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Catheter ablation of the heart using microwave energy

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O r d e r N u m b e r 9308629
C atheter ablation of the heart using microwave energy
Mirotznik, Mark Steven, Ph.D.
University of Pennsylvania, 1992
UMI
300 N. ZeebRd.
Ann Arbor, MI 48106
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Catheter Ablation of the Heart
Using Microwave Energy
Mark S. Mirotznik
in
B ioengineering
Presented to the Faculties o f the U niversity o f
P ennsylvania in Partial F ulfillm ent o f the R equirem ents for
the D egree o f D octor o f Philosophy
1992
\£cxJ—<,h /''VH
(Signature)
Supervisor of Dissertation
(Signature)
Co-Supervisor oi^Dissertation
1
/
,
1
Graduate Grot p Chairperson
.
_
(Signature)
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ii
Dedication
This thesis is dedicated to my parents, Alvin and Charlotte Mirotznik. Their love
and support over the last 27 years have allowed me to achieve more than I ever
believed possible.
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Acknowledgement
I extend ray most sincere appreciation to ray advisor, Dr. Kenneth R. Foster,
for his continual support and encouragement throughout the completion of this work.
Ken has been a caring advisor and a genuine friend.
I would also like to thank my
co-advisor, Dr. Nader Engheta. Dr. Engheta's positive outlook and sincere enthusiasm
for electromagnetics are a source of endless inspiration.
I also extend sincere thanks to my labmates; Dr. Jonathan Leonard and Dr.
Amanda Osborne and to the bioengineering staff, Gail, Nancy, Lisa, Monica, Kate and
Bill for providing an environment of warmth and friendship from which creativity
blossoms naturally.
To my roommates Tom, Yale, Casey and Mookie, I am truly thankful. Their good
humor and friendship have made living in West Philadelphia a genuinely enjoyable
experience.
I am particularly indebted to my girlfriend, Rukki, for the countless hours spent
proof reading and editing this thesis, while simultaneously being a constant source of
encouragement and love. For this I am truly grateful.
I would also like to thank Microwave Medical Systems and Arrow International
for loan of equipment and financial support.
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iv
Abstract
Catheter Ablation of the Heart
Using Microwave Energy
Author:
Advisor:
Mark S. Mirotznik
Kenneth R. Foster, Ph.D
Co-Advisor:
Nader Engheta, Ph.D
The heating properties of helically coiled antennas, for use in a catheter ablation
system, are studied both experimentally and theoretically. A theoretical model, based
on the sheath helix approximation, is presented and used to predict the antenna's
specific absorption rate (SAR) pattern as a function of the geometry of the antenna and
the electrical properties of the surrounding tissue. This model is then extended to
include the case of an insulating layer. In addition, a thermistor based SAR mapping
apparatus was constructed and used to perform experimental studies on helical
antennas immersed in aqueous electrolytes of various conductivities. Analytical results
agree well with the experimental data, demonstrating the validity of the model.
For these antennas, the SAR distribution strongly reflects the presence of standing
waves along the antenna. These patterns are found to be particularly sensitive to the
helical pitch angle and loss in the external medium. It is shown that, by adding a thin
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layer of insulation to the outside of the helical antenna, one can produce a more
uniform heating pattern which is insensitive to loss. This configuration appears to be
suitable for catheter ablation applications.
The microwave results are then compared to analytical and experimental results
from a radio frequency (RF) ablation device. It is shown that the helical antenna
offers the possibility of relatively uniform heating, whereas the RF device heats
predominantly at its tip.
In vitro experiments are performed in excised sheep hearts. Lesion sizes measured
in actual tissue samples agree favorably with calculated responses. These results
graphically illustrate that microwave ablation is able to produce larger lesion sizes than
presently available techniques. This ability may prove useful in the catheter treatment
of a variety of cardiac arrhythmias.
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Table of Contents
Page
Chapter 1: Introduction
1.1 Scope of this work
1.2 Overview of Thesis
1
2
3
Chapter 2: Background in Catheter Ablation
2.1 Cardiac Arrhythmias
Wolff-Parkinson-White Syndrome
Supraventricular Tachycardia
Ventricular Tachycardia
2.2 Catheter Ablation Techniques
DC- Electric Shock Ablation
Radio Frequency Ablation
Microwave Ablation
2.3 Helical Coil Antennas
5
5
6
7
8
9
10
11
14
15
Chapter 3:
3.1
3.2
3.3
3.4
20
20
23
28
29
Theoretical Background
Physical Principles of Microwave Heating
Microwave Dielectric Properties of Tissue
Microwave Dielectric Properties of Saline Water Solutions
Temperature Dependance of Complex Permittivity
Chapter 4: Analytical Methods
4.1 Analytical Antenna Modeling
4.1.1 Uninsulated Helical Antenna
Helical Sheath Model
Formulation
Application of Boundary Conditions
Electric and Magnetic Field Solutions
Determinantal Equation
Effect of Feedpoint and Termination
Total Electric and Magnetic Fields
Summary
4.1.2 Insulated Helical Antenna
Antenna Model
Formulation
Application of Boundary Conditions
Electric and Magnetic Field Solutions
Determinantal Equation
32
32
32
34
37
42
43
47
52
60
61
62
64
64
67
68
71
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vii
4.2
4.3
Chapter 5:
5.1
5.2
5.3
Chapter 6:
Effect of Feedpoint and Termination
Summary
Simple Analytical Model of RF Ablation
Summary
Analytical Results
Results from Uninsulated Helical Sheath Model
5.1.1 Dispersion Characteristics
Numerical Method
General Properties of the Solutions
Numerical Results
Summary
5.1.2 Electric Field Distributions
5.1.3 SAR Distributions
Results from Insulated Helical Sheath Model
5.2.1 Dispersion Characteristics
Numerical Results
5.2.2 Electric Field Distributions
5.2.3 SAR Distributions
Summary
Experimental Methods
6.1 Measurement of Specific AbsorptionRate (SAR)
6.1.1 SAR Mapping Apparatus
6.1.2 Data Analysis
6.2 Measurement of Input Impedance
6.3 Measurement of Microwave Dielectric Properties
Chapter 7:
7.1
7.2
7.3
7.4
72
72
73
78
Experimental Results
Helical Antennas
7.1.1 Uninsulated Helical Sheath Antenna
SAR Distributions
Input Impedance
7.1.2 Insulated Helical Sheath Antenna
SAR Distributions
RF Ablation Measurements
Dielectric Measurements
In Vitro Measurements
80
80
81
81
83
85
89
91
97
104
104
105
108
110
117
118
118
118
124
130
133
138
138
139
139
148
151
151
158
162
162
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Chapter 8: Conclusion
Summary of Results
Significance of Results
Future Studies
171
171
172
173
Appendix A: Heat Transfer Analysis of Thermistor Based SAR Mapping 174
Apparatus
Appendix B; Expansion Coefficients in Open Ended CoaxialProbe Model 180
References
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181
ix
List of Tables
Table 7.1:
Table 7.2:
Helical antennas used for experimental measurements
Complex permittivity of NaCl solutions
Page
139
140
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List of Figures
Figure 2.1:
Figure
Figure
Figure
Figure
2.2:
2.3:
2.4:
2.5:
Figure 3.1:
Figure 3.2:
Figure 3.3:
Figure 3.4:
Figure 4.1:
Figure 4.2:
Figure 4.3:
Figure 4.4:
Figure 4.5:
Figure 4.6:
Figure 4.7:
Figure 5.1:
Figure 5.2:
Figure 5.3:
Figure 5.4:
Figure
Figure
Figure
Figure
5.5:
5.6:
5.7:
5.8:
Typical reentrant tract formation which leads to ventricular
tachycardia
Typical catheter used for DC electric shock ablation
Typical radiofrequency (RF) ablation system
Typical microwave catheter ablation device
Illustration of a typical helical antenna studied in this work
Page
7
10
12
14
16
The real part of the complex permittivity and conductivity
24
versus frequency
Dielectric properties of muscle and blood as a function of
26
frequency
Dielectric constant and conductivity of aqueous NaCl
27
solution, muscle and blood as a function of frequency [Foster and
Schwan, 1986]
Conductivity of 0.8% NaCl as a function of frequency for
31
temperatures ranging from 25 to 55°C.
Helical antenna immersed in an external lossy medium
Helical sheath model of antenna immersed in an external
lossy medium
Illustration of forward and backward traveling waves along
sheath helix antenna model
Insulated helical antenna immersed in an external lossy medium
Insulated helical sheath model of antenna immersed in an
external lossy medium
Model of an RF ablation device
An approximate model of Figure 4.6
Dispersion characteristics of slow and fast mode lqb vs.(3b
Dispersion characteristics of slow and fast mode propagation
constant vs. pitch angle
Dispersion characteristics of slow and fast mode propagation
constant vs. sheath radius
Illustration of the antenna geometry used for the electric field
calculations
Magnitude of electric fields at various frequencies
Magnitude of electric fields at various pitch angles
Magnitude of electric fields for various loss tangents
Illustration of the antenna geometry used for the SAR
calculations
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33
36
52
63
65
74
76
86
88
90
92
93
95
96
97
Figure 5.9: Normalized SAR distribution at various pitch angles
Figure 5.10: Normalized SAR distribution for various loss tangents
Figure 5.11: An illustration of the insulated helical sheath model used
for the dispersion calculations
Figure 5.12: Dispersion characteristics of slow and fast mode of insulated
antenna vs. insulation thickness
Figure 5.13: An illustration of the antenna geometry used for the electric
field calculations of the insulated antenna
Figure 5.14: Magnitude of electric field for insulated antenna for various
insulation thicknesses
Figure 5.15: Illustration of geometry used in the SAR calculations for the
insulated antennas
Figure 5.16: Normalized SAR distribution of insulated antenna for various
insulation thicknesses
Figure 5.17: Comparison of normalized SAR distributions for insulated and
uninsulated helical antennas in various lossy media
100
103
105
Figure
Figure
Figure
Figure
Figure
Thermistor based SAR mapping apparatus
Positioning table
Thermistor probe used for SAR measurements
Electronic circuit used to record thermistor temperature
Heat transfer model used to subtract the thermal artifact
out of the thermistor temperature measurement
Illustration of how the measured thermistor temperature will
differ from the actual temperature of the external medium
Measured temperature vs. time curves for several different
input power levels
The initial and second slopes identified in Figure 6.7 vs.
input power
Reference plane for input impedance measurements
Experimental setup used to measure input impedance
Experimental setup used to measure complex dielectric
constant of tissue at microwave frequencies. The measurement
is based on the open-ended coaxial probe technique
119
121
122
123
125
Measured and calculated SAR distributions for antennas of
various pitch angles in distilled water
Measured and calculated SAR distributions for Antenna #3
(in Table 7.1) in distilled water and various saline solutions
Measured and calculated SAR distributions for Antenna #4
(in Table 7.1) in distilled water and various saline solutions
Measured resistive and reactive components of the input
impedance vs. frequency for antennas with various pitch angles
immersed in 0.8% saline
142
6.1:
6.2:
6.3:
6.4:
6.5:
Figure 6.6:
Figure 6.7:
Figure 6.8:
Figure 6.9:
Figure 6.10:
Figure 6.11:
Figure 7.1:
Figure 7.2:
Figure 7.3:
Figure 7.4a:
107
108
109
110
113
116
127
128
129
130
132
134
145
147
149
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Figure 7.4b:
Figure 7.5:
Figure 7.6:
Figure 7.7:
Figure 7.8:
Figure 7.9:
Figure 7.10:
Figure 7.11:
Figure 7.12:
Figure 7.13:
Figure 7.14:
Figure A.1:
Measured resistive and reactive components of the input
150
impedance vs. frequency for antennas with various pitch angles
immersed in 0.4% saline
154
Measured and calculated SAR distributions of uninsulated and
insulated antennas in distilled water for Antennas #1,#3 and #4
(in Table 7.1)
Measured and calculated SAR distribution of uninsulated and
157
insulated antennas in 0.8% NaCl solution for Antennas #3 and #4
Illustration of the RF catheter geometry used for the SAR
158
measurements
Measured and calculated SAR distributions of the RF catheter
159
in 0.4% and 0.8% NaCl solution
Measured and calculated SAR distributions for the RF catheter
161
and the insulated helical antenna (Antenna #3) in 0.8% NaCl
solution
The experimental setups used for microwave and RF ablation
163
studies
Illustration of lesion geometry used in lesion size measurements 165
167
Measured lesion de"th and SAR pattern for Antenna #1 with
and without insul*.
Measured lesion dt
and SAR pattern for Antenna #3 with
168
and without insulaL i
Measured lesion depth and SAR pattern for the insulated
170
Antenna #3 and the RF catheter
Spherical thermistor immersed in a homogenous lossy medium
and exposed to a uniform electric field
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174
List of Symbols
C h ap ter 3:
1.
2.
3.
4.
5.
6.
a e = effective electrical conductivity of lossy media
p = tissue density
e* = complex permittivity
to = radian frequency
E = electric field vector
SAR = specific absorption rate
C h ap ter 4:
Noninsulating Antenna
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14
15.
e, = permittivity of interior region of helical antenna
ee = permittivity of lossy exterior region ofhelical antenna
a = radius of inner core of helical antenna
b = outer radius of helical antenna
a = helical pitch angle
p = helical pitch
L = length of helical antenna
ne= electric Hertz vector
11”= magnetic Hertz vector
I,, = modified Bessel function of the first kindof order n
K„ = modified Bessel function of the second kindof order n
I, = total axial current flow
(5 = propagation constant
lq = wavenumber of interior region
kj = wavenumber of exterior region
16.
u = V(P2 - k,2)
17.
v = V(P2 - kg2)
Insulating Antenna
18.
19.
20.
21.
22
23.
24.
d = thickness of insulation
£t= permittivity of interior region
62= permittivity of insulating region
£3= permittivity of exterior lossy region
lq = wavenumber of interior region
kj = wavenumber of insulating region
k3 = wavenumber of exterior lossy region
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xiv
25.
26.
27.
u = V(p2 - kj2)
x = V(p2 - k22)
v = V(p2 - k32)
C hapter 5:
1.
tan(y) = loss tangent of external lossy medium
C hapter 6:
1.
2.
3.
4.
5.
6.
7.
8.
9.
0,,, = electrical conductivity of thermistor
k*,, = thermal conductivity of thermistor
otu, = thermal diffusivity of thermistor
c m = electrical conductivity of outside medium
]£„, = thermal conductivity of outside medium
pm = density of outside medium
Z0 = characteristicimpedance of transmission line
Zfc = input impedance tohelical antenna
= power reflection coefficient
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1
Chapter 1: Introduction
In the past, pharmacological and surgical treatments were the only alternatives for
diseases such as cardiovascular disease, colorectal cancer and endobronchial cancer.
Surgery for some of these patients, depending on the severity of their illnesses, posed
a considerable risk. Over the last 50 years, attempts to treat high risk patients without
subjecting them to major surgical intervention have led to a range of nonsurgical
techniques using catheters.
One promising area of investigation is the treatment of certain cardiovascular
diseases resulting from arrhythmias. The idea is to use a catheter to ablate (destroy by
heating) the diseased cardiac tissue near the catheter tip. Recent advances in the
techniques of electrode catheter mapping have allowed the catheter to be localized near
arrythmogenic cardiac tissue. This tissue can then be ablated to produce the desired
therapeutic effect. A range of catheter ablation techniques have been explored,
including the use of direct current (DC) electric shocks, cryotherapy, radiofrequency
energy (RF) and lasers. The common goal of all these techniques is to destroy
abnormal tissue sites while sparing neighboring healthy tissue. The effectiveness of
any of these techniques depends on the type and location of the arrythmogenic site
The aim of this thesis is to complete a careful study into the design and
application of a relatively new catheter ablation technique which uses microwave
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2
energy. The goal is to design a microwave antenna that is able to ablate larger
volumes of tissue than is currently possible with other catheter ablation techniques.
This ability may allow catheter treatment of a class of arrythmias (ventricular
tachycardia) which is untreatable with current catheter ablation techniques.
1.1 Scope of this work
The ability of a microwave ablation device to produce a desired heating pattern
depends on a variety of factors. These include the geometry and operating frequency
of the antenna and the electrical properties of the tissue. Presently, however,
microwave ablation is still in its infancy and most of these factors have not been
carefully studied. Moreover, a careful comparison between microwave and
radiofrequency ablation is needed to address the relative merits of the former.
To better understand the significance and limitations of microwave ablation, it is
necessary to have a clearer understanding of the heating characteristics of the
microwave ablation antenna. This study focuses on a particular antenna design, the
helically coiled antenna, whose heating properties have not been previously
understood. This work answers the basic question of how the geometry of the
antenna, the electrical properties of the tissue and the frequency of operation effect the
heating characteristics of the antenna. Additionally, I compare the heating patterns of
microwave antennas with those of commercially available RF devices. This research
follows the sequence:
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1)
Present an analytical model for insulated and uninsulated helical
antennas immersed in a general lossy medium.
2)
Experimentally study the heating characteristics of helical antennas to
validate the analytical models.
3) Perform in vitro studies on excised sheep hearts, to qualitatively estimate
the lesion sizes microwave ablation is capable of producing.
4) Compare the analytical and experimental data from the microwave ablation
results to those from commercially available RF catheters. This comparison
allowed me to evaluate the relative merits of the different techniques.
1.2 Overview of Thesis
The remainder of this thesis presents the results obtained from the above study
sequence. Chapter 2 presents the physiological and technical background underlying
catheter ablation. It includes a survey of previously investigated catheter ablation
techniques including studies in microwave ablation. Also included is a detailed
description of the helical antennas studied in this work. The next chapter addresses the
theoretical background of microwave ablation. A presentation of the physical
principles underlying microwave heating is followed by a discussion of the electrical
properties of cardiac tissue at microwave frequencies. Chapter 4 presents the
analytical models used during this study. It begins with analytical models for the
helical antenna with and without insulation followed by a simple analytical model for
commercially available RF catheters. In Chapter 5, the theoretical results which follow
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the analytical antenna models is presented. These results consist of the dispersion
characteristics, the electric Held distributions and the SAR patterns for the uninsulated
and insulated helical antenna. Chapter 6 describes the experimental techniques used to
validate the analytical models. After the analytical and experimental methods have
been explained, Chapter 7 presents and discusses the experimental results obtained.
From these results, Chapter 8 draws pertinent conclusions regarding the utility of
microwave ablation.
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5
Chapter 2: Background in Catheter Ablation
This chapter addresses some of the medical and technical aspects of catheter
ablation. The first section describes a few of the most common cardiac arrhythmias
for which catheter ablation techniques have been used. The next section describes
some of the most commonly investigated catheter ablation techniques. The last section
discusses the microwave antenna studied in this work, the helical coiled antenna.
2.1 Cardiac Arrhythmias
Cardiac arrhythmias are, by definition, any variation from normal cardiac rhythm.
This definition encompasses a wide variety of cardiac diseases, some of which have
been successfully treated using catheter ablation techniques. In this section, a few of
the most common cardiac arrhythmias which are treatable using catheter ablation are
described. In addition, there is a description of a class of arrhythmias, termed
ventricular tachycardia, which are presently not treatable using catheters.
Wolff - Parkinson - White Syndrome
The Wolff-Parkinson-White syndrome (WPW) is a functional disorder affecting
many young people in the United States1. This disorder, it is believed, stems from an
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accessory muscle bundle (bundle of Kent) connecting the atria to the ventricles. Rapid
depolarization over this bundle results in ventricular preexcitation. Consequently,
WPW patients have frequent attacks of supraventricular or even ventricular
tachycardia.
Conventional treatments, such as open heart surgery or drug therapy, are found to
have either too high a risk or undesirable side effects. This has motivated the use of
catheter ablation. With this technique, the ablation catheter first locates the accessory
pathway and then deposits enough energy to destroy it. The accessory pathways are
typically thin muscle bundles lying anywhere within the myocardium. Consequently,
the ablation catheter needs only to produce a small discrete lesion large enough to
reach this pathway. Presently, RF catheters are in wide clinical use in the treatment of
WPW syndrome. They have an extremely high success rate ( > 90 %) and do not
subject the patient to unnecessary risk2,3,4.
Supraventricular Tachycardia
This class of arrhythmias includes all tachyarrhythmias which originate above the
ventricle. While the mechanism behind the tachyarrhythmia varies depending on the
exact nature of the disease, the treatments have certain similarities. For many cases of
supraventricular tachycardia, the solution is to ablate the AV node. By doing, this the
physician effectively separates the conducting system between the atria and the
ventricle. Hence ensuring that the supraventricular tachycardia does not interfere with
the otherwise normal contraction of the ventricle.
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A variety of catheter ablation techniques have been introduced to ablate the AV
node in patients with supraventricular tachycardia5,6,7. These techniques, like those
used in the treatment of WPW, need only produce a small discrete lesion at the AV
node to successfully disrupt conduction. Techniques using DC-electric shocks and RF
energy have been used and are discussed in more detail below.
Ventricular Tachycardia
Of all the arrhythmias mentioned here this is the most life threatening and the
most difficult to treat. Each year, several hundred thousand people in the United
States die of ventricular fibrillation (sudden death), often the result of ventricular
tachycardia (VT). This condition is primarily due to rapid impulse formation in a
ventricle. Ventricular contractions during VT are generally greater than 100 beats per
Infarct
Normal
Pathway
Unidirectional
Block
Delayed
Conduction
Proximal
Reexcitation
Figure 2.1 Typical reentrant tract formation which leads to ventricular tachycardia.
