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Controlled microwave heating of inhomogeneous materials in medical and space applications

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CONTROLLED MICROWAVE HEATING OF
INHOMOGENEOUS MATERIALS IN MEDICAL AND
SPACE APPLICATIONS
by
Zhen Li
Department of Electrical and Computer Engineering
Duke University
Date:
Approved:
..
Rhett George/
Qing H. Liu
W. Deverfiuy Palmer
Ste
Dissertation submitted in partial fulfillment of the
requirements for the degree of Doctor of Philosophy
in the Department of Electrical and Computer Engineering
in the Graduate School of
Duke University
2008
UMI Number: 3371383
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UMI
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Copyright © 2008 by Zhen Li
All rights reserved
ABSTRACT
CONTROLLED MICROWAVE HEATING OF
INHOMOGENEOUS MATERIALS IN MEDICAL AND
SPACE APPLICATIONS
by
Zhen Li
Department of Electrical and Computer Engineering
Duke University
Date:
Approved:
William T^. Joine^f Supervisor
Qing H. Liu
(A/ • 'Qzve<T*A>^ \iJL^^
W. D&yereux Palmer
Stephen Smith
An abstract of a dissertation submitted in partial fulfillment of the
requirements for the degree of Doctor of Philosophy
in the Department of Electrical and Computer Engineering
in the Graduate School of
Duke University
2008
Abstract
In microwave-induced heating of materials there are two applications for medical
and space use that are quite interesting as well as scientifically important. These
applications are the treatment of cancer in humans and the melting of thick layers of
ice.
Aside from the fact that both applications involve raising the temperature of a
material using microwaves, these applications have many other features in common.
The depth of penetration of microwave energy into the material is of great importance in both applications. Furthermore, the composite depth of penetration in each
material (biological tissue and ice) is determined by the composition of materials
in each application. The major components of biological tissue (muscle, fat, blood
and bone) have individually determined penetration depths that may be combined
in a know way to obtain composite penetration depth. Likewise, for ice melting,
the individual depths of penetration in melted ice, partially melted ice and solid ice
may be calculated separately and then combined by a known method to obtain the
depth of penetration in the composite material. These depths of penetration play a
major role at which frequencies to use for each application. In both applications the
choice of antenna or applicator, the impedance match to the source and the antenna
radiation pattern are of fundamental importance. Another common feature of the
two applications is that the required induced temperature rise is approximately the
same, an increase from 37°C to 43°C for cancer therapy and an increase from — 5°C
iv
to 1°C for ice melting. An obvious difference between the two is that ice melting
involves a phase of material, whereas cancer therapy does not.
Both applications induce heating patterns and electromagnetic field distributions
in materials that are conveniently displayed and analyzed using electromagnetic simulation software called High Frequency Structure Simulator (HFSS - Ansoft Corp).
However, to preserve the definition of each application, and to make the analysis as
clear as possible, the two applications are herein documented separately.
In the first application, an improved radio-frequency hyperthermia system for
therapeutic tumor heating is investigated. The existing hyperthermia system is a
cylindrical phased-array applicator, which operates at 140 MHz and consists of eight
dipole antennas connected in parallel pairs, distributed uniformly around the cylinder. The system provides radial power steering by a four channel independent control
of power and phase. When used in conjunction with Proton Resonance Frequency
Shift (PRFS) Magnetic Resonance Imaging methods (MRI), patient heating within
the tumor and surrounding healthy tissue can be monitored and corrected in real
time to optimize hyperthermia treatment. To prevent crosstalk between a hyperthermia system and a MRI radio frequency (RF) coil, a bandpass filter which passes
frequencies around 140 MHz and rejects frequencies around 64 MHz is designed and
added to each channel of the existing system. And due to the complexity of the load,
such as the position of the patient and the size of the tumor, etc., an impedance
matching network is integrated into the existing applicator. The matching network
v
successfully maximizes power delivered from each channel into a patient. To improve
preplanning of treatment, a simulation with HFSS including a realistic human-body
model is made. Then the electromagnetic field results from HFSS can be used by
ePhysics (Ansoft Corp) to predict temperature distributions as a function of time in
the tumor and the surrounding healthy tissue, taking into account blood perfusion
and water cooling. Simulation results are compared with results of patient treatments. Meanwhile the results can be used to choose the appropriate settings of each
antenna in advance for an individual patient.
In the second application, we explore the feasibility of using microwave energy to
bore through thick layers of ice. Microwave energy is capable of achieving a composite
depth of penetration of approximately 0.1 m at an operating frequency of 2.45 GHz,
a frequency at which waveguide dimensions are practical and high-power sources are
more readily available than at higher frequencies. Since ice has a very large depth of
penetration and water has a very small depth of penetration at frequencies below 10
GHz, this presents a challenging problem. The problem is compounded because some
of the places where this technique could be used may be on Mars or Europa where
the ice is hundreds of kilometers thick. We simulated and tested our calculations and
assumptions at 2.45 GHz using a 1300-watt microwave oven converted to transmit
all output power into a rectangular waveguide terminated in a dome-shaped, openended probe pressed against a large block of ice. From multiple tests the melting rate
in average is 0.75 inches/minute. Therefore, microwave-induced heating for melting
vi
deep layers of ice could be a viable alternative to other methods that have been used
such as drilling and electrical resistance heating. In the end, we propose a method
to combine the microwave heating and the electrical resistance heating to speed up
the melting process.
vn
Acknowledgements
This project was supported by NIH grant 5PO1-CA042745. I would like to express
my gratitude to all those who gave me the possibility to complete this thesis. Firstly,
I want to thank Electrical and Computer Engineering Department and Department
of Radiation Oncology at Duke University for giving me the permission to do the
necessary research work.
I am deeply indebted to my advisor and mentor Dr. William T. Joines, whose
encouragement, invaluable guidance, and stimulating suggestions helped me in all the
time of my research. During the past four years, I have acquired a great deal from him
of technical knowledge, philosophical insights, and art of dealing with complicated
situations both in research and in life. It is a great honor to be his student. I am
also grateful to Dr. Rhett George, Dr. Qing H. Liu, Dr. W. Devereux Palmer and
Dr. Stephen Smith for kindly serving on my committee.
Also, I would like to express my appreciation to a large number of collaborators
at Department of Radiation Oncology in Duke University Medical Center who participate in collaborative efforts that contribute to the investigation reported here.
Special thanks to my mentors Professor Paul R. Stauffer and Dr. Paolo F. Maccarini
for their support, valuable comments and suggestions. This thesis would not be possible without clinical data provided by many people. They include Omar. A. Arabe,
Dr. Kung-Shan Cheng, Dr. Vadim Stakhursky, Dr. James MacFall, Dr. Brian J.
Soher, and Cory Wyatt. Next, I would like to thank my research group members in
viii
Electrical and Computer Engineering Department, Steven Keller, John Stang, and
Tao Zhao, as well as many graduate students in our department. Each of them provided valuable friendship and support to me during these years. Because of them,
research and work has been more fun than fun!
During my time as an intern at the Ansoft Corporate Headquarters in the summer
of 2007,1 learned a great deal from my mentor, Dr. Martin Vogel, who taught me how
and where I can improve my research in the most efficient way. Meanwhile he also
taught me a bit more about the difference between the industry and academic world
and what to expect from a career in both worlds, which is absolutely invaluable at
this point in my life. I also gratefully acknowledge the support and helpful discussions
from the software development group at Ansoft Corporation.
Last but not least, I want to thank my husband Hao Hu for his love, patience, and
understanding; thanks to my parents, my brother and his girlfriend for their constant
encouragement and support; and thanks to all my close friends, whose support and
enthusiasm for life helped me in many ways.
For all these mentioned above, I will be eternally grateful.
IX
Contents
Abstract
iv
Acknowledgements
viii
List of Figures
xiv
List of Tables
xxi
1
2
Introduction of Hyperthermia — A Medical Application of MicrowaveInduced Heating
1
1.1
Historical Background of Hyperthermia Therapy
1
1.2
Rationale for Clinical Hyperthermia
3
1.3
Technical Aspects of Clinical Hyperthermia Treatment
6
1.4
Electromagnetic Heating
9
1.5
The Composite Depth of Penetration in a Mixture of Biological Materials 11
1.6
Thermometry
13
1.7
Modeling and Treatment Planning
15
1.8
Contribution
16
Bandpass Filter Design for a Hyperthermia System
18
2.1
Overview of a MRI Compatible RF Hyperthermia System
18
2.2
Introduction of Band Pass Filter Design
21
2.3
Filter Design Using Q Tapering of Sections
23
2.4
Half-wavelength Tapped-Stub Resonator
24
2.5
Replacing the Open Stubs with Capacitors
28
2.5.1
28
Resonant Frequency and Q
x
2.5.2
Replace A/4 Transmission Line by a Series Inductance and Capacitors to Ground
30
2.5.3
Derive New Expression for Q of Each Resonant Section . . . .
34
2.5.4
Replace Remaining A/4 Transmission Line by a Series Inductance and Capacitors to Ground
37
Replace Inductors with the Shortest Transmission Line . . . .
39
2.5.5
2.6 Results and Conclusion
40
2.6.1
Comparison of Measured and Modeled Results
42
2.6.2
Discussion and Conclusion
44
2.7 Filter Design for MRI Compatible RF Hyperthermia System
3 3D Modeling for Clinical Hyperthermia Treatments
45
51
3.1 Overview of 3D Modeling
51
3.2
Mathematical Formulations
53
3.2.1
Power Deposition Modeling
53
3.2.2
Thermal Modeling
55
3.2.3
Numerical Methods for Solving Maxwell Equations and Bioheat
Transfer Equation
57
3.3 Ansoft Packages
59
3.4
60
Electromagnetic Model for a Homogeneous Medium
3.4.1
Electromagnetic Model and Power Deposition in a Homogeneous Medium
60
3.4.2
Experiments of Heating a Gel Filled Phantom
64
3.4.3
Results and Discussion
65
3.5 Electromagnetic Model for a Heterogenous Medium
3.5.1
Electromagnetic Model and Power Deposition in a Patient Body
Model
xi
67
67
3.5.2
Temperature Distribution in a Patient Body Model
74
3.5.3
Simulated Results and Discussion
82
4 Optimized Hyperthermia Treatment Planning
89
4.1 Overview of Treatment Planning
89
4.2
90
Procedures to Optimize the Antenna Settings
4.3 Results and Discussion
93
5 Wide-Band Input Impedance Matching Circuit Design for a Hyperthermia System
95
5.1 Introduction
95
5.2
97
Antenna Input Impedance Measurements
5.3 Theory
5.3.1
Lumped Element Circuits That Are Equivalent to a Quarter
Wavelength Transformer
99
Lumped Element Circuits That Are Equivalent to Two Cascaded Quarter Wavelength Transformers
101
Replace the Lumped Elements by Relatively Short Sections of
Transmission Line
103
Final Designs of Impedance-Matching Networks with Dimensions and
Component Values
105
5.4.1
108
5.3.2
5.3.3
5.4
99
Final Design Format
6 Melting of Ice - A Space Application of Microwave-Induced Heatingll6
6.1 Introduction
116
6.1.1
Wave Propagation in Ice
125
6.1.2
Wave Propagation in Water
127
6.1.3
The Composite Depth of Penetration for Mixtures of Ice and
Water
129
xii
6.2
Melting Time Required for the Composite Layers
134
6.2.1
136
Laboratory Measurements to Confirm the Model
6.3 Discussion and Conclusion
137
7 Discussion and Conclusion
141
Bibliography
143
Biography
150
xin
List of Figures
1.1
Schematic of power delivery system
9
1.2
An annular phased array applicator
10
1.3
Electromagnetic waves propagate through cascaded materials of total
depth of d
12
A block diagram of the MRI compatible radiofrequency (RF) heating
system
20
2.2
Quarter wavelength tapped-stub resonator
24
2.3
Half wavelength tapped-stub resonator
25
2.4
A three section half wavelength tapped-stub resonator
26
2.5
PUFF simulation of a three section half wavelength tapped-stub resonator
27
2.6
Half-wavelength tapped-stub resonator with capacitive loading
28
2.7
A three section half-wavelength tapped-stub resonator with capacitive
loading
30
PUFF simulation of a three section half-wavelength tapped-stub resonator with capacitive loading
31
2.1
2.8
2.9
A A/4 transmission line equivalent circuit: shunt Co-series Lo-shunt Co. 31
2.10 Replace A/4 transmission line by a series inductance and capacitors to
ground
33
2.11 Add all capacitors in parallel in Figure 2.10
33
2.12 PUFF simulation of A/4 transmission line in Figure 2.8 replaced by a
series inductance and capacitors to ground
34
xiv
2.13 PUFF simulation after using derived new expression for Q of each
resonant section
36
2.14 Replace all remaining A/4 transmission lines by a series inductance
and capacitors to ground
37
2.15 PUFF simulation of replacing all remaining A/4 transmission lines by
a series inductance and capacitors to ground
38
2.16 The input impedance of inductance and a transmission line
39
2.17 Replace inductors with the shortest transmission line
40
2.18 PUFF simulation of replacing inductors with the shortest transmission
line
2.19 Designed n = 3 band pass filter
41
42
2.20 Simulated and measured results of the designed board of n = 3 band
pass filter working at f0 = 205 MHz
43
2.21 The PUFF simulation results in frequency range from 20 MHz to 240
MHz of an n = 3 band pass filter which has Butterworth response with
QT = 10 and centered at /<, = 200 MHz
46
2.22 PUFF simulation result of a n = 3 band pass filter which has Butterworth response with BW = 60 MHz and centered at / 0 = 140 MHz
connected to a n — 3 high pass filter which works at /o = 140 MHz. .
48
2.23 A designed board of n = 3 band pass filter connected with a n = 3
high pass filter, working at / 0 = 140 MHz
49
2.24 Measured results of the designed board of n = 3 band pass filter connected with a n = 3 high pass filter, working at /o = 140 MHz
50
3.1
A schematic diagram in HFSS of a annular phased array limb applicator. 62
3.2
HFSS simulation results in the xy Plane with different 4 Channel Phases. 62
3.3
Matlab plots of hotspot regions in the xy plane with different 4 Channel
Phases
xv
63
3.4
12 cm diameter muscle equivalent phantom inside 23 cm diameter RF
applicator surrounded by water
65
MRI PRFS imaging results showing relative temperature changes due
to each of the six settings of the RF applicator
66
A anatomical reconstruction of a patient's leg with sarcoma inside.
This figure is provided by Dr. Vadim
68
A schematic diagram in HFSS of a human body being placed inside
an annular phased array limb applicator inside MRI machine
70
A detailed schematic diagram in HFSS of a lower leg placed inside an
annular phased array limb applicator
71
(a). An original geometry of tumor reconstructed from a patient's CT
scan. (b). Reduced geometry information of the tumor
71
3.10 A detailed schematic diagram in HFSS of a lower leg with tumor inserted at the appropriate location compared with the CT scan of that
patient placed inside an annular phased array limb applicator
72
3.11 (a). E field distribution (b). SAR distribution when four inputs are in
phase
74
3.12 Simulation strategy: Step 1: 3D FEM EM simulator-HFSS solves for
field quantities in area of interest. Step 2: 3D FEM thermodynamic
simulator-ePhysics takes field inputs and provides temperature maps
by solving bio-heat transfer equation in area of interest
77
3.13 (a). Anatomic MRI of a patient's lower leg. (b). Baseline temperature
change map after 4 minutes of imaging without application of heat,
temperatures in the leg have remained stable
80
3.14 (a). Simulated temperature field distribution, (b). Temperature
change map at approximately 15 minutes into treatment, heat is focused in tumor region, but more so on opposite side of leg
81
3.5
3.6
3.7
3.8
3.9
xvi
3.15 Patient Treatment Case I: 18 minutes with equal phases, equal powers.
Simulation vs. Measurement: General correlation of heating trend but
poor agreement found between simulated and measured results in both
the tumor and the healthy tissue when fixed perfusion rate assumed
in the simulation
83
3.16 Patient Treatment Case II : 25 minutes with variable power; equal
phases. Measurement vs. simulation. Power inputs were varied to
maintain a constant temperature in tumor. Poor correlation after first
8 minutes of heating was thought to be due to assumption of fixed
perfusion during the heat treatment
85
3.17 The effect of perfusion: doubling the tissue perfusion factor in patient
treatment case I and II yields better correlation between measurement
and simulation for both clinical trials
86
4.1
4.2
4.3
Drive one channel first and find the phase that puts most field in the
tumor
90
E field distribution when phases of each channel are optimized: Channel 1: 0°, Channel 2: 70°, Channel 3: 90°, and Channel 4: 5°
91
SAR distribution when phases of each channel are optimized: Channel
1: 0°, Channel 2: 75°, Channel 3: 95°, and Channel 4: 5°
92
4.4
Phases optimized experimentally
92
4.5
Phases optimized with HFSS
93
5.1
The A/4 transformer in (a) is equivalent to each of the LC circuits in
(b), (c), (d), and (e). For each the equivalence is Zot = OJQL = \/{ujQC). 100
Lumped element replacement of two cascaded A/4 transformers, where
Zs = 50 Q, and ZL = 19.17 fl. (a). Cascaded transformers yielding
a maximally-flat passband impedance match, where Z 0 i = 39.344 fl
and Z02 = 24.362 fl. (b). The lumped element replacement where
d = 28.89 pF, L 2 = 44.73 nH, C 3 = 75.55 pF, L 4 = 27.69 nH, and
C5 = 46.66 pF
103
5.2
xvn
Simulated return loss (Sn in dB) of the single-stage networks in Figure
5.1 for Zs = 50 ft and ZL = 14.43+J8.27 ft (a series R and L), or ZL =
19.17 ft 11 j'8.27 ft (a parallel R and L). On the left of/ 0 = 140 MHz, the
top curve corresponds to Figure 5.1(e) with ZL = 14.43 + j 8 . 2 7 ft and
ojod = l/26.86ft, UJQL2 = 26.86 ft, co0C3 = 1/35.13Q. The next curve
down corresponds to Figure 5.1(d) with ZL = 19.17 ft \\ J8.27 ft, and
w 0 ^i = 30.96 ft, UJ0C2 = l/30.96ft, and u0L3 = 466.22 ft. The third
curve down corresponds to Figure 5.1(c) with ZL = 14.43 + j'8.27 ft
and UQLI = 26.86 ft, u0C2 = l/26.86ft, LU0L3 = 18.59 ft. The bottom
curve corresponds to Figure 5.1(b) with ZL = 19.17 ft || J8.27 ft, and
LOQCX = l/30.96ft, LO0L2 = 30.96 ft, and LO0CS = l/16.078ft
The dot-dash curve is simulated return loss (Su in dB) versus frequency for the five lumped-element replacement of two A/4 transformers as in Figure 5.2(b). Here, w 0 Ci = l/39.344ft, u0L2 = 39.344ft,
u0C3 = l/15.05ft, LOQU = 24.362ft, UJQC5 = 1/14.095. The solid
curve is simulated return loss for the same circuit except the series
inductances are replaced by sections of transmission line, as Z02 =
85ft, l2 = 0.069A replaces L2, and Z0i = 85ft, Z4 = 0.044A replaces
L 4 . The dash-dash curve is the bottom-left curve from Figure 5.4,
repeated here as a guide for reference. For each circuit Zs = 50ft and
Z L = 9.17ft||j33.448ft
The dot-dash curve is simulated return loss (Su in dB) versus frequency for the five lumped-element replacement of two A/4 transformers as in Figure 5.2(b). At / = 140 MHz, w 0 Ci = l/39.485ft,
UJ0L2 = 39.485ft, LU0C3 = 1/15.17ft, UJQU = 24.625ft, u0C5 = 1/14.53.
The solid curve is simulated return loss versus frequency for the same
circuit, except the series inductances are replaced by sections of transmission line, as Zo2 = 85ft, l2 = 0.069A replaces L2, and Z04 =
85ft, /4 = 0.044A replaces L 4 . The dasked curve is the simulated
return loss when the three capacitors are replaced by open-circuited
sections of transmission line, as Z01 = 39.485ft, l\ = 0.125A, ZG3 =
15.17ft, h = 0.125, Z05 = 14.53, k = 0.125A
xvin
5.6
5.7
5.8
6.1
6.2
A diagram of the circuit that would yield the return loss represented
by the solid curves in Figure 5.4 and Figure 5.5. The input (Zin) is fed
from a 50-ohm cable into a parallel-plate section that has Z0 = 50Q and
w = 4.16 mm. The capacitors (Ci = 28.89 pF, C 3 = 75.56 pF, C5 =
80.65 pF at f0 = 140 MHz) may be chip capacitors that are embedded
in the dielectric between the strips of width w = 1.97 mm (for Z02 =
Z04 = 85Q). The length l2 = 0.069A = 8.00 cm and /4 = 0.044A = 5.10
cm. With G-10 epoxy-glass dielectric between the strips and 2d =
1/16 inch = 1.59 mm, ed = 4.4 and eE = 3.41 for w = 1.97 mm. . . .
113
A variation of the circuit in Figure 5.6 that will yield the return loss
represented by the solid curves in Figure 5.4 and Figure 5.5. This
is the same as in Figure 5.6, except that new values of capacitance,
d = 20.87 pF, C3 = 67.54 pF, C5 = 72.63 pF at f0 = 140 MHz are
each added in parallel with the open-circuited transmission lines to
produce the same capacitance given in Figure 5.6. The input on the
left is into a parallel-plate section that has ZQ — 50Q and w = 4.16 mm.
