0017-9078/79/ 12014743/%02.00/0
Healfh Physics Vol. 37 (December), pp. 743-750 Pergarnon Press Ltd., 1979. Printed in the U.S.A. @ Health Physics Society
DESIGN OF APERTURE SOURCES FOR DEEP HEATING USING ELECTROMAGNETIC ENERGY HENRY S. HO
U.S. Department of Health, Education and Welfare, Public Health Service, Food and Drug Administration, Bureau of Radiological Health, 5600 Fishers Lane, Rockville, MD 20857 (Received 18 August 1978; accepted 14 May 1979)
Abstract-Currently, there exists interest in the use of electromagnetic energy (nonionizing) for research. One of the most important problems facing such applications is the proper design of applicators which deliver deep penetration of electromagnetic energy into the tissues. At the present, microwave aperture sources used for these applications often have shallow energy-penetration characteristics. In contrast to aperture sources with deep energy-penetration characteristics, aperture sources with shallow energy penetration require higher input power, allow larger scattered field into the environment, and cause often-unwanted higher heating to the surface tissues. In the present theoretical investigation, source frequency, aperture size and field distribution are parameters used for designing aperture sources which deliver deep penetration of electromagnetic energy into different sizes of spherical tissue-equivalent bodies. The source frequencies used in this calculation range from 10 MHz to 10 GHz. ISM frequencies (for unlicenced use in industrial, scientific and medical applications) in this range are included in the calculation. Three types of sources are used: plane wave “Cap” aperture, and “Belt” aperture. The “Cap” aperture is a circular aperture shaped like a polar cap in contact with the irradiated sphere. The “Belt” aperture is a loop source that wraps around the irradiated sphere. Four different sizes and three different aperture field distributions of each aperture are used. Twelve sizes of the tissue-equivalent sphere are used with radii ranging from 0.5 to 10.0 cm. For each size of the sphere, four cases are considered: a single-layered muscle sphere, and three triple-layered spheres with muscle, fat and skin layers. The thicknesses of the fat layers of the three triple-layered spheres are respectively 10, 20 and 30% of the radius of the muscle sphere. The thickness of the skin layer is 1.0mm in each case. The results indicate a strong resonance type of dependence on source frequency for deep electromagnetic energy penetration. This resonance frequency decreases with increased sphere size. The energy penetration is also found to be a strong function of the aperture size. With optimum design, the aperture sources can produce deeper energy penetration characteristics than obtained with plane wave sources. The optimum energy penetration into the smaller size spheres (less than 5.0cm radius) is found to be much greater than that for the larger size spheres. In general, the optimum deep energy penetration characteristics of the triple-layered spheres are not as good as those of the single-layered spheres. An improvement over the energy penetration characteristics of some of the existing applicators can be obtained by using the optimum aperture frequency, size, shape and field distribution reported in this investigation.
INTRODUCTION
of nonionizing electromagnetic energy for research has been a topic of increasing interest (Ba76; C076; Dc70; Gu74;
THE
USE
Le70; Sz76; Ve76). A n important problem encountered in such applications is the design of applicators which deliver penetrating electromagnetic energy into tissues, since the
743
744
DESIGN OF APERTURE SOURCES FOR DEEP HEATING
location of the tissues where irradiation is desired may be deep within the body. The testing and design of applicators for deep heating of tissues has been a continuing effort (Le70; De70; Ch76; Gu66; Gu71; Gu75; Ho71; Ka76). Source frequency, aperture size and aperture field distribution have been used in separate investigations as design parameters. Also, the size of the biological body is found to be an important factor in determining the optimum source frequency and applicator characteristics which produce deep tissue-heating (Ho71; Ho75a). The present theoretical investigation used a systematic approach of varying source frequency, aperture shape and size, and aperture field distribution to seek aperture sources which deliver deep penetration of electromagnetic energy into different sizes of spherical tissue-equivalent bodies. METHODS
The method for.calculating the dose rate (mW/g) in an aperture irradiated dielectric sphere has been reported (Ho75). Results from this calculational method were found to be in general agreement with those obtained from experiments using the thermographic method (Ho77a). Calculations of dose rate in plane wave irradiated dielectric spheres have been reported (Ho75a; Sh7 1). The calculated results were also found to be in general agreement with experimental data from thermographic studies (Jo72). In the present theoretical investigation, three different types of sources were used: plane wave, “Cap” type aperture, and “Belt” type aperture. The “Cap” aperture is a circular aperture shaped like a polar cap in contact with irradiated sphere. The “Belt” aperture is a loop aperture source that wraps around the irradiated sphere. Figure 1 shows these three types of sources and the tissue-equivalent sphere. The angle 8,, indicated in Fig. 1 determines the size of the aperture source. Three different aperture field distributions designated as types A, B and C were included in this calculation. The mathematical expressions describing these field distributions for the “Cap” and the “Belt” type of aperture sources are shown in equations (1) and (2) respectively.
