo
metric relationship between relative \elocity fluctuations of different sized particles m a
mixture [17] There is no similar measured relationship for the mean relative movement
of particles so this creates a problem for the use of disparate tracer particles
There is an apparent solution to the latter problem if larger particles rise relative
to equal density counterparts and denser particles sink relative to their same sized
lighter counterparts the two effects have the potential to cancel one another out In
fact some experimental research suggests specific combinations of density and size
ratios for which there is no such relative movement [18] This suggests for effective
use of retroreflcctors as tracers even when they are larger than those in the granulai
materials system of interest one may simply construct them using filler materials of a
greater material density than that of the bulk particles The focus of tins section is to
investigate this proposal
The most common experimental systems for studying granular segregation m dense
sheared sy stems in\ oh e free surface gravity driven boundary layer flow Here we study
segregation m free surface gravity d m en flow in a drum Our physical experiments take
place m a thin transparent circular drum (diameter D ss 300 mm thickness t ~10 mm
material acrylic) filled halfway with one of two types of binary mixtures one where
the particles differ only in density (plastic and steel beads all of diameter d = 2 mm)
the other where the particles differ only in size (plastic beads whose diameters arc
d = 2 & 3 mm) We rotate the drum at u sa 1 rpm which generates a thin flat flowing
__. (?j
jo
f lv
teL_(ms) x^O1
-JM.
n
id
f j i / \m/$ix1(f3
Fig. 2 Experimental results of segregating mixtures of particles (a) A sketch of the rxpen
men) % rotating drum halfway filled At any time a thin flowing laj^r of bead1! (A) flow over
most of the beads whuh arc rotating with the drum (B) (b d) images taken of 3 mm (dark)
& 2 mm (bright) plastic beads (e g) corresponding segregation flux in the y direction first
mixed then rotated in a drum after (b,e) 1/4 rot (c,f) A/4 rot (d g) � 10 rot (h j) images
taken of 2 mm steel (dark) &; plastic (bright) beads (k rn) corresponding segregation flux in
1he y direction first mixed then rotated in a drum after (h k) 1/4 rot (i 1) 3/4 rot (j,ni) ~ 10
rot
layer that is relatively uniform m the x direction (see Fig 2(a)) in the center of the
drum While the drum rotates we focus a high speed high resolution digital camera
on this region of the flowing layer and at e\ery half rotation we take 1024 images at
500 fps All results shown represent the average of three sets of such experiments
During the first half drum rotation all beads enter the flowing layer wcll-rnixed
as m Fig 2(b) (2 & 3 mm plastic particles) and m Fig 2(h) (2 mm plastic &; 3 steel
particles) For each experiment we locate and track the beads from one linage to the
next From this, we calculate the average segregation flux of each component relative
to the mixture /,Z\u 7 = f1 (vt ? vraix) where / , and vt represent the average volume
fraction and 'vertical velocity respectively, of component i and vmiT is the average
velocity of mixture (The velocity 1? = ux.? uy Sec Fig 2(a) for component directions )
The relative movement of the different components is apparent m the flux when the
particles are well-mixed (Fig 2(e k)) The smaller particles exhibit a relatively large
negative flux as they sink (with gravity), and the flux of the larger particles is positive
Similarly the denser (steel) particles exhibit a large negative net flux, and the flux of
the less dense (plastic) particles is positive ((Fig 2(k)) As commonly observed this
quickly leads to the unmixing or segregation of the components Tigs 2(c d) and (i,])
leaving the larger or less dense particles on top As the components sort the average
relative movement or flux decreases essentially to zero (Figs 2 (f g) and (l,m))
From these experimental results, one could be further convinced that the relative
movement due to particle size and density could cancel one another if larger particles are
also denser It is difficult to vary only density or size without changing other properties
such as friction that might affect segregation Therefore to study the relative average
particle motion - the flux - as it varies with relative particle size and/or density, we
use computational experiments based on the Discrete (or Distinct) Element Method
(DEM), first proposed by Cundall and Strack [19] The method allows for systematic
variation of particle properties through a simple 'soft sphere force law that models
/ Ai
(ms) xlO
F i g 3 S i m u l a t e d \ o l u m e friction / a n d segregation flux / AT ploLs at ~ 1/2 r o t a l i o n The
first row shows t h e volume fractions and 1he second row shows t h e segregation flux in t h e y di
reel ion P a r t i c l e s density r a l i o i s p ~~ p ie srr/p e sd S e ~ 3 1 w i t h ( / r ? DdP se /Dtps dr -a= (a) 1 (b) 1 4 (c) 1 5 ( 1) 1 6 (c) 1 8 a n d (f) 2
particle particle interactions We use a nonlinear force model that incorporates Hert/ian
contact theory and material properties into the contact coefficients as in Ref [20]
The computational domain involves a circular drum w ith periodic boundaries in the
axial direction to eliminate the side wall effect [17] The drum size is smaller than the
physical experiments (here D = 72 mm) to reduce the computational time Accordingly
the rotational \elocity is increased according to scaling laws proposed by Tabcrlet et
al [21] so that u ss 16 rprn Simulations are performed using beads with density ratio
of pr = Pdenser/Plcssdcnsc = 3 1 a n d t h e S17e r a t i o of dr
= f^densei /d] e ssden;=e r a n g i n g
from 1 3 the smaller (less dense) particles arc 2mm in diameter The average particle
concentration is fixed at 50 50 bj volume As for the experiments the drum is filled
halfway with the mixture of particles and rotation is commenced Results ire averaged
over three such computational experiments under each set of conditions
Tigurc 3 shows f, (first row) and flAvl
(second row) at ~ 1/2 rotation when the
systems are still well mixed for dr ranging from 1 2 The plots for f1 show these 6
mixtures to start relatively well mixed The plots for f Av% show markedly different
behavior with changing dr When dr = 1 results are qualitatively and quantitatively
similar to those shown in 2(k) Qualitatively fAv < 0 for the dense particles and
fAv > 0 for the less dense particles "When d, = 2 the migration flux of denser particles
is essentially positive throughout the flowing la\cr indicating that density effects are
reversed due to size effects For intermediate values of dr however these two effects
do not cancel In these cases for the denser particles fAv > 0 in the deeper region
(y > b mm) and fAv < 0 close to the free surface (y < 6 mm) This indicates that
si7e and density effects dominate in different regions of the flowing layer Similar dT
dependent behavior is observed for other density ratios [22] The computational lesults
are consistent with experimental results from monosized systems reported here The
7
variation of dominant scgicgation effects in different regions of the flowing layer is hkclv
responsible for the 'banding segregation reported in Rcf [23] However additional
experiments with mixtures of particles differing in both s u e and density would be
useful for further testing these results
There arc a number of possible explanations for the variations of the relative flux
of the components across the flowing layer For example the flowing layer itself is
not uniform in the j-direction The porosity, shear rate, and velocity fluctuations arc
greatest near the free surface [17] and decrease with increasing depth below the surface
It is likely that not only are size- arid density- dependent fluxes arc influenced not only
by gravitv but by volume fraction and velocity gradients and related effects as well It
is difficult to isolate these effects experimentally and correspondingly existing models
for size- and density- dependent segregation [15], [16] do not yet account for effects
associated with solids fraction or velocity gradients
In any case it appears that if the tracer particle is larger than the particles of
interest theie is not a single value for the tracer density that will cause it to drift with
a smaller counterpart at all regimes of dense granular flow Instead a more complicated
solution is required It may be that one would need different tracer particles for different
parts of the flow A senes of experiments (computational and/or experimental) would