The capacitors are embedded in the dielectric between the strips on
each surface. With G-10 epoxy-glass dielectric between the strips and
2d = 1/16 inch = 1.59 mm, e^ = 4.4 and CE = 3.41. The wider lines
are Z0 = 50fl of width w = 4.16 mm, and the length I = A/36 = 3.12
cm. The narrower lines are Z0 = 85Q of width w = 1.97 mm. The
length l2 = 0.069A = 8.00 cm and U = 0.044A = 5.10 cm. The total
length of the circuit board may be made more compact by serpentining
li and U
114
The network in Figure 5.7 constructed to approximate scale using
copper-foil tape on epoxy-glass substrate. The input on the left is
from the 50-ohm source and the output on the right is to the antenna
array
115
The Subglacial Lake Vostok System (Excerpted from Science, 2005,
310:28)
119
The primary elements of the microwave and resistance heating probe
(not in scale)
123
6.3
The conductivity of ice
128
6.4
Depth of penetration of ice and water (log scale)
130
xix
6.5
(a). Melted water distribution in a unit volume, (b). Three-layer
model (water | water and ice | ice)
131
6.6
Depth of penetration in mixtures of water and ice (log scale)
132
6.7
Depth of penetration in a mixture of 3 layers (log scale)
133
6.8 Simulation of absorbed microwave energy in: (a), pure ice (b). impure
ice with conductivity of 0.3 S/m
6.9
135
(a). Permittivity and (b). Conductivity of 1% and 2% sugar water
after being frozen and at room temperature
137
6.10 A 1% sugar ice block (12 x 6.5 x 3 inches) under the dome-shaped
probe terminating the waveguide
138
6.11 1.8 inches 1% sugar ice was melted after 2minutes and 24 seconds. . . 138
6.12 A probe which combines microwave heating and resistance heating. . 140
xx
List of Tables
1.1
Properties of biological materials
13
3.1
Material dielectric properties
73
3.2
Material thermal properties
78
3.3 Perfusion
80
5.1 Antenna input impedance measurements
98
xxi
Chapter 1
Introduction of Hyperthermia - A
Medical Application of
Microwave-Induced Heating
1.1
Historical Background of Hyperthermia Therapy
Induced heat for cancer therapy is called "Hyperthermia". Hyperthermia is a therapy
in which tissue temperature is raised to 41°C or higher (approximately 42°C-45°C)
by external methods in opposition to the body's control process whose purpose is to
maintain temperature around the normal set-point [1].
The use of heat as a cancer therapy dates back to the ancient Egypt, India, and
Greece. The earliest references to treat cancer with hyperthermia can be found in
Egyptian Edwin Smith papyrus scrolls dated back to 3000 BC describing a breast
cancer patient treated with immersion in hot water, or with a "fire drill" which was
used to burn away the tumor [2]. Meanwhile since around 3000 BC, the traditional
medicine practiced in India (an Ayurvedic system) which involves a month-long pro-
1
gram of heating by steam baths, feeding with oils and rice, and the administration
of purgatives, has been used till nowadays [1]. Greek physicians recommended the
use of heat when surgery was not possible. They refer to the use of high temperature therapy as hyperthermia. This simply means heating body tissue considerably
above its normal temperature. People found out that the total body hyperthermia
in the form of hyperpyrexia (fever) has been beneficial in many diseases, cured some
infection with pyrogenic bacteria and even produced dramatic tumor regressions. In
1866, Dr. W. Busch, a German physician, described the case of a patient who had
histologically verified sarcoma of the face which completely disappeared after a high
fever associated with a skin infection called erysipelas [3]. Thus the Busch paper
becomes the first article which indicated that temperatures might selectively destroy
tumor tissue [4]. Similar reports were published by others 20 years later (Fehleisen,
1883; Bruns, 1888; Coley, 1893; and Westermark, 1898 etc.). More recently in 1893,
Dr. William Coley in the United States began to create bacterial toxins which would
induce high fevers. His reports on clinical trials on inoperable cancer patients showed
that the five year survival rate went from 28 to 64 percent depending on whether the
fever was less than or greater than 38.5°C [5]. During the 1920's, several investigators
began to study the effect of heat on animal tumors [6]. Then in the 1960s, a rationale
for using hyperthermia as a treatment for malignant diseases started to be developed.
In late 70s and early 80s, there were several clinical trials showing that hyperthermia combined with radiation produced better results than radiation used alone.
2
Thus, in 1984 hyperthermia was given legal status as an approved medical procedure. However, those results on clinical trials were not confirmed by U.S. phase
III trials. Therefore, people's interests on hyperthermia waned. Although it was
still used in some cancer centers, it had been ignored by most oncologists and unknown to the public. Until the end of 1990's, it has been realized that those negative
results were due to inadequate equipments and quality assurance procedures. Meanwhile, new positive phase III trials on three European and one American showed
that the use of hyperthermia in combination with radiation therapy results in superior tumor response, tumor control, and survival as compared with radiation therapy
alone [7]. Finally the situation of hyperthermia started to change. In the past 15
years, the technologies to deliver effective heating into interested regions, especially
to the deeper tumors have been investigated. The use of computer modeling makes
it possible for researchers to direct and control the heat and temperature inside the
tumors. Meanwhile noninvasive thermometry is being developed. Writing a thermal
prescription finally becomes possible. All these developments raise the expectations
of hyperthermia as a treatment modality.
1.2
Rationale for Clinical Hyperthermia
The rationale for using hyperthermia as a treatment for malignant diseases is that
there are some differences in the blood supply and vasculature in tumors and normal
tissues [1]. In normal tissues, blood flow dissipates part of the heat; in a tumor, how3
ever, blood flow is frequently disorganized and heterogeneous. Since blood flow is an
important part of the cooling mechanism, some regions within the tumor will have a
reduced capacity for cooling and may become hotter than surrounding normal tissues.
On the other hand, there may be an increase of blood flow in the normal tissues due
to the body's control process whose purpose is to maintain the normal temperature.
This would increase the temperature difference between tumors and adjacent normal
tissues. Therefore applied heat results in a relatively large temperature rise and the
tumor is weakened. Secondly, people found out that malignant cells are reliable more
sensitive to heat than normal cells. Bolstered by research in the 1980's emphasizing
the cell killing potential of heat, researchers focused on high temperature (> 42°C)
treatments intended to induce cell death. Unfortunately, this approach was limited
by a number of biological and commercial factors and, as a result, interest in hyperthermia began to wane by the mid-1990's. Fears of thermotolerance, for example,
limited the number of heat fractions to about two per week. Thermotolerance in
surviving cells increases with temperature; however, it is now known to be limited
in mild-temperature hyperthermia. High heat also causes vascular damage thereby
cause the development of hypoxic cells. And the presence of oxygen is critical to
both radiation- and chemotherapies. For example, oxygen is necessary to stabilize
the radiation induced hydroxyl radicals that can directly cause DNA damage and
interfere with DNA repair. In contrast, these hypoxic cells which are lack of oxygen
are likely to switch to anaerobic metabolism. The end of the process of that makes
4
the tumor region becomes low pH and deprived of nutrients. Therefore tumor region
is easily to be killed by hyperthermia. It is now thought that mild hyperthermia leads
to increased perfusion and increased p 0 2 (reoxygenation) of fast-growing, hypoxic
tumors thus increasing radio- and chemo-sensitization. Because of the threat of vascular damage and hypoxia, heat was often applied after radiation which reduces the
effectiveness of the hyperthermia. And finally, studies have shown that mild hyperthermia results in the denaturation (unfolding) and eventual aggregation of nuclear
proteins which interferes with mitosis, DNA transcription, and DNA repair. Limited thermotolerance, reoxygenation effects, and its denaturation and aggregation
potential are the key biological factors causing scientists to rethink adjuvant mild
hyperthermia.
It is now realized that tissue temperature in this range does not instantly destroy
the cells, however it reduces the ability for the cells to divide. Hyperthermia is not
a form of cauterization or surgery [4]. Nevertheless, when hyperthermia is used in
combination with radiation therapy, chemotherapy or surgery, there is a dramatic
improvement in response rates.
5
1.3
Technical Aspects of Clinical Hyperthermia
Treatment
A typical course of clinical hyperthermia treatments consists of 4-8 heating sessions
spread over a period of several weeks. The first hour of a two-hour session is used for
patient preparation, such as placement of thermal monitoring probes in and around
the tumor volume, and the RF applicator around the tumor region. After the patient is prepared, the power is turned on to the hyperthermia antenna(s) and the
tumor is heated by radiated electromagnetic energy. The tumor should be heated for
approximately 30-60 minutes at a temperature of 42°C to 45°C if hyperthermia is
combined with radiation therapy or chemotherapy. When hyperthermia is used alone,
the tumor should be heated up at the temperature higher than 48°C for the same
amount of time. And approximately 15 minutes (maximum) is available prior to the
actual delivery of RF energy to the tumor for manual control of the RF electric-field
distribution within the patient target tissue [8].
Techniques in clinical hyperthermia can be classified into three broad categories
based on the locations of the tumors. There are whole body, localized and regional
hyperthermia. In this paper, we focus on the design and analysis of an improved regional hyperthermia therapy system. A regional hyperthermia system is used to heat
a large portion of the trunk or whole limbs. The most difficult task of implementing
reginal hyperthermia is to concentrate electromagnetic power in the deep-seated raa-
6
lignant tumors with minimal energy delivered to the surrounding normal tissue. To
make the energy focused in a small region, which is proportional to the wavelength,
the working frequency of the antennas should be as high as possible. However, the
depth of penetration decreases when frequency increases. Which means the high
frequency electromagnetic waves cannot penetrate into the deep-seated malignant
tumors. This becomes the major problem in heating a deep-seated tumor in regional hyperthermia treatments. The undesired higher temperatures may occur in
various spots in the surrounding normal tissue, which can generate burns, blisters,
discomfort, or pain in the patient. Although most of these side effects are temporary,
techniques to reduce them are necessary in hyperthermia treatment.
For years, though the principles of tumor heating were widely understood, the
technology to direct the heat in a concentrated area lagged behind the theory, especially for the deep-seated malignant tumors [1] [9] [10] [11] [12]. A limited range of
applicators restricted the locations to which hyperthermia could be reliably applied.
Inflexible and klunky controls made beam focusing and steering a challenge. Delivering the high-power energy into the deep-seated tumors in order to achieve hightemperature hyperthermia also presented a challenge. The absence of robust computer simulations often left clinicians to deal with epidermal "hot spots" -unexpected
burns on the exterior surface (air-dermis interface) of the patient's skin. The absence
of non-invasive thermometry forced hyperthermia technicians to rely on limited (localized), in-situ temperature probes. Insurance-controlled reimbursement rates and
7
restrictive cost codes have also played a role in encouraging original equipment manufacturer's to forego development plans. Happily, many of these technical challenges
have been addressed in the last ten years and promising solutions are emerging. This
paper will present several of these equipment solutions in the following case study.
In regional hyperthermia for deep-seated tumors treatment, the electromagnetic
mini annular phased array (MAPA) which works at the frequency of 60 — 150 MHz
has been developed and used for many years [13] [14] [15] [16] [17]. To focus the heat
into the tumor site, researchers found that the driving phases and amplitudes of the
MAPA must be set up carefully. Lots of work has been done in a homogeneous load
then patient-specific computational analysis to determine and optimize the driving
phases and amplitudes of the MAPA [18] [19] [20] [21]. For treatment planning purpose, medical expertise is required to build a three-dimensional patient model, which
potentially causes a number of errors in the model. The difficulties of building a
complex hemodynamic system of the patient may also impact on the effectiveness
of the clinical treatment [22] [23] [24] [25]. Those difficulties also include our lack of
knowledge of a large number of physical parameters because many of them can not
be measured non-invasively. Even to solve the bioheat transfer equation in the simplest thermal models, we need to know the spatial distribution of blood flow which
is difficult to estimate correctly [26]. Those difficulties and possible solutions based
on the recent development of computational resources and human body model will
be addressed in this paper.
8
1.4
Electromagnetic Heating
In Figure 1.1, a schematic overview of the radio frequency (RF) power delivery system is presented. It has been demonstrated that patient tumors can be heated
non-invasively and with good localization using a mini annular phased-array applicator (MAPA) with four pairs of U-shaped dipole antennas as shown in Figure 1.2
[27] [13] [28]. This applicator is able to focus and output electromagnetic waves to
a portion of a patient undergoing treatment, and deposit RF energy at 140 MHz
primarily to heat such portion. Out-going electromagnetic waves propagation in the
applicator
skin
(dermis)
temperature probe
tumor
Figure 1.1: Schematic of power delivery system.
z-direction through a material will have the field components
E+(z) = Ebe*" -7 * =
Eoe-azej^-0z\
(1.1)
where the propagation constant is
7 = y/jufj,(a + jue) = a+ j/3.
9
(1.2)
\
F i g u r e 1.2: An annular phased array applicator.
The definitions and units of the quantities are:
a
=
attenuation constant (Np/m) ;
j3 = phase constant (rad/m) ;
/j, =
a
permeability of the material (henries/meter) ;
= conductivity of the material (siemens/meter) ;
e =
permittivity of the material (farads/meter) .
The basic mechanism of electromagnetic heating can be expressed by a modified
Ohm's law, which determines the tissue current density J for a given electrical field
E and tissue conductivity a as J = aE. The current creates a local power deposition
having a density when passing through a lossy medium
p = i/a\J\2 = a\E\2
10
(W/m3).
(1.3)
The tissue conductivity a depends on the water content of the tissue and the choice of
the frequency [1]. Direct measurements of a and e for malignant and normal tissues
were reported by several groups [29] [30] [31]. All of their reports have shown that
there are differences in electrical properties between malignant and adjacent normal
tissue. Both a and e are generally greater in malignant cancerous tissue than in
normal tissue. The local power deposition is closely related to the specific absorption
rate (SAR) by P — p x SAR where p is the tissue density. Therefore the SAR
generated by the MAPA will produce a temperature difference between malignant
and normal tissue.
1.5
T h e Composite Depth of Penetration in a Mixt u r e of Biological Materials
As we mentioned earlier, the most difficult task of implementing a regional hyperthermia is to choose the working frequency of the applicator in order to allow the
electromagnetic power to concentrate into the deep-seated tumors. One thing has
to be answered first is how to achieve required depth of penetration. The depth of
penetration or skin depth (8) is defined as the depth a electromagnetic wave travels
in a lossy medium to reduce the current density to 1/e or 36.8%, or where the power
density has dropped to 13.5% of the starting value at the surface. Therefore,
<5 = 1 .
a
11
(1.4)
Equating real and imaginary from both sides of Equation 1.2, we can write a and
0 as
1 \W
a = u^}Ie-< -
(1.5)
\UJEJ
and
1/2
where a can be used to calculate the depth of penetration. For electromagnetic
waves propagating through cascaded materials of total depth of d and the composite
propagation constant 7 as shown in Figure 1.3, the equivalent electrical depth through
two layers of materials of total depth d = d\ + d<i is:
.
l
Wave Propagation
1
Material 1
dl
>1
d2
Material 2
Figure 1.3: Electromagnetic waves propagate through cascaded materials of total
depth of d .
jd = 7ic?i + 7 2 d 2 -
(1.7)
ad + jfid = at\di + jfcdi + a 2 d 2 + j(h<k-
(1.8)
Since 7 = a + j(3,
Equating real parts and using a = 1/6 yields,
1
Ft
1 - Fi
S
Si
62
12
(1.9)
Properties
Muscle
Fat
Blood
Bone
Relative Permittivity
63.64
5.88
72.05
25.86
Conductivity (S/m)
0.77
0.037
1.26
0.18
Thickness (cm)
6
2
0.1
2
Depth of Penetration (cm)
5.50
34.79
3.57
14.99
Table 1.1: Properties of biological materials.
where Fi — d\/d is the fractional volume of material 1, and 1 — F\ = d^jd is the
fractional volume of material 2.
Therefore, we can calculate the composite of effective depth of penetration within
a several layer mixture of muscle, fat, blood, and bone, with the knowledge of electric
properties and the thickness of each biologic material as shown in Table 1.1. Since the
depth of penetration decreases with increasing frequency, to achieve required depth
of penetration for deep-seated tumor hyperthermia, 50-200 MHz has been chosen by
most of researchers. In our case at the frequency of 140 MHz, by using Equation 1.9,
the depth of penetration in this mixture of biological materials is 7.71 cm.
1.6
Thermometry
In clinical hyperthermia, knowledge of temperatures obtained and retrospective analysis is crucial. Therefore, excellent thermometry is just as important as is the development and improvement of practical annular phased array applicators. During
13
clinic treatments, various of invasive thermometry technologies have been used such
as thermocouple, electromagnetic, thermistor, and fiberoptic. In those technologies,
it appears that fiberoptic probes are most ideal for electromagnetic field. Fiberoptic
probes are able to collect a large amount of temperature data from a single invasive catheter during a treatment. However, the dwell times need to be sufficient in
order to establish thermal equilibrium before moving the probe to the next measurement position. And artifacts can occur if good thermal contact is not maintained.
Moreover, three dimensional information about temperature in malignant and normal tissues is not available [1]. For years, researchers and practitioners have not been
satisfied with the limited amount of information for control and analysis of invasive
thermometry technologies. More and more work has been done in noninvasive temperature monitoring, for example computerized axial tomography (CT), Ultrasound
(US), applied potential tomography (APT), and magnetic resonance imaging (MRI)
[32]. During the clinic treatments in radiation oncology department at Duke University, temperature within the tumor and surrounding healthy tissue is monitored
using Proton Resonance Frequency Shift (PRFS) MR imaging methods (MRI). This
method allows us to monitor and correct the temperature in real time to optimize
hyperthermia treatments.
14
1.7
Modeling and Treatment Planning
Inspired by the dream that in the future one might be able to predict accurately
the complete spatial and time dependence of the temperature distribution before
a clinical hyperthermia treatment for an individual patient, much work has been
done into computer aided modeling and simulation. Using computational models
can benefit in both clinical and engineering settings. To achieve these goals, two
steps are required. The first step is to determine the E field distribution, the power
deposited per unit volume (or unit mass) of tissue or the SAR distribution. Secondly,
using the knowledge of spatial and time dependent SAR distribution, coupled with
the thermal properties and physiological nature of the patient, one can predict the
developing and the steady state of temperature distribution by using appropriate
heat transfer equations. Ideally, we need accurate anatomic and physiology models
for specific patients, and complete understand the electrical properties and thermal
properties of malignant and surrounding normal tissue.
Clearly, a very complex
model is required which takes into account heat transfer process between the body
and the environment as well as the response for the thermoregulatory system [33] [34].
Moreover, we need to understand the EM interaction between power sources and
patient, as well as the thermal interaction within the patient's body [32]. However,
some knowledge is not completely obtained by researchers.
Although difficulties exist in computer aid modeling and simulation, more and
more researchers have realized that computer simulation is one of the promising
15
methods for treatment preplanning. Treatment planning for hyperthermia involves
the following steps: 1) generating a model which includes the information about
an individual patient, 2) simulating the E field/SAR distributions induced by RF
antennas, 3) determine the three dimensional temperature distribution inside the
patient, 4) optimizing the antenna settings and finally reduce hot spots in normal
tissue and guarantee a required heat in the tumor area, and finally 5) calculating
the effect at the cellular level [35]. The first three steps are addressed in chapter
2 and 3. In chapter 4, we investigate how simulation results can help technicians
determine the optimal antenna steering parameters during treatment preplanning
to achieve best hyperthermia results. In this article, we demonstrate the power of
RF simulations for treatment planning. 3D modelings with realistic patient anatomy
have been undertaken. Simulation results are compared with the clinical data. These
studies have shown that modeling is a promising method to pre-plan hyperthermia
treatment. Further research needs to be done at the cellular level.
1.8
Contribution
In radiation oncology department of Duke University, an annular phased array limb
applicator is being used in conjunction with Proton Resonance Frequency Shift
(PRFS) MR imaging methods for hyperthermia research. Temperature within the
tumor and surrounding healthy tissues can be monitored and corrected in real time to
optimize hyperthermia treatments. In the following chapters, the author illustrates
16
the design of filters, and input impedance matching circuits to improve the existing
hyperthermia system. Then in order to increase the treatment quality and efficiency,
a series of 3D electromagnetic and thermodynamic simulation models are done for
treatment preplanning. The main tasks are completed and presented in this thesis
are:
1. Design filters which are used to prevent the cross talking between the limb
applicator and the MRI machine.
2. Simulate the E field distributions generated by the annular phased array limb
applicator in a homogenous medium and then in a more complex human body model
when the applicator is used inside the MRI machine.
3. Transform CT imaging data of a patient into a model in which simulations can
be carried out.
4. Predict the temperature distribution in the patient, taking into account blood
flow and specific heat generation rates of the various tissues.
5. Adjust the relative phases of each channel to optimize the temperature distribution inside the tumor.
6. Compare simulated results with clinical measurements.
7. Design wide-band input impedance matching circuits to maximize the transmitted power.
17
Chapter 2
Bandpass Filter Design for a
Hyperthermia System
2.1
Overview of a M R I Compatible R F Hyperthermia System
The monitoring and control of in vivo temperature has continued to be a significant
problem in hyperthermia treatment. Noninvasive measurement of temperature distributions within the tumor and surrounding healthy tissues can be achieved with Proton Resonance Frequency Shift (PRFS) MR imaging methods (MRI). This method
offers some distinct advantages. It allows three dimensional measurements, and large
amounts of data can be acquired in a relatively short time in complex geometric
objects. Therefore, the clinical use of PRFS MRI as a temperature indicator can
greatly enhance such applications.