where E, and Eb are respectively the surface field of the “Cap” and “Belt” apertures. The function g(4) defines the different aperture distributions, where
R(4)
= Eo = EolCOS
(411
= Eolcos (412))
Vlm for type A Vlm for typeB Vlm for typeC (3)
where Eo is a value determined by the net input power to the aperture source. There were four sizes of each aperture with 80 equal to 7~14,~ 1 2 3, ~ 1 4and r respectively. These large sizes of aperture source were used because previous investigations (Gu71; Ho71; Ho75b; Ho77b) have shown that small aperture sizes result in high heating at the surface of the tissue-body and produced shallow penetration characteristics. The frequency dependent dielectric properties of the muscle and fat tissues has been reported by Johnson and Guy (Jo72). In the present investigation, twelve sizes of muscle spheres were used with radii equal to 0.5, 1, 2, 3 , 4, 5 , 6, 6.5, 7, 7.5, 8 and 10cm respectively. Four cases were considered for each size of the muscle sphere: the single-layered muscle sphere, and three triple-layered spheres composed of fat
47 PLANE WAVE X
Y
Y
‘BELT’ APERTURE
‘CAP APERTURE
X
X
Y
FIG. 1. Plane wave, “Belt” aperture, and “Cap” aperture sources on tissue-equivalent spheres.
HENRY S.H O and skin layers on top of the muscle spheres. The thicknesses of the fat layers for the three triple-layered spheres were respectively 10, 20 and 30% of the radii of the muscle spheres. The thickness of the skin layer was 1.0mm in each case. Two values of the conductivity of the fat tissue have been reported for each source frequency. The lower values were used in the present investigation. However, a calculation was also made to compare the results using the higher and the lower reported values of the conductivity of the fat tissue. Fifteen source frequencies ranging from 10MHz to 10GHz were used. These frequencies were: 10, 27.12, 40.68, 100, 200, 300, 433, 750, 915, 1500, 2450, 500, 5800, 8000 and 10,000 MHz. A term “Energy Penetration Factor” (EPF) was defined. This index (EPF) is a dimensionless number defined as the quotient of the dose rate, b (Ve76) at the center of the sphere by the maximum dose rate at the surfaces of all tissue layers of the sphere. Hence a high value of EPF indicates deep penetration of energy absorption. The EPF value for each size of sphere as a function of source frequency, aperture shape and size, and aperture field distribution were calculated. Heating patterns in selected triplelayered tissue-equivalent spheres were also calculated. RESULT A N D DISCUSSION
The calculated result indicates that for each source frequency, the size O o = 77/4 yields the lowest E P F value. The sizes Oo = 37r/4 and 7~ generally yield higher EPF values. This finding is in agreement with reported theoretical and experimental results from previous applicator designs (Gu7 1; Ho71; Ch76). The EPF value depends on the source frequency in a resonant fashion. Figure 2 shows the EPF value vs source frequency and aperture size for the triple-layered sphere with 1.0cm muscle radius irradiated by “Belt” apertures with type A field distribution. The peak EPF value of 8.6 was obtained with a source frequency of 2,450 MHz and aperture size of 80=3?r/4. Deep heating pattern along the X - 2 plane of the