have to be performed to explore the relevant parameter space to determine which
tracers work best with which flow regimes Alternatively a much more sophisticated
framework for segregating particles m den&,e flows would have to be developed Then,
one would be able to map out the relationship between the movement of a disparate
tracer particle compared to that of its smaller counterparts Suggestions are included
in Section 4
4 S u m m a r y and Future Directions
We have presented a new measuring technique based on rctrorcflector particles that
provides three dimensional tracking information for fully three dimensional high solids
fraction granular materials The system has the potential for rotational as well as
translational information when the faces of an encased retr or effect or particle arc treated
distinctly The svstem is still under development, and issues such as temporal and
spatial resolution are not yet known and will depend in part on certain design issue
A few things are clear At this point a cost-effective system requires the use of tracer
particles no smaller than ~ 1 cm Because of this the most straightforward use of
this system is limited to two classes of granular materials (1) sheared systems of
particles ~ 1 cm or greater and (2) quasi-static systems of particles of any sizes where
one is concerned with whether or not particles move at all, rather than the details
of the movement If used m a sheared system of smaller particles, the relatively large
tracer particle would not be a perfect tracer The large tracer particle may drift m the
strcamwise direction with its smaller neighbors [22], but it would tend to drift against
gravity relative to its smaller neighbors Increasing its effective density could slow this
rise, stop it, and even cause it to move down relative to the neighbors However, as
we have shown in this paper, in a typical nonuniform system with varying gradients in
porosity and velocity there is not a single combination of size and density that would
match the tracer particle movement with those of its smaller neighbors throughout the
flow To increase the versatility of such a system to one w here the tracer particle might
be larger than the particles of interest in a sheared svstem one would need a method to
8
Fig 4 (a) Sketch of a split-bottom cell J? is the rotation speed of Lhc base (b) Sketch of
bulk shear band (black area) for (a) (c) Sketch of experimental results after as 100 rotations
showing larger (black) partirlcs segregated upward and toward the high shear zone (d) top
view (photo) of t he horizontal segregation aft cr i xravatmg 50% of t he material showing large
(darker) particles concentrated in the high shear /one
relate the movement of relatively smaller particles to the measured movement of tracer
particles To do this, we propose two possible directions, depending on the complexity
of the system
For a system rclativ cly uniform m shear rate and porosity one type of tracer particle
(single size and density) may be sufficient to track the system To determine which to
use, we need to study the effect of gravity on the relative movement of particles isolated
from a variation of shcai rate common to most experimental systems Tv pical systems
vised to study this relative movement {e g rotating drums) do not isolate gravitv from
volume fraction and velocity gradients The recently developed spht-bottoin cell [25]
provides a means for isolating some of these effects For example, recent experiments
in a split-bottom cell reveal that gravity-driven relative movement of different-sized
particles is suppressed when the solids fraction is high and the velocity gradient is
low [26] Vertical and horizontal segregation zones (See Tig 4 ) appear at different
timescales indicating the separation of different driving factors Segregation studies
using retrorefiector tracer particles in a split-bottom cell provide a means for mapping
gravity-driven tracer particle movement onto movement of smaller particles of interest
Alternatively for a system varying m shear rate and/or porosity the movement of
a single disparate particle compared with that of smaller particles of interest would
differ depending on the local shear rate or porosity There would be no simple mapping
of a single tracer particle movement to the movement of the particles of interest for
the whole system If this is the case it could be that the relative movements of tracer
particles of different densities could be interpreted together to indicate velocity fields
Systematic computational experiments could be designed where velocity gradients are
varied systematically to study the effect of these gradients on multiple tracer particle
movements m for example, Couctte geometries as described m Ref [27] to study
segregation in more energetic flows
Acknowledgments This work is supported by NSF through CMS-0623022, CMS0625313 and CMS-0625054
References
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9
3 Forlcrre, Y and Pouhquen, 0 Hows, of Dense Granular Media Annu Rev Fluid Mcch
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11 TOIJA M , Heltinga, J , Losert W 3D Imaging of Particle Motion During Penetrometer
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15 Savage, S B Lain C K K Particle si?e segregation in inclined chute flow of dry cohe
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R A theory for particle size segregation in shallow granular free-surface flows Proc Roy
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17 Hill, K M , Zhang, J Kinematics of densely flowing granular mixtures Phys Rev E 77,
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19 Cundall P A , St rack, O D L A discrete numerical model for granular assemblies
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20 Tsu]i, Y Tanaka, T Ishida T Lagrangian numerical simulation of plug flow of tohcsionless particles in a horizontal pipe Powder Technology 71, 239 250 (1992)
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22 Hill, K M Zhang, J in progress
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Jam, N , Ottino, J M , Lueptow, R M Combined size and density segregation and mixing
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24 Sarkar S Khakhar, D V Fxpcnmental evidence for a description of granular segregation
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26 Hill K M , Fan Y Isolating Segregation Mechanisms in a Split-Bottom Cell Phys Rev
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values for hbioganduhr tissue we
consider two estimates ol the, dicleetnc properties of fibroghndular
tissue T\pe A is a moderate estimate (also used in Rcf 9}
whereas type B is an extreme estimate with dielectric propeities
that aic significantlv higher than tho^c teported to date in the
literature
Wc describe all of the dispersive media piopertics in our
models using \ single pole Debye expression lor the complex
permittivity
z(<�)
2 4 6 8 10 1214 165
z err)
c^
lb)
Figure 1 3D FDTD model computed ot an VJRI denved numeucal
Imasi phantom (Phantom II) and an UWB amenm fa) Full \uw showing
the hieasi surface (b) Cross secliond! view showing (he breast interior
?Q\ e
JU)?
1 +
}OiTi
(l)
I able 1 summarizes the Dcbse paiameteis toi the dispersive
dielectric media in the models The Debvc parameters for muscle
(the 1 5 em thick chestv*all) and skin (a 2 mm thick laver) were
chosen to mimic the properties reported in Rcf 13 over the
frequency tange of interest
The degree of heterogeneity of bieast tissue \anes from patient
to patient bar completeness we investigate energy depositions m
tour numerical phantoms based on patients with the iollowing
bicast composition (i) almost entirely fat (11) scattered hbioglan
dului tissue (in) hetcroecncously dense and (iv) extremely dense
A cross sectional view of Phantom II is shown in Figure 1(b) Foi
each of the four phantoms v\e consider both type A and type B
dielectric propeities to repiesent the fibroglandular tissue In ad
dmon to the four numerical breast phantoms with \ uying tissue
TABLE 1 Debye Parameters Used in the FDTD Models
(Si)
Vltdia
Coupling medium [41
Breasl f u [31
FiLsioglandulai tissue t\pe \ |9[
hbroghndnlar tissue type B
Skin[9]
Muscular chestwall
Ph) lolngicil Naline (0 15 M) 141
2�
9 00-11 00
20 11-24 8"
42 94-52 48
57 00
'4 00
77 9
2 54
610 7 70
5 51-6 7*
1 98^4 8b
4 00
4 00
4 15
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 'Vol 49 No 1 January 2007
0 05
0 133-0 165
0 279-0 341
0 558-0 682
1 10
0 70
1 7'
DOI 10 1002/mop
N/A
7 00
7 00
7 00
7 23
7 00
8 97
146
I
i.b>
(b)
i j)
*
if
(u
<il)
Id!