Figure 2.1 shows a block diagram of a MRI compatible radiofrequency (RF) heating system which has being used in hyperthermia clinical treatments in radiation
oncology department in Duke medical center. This diagram only shows one channel
of the system; the other three channels are similar to the one shown here. A HP
18
8647A signal generator generates the initial (—4 dBm) signal for the system. This
signal is then amplified to 19 dB after passing pre-amplifier and split by a power divider into 4 channels. Each channel has its own attenuator and phase shifter. After
the phase and amplitude of the signal are set, a high power amplifier amplifies the
signal up to a maximum power of 160 Watts. A circulator is placed after the amplifier
can isolate the amplifier from the rest of the channel to prevent any damage caused
by impedance mismatches. At the output of the channel, a dual directional coupler
taps off a portion of the forward and reflected power. These signals are monitored
using the vector voltmeter and a labview program on a computer. The whole hyperthermia system is housed in the MRI equipment room. The outputs of each channel
are connected to the patch panel in the MRI room and then to the annular phased
array antenna applicator using approximately 25 feet of low loss cables. The working
frequency of antenna applicator for deep-seeded hyperthermia is from 125 — 160 MHz
and the MR imaging frequency is 64 MHz. Therefore a band pass filter is required to
be placed between the circulator and the dual directional coupler. The band pass filter not only removes any low frequency noise which could corrupt the MR image, but
also removes any higher frequency noise to produce quite effective heating. Cleaning
up RF interference outside the intended 125 — 160 MHz bandwidth is a critical factor
to improve the performance of the hyperthermia heating system and temperature
monitoring system.
19
Pre-Amp 4-Way Power Divider
HP
Signal Generator
->- Same as channel 4
MRI
machine
LCF Power Amplifier Band Pass Filter
Attenuator Phase Shifter ^
Circujator ,
, Directional Coupler
<
Computer
Vector Voltmeter
Inputs from
other channels
Switch
Figure 2.1: A block diagram of the MRI compatible radiofrequency (RF) heating
system.
20
2.2
Introduction of Band Pass Filter Design
[This Section follows closely the paper to be submitted for publication:
Zhen Li, William D. Palmer and William T. Joines*, Multi-section Bandpass Filters
using Capacitively-loaded Transmission Lines, to be submitted to IEEE Transaction
on Microwave Theory and Techniques, 2008.]
At frequencies in the kilohertz or lower megahertz region, the change in phase
due to the finite propagation velocity of an electrical signal is usually so small as
to be considered negligible for most physical structures. At these frequencies the
networks are termed lumped element networks [36]. However, at higher frequencies such as frequency range from 50-500MHz, lumped element inductors usually
have internal resonances, and the distributed nature of a physical structure is taken
into consideration, leading to the well known transmission-line theory. Stub filters
(shorted or opened stubs separated by sections of line) are quite reliable and easy
to manufacture, but their physical size is a disadvantage at these frequencies. Stub
filters may be made very compact if open sections less than a quarter-wavelength are
replaced by equivalent capacitors and all quarter-wavelength sections are replaced
by CLC equivalent circuits. Then the inductors are replaced by the shortest possible sections of equivalent transmission line. The size reduction process is illustrated
by a series of design examples, starting with a bandpass filter at 200 MHz that
uses half-wavelength tapped stubs and has multiple resonant sections separated by
quarter-wavelength sections of transmission line. By using this technique the filter
21
area is reduced from 243.67 square inches to 5.99 square inches, an impressive factor
of about 40x! Theoretical results are verified by measurements.
A desired network response versus frequency is achieved for multi-section bandpass networks by relating the frequency selective or Q of individual sections to the
total frequency selectivity QT, denned by
QT
= -j^~,
h - J\
(2.1)
where /o = V/1/2 is the central frequency, and BW = / 2 — f\ is the 3-dB bandwidth.
Each section of the bandpass filter has its own frequency-selective Q, which is
computed as if it was the only section connected between source and load.
The
individual section Q's are related to the total QT of filter by:
Qk = ^Qr
/c = l,2,3...n,
(2.2)
where Qk is the kth frequency-selective section of an n-section network, g^ are dimensional element values that are selected to produce a desired network response, such
as, Butterworth (maximally-flat magnitude), Chebyshev (equal-ripple magnitude),
or Thomson (maximally-flat delay). The g^ values are tabulated for a number of
different responses [37], but for a Butterworth response they are given quite simply
by [38]:
(Ik — 1 \
2fe = 2 s i n f - ^ - jir
k = l,2,3...n
.
(2.3)
From Equation 2.2 and Equation 2.3,
(2k — 1 \
Qk = QT sin I - ^ - j n
22
k = l,2,3...n
.
(2.4)
And for a Butterworth response, the transducer loss ratio is given by,
£2.3
2n
Q
<~7
(2.5)
Filter Design Using Q Tapering of Sections
To design a band pass network using Q tapering, QT and /o are known in a typical
filter design. Thus if we know Qk in terms of the parameters of individual resonant
sections, then the design can be completed.
A universal definition for Q is [39] [40],
peak energy stored
Q = UJ0
average power lost
(2.6)
For a network described in terms of admittance Y = G + jB, applying Equation
2.6 yields,
Q =
u_dB_
2G~o\J
(2.7)
where G is the total shunt conductance. And for a network described in terms of
impedance Z = R + jX, Equation 2.6 yields
Q =
u dX
2Rdu
(2.8)
ui=uo
where R is the total series resistance.
In the following sections the foregoing method will be used to design different
versions of a band pass filter that progressively becomes smaller and smaller in size.
23
2.4
Half-wavelength Tapped-Stub Resonator
A tapped-stub resonator circuit is created by changing the connection point of a
stub on the main transmission line. Without changing the resonant frequency, the
Q of the resonator can be changed by changing the tapping point without changing
the length of the stub. Thus, the characteristic impedance of the stub may be set
to any convenient value since Q is controlled by the tapping point. The simplest
tapped-stub resonator is a quarter wavelength from end to end across the main line
with one of shunt stubs shorted to ground and the other open [41] as shown in Figure
2.2. The half-wavelength tapped-stub resonator replaces the short on the shorted
stub with a quarter wavelength open section of transmission line to create a virtual
short at the original point. Thus, the half-wavelength tapped-stub resonator has two
open stubs with one stub less than a quarter-wavelength and the other greater than
a quarter-wavelength. The half-wavelength tapped-stub resonator is shown in Figure
2.3. Open stub sections that are less than a quarter-wavelength may be replaced by
Figure 2.2: Quarter wavelength tapped-stub resonator.
24
^
J^i ^ J e i
Figure 2.3: Half wavelength tapped-stub resonator.
capacitors [42]. Because the half-wavelength tapped-stub resonator has open stubs
on both sides of the main transmission line, we may replace all of the stub on one
side and part of the stub on the other side by capacitors.
First, consider the half-wavelength tapped-stub resonator without capacitive loading. The total electrical length of it is:
0 1 + 0 2 = 7r—= 7r-£.
<^0
(2.9)
JO
To analyze the tapped-stub, we introduce a tapping factor k, which gives the
proportional length of the stub on each side of the main line where 0 < k < 1 such
that:
9i = k^-,
(2.10)
and from Equation 2.9,
#2 = ( 2 - f c ) | ^ .
Note that k = 0 represents an untapped half-wavelength open stub.
25
(2.11)
The Q of a half-wavelength tapped-stub resonator is derived from the node admittance of the half-wavelength tapped-stub in Figure 2.3 given by:
Y = Yx + Y2 + 2Y3 = 2Y0 + jY01 (tan 62 + tan 0X) = G + jB.
(2.12)
Using Equation 2.12 and Equation 2.7, we could get the Q of the half-wavelength
tapped-stub resonator:
•KYQI
..
7T
2
TtYr01
Q = 4Y sec
K— = 4F cos 2 fcf'
0 ~~~ ' 2
0
(2-13)
Note from Equation 2.13 that as k —> 0, Q —» ^ ^ and as A; —> 1, Q —> oo.
To design an ra = 3, half-wavelength tapped-stub filter which has Butterworth
response with QT = 10 and centered at / 0 = 200 MHz. Take all lines to be of
characteristic impedance ZQ = 50 Q. As shown in Figure 2.4, by using Equation
2.13, Equation 2.10 and Equation 2.11, we can get Q\ = Qz = 5 and Q2 = 10, thus
yields 6n = #13 = 66.651°, 02i = #23 = 113.349°, 6U = 73.725°and 622 = 106.275°.
The PUFF simulation result of it is shown in Figure 2.5. From the simulation,
BW = 211 - 191 = 20 MHz, /„ = V191 x 211 = 200 MHz and QT = 200/20 = 10.
01
012
0h3
0:'21
0:'22
023
Figure 2.4: A three section half wavelength tapped-stub resonator.
26
*" ]/^~
V
h""
\
'
i
S11
OZ 1 "
;
..V...J
CQ -10
\ i
CO
...A.i
V
-15
...L.L.L
-20
-25
150
/ i
/ i
160
170
180
190
{
T
1
200
i\
210
220
i
230
240
250
Frequency (MHz)
Figure 2.5: PUFF simulation of a three section half wavelength tapped-stub resonator.
If this filter is constructed as microstrip on 1/16 inch epoxy-glass substrate which
has 4.8 dielectric constant using 50-Ohm lines, the effective permittivity is 3.58 and
a half-wavelength at 200 MHz is 39.64 cm (15.61 inches). Therefore, this filter would
be at least 15.61 inches in length and width and take up a total circuit board area of
243.67 square inches. For most application it would be prohibitively large for use at
200 MHz. However, in this paper we will progressively reduce the physical size while
maintaining the desired performance.
27
2.5
Replacing t h e Open Stubs with Capacitors
As is known, the input admittance of an open-circuited section of transmission line
is capacitive if the section is less than a quarter wavelength, or Yin = jY0ta,n (—) =
j'Yotan#. For the half-wavelength tapped-stub resonator there are two open stubs
that may be replaced with capacitors. The shorter stub is replaced entirely by a
capacitor (Ci)
an
d the longer stub is replaced by a quarter-wavelength section of
transmission line and a capacitor (C2), as shown in Figure 2.6.
Figure 2.6: Half-wavelength tapped-stub resonator with capacitive loading.
2.5.1
Resonant Frequency and Q
Referring to Figure 2.6, the combination of Ci, C2 and the quarter-wavelength section
determine the resonant frequency and Q of the circuit. The total admittance at the
common node to ground in Figure 2.6 is:
y - y, + y, + 2n - 2Y0 + frft
+
Ym * * * + ^
* ° *' ,
*oi + JU^Cy tan6>d
28
(2.14)
where 6a = 2/0
f/-. At / = /o, &d = TT/2 and Equation 2.14 becomes:
Y*
r = 2y0 + .?'U)Ci- ^ 0 01
^2
= G + jB.
(2.15)
At resonance 5 = 0, and Equation 2.15 yields the resonant frequency as,
/o
(2.16)
2ir\/CiC2
The Q of the circuit in Figure 2.6 as determined from Equation 2.14, the total admittance at the common node to ground, and Equation 2.7 is [42]:
Q
~ 8Yv [1 + n\lc2 + C2
(2.17)
The first term ( f ^ 1 ) is the Q of an effective A/4 shorted stub, and the remaining
term (i%\f§;
is t h e
+ f ^c^)
Q contributed by d and C2. From Equation 2.17,
it is clear that Q may be controlled by the ratio of C\ to C2, and from Equation 2.16
the center frequency, /o, may be controlled by the product of C\ and C2. Thus, Q
and /o may be controlled independently.
Generally, we solve Equation 2.16 and Equation 2.17 for the product and ratio of
C\ and C2 as,
VC^~2 = ^ r ,
(2.18)
27T/o
and
ICi_2
C~2~K
.l + ,ll
+
2n[^-Q-l
(2.19)
Furthermore, solve for C\ and C2 as:
•K
1+ +2
• f "(^°-i
29
^ 01
2TT/ 0
(2.20)
Yn
01
Co =
-l + i /l + 27r(^g-f)J}
2TT/0'
(2.21)
In Figure 2.4 we replace the open stubs. The resulting circuit is shown in Figure 2.7.
Using Equation 2.18 and Equation 2.19 and let Y0i = Yo, we obtain all the capacitors
as: Cii = 45.32 pF, C21 = 5.59 pF, C12 = 69.24 pF, C22 = 3.66 pF, Cl3 = Cu and
C23 = C21. Simulation of this filter design using PUFF is shown in Figure 2.8. From
the simulation, BW = 212.7 - 192.7 = 20 MHz, f0 = ^192.7 x 212.7 = 202.5 MHz
and QT = 202.5/20 = 10.12.
Cl1 $
U21
Cl2i
/22
Cl3S
/23i
Figure 2.7: A three section half-wavelength tapped-stub resonator with capacitive
loading.
2.5.2
Replace A/4 Transmission Line by a Series Inductance
and Capacitors t o G r o u n d
The remaining A/4 section of transmission line between C\ and C2 may be replaced
by a series inductance with equal capacitors to ground on each end as shown in Figure
2.9. To prove this, compare the ABCD matrix of the A/4 transmission line with the
ABCD matrix of the shunt Co-series Lo-shunt Co equivalent circuit.
30
1
m\my~
-n
"i _,
r'
^
i
i
i
^/
X
/ \
J'X"
f\
\
CO -10
\
/
i
-20
-25
150
•
•
i
•
•
170
180
i
i
i
i
i
i
i
.A.i
i
/
L.\,-L
/
•
/
160
' ' |
S11
S21 -
i
1
190
200
210
220
230
X
j V
240
250
Frequency (MHz)
Figure 2.8: PUFF simulation of a three section half-wavelength tapped-stub resonator with capacitive loading.
>. 4
.r
1
i
Figure 2.9: A A/4 transmission line equivalent circuit: shunt Co-series Lo-shunt C0.
31
With 6d = 7 T / 2 / / / 0 , the ABCD matrix of the A/4 section is:
A
B
cos8d
jZ01sin9d
(2.22)
C
D
jY0i sin 9d
cos 6d
And the ABCD matrix of the CQLQCQ network is:
A
B
C
D
1 - cu2L0C0
jtoLo
(2.23)
2
juC0(2 - UJ L0CO)
1-
2
UJ L0C0
These two matrices are equal term by term at / = /o if u>o = 1/y/LoCo , and
UJQLQ — ZQI
(2.24)
=
UJQCQ
which is the design equation for determining L 0
an
d Co- We can get L 0 = 50/u)0 =
39.789 nH and C 0 = l/(50w 0 ) = 15.916 pF at 200 MHz. As shown in Figure 2.10, we
replace the remaining section in Figure 2.9. Then adding all capacitors in parallel,
we can get the new capacitances as shown in Figure 2.11, which are C'n = C\\ +
Co = 45.316 + 15.916 = 61.232 pF, C'21 = C 21 + C0 = 5.590 + 15.916 = 21.506 pF,
C'l2 = C12 + C0 = 69.238 + 15.916 = 85.154 pF and C'22 = C22 + C0 = 3.658+15.916 =
19.574 pF. Again C'n = C'u and C'23 = C21. The PUFF simulation results for this
filter design are shown in Figure 2.12. However, the simulated results show that the
response is not maximally-flat since BW = 208.6 - 194.8 = 13.8 MHz, f0 = 210.6
MHz and QT = 14.6. This filter does not meet our specifications because the Q
expressions for the individual resonant sections are now only approximately correct
since we added in the CQLQCQ circuit to the existing one. To use the resonant circuits
32
S5C,3
Cl2i
Co
Co
Co
•|R[
Lo
Lo
•iRf
Lo
•|RI
Co
Co
iRf
C 21
C22
Co
C 23
Figure 2.10: Replace A/4 transmission line by a series inductance and capacitors to
ground.
C11
a2 5E
Lo
ci3^E
Lo
Lo
C22
C'23
Figure 2.11: Add all capacitors in parallel in Figure 2.10.
33
now consisting of Cn in parallel with C21 and LQ in series, we must derive new
expressions for Qk of these resonant sections.
0—
; VT' i
••
-5
ST -10
1
! [ !\
!
\
^
. . _ . . . ! . . . , . i.j
-20
IN
i
150
\
/...J...V.J
-15
-25
\ \
r—J^H
0)
\""'\
i
160
170
180
190
i I
200
i
210
i
1
—
S11
—
bzi
•
L
M
i ^ i
220
230
240
250
Frequency (MHz)
Figure 2.12: PUFF simulation of A/4 transmission line in Figure 2.8 replaced by a
series inductance and capacitors to ground.
2.5.3
Derive New Expression for Q of Each Resonant Section
When the A/4 transmission line between C\ and Ci is replaced by its lumped CQLQCQ
equivalent circuit, the result is a capacitance C1 in parallel with the series connection
of L0 and C'2, where Cx = CQ + C\ and C'2 = C0 + C2, and this combination is in shunt
with the main line. Thus, the total admittance at the common node connection is,
Y = G+jB =
2Y0+JLUC[-
1
juLQ +
j + , - ( M c i + ^ - . ^ c , ^ ) - (225)
1 - u2L0C2
ju>C2
34
From Equation 2.25 the resonant frequency, at which 5 = 0, is:
^o = 27T/0 = W ^ - i ^ .
(2.26)
And the Q from Equation 2.25 and Equation 2.7 is,
From Equation 2.26 and Equation 2.27, with Y0 = 0.02 S, f0 = 200 MHz and L0 =
39.789 nH,
= 31.831Q x 10- 12 ,
(C[ + C'2) ( ^ ) = ^
(2.28)
and
^
^
2
=
U
2
L Q
=
^
x
1010
( 2
2 g )
Dividing Equation 2.28 by Equation 2.29 yields,
C[ = 22.508 x 10-12v/<2,
(2.30)
and substituting this result into Equation 2.28, we obtain,
C
> = (QYQ/.Y0) ~ C-
(2 31)
-
Using Equation 2.30 and Equation 2.31 the new capacitances are: C'n = 50.329 pF,
C'21 = 23.276 pF, C'l2 = 71.177 pF and C'22 = 20.500 pF. The resulting simulation of
this filter design using PUFF is shown Figure 2.13. From the simulation, the response
is maximally-flat again, BW = 212.6 - 192.7 = 19.9 MHz, / 0 = \/212.6 x 192.7 =
202.4 MHz and QT = 202.4/19.9 = 10.17.
35
•s
uA
w
\ j
....X...
:/..
t
j
I
-15
/I...
-20
Ji
-25
150
/i
160
170
180
190
i
S11
S21 -
•\
CO -10
i
J — '
,
200
/
210
,
—
•
•
•
•
•
i
i
i
i
i
.
i
—
i\ i
i
!
i
X
i
i
i X
220
230
240
250
Frequency (MHz)
Figure 2.13: PUFF simulation after using derived new expression for Q of each
resonant section.
36
2.5.4
Replace Remaining A/4 Transmission Line by a Series
Inductance and Capacitors to Ground
Till now, all transmission lines have been replaced with lumped elements except
the two 50—Ohm A/4 transmission lines between the resonant section. Continuing
the previous example, using the equivalent circuit represented in Equation 2.24 to
replace these two 50-Ohm A/4 transmission lines with lumped CLC elements, we
add the capacitances thus created to the new one as shown in Figure 2.14. The new
capacitances are C'n = C[3 = 50.329 + C0 = 66.245 pF and C'12 = 71.177 + 2C0 =
103.009 pF. The values of the other capacitors remain the same. The simulation
On 5
C'13^
_rvrv\
Lo
H
C'22
Figure 2.14: Replace all remaining A/4 transmission lines by a series inductance
and capacitors to ground.
results for this filter design are shown in Figure 2.15, the response is maximallyflat, BW = 211.6 - 192.3 = 19.3 MHz, /„ = V211.6 x 192.3 = 201.7 MHz and
QT = 201.7/19.3 = 10.45.
37
00
w
150
160
170
180
190
200
210
220
230
240
250
Frequency (MHz)
Figure 2.15: PUFF simulation of replacing all remaining A/4 transmission lines by
a series inductance and capacitors to ground.
38
2.5.5
Replace Inductors with t h e Shortest Transmission Line
Since lumped inductors may create design problems at 200 MHz due to internal
resonances, to solve this problem we replace each of the five 39.789 nH inductors
with the shortest possible length of transmission line. To show this, we can compare
the input impedance of inductance and a transmission line, both are terminated by
a same load as shown in Figure 2.16. For inductance terminated in a load ZL, the
input impedance is,
zL
Figure 2.16: The input impedance of inductance and a transmission line.
Zi = jcuL + ZL.
(2.32)
And for a section of transmission line of length lt and characteristic impedance Zot
terminated in the same load has the input impedance as,
Zi — Ziot
ZL + jZptk/v
Zot+jZLlt/v'
(2.33)
If ZL/Zot t&n cult/v is kept appreciably less than unity, then,
Zi = ZL + jZot ta,nu;lt/v = ZL+ ju>L.
(2.34)
When Equation 2.33 and Equation 2.34 are equal, we get,
L = (Zot/uj) ta,ncolt/v.
