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Comparative theoretical performance for two types of regional hyperthermia systems
h. J. Radiarion Omhgy Biol. Pbys.. Vol. Printed in the U.S.A. All rights reserved.
I I, pp.1659-1671 Copyright
0360-3016/85 $03.00 + .OO 0 1985 Pergamon Press Ltd.
??Original Contribution
COMPARATIVE THEORETICAL PERFORMANCE FOR TWO TYPES OF REGIONAL HYPERTHERMIA SYSTEMS
KEITH D. PAULSEN,M.S.,JOHN W. STROHBEHN, PH.D.AND DANIEL R. LYNCH, PH.D. Thayer School of Engineering, Dartmouth
College, Hanover, NH 03755
Regional hyperthermia systems have drawn attention because of their potential for depositing power noninvasively in deep-seated tumors. Two such systems that have received clinical attention because of their ability to deposit significant amounts of power in tissue are magnetic induction devices and annular phased array applicators. In this paper, theoretical calculations for the specific absorption rate (SAR) and the resulting temperature distributions for these systems are compared. The finite element method is used in the formulation of both the electromagnetic and thermal boundary value problems. Six detailed patient models based on CT-scan data from the pelvic, viscera& and thoracic regions are generated to simulate a variety of tumor locations. In general, the annular phased array deposited more power within the tumor and produced better temperature distributions than the magnetic induction device. However, the ratio of the maximum power absorbed by the tumor to the maximum power absorbed in normal tissue does not appear to be high enough for either device to heat significant portions of perfused tumors to therapeutic temperatures under a wide range of physiological conditions. The results contained herein slhould aid the physician in comparative treatment planning with existing regional hyperthermia systems. Comparative thermal dosimetry, Regional hyperthermia.
been published, and the analysis that has been done has generally been carried out on idealized patient configurations. 2,3,6S1 1-14,22,24,31 Generally, reported results suggest difficulty in deep-seated heating in the torso, but satisfactory temperature rises in superficial tumors when magnetic induction devices are used.12,20-22,31 Annular phased array applicators have been reported to produce a nearly uniform electric field across the body, and have been modeled as such, suggesting that they should heat deep centrally located tumors the best.“3’5*16.33*34 The question of which of these two types of regional hyperthermia systems will produce the superior thermal dosimetry given the same tumor location heated under the same physiological conditions has been addressed by Roemer et. a1.24In this study, idealized power deposition and patient geometry were used with a wide range of physiological and anatomical variables. Quantitative results from these simulations agree with the qualitative statements made above for each type of device. These studies have been useful in setting some general guidelines for evaluating the potential efficacy of magnetic induction devices and annular phased array applicators. In this paper we compare two-dimensional theoretical
INTRODUCIION
the resurgent interest in hyperthermia as a cancer therapy, a number of different hyperthermia systems have emerged in the clinic. External devices that produce regional hyperthermia are particularly popular because of their noninvasive approach to heating deep-seated tumors. Two such systems that have been proposed as capable of depositing significant amounts of power in tissue are magnetic induction devices and annular phased array applicators.5,28-30,33,34 In the case of magnetic induction, tissue is heated by power deposited from eddy currents induced by magnetic fields. In one configuration these magnetic fields are generated inside the patient by a concentric conducting coil which wraps around the body section to be heated. Annular phased array devices are also large external applicators that fit around the diseased body section. Power is deposited in tissue by electric fields produced from concentric rings of inphase apertures. Although these two types of hyperthermia systems have received much clinical attention, only a modest amount of analysis on their theoretical performance has With
Presented in part at The: 4th International Symposium on Hyperthermic Oncology, Aarhus, Denmark, July 2-6, 1984. Supported in part by NIIH/NCI Grants CA23594, and NSF Grant EC%0258 18.
Reprint requests to: John W. Strohbehn. Accepted for publication 3 April 1985.
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calculations for the specific absorption rate (SAR) and the resulting steady-state temperature distributions produced by magnetic induction devices and annular phased array applicators in anatomical models based on CT scans of typical cancer patients. A number of detailed patient models from the pelvic, visceral, and thoracic regions were generated to simulate a variety of tumor locations and surrounding normal tissues that are representative of clinical situations. The methods and results contained herein are useful for both comparative thermal dosimetry, where the objective is to compare different types of hyperthermia systems for their ability to heat typical tumors, and for prospective thermal dosimetry, where the goal is to plan the treatment for a specific patient.32 METHODS
AND MATERIALS
Predicting temperature profiles is a two-fold problem; first, to predict the power deposition in tissues; and second, to predict the resultant temperatures. The second problem is common to all hyperthermia devices and has been formulated as a heat diffusion equation with a first order decay term that represents the crucial role of blood circulation in temperature regulation. We used a standard form of the bioheat transfer equation’.” whose finite element formulation we have previously employed.22,23 The first problem, the heat source calculation, tends to be device-specific. Our finite element formulation for this problem is explained in detail in Ref. 19, where we demonstrated its ability to conserve energy exactly, to faithfully reproduce the analytic dispersion relationship, and to accurately predict analytic solutions under representative conditions; hence, only the governing equations for each device will be reviewed here. Assuming a time variation of the form exp(-iwt), Maxwell’s curl equations in differential form become:
September 1985, Volume I I, Number 9
where k is the complex wavenumber: k2 = o*pP = w2pc + iups.