Figure 3 Pe ik Ltna\eras,ed S\ in ea h coronal shee (corresponding to
depth A) tor nch tissue type lor Phantom I (type A) ihiough IV (type A)
Figure 2 Una\ ei at,ed SA diitnbution of the cor nal slice com lining, the
ploba! peak absorption (mJ/kj,) for Phantrm 1 (i\pe A) ihiough IV (type A)
compositions we consider thiee scenarios where foreign materials
are present in the breast phantoms Foi the fust scenano wc obtain
an MRI of a patient with bicast implants and assign the dielectric
properties, of physiologic d saline (0 15 M) [14] to the region of the
implani Wc use the t>p^ B properties to represent the hbroglan
dular tissue in this phantom In the second and thud sccnanos
titanium suigiL.il marking clips commonly deploved in cxcisional
biopsy procedures are ainficially inserted m Phantom III We
assign the type S properties to the hbioghnduiar tissue in the
phantom for both of these scemrios Ihe two suigicai clips wc
consider die a 2 y 2 mm 2 horseshoe shaped clip [IS] and a 5 x
1 mm 2 line shaped clip The clips arc centered at A 5 0 em > ~
5 0 cm and
6 1 cm ( OS cm beneath the skin lavet and on the
axis of the antenna)
An PDTD simulation is conducted for each of the 11 breast
phantoms described abo\c The excitation waveform applied at the
feedpoint of the UWB hoin intenna is a modulated Gaussian pulse
with a temporal full width at half-maximum of 120 ps and a
spectral peak at 6 GHz The unavcraged SA during single pulse
cxposme is computed at everv voxel in the breast phantom as
follows
SA
E(r) J(f)dt
(2)
peak unavcraked SA in a coronal slice at depth x tor I specihed
tissue type These figiucs show that the spatial distribution of
una\cidged SA vanes with the distance from the antenna as well
as the tissue type As expected the absorption in the interior
tissues (fat and fibroglandular) is le^s than the absorption in the
sktn Vamtions in the absorption in the breast interim for different
phantoms aic relatively small Ihe peak undveraged SA consis
tently occurs m the skin liver and has simil u makniludc lor all
tour phantoms
Wc further investigate the absorption in fibioglandular tissue a->
a function of its diclcctnc properties Figuie 4 shows the peak
unaveraged SA value for the fibioglandular tissue in each coronal
slice of Phantom 111 with tvpe A and type B tissue properties The
energy absorbed in type B fibroglandular tissue is approximately
twice the encigy absorbed in type A but icmains significantly
lower than the absorption in the skm and fat
Next we evaluate absorption when foreign objects arc picsent
in the bicast In our first seen ino we consider the absoiption in the
brc is,t phantom eonl unmg a saline implant as depicted by Figuie
5 Figuie 6 u ) shows the unavciaged SA of the eoional slice
containing the peak absorption for this phantom The absorption
level at the tissue implant interface is elevated abov e othci interior
legions inside the breast Figure 6(b) shows the peak unavcraged
SA in each coronal slice for each tissue type and tor saline I h e
saline implant alteis the breast shapv. and distribution of the fi
broglandular tissue thereby modifying the interior scattering and
using the six field component approach [161 The tissue densitv p
is assumed to be 1 g/cm' L and J are the electric field and total
cuirent density vectors respectively and 1 is the duration ot the
simulation We also compute the peak 1 g SA for each ph-tntom
All absorption values aie normalized to I mj of radiated encrsv
3 RESULTS
Figuie 2 shows the spatial distribution ot unaveraged SA ovci the
eoional shee containing the global peak absoiption in mJ/kg lot
Phantoms 1 thiough IV with tvpc A fibroglandular tissue propei
tics The energy deposition as a function of tissue tvpe within each
phantom is shown in Figure 3 where each cuive leprcscnts the
DO 10 1002 mop
Figure 4 Peak una\eraj_ed SA in the fibroglandular tissue in eai.h
coronal 玥ce {corresponding to depth x) of Phantom 111 for lv\o types of
libroglandular tissue properties (tvpe A and B)
MICROWAVE AND OPTICAL TECHNOI OGY LETTERS
Vol 49 No 1 January "007
147
10u
? *r
<
AQ
A)
6
B
10 12
14
l (an;
ISI'S
>j ^
0
Figure 5 Cioss s u una! view of the ^D FDTD mode! comprised ol an
MRI demed mime L J breast pinnlorn 0>Pe &J Lfnfdimm, a saline im
plant
absorption piopcrtics As a result the SA lc\cls in fibroglandular
tissue (type B) in this phantom aic higher than those obseived in
Figme 4 tor Phantom HI ftjpe B)
In our second scenario \vc evaluate the situ ition where metallic
suigical clips arc tntioduccd ai i sh illou location in the subculi
ncous fat lajcr of Phantom III (t>pc B) Wc considered several
orientations ot the two clips described in the picvious section and
found that the absorption is highest when the clips are oncntcd in
the x direction Wc report the results tor this orientation Hgurc 7
shows that the piesence of these clips iaiScs Ihe level of unaver
aged SA in ihe \itmity of the clips Clculy the ib&orption ehar
actcristics depend on the specific shape of the clip The line chp
induce1; two localized absorption peaks at the ends of the clip Ihe
horseshoe clip induces a single localized absorption peak between
the two prongs Ihe v ilues of the peik absorption arc eompaiable
for both clips These sharp increases in absorption aic highly
s
G
TTjimMfQ
a
10
z cm)
\2
(a)
to
40
?0
(b)
Figure 7 Peak uni\eiaged S \ m each coronal slice foi each tissue tvpe
of Phiniom III (tvpe B) with a fa) line shaped clip nd (b) hnst^hoe
shaped chp centeied at K 50cm s ? s 0 cm and
6 t cm
localized and therefore h ive little impact on the 1 g SA around the
chp region The peak 1 g SA remains in the skin region
Tabic 2 summarizes the peak una\eragcd and peak 1 g SA
noimahzcd to I ml of ladiatcd energy fiom a s i n j c UWB pulse
for all numerical phantoms The variation in the shape si?e and
tissue composition of the phantoms results in onh minor variation
in the peak absorption values and the foreign objects have no
noticeable impact on the peak 1 g SA
The results of Table 2 along with the exposure limits established bv IFFF standard C9:> 1 [17] make it possible to assess the
safety of futuic clinical systems The 1FFF peak 1 g SA limit foi
a 6 min exposure is 576 J/kg [17] This hmit is ~ 2 8 000 times
highci than the peak 1 L SA fiom i single 1 mJ UWB pulse in
Ttble 2 With these numbers wc can predict limits on die approx
imate amount of energy radiated in each pulse the numbci of
TABLE 2
80
c
a)
SA in mJ/kg for 1 mJ of Radiated Energy
Computed During Single-pulse Exposure
4(l
EM Model
Peak
l ! iiaveraj,ed
SA
Pe_k
lgSA
68 �
68 17
80 i9
80 " 0
7.06
71 (P
84 47
84 48
63 46
108 6
92->2
1810
18 .0
' 1 75
2171
18 12
1811
20 81
20 81
17 72
18 11
J819
tr
20
:
?
%
(b)
Figure 6 (a) Lnaveraged SA di tnbuuon of die coronal slice containine.
ihe global peak absorption (mJ/kg) for the phantom (tvpe B) containing the
salme implant (b) Peak unavuaged SA in eiih coronal slue fee rrcspond
ine lo depth x) for each tissue tvpe and the implant
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
Phantom
I ttype A)
I (type B)
il (type A)
i[ (type B)
[[I (lype A)
III (tvpe B)
i\ (type Al
IV (tvpe B)
(tvpe B) unit breast impl ml
ill (type B) with horseshoe shaped clip
III (ty ie B) with line shaped clip
MICROWAVE AND OPTICAL TCCHNOl OGY LETTERS / Vol 49 No 1 January 2007
DOM 0 1002 mop
148
putsch ladiarcd p e r a n t e n n a
ana>
a n d the n u m b c i of a n t e n n a s in an
Fot e x a m p l e if each p u l s e c a i n e s 1 m j o f e n e r g v
it w o u l d
he p e r m i s s i b l e t o c o u p l e u p to 28 0 0 0 p u l s e s into the b r e a s t o v e r a
6 m m peiiod
sccmno
In a pi ac t i e d U W B
i n u r o w a v e radar
9
imaging
an array of u n l c n n a s s u n o u n d s the b i c i s t v o l u m e and
e a c h c l e m e n t sequentially i l l u m i n a t e s the b r e a s t
A typical a n ay
may c o n t a i n on the ordci of 50 a n t e n n a s s u g g e s t i n g that up to 5 6 0
10
p u l s e s c o u l d be Transmitted by e a e h a n t e n n a w i t h o u t e x c e e d i n g the
p e a k 1 g S A l i m i t s u c g t sted in the J b b b e x p o s u i e g u i d e l i n e
Note
l i n t the level of c x p o s u u of 5 6 0 pul&cs p e r a n t e n n a is m u c h h i g h e r
11
than w e a n t i c i p a t e n e e d i n g for this a p p l i c a t i o n
12
4 CONCLUSIONS
W c have i n v e s t i g a t e d the a b s o r p t i o n of short ( 1 2 0 ps
earner)
miciowavc
pulses
in a n a t o m i c a l l y
b i e a s t p h a n t o m s in a n effoit t o f o r m a l K
realistic
6GH/
n
numerical
e \ a l u a t c the safety of
U W B m i c r o w a v e breast e n i c e r d e r a t i o n teehnolog> o p e r a t i n g in
14
the 1 11 G H z rariL.e W e h a v e found t h a t the S A d o e s n o t \ a r y
greatly with p a t i e n t t o p i t i e n t variations in b r e a s t s h a p e
composition
or fibroglandular
diclcetne properties
tissue
While
15
the
specific c h a r a c t c n s n c s ( a n t e n n a latitat ion patterns c o u p l i n g m e d i a
properties
etc ) of future clinical s\ s t e m s m a y differ from t h o s e
a s s u m e d t o r this c o m p u t a t i o n a l sttid\
the S A values are n o t
16
e x p e c t e d to vary s i g n i f k a n t K as i function of t h o s e e h a r a e t e n sties
The n o r m a l i z e d S A values l c p o r t c d in this p a p e r c a n b e scaled to
a c e o u n t for the total n u m b e r of p u l s e s l a d i a t c d a n d d i t f e i c n r p u l s e
energies
p r o v i d i n g v a l u a b l e g u i d a n c e in the d e s i g n of
futuie
clinical s v s t e m s that arc in c o m p l i a n c e with safety s t a n d a r d s
Foi
a n t i c i p a t e d e m b o d i m e n t s of s u c h a s y s t e m w e c o n c l u d e that U W B
m i c r o w a v e breast c a n c e r detection m o d a l i t i e s p o s e n o health n s k
17
horn inlenna with curved hunching plane for pulse radiation IFFF
Antennas W i r e l e ^ Propig I ett v 200^1 2">9-262
VI Converse h i Bond B D Van Veen m d S L Harness \ com
puialional study of tiltiawideband veisus nanowband microwave hy
pcrtliemin for bieast cancel treatment IEEE Tians Microwave Theorv
Tech M (200b) 2169-^lSO
\ \ T Jomes ^ Zhang C Li and R L Jirile The measured electrical
properties of normil ind malignant human tissues from ^0 lo 900
MH? Mtd Phys (1994) 5 4 7 - " 0
A J Surowiec S S Stuchly J R Barr and A Swamp Dielectiu
propeities oi breast carcinoma m d die surrounding tissues IEEE Fi ns
Biomed Eng l a ("1988) 257-263
S Chaudh^ry R Mishia A Swamp and J T h o r n s Dielectric
pioperlies of n o t m J md malignant human brea I tissue at radiowave
m d microwave frequencies Ind T Riochem Biophys 21 (1984) 7 6 - 7 9
S Gibnel R W I an m d C Gabriel The dielectric properties oi
bioloeuil tissues UI Parametric models for the dicleclnc spectrum of
tissues Phys Med Biol 41 (1996) 2271-229-.