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minute and may be as high as 150 to 175. If sustained, VT can degenerate to
ventricular fibrillation and death.
This tachycardia often results from an impulse repetitively circling a reentry loop.
Figure 2.1 shows a typical reentrant tract formation which can lead to VT. It is
presently believed that abnormal tissues which border transmural infarcts are a major
source of this formation. Electrophysiological studies have shown that reentrant
circuits require the formation of separate conduction paths around a transmural infarct8,
with a unidirectional block and a slowed impulse conduction velocity in one pathway.
This combination can lead to reexcitation of the proximal node and, consequently, an
impulse which repetitively circles around the reentrant circuit9.
Long-term management of patients with recurrent ventricular tachycardia is a
challenging therapeutic problem. Usually, antiarrhythmic drugs are initially prescribed,
but many patients either fail to respond or cannot tolerate the drug therapy. Invasive
therapies include open-chest surgical intervention or the placement of automatic
implantable cardioverter defibrillator (AICD). The surgical procedure is designed to
excise or ablate the reentrant pathways whereas the implantable defibrillator is used to
shock the heart into a normal sinus rhythm when the onset of tachycardia is detected.
The success rate of these procedures is approximately 15% with a relatively high
operative mortality rate of 7-9%10. Moreover, due to additional medical problems, a
significant subset of VT patients are not ideal candidates for either procedure.
Consequently, a relatively noninvasive therapy such as catheter ablation is highly
desirable.
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A number of groups have reported varying success in their attempts at catheter
ablation of VT foci111213. For this procedure, multipolar electrode catheters are
inserted into the right or left ventricle. VT is induced by using standard stimulation
protocols and the catheters are manipulated within the ventricles to determine the exact
foci of the VT. Once this foci has been located, the ablation catheter is manipulated to
that location and used to apply large amounts of energy directly at the tachycardia
foci. Previous studies using low frequency (DC) electric shocks or RF energy have
shown modest success rates (< 50%) with several additional complications11,12,13.
Because of these drawbacks the procedure has not gained clinical acceptance. It is
believed, among other things, that presently available ablation devices are incapable of
producing lesion sizes necessary to successfully treat this disorder. Unlike the
situation with WPW treatment or AV nodal ablation, ventricular tachycardia foci can
be quite large, and can necessitate an ablation area which is larger than currently
available devices are able to produce. This is the primary motivation for investigating
microwave ablation devices.
2.2 Catheter Ablation Techniques
A variety of catheter ablation techniques have been introduced for the management
of patients with cardiac arrhythmias. These techniques include the use of large direct
current (DC) electric shocks, radiofrequency (RF) energy and microwaves. In this
section, each of these techniques is examined in detail. I also include a review of
previously reported studies which use these techniques.
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DC - Electric Shock Ablation
The first catheter ablation procedures used low frequency electric shocks14. Figure
2.2 shows a typical catheter used in these initial experiments. As shown in the figure,
the catheter is placed along the endocardium and large DC - electric shocks, ranging
from 30-200 J of energy, are applied via two catheter electrodes. In most cases, two
additional EKG mapping electrodes are included. These electrodes are used to help
the physician locate the arrhythmogenic site.
Tissue
V
Mapping Electrodes
Figure 2.2
Typical catheter used for DC - electric shock ablation.
Initial approaches used high-energy DC shocks, with good results, to ablate the
AV node in patients with supraventricular tachycardia. Data accumulated from a
world-wide voluntary catheter ablation registry reports over 500 attempted catheter
ablations of the AV node using this method15. Overall, the results show that
arrhythmia control was achieved in 85% of the patients. High-energy shocks were
also applied, with moderate success, to ablate accessory pathways in patients with
Wolff-Parkinson-White Syndrome. Fisher et al. delivered shocks, ranging from 40 to
150 J, to 20 patients with WPW16. Complete arrhythmia control, without need for
antiarrhythmic drugs, was achieved in 75% of the patients.
However, the use of DC shock has been associated with significant complications.
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These include induction of arrhythmias17, thromboembolism18, transmural necrosis and
cardiac perforation16. The DC energy is also difficult to control and is associated with
a high incidence of catheter damage19.
Attempts at treating ventricular tachycardia using DC-electric shock ablation have
been met with a limited success rate. The most comprehensive study reporting the
results of this comes from a voluntary international registry20. In 164 patients with
VT, the overall incidence of complete tachycardia cure (without the need for
supplemental antiarrhythmic drugs) was 18%. An additional 41% improved with a
supplement of antiarrhythmic drug therapy.
Radio Frequency Ablation
The moderate success of electric shock ablation encouraged investigators to
search out alternative energy sources that could be incorporated into a catheter ablation
system. The use of radiofrequency (RF) energy was the next major advance in
catheter ablation technology. RF ablation was introduced because the energy delivered
can be more accurately controlled and the lesions produced can be well circumscribed.
Several groups, employing a variety of techniques, have described catheter ablation
with radiofrequency. For example, Huang et al. used 750 kHz RF energy from an
electrosurgical generator in the bipolar mode (exactly analogous to the DC-shock
ablation catheter except operating at a much higher frequency, see Figure 2.2) to ablate
the AV node in dogs21. Complete heart block occurred in most of the dogs used in
these studies.
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More recent studies of RF ablation in humans have used standard
electrophysiological catheters operating in a unipolar mode22,23,24. Figure 2.3 shows a
typical RF catheter ablation system operating in the unipolar mode.
T ic c i
ip
Ground Plane
Mapping Eledrodi
Figure 2.3 Typical radiofrequency (RF) ablation system.
The RF currents (typically between 350 kHz - 1.0 MHz) are passed between one
electrode placed at the distal end of the ablation catheter and a ground electrode fixed
on the patient's back.
Jackman et al. “ used this arrangement in the treatment of 166 patients with
Wolff-Parkinson-White syndrome. In 164 of these, accessory-pathway conduction was
eliminated resulting in a successful treatment. Complications from the application of
RF energy occurred in only three patients. There were no associated mortalities.
It became apparent that RF ablation had many distinct advantages over DCelectric shock: 1) RF currents (unlike the low-frequency currents) are unable to excite
cells and thus cannot produce painful tetanic muscle stimulation ; 2) RF currents
cannot directly induce fibrillation; 3) The RF lesion’s location and size are more
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controllable and, therefore, the risk of perforating the ventricular wall is remote.
Presently, RF ablation is in wide clinical use. However, due to the nature of the
RF lesions (small discrete lesions concentrated near the tip of the catheter) the
procedure has been limited to bypass tract ablations. These ablations include
accessory pathway ablation in Wolff-Parkinson-White Syndrome, ablation of the His
bundle and ablation of the AV node.
Experience in the treatment of ventricular tachycardia with RF energy has been
limited to a small number of patients. Borggefe et a l reported successful
radiofrequency ablation in two out of five patients. Morady et al.n recently reported
favorable outcomes in only 45% of 31 patients with VT using RF ablation treatments.
One of the main problems indicated by Morady and Borggefe is the exact localization
of the arrhythmogenic focus, i.e., the reentry circuit of the tachycardia. Since the RF
lesions are small discrete lesions, if the catheter is not positioned exactly over the
arrhythmogenic focus then the procedure is not successful. Moreover, the patients
reported by Morady and Borggefe represent a highly selective group with a single type
of monoraorphic tachycardia. This type of tachycardia stems from a single focus. In
constrast, in many cases of VT, there may be several foci located near an infarcted
region. In these situations, the small lesions produced by an RF catheter make it
impossible for a single ablation procedure to eliminate all of the necessary foci.
Consequently, several investigators have turned to energy sources which are capable of
ablating larger regions of tissue. One promising source is the use of microwave
energy.
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14
Microwave Ablation
The idea of using microwave energy to facilitate tissue heating is by no means
new. In the hyperthermia treatment of cancer, some invasive (interstitial)
radiofrequency and microwave devices have been developed in order to heat deepseated tumors. Several investigators have compared devices using RF energy to those
using microwaves26,27,28. In particular, Stauffer et al. showed that microwave devices
are capable of heating much larger volumes of tissue than the RF devices. From these
earlier studies evolved the idea of incorporating microwave energy into a catheter
ablation device.
A typical microwave catheter is shown in Figure 2.4. The microwave energy,
typically 915 MHz or 2.45 GHz, is released via a microwave antenna placed at the
catheter tip. The objective is to produce a uniform heating pattern along the entire
1 in n itrs
Volumetric
Heating
Figure 2.4 Typical microwave catheter ablation device.
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length of the antenna, such that a large region of tissue can be ablated.
Previous work in microwave catheter ablation is limited to only a few studies29,30.
In particular, Landberg et a l recently reported the use of a microwave catheter for AV
nodal ablation in dogs. Landberg used a modified helical coiled antenna, operating at
2.45 GHz, to successfully block AV nodal conduction in 6 out of 6 dogs used in this
study. To date, the use of microwave catheters in the treatment of VT has not been
studied.
Studies using microwave catheters have been hampered by a lack of good
theoretical models to predict the interaction between the antenna and lossy tissue.
This work provides a theoretical model for a particular antenna design, a helically
coiled antenna. This antenna (similar to the one used by Landberg) is described in the
next section.
2.3 Helical Coiled Antennas
Helical antennas are well known for their applications in communications, where
they have been studied for over 50 years. Quite a different application involves their
use for heating. Little work has been done to characterize such helical antennas in
lossy media, and most previous reports are experimental in nature. Satoh et al?1 along
with Wu and Carr32 described the heating patterns of several helical antennas used as
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16
short circuit termination
Helically wound wire
inner core
dielectric
outer shield
coaxial transmission line
Figure 2.5 Illustration o f a typical helical antenna studied in this work. The antenna is fabricated by
wrapping a thin wire around the exposed dielectric of a coaxial transmission line in a helical fashion.
The wire is then soldered to the inner core of the coaxial line at the distal tip of the antenna (short
circuit termination) and fixed to the outer shield at its base. The pitch angle a is used to define the
angle between the helical wire and the plane normal to the antenna axis.
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interstitial hyperthermia applicators. Figure 2.5 shows a typical helical antenna design
used by Satoh and Wu. The details of this antenna are presented in the Analytical
Methods chapter.
The results from these experimental studies show a relatively uniform heating
pattern along the length of the antenna with a shallow depth of heating. For their
application of hyperthermia, where the goal is to achieve the greatest depth of heating,
other antenna designs are preferable. For catheter ablation, where great depth of
heating is often neither required nor desirable, helical antennas may be preferable.
However, Satoh and Wu did not present a comprehensive theoretical or numerical
analysis of the antenna characteristics as functions of helical pitch or other design
parameters. There is a need for a more general analysis of such antennas, in order to
describe their heating characteristics as functions of antenna geometry and dielectric
properties of the lossy medium.
There is a considerable amount of literature relevant to the theoretical problem.
However, due to the complicated boundary conditions imposed by the actual wire
wound helix, all studies have relied on approximate models. One such model,
originally studied by Sensiper33, approximated the actual wire wound helix by an
anisotropically conducting sheath. The sheath is assumed to be perfectly conducting at
some angle a parallel to the actual helical wire and perfectly insulating normal to that
direction. Sensiper obtained the field distributions and dispersion characteristics
assuming the antennas were radiating into free space. The antennas studied by Sensiper
did not include an inner core and were assumed to be infinite in length.
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18
Neureuther et al?* extended Sensiper’s model to include a conducting core (the
case of interest here). He also studied a more physically realistic, but mathematically
difficult, model consisting of a perfectly conducting spiral tape, and showed that the
sheath model was an excellent approximation. Neureuther et al., like Sensiper,
assumed the antennas were radiating into free space and were infinite in length.
Perini35 carried out an extensive theoretical and experimental study of helical
antennas. He used a spiral tape model with conducting core to compare calculated
results to experimental measurements. He was primarily concerned with the antenna's
radiation pattern and, consequently, only considered antennas radiating into free space.
He found that the results obtained under the assumption of an infinite length helix did
not agree satisfactorily with those determined experimentally. Perini suggested that
more accurate calculations could be obtained by taking into account end reflections.
However, he did not include these reflections in his model nor, to the best of my
knowledge, has any other investigator.
More recently, Hill and Wait36, carried out an elegant theoretical study on wave
propagation along coaxial cables with helical shields. Their model consisted of a
dielectric coated conductor which was shielded by a finite number of helices.
Utilizing a modal expansion technique, they solved for the propagation characteristics
of waves traveling along their antennas. They were particularly interested in the leaky
feeder technique used to provide radio communication in mine tunnels. Although that
is quite different from the application of interest here, the method used by Hill and
Wait is utilized and extended to the case of lossy medium in this work.
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19
Only a few investigators have studied the helical antenna immersed in a lossy
medium and these studies have been numerical in nature. Chen37 developed an
integral equation for an infinite length helical sheath antenna radiating into a lossy
medium. His equations could then be solved numerically for the antenna's current
distribution. Casey and Bansal38 extended Chen's work to the case of a finite length
helical sheath antenna in a general lossy medium. In addition, they developed a
numerical method based on the moment method for solving their integral equation.
The antennas considered by these investigators did not include a dielectrically coated
inner conductor or the effects of a coaxial feed point and short circuit termination, as
is the case here. However, the solutions reported by Casey and Bansal are used here
to check limiting cases for the model presented in this work.
The models presented in this thesis extends the analytical work of Hill and Wait,
Neureuther et al., Sensiper, and others to include the effects of a coaxial feed point, a
short circuit termination, an insulating layer and an external lossy medium. These
considerations, which are necessary for the present application of microwave catheter
ablation, have not, to the best of my knowledge, been studied by any previous
investigator of helical antennas.
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20
Chapter 3:
Theoretical Background
The mechanisms responsible for myocardial tissue damage which occurs during
ablation, depend on the ablation technique used. In RF and microwave ablation the
primary phenomenon responsible for cellular damage is excessive heating of tissue.
The first section of this chapter describes the physical principles underlying the
microwave heating of tissue. The discussion continues with an overview of the
dielectric properties of cardiac tissues at microwave frequencies. These properties are
then compared to those of saline solutions used to evaluate the antenna.
3.1
Physical Principles of Microwave Heating
In heating applications, the quantity of interest is the power, Pd, dissipated in the
medium. If we assume a nonmagnetic medium occupies some volume V, then the
total dissipated power is given by
Pd
‘ } J J c , \ E \ 2d v
Warn
[3.1]
where e is the instantaneous electric field vector in units of V/cm and a e is the
electrical conductivity of the medium in units of S/cm. The quantity being integrated,
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Pd = o j ^ l 2’ *s 1116 dissipated power density in units of Watts/cm3.
If the electromagnetic energy has a sinusoidal time variation (time-harmonic), then
the instantaneous electric field vector can be related to its complex phasor equivalent
in a very simple manner by
E { x M ) = R e [ E ( x ^ at]
[32]
where e represents the complex phasor form of the electric field, to is the angular
frequency ( to = 2 n f) and j= V -l. Throughout this thesis, the time-harmonic case will
be assumed and the term e**0*will be omitted for convenience. The dissipated power
density can also be related to the complex electric field by
P, - k
*
|£ |2 ~ s
cm3
M
In Equations 3.1- 3.3, cre represents the total or effective conductivity of a general
lossy material. This effective conductivity is actually composed of a static term, cts,
due to the ability of free charges to migrate under the influence of an electric field,
and an alternating part, a a, caused by the rotation of dipoles as they attempt to align
with an alternating applied electric field. The static conductivity contributes to the
ohmic or resistivelosses of a material, while the alternating conductivity contributes to
dielectric losses. The ratio of resistive to dielectric losses depends onthe material and
the frequency of the applied electric field. For most biological tissues, resistive
heating dominates up to several MHz after which dielectric effects begin to contribute.
At microwave frequencies (f>300 MHz), dielectric losses play a more significant role
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22
in the generation of heat.
When energy is deposited in tissue faster than it can be dissipated by thermal
conduction or convection, the inevitable result is an elevation of temperature. In the
early transient regime (where heat conduction and convection effects are negligible)
the temperature increase can be related to the applied power density distribution and
the thermal properties of the tissue by
q(xy& t) = pc
at
[3.6]
where T(x,y,z,t) = Time dependent temperature distribution ( °C)
q(x,y,z,t) = Applied power density distribution(Watts/cm3 )
p = Density of tissue (gm/cm3 )
c = Specific heat capacity of tissue (Joule/(gm °C))
Substituting [3.3] into [3.6], the rate of tissue temperature increase is found in
terms of the applied electric field and the effective conductivity of the tissue by,
SAR = f l ! ! ! ! - Ito v , c <L Z .
2p
M) dt gm
[3.7]
The left side of [3.7] is termed the specific absorption rate (SAR) and is used
extensively in biomedical applications to determine the amount of power deposited per
unit mass in biological tissue. The SAR distribution specifies the power deposition
patterns of antennas used in hyperthermia or ablation applications and is used
extensively in this work. At longer times, the temperature distribution will be different
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23
from the results shown in [3.7] due to the affects of thermal conduction and
convection. Thus, the SAR distribution can be experimentally measured by
determining the initial rate of temperature increase directly after the power is applied.
3.2
Microwave Dielectric Properties of Tissue
Propagation and absorption of electromagnetic energy within biological tissue
depends upon the electrical properties of the tissue. Biological tissue is essentially
nonmagnetic, so its permeability p is essentially the same as the permeability of free
space, p0 (= 4k
x
10 '7 Henrys/meter). However, the complex dielectric permittivity,
e*, of tissue is a complicated quantity depending on the type of tissue and the
frequency of the applied fields. The complex permittivity is expressed as
e* = e0( e'- j e#) where e0 is the permittivity of free space (=8.85 x 10'12
Farads/meter) and j= V -l. The quantity z' is the relative dielectric constant and the
imaginary part, z ‘ = oe /coe0, accounts for tissue losses.
A large amount of literature exists on the electrical properties of tissue. In
particular Foster and Schwan39 gave a thorough review of measured data and discussed
some of the mechanisms responsible for changes found in e*.
The dielectric constant, e', and conductivity, o e, of most soft tissues are
qualitatively similar in there frequency dependence. In Figure 3.1 (from [Foster &
Schwan, 1986]) the frequency dependence found in typical tissues is shown. The
frequency of interest here (915 MHz) corresponds, for muscle tissue, to the region
just before the beginning of the y dispersion. At this frequency, the cell membranes
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24
10.0
915 M H z
a S/m
FREQUENCY. Hz
Figure 3.1 Hie real part of the complex permittivity and conductivity versus frequency showing a, p
and v dispersions [Schwan & Foster, 1986].
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25
are shorted out and no longer contribute to the bulk permittivity. Hence, the bulk
permittivity at these frequencies, may appropriately be treated as a suspension of
proteins and other macromolecules in electrolytic solution.
Dielectric properties of tissue depend also on the particular tissue type. For
microwave ablation, the tissues of direct interest are cardiac muscle and blood.
In Figure 3.2, the electrical properties of canine muscle tissue are compared with the
those of whole blood as a function of frequency (data taken from Foster & Schwan
1986). The dielectric constant of blood and muscle show a broad dispersion with a
plateau region between 100 MHz and 1.0 GHz. The conductivity shows a slow
increase from a low frequency value of 1.0 S/m to a high frequency value at 10.0
GHz, of 10 S/m . Figure 3.2 shows that, at microwave frequencies, blood and muscle
have similar electrical properties. This fact justifies the assumption that muscle tissue
and blood form an electrically homogenous medium over the frequencies of interest
here.
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26
i° j
• Muscle
o — Whole Blood
b
0.1 —
0.01
1
0.1
10
frequency, GHz
1000
Muscle
- Whole Blood
s
1 100
a
tr
0.01
1
0.1
frequency, GHz
Figure 3.2 Dielectric properties of muscle and blood as a function of frequency,
[data taken from Foster and Schwan 1986]
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10
27
• -
o -1
CA
b
frequency, GHz
O K OOf ond 1.QX Noa OMftaee
frequency, GHz
Figure 3.3 Dielectric constant and conductivity of aqueous NaCl solution, muscle and blood as a
function of frequency. [ data taken from Foster and Schwan 1986]
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28
3.3
Microwave Dielectric Properties of Saline Water Solutions
To facilitate the placement of temperature and electric field probes, sodium
chloride solutions were used as an electrical tissue phantom. In this section the
electrical properties, at microwave frequencies, of different concentrations of saline
solutions are compared with those of tissue.
The complex permittivity as a function of frequency, water temperature and
salinity, can be calculated from the equations published by Stogryn40. These equations
assume the complex permittivity of saline solutions can be represented by an equation
of the Debye form given by
€ * = € „ + (6* ~ € J - y A .
1 + you
coe^
where es and
permittivity,
[3.8]
are the low and high frequency limit, respectively, of the
cs
is the low frequency conductivity and
t
is the relaxation time constant.
Stogryn obtained equations for the parameters in the Debye expression by interpolating
measured data over a broad range of frequency, temperature, and salinity ranges.