39
(2.35)
Thus to replace the inductance LQ = 39.789 nH with a section of transmission line
at 200 MHz, we choose Zot — 150 Ohms, then solve for lt as
lt =
(V/OJQ)
50
t a n - 1 (wLo/Zot) = 7.958 x lO" 10 — - = 2.653 x 1 0 _ 1 V
150
(2.36)
Using 1/16 inch epoxy-glass microstrip with dielectric constant of 4.8, the velocity
of propagation along the ZQt = 150 Ohm section is v = 3 x 10 8 /V3.069 = 1.712 x 108
m/s, and lt = 2.56 x 10" 10 x 1.712 x 108 = 0.0438 m = 4.38 cm = 1.73 inches. The
width of the Z$t line is u% = 0.152 mm = 0.006 inch. This filter design as shown
in Figure 2.17 was also simulated using PUFF, and the results are shown in Figure
2.18. From the simulation, the response is maximally-flat, BW = 213.5 — 193.5 = 20
^
C'21-
C'ii
^
C'12
C'22<
T
C'13
C23;
Figure 2.17: Replace inductors with the shortest transmission line.
MHz, /o = V193.5 x 213.5 = 203.25 MHz and QT = 203.25/20 = 10.16.
2.6
Results and Conclusion
This section describes the data collection for simulated and measured results. Measured data were collected from circuits, as shown in Figure 2.19, constructed in 5 x 3
40
CQ -10
CO -15
-20
-25
150
160
170
180
190
200
210
220
230
240
250
Frequency (MHz)
Figure 2.18: PUFF simulation of replacing inductors with the shortest transmission
line.
41
Figure 2.19: Designed n = 3 band pass filter.
in microstrip using G-10 Epoxy with a two sided 1-oz rolled copper cladding. The
relative dielectric constant was 4.2 and substrate thickness of (1/16) . The capacitors
(EIA0603) used were surface mounted multilayer ceramic capacitors (Panasonic, Inc).
Each capacitor had a thickness of 1.6 mm. Measured data was collected using the
Agilent Technologies E8362B network analyzer. The network analyzer was properly
calibrated. Simulated results were collected using computer aided design software
package for microwave integrated circuits called "PUFF". The modeled circuits were
also in a microstrip format with a dielectric constant of 4.2 and substrate thickness
of(1/16)".
2.6.1
Comparison of Measured and Modeled Results
To compare our theoretical results with measured and modeled results, a three section
half-wavelength tapped-stub filter with capacitive loading was created. Figure 2.20
42
X
l\
-15
/
/
/
If
:
1
1
i
;
i\
150
I
160
170
180
190
s
•
200
\
\
v
1
1
1
1
v
v
1
1
i
oc
IV ^
1
' It
r' 1' 1
'
Simulated S11
Simulated S21
Measured S11 .
Measured S21
Y
; ;1 - \
/
en
N
'
•
-
CD
•'"•
x
\
\
s
•
v :
V
N
l_i
1
210
220
230
I
240
250
Frequency (MHz)
Figure 2.20: Simulated and measured results of the designed board of n = 3 band
pass filter working at /o = 205 MHz.
shows measured and modeled data as a function of frequency using the capacitance
values as C'n = C'13 = 68 pF, C'12 = 100 pF, C'2l = C'2Z = 22 pF and C'22 = 20
pF. Note that there is a good agreement between modeled and measured results.
Both results show that the response is maximally-flat, BW = 19.3 MHz, /o = 205
MHz and QT = 10.6. Discrepancies between modeled and measured results can
be caused by the losses which are not included in the model such as the dielectric
losses, connector losses and capacitance losses. Also, the fact that all the lengths and
widths of transmission lines are exact in the simulation, whereas lengths and widths
are only approximate during manufacturing, causes some disparity between modeled
and measured results.
43
2.6.2
Discussion and Conclusion
By using those steps mentioned before, we successfully reduce the board size by a
factor of 40.68, from 243.67 square inches to 5.99 square inches. Comparing the design
version for each step, we find that in Figure 2.5 and Figure 2.8, the 3 — dB bandwidth
is 20 MHz and the simulated values of QT remains at the design value of 10. That
is because the correct expression for the individual Qk of each section was known
and used in the Q-tapering design. However, in Figure 2.12 the 3 — dB bandwidth
is 14 and QT becomes 14. The reason is because the Q expression for the individual
resonant sections is only approximately correct since we added in the CQLQCQ circuit
to the existing one. To use the resonant circuits now consisting of Cn in parallel
with C'2\ and L0 in series, new expression for Q of each individual resonant section
has been derived. By using the new expression, we can see that both the 3 — dB
bandwidth and the QT remain at the design values as shown in Figure 2.13. Then we
replaced the remaining two 50-Ohm, quarter-wavelength lines between each resonant
section with the equivalent CQLQCQ circuit and added the capacitances to the existing
ones. For this replacement we did not need to derive new expression for the Q of each
section, because this change does not change the Q. The Q of a quarter-wavelength,
ZQ line terminated in ZL is [39]
Q=l
ZQ
_ ZL_
ZL
ZQ
(2.37)
Since in this case ZL = ZQ, the transmission line section does not contribute any Q.
After transforming the transmission line section to the CQLQCQ equivalent by using
44
tdoLo = Z0 =
1/UJQCQ
and deriving the Q in accordance with Equation 2.7, we get
the result of Q as,
v
2
—
U)QCQZL
ZQ
_
Z>L
Z^
(2.38)
ZQ
Thus since Z0 = ZL, the transmission line and the lumped-element equivalent have
no selectivity even though the two expressions differ by the multiplying factors ir/8
and 1/2. Then in the last design step, all lumped inductors were replaced with the
shortest possible length of transmission lines to avoid internal resonances. A reduced
sized filter which satisfies all design values is achieved as shown in Figure 2.18.
Finally theoretical results are verified by measurements as shown in Figure 2.20.
By using this technique the filter area is reduced from 243.67 square inches to 5.99
square inches, an impressive factor of about 40x! And since the remaining segments
are quite narrow, 0.006 inch, a further reduction in area is easily achieved by zigzaging the lines or using serpentine lines. However there is a limit in size reduction,
since the adjacent lines should be kept approximately four substrate thickness apart.
2.7
Filter Design for M R I Compatible R F Hyperthermia System
The PUFF simulation results in frequency range from 20 MHz to 250 MHz of the
previous design, an n = 3, band pass filter which has Butterworth response with
QT = 10 and centered at /o = 200 MHz, are shown in Figure 2.21. From it, we can
45
see that the band pass filter successfully passes the signals around center frequency
/o = 200 MHz with a designed bandwidth of 20 MHz. However in the lower frequency
range such as / ^ 120 MHz, signals can not be totally rejected.
/*"«•». _
!
/
i/
v.'-
1
\
^.A
-5 -
r
U~—
IT
I
i
\
\
\
\
\
-20
•
S11
S21
40
60
r
/
\
\
\
\
\
\
\
\
W -15
20
i
j...
^ -10
CO
T3
-25
—
80
100
120
140
i
...J..
t
\
\
i
i
i
\
r
j
i
i
160
i 1
200
""""V"
\
\
220
240
Frequency (MHz)
Figure 2.21: The PUFF simulation results in frequency range from 20 MHz to 240
MHz of an n = 3 band pass filter which has Butterworth response with QT = 10 and
centered at / 0 = 200 MHz.
If such a band pass filter is used in the MRI compatible radiofrequency heating
system, the low frequency noise could completely corrupt the MR images. To solve
this problem, a high pass filter which works at the same central frequency as band pass
filter does is connected serially to it. Therefore, the noise either at the lower frequency
or at the higher frequency can be significantly reduced. For our MRI compatible
46
radiofrequency heating system, using the method we previously mentioned in this
chapter, and selecting the available capacitance in the market, we designed a n = 3
band pass filter which has Butterworth response with BW — 60MHz
and centered
at /o = 140 MHz. Then a n = 3 high pass filter working at / 0 = 140 MHz was
connected to the band pass filter.
Measured data were collected from circuits constructed in microstrip G-10 Epoxy
with a two sided 1-oz rolled copper cladding. The relative dielectric constant is 4.2 and
substrate thickness of (1/16)". The capacitors (EIA0402) used were surface mounted
multilayer ceramic capacitors manufactured by Panasonic, Inc. Each capacitor had
a thickness of 1 mm. They are mounted directly onto the surface of printed circuit
boards (PCBs). Measured data was collected using the Agilent Technologies E8362B
network analyzer. The network analyzer was properly calibrated. Simulated results
were collected using PUFF. The modeled circuits were also in a microstrip format
with a dielectric constant of 4.2 and substrate thickness of (1/16) . The simulation
results in PUFF are shown in Figure 2.22.
When a board is designed, a further reduction in area is easily achieved by zigzaging or serpentining the line. However there is a limit in size reduction, since the
adjacent lines should be kept approximately four substrate thickness apart, and since
some minimum area is needed for capacitors. A 5" x 3" board is built as shown in
Figure 2.23.
The measurement results are shown in Figure 2.24. Note that there is a excellent
47
Fl
= F2 : PLOT =
Points 500
Smith radius 1
f 119 9198 MHz
• Sll -15 85dB 77. 1°
XS21 -0 lldB -35. 1°
: LAYOUT
42
f
Tine
a
b
c
d
e
f
«
h
i
F4 : BOARD
zd
50.000 ft
fd 120.000 11Hz
er
4.800
h
1.590 mm
s
1000.000 mm
c
0.000 mm
Tab microstrip
f
Ii
to
M
%g•
6 6 6 666
3 1 . 0 sees
—
F3 : PARTS =
lumped 45pF
limped 68pF
tline 50ft 45°
lumped 110pF
lumped 120pF
tline 60ft 45°
tline 50ft 45°
tline S5ft 45"
tline 70ft 45°
=
3
file : FILTER5
•~w
.
j
^
—
!;
i
|S|
dB
-90
20
f MHz
200
Figure 2.22: PUFF simulation result of a n = 3 band pass filter which has Butterworth response with BW = 60 MHz and centered at /o = 140 MHz connected to a
n = 3 high pass filter which works at f0 = 140 MHz.
48
Figure 2.23: A designed board of n = 3 band pass filter connected with a n = 3
high pass filter, working at / 0 = 140 MHz.
agreement between modeled and measured results. Discrepancies between modeled
and measured results can be primarily attributed to losses not accounted for in the
model, such as dielectric losses, capacitance losses, and contact losses.
49
Marker: 1 of 3
Start
''-j £ j i»J
Marker 3 j 140.000000 MHz
Q
Marker 1
Marker 2
Marker 3
rZi PNA Series Network Anary.
Off
7-3 ;"J'-!.'J~. 5:25PM
Figure 2.24: Measured results of the designed board of n = 3 band pass filter
connected with a n = 3 high pass filter, working at /o = 140 MHz.
50
Chapter 3
3D Modeling for Clinical Hyperthermia
Treatments
[This Chapter follows closely the paper to be submitted for publication:
Zhen Li, Martin Vogel, Paolo F. Maccarini, Omar A. Arabe, Vadim Stakhursky, Devin
Crawford, Williams T. Joines*, and Paul R. Stauffer*, Modeling and Dosimetry
for Validation of a Commercial Hyperthermia Treatment Planning System, to be
submitted to Medical Physics Journal, 2008.]
3.1
Overview of 3D Modeling
Computational models of power depositions and temperature distributions in human
bodies have helped researchers to understand and improve the hyperthermia treatments significantly [43] [44] [45]. This chapter focuses on the development of computational models for characterizing power deposition and temperature distribution
patterns in a human body by a hyperthermia applicator. Before discussing about
how to develop those models, one question has to be answered first. Why one would
want to develop computational models for hyperthermia treatment in the first place?
From [1], the motivation for using computer-aided models arises for solving both
51
engineering and clinical problems.
From an engineering point of view, computational models are crucial in the design,
development and improvement of the hyperthermia applicators. Optimization is well
suited to computational models in a low cost manner since the time, effort and
expense spent on laboratory experiments can be reduced significantly. Meanwhile, in
clinical treatments, the present invasive technologies are impractically to make three
dimensional detailed SAR or temperature measurements throughout the treatment
region, especially for deep-seated tumors. Moreover, in terms of tumor size, location,
type, shape, and blood flow, etc., the treatment outcome varies from patient to
patient. Computational models can provide a method to predict the possibility of a
successful treatment for each specific patient or compare the effectiveness of various
applicators on a particular tumor site.
The extensive potential of computational models in hyperthermia has been best
summarized by the identification of four areas where modeling would play a role in
improving power delivery and evaluating resulting dosimetry. These four areas are
comparative, prospective, concurrent, and retrospective hyperthermia dosimetry [1].
The goal of comparative dosimetry is to compare the abilities of different hyperthermia applicators under the same clinical situation. Such simulations can be done using
standard patient models which only contain the most significant anatomic features
and electrical and thermal properties of each part of "typical" patients. Then major
characteristics of the power deposition for each applicator can be compared, there-
52
fore the guidelines for the use of one system over another can be established. On the
other hand, prospective dosimetry incorporates detailed information about one particular patient, such as the patient's anatomy, the expected blood perfusion, and the
power deposition. Such simulations are used to plan the treatment for one specific
patient. Treatment can be optimized by maximizing the tumor temperature distribution while minimizing the damage of surrounding normal tissue. In concurrent
dosimetry a feedback control system is established. First, a complete temperature
fields is calculated based on the measured temperatures at discrete locations during
the treatment. Then power deposition can be modified to improve the therapeutic
temperature rise in the tumor. In retrospective dosimetry, a complete temperature
fields profile is also inferred from the measured data, but the inference occurs after the
treatment. One can receive all the information about the meaningful clinical evaluations of the equipment's performance and the efficacy of the hyperthermia treatment
[46]. In this chapter, the author will show how simulations can benefit in the areas
of prospective dosimetry and retrospective dosimetry.
3.2
3.2.1
Mathematical Formulations
Power Deposition Modeling
As mentioned earlier, the first step process of modeling of hyperthermia treatment
is to compute the power deposition patterns produced in the body by the heating
53
source.
The foundation of EM theory lies in the four first-order partial differential Maxwell
equations. Only two of them are needed to uniquely define the electric and magnetic
field intensity. They are:
VxE
VxH
= -p—
(3.1)
dE
= e—+oE,
at
(3.2)
where E is the time-varying electric field intensity, H is the time-varying magnetic
field intensity, /J, is the permeability, e is the permittivity, and a is the electrical
conductivity.
Equation 3.1 and Equation 3.2 are also referred to as the time-domain form of
the Maxwell equations.
Our EM hyperthermia systems have sources which vary
harmonically in time. However, the propagation problem can be solved in a simplified
form in frequency domain as:
V x £ = jufiH
(3.3)
V x H = -jtoe*E,
(3.4)
where E is the complex amplitude of the electric field intensity, H is the complex
amplitude of the magnetic field intensity, e* = e + ja/cu is the complex permitivity
and u) is the radian frequency. In the electromagnetically induced hyperthermia, //
is a constant, but e and a of different tissue vary with the frequency [30][47][48][49].
To solve Equation 3.3 and Equation 3.4, one must know certain boundary conditions at interfaces between different tissues. Inside the body, when sources are
54
present on a boundary, the conditions on the electric and magnetic field intensity at
a tissue interface are:
h • (cj^i - e*2E2) = p
(3.5)
h x (Ei - E2) = 0
(3.6)
fix (H^
(3.7)
H2) = J
h • (fnHx - fi2H2) = 0,
(3.8)
where n is a unit vector normal to the interface, the subscripts distinguish the two
tissues at the interfaces of the boundary, p is the charge density and J is the surface
current. The conservation of charge is maintained through the continuity equation
as,
V • J = jujp.
3.2.2
(3.9)
Thermal Modeling
Once the absorbed power density or SAR has been found, the second step process
of modeling the hyperthermia treatment, which is to compute the temperature distribution due to the thermal conduction and blood flow, can be accomplished. The
information of absorbed power density can be used in conjunction with the appropriate heat transfer equation to calculate the temperature distributions [34].
In [50], Bowman has given an excellent discussion of the bioheat transfer equation
as related to hyperthermia, including descriptions of its derivation and underlying
55
assumptions. The bioheat transfer equation in differential form is:
Ptct
dT(r t)
^ ' = QP(r,t) + Qm(r,t) + V(fc • VT) - wbcb(T - Tb).
(3.10)
The definitions and units of the quantities are:
T(r, t)
r
— temperature of the tissue (°C) ;
=
spatia coordinates (m) ;
pt = density of tissue (kg/m 3 ) ;
ct,Cb = specific heat of tissue and blood, respectively (J/kg -° C) ;
Qp
= power absorbed per unit volume of tissue (W/m 3 ) ;
Qm
= power generated per unit volume of tissue by metabolic process (W/m 3 ) ;
k
=
thermal conductivity (W/m -° C) ;
wb
=
mass flow rate of blood per unit volume of tissue (kg/m 3 • s) ;
t
=
time (s) ;
Tb
= temperature of the arterial blood entering the control volume .
The term on the left describes the rate of change in the stored internal energy of the
tissue, and the term V(k • VT) describes heat transfer due to conduction. Because
the metabolic heat generation is generally much smaller than the external heat deposited, the term Qm can be neglected [51]. In Equation 3.10, the term WbCb(T — Tb)
is concerned with blood flow mechanisms which have been discussed by several researchers such as Bowman [50], Chen [52], and Weinbaum [53]. The term WbCb(T — Tb)
describes a large percentage of the blood flow effects in a simple manner under the
56
assumption that the blood enters the control volume at some arterial temperature TJ,
and then becomes equilibrium at the tissue temperature, meanwhile when the blood
leaves the control volume it carries away energy.
In our hyperthermia application, electromagnetic radiation is the external power
source. Therefore,
Qp(r,t) = a(r)\E(r,t)\2
(3.11)
where a = electrical conductivity (mho/m) and E(r, t) = electric field density (V/m).
3.2.3
Numerical Methods for Solving Maxwell Equations and
Bioheat Transfer Equation
Now after that the basic equations need to be solved have been discussed, the next
question to be answered is how to solve those equations. Since 1989, high-frequency
simulators to solve EM and bioheat problems have been on the market. In the past
twenty years, the rapid development of computer hardwares and new algorithms
makes it possible for software vendors to introduce many diverse electromagnetic
software packages [54]. There are several methods that have been used in commercial packages, such as finite difference methods, finite element method (FEM), finite
differences time-domain (FDTD), and moment method [34]. And based on [55], finite differences and finite elements are two methods chosen by most of researchers
for solving the bioheat transfer problems.
It is difficult to rank one of the method or commercial package as superior to oth57
ers, since each method or commercial package has its own strengths and weaknesses.
Most researchers choose FDTD or FEM to solve realistic hyperthermia problems.
Generally speaking, methods such as FDTD can solve larger problems with limited
memory, storage and computer time, but may have difficulty conforming to complex
curved surfaces. On the other hand, FEM is usually used to model complex structures
with curved boundaries, but it requires so much memory [1]. For years, FDTD is quite
adequate to simulate the homogeneous models with regular boundaries in order to
help engineers understand, develop and improve the system performances at the stage
of developing the hyperthermia applicator and to be used in the study of comparative thermal dosimetry. However when efforts move into treatment planning, more
complex nonhomogeneous models for specific patients must be implemented. As a
result many researchers feel that there are more and more advantages to choose FEM
to solve hyperthermia EM problems [56] [57] [58]. For example, when computational
realistic patient models are implemented, the anatomical and tissue complexities are
accommodated in a general way. Therefore, from a user's point of view, solving the
complex problems is just as easy as solving the simple problems. The other important
advantage of FEM is it can be easily used in conjunction with graphical systems such
as CT scans. In the following chapter, the author will show that how this information can be used to facilitate specific patient treatment planning. The disadvantages
of FEM compared to FDTD are: 1) there will be greater efforts on conforming the
complex nonhomogeneous models for specific patients and 2) greater computation
58
overhead [34]. However, nowadays the rapid development of high-speed computer
systems with a large memory provide us a good opportunity of choosing FEM based
software packages.
3.3
Ansoft Packages
A suite of 3D electromagnetic and thermodynamic simulation package is chosen for
our hyperthermia research purposes. The package from Ansoft corporation includes
High Frequency Structure Simulator (HFSS), ePhysics and a human body model.
HFSS is a commercial FEM solver for electromagnetic problems. It is one of the most
popular and powerful simulation tool used for the design of antennas, RF/microwave
components and high-frequency IC packages. The commercial software ePhysics , a
software designed for coupled thermal and stress analysis for electromagnetic applications, is used to simulate the temperature distribution. Once the HFSS simulation
is done, the electromagnetic losses in the model are known. These will serve as heat
sources for ePhysics through a dynamic link.
In this chapter, the author will show how to get the electromagnetic field results
from HFSS and how those results can be used by ePhysics to predict temperature
distributions as a function of time in the human body model which includes tumor
and the surrounding healthy tissue, taking into account blood perfusion and water
cooling. This will be compared with the results of patient treatments.
59
3.4
Electromagnetic Model for a Homogeneous Medium
As mentioned before, the ability to simulate hyperthermic treatments can help the
researchers to understand and improve hyperthermia therapy significantly. The role
of modeling becomes more important when the clinical treatments become more complex and delivering the heat only into the tumor region becomes more complicated.