J HiUnnd Simple sensoi system for measuring the dielectric pioper
ties of s d m e solutions Mtas Set Tcchnol (L997) 901 910
D M Lanners K k Amrami R S Jonsgaaid J J Gisvold and J P
Felmlee Safety and MRI artifict evaluation at 1 D T of metallic
mount inu she uh of a m irking clip madvcrlentH deployed it sleieo
tactic biopsy Am J Roentgenol (200^) 8 2 5 - 8 2 9
K Caputa M Okomewski and M A Stuchly An aleonthm for
compulsions of the power deposition in human tissue IEEE Antennas
Piopag Mag 41 (1999) 102-107
IEEE Standaid for safety levels widi respect lo human exposure to
radio frequency electromagnetic fields 3 kHz to 00 G H / IEEE
SLmchrdC95 I 1999
<Q 2006 Wilev Periodicals Inc
t o the p a t i e n t
ACKNOWLEDGMENTS
1 his w o r k w a s s u p p o r t e d b \ the N a t i o n a l Institutes of H e a l t h u n d e i
g i a n t H ! C A 1 1 0 9 1 2 a w a i d e d b y the N a t i o n a l C n i c e r Institute and
the N i t i o n - d Science F o u n d a t i o n u n d e r g r a n t B E S 0 2 0 1 8 8 0
RFFFRFNCFS
1 S C H i g m s s A laflove jiid J E Bridges 1 wo dimensional F D I D
analysis of a pulsed rwuowave conlocal svsiem lor bieasl cancer
detection Fixed locus and antenna array --ensorv IECE Trans Biomed
hn fo (1998! 1470-147b
2 F C Fear md M A Sluchly Microwive system lor breisl tumor
detection ICEC Microwave Guided Waxe Lett 9 (1999) 4 7 0 - 4 7 2
"i E J Bond \ Li S C Hagness and B D Van Veen Microwave
imaging v n space time bcamforming lor eirlv detection ot breisi
cancer IEEE Trans Antennas Propag (2001) 1690 1705
4 X Li S K Davis S C Hagness D W v a n d e r W e i d e and B D Van
Veen Microwave imiging v n space lime beamforitung Experimental
investigation of fumoi detection m mull layei breast phantoms IFFF
Trans Microwave Theorv Tech {20041 1856 186a
5 J M Sill and E C Fear Tissue sensing adaptive ladai lor breast cancer
detection?F^penmenlal investigation of simple lumoi models IFFF
Tians Microwave Theoiv Tech 53 (200^) 1 3 1 2 - ^ 1 9
6 A Taflove and S C Hagness Computational electrodynamics The
finite difference time domiin method 3id ed Artech House N r r
wood MA 200^
7 C Zasliow S K Davis and S C Magnets Safety assessment ol breast
cancel detection via i] lira wideband m i u o w a v e ridar opoeraung in
swept frequency mode in Proceedings o1 I F F F Inlemilional Sympo
sium on Antennas md Propagation Albuquerque N M Jul\ 2006 in
press
8 X Li S C Hagness M K Choi and D W v a n d e r W e i d e Numeric i]
and experimental investigation of an ultravvideband ridged pynmidal
DOM 0 1002 mop
MICROWAVE AND OF
APPLICATION OF THE FOLDY-LAX
MULTIPLE SCATTERING METHOD TO
THE ANALYSIS OF VIAS IN BALL GRID
ARRAYS AND INTERIOR LAYERS OF
PRINTED CIRCUIT BOARDS
C-J Ong,1 D Miller,2 L Tsang,1 B Wu,1 and C -C Huang2
1
Department ot Electrical Engineering
Un versity of Washington
Paul Allen Center PoomAblOOR
C a n p u s Box 3 5 2 5 0 0
Seattle WA98195 2500
* Intel Ooiporation
Jones Farm o 2111 N E 25th Avenue
Hillsboro OR 97124 D961
Received 12 Mav 2006
ABSTRACT The authors apfhed iht method of Tolds?Lax multiple
scattering equations to multiple ius in hall i,ud ana) s and the interior
lasers of printed aicmt boards The method gives the Mattering pat am
elets of the atra\ The result1; ate w lifted with Ansoft s NFS') with \en
little difference between the Fold) Lax approach and the HF&& results
The CPL required for the method is only a small fraction of tht time
that HFb& tequila
For a 16 X 16 arias- ot itus the method calculates
all the $ pa/ametei s of tht 512 potts m 4 mm for 10 frequencies on u
Pentium 3 2 Gfh PC O 2006 Wiley Periodicals Inc Microwave Opt
Technol Lett 49 225-211 2007 Published online in Wiley fnlerScience
(www inierscience vviley com) DOI 10 1002/mop 22091
Key words \ia\ multiple scattermf,
punted an uit hoards
signal mtei,iit)
ball },tid
TfCHNOLOGY LETTERS / Vol 49 No 1 January 2007
attuys
225
Safety A s s e s s m e n t of B r e a s t C a n c e r D e t e c t i o n v i a
U l t r a w i d e b a n d M i c r o w a v e R a d a r O p e r a t i n g in
Swept-Prequency M o d e
Eail Zastrow*, Shakti K Davis and Susan C Hagncss
Department of Elccti ical and Computer Engineering
University of Wisconsin Madison W I 53706
Email cpratoomQcae wise edu
Introduction
Ultrawideband (UWB) nnciowave radar is a promising modality for detecting cailystagc breast cancer [1] In our current prototype [1], we synthesize an antenna array
by scanning a single antenna to each array position and sequentially transmitting
a swept-fiequency signal and receiving the backscattcr Our U W B tadar operates
m the 1-11 GHz frequency band Whrle it has been assumed t h a t low-power U W B
microwave bieast cancer detection technology poses no health risk, it is important to
formally evaluate the absorption of electromagnetic energy in the breast to establrsh
t h e safety of such exposure prior to clinical implementation In this paper, wc report
the results of hmte-diffcrcnce trmc-domain (FDTD) [2] rnvestigations of the specific
absorption l a t e (SAR) in 3-D numerical breast models due to microwave radiation
m the 1-11 GHz frequency band
Models and Methods
In our d a t a acquisition scenario a patient lies prone with an antenna array surrounding the breast We represent this scerrarro numcrrcally by modeling an anatomrcally
realrstic breast with 2-mm-thick skm and a 1 5-cm-thick muscular chestwall T h e
breast is immersed m a low-loss couphng medium and a numerical representation of
our U W B pyramidal horn antenna [3] is placed near the bieast T h e antenna feed
is exerted with a resistive voltage source [2] For our safety assessment we position
the antenna with t h e a p e i t u r e approxrmately 2 5 cm away from the breast centered
on the xy-plane as lllustiated in Figure 1(a)
Normal breast tissue is a highly heterogeneous mrxture of fatty and frbroglandular
trssues Wc derrve an anatomrcally realrstrc breast model by basing the interior
on a 3-D MRI of an actual patient Breast tissue composition varies from patient
to patient and to some extent wc expect the powci deposition to depend on the
composition To investigate this hypothesis, we constiuct four numencal phantoms
based on patients with the following categories of breast composition (I) almost