In Figure 3.3, the dielectric permittivity e' and conductivity cre, of various
concentrations of sodium chlorine solutions (at 25°) are compared with those of blood
and muscle tissue, as a function of frequency. The figure shows that, between 1.0 and
10.0 GHz, the conductivity of 0.8% NaCl agrees well with the conductivity of blood
and muscle tissue. In the same frequency range the dielectric permittivity of the NaCl
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29
solutions is slightly higher than that of tissue (by 5 to 10 dielectric units), but varies
only slightly with NaCl concentration. Subsequent analysis will show that this small
difference does not significantly change the heating patterns for the microwave
antennas studied here.
3.4
Temperature Dependance of Complex Permittivity
The dielectric properties of tissue is known to vary as a function of temperature.
In the frequency range of 0.5 - 5.0 GHz, the conductivity of high water content tissue
has a temperature coefficient which varies from 0.5-2%/°C. The dielectric permittivity
reflects that of water, which has a very small temperature coefficient. Since the SAR
calculations are dependent on conductivity, it is obvious from [3.3] that the SAR will
also be a function of temperature. However, if a temperature dependent conductivity
is included in Maxwell's equations, then the equations become non-linear and
extremely difficult to solve. I will estimate the maximum change in conductivity that
is likely to occur during the ablation process (during the ablation process tissue
temperatures may increase as much as 20-30°).
Since, at microwave frequencies, the electrical properties of high water content
tissue reflect that of electrolytic NaCl solutions, the equations of Stogryn were used to
calculated the conductivity as a function of frequency and temperature. In Figure 3.4,
the calculated conductivity of 0.8% NaCl solution as a function of frequency is shown
for a range of temperatures.
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The results show a slight temperature coefficient around 1.0 GHz. This results
from the cancellation of two different temperature dependent mechanisms. As
discussed earlier, the total conductivity arises from two different mechanisms: the
movement of ions under the influence of an externally applied electric field and the
rotation of electric dipoles (of water) with the applied electric field. Both mechanisms
are dependent on temperature, but show quite different dependencies. The
conductivity due to the movement of ions has a positive temperature coefficient in this
frequency range, whereas the conductivity due to the alignment of dipoles has a
negative temperature coefficient in this frequency range. In the neighborhood of 1.0
GHz, the two temperature coefficients approximately cancel each other out, resulting in
only a slight total temperature coefficient. It is fortunate that the microwave antennas
used in this study are being driven at 915 MHz, near the region of small temperature
dependence. Consequently, it is hypothesized that temperature elevation will cause
only a small change in the electrical properties of tissue, which will not significantly
alter the antenna's SAR pattern. In the experimental section, care was taken to
monitor the reflection coefficient of the microwave antennas during the time course of
ablation, to confirm the conclusions of this section.
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31
3.0
T em p eratu re
C
o - 25°
35
45'
2.5
55
\
E
■ >
2.0
o
3
XJ
c
o
o
1.5
1.0
0.5
1.5
1.0
F requency
2.0
GHz
Figure 3.4 Conductivity of 0.8% NaCl as a function o f frequency for temperatures ranging from 25°C
to 55°.
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32
Chapter 4: Analytical Methods
This chapter describes the analytical methods used in the study. The chapter
consists of two sections. The first section describes the analytical antenna modeling
for the insulated and uninsulated helical antenna. The second section presents a simple
analytical model of presently available RF ablation catheters.
4.1 Analytical Antenna Modeling
To understand the heating characteristics of helical antennas, the underlying
theory will be presented. I present an analytical model which, given the various
parameters of helical antennas and electrical properties of the tissue, can approximately
predict the SAR distribution in the lossy tissue medium. I then extend the model to
the case where a layer of insulation is added to the outside of the antenna.
4.1.1 Uninsulated Helical Antenna
An uninsulated helical antenna for catheter ablation applications is shown in Figure
4.1 This antenna is fabricated from a coaxial transmission line with inner and outer
conductors of radii a and b, respectively, which are separated by a (loss-free) dielectric
medium of permittivity e, and permeability p0. At the end of this transmission line,
the outer conductor is stripped back a distance L and the helical antenna placed over
the line.
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33
— H
2a
2b
Figure 4.1 Helical antenna o f length L, outer radius b, inner radius a, helical pitch angle a and pitch p,
immersed in an external lossy media.
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34
The antenna is connected at the distal end to the inner conductor of the coaxial line,
and at the proximal end to the outer conductor of the transmission line. Thus, this
antenna has length L, and in this arrangement it can be regarded as being terminated at
one end by the coaxial feedpoint, and at the other by a short circuit. The medium
outside the helical coil is considered homogeneous, isotropic, linear, nonmagnetic and
lossy, characterized by complex permittivity ee* = e/+ j e / and real permeability p0
To describe the helix, as is usually done, I define the pitch, p, as the distance
between adjacent coils, and the pitch angle, a , as the angle the helix makes with the
plane normal to the helical antenna axis (shown in Figure 4.1). The pitch angle is
related to the pitch by
. - i / 2 rc b ,
a = cot (----- )
P
where b is the radius of the helix.
If Maxwell’s equations could be formulated in an appropriate coordinate system in
which the surface of the wire is described by keeping one of the coordinates constant,
then an exact solution could be obtained using techniques similar to those used in
waveguide problems. While it is possible to formulate the problem in a proper
coordinate system, it appears the resulting equations cannot be easily solved exactly.
Consequently, investigators must rely on approximate models when analyzing helical
antennas.
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35
Helical Sheath Model
One approach has been to replace the physical helix with an anistropically
conducting cylindrical sheath33,34. The sheath model shown in Figure 4.2, is assumed
to be perfectly conducting at an angle a which is parallel to the helix wire ( denoted
by unit vector
) and perfectly insulating normal to that direction (denoted by unit
vector a j . The short circuit termination is modeled approximately by a perfectly
conducting cap at the end of the antenna (shaded region).
In this section, I
describe an analytical model for the helical sheath antenna immersed in lossy media,
and then extend the analysis to include a coaxial feed point and a short circuit
termination. A modal expansion technique is utilized. This method is based on the
techniques used by Hill and Wait, Casey41, Delogne42 and others in treating loosely
braided coaxial cables with helical shields. The procedure is outlined in the following
steps.
1. Solve Maxwell's equations in the source-free region with the appropriate
coordinate system.
2. Apply the necessary boundary conditions. Specifically, the tangential electric
field must vanish on the surface of all perfect conductors. For the sheath
helix, in particular, the tangential electric field component in the direction of
a„ must be zero.
3. Formulate the determinantal equation. Solving this determinantal equation
yields which wave guide modes can exist along the helical structure.
4. Expand the fields at the coaxial feed point into a sum of the allowed guided modes.
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36
5. Introduce a set of reflected modes such that the net tangential electric field
vanishes at the short circuit termination.
6. Add all the forward and reflected modes together to calculate the total electric
and magnetic fields present in the lossy exterior media. The SAR can then
be easily calculated using Equation 3.7.
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37
z=L
Z=0
h— H
2a
2b
Figure 4.2 Helical sheath model of length L, outer radius b, inner radius a and helical pitch angle a,
immersed in an external lossy media. The sheath helix model defined as an anisotropically conducting
cylinder, which is perfectly conducting at an angle a w.r.t. to the plane normal to the antenna axis and
perfectly insulating normal to that direction. A perfectly conducting cap models the short circuit
termination.
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38
Formulation
In a source-free homogenous region, the time harmonic form of Maxwell's
equations are written as
VxE = -ju\iH
Vxtf =jae*E
I4-2)
V*£ = 0
[4-3^
V-tf = 0
t4-4!
where e* and p are the complex permittivity and permeability of the region.
It is well known that due to the divergenceless properties of the source free Maxwell's
equations ( Equations 4.3 and 4.4) the electric and magnetic fields may be expressed
in terms of electric and magnetic Hertz vector potentials IP and IT”, respectively,
by43.44.45
e
h
=VxVxir - j<onVxnm
^
=y we* Vxiie + Vxyxir*
^
Substituting [4.5] and [4.6] into [4.1] and [4.2], one obtains the following set of
decoupled equations in terms of either IP or IT” given by
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39
VxVxne - vcv-ep) - k2ne =o
[4.7]
VxVxIF - V(V-IP) - *2D* = 0
[4.8]
Here, jfc = o>/jxe* represents the complex wavenumber of the medium. Solutions to
[4.7] and [4.8] when inserted into [4.5] and [4.6] provide general solutions to
Maxwell's equations in a source free region. Thus the next step is to solve these
equations in the appropriate coordinate system.
I use a circular cylindrical coordinate system, defined in the usual manner, by
coordinates (p,<)>,z), shown in Figure 4.2. The unit vectors a/7 and ax are related to
the unit vectors in the cylindrical coordinate system ap, a*, and a* by
&u = az sin(a) +
cos(a)
[4.9]
ax = az cos(a) -
sin(a)
[4.10]
where a is the helical pitch angle defined earlier.
For an antenna, or waveguide, of infinite length whose cross section is uniform
along the z direction, it can be shown that only the z component of the Hertz vectors
IT and IF 1are necessary to obtain a general solution to Maxwell's equations3,4. Thus, if
the Hertz vectors are assumed to have only a z component, the electric and magnetic
field components in cylindrical coordinates are given by [4.5] and [4.6] as
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
X
lii t i S
p *8p
r
H .ll]
p a*
1
j 2i
p ozdy
E
H
dp
, . ^ +
dz2
=
p
X, - *
p
j
3<j)
^
ap
k%
14.13]
+ ¥H L
dzdp
[4-14]
♦ i f £
[4.15]
p a z ft
Hz = ^ - + k 2I%
dz2
[4-16]
In addition, Equations [4.7] and [4.8] simplify to the scalar Helmholtz equation given
by
(V2 + k 2)% - i - i ( p — ) * — —
* —
p 3 p K dp
p> a* 2
*2
< * ♦ * * .
+ *2I ? - 0
I f p f C , ♦
p 3p
3p
. o
p2 3<j,2
[4-17]
14181
az2
where the vector identity VxVxA = V(Vvl) - V2/! has been utilized.
As in [Hill and Wait], the solutions to [4.17] and [4.18] are obtained using a
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41
standard separation of variables approach which assumes solutions of the form
HZ = P(p)-3>(<J))-Z(z)
[4.19]
Substituting [4.19] into [4.17] or [4.18] and separating the equation yields three
ordinary differential equations in terms of <(>, z and p .
—
+ n 2® = 0
[4.20]
— + p2Z = 0
d z2
[4.21]
P y K p f ) ~ [(P2- * V + » 2]P = 0
dp
dp
[4.22]
Here, n is an arbitrary positive or negative integer and P is the unknown propagation
constant.
The solutions to [4.20] and [4.21] can be expressed in exponential form:
®(4>) = e ~J " * and Z(z) = e J p z. The solutions of [4.22] are the modified Bessel
functions of order n and argument J $ 2- k 2- The general solutions to [4.17] and [4.18]
are thus given by
l£(P><M = [An / „ ( / F P p ) + Bn Kn( ^ P p)] e 'j P * e-J" ♦
[4.23]
n zw( p , ^ ) = [Cn U < / f T 2p) + Dn * n( / F F p ) ] e-J
e-J
where I,, and K„ are the modified Bessel functions of the first and second kind
respectively, and A„ , Bn ,Cn and Dn are unknown coefficients determined by the
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42
boundary conditions and source distribution [ Hill and Wait].
The general form of [4.23] is valid in both the interior (a< p <b), and exterior
(b< p < oo) regions. However, due to differences in electrical properties and boundary
conditions in the two regions, the actual solutions can be quite different. Consequently
as in [Hill and Wait], the fundamental solutions in the two regions are given by
a< p <b
I?(p,4«) = ]An
P) * K
[4.24]
+d„c.f/F^p)] t ->' !
rCfp.fe) =[c.
♦
b< p < <»
K M A
=F
n
* n( / F * ? P ) e-J P1 e -j" *
Y
[4.25]
K M * ) = Gn Kn( J W ^ P ) e - ^ z e - j n *
where, the subscripts i and e refers to the interior and exterior regions, respectively. In
forming the solutions in the exterior region, the modified Bessel functions I„, is
excluded to insure that the electric and magnetic fields remain finite as p approaches
infinity.
The electric and magnetic fields can now be calculated by substituting [4.24] and
[4.25] into [4.11] through [4.16]. The unknown coefficients
Bn, Cn, D„, F„ and Gn
are then related by applying the appropriate boundary conditions.
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43
Application of Boundary Conditions
Along a boundary between two different media the electric and magnetic fields
must obey certain boundary conditions. If both media have a finite conductivity, the
tangential electric and tangential magnetic fields must be continuous at the boundary.
If one medium has an infinite conductivity (a perfect conductor), then the tangential
electric field will vanish and the tangential magnetic field will be discontinuous by an
amount equal to the induced surface current density. These conditions are written
mathematically as
n x (E2 - Et) = 0
for finite Oj and c 2
[4.26]
n x (ff2 - £ ,) = 0
n x E2 = 0
CTj infinite and ct2 finite [4.27]
n x H2 = J S
where subscripts 1 or 2 denotes media 1 or 2 respectively, n is a unit vector normal to
the perfectly conducting surface, and Jt is the surface current density.
Applying the above boundary conditions to the helical sheath results in the
following six conditions:
i. At the surface of the inner conductor p = a
[4.28]
[4.29]
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44
ii. At the surface of the helical sheath p = b, with current I, flowing in the direction a;/
Ez(b)t = Ez( b \
[4.30]
= E Jb\
[4.31]
P
,
H M t = H A b \ - ^ - Sm-(g)
♦ *
* e
2*6
[4.33]
where the subscripts i and e again refer to the interior and exterior regions,
respectively, and a is the helical pitch angle defined earlier.
It must be remembered that since the sheath model is perfectly conducting along
the a„ direction, the tangential electric field along a„ should also vanish, (i.e. E„ = 0 ).
This boundary condition is used later in formulating the determinantal equation.
Electric and Magnetic Field Solutions
Applying the boundary conditions above to the fields calculated by [4.11]
through [4.16], one obtains a set of six simultaneous equations for the unknown
coefficients An, Bn, Cn, Dn, Fn and Gn. In principle, this set of six equations can be
solved directly to obtain all the coefficients in terms of It. However, this leads to a
horrible algebraic mess. A simpler approach, as done in Hill and Wait35, involves
satisfying the boundary conditions at p=a, Equations [4.28] and [4.29], separately.
This leads to the simple relationships
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where the variables u = \j$2 - k f and v =
- k] are defined for notational
convenience, and the prime refers to the first derivative with respect to the entire
argument.
Following the method used in Hill and W ait36 and using a similar notation, it is
convenient to define the variables
IJu a)
Zn(u p) = /„(« p) - f - j - Kn(u p)
1
Z'n(u p) = /„(« p) -
[4.35]
Kn(u p)
< (« a)
Substituting [4.34] and [4.35] into [4.24], one obtains a much simpler expression for
the Hertz vectors in the interior region, given by
n^C p,^) = A Z (u p) e ~J *z e~j n *
[4.36]
n*(ps^ ) = C „ Z > p) e~j Q2 e~J n *
Now, applying the boundary conditions at the helical sheath, Equations [4.30] [4.33], one obtains a set of four simultaneous equations for the unknown coefficients
Cn, Fn and Gn, instead of six. This set of equations was solved using a symbolic
manipulating program (Maple) and the following electric and magnetic field
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
components were obtained
b< p < oo
Ep - - ( ^
A, < (v P » e-Jt ' e-J' *
[4.37]
C„ < (v p) - i ! / l „ AT„(v p)) e-J * ‘e - l " ♦
[4.38]
C. K„(v p ) + j
£„ = U P<o
V
p
V
[4.39]
£ ; = -v 2 ^„ X„(v p)
ff„ -
€ (OR
JC„(v p) - J
H„ - -( j coe.v X. < (v
=
-V 2
P)
,
p
v C„ AT„'(v p))
+
KJy p)) « -J U e -J . ♦
C„ tf„(v p) e 'n ze~J n *
[4.40]
[4.41]
[4.42]
a< p <b
Eo =
^
P) ^ P h F „ Z > p ) ) ^ P V J M
[4.43]
= ( 7 p u u Gn Z*'(u p) - ^ F n Zn(u p)) e~J " e l * *
[4.44]
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47
[4.45]
Ez = -u 2 Fn Zn(u
ۥ(07*
„
# p - ( - ^ - ^ Zn(u p ) - j p « G „ Z > p))
^
.
.
[4.46]
H
= - ( j <o€j« F„ Z„'(« p) h- £ J L Gn Z*(u p))
[4.47]
= -k 2 G„ Z > p) e -j *ze-j n *
[4.48]
where
.4,, = y |iw /, « 2 Z„ [ sin(a)v «
(« Z„*
- v Z„*' *„)
[4.49]
+ cos(a) n P (v K ' Zn* - « Kn Z„')] / 2ttD*
Cn = /, [ p n Z„ Zn* Kn(v2- u 2) (i«2 * sin(<|>)- p « cos(4»)
[4.50]
+ <o2p «2 z ; ' cos(4>) v (€,. Kn z'n v - €e K'n z n «)] I 2%b D*
F = A " v2 Kn"
[4.51]
«2Z„
[4.52]
and
D* =
p2 «2 z;
z; Z * 2 («2 - v2)2
v 2 (« <
V
z;'
( « 6e
k' Z„
- v
e,
z '
)
and for notational convenience 7^ = Z„ (u,, b), Z^’= ^ ’(t^b), 2,,*= Zp’ ^ b )
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[4.53]
48
K,, = K„(vnb) and K j = K„ (vn b).
The solutions derived above for the electric and magnetic fields depend on the
arbitrary integer n. Each value of n corresponds to a different independent solution
and, in waveguide terminology, is referred to as a guided mode . The guided modes
with different n values will have different azimuthal variation due to the e j n* term.
The propagation constant, P, is still undetermined and requires an additional boundary
condition to completely specify it. The needed relation is termed the determinantal
equation or the dispersion relation.
Determinantal Equation
The determinantal equation can be derived from the boundary condition that on the
surface of the helical sheath the electric field component in the direction %, must
vanish. This condition is written as
Ez sin(a) +
cos(a) = 0
at p = b
[4.54]
Substituting [4.38] and [4.39] into [4.54] results in the determinantal equation
- y2 \
KJy b) sin(a) + [ j pw v C„ k '„(v p) - ^ - A n Kn(v p)] cos(cc) = 0
P
[4.55]
where A„ and C„ are given by Equations [4.49] and [4.50] respectively. The
propagation constant, P, which is complex in general, is calculated by determining the
roots of [4.55]. For any particular integer value for n (guided mode with azimuthal
variation e'jn*), Equation [4.55] may have several roots. Each of these roots
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49
corresponds to a guided mode with a different radial variation.
The set of guided modes described above provide only a partial solution to the
helical sheath problem. In addition to the guided modes there exists a set of radiation
modes needed to account for radiation phenomena. The complete solution is then
formed by summing all of the individual guided modes along with the radiation
modes. This is written as
«°
N
Ktai = £ E £ n,(P) e~JPvZ e ' J n * + radiation modes
»—-/>-i
«
Htotai = £
N
£
e~J
[4.561
L
1
e~j n * + radiation modes
n~-oop<i
where n and p represent guided modes with azimuthal variation n and radial variation
p. Also N represents the number of roots of Equation 4.55 given any particular value
for n.
The radiation modes become important when the antenna's far field ( observation
points several wavelengths away from the antenna) is of interest, whereas the guided
modes play are crucial role in the distribution of the antenna's near field. Since we are
interested in the heating characteristics seen near the surface of the helical antennas,
the radiation modes are not included in this analysis.
In principle, all of the guided modes along with the radiation modes must be
summed to exactly model the characteristics of the helical sheath. However, in
practice only a few of the guided modes may be needed to adequately approximate the
heating characteristics of the helical sheath. For the helical antennas considered here,
the dominant guided modes are those modes where n=0 (modes with no azimuthal
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50
variation). These dominant modes are examined in more detail in the next section.
Dominant Modes n=0
There are two reasons for believing the n=0 modes will be of importance here:
1) The electric and magnetic fields of the coaxial line source are independent of
azimuthal angle, <J>. It is easy to show that if the source fields are independent of <j>
then the modes excited by that source will also be independent of <|>.
2) Experimental measurements revealed no changes in field intensity as the helical
antennas were rotated in the <j>direction.
Consequently, I considered only those modes with n=0. Equations [4.37] - [4.55]
simplify for those modes to
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51
Ep - 'J Pp v A . <<v P> J * *
£«
c„ < (v p) «•*»■>
[4.57]
£; = -v 2 i i . * .(v p) p * M
- - / P„ v C„ < (v p) e 'n - 2
ff, - - J o « ,v ,4. J t f v p ) e 2" - '
[4.58]
H, = -v2 C„ K J y p) p2" * 2
a<p<b
£p - - i P . « F. z > p) ^
£t ■ J P„“ K 0„ z ;\u p) e~J i f
[4.59]
Ez = -» 2 F0 Z„(« p ) e ‘, s -‘
ffp “ -J Pp « G. z;'(» p) p2" * 2
H4 - - j . eI v F . z 4 * p ) « 2' , *‘
[4.60]
H ,= -u2 G „ Z > p) e ‘-'M
where the subscript 0 indicates the n=0 modes. The constants A0, C0, F0, G0 reduce
to Equation [4.61], where again It is the total surface current along the a„ direction of
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52
j It u Z0(u ft) sin(a)
Ao =
27tft CO v [ ee k 0' (v b) Z0(u b) u - €, K Jy b) z'0(u b) v ]
It Z*'(u b) cos(a)
2*ft v [ < ( v b) Z*'(u b) v - < ( v ft) Z > ft) « ]
[4.61]
j It v K0(v ft) sin(a)
2%b (0 [ ee < ( v ft) Z0(« ft) « - e,. ^ 0(v ft) Z'(u ft) v ]
/{ < ( v ft) cos(a)
2nft«[ <(v ft) z; («ft) v - <(v ft) z;(« ft)«]
the n=0 mode.