145 MUSCLE SPHERE RADIUS = I 0 Cm FAT LAYER THICKNESS = 0 2 Cm S K I N LAYER THICKNESS = 1 0 mm
TYPE A, ‘BELT’ APERTURE SIZE, 00
___________ ___
.......................... ~
-;lo[
n:4
n
2
.____________ 3n:4 n
FREQUENCY (GHz)
FIG. 2. Energy Penetration Factor (EPF) vs source frequency for the 1.0cm muscle radius, triple-layered tissue-equivalent sphere irradiated by type A, “Belt” aperture sources. triple-layered sphere with 1.0 cm muscle radius irradiated by this source is shown in Fig. 3. The heating pattern in the X-Y plane (not shown) is also as deeply-penetrating as that in the X - 2 plane. MUSCLE SPHERE R A D I U S = 1 .O crn F A T LAYER THICKNESS = 0.2 crn S K I N LAYER THICKNESS = 1.0 mrn EZo = 3770 VZ/rn2 D,,
= 102.9 rnW/g
TYPE A, 2450 MHz, ‘BELT’ APERTURE SIZE Bo = 3n/4 EPF = 8.6
FIG.3. Heating pattern in the X - 2 plane cross section of the 1.0 cm muscle radius, triple-layered tissue-equivalent sphere irradiated by a type A, 2,450 MHz, “Belt” aperture source, with size: Bo = 3&.
746
DESIGN OF APERTURE SOURCES FOR DEEP HEATING
As the radius of the tissue-equivalent sphere increases, the resonance frequency of the EPF is lowered and the peak EPF value is smaller than those of the small radii. Figure 4 shows the E P F vs source frequency and aperture size for the triple-layered sphere with 4.0cm muscle radius irradiated by “Belt” apertures with type A field distribution. The resonance curve of the EPF vs source frequency for the 4.0 cm radius case is wider with lower peak than the resonance curve for the 1.0cm radius case. The heating pattern in the X - Z plane of the triple-layered sphere with 4.0cm muscle radius shown in Fig. 5 indicates that concentrated heating by aperture sources in the interior of the sphere is possible even though some surface heating lowers the EPF value to 1.9. Figures 6 and 7 show the EPF vs source frequency and aperture size for the triple-layered sphere with 7.0 cm and 10.0 cm muscle radii irradiated by “Belt” apertures with type A field distribution. Again the resonance frequency and peak EPF value are lowered for larger sphere sizes. The peak E P F value of 0.32 for the 10.0cm radius sphere shown in Fig. 7 suggests that a sharply concentrated heating pattern in the interior of the biological bodies may be difficult to achieve with the type of
MUSCLE SPHERE RADIUS = 4.0 cm FAT LAYER THICKNESS = 0.8 cm SKIN LAYER THICKNESS = 1 .O mm Eo2 = 3770 VZ/m2
= 17.7 mWig
,,D
TYPE A, 915 MHz, ‘BELT’ APERTURE SIZE: Bc = n EPF : 1.9
FIG. 5 . Heating pattern in the X - Z plane cross section of the 4.0 cm muscle radius, triple-layered tissue-equivalent sphere irradiated by a type A, 915 MHz, “Belt” aperture source, with size: 0” = T.
MUSCLE SPHERE RADIUS = 7.0 cm FAT LAYER THICKNESS = 1.4 cm SKIN LAYER THICKNESS = 1 0 mm
TYPE A , ’BELT‘ APERTURE SIZE, 00
____________________ n/2
. . . . . . . . . . . . . . . . . . . . . . . . .
nl4
.-----------.mi4
n
MUSCLE SPHERE RADIUS = 4 0 C r n FAT LAYER THICKNESS 0.8 c r n SKIN LAYER THICKNESS 1 0 mm ~
~
TYPE A, ‘BELT’ APERTURE SIZE, 00 ...........
n/4
______ 3 n i 4
..........n/2 G ‘ 3
L
n
1~
0.4
L 0.