entuely fat (II) scattered fibroglandular trssue (III) heterogeneously dense, and
(IV) extremely dense A cut-away view of the Category III model is shown in Figure
1(b) T h e MRI voxel intensity is m a p p e d to a dielectric model via a piecewise linear
map [4] wheie we specify the median dielectric piopertics foi fat and fibroglandulai
tissue and assume a � 1 0 % variation about each median Since out radar system
operates at multiple frequencies we describe the dispersive media properties using
a smgle-pole Debye expression Table 1 summarizes the Debye parameters for t h e
150
dispcisive dielectnc media in the models
An F D T D simulation is conducted for each discrete frequency of nitcicst withm the
U W B lange of opeiation Once the simulation has reached the sinusoidal steady
state tho SAR is computed Following the six-held-component approach [5], we
calculate both peak 1-g and unaveiaged SAR values thioughout the numerical breast
p h a n t o m lepiesentmg each of the four breast compositions All absoiption values
arc noimahzed to 1 m W of radiated powci
Results and Conclusion
Figures 2(a) (c) (e) show the spatial distribution of unavcraged SAR over t h e coronal slice containing t h e global peak absorption of the Categoiy III breast p h a n t o m
for operating frequencies of 1, 6 and 11 GHz, respectively These SAR distributions
demonstrate how absoiption mcieases with frequency while penctiation depth decreases with ftequency Each curve in Figures 2(b) (d),(f) represents t h e peak SAR
m a coronal slice at depth x foi a specified tissue type T h e absoiption is greatest
m the skm layer at all depths Figuie 3 compares the spatial distribution of unavcraged SAR foi diffucnt bicast compositions These i t s u l t s suggest t h a t t h e breast
composition does not significantly affect the amount of powci deposition withm the
breast interior Table 2 summarizes the peak 1-g SAR for all breast models It
is interesting to note t h a t the laigest SAR values occur m the Category II breast
phantom
T h e SAR values leported in Table 2 can be leadily scaled to generate results for an
experimental setup with known radiated power As an illustration we determine
the peak 1-g SAR value for t h e Category III breast example under radiation at 6
GHz in a breast cancel detection scenario t h a t makes use of a network analyzer with
a p o i t powci setting of -17 d B m as the swept-frequency source Assuming perfect
power transfer we scale the values in Table 2 by 1/50 to obtain estimates of SAR
due to 0 02 m W of radiated powei This results in a peak 1-g SAR of 0 385 m W / k g
at 6 GHz
We conclude t h a t the absorption due to miciowave radiation in the 1-11 GHz b a n d
m t h e application of low-power U W B microwave breast cancer detection is well
below the suggested I E E E exposure limit of 1 6 W / k g [6]
References
[1] X Li, S K Davis, S C Hagncss, D W van der Weide and B D Van Veen,
"Microwave imaging via space-time bcamfornnng Experimental investigation
of tumoi detection in multi-layer breast phantoms,' IEEE Trans
Microwave
Theory Tech , vol 52, pp 1856-65 August 2004
[2] A Taflove and S C Hagness Computational
Electrodynamics
The FiniteDifference Time Domain Method, 3rd ed , Norwood MA Artcch House, 2005
[3] X Li, S C Hagness, M K Choi, and D W van der Weide, 'Numerical and
experimental investigation of an ultrawideband ndged pyramidal-horn antenna
151
with cm ved launching plane foi pulse radiation,' IEEE Antennas Wireless Propaqat Lett , vol 2, pp 259-62, 2003
[4] M Conveise, E I Bond B D Van Veen, and S C Hagncss, 'A computational
study of ultrawidcband versus narrowband microwave hyperthermia for breast
cancer treatment' IEEE Trans Microwave Theory Tech , submitted
[5] K Caputa, M Okomcwski, and M A Stuchly, 'An algorithm foi computations of the power deposition m human tissue ' IEEE Antennas Propagat Mag ,
vol 41, pp 102-7, August 1999
[0] 'IEEE Standard for Safety Levels with Respect to Human Exposure to Radio
Fiequency Electromagnetic Fields, 3 kHz to 300 GHz ' IEEE Std C95 1, 1999
Media
Coupling medium [1]
Fat [4]
Fibroglandular tissue [4]
Skm [4]
Chcstwall*
c9
2 54
10 00 �%
21 57 +10%
37 00
54 00
too
&s
T (ps)
2 54
7 00 �%
6 14 �%
4 00
4 00
0 05
0 15 �%
0 31 �%
1 10
0 70
7
7
7
7
7
00
00
00
23
00
"The Debyc parameters for the chestwall arc based on the tumor propeities in [4] since muscle
and malignant breast tissue aie electromagnetically similar
Table 1 Dcbyc parameters used in FDTD models
Breast model
Category I
Category II
Category III
Category IV
1GHz
6 38
1108
8 27
9 91
2GHz
8 08
10 68
9 39
9 50
6GHz
vin
20 89
19 25
19 42
10GHz
35 49
42 76
34 52
40 75
11 GHz
44 62
47 71
44 32
44 07
Table 2 Peak 1-g SAR m mW/kg as a function of frequency for 1 mW of radiated
power
(a)
(b)
Figure 1 3-D FDTD model comprised of an MRI-derivod miiiiei ical bi east phantom
(Category III) and an UWB antenna
152
Skin
? Fat
? Fibroglandular
.!';
^Sv^
10 12
z (cm)
14
4
x (cm)
(a)
(b)
-
Skin
oi60 ? Fat
.M
Fibroglandular
1 40
"V
a:
^20
10 12
z (cm)
4
x (cm)
14
(c)
(d)
10'
''
Skin
? 2 0 0 ? Fat
en
10� | 150
E
? 100
10 <
� 50
10 12
z (cm)
6
Fibroglandular
/\->
4
x (cm)
14
(e)
(f)
Figure 2: Unaveraged SAR for the Category III breast phantom at operating frequencies (a)-(b) 1 GHz, (c)-(d) 6 GHz, (e)-(f) 11 GHz. (a),(c),(e) Spatial distribution of SAR in mW/kg of the coronal slice containing the global peak absorption.
(b).(d),(f) Peak unaveraged SAR value in each coronal slice (corresponding to depth
x) for each tissue type.
12
10
x = 4 75 err
"6
| p f '/
4
4
6
8 10 12 14
z (cm)
(a)
L
10
z (cm)
(b)
1
Ikh !\ 1
8
5
10
z (cm)
15
(c)
Figuie 3 Unaveraged SAR distribution in mW/kg of the coronal slice containing
the global peak absorption at 6 GHz operating frequency in the (a) Category I (b)
Category II and (c) Category IV breast phantoms
153
Appendix B: Implementation of a 3D microwave imaging system for granular materials research
Included in this appendix:
C. Van Niekerk, E. Zastrow, S. C. Hagness, and J. T. Bernhard, "UWB radar target sensing
and imaging for granular materials research applications," to appear in Antennas and Propagation Society International Symposium 2010, IEEE.