The determinantal Equation [4.55] reduces to the following for n=0
[4.62]
w2 \i0 cos(a)2
K Jy ft) 2
Z > ft)
—2
v - ------------ « v
<(v ft)
z; («ft)
u sin(a)2
e
< ( v ft)
e
»
=Q
z'0(u ft)
u - e . ----------
' zo(« *)
The propagation constants, P0, of the n=0 modes are now calculated by
determining the roots of [4.62]. It should be noted that, although only the n=0 mode
is being considered, there may still be several roots to [4.62], each corresponding to a
mode with different radial variation. The approximate solution is thus the sum of all
modes with n=0 with the appropriate weighting function.
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53
- E fy p ) ci,r ‘
[4.63]
.p-1
where the subscript n=0 has been omitted, for simplicity.
Effect of Feedpoint and Termination
The above results describe the characteristics of waves that can propagate along an
infinitely long helical sheath structure. However, it is necessary to account for the
terminations of the helical antenna which, for present purposes, consist of a coaxial
feed point at one end and a short circuit at the other.
The effect of these terminations can be modeled by expanding the given source
backw ard traveling m odes
En »Hn
77
source field
E„ H,
forw ard traveling m odes
E n\ H n+
Figure 4.3 Illustration of forward and backward traveling waves along sheath helix antenna model,
fields on an orthogonal basis using orthogonality relations that can be obtained for
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54
modes in the helical sheath. In the next section, I present the such relations. This
specific analysis follows from a more general analysis given by Mclsaac46.
Orthogonality Relations
Consider any two different modes, viz., m4 and n* modes, propagating in the
helical sheath shown in Figure 4.3. The Lorentz reciprocity theorem, which is derived
in Appendix B, is used to relate them by3,4
[4.64]
(P. ♦ P„) /
/ [£> .< « » 4(P .40 - 4(P .+ ) x HnM ) ]• 4, p <#> dp = 0
P ” fi <jp=0
For those modes in which Pn * - Pm, the Lorentz reciprocity theorem implies that the
integral must evaluate to zero. That is
“
2n
/
/
[£„(p,40 x JyM(p,<j>) - £m(p,4))
X
Hn(p,4)) ]• az p d$ dp = 0
p » j <{>=0
[4.65]
For those modes in which P„ = - Pm the above integral may obtain a non-zero value.
In general, for a bidirectional reciprocal waveguide, the electric and magnetic
fields of an arbitrary source (represented by superscript s) can be expanded into an
infinite sum of forward and backward traveling modes (represented by
superscripts +,- respectively ):
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55
N
E °(p M = E E ( %
n --« p -l
^ ( p . 4 # e 'J ^
+K
e
~J
^
+ Radiation modes
[4.66]
iT M d
=
± f > v STV(p,<J)) e '; p ^
n--~ p-1
+ Radiation modes
+
bv
e'J^ )
[4.67]
For our helical sheath case where we take n=0 and ignore the radiation modes,
Equations [4.66] and [4.67] reduce to
« £ > ,
# W ) * E (S # > ) e
p‘ i
'J
M
+ h £;<p>
[4-681
+ bp » > ) e ~J
f4-69]
where the subscript n=0 has been omitted for convenience, and the <{>dependance
removed to illustrate that only those modes independent of azimuthal variation are
being considered.
The unknown coefficients \ and bp are obtained by applying the Lorentz
reciprocity theorem, Equation [4.64], to Equations [4.68] and [4.69]. This results in
the following expressions for a,, and bp as given in Maclsaac46.
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56
/[
E~x
S’ - £-'* «;] pip
ar ‘ ~ h
/ [ £ ,x a ; - e ; x
[470]
h;
\ Pi ?
J [ e ; * S ’ - e ’ x h 'p] p ip
h - —a _____________________________________
-----------------------------------P
00
[4.71]
/[ £;x s; - e;* s;i ?dP
Equations [4.70] and [4.71] are general orthoganality relations valid for any reciprical
waveguide. If possible, it is convenient to express these relations only in terms of the
forward traveling modes and source field. For the case of the sheath helix this can be
accomplished, by noting the relationship between the propagation constant and field
components of the forward and backward traveling waves given as
|3 0- = - P0+ , Ep‘= - Ep+, E,'= E*+, E- = Ez+, Hp'= - Hp+, H, = H,+ and H ^ H / .
Substituting these equalities into Equations [4.70] and [4.71] results in the following
expansion coefficients a,, and bp for the sheath helix;
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57
[4.72]
7>
2/ ( £ ; , ♦ e ; , h > ^
a
/( e ; ,
e *‘
-
e^
e;
-
e;
^
♦ e;
e
(> « / p
[4.73]
a
where Es and Hs refer to the known source fields, E+pp, E \ p, H+pp, H \ p and E'p
E ^ p, H p p and H*^p are the transverse field components of the forward and backward
traveling waves.
Introduction of the Feedpoint from the Coaxial Source
I assume that the helical antennas are driven by a coaxial line source. In
considering the source field distribution, I ignore higher order modes in the coaxial
cable, and I also use the normalized electric and magnetic fields. At the feedpoint of
the antenna z = 0 (i.e. the junction of the antenna with the inner conductor of the
coaxial line), the normalized electric and magnetic field distributions are assumed to be
Assuming that the waveguide is infinitely long, contribution of the coaxial source
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58
Hi =
e;
=o
— —
P
HI = 0
a<p<b
[4.74]
p>i>
to the forward traveling modes can be expressed as
^-1
[4.75]
/>»i
To obtain the unknown coefficients, a,,, I substitute the electric and magnetic fields
from the coaxial source, Equation [4.74], into the orthoganality relation, Equation
[4.72]. This results in
-/(K ,
[4.76]
ap ‘
2/ ( e
„
‘
h ;„
* e ;„
h ; , > P</P
Introduction of a Short Circuit Termination
The antennas are shorted at the proximal end (z=L) where the helix is connected
to the inner line of the coaxial cable. The reflections from this short circuit
termination can also be included in the model. For simplicity, I assume that only a
single reflection occurs at the end of the antenna and that the reflected wave does not
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59
significantly disturb the source fields at z=0. In a lossy external medium, this is
justified due to the rapid attenuation of both forward and reflected waves along the
antenna.
Since, I model the short circuit termination as a perfectly conducting cap at
z=L, the sum of theforward and reflected waves must then satisfy the condition that
the total tangential electric field vanishes at this termination. To satisfy this condition,
the tangential component of electric field for the reflected wave must be related to the
incident wave at z=L by
e ] = e ;p + e;4> = -£ p+p - <4>
f4-77]
where superscripts - and + refer again to the reflected and incident traveling waves,
respectively, and subscript t denotes the tangential component of electric field. Since
this effectively means that the reflection coefficient at z=L is essentially unity, the
tangential component of magnetic field, of the reflected wave, is related to those of
the forward traveling wave as
h;
= h ;$ + h $
= h ; p + h$
r4-78J
The reflected wave, defined in Equations [4.77] and [4.78], can now be interpreted
as a secondary source located at the antenna's termination, z=L. This secondary
source, denoted by superscript ss, can also be expanded into a sum of n=0 propagating
modes. However, in this case I choose the expansion in terms of modes propagating
in the - z direction. Hence,
The total incident electric and magnetic fields at z=L are obtained by substituting
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60
£ ”(P) - I 0, £,(P) « '*
p-1
[4.79]
/>-l
[4.76] into [4.75] and replacing z by L. Thus
[4.80]
e.
N
EP
+(p) e 'n >
-E
p -l
2/< 2? ;, h ; p + ^
N
- / ( K*
) prfp
e.— + " if ) if
C (P ) e '1 p;i
2/ (
h ; , * e ; , H; f ) p</p
[4.81]
The unknown coefficients, bp, for the reflected wave can now be obtained by applying
[4.77] through [4.81] to the orthogonality relation [4.73] and are given as
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61
~ f(P p ,p
tot + E+,p Hp, tot “ Ep, tot H $ ,p ~ E $,tot H p , p )P^P
a______________________________________________________________
| 4 .oZ
]
2! K , K
p
* K .p K p M
p
where the terras which contain subscript tot refers to the field components defined in
Equations [4.80] and [4.81]. The total reflected wave is now obtained by substituting
Equation [4.82] into [4.79].
Total Electric and Magnetic fields
After including the coaxial line source and the short circuit termination, the total
electric and magnetic fields are obtained as the sum of forward plus reflected modes as
4 , - **„ *
- X > , % *~n > .+ b, 4 e ' ' 1* )
I4-83!
p -1
where the coefficients a,, and bp are given by Equations [4.76] and [4.82] respectively.
The quantity of interest here is the specific absorption rate (SAR) which is now given
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62
N
* bp h;
)
[4.84]
/>"1
as
&
4i?
=
—
o | £ j
2p
1 *fl
2
—
[4.85]
Kg
where c and p are the conductivity and density of the outside medium respectively.
Summary
In summary the procedure for calculated the SAR pattern of the uninsulated helical
antenna is outlined in the following steps:
1)
The propagation constants for the dominant are calculated by
determining the roots of the determinantal Equation [4.62].
2)
are
3)
The electric and magnetic fields associated with each of these modes
then formulated using Equations [4.57] - [4.61].
The coaxial line source is then expanded into each of the dominant
modes by Equations [4.74] - [4.76].
4)
A set of reflected modes due to the short circuit termination are then
derived by Equations [4.79]-[4.82].
5) All of the forward and reflected modes are then summed to get the total
electric and magnetic fields, Equations [4.83]-[4.84] .
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63
6) Finally, the specific absorption rate (SAR) in the exterior lossy media is
determined by Equation [4.85].
4.1.2
Insulated Helical Antenna
This section investigates the electrical properties of insulated helical antennas
which are immersed in a lossy dielectric medium. I extend the previous analytical
model based on the uninsulated helical sheath approximation, to include a thin layer of
insulation. In comparison to an uninsulated antenna, the presence of a thin insulating
layer can significantly alter the field distribution of the antennas, the mode structure of
the antennas, and the SAR pattern in the outside medium. I will illustrate that the
insulated helical antenna may offer the possibility of short-range and relatively uniform
heating in the outer media. In subsequent chapters, it will be shown that these
properties make it well-suited for catheter based applications in biomedicine.
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64
Insulating
layer - -
e 3>^3
Figure 4.4 Insulated helical antenna of length L immersed in an external lossy media,
insulation is assumed to be lossless with a permittivity of e* and thickness (c-b).
The layer
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65
Antenna Model
The antenna to be considered is shown in Figure 4.4. Extending the previous
analysis for uninsulated antennas, the antenna is considered to be covered by an
insulating layer of thickness d with lossless dielectric medium of permittivity e^. The
outside medium is infinite in extent, lossy and nonmagnetic, with permittivity
£3’ = Ej' - j £3" and permeability p0 The inside dielectric medium is assumed lossless
of permittivity ey Following the previous analysis, I model the helical antenna in
cylindrical coordinates (p,<t>,z) by a sheath helix shown in Figure 4.5.
Formulation
I utilize the same modal expansion technique used before to solve for the total
electric and magnetic fields present in now three regions; inner dielectric (a<p<b),
insulating layer (b<p<c) and lossy outside medium (c<p<°°). These regions are
denoted as 1,2 and 3, respectively. The electric and magnetic Hertz vectors must
satisfy the scalar Helmholtz equation in each of the three regions.
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66
z=L-
£ 3»G 3
2=0
Figure 4.5 Insulated helical sheath model. This figure is identical to the uninsulated helical sheath
model shown in Figure 4.2, with the addition of a layer of lossless insulation of permittivity e* and
thickness (c-b).
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67
(V* + k 2)l£ =
^
P aP p aP
(V2 + fc2) l £ = i l ( p i )
^
p
dp H dP
p2ad>2
^
as2
+ k 2^
=0
t4-863
+ -L .?? 5 l + . ^ E l +k2! ^ = 0 t4-8?]
p2
a<|,2
dz2
The solutions to [4.86] and [4.87] in each region are given by:
a<p<b
n'(p.4v) - [ D , K J x p) ♦ F, I„(x p) ] e ' J " * « ' » «
n -(p ,(M - [
d ; K,(x
[4 gg]
p) ♦ f ; 1„ (x p) ] e '1 "* e
b<p<c
n*(p,^) = [ fl„ K fa p) + C„ /„(* p) ]
«-•'!>«
n"(p,<t>^) » [ b ; k ,( x P) ♦ c; /„(* P) ] « >"♦
[4.89]
c<p<
IT(p,(j,^) = 4 J n( v p ) e ^ ^ ^ J
[4.90]
n m( p , 4 ) ^ ) = A ; K „ \ v p ) * / * ♦ e V M
where
u = y p 2-*,2,
* = /p M £
v = ^ p 2-*32
and K„ and I„ are the modified Bessel functions of the first and second kind,
respectively, and n is an arbitrary positive or negative integer.
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[4.91]
68
Application of Boundary Conditions
\ \ Bn, Bn’, Cn, Cn*. D„, Dn’, Fn and Fn* are obtained
The unknown constants,
in terras of the total current I, flowing in the direction a,, by applying the appropriate
boundary conditions to the electric and magnetic fields at the interfaces
p = a, p = b and p = c. Thus:
i.
At the interface p = a the tangential electric fields Ez and E+ vanish.
=E Ja\ = 0
[4.92]
ii. At the sheath interface p = b, with current I, flowing in the direction a//( the
tangential electric fields are continuous and the tangential magnetic fields are
discontinuous.
E f i ) i = E^(b)2
[4.93]
where again a is the helical pitch angle of the insulated helical antenna,
iii. At the interface between the insulation and the exterior lossy medium, the
tangential electric and tangential magnetic fields are continuous.
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69
Ez(c)2 = Ez(c)3
= Et (c)3
Hz(c)2 = Hz(c)s
H^(c)2 = ff*(c)3
[4.94]
Solutions for Electric and Magnetic Fields
The insulated helical antennas are also being driven by a coaxial line source.
Consequently, since the symmetry considerations discussed for the uninsulated helical
antennas are still valid, only modes independent of azimuthal angle <|) will be
considered (i.e. n=0). The solutions presented below for n=0 are valid for all modes
with radial variation p, but for convenience I omit the subscript p.
Applying the boundary conditions found in Equations [4.92] to [4.94] leads to the
following electric and magnetic field solutions for the modes where n=0:
a<p<b
E, - -JK%DozXkp***
Et -•/>„<■> K D 'o t i W
* *
Ez - - u l D„
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[4.95]
70
B , - -J K u0 d ; z ; ( u oP)e-J^
= "7«€i uQ Do Z'(u0p)e
hz
[4.96]
= - u l d ; z ;( u09)e-J>*
b<p <c
Et - -J K \
K lw W .
E„= jp.w *„ [s ; < < *.p )-c ; 4'(i0p)]e *
[4.97]
B, - -*? [fl, % p ) » C 0 ;„(j,p)]e *
- -7P„ * . [ « ; < k p ) <
»*
/ X p )]<
- -j< * V . IB, K '( V ) * C , ^ . p ) ] e ^
[4.98]
ff; - - J 2 [B; « „ ( « „ p ) < / . ( j y > ) ] « *
c<p
Ep " -7'Pp v0
* - > oP) ^
E , - jp .w v„ /]„■ K^r,p)e'JP'‘
E, = -v2 4 , Kp(v„p)e*
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I4-" !
71
H , - -]» . v. a ; K f a j e * * '
Ht ■ -J“ e3v. j4. * :»(voP)<! ^
hz
[4.100]
- -v„2 a ; A y v „ p ) e *
The constants A0, A0*, B0, B0‘, C0, CG*, Dc and D0*are given as:
A
= j €^ f sin((x)Xo“0 Zo(u0b)U0(cx^K iicx^ °
2it£> <x>v0 Ql
, _ /, cos(a)*0 Z0* ( « ^ ) [ ^ 5 ( « ^ ( a o ) - / 0( « X ( « » ) ]
2rcfc v0 (?2
B = j Jt sin(«)«0
~
2ltf> (jiXQ Ql
°
B.
. = h « » (« ) ^ ( # , ljc x } K 0(cvJ - x 0 IJjcxJK & cvjl
2nb x0 Q2
[4.101
_ j I, sin(a)«0 Z0(u0b)[e2v0K0(cvJK!,(cxJ - ejcJKfcvJKJicxJH
c .2tc6 ojc0 <?j
c
_ A cos(a) z;W > )[* o KjLcvJKJLaJ - v. W < ( « o ) ]
2nb x0 Q2
D _ Jh8fa(«W yw y, - €3x0<(cv0)^]
°
2lti> (|)M0 Qj
2j* = h c o s(a)[j:X (c0 ^ 3 ~
2itf»
q2
where:
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72
Q{ =
+ £1e^ X ( < * X ( Wo W
-
' W
C2 =
+V o W
^
W
[ 4102]
) ^
c ( “. W 4
- x 0vpK0(cvJZ*'(u0b)W2 - x 0u0K'0{cv^Z *(u0b)W3
and
wx
=W
W
"
=W < ( « .) " f e w
W3 = l'0(bx^K0(cx^ - l 0(cx^K ,0(bxt)
[4.103]
W4 = jfcxJK 'C cxJ - I'icxJK'CbxJ
where I0 and K„ are the zeroth order modified Bessel functions of the first and second
kind respectively. For the limiting cases where c = b or ^ = £3, the solutions for the
insulated helical sheath reduce to those obtained previously for the uninsulated
antenna.
Determinantal Equation
The determinantal equation for the insulated helical antenna is constructed using
the same boundary condition as the uninsulated case, namely that on the surface of the
helical sheath the electric field component in the direction a„ must vanish. Thus:
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73
£>
2sin(oc) +
cos(a) = 0
at p=b
[4.104]
i|x0w D* Z*(u0b) cos(a) - u0 D0 Z0(uob) sin(a) = 0
The propagation constants, p0, of the n=0 modes for the insulated antennas are now
calculated by determining the roots of Equation [4.104]. Analogous to the uninsulated
results Equation [4.104] may have several roots each having a different radial
variation. The total fields are then approximated summing all modes where n=0.
Feedpoint and Termination
The feedpoint and short circuit termination for the insulated antenna are accounted
for by using the same approach as for the uninsulated antenna. To briefly review the
procedure; 1)
Expand the coaxial line source into a sum of forward traveling modes
using Equations [4.73] - [4.75]. 2) Calculate the reflected modes by insuring the net
tangential electric field on the short circuit termination vanishes, using Equations
[4.80] - [4.82]. 3) The total fields are then formed by summing the forward and
reflected waves together.
Summary
In summary, the procedure for calculated the SAR pattern of the insulated helical
antenna is outlined in the following steps;
1)
The propagation constants for the dominant radial modes are first
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74
calculated by determining the roots of the determinantal Equation
[4.104].
2)
The electric and magnetic fields associated with each of these modes
are then calculated using Equations [4.95] - [4.100].
3)
Using Equations [4.74] - [4.76] the coaxial line source is expanded into
each of the dominant modes.
4)
A set of reflected modes due to the short circuit termination are then
calculated using Equations [4.79] - [4.82].
5) All of the forward and reflected modes are now added together to
calculate the total electric and magnetic fields using Equations [4.83]-[4.84] .
6) Finally, the specific absorption rate (SAR) in the exterior lossy media is
calculated using Equation [4.85].
4.2 Simple Analytical Model of RF Ablation
To better comprehend the significance of the microwave antenna results and to
investigate its merits relative to presently available RF techniques, I developed an
analytical model describing an RF ablation catheter.
Figure 4.6 presents an illustration of a currently available RF ablation catheter
operating in a unipolar mode. The geometry of the problem is also shown in Figure
4.6. The tip of the catheter is a hemispherical electrode of radius b. A grounding
plane is placed a distanced D away from the electrode tip. The interior region is
assumed to be filled with a homogenous tissue medium of permittivity e and
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75
RF Ablation Model
Tissue
Figure 4.6 Model of an RF ablation device, consisting of a hemispherical tip electrode of radius b,
placed a distance D from a grounding plane. The space between the tip electrode and grounding plane
is assumed to be filled with tissue.
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76
conductivity o.
The operating frequency for a typical RF ablation device is 500 kHz. At this
frequency, the wavelength, k, is approximately 60 meters in tissue. This wavelength
is several orders of magnitude larger than the largest dimension of the devise.
Consequently, a quasi-static approximation is well justified. The standard procedure
for solving quasi-static problems is outlined in the following steps.
1)
Solve Laplace's equation in the tissue medium for the scalar
potential O.