0.2
t,
0.0
>
0.01
0.1
1 .o
10.0
FREQUENCY (GHz)
FIG. 6. Energy Penetration Factor (EPF) vs source frequency for the 7.0cm muscle radius, triple-layered tissue-equivalent sphere irradiated by type A, “Belt” aperture sources. FREQUENCY (GHz)
FIG. 4. Energy Penetration Factor (EPF) vs source frequency for the 4.0cm muscle radius, triple-layered tissue-equivalent sphere irradiated by type A, “Belt” aperture sources.
single frequency aperture sources used in this calculation. However, a relatively uniform interior heating pattern can still be achieved. Figure 8 shows the heat-
HENRY S. HO
747
tern in the X-Y plane (not shown) was found to be even more uniform than that in the X - 2 TYPE A, ‘BELT’ APERTURE SIZE, 00 plane. As is indicated by the result shown in . . ..... ~ ....... ~ .... ni4 ~ ~ ~ ~ ~ 31114 Fig. 7, this heating pattern cannot be attained _______ _____ ______ n;2 .________ ---. n for the 10.0cm radius sphere by using relatively higher frequencies even if the optimum aperture dimensions and field distributions are used. An even higher surface heating vs internal heating than indicated in Fig. 8 would be produced. The source frequency for maximum EPF value vs muscle sphere size of triple-layered sphere irradiated by “Belt” aperture is shown in Fig. 9. The optimum source frequency decreases as the sphere radius increases. The calculated result also indicates similar sourcefrequency dependence of the EPF values between the “Belt” and the “Cap” apertures as FREQUENCY (GHz) well as the plane wave source. However, the FIG. 7. Energy Penetration Factor (EPF) vs “Belt” and “Cap” apertures have higher source frequency for the 10.0cm muscle radius, maximized EPF values than the plane wave triple-layered tissue-equivalent sphere irradiated source. Figure 10 shows the maximized E P F by type A, “Belt” aperture sources. values vs sphere size of type A “Belt” and “Cap” apertures, and the plane wave source. MUSCLE SPHERE RADIUS = 10.0 Cm The low EPF values for the large spheres FAT LAYER THICKNESS = 2.0 cm irradiated by the plane wave source is in SKIN LAYER THICKNESS = 1.0 mm EZo = 3770 V2/mZ agreement with previously reported results =, ,D , 6 . 6 4 mW/g for large tissue-equivalent spheres (25 cm MUSCLE SPHERE RADIUS = 10.0 cm FAT LAYER THICKNESS = 2.0 crn SKIN LAYER THICKNESS = 1.0 m m
~
~
TYPE A, 200 MHz, ‘BELT’ APERTURE SIZE: 96 = 3ni4 EPF = 0.32
FAT LAYER THICKNESS = 20% OF MUSCLE SPHERE RADIUS SKIN LAYER THICKNESS = 1 0 m m
TYPE A, ‘BELT’ APERTURE FREQUENCY FOR MAXIMIZED EPF VALUE
-1
Y FIG. 8. Heating pattern in the X-Z plane cross section of the 10.0 cm muscle radius, triple-layered tissue-equivalent sphere irradiated by a type A, 200 MHz, “Belt” aperture source, with size: 00 = 24.2 cm
37~14.
0.01
0
ing pattern in the X - 2 plane of the 10.0cm radius sphere irradiated by a type A, 200 MHz-“Belt”-aperture source with an aperture size of: & = 3d4. The heating pat-
2
4
6
8
10
MUSCLE SPHERE RADIUS ( c m )
FIG.9. Source frequency of type A, “Belt” aperture source for maximized EPF values vs muscle sDhere radius.