K. M. Hill, Y. Fan, J. Zhang, C. Van Niekerk, E. Zastrow, S. C. Hagness, and J. T. Bernhard,
"Granular segregation studies for the development of a radar-based three-dimensional sensing
system," Granular Matter, vol. 12, no. 2, pp. 201-207, Apr. 2010. doi: 10.1007/sl0035-0100167-x
154
U W B R a d a r T a r g e t S e n s i n g a n d I m a g i n g for G r a n u l a r
Materials Research Applications
C Van Niekcrk* 1 , E Zastiow 2 S C Hagncss 2 , and 7 T
1
Bernhaid1
University of Illinois at U i b a n a - C h a m p a i g n , U r b a n a IL 61801
2
University of Wisconsin at Madison Madison, WI 53706
E-mail cvanmc2@illmois cdu
Introduction
Granular materials research involves the study of dynamic movement of objects with
gianulai shape and chaiacteirstics Researchers in this held of study tely on accurate
experiments to validate theoietical models or solve problems empirically Current
expciimcnts aie either expensive (e g , MRI or X-ray technologies), limited in scope
(e g High-Speed High-Resolution Photography which is limited to 2D experiments
due to granular material opacity) or extremely tedious and time-consuming
In
this papci we investigate a fiist-gcneiation p i o t o t y p e o( a ladai system t h a t will
provide a minimally invasive fully automated mcasuiement of individual and bulk
particle movement in a 3D volume T h e radai system [1] comprises inexpensive
tracer particles as targets a test signal geneiation and measurement unit and a
post-piocessing unit for imaging T h e proposed target is a square rctrorcfiector
which is made up of three oithogonal square metal plates (sec Figure 1) An array
of wideband antennas surrounding the testbed is operated in monostatic mode using
swept-frcquency VNA measurements t h a t arc processed to mimic an ultrawideband
(UWB) bandpass pulse In oui fust-generation prototype we synthesize a linear
array by moving the testbed relative to a single antenna The testbed contains one
or moic targets deployed m a free-space (rather t h a n granular material) volume
Wc perform delay-and-surn beamforrmng to reconstruct an image of the testbed
Images aie geneiatcd foi the rctioieflcctoi at two distinct onentations - (normal
and oblique) relative to the array
T h e retroreflector
T h e simplf- geometry of the ietioipflre toi with its ught-anglcd trihedral coiners is
known to positively lemforcc a strong monostatic radar cross section (RCS) from
almost all incident angles [2] Numerous papers have shown t h a t any deviation from
t h e classic geometry (l e orthogonal plates) results in a decrease in RCS [3] While
its operation is well understood and known exactly when it is several wavelengths
in size, its performance is less familiar when t h e dimensions of the refiorefiertoi
are sub-wavelength, as is the case m this application [4] For use as a radar target
in granular materials experiments, the target has to be encased in spherical shell
to facilitate case of motion during t h e experiment
T h e size of letioreflcctor is
ultmutely limited by the size of granular materials under test If t h e retioflectoi
is significantly larger t h a n a gianular m a t e n a l particle its movement will not be
representative of that of the granular material Plastic refroieftcctor elements were
manufactured using a rapid prototyping process T h e retrorefiectoi targets were
manufactured to have a square plate length of 12 7 m m (or plate diagonal of 18
155
m m ) T h e taigets were then coated with several layeis of silver paint this coating
ensures a good mctalizcd target (1 e the target wall produces stiong inflection and
minimal transmission chaiacterrstics)
When analyzing the target s RCS performance we are primarily concerned with only
monostatic r c t u i n since the letioieflectoi s structuic is biased to stiong backscatter
returns Here we limit our comrncntaiy to the monostatic RCS frequency response
(5 to 15 GHz) at normal incidence and then the monostatic RCS spatial response
foi one q u a d i a n t (oi t i i h e d i a l c o m a ) of the letioieflectoi at fixed hcqucncics of
5 10 and 15 GHz T h e backscattei i c t u i n fiom the retioicflcctor increases with
frequency in a monotomc fashion There is howcvci, a large null at the ft equency
t h a t c o n e s p o n d s to a edge length of loughly a half wavelength At this frequency the
letioieflectoi expciionccs maximum diffiaction at edges paiallcl to t h e polarization
direction of the incident wave Since diffiaction is a phenomenon where encigy is
ladiated in all directions equally (I e , similar to a isotropic ladiator) the amount of
scattered energy is substantially reduced in t h e backscatter direction Meanwhile,
t h e angular monostatic R C S lesponse shows a deciease in vailability as t h e electrical
size of t h e letioieflectoi is shiunk m clcctiical size In other words, toward the lowei
end of the hequency langt the letioieflectoi looks like a small metal sphere (l c , no
angle dependency)
Delay-and-sum beamforming
T h e frequency-domain Sii d a t a recorded at all N antenna locations is fust transformed into time-domain A modulated Gaussian pulse (center frequency = 10 GHz,
full-width half-maximum = 8 GHz) is assumed to be the desired incident waveform
T h e synthesized discrete time-domain wavefoim at each channel includes the incident wave the leflection fiom the expoiimcntal fixtuie and the backscatter from
the target We isolate the target backscattei by subtracting a reference waveform
collected at each channel in the absence of the testbed This yields a calibrated
dataset containing only t h e backscatter from the target collected fiom N channels,
A\,Ai
,AJV as illustrated m Figure 2(a) Each time-domam signal contains M
time samples At each scan location, r, in the imaging region, the discrete-tune delay
needed to achieve a synthetic focus at r is T?(r) = 2d?(r)/(vAt),
where dn = |r?r?|
is the distance between r and t h e transmit/receive nth antenna located at r ? v
is the propagation speed in the background medium (I e free space) and At is
the time-sampling interval T h e calibrated wavefornrs Ai,
,AN are time-shifted
to time-align all N signals and scaled to compensate for the radial spreading of
the wave traveling fiom r ? to r T h e time-aligned and scaled waveforms A\
A'N
(illustrated in Figure 2(b)) are then summed to obtain the beamformer waveform,
z m
\ ] = E n = i ^ n ( m ) (illustrated m Figure 2(c)) Finally the energy in the bcamforrnei o u t p u t calculated as p(r) = ~^z{m]2, where t h e summation is performed
over an appropriate time window
156
Experimental implementation using a linear array configuration
The goal of this experiment is accurate localization and imaging of the rotioieficctoi
taigct in the experimental volume For thrs experiment the target is m a static
position and placed with specific orientation relative to the sensing linear array Two
distinct orientations are analyzed and are desrgnatcd normal (one of the vertical
plates arc parallel to plane of the antenna array) and oblique (which is normal
orientation shifted by 45�) A distance of 20 cm exists between the plane of the
airay and the target Presently, the linear array rs implemented synthetically by
using one stationary antenna and moving a single target to eight seperate positions
in the measurement space This implementation not only produces a cost saving
for the prototype system but also eliminates potential array coupling issues The
major disadvantage is that there are unavoidable placement errors due to the manual
movement of the target Also, the experiment takes much longer to complete than
if it were automated
The specific arrangement of the experiment is depicted m Figure 3, which shows the
measurement space wrth grid foi both orientations The target position is shown
by cross hairs (at -10 cm on y-axrs and 20 cm on x-axis) and the eight synthesized
antennas are shown by x markers on y-axis Figure 4 shows resulting radar images
for both orientations The cross hairs indicate the exact position and onentatron
of the target while the experimental result is shown by a deep red spot For the
normally oriented rotioieflector the image shows a localization error of less than
1 cm with the image target center is further back and slightly to the right than the
true situation Meanwhile for the oblique case the result is much more accurate
wrth error less than 0 5 enr Both orientations also show a fair amount of image
ghosting but the target is clearly discernible from the ghost image
Conclusion
A prototype system has been shown to work using a hncar array and single target,
albeit with sonic localization error This error can be accounted for by the inherent
inaccuracy of placing the target at the correct position and face angle with manual
means Thrs error wrll be eliminated by implementing the actual array
References
[1] K M Hill, Y Fan, J Zhang, C Van Niekerk, E Zastrow S C Hagncss J T
Bernhard, 'Granular Segregation Studies for the Development of a Radar-Based
Three-Dmicnsional Sensing System,' Granular Matter, 2010 (in press)
[2] G T Ruck, D E Barrick, W D Stuart and C K Krrchbaum, Radar Cross
Section Handbook, vol 2 New York, NY Plenum 1970
(3] W C Anderson, 'Consequences of nonorthogonahty on the scattering properties of dihedral reflectors IEEE Transactions on Antennas and Propagation,
vol 35, no 10, pp 1154-1159, 1987
157
[4] R Green 'The echo area of small icctangular plates with linear slots,' IEEE
Ttaasactions on Antennas and Piopagatton vol 12, no 1 pp 101-104 1964
5
%-
(a)
Figure 1 (a) Squaic ictioieflcctoi
(b)
(b) Silvci spiay-pamtcd utioicflcttoi
Figure 2 (a) Time-doniam signals (b) Time-aligned signals for scanned location r