V2® = 0
2)
Express the electric field in terms of the scalar potential O.
E = -V®
3)
[4.105]
[4.106]
Use electric field to calculate SAR pattern.
SAR = — o |E |2
2p
Kg
[4.107]
The geometry shown if Figure 4.6 does not lend itself to a closed form analytical
solution to Laplace's equation. However, if the distance, D, is much larger than the
radius of the hemispherical tip electrode, b, the following model is a valid
approximation.
The approximate model shown in Figure 4.7 consists of the same hemispherical tip
electrode surrounded by a larger hemisphere a distance D away. The space between
the two electrodes is assumed to be filled by tissue. The inner electrode is held at a
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77
Tissue
SAR «
Figure 4.7 An approximate model of Figure 4.6, consisting of the same hemispherical tip electrode of
radius b surrounded by a larger hemisphere of radius D. The inner electrode is at potential V0, whereas
the outer electrode is fixed at ground potential. The space between the two hemispheres is assumed to
be filled with tissue medium.
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78
constant potential of V0, while the outer electrode is fixed at ground potential. Both
electrodes are assumed to be perfect conductors. It is also assumed that current flows
only radially between the two electrodes ( i.e. a perfectly insulating boundary along the
flat surfaces of the hemispheres ). Consequently, the electric field will have only a
radial component. The problem is stated mathematically as
[4.108]
^®(M>.6) ‘ - y ( r 2~ ) *
— ~ ( s in ( 4 > ) ~ ) + ■ 1
- 0
r 2 dr
dr
r 2sm(<J)) &1>
r 2sin2(<]>) 502
It is clear from Equation [4.106] that if the electric field has only a radial
component then the scalar potential O will vary only in the radial direction.
Consequently, Equation [4.108] simplifies to
V ^ fr) =
r 2 dr
dr
=0
[4.109]
with the following boundary conditions
<b(b) = V0
0 < <]>< 7t, - n/2 <0< n/2
<b(D) = 0
0 < <p < 7C, - tc/2 <0< n/2
The solution to Equation [4.108] is given by
=
i
Id
°
^
b<r <D
[4.110]
1
The electric field in the region between the electrodes is obtained using Equation
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79
[4.110], and is given by
1 ------ f 72
~D
r
b<r <D
[4.111]
~b
Taking, the outer radius D to be far larger than the radius of the inner electrode b,
results in the following approximate form
E(r) « -
ar
b<r <D
[4.112]
r
The SAR pattern of the RF catheter is now obtained using Equation [4.107] as
[4.113]
where a and p are the conductivity and density of the tissue medium respectively.
According to Equation [4.113] the SAR from RF catheters drops off as r4 away
from the electrode tip. This rapid attenuation in SAR explains why RF ablation
produces small discrete lesions located near the tip of the catheter.
4.3
Summ ary
In this chapter, the analytical methods used for this study were derived. Analytical
antenna models based on the sheath helix approximation were developed to calculate
the SAR distributions of insulated and uninsulated helical antennas. In addition, an
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analytical model of a RF ablation catheter was presented. In the following chapters
the models presented here are presented in comparison with experimental results.
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81
Chapter 5: Analytical Results
This chapter presents the results which follow from the analytical antenna models
derived in Chapter 4. It consists of two sections. The first presents the theoretical
results obtained from the uninsulated helical sheath model. The second shows the
results for the insulated case. Each section calculates the antenna's dispersion
characteristics, its electric field distribution and its SAR pattern under a variety of
configurations. For the present application, it is of particular importance to investigate
how these properties change with respect to loss in the external medium, operating
frequency, pitch angle, antenna radius and insulation thickness. The dependence on
these parameters will indicate how the actual helical antenna performs with respect to
changes in configuration. Chapter 6 will present the experimental methods and
Chapter 7 will compare the analytical results presented here to the experimental
results. Results from the RF ablation model (derived in Section 4.3) will also be
discussed in Chapter 7.
5.1 Results From Uninsulated Helical Sheath Model
This section presents the theoretical results of the uninsulated helical sheath model
derived in Section 4.1. Using this model, I calculate the dispersion characteristics, the
electric field distributions and the SAR patterns of the uninsulated helical sheath.
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82
5.1.1 Dispersion Characteristics
The dispersion characteristics of an antenna or waveguide characterize the
existence and the general nature of waves which can propagate along the structure.
The propagation constant, p, is used to quantify these characteristics. It can be
determined by calculating the roots of the determinantal equation. For the dominant
modes (n=0) of the uninsulated helical sheath antenna, the determinantal equation is
given by Equation 4.62. The intent here is to investigate how the propagation constant
of the uninsulated antenna varies with loss in the external medium, frequency, pitch
angle and antenna radius.
Numerical Method
A general closed form solution to Equation 4.62 appears not to be possible.
Consequently, I rely on numerical techniques. I develop a numerical method to solve
for the complex propagation constant, p. The method is based on a modified NewtonRaphson procedure47, and is implemented using the mathematical software package
Matlab [MathWorks, Inc].
The Newton-Raphson algorithm is an iterative procedure normally used to locate
real roots. I modify the procedure to make it applicable for finding roots in the
complex plane.
To accomplish this, I first write the determinantal equation in the form
D(P,p|,p2,p3,..,p„) = 0, where pj though pn are known parameters (such as size,
frequency, pitch angle, etc.). The propagation constant, which is complex in general,
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83
can be written as
p = pr + j p ,
[5.1]
where pr and ft are the phase constant and attenuation constant, respectively.
Likewise, the deterrainantal equation can be separated into real and imaginary parts
given by
£ (P r> P p P v P v
•• » Pn)
= D r +j Di
When given an initial guess for the solution, the Newton-Raphson computes a
corrected value,
pr = pf + Apr
p r
= pf
*
Ap.
where APr and Aps are correction terms.
These correction terms are calculated by applying a first order Taylor expansion to
both the real and imaginary parts of the determinantal equation. The following set of
simultaneous equations results:
3D
3D
-D, =
3p’
.
3D.
3D.
-D . = — iA Pr + — ^Apf
'
ap r
3P;
[5.4]
where the partial derivatives are calculated by a central difference method.
Solving these equations gives the correction terms. This procedure is then iterated
until the procedure adequately converges to a root. For present purposes, I assume
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84
convergence when both I Pnew - P°ldl < 10 6 and I D(P“ W, Pi,..,pn) - D(p0ld, plf..,pn)l
< 10 12. To insure that the result is a true root, the alteration of sign of the real and
imaginary parts is checked in the vicinity of the root.
Verification of Numerical Method
The accuracy of the numerical technique was checked by examining some
limiting cases. For the special case where the inner and outer media are identical and
lossless, Equation 4.62 reduces to that reported earlier by Neureuther et al.34. For this
case, the results of the present technique agree well with Neureuther's et al34.
solutions. Additionally, when the inner conductor does not exist (a=0), Equation 4.62
reduces to that reported by Sensiper33. This case was also checked and the results
obtained here are identical to those obtained by Sensiper. It was therefore concluded
that the numerical method worked properly and hence was utilized in finding solutions
for the cases of interest here.
General Properties of the Solutions
Before proceeding with the numerical results, it is useful to consider some general
properties of the solutions. In considering these general properties, I distinguish
between antennas or waveguides in lossless and lossy media. Only the former case
was discussed by Neureuther et al.34.
lossless media In the case of a lossless external medium, where
Rel kj I >Rel kj, the propagation constants of the n=0 modes are real and greater than
the wave number of the external medium k,.. The corresponding waves propagate
more slowly along the antenna than in the medium and are the well known slow
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85
modes of helical structures. For guided modes where n>0, the wave numbers can be
complex. This case is studied in some detail in34.
lossy media
For a lossy external medium, where I k, I >1 kj I ( the case of
interest here), the propagation constants of the n=0 modes are, in general, complex and
their magnitudes are not necessarily greater than the wave number of the external
medium. In this case, the following three distinct regions can be distinguished: the
very fast mode region, Pr< Re( k,)< Re( k j; the fast mode region, Re( lq)< |3r< Re(k,.);
and the slow mode region, Re( kj)< Re( ke)< Pr.
The very fast mode region corresponds to waves which travel along the antenna
faster than plane wave propagation in both the external lossy medium and the internal
dielectric. These waves are found to be improper and do not correspond to physically
realistic solutions of interest here.
The fast mode region corresponds to waves propagating faster than plane wave
propagation in the external medium1, but slower than it in the internal dielectric. It
appears that this mode in our problem can only exist if the outside medium has loss.
Consequently, it has not been reported in previous studies dealing with helical
antennas radiating into free space.
The slow mode region corresponds to waves which travel slower than plane wave
propagation in both the external medium and the internal dielectric. These waves,
which also exist in the lossless case, are the primary contributors to the antenna's
1 The term fast mode generally referrs to modes with phase velocities greater than both the internal and
external medium. Here, I use the term fast mode to refer to modes with phase velocities greater than the
external medium, but less than the internal medium.
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86
heating properties.
For all the helical sheath antennas investigated here, only two distinct propagating
modes are found to exist. Based on the definition given above, one in the fast mode
region and the other is in the slow mode region. The total solution is formed by
summing the two modes. In the numerical results which follow, the characteristics of
each of these modes are investigated as a function of the antenna design parameters
and the electrical properties of the external medium.
Numerical Results
The effects of loss, operating frequency, pitch angle and antenna radius on the
propagation characteristics of the uninsulated helical antennas are investigated. The
dependence on these parameters will give an indication of the actual antenna heating
performance with respect to configuration changes. It should be noted that only the
dominant modes, n=0, are considered in the results and discussion which follow.
Effect of Varying Frequency and Loss
Figure 5.1 illustrates how the two modes of
propagation (slow mode and fast mode) are affected by changes in frequency. Here,
Pb vs. kjb (ki=toV(|i0ei)) is used to normalize the results with respect to antenna radius,
b, and inner medium permittivity,
In this figure, the pitch angle is fixed at 20°, the
ratio of outer to inner core radii is fixed at b/a=3.0, the real part of the outside
medium's permittivity is taken to be 30 times that of the inside insulation,
z j /e / = 30, and the loss tangent, tan(y)=z'lz', of the outside medium is varied from
0.1 to 0.7.
Several points can be made about this figure. First, the phase constant (Pr) and
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87
F ast Wave
0.6
tan(y) Ra(flb) ImQib)
0.4
fib
0.2
0.0
-
0.2
0.0
0.1
0.2, .
k.b
0.3
0.4
Slow Wave
B
tanM Refffb) Imfflbl
6
4
fib
2
0
-2
0.0
0.1
0.2, .
i
0.3
0.4
Figure 5.1 Slow and fast mode k,(= o /c v ^ b vs Pb diagram for b/a=3, pitch angle a=20°, and
ee7e/=30.
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88
attenuation constant (ft) are nearly linear functions of frequency for both the slow and
fast modes. However, the slow mode is much more sensitive to frequency changes as
is seen by the steeper slopes. Second, the attenuation constant of the slow mode is
much larger than that of the fast mode. Consequently, the slow mode will release its
energy to the exterior medium more rapidly. Third, the slow mode shows a higher
sensitivity to changes in loss than the fast mode, particularly in its attenuation constant.
Consequently, the fast mode will propagate in a very lossy medium with little
attenuation whereas the slow mode will release its energy quickly.
Effect of Varying Pitch Angle and Loss
Figure 5.2 illustrates how the two modes
of propagation are affected by changes in the pitch angle, a. Here, b/a is 3.0 with
b=0.1 cm, e j /&/ = 30 with e/=2, and tan(Y)=e#/e/ is once again varied from 0.1 to
0.7. In addition, the frequency is fixed at 915 MHz (the frequency used in the
experimental measurements) and the pitch angle is varied from 5° to 40°.
Clearly, for the slow mode, as a decreases (corresponding to a more tightly coiled
helix) the phase constants and attenuation also increase.. This observation is consistent
with the results reported earlier by Neureuther et a l . The effect becomes much more
pronounced at smaller pitch angles (5° < a < 10°) when the helix is very tightly coiled.
The fast mode, however, shows little sensitivity to pitch angle. This suggests that
any changes in heating pattern caused by changes in pitch angle are primarily due to
the slow mode.
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89
F a s t Wave
0.6
c
0.4
o
-M
n
c
o
°
0.2
lmag(/3)
0.0
a.
0.2
10
30
Pitch Angle a deg.
20
40
Slow Wave
tanM
R o (ff)
Real(0)
a>
L.
Q.
Imag(/?)
-5
10
20
30
40
Pitch Angle a deg.
Figure 5.2 Slow and fast mode propagation constant vs. pitch angle for f=915 MHz, b=0.1 cm, a=0.03
cm, and €c7e/=30 with §'=2.
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90
Effect of Varying Antenna Radius
Figure 5.3 illustrates how the two modes of
propagation are affected by changes in the helical sheath radius.
Here, b/a is 3.0 , e j
lz( = 30 with e/=2, and tanCy^'/eMXS. In this figure the frequency is fixed at 915
MHz, the pitch angle is fixed at 20°, but the outer sheath radius, b, is varied from 0.03
to 0.3 cm. For catheter ablation applications, the radius of a realistic antenna should
be somewhere within this range.
The important point of this figure is that, as the radius changes by a factor of 10,
the propagation constants for both the slow and fast modes changes by, at most, 40%.
Thus, I conclude that the propagation constants for both the slow and fast modes are
rather insensitive to changes in sheath radius (at least for the antenna sizes of interest
here).
Summary
From the determinantal equation for the uninsulated helical sheath antenna, I
determine that two dominant modes of propagation exist in lossy media. One mode,
termed a slow mode, corresponds to the same slow modes found in lossless media.
The other is a newly discovered faster mode. The propagation constant of the slow
mode is sensitive to changes in frequency, pitch angle and loss of the external
medium, whereas, that of the fast mode is not. Also, both slow and fast modes are
insensitive to changes in sheath radius for the antenna diameters of interest here.
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91
Fast Wave
0.5
0.4
*»-
R eal(l)
0.3
CO
c
o
CJ
0.2
c
o
Vj
o
o>
O
a.
0.1
k_
o.o
a
Q_
-
lmag(/S)
0.1
0.05
0.10
0.15
0.20
0.25
0.30
Sheath radius b (cm )
Slow Wave
Real(/9)
c
a
01
c
o
o
c
o
□
OI
a
a.
oL.
o-
lmag(/S)
-1
-2
0.05
0.10
0.15
0.20
0.25
0.30
Sheath radius b (cm )
Figure 5.3 Slow and fast mode propagation constant vs. sheath radius, for f=915 MHz, b/a=3,
e^ /e^ O with e/=2, pitch angle o=20° and the loss tangent tan(y)=0.5.
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92
5.1.2 Electric Field Distributions
In addition to the dispersion characteristics presented above, it is useful to consider
how the actual electric field distribution varies with respect to changes in the antenna
or the external medium. The dependence on the frequency, the pitch angle and the
loss in the external medium are investigated in this section. Using these results along
with the dispersion diagrams given above, one can gain some physical insight into the
characteristics of an actual wire wound helical antenna.
These results follow from the analytical model presented in Section 4.1. The
electric fields in the external medium are obtained using Equations 4.56 through 4.60
with the unknown propagation constants being calculated from the procedure described
above. For these plots, the electric fields are calculated at the feedpoint, z=0, as a
function of radial distance, p, from the antenna surface. Also, the antenna is assumed
to be semi-infinite in length with a coaxial source of unit voltage placed at z=0. The
coaxial source is included so that the electric fields obtained can be normalized with
respect to a fixed source voltage using the orthogonality conditions derived in Section
4.1.
Figures 5.5 through 5.7 indicate how, for both the slow and fast modes, the
magnitude of the electric field varies with changes in frequency, pitch angle and loss.
In these figures, the outer and inner radii of the antenna are fixed at 0.1 and 0.03 cm,
respectively. Also, eJ /&/ = 30 with e/= 2. Figure 5.4 illustrates the geometry of the
antenna used in these calculations (In these figures the arrows are used simply to
indicate the envelope of the electric field magnitude, not its direction).
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93
Effect of Varying Frequency Figure 5.5 illustrates how the magnitude of the electric
z-0
ta n ( Y ) - ■
e l-6 0 .0
soiree voltage
f
V0- 1 .0 V o lt
JS
s e m i infinite in le n g th
Figure 5.4 An illustration of the antenna geometry used for the electric field calculations,
field in the external medium, varies with respect to frequency given a source of one
volt. Here, the pitch angle is fixed at 20°, the loss tangent of the outside medium is
fixed at 0.5 and the frequency ranges from 100 MHz to 10 GHz.
It is clear from the figure that the magnitude of the electric field at the surface of
the antenna increases with increasing frequency (assuming the voltage source remains
at unity). Although this is true for both slow and fast modes, it is somewhat less
pronounced in the slow mode. This figure also shows that, with increasing frequency,
the electric field attenuation in the radial direction is more rapid. In fact, for the 10.0
GHz slow mode, the electric field is
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94
Fast Mode
1.5
1.0
10.0
1.0
E
S
ui
0.5
O.o
0.0 ------------- 1-----r ”
0.00
i i i
....................
0.25
0.50
0.75
Radial Distance (cm)
1.00
Slow Mode
Frequency, GHz
1.5
o - 0.1
• - 1.0
* - 10.0
E
u
Ui
0.5
0.0 —
0.00
0.25
0.50
0.75
1.00
Radial Distance (cm)
Figure 5.5 Magnitude of electric field in external medium at various frequencies. Here, b=0.1 cm,
a=0.03 cm, eJ/^30 with e/=2, pitch angle a =20° and the loss tangent tan(y)=0.5.
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95
essentially zero at a distance of only 1.0 ram from the antenna surface. Consequently,
it is important to choose a frequency range which provides the proper heating depth
for the desired application. The antennas in this study were operated at 915 MHz.
Figure 5.5 indicates that, at this frequency, significant heating occurs in the first few
millimeters from the antenna. This depth of heating is believed to be adequate for
most of the cardiac arrhythmias treatable by catheters.
Effect of Varying Pitch Angle Figure 5.6 indicates how the magnitude of the electric
field varies with changes in pitch angle. Here, the loss tangent is fixed at 0.5, the
frequency is fixed at 915 MHz and the pitch angle is varied from 10° to 30°. This
figure clearly indicates that, as the pitch angle decreases, the magnitude of the electric
field distribution increases. This is true for both slow and fast modes, however, much
more pronounced for the former. Consequently, for catheter ablation applications,
greater heating depths can be achieved by decreasing the helical antenna's pitch angle.
Figure 5.6 also shows that, for the pitch angles studied here, the magnitude of the
electric field of the slow mode is greater than that of the fast mode. This suggests that
heating is primarily due to the slow mode.
Effect of Varying Loss
Figure 5.7 illustrates the effect of varying the loss of the
external medium. In this figure, the pitch angle is fixed at 20°, the frequency is fixed
at 915 MHz and the loss tangent is varied from 0.1 to 0.7. The plot shows that the
magnitude of the electric field distribution in the transverse plane for both slow and
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96
Fast Mode
0.5
Pitch Angle a
o - 30°
• - 20 °
0.4
E
0.3
§
HL
0.2
0.1
0.0
-
>—
0.00
0.25
0.50
0.75
Radial Distance (cm)
Slow Mode
4.0
Pitch Angle a
o - 30°
•
- 20 °
3.0
E
o
1.00
2.0
uj
1.0
0 .0 I—
0.00
0.25
0.50
0.75
Radial Distance (cm)
1.00
Figure 5.6 Magnitude of electric field in external medium at various pitch angles. Here, b=0.1 cm,
a=0.03 cm,
with e/=2, f=915 MHz and the loss tangent tan(y)=0.5.
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97
Fast Mode
0.4
E
o
loss
o
•
•
•
tangent tan(y)
- 0.1
- 0.3
- 0.5
- 0.7
0.2
0.0
0.00
0.25
0.50
0.75
Radial Distance (cm)
1.00
Slow Mode
1.5
loss tangent tan(?)
o - 0.1
1.0
* - 0.3
* - 0.5
* - 0.7
0.5
0.0 ■—
0.00
0.25
0.75
0.50
Radial Distance (cm)
1.00
Figure S.7 Magnitude c f electric field in external medium for various loss tangents. Here, b=0.1 cm,
a=0.03 cm, ej/e'=30 with e/=2, pitch angle a=20°, f=915 MHz and the loss tangent ranges from 0.1
to 0.7.
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98
fast modes is insensitive to changes in external medium loss. It should be noted
however, that while the field distribution in the transverse plane is insensitive to loss,
the fields will decay as they propagate in the longitudinal direction. This attenuation
is sensitive to external medium loss as indicated by the dispersion diagram in Figure
5.2.
5.1.3 SAR Distributions
For catheter ablation, the quantity of direct interest is the specific absorption rate
(SAR). This section investigates how the SAR pattern of the uninsulated helical
sheath antenna is affected by changes in pitch angle and loss in the external medium.
z*=0
0
e0
z=3.0 cm
tan(Y)*» —
*
e'=60.0
*
source Held
Vo-1.0 Volt
p -0
p=0.4 cm
Figure 5.8 An illustration of the antenna geometry used for the SAR calculations.
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The procedure summarized at the end of Section 4.1 is used to calculate these patterns.