DESIGN OF APERTURE SOURCES FOR DEEP HEATING
148
F A T LAYER THICKNESS = 20% OF MUSCLE SPHERE R A D I U S S K I N LAYER THICKNESS = 1 0 rnm ........-. TYPE . A BELT APERTURE .__________.TYPEA C A P APERTURE -------PLANE WAVE
h
u. LI
>E
on
ag 5y
nu i Z
2; rt, x
Healfh Physics Vol. 37 (December), pp. 743-750 Pergarnon Press Ltd., 1979. Printed in the U.S.A. @ Health Physics Society
DESIGN OF APERTURE SOURCES FOR DEEP HEATING USING ELECTROMAGNETIC ENERGY HENRY S. HO
U.S. Department of Health, Education and Welfare, Public Health Service, Food and Drug Administration, Bureau of Radiological Health, 5600 Fishers Lane, Rockville, MD 20857 (Received 18 August 1978; accepted 14 May 1979)
Abstract-Currently, there exists interest in the use of electromagnetic energy (nonionizing) for research. One of the most important problems facing such applications is the proper design of applicators which deliver deep penetration of electromagnetic energy into the tissues. At the present, microwave aperture sources used for these applications often have shallow energy-penetration characteristics. In contrast to aperture sources with deep energy-penetration characteristics, aperture sources with shallow energy penetration require higher input power, allow larger scattered field into the environment, and cause often-unwanted higher heating to the surface tissues. In the present theoretical investigation, source frequency, aperture size and field distribution are parameters used for designing aperture sources which deliver deep penetration of electromagnetic energy into different sizes of spherical tissue-equivalent bodies. The source frequencies used in this calculation range from 10 MHz to 10 GHz. ISM frequencies (for unlicenced use in industrial, scientific and medical applications) in this range are included in the calculation. Three types of sources are used: plane wave “Cap” aperture, and “Belt” aperture. The “Cap” aperture is a circular aperture shaped like a polar cap in contact with the irradiated sphere. The “Belt” aperture is a loop source that wraps around the irradiated sphere. Four different sizes and three different aperture field distributions of each aperture are used. Twelve sizes of the tissue-equivalent sphere are used with radii ranging from 0.5 to 10.0 cm. For each size of the sphere, four cases are considered: a single-layered muscle sphere, and three triple-layered spheres with muscle, fat and skin layers. The thicknesses of the fat layers of the three triple-layered spheres are respectively 10, 20 and 30% of the radius of the muscle sphere. The thickness of the skin layer is 1.0mm in each case. The results indicate a strong resonance type of dependence on source frequency for deep electromagnetic energy penetration. This resonance frequency decreases with increased sphere size. The energy penetration is also found to be a strong function of the aperture size. With optimum design, the aperture sources can produce deeper energy penetration characteristics than obtained with plane wave sources. The optimum energy penetration into the smaller size spheres (less than 5.0cm radius) is found to be much greater than that for the larger size spheres. In general, the optimum deep energy penetration characteristics of the triple-layered spheres are not as good as those of the single-layered spheres. An improvement over the energy penetration characteristics of some of the existing applicators can be obtained by using the optimum aperture frequency, size, shape and field distribution reported in this investigation.
INTRODUCTION
of nonionizing electromagnetic energy for research has been a topic of increasing interest (Ba76; C076; Dc70; Gu74;
THE
USE
Le70; Sz76; Ve76). A n important problem encountered in such applications is the design of applicators which deliver penetrating electromagnetic energy into tissues, since the
743
744
DESIGN OF APERTURE SOURCES FOR DEEP HEATING
location of the tissues where irradiation is desired may be deep within the body. The testing and design of applicators for deep heating of tissues has been a continuing effort (Le70; De70; Ch76; Gu66; Gu71; Gu75; Ho71; Ka76). Source frequency, aperture size and aperture field distribution have been used in separate investigations as design parameters. Also, the size of the biological body is found to be an important factor in determining the optimum source frequency and applicator characteristics which produce deep tissue-heating (Ho71; Ho75a). The present theoretical investigation used a systematic approach of varying source frequency, aperture shape and size, and aperture field distribution to seek aperture sources which deliver deep penetration of electromagnetic energy into different sizes of spherical tissue-equivalent bodies. METHODS
The method for.calculating the dose rate (mW/g) in an aperture irradiated dielectric sphere has been reported (Ho75). Results from this calculational method were found to be in general agreement with those obtained from experiments using the thermographic method (Ho77a). Calculations of dose rate in plane wave irradiated dielectric spheres have been reported (Ho75a; Sh7 1). The calculated results were also found to be in general agreement with experimental data from thermographic studies (Jo72). In the present theoretical investigation, three different types of sources were used: plane wave, “Cap” type aperture, and “Belt” type aperture. The “Cap” aperture is a circular aperture shaped like a polar cap in contact with irradiated sphere. The “Belt” aperture is a loop aperture source that wraps around the irradiated sphere. Figure 1 shows these three types of sources and the tissue-equivalent sphere. The angle 8,, indicated in Fig. 1 determines the size of the aperture source. Three different aperture field distributions designated as types A, B and C were included in this calculation. The mathematical expressions describing these field distributions for the “Cap” and the “Belt” type of aperture sources are shown in equations (1) and (2) respectively.