(c) Bcamfoimer output for scanned location r
I T TTT I I T
1
2
3
4
5
(a)
6
7
8
TI I I TTI T
1
2
3
4
S
6
7
8
(b)
Figuif 3 Experimental setup with rctioioflectoi of different orientation (a) Normal
orientation (b) Oblique orientation
Figure 4 Beamformer image for the two experiments with retrotoflcctoi of different
orientation (a) Normal orientation (b) Oblique orientation
Granular M a t t e r manuscript N o
(will be inserted by the editor)
Granular Segregation Studies for the Development of a
Radar-Based Three-Dimensional Sensing System
K M . Hill*, Y Fan*, J. Z h a n g j , C Van
N i e k e r k | , E . ZastrowJ, S. C. HagnessJ, and J
T. B e r n h a r d t
Received date / Accepted date
A b s t r a c t The behavior of dense granular materials is difficult to measure in threedimensions due to the opacity of the materials \ \ c present a new radar-based sensing system that has the capability of measuring three-dimensional particle movement
throughout the bulk of high solids fraction granular s> steins A key component of the
new system involves letroreficctors imbedded in objects resembling the particles in the
bulk granular systems These embedded rctroreficctors may be used as tracers in systems comprised of relatively large particles However in systems of smaller particles
the most versatile use of this new sensing system requires an understanding of the details of relative particle movement based on particle size and other particle properties
Towards this, we present new ongoing experimental and computational results toward
building a versatile sensing system foi high solids fraction granular systems We then
comment on additional research needed on the behavior of the components in granular
mixtures for a fully versatile sensing system
K e y w o r d s Remote sensing, dense granular materials, segregation
P A C S 42 68 Wt 47 57 Gc
81 05 Rin
1 Introduction
Over a centurv of research has provided a wealth of insight on the behavior of granular
materials Constitutive laws based on kinetic theory have been relatively successful at
modeling the behavior of collisional particulate flows [1] Constitutive laws based on
plasticity theory have been relatively successful at modeling small deformations [2]
However, an appropriate framework for modeling the intermediate regime of sheared
flows at relatively high solids fractions remains a matter of debate [3j-[5] Theoretical
discrepancies are hard to resolve because of the paucity of data it is difficult to measure
the kinematics of granular materials m three-dimensions due to their opacity
*University of Minnesota Minneapolis MN 55414
"("University of Illinois Urbana IL 61801
tUniversity of Wisconsin Madison, WI 53706
Fig 1 Schematic of one embodiment of the new three dimensional sensing system Ihe image
at the right is a sketch of the tr icer particle consisting of an embedded ret rentier tor described
in the text As shown the basir design consists of three orthogonal intersecting plates
Experimental techniques designed to provide further insight and computational
model validation of granular flow come m many forms For example magnetic resonance imaging (MRI) [6] positron emission tracking studies [7], and x-ra>s [8] have
been used to measure granular flow m three dimensions However, these techniques
arc restrictive in terms of system si^c and/or particle t j p e and can be prohibitively
expensive Recently particle tracking from two-dimensional images taken using digital
cameras have repealed much of the structure and kinematics of granular flow [9] the
method is less restnetn e m terms of particle properties, but due to the opacity of granular materials it cannot be used for tlircc-dimcnsional studies The behavior of granular
systems has been shown to be influenced by their boundaries [10], which restricts this
technique to two-dimensional behavior and the behavior of three-dimensional flow near
boundaries Finally, confocal microscopy in conjunction with index-matched particles
and fluids has recently shown some promise [11] Howevei due again to the opacity of
the granular materials this technique can only be used li the particles arc cmerscd in
an index-matched fluid so it is restricted to wet granular flows
To address the evident need for a robust method to collect three-dimensional experimental data on dry dense granular materials, we introduce a new sensing system
currently under development The sensing system depicted m Fig 1 is based on an
ultrawideband (UWB) radar imaging technique for localizing and tracking deployed
targets and is comprised of three components (1) passive radar targets that serve as
tracer particles interspersed throughout the volume of interest (2) an array of wideband antennas that are positioned outside the volume, and (3) a signal generation and
processing system that sequentially excites the wideband antennas and then records
and processes the returned signals
In this paper, we present the new radar system and design requirements of the
passive radar targets / tracer particles The issues are two-fold and specifically involve
the electromagnetic and material properties of the granular system Section 2 concerns
some of the most critical electromagnetic design issues surrounding the radar targets
As will be described to address these requirements in a relatively cost-effective manner
these tracer particles need to be relatively large (on the order of 1 cm) and the most
direct use of this sensing system is in systems of coinparably-sized particles (approximately 1 cm in diameter) However, for many applications where tins sensing system
would be useful, the particles of interest are significantly smaller For quasi-static systems where the primary interest involves whether or not there is local translational or
rotational movement, the tracer particles may still be used For continuously deforming
3
systems where the details of the displacements are of interest, the use of larger tracer
particles in a matrix of smaller particles may piescnt some problems
Section 3 addresses some of the material design issues related to tins issue Specifically, particles of dispaiatc properties move differently from their neighbors Thus
m these cases, the radar targets would not necessarily act as pure tracer particles
that move with the material of interest Giavity, velocity giadients, poiosity gradients
and associated granular temperature gradients, as well as simple geometric details of
the particle displacements all appear to affect the kinematics of components in dense
sheared granular mixtures Many of these factors are only margin ally-well understood
In section 3, we investigate rather naive solutions to this design issue for free surface
gravity-driven granular flow This is very much a work m progress and requires additional work m the relative behavior of mixture components within dense sheared
granular mixtures for a fully versatile sensing system for dense sheared granular flows
We conclude the paper with a description of additional research needed
2 E l e c t r o m a g n e t i c I s s u e s R e g a r d i n g T r a c e r Particle D e s i g n
A key component of the radar-based sensing system involves radar targets consisting of
rctroreflcctors embedded in particles Standard retrorcflcctors arc comprised of three
orthogonal intersecting metal planes (see Fig 1) and are known to strongly reflect
incident radar signals Such retioreflcctors were deposited on the surface of the moon
by Apollo missions 11, 14, and 15 to enable precise distance measurements using lasers,
and they arc also commonly used for nautical safety, mounted to masts or cabins of
small sea craft [12] For rctrorcflcctois to be adapted for granular material studies
several critical parameters must be considered
The size of the retroreflector compared with the operating wavelength A = vj f, is an
important determinant of the system's sensing capabilities Here, v is the propagation
velocity of the signal from the radar antenna through the bulk granular material to
the retroreflector, and f is the operating frequency of the radar The effective relative
permittivity of the bulk material, n, decreases the propagation velocity relative to
c the velocity in free space (e g v = c/y^eft) a " d therefore decreases the operating
wavelength relative to the free-space wavelength, Ao = c/f The relative permittivity
of air is very close to unity The relative permittivity of some materials used m granular
experiments range from 2 - 4 for plastic, 5 5 - 7 for glass and 10 5 - 15 for zirconium
silicate [13] The effective permittivity of bulk granular materials is a weighted average
of that of the solid and that of air depending on the size and composition of the
beads We found that for 2 5 mm diameter beads, the bulk effective permittivity for
plastic glass, and zirconium silicate beads are 2 4 3 0, and 3 4, respectively [14] This
causes the retroreflector to appear electrically larger (I c resulting in a larger radar
return signal) when embedded m the bulk medium than if it were m air for a given
signal frequency The larger the retroreflector is compared to A, the larger its radar
cross section an indicator of the radar return signal Reasonable detection results are
produced when the lateral dimension of the retroreflector is > A/2
For a fixed retroreflector size, these relationships largely determine the minimum
operating frequency of the system radar (and the cost of the system) For example
a retroieflector with a lateral dimension of 10 mm corresponds to a minimum radar
operating frequency of ~ 1 5 GHz in air, a relatively accessible radar system While the
requirements are not quite as restrictive m bulk granular materials the principle is the