In general, there are two steps in the simulation studies on hyperthermia research:
1) initial analysis based on simplified models for homogeneous medium, and 2) simulations on detailed complex models where as much information about the patient
as possible is included. Since 1980s, researchers in hyperthermia field started doing
simulations on simple homogeneous models, whose goal is to understand the basic
mechanisms of complicated processes. The homogenous models allow us to compare
the theory and the experiment which can be constructed in laboratory. For example,
in the following sections, we will see how well the theoretical predictions compare
with phantom experiments. These models also provide us a fundamental knowledge
on how more complex models including human body can be implemented.
3.4.1
Electromagnetic Model and Power Deposition in a Homogeneous Medium
The mini annular phased array (MAPA) applicator we used in clinical treatments
is based on the design in [14]. It consists eight copper foil strip dipole antennas
connected in parallel pairs and printed on the inner surface of a cylindrical plastic
60
shell. The tapered antennas are made of 0.03 mm copper foil. Each antenna pair is
fed by coax cables (RG-233/U) at the center of U-shaped elements and each cable
has a stub for impedance matching. Each antenna pair forms one separate channel
fed by a separate amplifier and phase shifter.
A water bolus, which is a closed
silicone membrane containing deionized water, is attached to the internal side of the
cylindrical plastic shell. Deionized water fills the whole space between the patient and
the inner side of the plastic cylinder. It works as a cooling device for patient's skin as
well as an impedance matching device for directing the RF waves into a patient. The
antennas are separated from deionized water by an insulating layer with thickness of
0.5 mm.
To build the electromagnetic model, the applicator with folded dipoles and feed
network was first drawn in a mechanical CAD program. Then the drawing file was
translated and imported into the electromagnetic simulator-HFSS. The MAPA is
coherently driven at 140 MHz [14]. Using a technique called pushed-excitations, the
amplitude and phase inputs into each dipole can be adjusted. A schematic diagram
in HFSS of a annular phased array limb applicator is shown in Figure 3.1. In the
simulation setups, 40 W power was applied at 140 MHz to each of four channels. The
relative phases (0° —180°) of first one channel, then two channels were investigated as
shown in Figure 3.2. Then the solution data were exported into a Matlab program,
which showed the position (*) and magnitude of local SAR maximum (SARmax),
and 50 percent of SARmax contours for each case, details are seen in Figure 3.3.
61
Figure 3.1: A schematic diagram in HFSS of a annular phased array limb applicator.
4 Channel Phases: 0,0,0,0
4 Channel Phases: 0, 0, SO, 0
4 Channel Phases: 0, 0,180,0
Figure 3.2: HFSS simulation results in the xy Plane with different 4 Channel Phases.
62
4 Channel Phases: 0,0,0,0
0.1
.
4 Channel Phases: 0,0,90,0
4 Channel Phases: 0,0,180,0
y4- Perimeter.pf Applicant
0.05
%
0
-0.05
-0.1
(0
d \ V.L/I / ;
X;
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t
o
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MaxSAR:24.330W*g
@C-0.002,-0.001)
0.5'MaxSaR:12.194Wftg
•
-0.05
0
0.05
xpos (m)
0.1
-0.1
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-0.05
-0.1
^ - P e r i m e t e r lot Applidatto.
,<b- 75%ApplicatorStze
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-0.1
-0.05
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xpos (m)
d
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-0.1
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0.1
xpos (m)
c
4 Channel Phases: 135,1350.0
0.1
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0.05
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o
c
MaxSAR:21.689WJkB
<3 (-0.008,-0.006)
0.5*MaxSaR:10.870WAg
*
•
0
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KM
,
-0.05 0
0.05
xpos (m)
b
0.1
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-0.05
-0.1
»
-0.05
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0~DS
xpos (m)
0~T
-0.1
-0.05
0
MaxSAR:9.733W*g
@t-0.045,-0.047)
O.S'MaxSaR:4.878Wfkc
0.05
0.1
xpos (m)
f
Figure 3.3: Matlab plots of hotspot regions in the xy plane with different 4 Channel
Phases.
63
3.4.2
Experiments of Heating a Gel Filled P h a n t o m
An important but often easily ignored consideration is how well the simulation results compare with the phantom experiments. Since 1999, systems measuring electric
fields within a phantom have been presented by several groups [15] [59] [60]. Other experiments aimed at examining specific absorption rates (SAR) pattern in a phantom
have been discussed [61] [62] [63]. In our study, we attempt to explore the control of
electric field distribution for our limb applicator when it is used in conjunction with
Proton Resonance Frequency Shift (PRFS) MR imaging methods (MRI).
A phantom constructed from gel (8.39% Tx-150, 15.79% Polyethylene, 74.92%
H2O, and 0.9% N a Cl) with the dielectric properties of muscle was placed concentrically in the MAPA applicator and placed within the GE 1.5T MRI system. For
effective matching, the space within the 23 cm diameter cylindrical applicator was
filled with water all around the 12 cm diameter phantom, held within an expandable
thin plastic membrane. An example MRI of the gel phantom is shown in Figure
3.4. During the experiments, 40 W power was applied for 2 minutes at 140 MHz to
each of four antennas. The relative phases (0° — 180°) of first one channel, then two
channels were investigated and compared with simulation results as shown in Figure
3.5. Power was left off for approximately 4 minutes between heat trials. PRFS gradient echo images with TR = 117 ms, TE = 20 ms, 128 x 128 matrix and 4 NEX,
were acquired by the MRI system before and after each power interval to determine
temperature changes due to RF power deposition.
64
F i g u r e 3.4: 12 cm diameter muscle equivalent phantom inside 23 cm diameter RF
applicator surrounded by water.
3.4.3
Results and Discussion
Figure 3.2 shows the HFSS simulation graphical outputs, where higher RF power
deposition (i.e. increased temperature) is shown in orange. To show the details of
the output information, we exported the solution data into a Matlab program. Figure
3.3 shows contour plots of where the RF power deposition is at least 50 percent of
the maximum value and the position (*) and magnitude of local SAR maximum
(SARmax). In the end, Figure 3.5 shows the actual relative temperature changes
in the gel phantom due to various settings of the MAPA. The greatest temperature
changes are shown in yellow in these images.
From simulated and measured data, we find that 1) at 140 MHz, SAR can be
adjusted to move a single 9 cm diameter focal hot spot around within 75 percent of the
array diameter by adjusting relative phase of four inputs, 2) local SAR is maximized
65
4 Channel Phases: 0,0, 0,0
4 Channel Phases: 45, 45, 0, 0
4 Channel Phases: 0,0,90,0
4 Channel Phases: 0,0,180, 0
4 Channel Phases: 90, 90, 0, 0
4 Channel Phases: 135,135, 0, 0
Figure 3.5: MRI PRFS imaging results showing relative temperature changes due
to each of the six settings of the RF applicator.
66
when all 4 inputs are in phase, 3) with four antennas in phase, the local SAR is
centered within the applicator with an maximum SAR (SARmax) of 24.3 W/kg at the
center and a full width at half maximum (FWWM) of approximately 9 cm diameter,
4) the SAR peak shifts away from the antenna(s) with increased phase. Further
increases in phase cause energy to split into two separate regions. 5) due to large air
bubble and asymmetry of the phantom, simulation and experimental results differ
when phase combinations are 0-0-180-0 and 135-135-0-0. In other cases, simulations
match experimental measurements well. Finally, after we fully understand the how to
control locating the hot spot in a homogeneous medium, our next step is to simulate
realistic heterogeneous human body model inside the antenna applicator.
3.5
3.5.1
Electromagnetic Model for a Heterogenous Medium
Electromagnetic Model and Power Deposition in a Patient Body Model
Next to investigate the detailed complex model, a geometric construction of a 3D patient model is required. Typically, this model has to be made by utilizing
computed tomography (CT) or other medical imaging modalities so that the model
can include all the information about each structure and target volume [64]. In CT
scan data, usually the information of patient anatomy is shown as pixel densities
[65]. For electromagnetic simulation purposes, a more common approach to build
67
the anatomical structure is to generate the contour manually or automatically [66].
Each 3-D image is a data collection of 2-D image files. On that 2-D plane, a number
of closed circuit contours define each type of tissues with a finite thickness. In the
department of radiation oncology in Duke medical center, a series of C++, MATLAB
and VB scripts have been developed by Dr. Vadim Stakhursky to draw contours of
individual patient anatomical structure. For example, an application to construct
the geometric structure through these contours of a patient's leg with sarcoma in it
is shown in Figure 3.6.
Figure 3.6: A anatomical reconstruction of a patient's leg with sarcoma inside. This
figure is provided by Dr. Vadim.
Such a patient model is reconstructed from CT data where the voxel size is of
68
order of 1 mm 3 . Therefore, the patient body model can be very accurate. However,
during electromagnetic simulation process such a detailed model requires too much
memory and simulation time. To solve this problem in an early stage of research, a
recently released 300-component human body model is called by the EM simulator.
The human body model is placed inside an annular phased array limb applicator
inside MRI machine as shown in Figure 3.7. Therefore, this model is not in free
space but in a metal cylinder with open ends. The cables which feed the antennas
and their tuning stubs are present in Figure 3.7. This model requires a lot of memory.
Therefore, we supplied two additional models with a modest level of de-featuring,
removing details smaller than 2 mm or smaller than 4 mm respectively, which did
not make any differences in terms of simulation results in interested region. For this
application, to reduce simulation time, all non-essential body components are turned
off. A detailed lower leg inside of MAPA is shown in Figure 3.8 where calf muscle is in
red, shin muscle is in orange, fibula and tibia bones are in gray. A geometrical model
of the sarcoma is created from a patient's CT data in Figure 3.6, then the geometry
information is reduced to increase the simulation time as shown in Figure 3.9. Then
the tumor volume is inserted into the human body model at the appropriate location
compared with the CT scan of that patient as shown in Figure 3.10.
From [67] [68], the dielectric properties of body at frequency 140 MHz are shown
in Table 3.1. After the electrical properties are defined for each component of the
model, the EM simulation is run. The FEM based EM simulator first produces a
69
Figure 3.7: A schematic diagram in HFSS of a human body being placed inside an
annular phased array limb applicator inside MRI machine.
Figure 3.8: A detailed schematic diagram in HFSS of a lower leg placed inside an
annular phased array limb applicator.
(a)
(b)
Figure 3.9: (a). An original geometry of tumor reconstructed from a patient's CT
scan. (b). Reduced geometry information of the tumor.
71
Figure 3.10: A detailed schematic diagram in HFSS of a lower leg with tumor
inserted at the appropriate location compared with the CT scan of that patient
placed inside an annular phased array limb applicator.
72
Tissue
Relative Permittivity
Conductivity [S/m]
Muscle
63.64
0.77
Bone
25.86
0.18
Marrow
6.2
0.024
Skin
63.5
0.53
Blood
72.05
1.26
Tumor
74
0.89
40
0.4
Rest (high water content
but includes some fat)
Table 3.1: Material dielectric properties.
tetrahedra mesh for each model component using an adaptive meshing algorithm.
This algorithm automatically adds more tetrahedra to regions experiencing large
changes in the electric and magnetic field quantities being solved. Once the mesh
is complete, the field solver solves Maxwell's equations for each tetrahedron. The
solved 3D EM field model is then linked to the 3D thermodynamic solver. Data
linking allows changes in the EM model, for example amplitudes and phases input
into the dipole pairs, to be automatically updated in the 3D FEM thermodynamic
model. The resulting field quantities are then used to produce the SAR inputs in the
thermodynamic simulator. From the simulation, when the four inputs are in phase,
the E field distribution and local SAR is concentric within the applicator are shown
73
in Figure 3.11.
son r
n
• , . "
&
"
i
'
:
' '
'
n
—-S-X .,
./'
T.S003H.MI
(.soaoc-cai
/**''
'•-\
\
3.eeoos>oai
L•
Breo*-«oi
fr
l.BCQSatCOl
1
,;
•>''
:
1
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• 1
.V
\,
\
x /
.'"/
< * * , —•;=>' '
>
s
•
(a)
^
-
—
.
.
(b)
Figure 3.11: (a). E field distribution (b). SAR distribution when four inputs are
in phase.
3.5.2
Temperature Distribution in a Patient Body Model
After the HFSS simulation is done, the electromagnetic losses in the model are known.
These will serve as heat sources for ePhysics through a dynamic link as shown in
Figure 3.12. Since,
MTWFAT
E
SAR=°W W
+\\2
(W/kg),
(3.12)
where a is electrical conductivity (S/m) and E(r,i) is electric field density (V/m).
Then combined with Equation 3.11, neglected the term Qm in Equation 3.10, the
Bowman bioheat equation becomes as,
dT(r,t)
= k-V2Tpc- dt
ppbcbF(T -Tb)+p74
SAR,
(3.13)
where T is temperature (°C), t is time (s), p is tissue density (kg/m 3 ), k is thermal
conductivity (W/(m-K)), c is the tissue specific heat (J/(kg-K)), F is the blood flow
rate or perfusion (m 3 /(kg-s)), and the subscript "b" refers to blood. Therefore the
SAR data from the electromagnetic simulator can be "linked" to a thermodynamic
simulator and the bioheat transfer equation is solved for changes in temperature.
This energy balance Equation 3.13 relates the rise in temperature over time at a
given region of interest to the heat inputs (power deposition or SAR) and heat losses
from thermal conduction and convection (blood perfusion).
In solving Equation 3.13, five sets of variables must be specifies. There are: 1)
tissue thermalphysical properties such as thermal conductivity^), specific heat(c),
specific mass(/9), 2) blood perfusion values to the various normal tissues and to the
tumors, 3) initial and thermal boundary conditions for the thermal field, 4) power
deposition pattern, which can be obtained by pointing ePhysics to the HFSS project
and 5) during what time the RF signal is on and with what relative strength to run
the simulation.
Of the three thermal parameters, mass density is probably the most accurate,
followed by specific heat. These are largely based on their chemical composition,
which is well known. The specific heat of the tumor is based on two data points,
only three percent apart, for fibrosis and adenocarcinoma. The thermal conductivity
has more uncertainty [69] [70] [71]. For instance, for muscle on source lists 0.38 and
another lists 0.45-0.54. So the chosen value of 0.45 has an uncertainty of more than
75
10 percent. Marrow has been assumed to be similar to muscle, since no reference
could be found. The thermal conductivity of the tumor is based on two data points,
only two percent apart: one for a sarcoma in a hamster and one for human colon
cancer. The thermal conductivity of the rest of the leg is an estimate, based on the
fact that that of fat is only 0.2.
When setting up the ePhysics project, we can point to the HFSS project, and
ePhysics will get the geometry information. The thermodynamic simulator uses the
same 3D applicator-body model as the EM simulator. A mesh is produced and the
temperature changes within each tetrahedron as a function of time are derived. No
special operations are needed.
Blood perfusion rate is the rate at which blood perfuses to different organs varies
widely. From [72], we can get the perfusion values of different organs as shown in
Table 3.3. Basically, the higher blood perfusion rate of the tissue is, the greater the
cooling effect. The differences between the perfusion rate of the normal tissues and
that of tumors help us to heat tumors without causing thermal damage to surrounding
normal tissues. Studies on blood perfusion in tumors show that the value varies
significantly with type, phase, temperature and the size of the tumor [73] [74] [75].
But no value for human tumor, especially our patient's particular sarcoma, could
be found. We assume that the tumor gets a little less blood flow than muscle does.
Not unreasonable, since muscle needs a lot of blood to facilitate the cooling effect.
Also as researchers already know, blood perfusion rate depends on a wide variety
76
Lin&
1. Electromagnetics
(E,H fields)
2. Thermodynamics
(temperatures)
.Tumor (green)
(Tumor generated from CT data)
^"^^l'K^^^^^^^^^ jJ "/'"'•'-'' — D e r m i s (orange)
A
Tibia & fibula
(grey)
i
r
i
Applicator dipole pairs
(Lucite platform Sfeed network not shown)
uscles (red)
Grey area defeatured to reduce
ZJ
LA
Figure 3.12: Simulation strategy: Step 1: 3D FEM EM simulator-HFSS solves
for field quantities in area of interest. Step 2: 3D FEM thermodynamic simulator-ePhysics takes field inputs and provides temperature maps by solving bio-heat transfer
equation in area of interest.
77
Tissue
Mass Density
Thermal Conductivity
Specific Heat
[kg/m3]
[W/(m°C)\
[W/(kg°C)]
Muscle
1047
0.45
3550
Bone
1990
0.29
970
Marrow
1040
0.45
3550
Skin
1125
0.31
3000
Blood
1058
0.49
3550
Tumor
1047
0.55
3560
1020
0.4
3200
Rest (high water content
but includes some fat)
Table 3.2: Material thermal properties.
78
of factors, including some local factors which are pH, temperature, and O2 of the
tissue, and some external factors which directly or indirectly affect local flow such
as hormones, heart rate, blood pressure, and skin temperature. In all these factors,
the effect of local tissue temperature on muscle perfusion is the easiest to study. To
provide a more realistic model of variable tissue perfusion during heat treatments,
a temperature dependent perfusion model was created based on perfusion data of a
dog's prostate from the CRC Handbook of Thermal Engineering.
According to the
model, the perfusion F in Equation 3 was multiplied by a temperature-dependent
factor ranging from 1 to 1.52. The temperature dependent perfusion model was used
to account for the clinical observation that perfusion increases in response to gentle
heating. In addition, the perfusion value for the skin layer was assumed to increase
by a factor of five when the skin is warmed. However, due to the overall mass of the
skin, this additional perfusion had little effect on the simulation results.
It has been demonstrated that patient tumors can be heated non-invasively and
with good localization using a phased-array applicator with four antennas depositing
RF energy at 140 MHz. When used in conjunction with Proton Resonance Frequency Shift (PRFS) MR imaging methods (MRI), patient heating within the tumor
and surrounding healthy tissue can be monitored in real time during hyperthermia
treatment. An example of one such treatment is shown in Figure 3.13. The simulated
temperature distribution is compared with the MR imaging as shown in Figure 3.14.
79
Tissue
Perfusion cm3blood/(second -cm? tissue)
Muscle
4.17 x 10"4
Bone
3.33 x 10- 4
Marrow
not found, assume same as muscle
Skin
4 x 10 -4 , but five times larger when warm
Tumor
3 x 10~4, not found, assume a little less than other organs
Rest (high water content
but includes some fat)
Assume same as muscle
Table 3.3: Perfusion.
(a)
(b)
Figure 3.13: (a). Anatomic MRI of a patient's lower leg. (b). Baseline temperature
change map after 4 minutes of imaging without application of heat, temperatures in
the leg have remained stable.
80
(a)
(b)
Figure 3.14: (a). Simulated temperature field distribution,
(b). Temperature
change map at approximately 15 minutes into treatment, heat is focused in tumor
region, but more so on opposite side of leg.
81
3.5.3
Simulated Results and Discussion
Patient T r e a t m e n t : C a s e I
The first case was used as a baseline to determine the correlation between measurement and simulation. Two in situ probes were used. The first was located centrally
in tumor at the upper right and the second was located in healthy tissue to the left of
center in the leg. During the first 18 minutes of treatment, the four dipole pairs were
driven with equal amplitude and phase at 140 MHz. As expected, this resulted in
a beam that was focused centrally in the roughly cylindrical volume of interest and
heated the surrounding tissue almost equally, except as modified by heterogeneous
electrical and thermal tissue properties. Both the healthy tissue and malignant tissue
were heated. This behavior is clearly shown in the MRI time sequence in Figure 3.14.
In Figure 3.15, the temperature data for the in situ probes is compared to the simulation results. Here, the perfusion values shown in Table 3.3. and the temperature
dependent model were used in the simulation. A high correlation between simulation
and measurement was found for both the tumor and the healthy tissue. These results
were encouraging and the investigators were able to proceed to a subsequent, more
complex clinical trial.
Patient Treatment: Case II
In the second clinical study, an attempt was made to maintain a constant temperature
rise in tissue around the in-situ "tumor" probe by adjusting the input power to the
82
0
2
4
6
8
10
Time (min)
12
14
16
18
Figure 3.15: Patient Treatment Case I: 18 minutes with equal phases, equal powers. Simulation vs. Measurement: General correlation of heating trend but poor
agreement found between simulated and measured results in both the tumor and the
healthy tissue when fixed perfusion rate assumed in the simulation.
83
dipole pairs up and down during the treatment. The four dipole pairs were driven
with equal power and phase. For the first two minutes, thirty watts were applied to
each of the four dipole pairs. From minutes two to five, twenty watts were applied,
and so on as indicated in Figure 3.16, in an attempt to maintain constant temperature
of the tumor. After the treatment, the power changes required to maintain steady
temperatures were simulated. As shown in Figure 3.16, there is fairly tight correlation
between measurement and simulation for the first ten minutes but after that, the
curves begin to diverge.
After studying the data and their sensitivity to various parameters, it was postulated that the effect of perfusion was still being under-estimated, even with the
temperature dependence mentioned earlier. Subsequent simulation studies were performed to investigate this.
Since the sensitivity study strongly hinted that the perfusion values were too low
and since there was not enough information to include detailed modeling of complex
arteries and veins during this trial, an iterative series of simulations was conducted
with increasing perfusion factors. A marked improvement in the correlation in these
two cases was observed using a perfusion value that was double the initial value. Both
cases were re-simulated with the new perfusion factors and compared to the measured
results. As shown in Figure 3.17, both cases demonstrated a marked improvement in
the correlation of simulated and measured data.