where E, and Eb are respectively the surface field of the “Cap” and “Belt” apertures. The function g(4) defines the different aperture distributions, where
R(4)
= Eo = EolCOS
(411
= Eolcos (412))
Vlm for type A Vlm for typeB Vlm for typeC (3)
where Eo is a value determined by the net input power to the aperture source. There were four sizes of each aperture with 80 equal to 7~14,~ 1 2 3, ~ 1 4and r respectively. These large sizes of aperture source were used because previous investigations (Gu71; Ho71; Ho75b; Ho77b) have shown that small aperture sizes result in high heating at the surface of the tissue-body and produced shallow penetration characteristics. The frequency dependent dielectric properties of the muscle and fat tissues has been reported by Johnson and Guy (Jo72). In the present investigation, twelve sizes of muscle spheres were used with radii equal to 0.5, 1, 2, 3 , 4, 5 , 6, 6.5, 7, 7.5, 8 and 10cm respectively. Four cases were considered for each size of the muscle sphere: the single-layered muscle sphere, and three triple-layered spheres composed of fat
47 PLANE WAVE X
Y
Y
‘BELT’ APERTURE
‘CAP APERTURE
X
X
Y
FIG. 1. Plane wave, “Belt” aperture, and “Cap” aperture sources on tissue-equivalent spheres.
HENRY S.H O and skin layers on top of the muscle spheres. The thicknesses of the fat layers for the three triple-layered spheres were respectively 10, 20 and 30% of the radii of the muscle spheres. The thickness of the skin layer was 1.0mm in each case. Two values of the conductivity of the fat tissue have been reported for each source frequency. The lower values were used in the present investigation. However, a calculation was also made to compare the results using the higher and the lower reported values of the conductivity of the fat tissue. Fifteen source frequencies ranging from 10MHz to 10GHz were used. These frequencies were: 10, 27.12, 40.68, 100, 200, 300, 433, 750, 915, 1500, 2450, 500, 5800, 8000 and 10,000 MHz. A term “Energy Penetration Factor” (EPF) was defined. This index (EPF) is a dimensionless number defined as the quotient of the dose rate, b (Ve76) at the center of the sphere by the maximum dose rate at the surfaces of all tissue layers of the sphere. Hence a high value of EPF indicates deep penetration of energy absorption. The EPF value for each size of sphere as a function of source frequency, aperture shape and size, and aperture field distribution were calculated. Heating patterns in selected triplelayered tissue-equivalent spheres were also calculated. RESULT A N D DISCUSSION
The calculated result indicates that for each source frequency, the size O o = 77/4 yields the lowest E P F value. The sizes Oo = 37r/4 and 7~ generally yield higher EPF values. This finding is in agreement with reported theoretical and experimental results from previous applicator designs (Gu7 1; Ho71; Ch76). The EPF value depends on the source frequency in a resonant fashion. Figure 2 shows the EPF value vs source frequency and aperture size for the triple-layered sphere with 1.0cm muscle radius irradiated by “Belt” apertures with type A field distribution. The peak EPF value of 8.6 was obtained with a source frequency of 2,450 MHz and aperture size of 80=3?r/4. Deep heating pattern along the X - 2 plane of the