Since, the experimental results are obtained at one frequency, 915 MHz, the effect of
changes in frequency is not considered here.
For these calculations, the antenna is assumed to be 3.0 cm in length with outer
and inner radii of 0.1 cm and 0.03 cm, respectively. Figure 5.8 illustrates the
geometry of this antenna. As before, the real part of the permittivity of the outside
medium is taken to be 30 times greater than that of the inside insulation, e j /e/ = 30
with &/= 2. The SAR distributions are calculated as a function of radial distance, p,
from the antenna surface and longitudinal distance, z, along the axis of the antenna. It
is of particular interest here to compare the pattern of the SAR distribution as a
function of pitch angle and of loss. For this reason, I normalize each pattern such that
it has a maximum value of one.
Effect of Varying Pitch Angle Figure 5.9 indicates how the SAR distribution varies
with changes in pitch angle. Here, the loss tangent is fixed at 0.1, the frequency is
fixed at 915 MHz and the pitch angle ranges from 10° to 30°.
Several observations can be made regarding these figures. First, the results show a
distinct standing wave pattern along the length of the antenna. This sinusoidal
variation in SAR has been observed experimentally by other investigators48,49 and in
this work.
Second, the spatial frequency of the standing wave depends strongly on the pitch
angle. As the pitch angle decreases, the spatial frequency increases. Physically, this
phenomenon corresponds to waves which propagate more slowly as the pitch angle
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100
A. Pitch angle a=30°
mm
jliiiill
|||»
B. Pitch angle a=20°
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101
C. Pitch angle a=10°
Figure 5.9 Normalized SAR distributions at various pitch angles. Here, b=0.1 cm, a=0.03 cm, L=3.0 cm,
eJ/^30 with e/=2, f=915 MHz and the loss tangent is tan(Y)=0.1.
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102
decreases. This observation is consistent with the dispersion characteristics of the slow
mode.
Third, the SAR pattern attenuation in the radial direction is more rapid for the
smaller pitch angles. Thus, to heat tissue at extended depth, one must either increase
the pitch angle of the antenna or wait for the effects of thermal conduction to carry
energy deep into the tissue. For the catheter ablation treatment of ventricular
tachycardia, this does not pose a significant problem. As mentioned in Chapter 2, the
reentrant tract formations are believed to lie near the endocardial surface.
Consequently, there is no direct need for heating at large depths.
Effect of Varying Loss
Figure 5.10 indicates how the SAR distribution varies with
loss in the external medium. Here, the frequency is 915 MHz, the pitch angle is 10°
and the loss tangent ranges from 0.1 to 0.7. Clearly, as the loss tangent increases the
SAR peaks shift toward the antenna's distal tip. In fact, when the loss tangent is
comparable to muscle tissue, tan(y)=0.5, almost all of the energy is located near the
tip.
Physically, this phenomenon can be explained by examining the propagation of the
dominant modes along the helical structure. At the coaxial feedpoint, z=0, the fast
mode is excited strongly by the coaxial source. As shown earlier, this mode has a
small attenuation constant which is insensitive to loss in the external medium.
Consequently, the fast mode carries most of its energy to the end of the antenna with
little loss to the external medium. At the distal end of the antenna, a reflected slow
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103
A. Loss tangent, tan(Y)=e#/ e - 0.1
B. Loss tangent, tan(y)=e#/ e - 0.3
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104
C. Loss tangent, tan(Y)=e#/e'= 0.5
D. Loss tangent, tan(y)=e#/e/= 0.7
Figure 5.10 Normalized SAR distributions for various loss tangents. Here, b=0.1 cm, a=0.03 cm, L=3.0
cm, eZ/ei-30 with e/=2 the pitch angle o=10° and f=915 MHz. Here, the loss tangent is varied from
0.1 to 0.7.
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105
mode is excited in order to satisfy the short circuit boundary condition there. This
mode has a relatively large attenuation constant which becomes larger as the loss in
the external medium increases. Hence, this reflected slow mode loses its energy
rapidly to the external medium and is responsible for the large hot spot seen at the
antenna's tip. The present application of catheter ablation, calls for a more uniform
heating distribution than the uninsulated helical antenna exhibits. It will be shown in
the next section, that a thin layer of insulation can be used to produce such a heating
pattern.
5.2 Results From Insulated Helical Sheath Model
This section presents the theoretical results of the insulated helical sheath model
derived in Section 4.2. Using this model, I calculate the dispersion characteristics, the
electric field distributions and the SAR patterns of the insulated helical sheath.
5.2.1 Dispersion Characteristics
The intent of this section is to investigate how the dispersion characteristics of the
helical sheath antenna change due to the addition of an insulating layer. These
properties are determined by solving the determinantal equation, Equation 4.104, given
in Section 4.2. The numerical method described above is used to calculate the
propagation constant, |5, as a function of insulation thickness and loss in the external
medium.
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Numerical Results
Figure 5.11 illustrates the geometry of the insulated helical sheath antenna studied
here.
insulating layer
infinite In length
+z
Figure 5.11 An illustration of the insulated helical sheath model used.
The insulated helical sheath model consists of the helical sheath antenna studied above,
with an insulating layer surrounding the antenna. The insulating layer is assumed to
be lossless with a permittivity equal to that of the internal dielectric, e / ^ / . The
external medium is taken to be lossy with complex permittivity
e3’=e3/-
It is also assumed that the real part of the permittivity of the external
medium is greater than the permittivity of the internal dielectric and insulating layer,
Under these assumptions, only two distinct propagating modes are found to exist.
These modes, as in the uninsulated case, consist of one in the fast mode region and
another in the slow mode region. The numerical results which follow investigate the
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effect of insulation thickness and loss in the external medium on each of these modes.
Effect of Insulation Thickness and Loss Figure 5.12 illustrates how the two modes of
propagation are affected by changes in the thickness of the insulation and loss in the
external medium.
Here, the outer radius, b, and inner radius, a, are taken to be 0.1
and 0.03 cm, respectively, ^ /e / = 30 with e/= ^ = 2 , and tan(y)=e3#/e3/ is once
again, varied from 0.1 to 0.7. In this figure, the frequency is fixed at 915 MHz and the
pitch angle is fixed at 20°, but the insulation thickness, d=c-b, is varied from 0.001 to
0.1 cm.
Several important observations can be made regarding Figure 5.12. First, the slow
mode is sensitive to the addition of an insulating layer, whereas the fast mode is not.
Second, as the insulation thickness increases, the attenuation and phase constant of the
slow mode decrease. This results in a slower release of energy and a decrease in
wave number for thicker insulations. Third, as the insulation thickness increases, the
slow mode becomes less sensitive to loss in the external medium. In fact, as the
insulation thickness becomes greater than 0.025 cm, both modes are essentially
independent of the external medium. I conclude from these results that, by judiciously
choosing a proper insulation thickness, one can adjust the attenuation constant of the
slow mode to produce a more uniform heating distribution.
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108
Fast Mode
0.5
0.4
0.3
Lobb ta n g e n t
0.1 0.3 0.5 0.7
0.2
0.1
0.0
-
0.1 —
0.000
0.025
0.075
0.050
insulation thickness, d (cm)
0.100
S lo w M ode
2.5
Lo
bb
ta n g e n t
0.1 0.3 0.5 0.7
2.0
1.5
1.0
0.5
Ol
0.0
Imag(jJ)
-0 .5
-
1.0 —
0.000
0.025
0.050
0.075
0.100
Insulation thickness, d (cm)
Figure 5.12 Slow and fast mode propagation constant vs. insulation thickness. Here, f=915 MHz, b=0.1
cm, a=0.3 cm, e3V€/=30 with e/=€2/=2, pitch angle a=20° and the loss tangent is varied from 0.1 to
0.7.
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109
5.2.2 Electric Field Distributions
These results follow from the analytical model presented in Section 4.2. The electric
fields in the external medium are obtained using Equations 4.99 through 4.103, with
the unknown propagation constants being calculated by the procedure described above.
Like the previous electric field plots, the values are determined at the feedpoint, z=0,
as a function of radial distance, p, from the outer surface of the insulating layer. Also,
the antenna is assumed to be semi-infinite in length with a coaxial source of unit
voltage placed at z=0. Figure 5.13 illustrates the geometry of the antenna used in
these calculations.
tan(Y)'
4 - 6 0 .0
►
sem i Infinite !n length
source voltage
V „ - 1 .0 V o lt
In s u la tin g la y e r
Figure 5.13 An illustration of the antenna geometry used for the electric field calculations of the
insulated antenna..
Effect of Insulation Thickness Figure 5.14 shows how the magnitudes of the electric
field distributions of the two dominant modes are affected by insulation thickness.
Here, the outer radius, b, and inner radius, a, are taken to be 0.1
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F a s t M ode
0.4
0.3
Insulation Thickness (cm )
E
°
0.2
•
-
•
-
0.01
0.001
Ll I
0.1
-
0.0
—
0.00
0.25
0.50
0.75
Radial Distance (cm)
1.00
Slow Mode
1.00
Insulation Thickness (cm )
0.75
•
-
-
-
0.01
0.001
>_ 0.50
ui
0.25
0.00 *—
0.00
0.50
0.75
0.25
Radial Distance (cm )
1.00
Figure 5.14 Magnitude of electric field in external medium for various insulation thicknesses. Here,
b=0.1 cm, a=0.03 cm, e3//e/= 30 with e,/=e2/=2, pitch angle a=20°, f=915 MHz and the loss tangent
tan(y)=0.5.
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I ll
and 0.03 cm, respectively and z j /e / = 30 with e/= &/=2. In this figure, the
frequency is 915 MHz, the pitch angle is 20°, the loss tangent is 0.5 and the insulation
thickness is varied from 0.001 to 0.1 cm.
Clearly, for the slow mode, as the insulation thickness increases, the magnitude of
the electric field at the surface of the insulating layer decreases. It should be noted
however, that these plots are the electric field distribution at the antenna's feedpoint,
z=0, and will attenuate along the length of the antenna as e^‘z- The electric field
distribution of the fast mode, as in the previous results, shows little sensitivity to
insulation.
5.2.3 SAR Distributions
This section investigates how an insulating layer affects the SAR pattern of the
helical sheath antenna. The complete procedure summarized at the end of Section 4.2
is used to calculate the SAR as a function of insulation thickness and loss.
p -0
insulating layer
Figure 5.15 Illustration of geometry used in the SAR calculation for the insulated antennas.
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112
Figure 5.15 illustrates the geometry of this antenna. For these calculations, the
antenna is assumed to be 3.0 cm in length with an outer radius, b, and inner radius, a,
taken to be 0.1 and 0.03 cm, respectively, e3/ /e / = 30 with e/= e / =2 and the
frequency is fixed at 915 MHz. The SAR distributions are calculated as a function of
radial distance, p, from the insulation surface and longitudinal distance, z, along the
axis of the antenna. Here, I examine the SAR distribution as a function of insulation
thickness and loss. As done in the uninsulated case, the SAR patterns are normalized
to a maximum value of unity.
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113
A. Uninsulation
/
llliP
B. Insulation thickness d=0.001
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>-
C. Insulation thickness d=0.01
i M
E
I I I -P-
:: :
D. Insulation thickness d=0.1
Figure 5.16 Normalized SAR distributions for various insulation thicknesses. Here, b=0.1 cm, a=0.03
cm, L=3.0 cm, e3//e/= 3 0 with €/=e2'=2 the pitch angle o=20°, f=915 MHz and the loss tangent
tan(Y)=0.1. Here, the insulation thickness is varied from 0.001 to 0.1 cm.
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115
Effect of Insulation Thickness Figure 5.16 illustrates the effect of insulation thickness
on the SAR distribution. Here, the pitch angle is 20° and the insulation thickness is
varied from 0.0 to 0.1 cm. As in the uninsulated case, the SAR pattern shows a
distinct standing wave pattern whose wavenumber varies with insulation thickness. As
the thickness increases, the wavenumber decreases, resulting in less cycles of the
standing wave.
Effect of Insulation Thickness and Loss Figure 5.17 compares the effects of loss on
the SAR distributions of the insulated and uninsulated antennas. Here, for both
antennas, the pitch angle is 10° and the loss tangent is varied from 0.1 to 0.7. For the
insulated antenna, the insulation thickness is fixed at 0.01 cm.
These figures show how adding an insulating layer decreases the sensitivity to
loss. For the uninsulated antenna, as shown earlier, increasing loss shifted the SAR
distribution towards the antenna's tip. This resulted in an undesirable SAR pattern for
catheter ablation applications. However, the SAR pattern of the insulated antenna is
insensitive to changes in loss. Thus, by adding a thin layer of insulation, one can
achieve a nearly uniform heating pattern along the length of the antenna, even for loss
tangents comparable to that of heart tissue.
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Uninsulated
Insulated
A. Loss tangent, tan(Y)=e#/e'= 0.1
B. Loss tangent, tan(y)=e#/ e - 0.3
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^
Uninsulated
Insulated
C. Loss tangent, tan(y)=erle'= 0.5
D. Loss tangent, tan(Y)=e'/e'= 0.7
Figure 5.17 Comparison of normalized SAR distributions for insulated and uninsulated helical antennas
in various lossy media. Here, c=0.11 cm, b=0.1 cm, a=0.03 cm, L=3.0 cm, €3//e/=30 with e /= e 2/=2
and the pitch angle a=10°and f=915 MHz. Here, the loss tangent is varied from 0.1 to 0.7.
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118
Summary
This chapter presented some analytical results from the helical sheath antenna
model presented in Chapter 4. The results, which included dispersion diagrams,
electric field plots and SAR distributions, reveals several interesting observations.
First, when the antennas are immersed in an external lossy medium, there exist
only two dominant (n=0) modes of propagation. One mode, corresponds to a
previously reported slow mode found in lossless medium. The other is a newly
discovered faster mode, which appears only to exist when the external medium has
loss. The propagation constant and electric field distribution of the slow mode were
found to be sensitive to changes in the antenna configuration and the electrical
properties of the external medium, whereas those of the fast mode were not. It was
also determined that the slow mode contributes primarily to the heating of the external
medium.
Second, the SAR distributions for the uninsulated antennas show a significant shift
in the heating pattern as the external medium became more lossy. This resulted in an
undesirable heating pattern for the present application of catheter ablation.
Lastly, it was discovered, that by adding a thin layer of insulation to the outside of
the helical antenna, one can produce a more uniform heating pattern which is
insensitive to loss in the external medium. This configuration appears to be suitable
for catheter ablation applications.
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119
Chapter 6: Experimental Methods
This chapter describes the experiments that were performed. It consists of three
sections. The first section describes the apparatus used to measure SAR patterns, the
second describes the input impedance measurements; the third section describes the
measurement of the microwave dielectric properties of normal and coagulated heart
tissue.
6.1 Measurement of Specific Absorption Rate (SAR)
To confirm that the calculated SAR patterns of the helical coil antenna and RF
ablation catheter were correct, I designed and built a system to measure the SAR
directly. This section consists of two parts. In the first part the hardware of the SAR
mapping apparatus is described. The second part explains the methods used to correct
for artifacts introduced by the thermistor probe.
6.1.1
SAR Mapping Apparatus
A block diagram of the experimental apparatus is shown in Figure 6.1. The antennas
were mounted in a tank filled with aqueous electrolyte of varying
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120
(x,y,z) Positioning Command
Vectra
Computer
Thermistor Signal
Thermistor
Digital Pulse
915 MHz
Microwave
Generator
Tttt
' Aiteua
Microwave Energy
Blectroltfe
Solatiga
Figure 6.1 Thermistor based SAR mapping apparatus.
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121
conductivities. In Chapter 2, this solution was shown to be adequate as a muscle
phantom in the frequency range used in this study. The probe consisted of a small
thermistor encased in a glass micropipette, whose thermal response time was less than
0.1 seconds. The leads of the thermistor were a twisted pair of shielded wires which
were aligned perpendicular to the field of the antenna. This arrangement was found to
be sufficiently immune from interference to permit accurate measurements of the
antenna SAR patterns. The probe was mounted on a translating platform which was
controlled by stepping motors. The entire measurement process, including movement
of the probe and the recording and analysis of the thermistor output, was controlled by
a laboratory computer (Hewlett-Packard Vectra) running ASYST.
To measure the SAR pattern, I recorder the transient temperature increase in the
outside medium following a short pulse (0.5 sec) from either a 30 Watt 915 - MHz
microwave transmitter or a 30 Watt 500-kHz RF generator. The thermistor probe was
then repositioned to record the local SAR at a new position. Using this apparatus, I
could map the three-dimensional SAR pattern of an antenna with a 0.5 mm spatial
resolution over a total time period of a few hours. The whole process was done under
computer control. A more detailed description of the specific hardware follows.
Hardware
The hardware for the SAR mapping apparatus consisted of the x-y-z positioning
table, thermistor probe, power generators, computer and data acquisition system with
associated electronics. A few of these components are discussed in detail below.
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122
Positioning Table
Accurate measurement of the antenna's SAR distribution requires precise
positioning of the thermistor relative to the antenna. The device shown in Figure 6.2
was able to position the thermistor in three dimensions with the necessary accuracy.
This device is described in detail by Cheever 198950 and will be discussed here briefly.
Figure 6.2
Positioning table
The antenna mapping system was constructed using an x-y plotter drive
mechanism for transverse motion and a stepper motor mounted on the plotter pen
carriage for vertical, z-axis, positioning. The x-y plotter was able to position the
thermistor in the x-y plane with an accuracy of 0.1 mm. The stepper motor allowed
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123
positioning in the z-axis with an accuracy of 0.04 ram.
The x-y-z positioning was under computer control. Given the required x, y and z
coordinates at which to move the thermistor, the computer would translate these
coordinates into the proper plotter and stepper motor commands. The plotter
possessed its own language which defined movements. These commands were sent
via a serial line from the computer. The z-axis movement was accomplished by
calculating the appropriate number of step increments to send to the stepper motor.
This sequence of steps was sent to the stepper motor controller via a digital I/O port
on the data acquisition system which in turn incremented the stepper motor.
Thermistor Probe
A thermistor probe was constructed by securing a small thermistor at the tip of a
glass micropipette. A schematic of the probe is shown in Figure 6.3. The thermistor
had a diameter of 0.25 mm and a measured thermal response time of 0.08 sec. It was
Therm istor
G lass Micropipette
0.25 mm
Twisted Fair Insulated W ires
Epoxy
Figure 6.3 Thermistor probe used for SAR measurements.
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124
secured and sealed by a layer of epoxy placed at its base. The wire leads were
insulated and twisted to reduce electrical interference.
Electronics
Any temperature changes are reflected as changes in the thermistor resistance.
The circuit shown in Figure 6.4 was designed to transform the resistive changes of the
thermistor into an appropriate voltage signal which was capable of being sampled by
the computer's data acquisition unit. The first stage was a transducer bridge circuit
used to obtain an output voltage proportional to temperature variations. In this case, a
potentiometer was added to the bridge so that the bridge could be balanced at some
reference temperature and then calibrated to read variations above and below that
reference. The bridge output was sent though an instrumentation amplifier (variable
gain) and then passed through an active two-pole low pass filter with a 1.0 kHz cutoff
Vrr = 2.0 V
6.0 KQ
f
9.6 KQ
—
o |
14.0KQ
7.4 KQ
5.0 KQ
''I --------W V - p A A r
vw
9.6 KQ
out
14.0 KQ
1.0 KQ
1.0 KQ
S i— V W i — V W -1
o I
Figure 6.4 Electronic circuit used to record thermistor temperature.
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125
frequency. This temperature signal (Vout) was then sampled by a multichannel
12-bit analog-to-digital converter (Data Translations DT2800) at 100 Hz using an HPvectra™ computer with the data acquisition software ASYST™.
6.1.2
Data Analysis
Thermistor probes have been used by a variety of investigators to facilitate SAR
measurements. In particular, Bowman et a/.51 studied the accuracy of using thermistor
probes and reported some potential problems when the probes were inserted into
strong electromagnetic fields. Bowman's chief problem was that due to differences in
the electrical and thermal properties of the thermistor and the external phantom
material the measured temperature does not purely reflect the heating of the external
medium (the desired phenomenon), but rather a combination of thermistor and external
medium heating. This section examines this thermal artifact in more detail.
Thermal Artifact
Due to differences in electrical and thermal properties between the thermistor and
external medium, the recorded temperature will reflect a combination of thermistor and
external medium heating. However, since it is desirable to measure only the external
medium temperature uncontaminated by the presence of the thermistor, a heat transfer
model was developed to extract the external medium temperature from the recorder
temperature signal.
The model shown in Figure 6.5 consisted of a spherical thermistor of radius R,
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126
^ th
®th» Kh» **th \
®m> ®m» P
►
Figure 6.5 Heat transfer model used to subtract the thermal artifact out of thermistor temperature
measurement.
electrical conductivity
coefficient of heat conduction
and thermal diffusivity
immersed in an uniform electric field of strength E0 and surrounded by an external
medium. The external medium was assumed to be infinite in extent with electrical
conductivity a m, coefficient of heat conduction k,,,, specific heat cm and density pm.
Initially, the thermistor and external medium were assumed to be in thermal
equilibrium at temperature, Tj, and at time t=0 the electric field was turned on.