4
same A smaller ret r ore fleet or provides a smaller return signal and requires a higher
frequency ladar system typically more expensi\c Hence to some extent minimizing
costs associated with maximum signal strength means lnaximi/mg tracer particle size
Tor many basic granular materials studies there is little restriction on particle size
except for practical limits on the system size However for certain applications the
si/e of the particles of interest is small enough (such as sind < 0 5 rnm) that matching
the retrorcfltctor particle size to the bulk particle si/e would require an unpractically
high frequency radar signal Tor these cases retrorcflcctor tracer particles would ha\c
to be larger than those m the bulk so that they are detectable with less expensive radar
equipment There arc several apphc itions where the details of the movement is less
important than the detection of any increment at all such as slope failure or adjacent
excavation m dense construction zones Tor these cases no special interpretation of
the tracer particle is needed However m certain powder processing applications one
may want more details of the movement of particles m the bulk As mentioned larger
retrorcnector particles would not m general act as pure tracer particles that move with
the material of interest If the movement of larger tracer particles were considered
identical to the mo\emcnt of the background particles of concern one would be misled
as to the overall beha\ lor of the system In the next section we present granular
materials studies performed to nnestigate a potential simple solution to this problem
3 Retroreflector Tracer Particle D e s i g n size and density
It is well known that the lelatrvc size and density of a particle affects the movement
of that pirticlc relative to others of disparate properties Most studies on the relative
movement of disparate particles concern their mean relative mo\emcnt
large parti
clcs tend to rise lelative to smaller particles [15] and denser particles tend to sink
relative to their les-s dense counterparts [16] Velocity variances also vary with particle
property Recent experimental and computational results suggest there is a simple geo
metric relationship between relative \elocity fluctuations of different sized particles m a
mixture [17] There is no similar measured relationship for the mean relative movement
of particles so this creates a problem for the use of disparate tracer particles
There is an apparent solution to the latter problem if larger particles rise relative
to equal density counterparts and denser particles sink relative to their same sized
lighter counterparts the two effects have the potential to cancel one another out In
fact some experimental research suggests specific combinations of density and size
ratios for which there is no such relative movement [18] This suggests for effective
use of retroreflcctors as tracers even when they are larger than those in the granulai
materials system of interest one may simply construct them using filler materials of a
greater material density than that of the bulk particles The focus of tins section is to
investigate this proposal
The most common experimental systems for studying granular segregation m dense
sheared sy stems in\ oh e free surface gravity driven boundary layer flow Here we study
segregation m free surface gravity d m en flow in a drum Our physical experiments take
place m a thin transparent circular drum (diameter D ss 300 mm thickness t ~10 mm
material acrylic) filled halfway with one of two types of binary mixtures one where
the particles differ only in density (plastic and steel beads all of diameter d = 2 mm)
the other where the particles differ only in size (plastic beads whose diameters arc
d = 2 & 3 mm) We rotate the drum at u sa 1 rpm which generates a thin flat flowing
__. (?j
jo
f lv
teL_(ms) x^O1
-JM.
n
id
f j i / \m/$ix1(f3
Fig. 2 Experimental results of segregating mixtures of particles (a) A sketch of the rxpen
men) % rotating drum halfway filled At any time a thin flowing laj^r of bead1! (A) flow over
most of the beads whuh arc rotating with the drum (B) (b d) images taken of 3 mm (dark)
& 2 mm (bright) plastic beads (e g) corresponding segregation flux in the y direction first
mixed then rotated in a drum after (b,e) 1/4 rot (c,f) A/4 rot (d g) � 10 rot (h j) images
taken of 2 mm steel (dark) &; plastic (bright) beads (k rn) corresponding segregation flux in
1he y direction first mixed then rotated in a drum after (h k) 1/4 rot (i 1) 3/4 rot (j,ni) ~ 10
rot
layer that is relatively uniform m the x direction (see Fig 2(a)) in the center of the
drum While the drum rotates we focus a high speed high resolution digital camera
on this region of the flowing layer and at e\ery half rotation we take 1024 images at
500 fps All results shown represent the average of three sets of such experiments
During the first half drum rotation all beads enter the flowing layer wcll-rnixed
as m Fig 2(b) (2 & 3 mm plastic particles) and m Fig 2(h) (2 mm plastic &; 3 steel
particles) For each experiment we locate and track the beads from one linage to the
next From this, we calculate the average segregation flux of each component relative
to the mixture /,Z\u 7 = f1 (vt ? vraix) where / , and vt represent the average volume
fraction and 'vertical velocity respectively, of component i and vmiT is the average
velocity of mixture (The velocity 1? = ux.? uy Sec Fig 2(a) for component directions )
The relative movement of the different components is apparent m the flux when the
particles are well-mixed (Fig 2(e k)) The smaller particles exhibit a relatively large
negative flux as they sink (with gravity), and the flux of the larger particles is positive
Similarly the denser (steel) particles exhibit a large negative net flux, and the flux of
the less dense (plastic) particles is positive ((Fig 2(k)) As commonly observed this
quickly leads to the unmixing or segregation of the components Tigs 2(c d) and (i,])
leaving the larger or less dense particles on top As the components sort the average
relative movement or flux decreases essentially to zero (Figs 2 (f g) and (l,m))
From these experimental results, one could be further convinced that the relative
movement due to particle size and density could cancel one another if larger particles are
also denser It is difficult to vary only density or size without changing other properties
such as friction that might affect segregation Therefore to study the relative average
particle motion - the flux - as it varies with relative particle size and/or density, we
use computational experiments based on the Discrete (or Distinct) Element Method
(DEM), first proposed by Cundall and Strack [19] The method allows for systematic
variation of particle properties through a simple 'soft sphere force law that models
/ Ai
(ms) xlO
F i g 3 S i m u l a t e d \ o l u m e friction / a n d segregation flux / AT ploLs at ~ 1/2 r o t a l i o n The
first row shows t h e volume fractions and 1he second row shows t h e segregation flux in t h e y di
reel ion P a r t i c l e s density r a l i o i s p ~~ p ie srr/p e sd S e ~ 3 1 w i t h ( / r ? DdP se /Dtps dr -a= (a) 1 (b) 1 4 (c) 1 5 ( 1) 1 6 (c) 1 8 a n d (f) 2
particle particle interactions We use a nonlinear force model that incorporates Hert/ian
contact theory and material properties into the contact coefficients as in Ref [20]
The computational domain involves a circular drum w ith periodic boundaries in the
axial direction to eliminate the side wall effect [17] The drum size is smaller than the
physical experiments (here D = 72 mm) to reduce the computational time Accordingly
the rotational \elocity is increased according to scaling laws proposed by Tabcrlet et
al [21] so that u ss 16 rprn Simulations are performed using beads with density ratio
of pr = Pdenser/Plcssdcnsc = 3 1 a n d t h e S17e r a t i o of dr
= f^densei /d] e ssden;=e r a n g i n g
from 1 3 the smaller (less dense) particles arc 2mm in diameter The average particle
concentration is fixed at 50 50 bj volume As for the experiments the drum is filled
halfway with the mixture of particles and rotation is commenced Results ire averaged
over three such computational experiments under each set of conditions
Tigurc 3 shows f, (first row) and flAvl
(second row) at ~ 1/2 rotation when the
systems are still well mixed for dr ranging from 1 2 The plots for f1 show these 6
mixtures to start relatively well mixed The plots for f Av% show markedly different
behavior with changing dr When dr = 1 results are qualitatively and quantitatively
similar to those shown in 2(k) Qualitatively fAv < 0 for the dense particles and
fAv > 0 for the less dense particles "When d, = 2 the migration flux of denser particles
is essentially positive throughout the flowing la\cr indicating that density effects are
reversed due to size effects For intermediate values of dr however these two effects
do not cancel In these cases for the denser particles fAv > 0 in the deeper region
(y > b mm) and fAv < 0 close to the free surface (y < 6 mm) This indicates that
si7e and density effects dominate in different regions of the flowing layer Similar dT
dependent behavior is observed for other density ratios [22] The computational lesults
are consistent with experimental results from monosized systems reported here The
7
variation of dominant scgicgation effects in different regions of the flowing layer is hkclv
responsible for the 'banding segregation reported in Rcf [23] However additional
experiments with mixtures of particles differing in both s u e and density would be
us
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