145 MUSCLE SPHERE RADIUS = I 0 Cm FAT LAYER THICKNESS = 0 2 Cm S K I N LAYER THICKNESS = 1 0 mm
TYPE A, ‘BELT’ APERTURE SIZE, 00
___________ ___
.......................... ~
-;lo[
n:4
n
2
.____________ 3n:4 n
FREQUENCY (GHz)
FIG. 2. Energy Penetration Factor (EPF) vs source frequency for the 1.0cm muscle radius, triple-layered tissue-equivalent sphere irradiated by type A, “Belt” aperture sources. triple-layered sphere with 1.0 cm muscle radius irradiated by this source is shown in Fig. 3. The heating pattern in the X-Y plane (not shown) is also as deeply-penetrating as that in the X - 2 plane. MUSCLE SPHERE R A D I U S = 1 .O crn F A T LAYER THICKNESS = 0.2 crn S K I N LAYER THICKNESS = 1.0 mrn EZo = 3770 VZ/rn2 D,,
= 102.9 rnW/g
TYPE A, 2450 MHz, ‘BELT’ APERTURE SIZE Bo = 3n/4 EPF = 8.6
FIG.3. Heating pattern in the X - 2 plane cross section of the 1.0 cm muscle radius, triple-layered tissue-equivalent sphere irradiated by a type A, 2,450 MHz, “Belt” aperture source, with size: Bo = 3&.
746
DESIGN OF APERTURE SOURCES FOR DEEP HEATING
As the radius of the tissue-equivalent sphere increases, the resonance frequency of the EPF is lowered and the peak EPF value is smaller than those of the small radii. Figure 4 shows the E P F vs source frequency and aperture size for the triple-layered sphere with 4.0cm muscle radius irradiated by “Belt” apertures with type A field distribution. The resonance curve of the EPF vs source frequency for the 4.0 cm radius case is wider with lower peak than the resonance curve for the 1.0cm radius case. The heating pattern in the X - Z plane of the triple-layered sphere with 4.0cm muscle radius shown in Fig. 5 indicates that concentrated heating by aperture sources in the interior of the sphere is possible even though some surface heating lowers the EPF value to 1.9. Figures 6 and 7 show the EPF vs source frequency and aperture size for the triple-layered sphere with 7.0 cm and 10.0 cm muscle radii irradiated by “Belt” apertures with type A field distribution. Again the resonance frequency and peak EPF value are lowered for larger sphere sizes. The peak E P F value of 0.32 for the 10.0cm radius sphere shown in Fig. 7 suggests that a sharply concentrated heating pattern in the interior of the biological bodies may be difficult to achieve with the type of
MUSCLE SPHERE RADIUS = 4.0 cm FAT LAYER THICKNESS = 0.8 cm SKIN LAYER THICKNESS = 1 .O mm Eo2 = 3770 VZ/m2
= 17.7 mWig
,,D
TYPE A, 915 MHz, ‘BELT’ APERTURE SIZE: Bc = n EPF : 1.9
FIG. 5 . Heating pattern in the X - Z plane cross section of the 4.0 cm muscle radius, triple-layered tissue-equivalent sphere irradiated by a type A, 915 MHz, “Belt” aperture source, with size: 0” = T.
MUSCLE SPHERE RADIUS = 7.0 cm FAT LAYER THICKNESS = 1.4 cm SKIN LAYER THICKNESS = 1 0 mm
TYPE A , ’BELT‘ APERTURE SIZE, 00
____________________ n/2
. . . . . . . . . . . . . . . . . . . . . . . . .
nl4
.-----------.mi4
n
MUSCLE SPHERE RADIUS = 4 0 C r n FAT LAYER THICKNESS 0.8 c r n SKIN LAYER THICKNESS 1 0 mm ~
~
TYPE A, ‘BELT’ APERTURE SIZE, 00 ...........
n/4
______ 3 n i 4
..........n/2 G ‘ 3
L
n
1~
0.4
L 0.