The fields internal to the thermistor, E^, will be different than the external fields
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127
and can easily be calculated by52,
Ea
34=—
E„
[6.1]
24 + 4
where e** = e*' - j a j (to e0 ) and em* = e j - j o m/ (to e0 ) are the complex
permittivity of the thermistor and external media respectively. The goal of this
analysis is to calculate the average temperature of a thermistor immersed in a uniform
external electric field.
A heat transfer analysis, described in detail in Appendix A , finds the average
temperature, T,ve,within the thermistor to be
a Tt * * £ [ 2 .
n4 4
where 5 =
- — ][1 -
e {«
** ] + S
t
[6-2]
«*
° m is the rate of temperature increase in the external medium
2 PmCm
Q = M
and
a*
2
is the time averaged power density dissipated in the
thermistor.
Without the presence of the thermistor the external medium temperature, T , ^ , is
simply given as
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r — i - T> * s ‘
[M 1
By comparing Equations [6.2] and [6.3], it is clear that the temperature measured by
the thermistor differs from the actual temperature of the external medium by an
Measure temperature signal
using thermistor
o.
Actual temperature signal
time
Figure 6.6 Illustration of how the measured thermistor temperature will differ from the actual
temperature of the external medium.
exponentially decaying transient component and a constant offset. This is illustrated
in Figure 6.6.
The quantity of interest here is the SAR in the external medium. By definition, this
is given by the rate of temperature increase multiplied by the specific heat of the
external medium ( SAR = cmS ). Therefore, measuring the slope of the thermistor
signal after the transient component has sufficiently died out, results in a quantity
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129
directly proportional to the SAR in the external medium.
To verify this prediction of the model, I performed the following experiment.
The thermistor probe was positioned and fixed in place next to a microwave antenna.
A 915 MHz microwave generator was then used to pulse microwave energy at several
26.0
Second Slope
25.0
Input Power, W atts
40.0 Watts
O
6>
<D
X
J
24.0
30.0 Watts
a>
a.
E
20.0 Watts
23.0
10.0 Watts
22.0
Initial Slope
Power
On
21.0
0.00
0.25
Power
Off
0.50
0.75
1.00
Time, se c o n d s
Figure 6.7 Measured temperature versus time curves for several different input
power levels.
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130
different power levels for 0.5 seconds each2. The resulting temperature signals were
recorded as a function of time (Figure 6.7).
From these curves, I calculated the slope of the initial temperature rise and the
steady state temperature rise (identified in Figure 6.7 as the second slope). These
values were then plotted as a function of the input power. The results shown in Figure
7.0
0.0
O
a)
o
— initial slope
•
- seco n d slope
5.0
■a
3.0
2.0
1.0
0.0i
40
Input Pow er Watts
Figure 6.8 The initial and second slopes identified in Figure 6.7 verses input power.
2 The microwave generator was custom built by Microwave Medical System, Littleton
MA.
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131
6.8 illustrate the utility of the model.
The second slope shown in Figure 6.8 is nearly a linear function of input power,
as predicted by the heat transfer model. This is a necessary requirement for accurately
measuring SAR patterns. If the initial slope was used, as shown in Figure 6.8, the
SAR pattern would be highly distorted by the non-linear relationship to input power.
6.2 Measurement of Input Impedance
The SAR mapping apparatus described in Section 6.1 was used to measure the
normalized distribution of energy released by the ablation device. This, however, does
not complete the entire picture. It is also necessary to consider what percentage of the
energy supplied by the generator is actually being released by the antenna. Since, a
considerable amount of the supplied energy may be reflected back into the generator,
the actual energy being released by the antenna may be too little to produce an
adequate ablation. It is possible to calculate the amount of reflected energy from
Z=0
Z=L
Figure 6.9 Reference plane for input impedance measurements.
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132
HP
8720
Network
Analyzer
GPIBBns
Apple
Macintosh n
Computer
Figure 6.10 Experimental setup used to measure input impedance.
knowledge of the antenna's input impedance. In this section, I describe the
experimental setup used to measure the input impedance of insulated and uninsulated
helical antennas radiating into a variety of external media.
Using a standard transmission line approach, the input impedance is defined as
the impedance looking into the antenna at the plane z=0 ( shown in Figure 6.9 ). The
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133
input impedance which is a complex quantity, z
both the input resistance
=
+j
represents
and the input reactance X ^ ,. The percentage of
reflected power is related to the input impedance through the simple relationship,
|j . 5p;p
% Reflected Power = r /wer x 100 = ----------
— x 100
[6.4]
U + _^|2
Here, Z0 is the characteristic impedance of the transmission line (Z0= 50 £2 typically)
P
is the power reflection coefficient defined as Tpower = ——• where Pref is
and
^inc
the reflected power and
the incident power.
Figure 6.10 illustrates the test fixture used for the input impedance measurements.
The antennas were immersed in a basin filled with electrolytic NaCl solution. The
basin was made large enough to insure that any reflections off its sides or top did not
significantly disturb the antenna's input impedance. A flexible 50 £2 coaxial cable was
used to attach the antenna to a Hewlett Packard 8720 Network Analyzer. The network
analyzer was calibrated at the reference plane ( shown in Figure 6.9) using three
factory standard loads — a short circuit, an open circuit and a 50 £2 termination. An
Apple Macintosh II computer running the data acquisition program Labview™ was
programmed to control the network analyzer. The network analyzer swept through the
frequency range 130.0 MHz to 3.0 GHz recording the input impedance every 50.0
MHz.
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6.3 Measurement of Microwave Dielectric Properties
The SAR calculations depend on the dielectric properties of the medium into
which the microwave antenna is radiating. During the time course of ablation, the
dielectric properties of heart tissue may change due to tissue coagulation. Therefore, it
was necessary to measure these properties at the low microwave frequencies for both
normal and coagulated heart tissue.
To accomplish this, I used an open ended coaxial probe technique developed by
Tanabe et al.. 53 The probe (typically a length of the common 3.6 mm OD semirigid
coaxial line) was placed against the unknown sample and its complex reflection
coefficient, T, was measured with an automated network analyzer (ANA). This
technique relies on the fact that the reflection coefficient of the coaxial probe is
strongly dependant on the dielectric properties of the sample. Given the reflection
coefficient and a good electrical model for the coaxial probe, one cal calculate the
complex dielectric constant of the medium.
The instrument used to implement the coaxial probe technique is shown in Figure
6.11. For these measurements the reflection coefficients were measured using a
Hewlett- Packard 8410 A Network Analyzer. A computer program was written
( Miranda, 1990) on a Hewlett-Packard 9000 series computer, to calibrate the network
analyzer, record the reflection coefficients and calculate the complex dielectric
constant.
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135
To Computer
To Computer
A
HP8410A
Network
Analyzer
HP5-I42A
Freqtjency
Counter
HP8620C
Sweep
Oscillator
6412 A
Display
862090A
RF Plug-In
"
HP8743 A
Reflection /
Frequency
Converter
Transmission
Test Unit
Reflection Port
Transmission Port
r~
i
Coaxial Probe
Saline
7
Figure 6.11 Experimental setup used to measure the complex dielectric constant o f tissue at microwave
frequencies. The measurement is based on the open-ended coaxial probe technique developed by
Tanabe3.
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136
In order to back calculate the dielectric properties from the measured reflection
coefficient, a good electrical model for the coaxial probe is required. While no
rigorous closed-form solution exists, several approximate models are available.
Marcuvitz54 expressed the admittance of the probe as an integral over its aperture; this
approximation was rederived in equivalent forms by Levine and Papas55 and Misra56.
Marcuvitz's approximation can be expanded into a series that is convenient for
numerical solution, and in this form can be used in experimental studies employing the
probe technique. According to Marcuvitz's approximation, the admittance at the plane
separating the coaxial probe and the sample (z=0 in Figure 6.11) is
Y = G +jB
71
[6.5]
a v
- Si(2k0y/e a sin(—)) - Si(2k0\fe b sin(—))] dQ
2
2
In these expressions, a and b are the inner and outer radii of the line, respectively; k„
is the propagation constant in free space, k ^ rc f/c where c is the velocity of light in
vacuum and f is the frequency; e and ec are the relative permittivities of the material
under test and the dielectric in the transmission line, respectively; J0 is the Bessel
function of order zero; and Si is the sine integral; Y0 is the characteristic admittance of
the line (Y0 = 0.02 S in these experiments). In this model, k0, ec, Y0, a and b are
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137
known parameters, G and B are measured quantities and e is the unknown
permittivity. Equation [6.5] was expanded in a power series in e in order to
numerically calculated e from the other known and measured quantities. The power
series given by Misra et al.56 is valid over the frequency range and probe dimensions
used in this study.
For these experiments, probes were constructed from a semirigid 50 £2 coaxial line
(3.5 mm OD line with a type SMA connector) of length 6.0 cm. The end distal to the
connector was machined flat and polished with a fine crocus cloth. The probe was
then connected to the test cable of the ANA (automated network analyzer). The
reference plane of the measurement was defined by shorting the end of the probe with
aluminum foil and adjusting the electrical delay of the ANA until a constant 180°
phase angle was observed.
The reflection coefficients from three standard load each with a known reflection
coefficient were used to correct for imperfections in connectors and the network
analyzer. Additional test samples with known dielectric properties were used to access
the accuracy of the technique. Over the range of frequencies used in this study, the
technique was found to be accurate to within 6.0% of the known values. This was
considered acceptable for the present study.
The dielectric measurements were performed on freshly excised sheep hearts (0 - 2
hrs old) that were obtained from a local slaughterhouse and put on ice for less than 1.0
hour prior to the experiment.
For uncoagulated tissue measurements, the left ventricle was excised and sliced
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into 3 cm x 3 cm sections with thicknesses ranging form 1 cm - 2.0 cm. The slices
were then immersed in a tank filled with 0.9% physiological saline at 25°C. The
tissue was left in the tank at least 30 minutes prior to measurements to insure that it
reached thermal equilibrium with the temperature of the external medium. After the
coaxial probe was properly calibrated, it was pressed firmly against the epicardial
surface. The dielectric measurements were then recorder at a variety of frequencies.
The procedure was then repeated on the endocardial and myocardial surfaces.
For coagulated tissue measurements, the left ventricle was again excised and sliced
into 3 cm x 3 cm sections. However, this time, the heart tissue was cooked in a
microwave oven at 300 watts for 10 minutes. It was then cooled for 30 minutes at
25°C prior to dielectric measurements. At this point the tissue was visibly coagulated.
The tissue was then immersed in the tank of physiological saline and the same
measurement process, as that for uncoagulated tissue, was performed.
The results for the dielectric properties of coagulated and uncoagulated tissue's
dielectric properties are presented in Chapter 6 (the results chapter).
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139
Chapter 7: Experimental Results
This chapter presents the experimental results obtained during the course of this
study. It consists of four sections. The first begins by presenting the experimental
measurements for the uninsulated and insulated helical antennas described in Chapter
6. It then compares these experimental results to the analytical results of Chapter 5.
The second section presents experimentally measured SAR patterns for an RF ablation
device and compares these to the results calculated by using the analytical model
derived in Section 4.3 . The third section briefly summarizes the complex permittivity
measurements for normal and coagulated heart muscle at microwave frequencies.
Finally, the last section shows the results of the in vitro experiments which were
performed.
7.1 Helical Antennas
This section presents the measured results for the uninsulated and insulated helical
antennas. These experimental results consist of SAR patterns and input impedance
measurements. To validate the analytical models developed in Chapter 4 , 1 compare
the experimentally obtained SAR patterns with the calculated results in Chapter 5.
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140
7.1.1 Uninsulated Helical Sheath Antenna
A series of helical antennas were fabricated and used in these experiments. Their
physical characteristics are summarized in Table 7.1. The antenna was constructed by
placing a helically wound, 0.01 cm diameter, copper wire around the exposed
dielectric of a standard semirigid coaxial line. The helix was wound using a precision
spring-winding facility at Arrow International (Reading, PA), with pitch angles ranging
from 5.25° to 17.1°. All the antennas were of length L=3.0 cm with an inner
conductor of radius a=0.03 cm and outer conductor of radius b=0.095 cm. The
dielectric core was made of teflon which was assumed to have a dielectric constant
£i=2.1. For all these experiments, the frequency was fixed at 915 MHz.
Length,
Radius of inner
Radius of outer
Pitch angle, a,
L, (cm)
conductor,a, (cm)
conductor,b, (cm)
deg.
Antenna #1
3.0
0.03
0.095
17.1
Antenna #2
3.0
0.03
0.095
11.2
Antenna #3
3.0
0.03
0.095
8.6
Antenna #4
3.0
0.03
0.095
5.25
Table 7.1 Geometry o f helical antennas used for experimental measurements
SAR Distributions
The apparatus described in Section 6.1.1 was used to measure the SAR patterns of
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141
the helical antennas described in Table 7.1. It is of particular interest, for the present
application, to investigate how the SAR patterns of these antennas vary with respect to
changes in pitch angle and loss in the external medium, and to compare these
experimental results to the analytical model of Section 4.1. Table 7.2 summarizes the
dielectric properties of the various concentrations of NaCl solutions used in these
experiments. These properties were calculated from the equations given by Stogryn40
(which were discussed in Section 3.3 and used for the analytical calculations). The
calculated and measured SAR patterns are normalized in the same manner as described
in Chapter 5.
Concentration of NaCl solutions (wt./wt.)
distilled
water
0.2%
NaCl
(wt/wt)
0.4% NaCl
(wt/wt)
0.6% NaCl
(wt/wt)
0.8% NaCl
(wt/wt)
1.0% NaCl
(wt/wt)
Complex
Permittivity
E^E'-je'
78.2-j3.41
77.5-J10.3
76.8-jl7.1
76.2-j23.8
75.5-j30.4
74.9-J36.9
Loss Tangent
tan(y)=E//E/
0.044
0.13
0.22
0.31
0.40
0.49
Table 7.2 Complex permittivity and loss tangent of various concentrations of NaCl solutions. For
reference, the complex permittivity of muscle tissue at 915 MHz was measured to be approximately
E*=56-j27.
Effect of Pitch Angle In Figure 7.1, the SAR patterns measured for the antennas in
Table 7.1 immersed in distilled water are compared to the calculated SAR patterns.
Clearly, the analytical results are in good agreement with experimental data,
demonstrating the validity of the sheath helix model.
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Measured
Calculated
A. Antenna #1, pitch angle a=17.1
B. Antenna #2, pitch angle a=11.2'
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Measured
Calculated
mm
C. Antenna #3, pitch angle a= 8.6‘
D. Antenna #4, pitch angle a=5.25°
Fto* 7.1 Measured and calculated SAR distribudons fo, antennas of various ptteb angles in disdlled
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143
144
As discussed in Chapter 5, the SAR pattern shows a distinct standing wave
pattern along the length of the antenna and its wavenumber increases as the pitch
angle decreases. This implies a standing wave with higher spatial frequency for more
tightly coiled helices.
Figure 7.1 also shows that the majority of the energy is held close to the helical
surface. The penetration depth at 915 MHz is shown here to be only a few
millimeters, and decreases as the pitch angle decreases. Consequently, if a deep lesion
is required, one must rely on the effects of thermal conduction.
Effect of Loss
Since the conductivity of muscle tissue is much greater than that of
distilled water, the SAR plots shown above do not reflect the pattern of the actual
antenna when used for ablation. Figures 7.2 and 7.3 illustrate how tissue loss would
change the SAR pattern of the uninsulated helical antenna.
In Figure 7.2, Antenna #3
(a= 8.6°) is immersed in solutions ranging from distilled water to 0.8% saline. As
predicted by the analytical results, as the conductivity of the external medium
increases, the heating pattern shifts toward the antenna's tip. In fact, when the
conductivity is similar to muscle tissue (0.8%) almost all of the heating takes place at
the tip.
Figure 7.3, shows the same phenomenon for Antenna #4 (a=5.25°). In this case
however, the shift in the heating pattern is ever more pronounced than for Antenna #3.
This is consistent with the analytical results which predict larger attenuations with
decreasing pitch angle.
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Measured
Calculated
A. Antenna #3 in distilled water
B. Antenna #3 in 0.2% (wt/wt) NaCl
solution
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145
Measured
Calculated
V
C. Antenna #3 in 0.4% (wt/wt) NaCl
solution
D. Antenna #3 in 0.8% (wt/wt) NaCl
solution
Figure 7.2 Measured and calculated SAR distributions for Antenna #3 in distilled water and various
saline solutions.
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Measured
Calculated
A. Antenna #4 in distilled water
B. Antenna #4 in 0.2% (wt/wt) NaCl
solution
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Measured
Calculated
148
C. Antenna #4 in 0.4% (wt/wt) NaCl
solution
D. Antenna #4 in 0.8% (wt/wt) NaCl
solution
Figure 7.3 Measured and calculated SAR distributions for Antenna #4 in distilled water and various
saline solutions.
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149
In p u t Impedance
To gain a deeper understanding of the heating characteristics of the helical
antenna, it is necessary to also consider the input impedance. The experimental setup
described in Chapter 6 was used to measure the input impedance of the uninsulated
helical antennas described in Table 7.1.
Unfortunately, the helical sheath model is unable to adequately predict the
measured input impedance. This is not surprising since the input impedance is far
more sensitive to current distribution near the feed point and to angular variations in
electric field than the SAR distribution. The helical sheath model assumes no
azimuthal variation in electric field and current distribution. Moreover, higher order
modes in the helical structure and the coaxial transmission line are not considered here
and could significantly affect the input impedance. In order to accurately predict the
input impedance, the helical sheath model should be replaced by a more realistic (and
complicated) model, such as a helical tape model.
In Figure 7.4a, the measured resistive and reactive components of the input
impedance are plotted as a function of frequency. The antenna pitch angle varies from
5.25° to 17.1° and the outside medium is 0.8% saline. Figure 7.4b shows the same
antennas radiating into 0.4% saline. The results show an insensitivity of input
impedance to changes in helical pitch angle and loss in the external medium. This
most likely reflects the contribution of the fast mode since it is also rather insensitive
to variations in pitch angle and loss.
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150
140
Helical Pitch Angle deg.
o - 14.B
120
|
100
.c
o
ua>
c
80
a
.52
*01
u
a:
0.16
0.60
1.04 1.4B 1.92
Frequency GHz
2.36
2.80
60
40
cn
|o
Helical Pitch Angle deg.
o - 14.8
20
0)
2
o
a
-M
o
a
a -2 0
O '
-4 0
-6 0
-B0
0.16
0.60
1.04 1.4B 1.92
Frequency GHz .
2.36
2.80
Figure 7.4a Measured resistive and reactive components of the input impedance vs. frequency for
antennas with various pitch angles immeresed in 0.8% saline.
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151
140
Helical Pitch Angle deg.
•2
60
0.16
0.60
1.04
1.48
1.92
2.36
2.80
Frequency GHz
Helical
» -2 0
1.04 1.48 1.92
Frequency GHz
2.36
2.B0
Figure 7.4b Measured resistive and reactive components of the input impedance vs. frequency for
antennas with various pitch angles immeresed in 0.4% saline.
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152
7.1.2 Insulated Helical Sheath Antenna
An insulating layer was formed by tightly wrapping the antennas, described in
Table 7.1, in a thin layer of Teflon tape (insulation thickness d=0.01 mm, permittivity
£2=2.1). Here, I intend to investigate the effect of this insulating layer on the SAR
pattern and input impedance of the helical antenna. I also compare the measured
results to the analytical model developed in Section 4.2.
SAR Distributions
The SAR patterns of the insulated antennas were measured using the same
apparatus and method used for the uninsulating antennas.
Effect of Insulation and Pitch Angle
Figure 7.5 shows the effect of insulation on
three antennas (a=17.1°, 8.6° and 5.25°) immersed in distilled water. Here, the
measured results are compared to the calculated results.
First of all, the insulation dramatically alters the antenna's SAR pattern.
Secondly, the measured and calculated results are in fairly good agreement, with the
exception of an additional peak in the SAR pattern of the calculated results. This
discrepancy is most likely due to inaccuracy in measuring the insulation thickness. As
shown in Chapter 5, a very small change in this thickness can significantly alter the
antenna's SAR pattern.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Calculated
Measured
153
A. Antenna #1, uninsulated in distilled
water.
1
m m
B. Antenna #1, insulated in distilled water
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Measured
Calculated
C. Antenna #3, uninsulated in distilled
water.
D. Antenna #3, insulated in distilled water
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154
Calculated
Measured
l
V s3
.O
-cC O 1
E. Antenna #4, uninsulated in distilled
water.
»*'\\V .v
F. Antenna #4, insulated in distilled water.
Figure 7.5 Measured and calculated SAR distributions of uninsulated and insulated antennas in distilled
water for Antennas #1, #3 and #4.
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156
Effect of Insulation and Loss Figure 7.6 compares the normalized SAR patterns of
Antenna #3 and #4 for the insulated and uninsulated cases when immersed in 0.8%
NaCl solution.
It is evident that a thin layer of insulation greatly reduces the effect of loss on the
antenna's SAR pattern. As seen earlier, the SAR peaks of the uninsulated antenna
rapidly shifts toward the antenna's tip with increasing conductivity of external medium.
In the insulated antennas, however, this effect is greatly reduced. In fact, the
measured and calculated results show no significant change in the normalized SAR
pattern as the loss of the exterior region approaches that of tissue. This result has
significant implications for the prospective biomedical application of catheter ablation.