For magnetic induction devices, it is assumed that the magnetic field is directed down the long axis of the patient; thus, the electric field is confined to the transverse or CT-scan plane. In this plane, & in eqn (2) is a vector quantity in which continuity in its parallel component and discontinuity in its perpendicular component must exist at all tissue interfaces where the electrical properties change abruptly. We have successfully solved eqn (2) on finite elements incorporating the appropriate boundary conditions at each tissue interface [ 191; however, because of the large number of different tissue regions in a typical CT-scan, we also adopted a second numerically simpler but less elegant approach: calculate @ via finite elements; then differentiate to find &. Because CL is effectively constant in tissue, @ is continuous across all tissue interfaces-hence the added numerical simplicity. We can isolate @ in the same fashion as & above by combining eqns (la) and (1 b) giving:
px($yxy)-H-0
(3)
Because the magnetic field is assumed unidirectional and perpendicular to the plane of analysis (@ = H,(x, y)~), eqn (3) reduces to a scalar equation in Hz:
8 can be isolated by taking the curl of eqn (la) and substituting (lb) which results in (assuming CLconstant)
At the device boundary, Hz = .I,, the amplitude of the current per unit length in the coil, which we assumed known and constant. Operationally, we solve eqn (3a) for @ on finite elements, then take the curl of this solution to obtain &, the desired quantity, via eqn (lb). The drawback in this simpler approach is the loss of accuracy in & as a result of the necessary differentiation of @. An additional consequence is that & will be discontinuous across all element boundaries on the simple elements we employ. Nonetheless, we have found essentially the same accuracy between the two approaches when compared to analytic solutions under representative conditions.” Further, we have found that virtually identical temperature profiles were produced in a four region, CT-based patient model regardless of which method was used to compute the SAR distribution. For annular phased array applicators, the electric field is assumed to be polarized down the long axis of the patient and we solve directly for E,. The double curl in eqn (2) reduces to V2 and the electromagnetic problem is one of solving a scalar Helmholtz equation in Ez:
V x (0 x @ - k2& = 0
V’E, + k2Ez = 0
0 X & = iwp@
(la)
0 X fl=
(lb)
-it.&&
&
is the time-invariant complex amplitude electric field E-1: is the time-invariant complex amplitude magnetic field is the magnetic permeability p t* = t + is/o is the complex permittivity u is the electrical conductivity is the permittivity t frequency w E tr
of the of the
i
(2)
(4)
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Comparative theoretical performance 0 K. D. PAULSEN etal.
At the device boundary, we assume that the electric field distribution is known and can be represented across each aperture by a half-wavelength cosine function: E, = E. cos (ra/L)
(5)
where L a
the length of a segment is the distance from .the center of a segment. is
Because of the unidirectional nature of & in this problem, E, is continuous across tissue interfaces; hence the finite element formulation for eqn (4) becomes the analog of that for eqn (3a).19
Table Perfusion Fat
Muscle
Bone
Both of these heat source problems and their subsequent heat diffusion problems were solved on six finite element models that were generated from CT-scans of actual cancer patients. The finite element discretization of each patient’s anatomy has been published previously. 23Two-dimensional power deposition patterns were calculated for each of the six body cross-sections for each of the two types of regional hyperthermia systems. The concentric coil device was assumed to operate at 13 MHz, whereas the annular phased array applicator was assumed to operate at 100 MHz with all apertures driven inphase. The numerically calculated SAR distributions were then used as the source input for the
1. HEP rating
rates Rectum
Tumor
cc
Relative
power level
AA
cc
AA
1 = 245 W/m 1.0 1.0
1 = 266 W/m 1.5 1.6
Pelvic model A .03*q * *
2.1
0
1.8-f
0 2.7 20
P P P
G P P
lot
0 2.1 20
P P P
G P P
2.3 2.3 2.3
3.3 3.3 3.3
0 2.7 20
P P P
F P P
3.6 3.6 3.6
4.7 4.7 4.7
:
5**t *. *. :
15
5
10*-t *. *, :
21
10
15*,t *. *, :
54
15
W
0 2.7 20
P P P
F P P
4.1 4.1 4.1
6.2 6.2 6.2
30* *, *, :
65
30
45
0t 2.1 20
P P P
G F P
7.8 7.8 7.8
9.5 11.3 11.3
t
Pelvic model B 2.7*q *, *. :
0
1.8
0 2.1 20
F P P
G G P
5* * *
15*q *, *, :
5
10
0 2.1 20
P P P
G G P
3.1 3.1 3.1
2.8 6.0 7.8
lo* * *, t
27* *. t *
10
18
ot 2.1 20
P P P
G G P
5.0 5.0 5.0
3.8 8.0 10.4
15* * *.