0.2
t,
0.0
>
0.01
0.1
1 .o
10.0
FREQUENCY (GHz)
FIG. 6. Energy Penetration Factor (EPF) vs source frequency for the 7.0cm muscle radius, triple-layered tissue-equivalent sphere irradiated by type A, “Belt” aperture sources. FREQUENCY (GHz)
FIG. 4. Energy Penetration Factor (EPF) vs source frequency for the 4.0cm muscle radius, triple-layered tissue-equivalent sphere irradiated by type A, “Belt” aperture sources.
single frequency aperture sources used in this calculation. However, a relatively uniform interior heating pattern can still be achieved. Figure 8 shows the heat-
HENRY S. HO
747
tern in the X-Y plane (not shown) was found to be even more uniform than that in the X - 2 TYPE A, ‘BELT’ APERTURE SIZE, 00 plane. As is indicated by the result shown in . . ..... ~ ....... ~ .... ni4 ~ ~ ~ ~ ~ 31114 Fig. 7, this heating pattern cannot be attained _______ _____ ______ n;2 .________ ---. n for the 10.0cm radius sphere by using relatively higher frequencies even if the optimum aperture dimensions and field distributions are used. An even higher surface heating vs internal heating than indicated in Fig. 8 would be produced. The source frequency for maximum EPF value vs muscle sphere size of triple-layered sphere irradiated by “Belt” aperture is shown in Fig. 9. The optimum source frequency decreases as the sphere radius increases. The calculated result also indicates similar sourcefrequency dependence of the EPF values between the “Belt” and the “Cap” apertures as FREQUENCY (GHz) well as the plane wave source. However, the FIG. 7. Energy Penetration Factor (EPF) vs “Belt” and “Cap” apertures have higher source frequency for the 10.0cm muscle radius, maximized EPF values than the plane wave triple-layered tissue-equivalent sphere irradiated source. Figure 10 shows the maximized E P F by type A, “Belt” aperture sources. values vs sphere size of type A “Belt” and “Cap” apertures, and the plane wave source. MUSCLE SPHERE RADIUS = 10.0 Cm The low EPF values for the large spheres FAT LAYER THICKNESS = 2.0 cm irradiated by the plane wave source is in SKIN LAYER THICKNESS = 1.0 mm EZo = 3770 V2/mZ agreement with previously reported results =, ,D , 6 . 6 4 mW/g for large tissue-equivalent spheres (25 cm MUSCLE SPHERE RADIUS = 10.0 cm FAT LAYER THICKNESS = 2.0 crn SKIN LAYER THICKNESS = 1.0 m m
~
~
TYPE A, 200 MHz, ‘BELT’ APERTURE SIZE: 96 = 3ni4 EPF = 0.32
FAT LAYER THICKNESS = 20% OF MUSCLE SPHERE RADIUS SKIN LAYER THICKNESS = 1 0 m m
TYPE A, ‘BELT’ APERTURE FREQUENCY FOR MAXIMIZED EPF VALUE
-1
Y FIG. 8. Heating pattern in the X-Z plane cross section of the 10.0 cm muscle radius, triple-layered tissue-equivalent sphere irradiated by a type A, 200 MHz, “Belt” aperture source, with size: 00 = 24.2 cm
37~14.
0.01
0
ing pattern in the X - 2 plane of the 10.0cm radius sphere irradiated by a type A, 200 MHz-“Belt”-aperture source with an aperture size of: & = 3d4. The heating pat-
2
4
6
8
10
MUSCLE SPHERE RADIUS ( c m )
FIG.9. Source frequency of type A, “Belt” aperture source for maximized EPF values vs muscle sDhere radius.
DESIGN OF APERTURE SOURCES FOR DEEP HEATING
148
F A T LAYER THICKNESS = 20% OF MUSCLE SPHERE R A D I U S S K I N LAYER THICKNESS = 1 0 rnm ........-. TYPE . A BELT APERTURE .__________.TYPEA C A P APERTURE -------PLANE WAVE
h
u. LI
>E
on
ag 5y
nu i Z
2; rt, x