Clearly, due to the reduction in tip heating, the insulated antenna produces a relatively
uniform heating pattern even when immersed in a medium as conductive as tissue.
Consequently, insulated helical antennas may offer the possibility of treating cardiac
arrhythmias (such as ventricular tachycardia) which require relatively large lesion
sizes.
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Measured
Calculated
A. Antenna #3, uninsulated in 0.8%
(wt/wt) NaCl solution.
B. Antenna #3, insulated in 0.8% (wt/wt)
NaCl solution.
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Measured
Calculated
158
5&>
C. Antenna #4, uninsulated in 0.8% (wt/wt)
NaCl solution.
iccD. Antenna #4, insulated in 0.8% (wt/wt) 1^£1*
solution.
Figure 7.6 Measured and calculated SAR distributions of uninsulated and insulated antennas in 0.8%
NaCl solution for Antennas #3 and #4.
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159
7.2 RF Ablation Measurements
To better comprehend the significance of the microwave antenna results with
respect to presently available RF techniques, I measured a series of SAR patterns for
the RF device. The SAR mapping apparatus, described in Section 6.1.1, was used to
obtain the patterns. The RF catheter used in these experiments was a standard
quadrapole catheter (manufactured by the Bard corporation) which is used clinically in
RF ablation procedures. The catheter was driven by a 100 Watt, 500 kHz RF source.
It was immersed in a basin filled with NaCl solution and oriented perpendicular to a
grounding plane which was placed 15.0 cm from the catheter tip. Figure 7.7 illustrates
the geometry of the RF catheter used for these experiments.
The SAR patterns were measured in both 0.4% and 0.8% NaCl solutions, and were
catheter tip electrode
b=3.0mm
p=0 T 3-0 mm
grounding plane
p=0.4 cm
z=2.'0 cm 2=3.0 cm
Figure 7.7 An illustration of the RF catheter geometry used for the SAR measurements,
normalized in the same manner as the microwave antenna results.
Figure 7.8 compares the measured SAR patterns to the results calculated from
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Measured
Calculated
160
sc*-
A.
RF catheter in 0.4% (wt/wt) NaCl
solution.
B.
RF catheter in 0.8% (wt/wt) NaCl
solution.
Figure 7.8 Measured and calculated SAR distributions of the RF catheter in 0.4% and 0.8% NaCl
solution.
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161
the analytical model derived in Section 4.2. Several observations can be made
regarding this figure. First, the measured and calculated results are in excellent
agreement. Second, the SAR of the RF device is largest at the tip of the catheter and
rapidly attenuates away from this point; it drops off as 1/r4 as predicted by the model.
Third, the normalized SAR patterns are independent of the conductivity in the external
medium. Consequently, the penetration depth of the RF device in tissue, or any other
lossy medium, will only be 2.0 to 3.0 mm.
Figure 7.9 compares the normalized SAR pattern of an RF catheter with that of an
insulated helical antenna. This figure clearly demonstrates that the microwave antenna
is capable of heating a much larger region than the RF device.
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Measured
Calculated
162
.O
A.
RF catheter in 0.8% (wt/wt) NaCl
solution.
B.
Insulated helical antenna in 0.8%
(wt/wt) NaCl solution.
Figure 7.9 Measured and calculated SAR distributions for the RF catheter and the insulated Antenna #3
in 0.8% NaCl solution.
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163
7.3 Dielectric Measurements
The open ended coaxial probe technique, discussed in Section 6.3, was used to
measure the complex permittivity of cardiac tissue at microwave frequencies. These
properties were measured for coagulated and uncoagulated tissue in order to determine
if the tissue's electrical properties are likely to change during the time course of
ablation.
Table 7.3 summarizes the average dielectric data obtained from 5 samples of raw
sheep heart muscle and 5 samples of coagulated heart muscle at 915 MHz.
Measurements were performed on the endocardial surface.
Complex Permittivity
*
/ • f
e =e -je
Uncoagulated
Endocardium
Coagulated
Endocardium
56.3 - j27.4
57.4-j26.8
Table 7.3 Summary o f dielectric properties for raw and coagulated sheep heart at 913 MHz.
The data illustrates that coagulation does not significantly alter the complex
permittivity of cardiac tissue at this frequency. Consequently, the antenna's SAR
pattern should not change during the time course of ablation.
7.4 I n Vitro Measurements
A series of in vitro experiments were performed. Their purpose was to estimate
the size of lesions likely to be produced by microwave ablation. These results could
then be correlated with measured SAR patterns. Additional experiments using RF
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164
In Vitro Experiments
Epicardial
surface
P e g s u s e d to hold
a n te n n a In p la c e
Helical
Antenna
Heart tissue sam ple
a. Microwave ablation setup
RF c a th e te r
RF tip e le ctro d e
P e g s u s e d to hold
a n te n n a In p la c e
Epicardial
surface
G rounding p la n e
Heart tissue sam ple
b. RF ablation setup
Figure 7.10 The setups used for microwave and RF ablation.
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165
ablation catheters were performed to provide a comparison for the microwave results.
The experiments were done on excised sheep hearts obtained from a local
slaughterhouse (0 - 2 hrs old). The left ventricles were excised and sliced into 8 cm x
8 cm sections, which ranged in thickness from 1.0 - 2.0 cm. As illustrated in Figure
7.10, the tissue slices were fixed in placed and the ablation device (either a
microwave antenna or an RF catheter) was placed along the epicardial surface. To
approximate the effect of intraventricular blood, the entire setup was immersed in a
tank of 0.9% NaCl solution at 25°C . An HP -vectra computer was used to pulse
microwave or RF energy to the ablation device for a set period of time (either 5.0,
10.0 or 30.0 seconds). The power levels of the microwave or RF device was adjusted
such that the total power being delivered from either was the same. This power was
measured and recorded during ablation to assess any changes due to tissue coagulation.
After the ablation was completed, the tissue was removed from the saline bath and the
lesions were excised and immediately placed in formalin for tissue fixation.
Lesion Size Determination
After two weeks, the tissue was removed from the formalin and the lesion was
carefully sectioned parallel to its base. All lesions were identified by a sharply
demarcated homogenous area of tissue coagulation. After sectioning through the
lesion's cross section, the depth, d, was measured every 2.0 mm along the antenna's
length. If, at any location, the lesion could not be visually identified, it was assigned a
depth of zero. Figure 7.11 illustrates the geometry of a typical lesion.
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166
epicardial su rfa c e
lesion
lesion d ep th
Figure 7.11 Illustration of lesion geometry used in measurements.
Results
Microwave Antenna Results In Figures 7.12A and 7.13A, lesion depth is plotted
verses location along antenna axis for several different heating times. These figures
compare the results for Antenna #1 and #3 with and without insulation. The measured
normalized SAR pattern for each antenna is given below each plot. The patterns is
included as a means of correlating the actual lesion size with the SAR plot. For these
experiments, the microwave power was set to 30 Watts and monitored during the
ablation process.
There are several observations which can be made regarding these experiments.
First, the depth of the lesions along the antenna axis correlates well with the SAR
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plots, particularly for the shorter heating times (5.0 and 10.0 seconds). Second, the
effects of thermal conduction become significant after 20 to 30 seconds of heating,
tending to produce a larger more uniform lesion. Third, the insulated antennas
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168
Uninsulated Antenna
Insulated Antenna
0.4
E
u
.—*
Heating Time sec.
o
0.3 -
c
o
'm
u
Heating Time sec.
E
o
— 5.0
10.0
•
-
•
- 30.0
c
o
5€)
- 3 0 .0
o
c
c
o
o
E
(U
c
V
0.
«c
u
CL
0.0
0.5
1.0
1.5
2.0
2JS
3.0
Length along antenna axis (cm)
I
0.1
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Length along antenna axis (cm)
S
Figure 7.12 Measured lesion depth and SAR pattern for Antenna #1 with and without insulation.
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169
Insulated Antenna
0.4
Uninsulated Antenna
0.4
Heatir.g Tima see.
E
o
E
u
0.3
co
*
m
e
o
c
o
- 30.0
Heating Time sec.
o
Hm
0.2
o
c
o
-l-l
10.0
•
-
v
- 30.0
-M
e
*8
cc
0.
0.3
c
o
e
ec
* -4
0.1
e
0.1
CL
0.0
0.0
0.5
1.0
1.5
2.0
2.5
Length along antenna axle (cm)
3.0
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Length along antenna axis (cm)
Figure 7.13 Measured lesion depth and SAR pattern for Antenna #3 with and without insulation.
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170
clearly produce a larger, more uniform lesion than the same antenna without insulation.
This effect, which is more pronounced in Figure 7.13, is of particular importance for
the catheter treatment of VT, which requires a large lesion size.
RF Results Figure 7.14 compares lesions produced by the insulated helical antenna to
those produced by an RF catheter. The RF source, like the microwave source, was set
at 30 Watts and monitored during the ablation process. The main finding from these
experiments is that the RF catheter produced a very localized lesion near the tip of the
catheter, whereas the microwave antenna produced a far larger lesion which extended
over its entire length.
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171
insulated Antenna
0.5
Heating Time eec.
E
c
o
m
o
o
co
33
0.2
E
e
ac
i
i
.
_0
o
c
o
s
0.2 -
-
e
0.1 -
o
▼ - 30.0
1----- 1-------1
0.4 . Heating Time eec. I
0 - 5.0
1
. ■ - 10.0
11
0.3
V -3 0 .0
E
ci 0.3
RF Catheter
c
o
*2
11
E
0.1
a.
a.
0.01i • eii» m * •
0.0 0.5 1.0 1.5
0.0
Length along antenna axis (cm)
-
•
—
2.0 2.5
3.0
Length along antenna axis (cm)
Figure 7.14 Measured lesion depth and SAR pattern for the insulated Antenna #3 and the RF catheter.
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172
Chapter 8: Conclusion
Over the past 10 years, a number of exciting new catheter techniques have
been introduced for the ablation of cardiac arrhythmias. Motivated by a need to ablate
large regions of tissue, this study has examined a relatively new technique using
microwave energy. Using combined theoretical and experimental methods, it has
focused on a particular antenna design, the helical coiled antenna. The properties of
such antennas immersed in a lossy medium have not been previously understood fully.
Analytical models based on a sheath helix approximation are described in Chapters 4
and 5 and experimentally verified in Chapter 7. These analytical and experimental
results are then compared to those of an RF ablation catheter as a means of estimating
the relative merits of the former.
Summary of Results
Near field SAR patterns in a homogenous lossy medium were calculated and
measured to characterize the antennas used in this study. It was found that, in general,
the SAR patterns strongly reflects the presence of standing waves. These patterns
depend in a complex way on the geometry of the antenna and the electrical properties
of the external medium.
. The patterns were found to be strongly sensitive to helical pitch angle, such that a
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173
tighter helix results in a higher propagation constant and a tighter standing wave
pattern. Another prominent feature is the high sensitivity of the antenna SAR pattern
to the loss of the external medium. This results, for the case of an uninsulated
antenna, in an antenna which heats predominantly at its distal tip. It was shown,
however, that if a thin layer of insulation is added to the outside of the helical antenna,
a more uniform heating pattern can result. This results even when immersed in very
lossy medium, such as tissue. Analytical and experimental results using an RF
ablation catheter, revealed a SAR pattern which was concentrated at the catheter’s tip.
In vitro experiments were performed on excised sheep hearts. These experiments
were done to correlate the SAR mappings with measurements of the induced tissue
lesions. It was found, that for short heating times (less than 10 seconds) thermal
conduction had little effect on tissue heating, consequently, the SAR patterns closely
matched the lesion geometry. Prolonged heating, on the other hand, lead to a more
diffuse heating distribution.
Significance of Results
The practical significance of this work is two fold. First, it was found that the
insulated helical antenna design offers the ability to ablate large regions of tissue.
This ability, which is not found in currently available ablation techniques, should be
useful in the treatment of ventricular tachycardia. Second, this study broadened our
understanding of helical antenna behavior in lossy matter. This may have practical
significance is other applications such as angioplasty or biotelemety.
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174
Future Studies
While this work has taken a step in the right direction, there are still many details
to be considered before microwave ablation becomes a clinical reality. First, further
studies are needed to quantify the effects of ventricular blood flow, heat conduction
and myocardial perfusion on the size of the induced lesion. Possibly a combined
electromagnetic/heat transfer model can be developed to account for these parameters.
Second, the possible dangers associated with this technique, such as the formation
of blood clots or induced catheter damage, should be accessed. It may be possible to
modify the helical antenna design ( such as shielding blood from the microwaves) to
minimize these potential hazards.
Third, a series of in vivo experiments should be performed in an animal model of
ventricular tachycardia to determine the effectiveness of the technique. These
experiments can also be used to estimate the optimal ablation parameters (frequency,
pitch angle, antenna length, power level) required to produce a particular lesion.
Clearly, microwave catheter ablation has potential in the treatment of certain
cardiac arrhythmias which are currently unbeatable using present techniques.
However, further engineering and medical studies are needed before this ambitious
goal is realized. This work has hopefully increased our understanding of the
capabilities of microwave ablation, and provided a foundation for further research.
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175
Appendix A: Heat Transfer Analysis of Thermistor Based SAR Mapping
Apparatus
As discussed in Chapter 6, a heat transfer analysis is utilized in subtracting out any
thermal artifact introduced by the presence of the thermistor. The model shown in
Figure A.1 consists of a spherical thermistor of radius, R, electrical conductivity, om,
coefficient of heat conduction, k^, and thermal diffusivity, o^, immersed in an uniform
electric field of strength, E0, and surrounded by an external medium. The external
medium is assumed to be infinite in extent with electrical conductivity, c m, coefficient
of heat conduction, k,,,, specific heat, cm, and density, pm. Initially, the thermistor and
external medium are assumed to be in thermal equilibrium at temperature, Ti( and at
^ th
Kh» ®th \
^m> Pm
►
Figure A .l Spherical thermistor immersed in a homogenous lossy medium and exposed to a uniform
electric field.
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176
time t=0 the electric field is turned on.
The fields internal to the thermistor, E*, will be different than the external fields and
can easily be calculated by,
-
--3e,<
E.
[A.1]
2ert + €w
(co e0 ) and e*’ = e j - j a j (to e0 ) are the complex
where e*’ = e*' - j
permittivity of the thermistor and external media respectively. The goal of this
analysis is to calculate the average temperature of a thermistor immersed in a uniform
external electric field.
The temperature distribution inside the thermistor, T(r,8,<l>), is determined by
solving the heat conduction equation with the appropriate boundary conditions. The
heat conduction equation is written in spherical coordinates as
l i f
r23r
i l ) * -J_-L (sm (0) i l ) + - J — H
dr
r!sio(0) 00
00
r!sin!(0) 0*1
cta dt
[A.2]
If the electric field distribution is assumed to be uniform both insideand outside the
thermistor (as the case here), then the resultant temperature distribution will vary only
in the radial direction. The heat conduction equation under this condition simplifies to
1 * 0 . 7)
r dr2
where, q =
♦^ - ± E
kA
[A.3]
aA dt
pa js the time averaged power density dissipated in the thermistor.
2
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177
The appropriate boundary conditions are
7(0, t) = finite
[A.4]
7 (R ,t) = Tt + S t
where S = ^
0|W is the rate of temperature increase in the external medium,
2PmC«
and T; is the initial thermistor temperature.
Before attempting to solve Equation [A.3] it is useful to first introduce the variable
U(r, t) = r [2(r, t) - TJ
[A.5]
Substituting Equation [A.5] into [A.3] and [A.4] results in
&E + r St = ——
dr2
[A.6]
dt
with the boundary conditions
U(0, t) = 0
[A.7]
U(R, t) = R S t
and the initial condition
U(r, 0) = 0
To solve Equations [A.6] and [A.7], I utilize the method of eigenfunction
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[A.8]
178
expansion. Using this method the function U(r,t) is expanded into a sum of
eigenfunctions, On(r), with time varying coefficients, bn(t), written as
OD
U(r,t) = £ > „(* ) ®„(r)
[A-9]
n-1
where the eigenfunctions are obtained by solving the appropriate eigenfunction
problem. For the present problem the eigenfunctions are obtained as
$>(r) = sin(— r)
R
[A. 10]
Substituting Equation [A. 10] into [A.9] results in
oo
t'W ) ■ £ *>.«) s i n ( ^ r )
[A.11]
&
n-1
Substituting this result into Equation [A.6], and collecting like terms, results in the
following differential equation for the unknown coefficients bn(t);
t
* M
f J2 *UMQ - ( f r ) -
[A.12]
Utilizing the orthogonality property of sinusoids this expression can be expressed for
any value of n as
^
K «)
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[A-13!
179
where,
- 2 a A Q R cos(/iit)
c, =
'*
kA n%
-2art nn S cos(/ni)
C2 =
Solving this first order differential equation for the unknown coefficients, bn(t),
results in
(nn)2,
b ^ = -2R3 cos(/m)( ^
(nn)3
_ _1] (1 - e *2 * ) + (n7c) 5 f ) tA-14l
kA
aA
R2
The thermistor temperature distribution can now be calculated by substituting Equation
[A. 14] into Equation [A. 11] and substituting that result into Equation [A.5]. This
results in the following thermistor temperature distribution
o>
T(r, t) = - 2 R 3 ( - ^ - — ) Y
Kh
ath «-1 (nit)3
- e
. ,m tr .
j
“rt ) --------------+ s t + Ti
r
[A. 15]
The measured thermistor signal actually reflects its average temperature.
Consequently, it is necessary to determine the average temperature using Equation
[A. 15] and [A. 16].
T J t) = - i -
it
/ 4n r2 n r , 0 dr
3
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[A. 16]
180
This results in
[A. 17]
*th
th "-1 (W7t)
By keeping only the first term in Equation [A. 17], I find the approximate average
thermistor temperature as
it*
*»
“*
It is this expression which is used in Chapter 6 in analyzing the thermal artifact
introduced by the thermistor.
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181
Appendix B: Derivation of the Lorentz Reciprocity Theorem
In deriving the orthoganality relations for the helical sheath it was necessary to
impose the Lorentz reciprocity theorem without derivation. I will now derive the
theorem for the particular case of interest here.
Consider any two different modes, viz., E„ H, and Ej, H2, propagating in the z
direction, shown in Figure 4.3, of a guiding structure (a helical sheath in this case). In
a source free region these fields will satisfy Maxwell's equations given as
V x Ex =
■H 1
V x UY = j a e • 4
[B.U
[B.2]
V x E2 = -ja m • H2
[B.3]
V x H2 = ja>e ■4
[B.4]
Utilizing the vector identity V-(4xB) = B'VxA - A-VxB (where A and B are
arbitrary vectors) we can expand the quantity v ( E ^ H J and
V- (4> < 4) “
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182
- Ey-VxH2
[B.5]
V* (E2xHy) = Hy'VxE2 - E2-VxHy
[B.6]
V- (£xx / y =
respectively.
Subtracting [B.6] from [B.5] results in
V* (EyxH2 - E2xHy) = H2 VxEy - Ey-VxH2 - H{-VxE2 + E^VxHy
[B.7]
Substituting equations [B.l] through [B.4] for the curl of the field vectors given on the
right hand side of [B.7] results in
V- (EyXH2 - E2xHy) = 0
[B.8]
The del operator in Equation [B.8] can be separating into its transverse, denoted by
subscript t, and longitudinal parts, given as
V,- (Eu xHy - E24xHu ) + ^ (E y x H 2 - E2xHy)-az = 0
[B.9]
Applying the divergence theorem to Equation [B.9] results in
~ V ^ i P ’ dl +
c
~
az ds = 0
[B.10]
s
The above expression must be true for any surface, s, with contour, c. If the surface
integral is chosen to be over the entire transverse plane, then the contour integral must
be evaluated at infinity. Since the fields must vanish at infinity the first integral in
Equation [B.9] must also vanish. This results in
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183
*> 2u
f / - |( ^ x f f 2 -
&z p d* dp = 0
[B.11]
p»0 $ -0
For the present case each mode is propagating in the z direction with a propagation
constant p. The fields can thus be written as
£ ,(p A
z)
= £ i ( p ,<B
« ,( P ,M - A ,(P ,«
(B 12]
4(p,<|>d = £ 2( p ,« e * *
S 2( p M
- J?2(P,4>) e *
Substituting Equation [B.12] into [B .ll] and preforming the derivative results in the
form of the Lorentz reciprocity theorem used in Chapter 4.
oo
( P i + P2 ) /
2n
/ (frpADxBjp*) - ^(p^)^i(p^))* a* p d<Mp =0
P “0
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184
1. F. H. Netter, The CIBA Collection o f Medical Illustrations, vol. 5, Ciba - Geigy
corporation, pp. 60-61, 1978.
2. W. M. Jackson, X. Wang, K. Friday, et al., "Catheter Ablation of Accessory
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12. M. Haissaguerre, J. F. Warin, P. Lematayer et al., "Catheter ablation of resistant
ventricular tachycardia: immediate results and long-term follow-up", PACE,
11:920, 1988.
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185
13. T. D. Sellers, D. Dilorenzo, P. Primerano, et al., "Catheter ablation of ventricular
tachycardia using high cumulative energy: Results in 28 patients with a mean
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