84
Time (min)
Figure 3.16: Patient Treatment Case II : 25 minutes with variable power; equal
phases. Measurement vs. simulation. Power inputs were varied to maintain a constant temperature in tumor. Poor correlation after first 8 minutes of heating was
thought to be due to assumption of fixed perfusion during the heat treatment.
85
Temperature Change in Tumor and Muscle
Temperature Change in Tumor
10
15
Time (min)
Case 11
Case I
Figure 3.17: The effect of perfusion: doubling the tissue perfusion factor in patient
treatment case I and II yields better correlation between measurement and simulation
for both clinical trials.
86
Discussion
A number of investigative pathways are renewing interest in adjuvant mild hyperthermia in the fight against cancer. Critical among these is the development of simulation
tools that allow clinicians the opportunity to optimize the heat dosage and prevent
patient hot spots. As argued in THE LANCET Oncology (August, 2002), "The
potential to control power distributions in vivo has been significantly improved by
the development of planning systems and other modeling tools." These simulation
tools are also being used to design new applicators and train the next generation of
medical researchers.
To achieve these goals, two steps are required. The first step is to determine
the E field distribution in heterogeneous tissue, which, when coupled with respective
tissue properties, determines the power deposited per unit volume (or unit mass)
(SAR). Secondly, using the knowledge of spatial and time dependent SAR distribution, coupled with the thermal properties, one can predict the transient and steady
state temperature distributions. Ideally, we need accurate patient specific anatomic
and physiologic tissue models, and complete understanding of the electrical and thermal properties of malignant and surrounding normal tissues. Clearly, a very complex
model is required. However, some of the critical information is not completely known,
such as blood perfusion. Studies on blood perfusion in tumors show that the value
varies significantly with tissue type, as well as temperature and other physiologic
conditions [75]. But no specific value for human tumor can be identified accurately
87
in advance. Of all these factors, the effect of local tissue temperature on muscle
perfusion is the easiest to study. Research on that has been done by different groups.
The information we are using for the temperature dependence of blood perfusion is in
the CRC Handbook of Thermal Engineering. It lists a couple of multiplication factors
for several temperatures for dogs' prostate. The initial perfusion increased 17% when
temperature exceeded 39.6°C, and 52% when temperature reached 41.7°C. For skin,
the perfusion increases by a factor of five when the skin is warmed. We also included
this perfusion increase in the skin in our simulations. However, that turned out to
have little effect on the tumor temperatures, because of the relatively small volume
of the skin.
Conclusions
In this study, a novel coupled electromagnetic and thermal simulation procedure
is described that couples 3D FEM electromagnetic and thermodynamic simulators
with accurate anatomic geometry and corresponding tissue properties contained in an
advanced human body model. An assumption of temperature dependent blood perfusion has been investigated. Two clinical hyperthermia treatments of an advanced
soft tissue sarcoma of the leg are simulated and results compared to simulations. The
comparison of simulated and measured thermal data are shown to have a high degree
of correlation if blood perfusion is considered, proving the importance of perfusion
modeling for clinical applications.
88
Chapter 4
Optimized Hyperthermia Treatment
Planning
4.1
Overview of Treatment Planning
Treatment planning system which emphasizes on the optimization of SAR or temperature distribution has been used for regional hyperthermia patients [76] [77]. These
studies are not only important for the design of better radiofrequency heating equipments, but also important when choosing appropriate applicator settings for an individual patient. Therefore computerized optimization becomes an extremely important part of each patient treatment when our complex multiple channel limb
applicator is used. Computerized optimization simulation results are able to suggest
a plan to maximize thermal dosage in the tumor region while minimize patient pain.
By using HFSS or ePhysics, both E field and SAR distributions and temperature
distribution can be optimized. Multiple targets can be assigned individual heating
priorities, and sensitive regions can be specified. In the following examples, two locations, one is in the tumor region the other is in the normal tissue, are selected. The
simulation results in these two locations are compared with the experiment results.
89
4.2
Procedures to Optimize the Antenna Settings
How can simulations tell the technician in advance how to drive the antennas? Drive
one channel first and find the phase that puts most field in the tumor as shown
in Figure 4.1. Then repeat for channel 2, 3 and 4. The combination of phases
obtained with this approach will be the one where the fields from the antennas add
constructively in the tumor, resulting in the highest SAR. In this case antenna we
Figure 4.1: Drive one channel first and find the phase that puts most field in the
tumor.
found the best setups for the phases are: Channel 1: 0°, Channel 2: 70°, Channel
3: 90°, and Channel 4: 5°. As we can notice in Figure 4.2 that E field is strongest
in and near the tumor. The absorbed power depends on the square of E, multiplied
by the conductivity. The tumor has a conductivity of 1 S/m while muscle has 0.72
90
Figure 4.2: E field distribution when phases of each channel are optimized: Channel
1: 0°, Channel 2: 70°, Channel 3: 90°, and Channel 4: 5°.
S/m at this frequency. Add to this the fact that the muscle has more blood perfusion
than the tumor and it becomes obvious that the tumor will get much hotter than the
healthy tissue. Figure 4.3 was generated with the best setting of phases: 0-70-90-5
and with power level 30 W (applied in clinical test).
The phase setup: 0-30-60-0 is the optimized setup we got experimentally during
the treatment. From simulation in Figure 4.4, we can see that after 7.5 minutes, if
we reduce the power from 28 W to 16.5 W. We could keep 47 °C in the tumor, and
42 °C in normal tissue.
91
Figure 4.3: SAR distribution when phases of each channel are optimized: Channel
1: 0°, Channel 2: 75°, Channel 3: 95°, and Channel 4: 5°.
Simulated Temperature in Tumor and Musole with Phase Setup as (WO/WO
50
48
^ ^ ^ ™ Temperature in Muscle
^ — Temperature in Tumor
! jf***\
: ~ 46
I 42
40
38
36
/
"J\
J
I
1 | !
;
j
;
|
i
i
20
i
25
\ \ \ \
V
i
i
10
15
Time (min)
Figure 4.4: Phases optimized experimentally.
92
4.3
Results and Discussion
Using simulation, we can find that the 0-70-90-5 setup will get better result. Figure
4.5 shows after 6.3 minutes, a shorter time than before, we can reduce the power
from 28 W to 15.1 W, a lower power than before. We are able to keep 47.5 °C in
the tumor, and 40 °C in normal tissue (was 42 °C in the experimentally optimized
case). Less power is used, and less energy is absorbed in the normal tissue.
Simulated Temperature in tumor and Muscle with Phase Setup as 0/70/9O'5
Time <min)
Figure 4.5: Phases optimized with HFSS.
This optimization procedure involves a complicated set of simulations. After we
assigned tissue properties for each part, calculated the electromagnetic field inside the
body for each settings for the limb applicator, the optimized SAR and temperature in
the tumor target and the surrounding healthy tissue can be obtained. This optimized
simulation results can be used to improve the probability of a successful treatment
for an individual patient. Moreover, a program made by Dr. Kung-Shan Cheng is
93
able to use MRI temperature images as a feedback control to correct the pre-setups
in real time. This method successfully reduces the time required for the controller to
steer the "hot spots" to the target tissue.
With the help of development of simulation tools and programs, one hopes that
one day the modeling is able to provide the pretreatment planning for individual
patient with a very high level of detail, accuracy and reliability.
94
Chapter 5
Wide-Band Input Impedance Matching
Circuit Design for a Hyperthermia System
[This Chapter follows closely the paper to be submitted for publication:
Williams T. Joines*, Zhen Li, Paolo F. Maccarini, and Paul R. Stauffer, Wide-Band
Impedance Matching of a Real Source to a Complex Load Using Lumped and Distributed Elements, to be submitted to IEEE Transactions on Microwave Theory and
Techniques, 2008.]
5.1
Introduction
Impedance matching antennas to maximize the transmitted or received power is a
frequently occurring problem that relies upon design, simulation and experimental
measurements to find a suitable solution. The amount of power radiated from an
annular phased-array applicator is load dependent, because the input impedance of
each channel of the applicator depends on the component and the geometry of the
material placed inside. If the antenna impedance is not close to the 50 Ohms, then
there is an impedance mismatch and part of the energy sent to the antenna is reflected
back into the system. Theoretically, to avoid reflection the input impedance of each
95
antenna pair should be as close as possible to 50 Ohms at the operating frequency of
140 MHz.
In our present application we have measured the complex input impedance (using
a vector network analyzer) to each of four pairs of dipole antennas within an annular
phased array under various load conditions. This array creates microwave-induced
hyperthermia for cancer therapy, and the various loads are the legs of volunteer test
subjects inserted into a region near the middle of the annular array.
As an impedance-matching element, a single A/4 transformer is broader in bandwidth than the stub tuners that are sometimes used in similar applications. Bandwidth is the frequency range, including the operating frequency, over which reflected
power is acceptably low. Maximizing the bandwidth is important because changing
load conditions might otherwise shift the range of low reflected power to a different
operating frequency. Multiple A/4 transformers would extend the impedance match
over even greater bandwidths. However, cascaded A/4 transformers, or even a single
A/4 transformer, would be prohibitively long at lower operating frequencies.
In our present application the operating frequency is centered at / = 140 MHz,
and the wavelength in air would be 214.29 cm. Thus, a quarter wavelength would
be 53.57 cm, or 21.10 inches, and to accommodate this length would be impractical
in most applications.
To reduce the size and retain the broadband properties of
the A/4 transformer we simulate its behavior by using more compact structures.
Specifically, we replace the A/4 transformer with a network of three lumped elements,
96
inductance (L) and capacitance (C). To achieve an even greater bandwidth, two
A/4 transformers are connected in cascade and replace with five lumped elements.
Next, the lumped elements are replaced with equivalent segments of transmission
line that are much less than A/4 in length. These equivalent replacements, from A/4
transmission lines to lumped L — C to small-length segments of transmission line, are
made to reduce the size of the impedance-matching network while maintaining the
broadband performance that would be obtained if we did use A/4 transformers.
5.2
Antenna Input Impedance Measurements
The input impedance to each of the four antenna pairs of MAPA is not well matched
to the 50 Ohms coaxial cables at 140 MHz. Furthermore, they vary from patient to
patient and with the position of the patient's limb placed inside the MAPA.
To start the broadband impedance matching process, we need to measure the
complex input impedance to each of the four pairs of dipole antennas within MAPA.
Since each channel has been connected to the amplifiers via 50 ohms coaxial cables,
which were soldered in the middle of each antenna pairs. We are unable to perform
a calibration directly at the input of antenna pairs. However by connecting a short
calibration standard at the input of each antenna pairs, we are able to know the exact
length of each additional coaxial cable. Then using port extensions to compensate for
the time delay (phase shift), and optionally the loss, caused by each coaxial cables,
we electrically move the measurement reference plane right to the middle of each
97
Subject
Test Subject 1
Test Subject 2
Test Subject 3
Test Subject 4
Test Subject 5
Antenna Pair
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
Ant 1 average
Ant 2 average
Ant 3 average
Ant 4 average
Grand average
Input Impedance (Q,)
15.4 + j 10.7 = 18.75 Z 34.79
10.4 + j 8.08 = 13.17 Z 37.84
16.4 + j 1.41 = 16.46 Z 4.91
28.5 + j 9.09 = 29.91 Z 17.69
10.9 + j 14.7 = 18.30 Z 53.44
11.1 + j 9.77 = 14.79 Z 41.35
14.7 + j 3.18 = 15.04 Z 12.21
20.9 + j 4.76 = 21.44 Z 12.83
16.7 + j 13.6 = 21.54 Z 39.16
14.6 + j 9.00 = 17.15 Z 31.65
13.9 + j 7.33 = 15.71 Z 27.80
17.1 + j 7 . 1 6 = 18.54 Z 22.72
16.2 + j 11.6 = 19.92 Z 35.60
11.0 + j 5.89= 12.48 Z 28.17
11.6 + j 4 . 2 4 = 12.35 Z 20.08
14.1 + j 3.82 = 14.6 Z 15.16
8.05 + j 10.5 = 13.23 Z 52.52
8.49 + j 5.47= 10.10 Z 32.79
11.7 + j 8.51 = 14.47 Z 36.03
11.1 + j 9.25 = 14.45 Z 39.81
13.4 + j 12.54 = 18.35 Z 43.10
11.18 + j 7.64 = 13.54 Z 34.36
13.90 + j 5.12 = 14.81 Z 20.21
18.40 + j 7.30 = 19.80 Z 21.64
14.43 + j 8.27 = 16.63 Z 29.83
Table 5.1: Antenna input impedance measurements.
antenna pair.
To produce the various load conditions that would be caused by different patients
and different limb sizes and positions, the legs of five volunteer test subjects were
inserted into a region near the middle of the MAPA, and the input impedance of
each antenna pair for each subject was measured at 140 MHz as shown in Table 5.1.
98
5.3
Theory
5.3.1
Lumped Element Circuits T h a t Are Equivalent t o a
Quarter Wavelength Transformer
As mentioned in Chapter 2.5.2, a A/4 transmission line is equivalent to the lumped
element circuit as shown Figure 5.1 when design Equation 2.24 is satisfied.
This
design equation also relates the other three element circuits in (c), (d) and (e) of
Figure 5.1 to the A/4 transmission line by making all of the ABCD matrices equal at
/ = /o- The LC networks in Figure 5.1 may be used as direct replacements for the
A/4 transformer if the frequency is not too high, or the LC elements may be replaced
by appropriate transmission line segments that are less than A/4 in length.
Note that the five input impedances to each antenna pair are averaged, and the
grand average of all input impedances is taken as the bottom line. This impedance,
14.43+j'8.27 ft, will be the load impedance (ZL) for any impedance-matching network
that has a series reactance {UJQL or 1/UQC)
as the last element nearest the load.
This allows the value of the last reactive element to be decreased by the amount
of the load reactance (j'8.27 Q). Likewise, if the last element of the impedancematching network is in parallel with the load, then ZL should be inverted to become
YL = 1/ZL
= 1/(14.43 + J8.27Q).
This yields YL = 0.052166 - jO.0298975 =
l/19.169fi + 1/J33.448Q, which represents the same load (14.43+ J8.27Q) expressed
as a resistance (19.169f2) in parallel with an inductive reactance (J33.448Q). Since the
99
(a)
L2
Li
L3
Cl±
CP
o
0
(c)
(b)
Cl
Ci
HI
Li
C3
1
II
o
L2
L3
(e)
(d)
Figure 5.1: The A/4 transformer in (a) is equivalent to each of the LC circuits in
(b), (c), (d), and (e). For each the equivalence is Z^ = UJQL =
100
1/(UJ0C).
susceptance of parallel elements may be added directly, this allows the susceptance
of the load (—jO.0298975) to be subtracted from the shunt susceptance of the last
element in the impedance-matching network. This value will be used in the following
examples to illustrate the use of the design equations that are developed, and a final
design is selected to match the input impedance of all antenna pairs of MAPA.
Example 1: In Figure 5.1, for Zs = Rs = 50 9. and ZL = RL = 19.445 Q,
use a A/4 transformer of characteristic impedance Zoi to form an input impedance
match, and then use lumped-element networks of the type shown in Figure 5.1(b)
to replace the A/4 transformer at / = 140 MHz. For Figure 5.1(a), at 6t = 7r/2 or
90 electrical degrees, a load resistance (RL) is transformed to an input impedance of
Zin = Z^/RL-
Setting this equal to Rs for an impedance match requires,
Zot = y/RsRL-
(5.1)
Therefore, the A/4 transformer impedance is Z^ = \/50 x 19.17 = 30.96 tt. In
the replacement network Figure 5.1(b) by using Equation 2.24, we can get LOQC\ =
UJQC3
= 1/30.96 n and LU0L2 = 30.96 Q. Thus, at / = f0 = 140 MHz, d
1/(2TT/ 0
5.3.2
= C3 =
x 30.96) = 36.72 pF, and L 2 - 3 0 . 9 6 / ( 2 T T / 0 ) - 35.20 nH.
L u m p e d Element Circuits T h a t Are Equivalent to Two
Cascaded Quarter Wavelength Transformers
Since multiple A/4 transformers would extend the impedance match over even greater
bandwidths, two cascaded A/4 sections of line between source and load are chosen
101
for this application. The input impedance match will be maximally flat in the pass
band if we transform RL through the two A/4 sections of characteristic impedance
ZQ\ and ZQ2 to obtain,
(5.2)
Rs =
and if we equalize the selectivity (Q) of each A/4 section, as [39]
Qi = Q2 =
8
Rs
ZQ\
IT
ZQI
Rs
8 RL
ZQ2
RL
(5.3)
Z02
Solving Equation 5.2 and Equation 5.3 yields the design equations to solve for ZQI
and Zno as
Zm — RQR
SllL>
(5.4)
Z02
(5.5)
and
—
RSRL,
Example 2: Again in Figure 5.1, for Zs = Rs = 50 Cl and ZL = RL = 19.445 Q,
use two cascaded A/4 transformers of characteristic impedance Zoi and Z02 to form
a maximally-flat input impedance match, and then use lumped-element networks of
the type shown in Figure 5.1(b) to replace the A/4 transformers at f = 140 MHz.
From Equation 5.4 and Equation 5.5, the A/4 transformer impedances are Z01 =
50 a75 19.17 0 - 25 = 39.344 fi and Z02 = 50 a 2 5 19.17 a 7 5 = 24.362 Q. In the replacement
network there will be five lumped elements. If these are numbered with subscripts 1
through 5, the central element is the sum of two adjacent elements as C3 = C\ + C5.
The calculations proceed using Equation 2.24 to obtain the following values of lumped
102
elements are Cx = 28.89 pF, L2 = 44.73 nH, C 3 = 75.55 pF, L 4 = 27.69 nH, and
C5 = 46.66 pF. The resulting networks are shown in Figure 5.2.
Zs
4
4
,01
Z()2
-WVVsi
ZL
(a)
Zs
-vwVs
L4
_rrrr\.
L2
_mm_
Ci±
C3
C5±
(b)
Figure 5.2: Lumped element replacement of two cascaded A/4 transformers, where
Zs = 50 Q and Z^ = 19.17 fl. (a). Cascaded transformers yielding a maximally-flat
passband impedance match, where Zoi = 39.344 Q and Z02 = 24.362 ft. (b). The
lumped element replacement where C\ = 28.89 pF, L2 = 44.73 nH, C 3 = 75.55 pF,
Li = 27.69 nH, and C 5 = 46.66 pF.
5.3.3
Replace t h e Lumped Elements by Relatively Short Sections of Transmission Line
Using the same method described in Chapter 2.5.5, a series inductance may be replaced by a relatively short section of transmission line under the following condition,
uoL = Zottan(27r/ t /A).
103
(5.6)
The shunt-connected L and C network elements may be replaced by sections of
transmission line terminated in a short-circuit and an open-circuit, respectively as,
u0L = Zot tan(u;olt/v) = Zottan(27rlt/X).
(5.7)
for a shunt-connected line of characteristic impedance Zot, length lt and terminated
in a short, and
LOQC
= — taxi(io0lt/v) = — tan(27r/ t /A).
(5.8)
for a shunt-connected line of characteristic impedance Zot and length lt terminated
in an open. Note in Equation 5.6, Equation 5.7 and Equation 5.8 that once UJQL and
LOQC are
specified, there are two unknowns: Zot and u>ok/v. One unknown may be
chosen for convenience, and the other can be calculated.
In Example 1, the series inductive reactance is LOOL2 = 30.96 Q. Thus, using
Equation 5.6, and choosing Zot = 85 ft, we calculate,
h = ^~ tan" 1 ^ ^
Z7T
= 0.0556A.
(5.9)
85
From Equation 5.8,
^
^
1
^ = . „ C 3 = — =
tan(27rJi/A)
^ - i U
,„ „„N
(5.10)
Choosing ZQt = 30.96Q, we calculate the length to the open-circuited end as,
/i = / 3 = ^ - t a n - 1 ^ ^ = 0.125A.
2TT
30.96
(5.11)
'
v
In Example 2, using Equation 5.6 and Equation 5.8, respectively, the transmission
line lengths and characteristic impedances are:
h = ~ tan" 1 ^ P
2-7T
85
104
= 0.069A
(5.12)
for U)QL2 = 39.344 and choosing ZQt = 85f2.
A
24 362
k = — t a n " 1 — ^ - = 0.0444A
In
85
(5.13)
for LUoLi = 24.362 and again choosing Zot = 85il.
Zi = £- tan" 1 ^ ^
2n
85
= 0.125A
(5.14)
for w 0 Ci = 1/39.344 and again choosing Zot = 39.344Q.
for u>0Cs = 1/15.047 and again choosing Zot = 15.047Q.
A
'» = ^
tan
24 S62
"'2l362=0-125A
< 5 ' 16 >
for LUQCS = 1/24.362 and again choosing Z 0 i = 24.362Q.
Note from the examples above that the series inductances are conveniently replaced by the relatively short and skinny sections of line, but the shunt capacitor replacements (to keep the length at A/8) require a relatively low characteristic
impedance, which may be inconveniently wider than a 50 Q transmission line. Thus,
the lumped-element capacitors may be a better choice.
5.4
Final Designs of Impedance-Matching Networks
with Dimensions and Component Values
As stated earlier, to improve power-handling capability and avoid internal resonances,
will use an equivalent segment of transmission line in place of each L in the impedance105
matching network. The two networks smallest in size and most convenient to manufacture are the shunt C, series L, shunt C and the shunt L, series C, shunt L. In
the latter, the series C must be a chip capacitor, so we would lose the flexibility of
using open-circuited segments. Also, the shunt L would require a segment of shorted
transmission line (an inconvenience). In the former, shunt C is either a chip capacitor
or an opened segment of transmission line, or a combination of the two (flexible and
convenient), and the series L is a narrow segment of transmission line that can be
serpentined to compact the structure. Therefore, we pattern our final design after the
C1L2C3 network in Figure 5.1(b) to simulate a A/4 transformer, and also in cascade
to yield the C1L2C3L4C5 network in Figure 5.2(b) to simulate two A/4 transformers.
The designs were carried out for all of the single-stage networks in Figure 5.1, and
the simulated results are shown in Figure 5.3. Clearly, the bottom curve to the left
of 140 MHz has the widest bandwidth for the input impedance match, and it is the
simulated response of the C1L2C3 network in Figure 5.1(b).
The return loss, called Su(dB)
in Figure 5.3, is 101og10 |p| 2 , where p is reflection
coefficient, and \p\2 is fractional power reflected. Thus, Sn(dB)
sponds to |p| 2 = 0.01, or 1% power reflected, and Sn(dB)
= —20dB corre-
= —30dB corresponds
to 0.1% power reflected. A return loss of 20 dB is considered to be an excellent
impedance match, and we will define our bandwidth as the frequency range over
which Sn(dB)
< —20dB. On this basis, the bandwidth of the lower curve in Fig-
ure 5.3 is 151-117=34 MHz. If f\ and f2 are the lowest and highest frequencies in
106
Frequency (MHz)
Figure 5.3: Simulated return loss (Sn in dB) of the single-stage networks in Figure
5.1 for Zs = 50 Q and ZL = 14.43 + J8.27 Q. (a series R and L), or ZL = 19.17 fl ||
J8.27 fl (a parallel R and L). On the left of / 0 = 140 MHz, the top curve corresponds
to Figure 5.1(e) with ZL = 14.43 + J8.27 Q, and OJ0CI = 1/26.86Q, u0L2 = 26.86 ft,
W0C3 = 1/35.13S1. The next curve down corresponds to Figure 5.1(d) with ZL = 19.17
n H J8.27 Q, and w 0 Li = 30.96 ft, UJ0C2 = l/30.96ft, and u;0L3 = 466.22 ft. The third
curve down corresponds to Figure 5.1(c) with ZL = 14.43+j8.27 ft and CJOLI = 26.86
ft, w o ^ = 1/26.86ft, w 0 L 3 = 18.59 ft. The bottom curve corresponds to Figure
5.1(b) with ZL = 19.17 ft || J8.27 ft, and UJ0CI = l/30.96ft, LO0L2 = 30.96 ft, and
a,0C*3 = 1/16.07811
107
the band, respectively, then the central frequency is taken as the geometric mean,
/o = \//i/2- In this case the central frequency is / 0 = \f\Yl x 151 = 133 MHz.
The input impedance match versus frequency for the C1L2C3L4C5 network simulating two A/4 transformers is shown in Figure 5.4 for lumped elements only, and
for the replacement of L2 and L4 with their transmission line equivalents. As a guide
to show the increase in bandwidth that is achieved, the lower left curve from Figure
5.3 is included in Figure 5.4 as well. In Figure 5.4, the 20dB bandwidth of the solid
curve is 172 - 127 = 45 MHz, and f0 = V127 x 172 = 148 MHz, or a 30% bandwidth
over which less than 1% of the input power to the antenna is reflected.
Figure 5.5 shows the simulated return loss achieved when all lumped elements are
replaced by transmission line sections. The capacitors are replaced by open-circuited
lines that are 0.125A in length and connected in shunt with the main line. Two of
the curves from Figure 5.4 are included in Figure 5.5 for a convenient comparison.
5.4.1
Final Design Format
For the format of the final designs we wish to minimize the metallization of printedcircuit boards that may contribute unwanted coupling to the antennas in the array.
Thus, we choose to realize the designs in parallel-plate transmission line, which has
two strips of equal width on each surface of a dielectric board. The characteristic
impedance of parallel-plate line for any strip width (w) and dielectric thickness (2d)
108
1
T
;
_i
90
;
I
100
;
I
110
;
I
120
;
I
130
1
i
1
•
lib
140
;,
1
•
LLI
150
;
I
160
1
;
i
170
r
;
;
I
i_
180 190
Frequency (MHz)
Figure 5.4: The dot-dash curve is simulated return loss (5n in dB) versus frequency
for the five lumped-element replacement of two A/4 transformers as in Figure 5.2(b).
Here,
UJQCI
= l/39.344ft,
U0C5 = 1/14.095.
LO0L2
= 39.344ft, u0C3 = l/15.05ft, w0L4 = 24.362ft,
The solid curve is simulated return loss for the same cir-
cuit except the series inductances are replaced by sections of transmission line, as
Z02 = 85ft, l2 = 0.069A replaces L2, and Z04 = 85ft, k = 0.044A replaces L4. The
dash-dash curve is the bottom-left curve from Figure 5.4, repeated here as a guide
for reference. For each circuit Zs = 50ft and ZL = 9.17ft||j33.448ft.
109
0
-5
i
i
i
__.L
'
_ J
:
S11
S22
S33
:
:
i
i
i
'_
'___
•
i
i
:
!
i
j..|...y.....i
:
:
: : : : :
i i i i l i
i
i
-r"
:
:
•
•
i
i
i
_..i
j
i
rosv
-i
-i
i-
i
'^-.-i.....Ap^-.-i'J----A
:
--;
-;
f
;
-;
*
-10
.
—— - t - * ~
\*- : / ; , -j>
V A/\
:
_/'__/ . _ i / _
-15
^ -20
CO
T3
"-' -25
^"^N :
/
: 7
I
:
•.._
J.—
(/> -30
-35
TTJ"
T
' T>1 1 7 "•"
"•
-40
! ! ! ! ! V/ i ; ! U ! ! !
—
-45 h
-50
90
100
110
120
130
140
150
160
170
180
190
Frequency (MHz)
Figure 5.5: The dot-dash curve is simulated return loss {S\\ in dB) versus frequency for the five lumped-element replacement of two A/4 transformers as in Figure
5.2(b). At / = 140 MHz, Lo0d = 1/39.485ft, u0L2 = 39.485ft, UJ0C3 = l/15.17ft,
CO0L4 = 24.625S7, UJ0C5 =
1/14.53.
The solid curve is simulated return loss
versus frequency for the same circuit, except the series inductances are replaced
by sections of transmission line, as Z02 = 85Q, \i = 0.069A replaces L2, and
Z04 = 85ft, U — 0.044A replaces L4. The dasked curve is the simulated return loss
when the three capacitors are replaced by open-circuited sections of transmission line,
as Z01 = 39.485ft, h = 0.125A, Z 0 3 = 15.170, h = 0.125, Z05 = 14.53, k = 0.125A.
110
is given by [78]:
r,, x
Z
° - "
F(9)
= ;
+
2407r/v/e/eo
1.308 + 0.667. n ft
+
tw
1.44)' I S '
(5 17)
'
and
Zo = F(9) =
"
7^lnU + «)^£1'
(5 18)
'
The effective dielectric constant for this transmission line is,
e
ed + l
ed-l
- = ££ = ^ r — + — .
Co
^
o
/i
(5.19)
i 12d
2A/1 +
/
U)
which also determines wavelength at a given line width, dielectric thickness and
frequency, as,
,
3 x 108
A= - r — .
,
(5.20)
For ZQ = 50 fi, e<i = 4.4, 2d = 1.59 mm, these equations yield, w = 4.156 mm and
eE = 3.64. For these parameters, if / = 140 MHz, then A = 112.32 cm. If Z0 = 85
CI, and ed, 2d and / are kept the same, then w = 1.97 mm, e^ = 3.41 and A = 116.04
cm.
A diagram of the circuit that would be constructed to yield the return loss represented by the solid curves in Figure 5.4 and Figure 5.5 is shown Figure 5.6. The
input (Zin) would be fed from a 50-ohm cable into a parallel-plate section that has
Z0 = 50Q. The capacitors ( d = 28.89 pF, C3 = 75.56 pF, C5 = 80.65 pF at
/o = 140 MHz) may be chip capacitors that are connected to each strip of width
w = 1.97 mm (to yield Z02 — ZQi = 85Q) and embedded in the dielectric between the
strips. The lengths l2 and I4 are 0.069A = 8.00 cm and 0.044A — 5.10 cm, respectively.
Ill
With G-10 epoxy-glass dielectric between the strips and 2d = 1/16 inch = 1.59 mm,
td — 4.4 and e# = 3.41 cm for w = 1.97 mm.
A variation of the circuit shown in Figure 5.6 is diagramed in Figure 5.7, where
open-circuited segments of 50f2 transmission line are connected in parallel with the
lumped-element capacitors to bring the total capacitance up to the values used in
Figure 5.6. Thus, the susceptance at each of these junctions will be,
uCnew + — tan (360°-) = uCold.
oU
(5.21)
A
With u> = 27r/o and I = A/36 = 112.32/36 = 3.12 cm for each open-circuited segment,
we determine Cnew from C0u as,
Cnew = Cold - 45.47 PF x tan 10° = Cold - 8.02 pF
(5.22)
From this equation the new capacitor values for use in Figure 5.6(Ci = 20.87 pF, C% =
67.54 pF, C 5 = 72.63 pF) are determined from the old values used in Figure 5.6(Ci =
28.89 pF, C3 = 75.56 pF, C5 = 80.65 pF). The open-circuited line segments in
Figure 5.7 may be made shorter or longer (length I) in Equation 5.21 to accommodate
available capacitor values.
Another view of the network in Figure 5.7 is constructed approximately to scale
in Figure 5.8 using copper-foil tape on 1/16 inch-thick epoxy-glass substrate. The
lines I2 and I4 are serpentined to compact the structure, and the circuit is identical on
the opposite side of the substrate. The capacitors would be inserted at the junction
points as indicated in Figure 5.7, shown in Figure 5.8.
112
£
" ^
TcX
r
* 1.
T 3
C
-*,
Figure 5.6: A diagram of the circuit that would yield the return loss represented
by the solid curves in Figure 5.4 and Figure 5.5. The input (Zin) is fed from a
50-ohm cable into a parallel-plate section that has Z0 = 50Q and w = 4.16 mm.
The capacitors {Cx = 28.89 pF, C3 = 75.56 pF, C5 = 80.65 pF at f0 = 140 MHz)
may be chip capacitors that are embedded in the dielectric between the strips of
width w = 1.97 mm (for ZQ2 = Z04 = 850). The length l2 = 0.069A = 8.00 cm
and k = 0.044A = 5.10 cm. With G-10 epoxy-glass dielectric between the strips and
2d = 1/16 inch = 1.59 mm, ed = 4.4 and eE = 3.41 for w = 1.97 mm.
113
Figure
5.7:
A variation of the circuit in Figure 5.6 that will yield the
return loss represented by the solid curves in Figure 5.4 and Figure 5.5.
This is the same as in Figure 5.6, except that new values of capacitance,
Cx = 20.87 pF, C3 = 67.54 pF, C 5 = 72.63 pF at f0 = 140 MHz are each added in
parallel with the open-circuited transmission lines to produce the same capacitance
given in Figure 5.6. The input on the left is into a parallel-plate section that has
Z0 = 50fi and w = 4.16 mm. The capacitors are embedded in the dielectric between
the strips on each surface. With G-10 epoxy-glass dielectric between the strips and
2d = 1/16 inch
= 1.59 mm, ed = 4.4 and eE = 3.41. The wider lines are ZQ = 50S1
of width w = 4.16 mm, and the length I = A/36 = 3.12 cm. The narrower lines
are Z0 = 85Q of width w = 1.97 mm. The length l2 = 0.069A = 8.00 cm and
l4 = 0.044A = 5.10 cm. The total length of the circuit board may be made more
compact by serpentining l2 and Z4.
114
A
i
'•'•
!
1
1
:1 1
i »0
i}
! i
i !
1
1 ;
i
:! j
;
*
'"<y{V
i
•5 1
Figure 5.8: The network in Figure 5.7 constructed to approximate scale using copper-foil tape on epoxy-glass substrate. The input on the left is from the 50-ohm
source and the output on the right is to the antenna array.
115
Chapter 6
Melting of Ice - A Space Application of
Microwave-Induced Heating
[This Chapter follows closely the paper to be submitted for publication:
Zhen Li, and Williams T. Joines*, Development of a Microwave Probe to Bore
Through Thick Layers of Ice, to be submitted to IEEE Transactions on Microwave
Theory and Techniques, 2008.]
6.1
Introduction
A new era of planetary surface exploration just began - searching for extra-terrestrial
life (ETL) beyond Earth. It is one of NASA's highest goals. Biologists believe that
terrestrial life began in ancient oceans of the Earth, implying that life can originate
in water.
As a result, any planet with the sign of existence of water or ice has
become a target of exploration. In our Solar System, Mars has permanent polar ice
caps, which vary greatly in size with the seasons. Until recently, it was believed that
both Martian polar caps consisted largely of dry ice about 120 kilometers thick, with
a small amount of water ice. One of the other bright objects in our solar system
is Europa, which is one of the natural satellites of Jupiter. In 2002, the magnetic116
field data collected by the space probe Galileo strongly indicates a liquid-water ocean
beneath Europa's frozen surface, which is an ice shell of probably 60 kilometers thick.
This liquid-water ocean is similar to the oceans found on Earth, and it is perhaps
as much as 50 kilometers deep and possibly capable of supporting simple life forms.
Thus, "to follow the water" in the search for extra-terrestrial life, scientists choose
Martian polar caps and the ocean beneath Europa's icy crust as the starting places
for the exploration. Finding that life exists or has existed on Mars and/or Europa
would answer some important questions in biology about the origin of life, such as,
"can life originate in other environments besides primitive earth?" Also if evidence
of life or past life is shown to exist in the Solar System, the search for ETL on extrasolar planets will be more promising. NASA is considering a proposal for a small
spacecraft that would land on Mars or Europa and melt its way through the ice,
collecting data as it descends, searching for clues of life or the evidence of past life.
In this project, one of the engineering goals is to investigate how to conquer the
challenge of ice penetration. Methods and technologies for accessing and exploring
environments beneath tens or hundreds of kilometers of ice cover are not well developed. As the first step, they could be developed and tested in the Earth's Polar
Regions such as the Antarctic.
Two methods have been used in recent research. The first one is drilling; the
other is conventional resistive heating.
As shown in Figure 6.1, drilling is the current plan used by the Russian ice core
117
drilling community for entering Lake Vostok in the Antarctic. Lake Vostok, beneath
an ice sheet 4 kilometers thick, has been locked up for more than 10 million years.
Russian scientists drilled through the ice, and collected data as the drill descended.
By extracting air from bubbles trapped in ice, scientists can reconstruct the past
composition of the atmosphere and can tell what the climate on Earth was like in
past [79]. In late 2007, they poked through and took the first sip of the lake water
underneath. However, because of contaminations researchers from several nations
fear that it is impossible to obtain untainted water samples. Such contaminations
exist because the borehole brims with 60 tons of drilling fluid, a soup of kerosene and
Freon that teems with foreign bacteria. Also other contamination may come from the
surficial microbes and the overlaying shallow icy habitats [80]. Besides, the required
considerable surface infrastructure of drilling may not be suitable for a space flight
mission.
The second method is conventional resistive heating. Melting ice is a process that
entails transferring heat energy to the ice at the rate of 80 calories per gram, to be
specific. If the pressure stays at one atmosphere, then ice at zero degrees Celsius
will turn into water at zero degrees Celsius once the heat is transferred. Although
it could avoid contamination and it has been used successfully by others, the energy
efficiency and speed of travel still need to be improved substantially. The reason
for these problems is that typical elements for resistive heating such as resistance
wires generate heat by resisting the flow of electricity through them. The generated
118
The Subelaciat Lake Vostok System
V-siuk Mcilion
ICE SHEET
Figure 6.1: The Subglacial Lake Vostok System (Excerpted from Science, 2005,
310:28) .
119
heat is then radiated onto the material beneath them. The conventional resistive
heating always heat the material from the outside. Because the characteristic thermal
conductivity of the material, there will always be a thermal gradient from the surface
to the core of the material being heated.
To overcome the limitations of the previous two methods, we propose a microwave
heating technique. Microwaves are able to penetrate objects, and pass through the
surrounding space without generating heat until they reach a receptive target, enabling a very rapid and high-intensity heat transfer throughout an item. With microwaves, no heat is applied per se. Instead microwave energy is transported as
electromagnetic waves in the range between 0.3GHz and 300GHz. Once they reach
their target, part of the energy is transmitted, part reflected and part absorbed by
the target where they are dissipated as heat. Heat is generated because the molecules
in the material can be considered to electric dipoles. They attempt to align themselves with the electrical field. Under the influence of this high frequency alternating
electrical field, the particles oscillate about their axes creating intermolecular friction
which manifests itself as heat.
In conventional heating the heat source causes the molecules to react from the
surface toward the center so that successive layers of molecules heat in turn. Microwaves, however, produce a volume heating effect, since all molecules are set in
action at the same time. Microwave heating offers advantages over surface heating in
many industrial situations. It is ideally suited for heating bulky products with a high
120
volume to surface ratio. Another advantage of microwave heating is that materials absorb microwaves unequally at the same frequency. Some material absorbs microwaves
readily, others do not. For melting ice purpose, by picking an appropriate frequency,
microwaves will transmit through the thin layer of liquid water on the surface of the
probe and be absorbed by the ice underneath the water. This allows more energy to
be transferred into the ice in comparison to the electric heating method. There are
other advantages of microwave heating for this project. For example glaciers are not
the same as frozen lakes; they can contain dust and rocks. Heating probes may have
difficulty passing them. However, using the microwave technique proposed we could
manage the accumulation of debris in front of the probe by melting pockets adjacent
to the path of travel. Since the direction of probe travel could be changed easily by
steering the microwave energy.
By calculation, we found that pure solid ice has a practical depth of penetration
(10 to 20 cm) at 150 GHz, which is an impractically high frequency.
However,
when applying a radiating microwave probe to the melting of ice, we assume that
the process of absorption of the microwave energy into the ice will establish three
distinct strata or layers within the ice. These then are the layers through which the
microwaves will propagate: 1) A thin layer of water will contact the probe (Most of
the water will be pushed away by the weight of the domed-shaped probe against the
ice), 2) Beyond the first layer will be a region of mixed ice and water (a range of
percentages are considered), and 3) Beyond the second layer will be solid unmelted
121
ice. Thus, the effective depth of penetration of the microwave energy will lie between
the small depth of penetration in liquid water and the large depth of penetration in
solid ice. To determine the composite or effective depth of penetration within the
three-layer mixture of water, water plus ice and ice, we first establish a range for the
depth of penetration in the second layer (water plus ice). This is a layer that has
absorbed an appreciable amount of microwave energy. Thus, the ice will be partially
melted. Using different percentages of water and ice, a reasonable range of depths of
penetration are determined for this layer. Next, for a range of fractional volumes for
the three layers, we calculate a range of composite depths of penetration. From these
assumptions we determine that the composite depth of penetration is approximately
10 cm at 2 GHz, 7 cm at 2.45 GHz, and 1 cm at 7.5 GHz.
To insure there is always a thin layer of water contacting the probe, a technique
which combines the microwave heating and the resistance heating is required. We
propose here a microwave and resistance heating probe as shown in Figure 6.2, where
the probe is suspended from a tether that is released from a spool on the surface
of the ice. Microwaves are generated from a magnetron within the probe, guided
through a rectangular waveguide terminated by a dome shaped probe. The probe is
made of material which has a dielectric constant similar to that of air. It will not
absorb any microwave energy. The dome shape is only for drilling purpose. The wires
of resistance heating elements (e.g., thin films of nichrome wire) are run back and
forward across the surface of the dome. While a thin layer of water is maintained
122
around the front of the probe, the excess water will be pumped to the surface. The
microwave and resistance heating probe unit and the tether are designed to allow the
probe to descend under its own weight while melting the ice that surrounds it. The
tether carries the electrical connections to the magnetron and resistance elements in
the probe, and allows the retrieval of the probe after the completion of the experiment.
Waiei Pimped
Out
Spool
Ice "
Ice
- Tether
Water
Magnetraon
—-~"
Waveguide,
Resistance
Heating "
Elements
\^/f—
Dome Shaped Probe
Ice
Figure 6.2: The primary elements of the microwave and resistance heating probe
(not in scale) .
The foregoing assumptions were simulated at 2.45 GHz, a practical frequency, in
a rectangular waveguide terminated in a dome-shaped, open-ended antenna probe
with resistance heating wires pressed against a block of ice. The waveguide may be
rectangular or square and from 3 to 5 inches on a side for operation in the TEIQ
mode (uniform E-field in aperture cross-section in one direction and a half sine wave
123
variation in the other direction). The waveguide could also be tapered to a larger size
and driven in the TE20 mode at 2.45 GHz. This mode would enhance the distribution
of energy across the aperture if needed. By operating in the TEW
or TE2o mode,
the E-field stays polarized in direction, and this would allow for wires of resistance
heating elements (e.g., thin films of nichrome wire) to be run back and forward across
the surface of the aperture or dome. If the wires are arranged perpendicular to the
E-field polarization, there is no appreciable interference between the two heating
modalities.
The resistance heating would insure that a thin layer of water is always produced
at the surface of the ice. The microwaves and the infra-red radiation from the resistance elements generate heat because the polar molecules oscillate about their axes
creating intermolecular friction that is manifested as heat. The microwaves have a
much greater depth of penetration and produce a heating effect over a much larger
volume than the infra-red radiation. This yields more energy to be transferred into
the ice than with electric resistance heating alone.
We have carried out preliminary experiments to explore the applicability of this
approach. The foregoing assumptions were tested at 2.45 GHz by using a 1300-Watt
microwave oven converted to transmit all output power into a rectangular waveguide
terminated in a dome-shaped, open-ended antenna probe pressed against a block of
ice. The block of ice is made from 1 percent sugar water, which has a depth of
penetration of approximately 0.1 meter.
124
6.1.1
Wave Propagation in Ice
At microwave frequencies ice is a lossy dielectric, such that e" /e = a/{toe) <C 1, and
a and /3 are closely approximated as,
.nr^
ire"
.27rVe
7 = a + j/3 <* —y=
+ J——
a fa
= -J^+JU^/JTE
.
.
(6.1)
The depth of penetration (8), also known as the skin depth, is defined as the
depth where e~az = e _ 1 , or z = 1/a = 5. Thus, at this depth the field intensity is
reduced to 1/e or 36.8% and the power density has dropped to 13.5% of the starting
valueat z = 0.
From Equation 6.1,
A l
d = - =
OL a
l
X
^
°^
j= = ^ — =
—
hj,
buna
ire
fao\
(6.2)
2V e
Ice has a large number of different crystalline structures, and its physical properties have been studied extensively. For example, by fitting ice measurement data
from 1 GHz to 100 GHz, Matzler and Wegmuller [81] determined the dielectric constant as e' = 3.175 at all microwave frequencies, and the following equation for the
loss factor e" as,
£ =
" {lt)+Bf8'
(6 3)
'
where fc is the frequency in GHz. The constants A, B, C vary with the temperature
and the purity of the ice. For example, for pure ice at -15°C:
125
e" = { ' ? ^ ^ , ) + 3 . 6 . 1 0 - V ^
(6-4)
For pure ice at -5°C:
6
'6 •10- 4
= I ^~
) + 6-5 • 1 { r 5 ^ ° 7
<6-5)
) + lm2 ' 10 " 4/ °°
(6 6)
For impure ice at -15°C:
S
'1.3-lO - 3
" = {"~k
'
For impure ice at -5°C:
/=(^^)+2.3.10-
4
/^
7
(6-7)
Combining Equation 6.2 and Equation 6.3 with e' = 3.175, the depth of penetration is
s=
A p ^ _ 0.170 _
r fr'~W
=
rr~=
~^
^-
W
0.170
ri
+ BfS
A
ATm
(6 8)
'
Thus for each case and any frequency from 1 to 100 GHz, the depth of penetration
is:
126
485.71
,
2.2
1 + 0.1029/g-
283.33
l + 0.1083/£2.07'
Pure ice at — 15°C;
Pure ice at —5°C;
(6.9)
S={
130.77
2.0'
1 + 0.0923/5
Impure ice at — 15°C;
65.38
I 1 + 0.0885/F'
ImPUre
^ ^ ~ 5 °'
From these equations the depths of penetration of pure and impure ice at -15°C and
at -5°C are plotted versus frequency in Figure 6.3.
For pure ice, Matzler and Wegmuller give e" = 0.00025 and a = 0.000034 S/m at
2.45 GHz [81]. Thus, the depth of penetration of solid, pure ice is 5 = 0.0053v/e7/cr =
277.8 m, and the power absorbed would be spread out over such a large distance that
melting would require too much time. However, as stated earlier, the composite depth
of penetration due to layers of water, water plus ice and solid ice is much smaller,
and it is within a practical range at 2.45 GHz.
6.1.2
Wave Propagation in Water
The attenuation constant for any material can be determined exactly as,
r
a = ^Ao -
£ ' + vW+~FF
127
1/2
(6.10)
The Conductivity of-15°C and -5°C Pure and Impure Ice
-15CC pure ice
5°C pure ice
15°C impure ice
-5°C impure ice
-
"
^
i
20
— i
40
60
Frequency(GHz)
Figure 6.3: The conductivity of ice.
128
1
80
100
and
5 =
\
=
;
14.81/ G • yj-e'
l
,
+ ^{ef
=
( f m )
+ {e"f
where Ao is wavelength in air. As examples, for pure liquid water at T = 0° C, at
/ = 100 GHz, e' = 6.2 and e" =* 8.7, a = 3135.01/m and 5 = 0.00032 m. At 2.45
GHz for pure liquid water, e' ^ 78, e" ^ 28, a = 79.61/m and 6 = 0.0126 m.
Based upon Equation 6.9 and Equation 6.11, and data from [81] [82] [83], the depth
of penetration in ice and in water is calculated and displayed in Figure 6.4 over the
frequency range from 1 to 100 GHz.
6.1.3
T h e Composite D e p t h of Penetration for Mixtures of
Ice and Water
As the microwave energy from the probe enters the surface of the ice, a thin layer
of water is formed against the surface of the probe. This thin layer of water exists
because most of the water will be pushed away along the sides of the probe due to its
weight and the curvature of the surface. Beyond this layer there is a region of mixed
ice and water followed by one of solid unmelted ice. The effective depth of penetration
of these composite layers will be between the small depth of penetration of water and
the large depth of penetration of ice. At our choice of operating frequency (2.45
GHz) a significant amount of energy can be transferred into the region just beyond
the liquid water layer to melt the solid ice.
To determine the composite or effective depth of penetration within the three-layer
129
The Depth of Penetration Of
-15°C and -5°C Pure/Impure Ice and 0°C Water
10
30
50
60 70 80 90100
Frequency(GHz)
Figure 6.4: Depth of penetration of ice and water (log scale) .
130
^ Water
25% water + 75% ice = Mixture 1
4 % rater + 99% mixture 1 = Mixture'
Ice
50% mixture 2 + 50% ice=Mixture 3
Figure 6.5: (a). Melted water distribution in a unit volume, (b). Three-layer model
(water | water and ice ] ice) .
mixture of water, water plus ice, and ice, we first determine the depth of penetration
in the second layer, the layer with the mixture of water and ice. This middle layer
between the liquid water and solid ice will have absorbed an appreciable amount of
microwave energy and the ice will be partially melted. The effective depth of penetration of this second layer will be between that of water and solid ice. By using
Equation 1.9, the depth of penetration in this layer for different mixture percentages
of ice and water is shown in Figure 6.6. Making a reasonable choice for the composition of this layer, we pick 25 percent water and 75 percent ice, the third curve up from
the bottom in Figure 6.6, to use as the depth of penetration in the middle layer versus
frequency. This curve is repeated in Figure 6.7 and labeled as Mix 1 to represent
the 2nd layer of the three layers. Also in Figure 6.7, Mix 2 is the combination of the
thin layer of water next to the probe and the layer represented by Mix 1, as obtained
131
using Equation 1.9. Here we chose 1 percent water and 99 percent Mix 1, and as
seen in Figure 6.7 the curves for Mix 1 and Mix 2 are approximately the same, as the
second curve up from the bottom. Finally, again using Equation 1.9, we combine Mix
2 (the first and second layers) with the third layer of unmelted ice (50 percent of each
seems a reasonable choice), and the effective depth of penetration versus frequency
is the third curve up from the bottom in Figure 6.7. With these choices of fractional
volumes for the three layers it is seen that the depth of penetration is approximately
10 cm at 2 GHz, 7 cm at 2.45 GHz and 1 cm at 7.5 GHz.
Depth of Penetration in mixtures of 0°C Water and -5°C Ice
water_0°C
m ix(50%water+50%ice)
m ix(25%water+75%ice)
m ix(10%water+90%ice)
m ix(5%water+95%ice)
m ix(1 %water+99%ice)
100
o
c
Q)
0.
•s
0.01
a
0.001
0.0001
2.45
5
10
60
80 100
Frequency(GHz)
Figure 6.6: Depth of penetration in mixtures of water and ice (log scale) .
132
Depth of Penetration in a mixture of 3 layers
(|Water|Water and lce|lce|)
Water 0°C
Mix1(25%Water+75%lce)
Mix2(1%Water+99%Mix1)
Mix3(50%Mix2+50%lce)
Impure ice _-5DC
5
10
30
60
80 100
Frequency(GHz)
Figure 6.7: Depth of penetration in a mixture of 3 layers (log scale) .
133
6.2
Melting Time Required for t h e Composite Layers
Using HFSS, the simulated power density in W/kg deposited into pure ice from our
waveguide probe delivering 1300 W at 2.45 GHz is shown in Figure 6.8(a), which
shows the maximum power density in the pure ice is 5 x 10~3 W/kg. This power
density, after a time delay, would establish a thin water layer and partially melted
ice layer we have used in our calculations and modeling. Once the layers are formed
and the depth of penetration becomes approximately 0.1 m, the HFSS simulation
shows that the distribution of power density to be as shown in Figure 6.8(b), where
the maximum power density is 3.5 x 103 W/kg at the probe-ice interface.
The time delay in forming the power density in Figure 6.8(b) from the density in
Figure 6.8(a) is the time required to raise the ice temperature to 0°C and then to
melt the ice at the probe surface.
For a given volume of ice, the time needed to melt the ice into water at 0° C is
determined as follows: Since a heat energy of 80 cal/gm is required for the melting,
we convert to J/m3 as, 80 cal/gm
x 1 gm/cm3
x 4.186 J/cal = 3.35 x 108
J/m3.
The microwave power dissipated within the ice per unit volume is determined from
the power transmitted in the z-direction through a cross-sectional area as,
Pt(z) = Pt(0)e~2az
= ^HfReWe-2"*
134
=
l
-\^ Re{r,)e-2az
(6.12)
SAR Field[W/kg]
I
5.0000e-0B3
4.6876e-003
4.3751e-003
4.0627e-003
3.7S02e-003
3.4378e-003
^^m
3.125te-003
^ ^ K 2.8129e-003
^ H
2.5005e-003
^ H
2.1881e-003
^ ^ | 1.8756e-003
^ ^ | 1.5632e-003
^ H
1.25B8e-003
^ H
9.3831e-00t
^^M
6.2588e-004
^ H
3.13tte-001
Figure 6.8: Simulation of absorbed microwave energy in: (a), pure ice (b). impure
ice with conductivity of 0.3 S/m.
135
in W/m . At any depth z the power dissipated in W/m is:
Pa{z) = - ^ ^
= 2aP 4 (0)e- 2 - = a ^ | £ | V
2
- = ^|£|V2-
(6.13)
For the composite layers of water, ice plus water and ice alone, the depth of penetration 6 = 1/a = 0.1 m, and a will be within the approximate range of 0.1 to 0.4 S/m.
The electric field intensity out of the waveguide and into the composite layers will be
approximately 15,000 V/m for a 1300-watt microwave source. Taking a = 0.3 S/m
yields Pa(0) = 0.335xl0 8 W/mz. Thus, t = (3.35xl0 8 J/m 3 )/0.335xl0 8 J/sec.m^) =
10 seconds would be required to produce the energy to melt the ice in this approximation of materials.
6.2.1
Laboratory Measurements to Confirm t h e Model
To produce a frozen material with an approximate depth of penetration of 0.10 m
at 2.45 GHz, we added 1% and 2% (weight/weight concentration) of cane sugar to
de-ionized water and froze this into large rectangular blocks (12 x 6.5 x 3 inches).
The sugar water solutions were measured before and after being frozen with the
HP85030B open-ended coaxial probe as shown in Figure 6.9. The open-ended probe
results show that 1% frozen sugar water has conductivity of 0.1 S/m at 2.45GHz.
Thus, these frozen blocks will serve our purpose for ice melting measurements.
To make the melting time measurements a rectangular waveguide from the microwave source was terminated in a dome-shaped probe made from Styrofoam with a
thin layer of epoxy glue applied to harden the curved surface. By adjusting the height
136
80-•
1/4
1Mugar-KT
IRSugar-F-awr
2P-3uaar-RT
2P-3ugar-F-A«r
ao.
12
—
1.0
"a 40-
s
u
?
OB
1P-8uBar-Roantanip
1Mujar-F-8»er
2P4Sugar-RoomtMflp
2P£ugar-FAver
*
5
20-
0-I-
1
1
1
1
2400
2420
2*40
2480
2480
250
2400
Frequency(MHz)
2420
2440
2480
2480
2500
FraqjancyfMHz)
(a)
(b)
Figure 6.9: (a). Permittivity and (b). Conductivity of 1% and 2% sugar water after
being frozen and at room temperature. .
of the jacks the probe was lowered to the top surface of the ice. With the source at
full power (1300 watts) the probe was continuously lowered as the ice melted, so that
water was pushed out of the region in front of the probe surface, as shown in Figure
6.10. After 2 minutes and 24 seconds, a 1.8-inch depth of ice was melted, leaving
the outline of the dome-shaped probe as shown in Figure 6.11. A number of tests
were carried out in this way, and the average melting rate was approximately 0.75
inches/minute.
6.3
Discussion and Conclusion
We have shown that microwave-induced heating for melting deep layers of ice could be
a viable alternative to other methods that might be used. Drilling could contaminate
137
Figure 6.10: A 1% sugar ice block (12 x 6.5 x 3 inches) under the dome-shaped
probe terminating the waveguide .
(a)
(b)
Figure 6.11: 1.8 inches 1% sugar ice was melted after 2minutes and 24 seconds.
138
the drill-hole and any samples that may be collected for study. Also, drilling would
require a considerable surface infrastructure that could prevent its use in outer space
(i.e., Mars and Europa). Electrical resistance heating used alone is ineffective. After
a thin layer of liquid water is generated around the probe the heat transfer to the ice
is blocked by the water which now acts as an insulator. Microwave heating potential
is transferred through layers of material in the form of an electromagnetic wave.
Microwave heating is ideally suited for heating bulky products with a high volume
to surface ratio. From the known electromagnetic properties of water and ice, and
composites of the two, we were able to select a practical microwave frequency of 2.45
GHz for testing our calculations and assumptions. In the present application the
microwave energy is absorbed as heat at it transmits through a thin layer of water,
a layer of partially melted ice and then solid ice. The overall or composite depth
of penetration of these layers is 0.1 m at 2.45 GHz. For laboratory testing we used
ice blocks made from 1% sugar water, which also has a depth of penetration of 0.1
m at 2.45 GHz. From multiple tests the melting rate in this material averaged 0.75
inches/minute.
From theory, calculations and simulations, microwave energy at 2.45 GHz applied
to the surface of pure or impure ice will create a thin melt layer and beyond that
layer a layer of partially melted ice before propagating into the solid unmelted ice.
There will be a time delay for this condition to be set up since the temperature at the
surface of the ice must be brought up to 0°C before the melting can begin. Once the
139
three layers are established the melting of the ice in front of the probe will process as
we have calculated, simulated and measured since the effective depth of penetration
will be near 0.1 m at 2.45 GHz. To speed up the process of establishing the distinct
layers, electrical resistance heating can be built into the probe surface to immediately
establish the thin layer of water (Figure 6.12) that is necessary to initiate the action of
the three-layer structure. The resistance wires in the probe surface would be oriented
perpendicular to the microwave electric field propagating out of the probe, so that
no interference between the two would occur. Further research is needed to test how
fast we can melt the ice when using this design.
Figure 6.12: A probe which combines microwave heating and resistance heating.
140
Chapter 7
Discussion and Conclusion
Controlled microwave heating of inhomogeneous materials in medical and space applications has been investigated. From Chapter 1-5, design and analysis of improved
hyperthermia therapy systems is presented. Such chapters have covered filter designs,
3D modeling for clinical hyperthermia treatments, optimized hyperthermia treatment
planning and wide-band input impedance matching circuit design for a hyperthermia
system. During this study, a high pass filter connected in series with a band pass
filter is designed, and size reduction is discussed. This filter was fabricated for a MRI
compatible RF hyperthermia system to prevent the cross talk between the hyperthermia applicator and the MRI machine. Excellent agreement exists between modeled
and measured results. In the first stage of the 3D modeling study, simulations using
a homogenous medium are investigated and results are proved to be acceptable by
phantom (artificial tissue) study. Then, a more complicated inhomogeneous medium,
a patient body model, was input into the hyperthermia applicator system, which in
turn was placed inside the MRI machine in our simulations. This realistic model covers as much information as possible, such as the cables that feed the antennas, tuning
stubs for each channel, and frequency-dependent materials (bones, muscles, and tumor etc). Simulated temperature distributions are compared with clinical data in
141
two clinical studies. In the end, a method using simulation to optimize hyperthermia
treatment planning is addressed. During a clinical study, we discovered by measurements that the input impedance of each channel of the hyperthermia applicator is
load dependent. To maximize the transmitted power (minimize reflections), a class
of broadband impedance matching networks was designed and developed for use at
the input of each antenna-pair in the phased array.
In the last chapter, microwave heating of ice-water mixtures for boring through
ice is presented. From the known electromagnetic properties of water and ice, and
composites of the two, we were able to select a practical microwave frequency of 2.45
GHz for testing our calculations and assumptions. In the present application the
microwave energy is absorbed as heat at it transmits through a thin layer of water,
a layer of partially melted ice and then solid ice. The overall or composite depth
of penetration of these layers is 0.1 m at 2.45 GHz. For laboratory testing we used
ice blocks made from 1% sugar water, which also has a depth of penetration of 0.1
m at 2.45 GHz. From multiple tests the melting rate in this material averaged 0.75
inches/minute. To speed up the melting process in future applications, we propose
that electrical resistance heating (wires perpendicular to E-field vector) be used in
combination with the microwave heating probe. Further research is needed to test
how fast we can melt the ice when using this design technique.
142
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Biography
Name: Zhen Li
Place of Birth: Beijing, China.
Date of Birth: December 30, 1976
Education:
Ph.D., Electrical and Computer Engineering, Duke University, June 2008.
Master of Science, Electrical and Computer Engineering, Duke University, September
2006.
Bachelor of Science, Biomedical Engineering, Capital University of Medical Sciences,
Beijing, China, June 1999.
Work Experience:
Intern, Ansoft Corporate Headquarters, Pittsburgh, PA, June 2007 - August 2007.
Associate Engineer, Office of Information Technology, Department of Medical Instruments, Jishuitan Hospital, Beijing, China, August 1999 - April 2002.
Presentations and Publications:
[1] Zhen Li, William T. Joines, and Paul R. Stauffer, Simulated Phase Control
of SAR Distribution within a Cylindrical Phased-Array, Printed-Circuit Antenna
Applicator with Four Input Channels, Duke Comprehensive Cancer Center's Annual
Meeting, p86, Nasher Museum, Durham, NC, March 12, 2006.
[2] Zhen Li, Paolo. F. Maccarini, Omar. A. Arabe, William T. Joines, and Paul
R. Stauffer, Control of SAR Distribution within a Cylindrical Annular Phased Array
(APA), Society of Thermal Medicine Meeting, p239, Washington DC, May 14, 2007.
[3] Zhen Li, and Martin Vogel, Fighting Cancel with Hyperthermia, Ansoft FirstPass System Success (Application workshops for high-performance electronic design),
Ansoft Corporate Headquarters in Pittsburgh, PA, August 23, 2007.
[4] Kung-Shan Cheng, Zhen Li, Paul R. Stauffer, William T. Joines, Mark W.
Dewhirst, Shiva K. Das. A Subspace Approach for Magnetic Resonance Thermal
Image (MRTI) Guided Feedback Control of Multi-Antenna Thermal Therapy, The
10th International Congress of Hyperthermic Oncology (ICHO), Munich, Germany;
April 7, 2008.
[5] Kung-Shan Cheng, Zhen Li, Vadim Stakhursky, Paul R. Stauffer , William T.
Joines, Mark W. Dewhirst, Shiva K. Das. Magnetic resonance temperature image
(MRTI) guided feedback controller for multi-antenna hyperthermia treatment in a
reduced order subspace, World Conference on Interventional Oncology (WCIO), Los
Angeles, CA, June 22, 2008.
[6] Kung-Shan Cheng, Zhen Li, Paul R. Stauffer , William T. Joines, Mark W.
Dewhirst, and Shiva K. Das. "Hyperthermia treatment for a patient with two shank
sarcomas treated by a fast pre-treatment optimization method." In: American Association of Physicists in Medicine (AAPM) - 50th Annual Meeting, Houston, TX,
2008.
150
[7] Zhen Li, William D. Palmer, and William T. Joines*, Multi-section Bandpass
Filters Using Capacitively-loaded Transmission Lines, to be submitted.
[8] Zhen Li, Martin Vogel, Paolo F. Maccarini, Omar A. Arabe, Vadim Stakhursky,
Devin Crawford, Williams T. Joines*, and Paul R. Stauffer*, Towards the Validation
of a Commercial Hyperthermia Treatment Planning System, to be submitted.
[9] Zhen Li, and William T. Joines*, Complex permittivity and depth of penetration of ice and water at microwave frequencies, to be submitted.
[10] William T. Joines, Zhen Li, Paolo. F. Maccarini, and Paul R. Stauffer, WideBand impedance matching of a complex load using lumped and distributed elements,
to be submitted.
151
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