54
15
2?5t 20
P P P
G G P
7.1 7.1 7.1
4.2 10.0 12.9
0t 2.7t 20
F P P
G G F
11.1 11.1 11.1
4.3 10.1 19.5
.03
36
t
30* * *, t
65
30
45
CC = Concentric coil; AA = Annular array; G = Good, F = Fair; P = Poor. *-t Indicate tissue reaching limiting temperatures for the concentric coil and the annular on two tissues usually means the limiting temperature was at an interface. All perfusion rates given in ml/l00 gm/min.
1 = 528 W/m 1.0 1.0
1 = 240 W/m 2.4 2.5
phased array cases, respectively.
A symbol
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Radiation Oncology 0 Biology 0 Physics
bioheat transfer equation to calculate the temperature profiles. As a thermal boundary condition, we assumed the patient was surrounded by water bolus, which was maintained at 20°C. We adopted the same protocol we used in a previous work23 for scaling the input power, varying normal and malignant tissue blood flow rates, and ranking the resulting temperature distributions. Only the essential points of our procedure will be reviewed. The input power was increased until either: 1. Tumor temperature > 60°C 2. Fat, muscle, or bone temperature 3. Visceral organs > 42°C
The required input power for each case was computed and reported, but no simulation was restricted on the basis of this value alone. It is difficult to relate our calculated values to any practical power requirements since our model is two-dimensional and our calculated values represent power absorbed by the body. Any physical device will have losses from reflected power and power radiated but not absorbed by the patient. We leave extrapolation of any practical power requirements from our two-dimensional data to those more familiar with the efficiency of existing physical systems. For normal tissue we first assumed basal blood perfusion values typical for the various tissue types (see the first case in Tables 1, 2, and 3). We then increased these
> 44°C
Table 2.
Perfusion Fat
Muscle
Bone
Viscera
Liver
HEP rating
rates
Kidney
Spleen
Aorta
Stomach
Relative
power level
Tumor
CC
AA
cc
AA
1 = 376 W/m 1.5 1.6
Visceral model A 2.F1_ *, t *, i
.03
15* * *,t
5
10
15
27
54
t 30
65 t
* *, * * * *
o*q * *.t
27
420
0 2.7 20
P P P
P P P
1 = 305 W/m 1.0 1.0
5*-t * *
27t t
420
0 2.7 20
F P P
F P P
2.7 2.8 3.8
2.1 3.2 4.4
10*,t *,
54
420
0 2.7 20
F P P
F F P
3.8 4.0 4.0
3.3 4.9 6.7
70
420
0 2.7 20
F P P
F F P
4.8 6.0 6.0
3.5 6.2 8.9
100
420
0t 2.1 20
F P P
F F P
6.2 8.0 8.0
3.8 7.8 14.8
1 = 340 W/m 1.4 1.4
*
t
t
15*-f *,
*
t
30* *, t *
Visceral model B 2.7* * *
0* * *
57
420
60
84
40
0 2.7 20
P P P
P P P
1 = 561 W/m 1.0 1.0
5*-/ *. *, :
15
5
57
420
60
84
40
0 2.1 20
P P P
F F P
2.5 2.8 2.8
2.1 3.6 7.4
1O*,f
27
10
57
420
60
84
40
0 2.7 20
P P P
F P P
3.6 4.3 4.3
2.4 4.0 10.2
15
57
420
60
84
40
0 2.7 20
P P P
P P P
4.4 6.3 6.6
2.6 4.2 12.6
30
57
420
60
84
40
0 2.7 20
F P P
P F F
6.4 8.4 8.4
3.2 5.0 15.0
.03t :
: 15*-t *, t *
54
30*q *, t *
65
* * * *
* *
Symbols: same as Table 1. All perfusion rates given in ml/100
gm/min.
Comparative theoretical performance 0 K. D. PAULSENet al.
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Table 3. Perfusion Fat
Bane
Muscle
Lung
Heart
Tumor Thoracic
.03
5
2.7*%1 *, *. ;
0* *. *,
15*q *, *, :
10* * *
27t
15* * *
34.t
30* * *
65t
:
:
:
*,
AA
cc
AA
model A
0 2.7 20
P P P
P P P
L = 678 W/m 1.0 1.0
1 = 768 W/m 1.2 1.3
5* * *
433
84
0 2.7 20
P P P
F F P
2.4 2.4 2.4
1.8 2.6 3.0
10* * *
433
84
0 2.7 20
P P P
F F P
3.1 3.1 3.1
2.3 3.2 4.0
15* * *
433
84
0 2.7 20
P P P
F F P
3.6 3.6 3.6
5.1 4.3 6.1
30* * *
433
84
0 2.7 20
P P P
G F P
5.3 5.3 5.3
3.5 4.7 7.4
5
model B
0
433
84
0 2.7 20
P P P
P P P
1 = 660 W/m 1.0 1.0
1 = 746 W/m 1.0 1.0
51
433
84
0 2.7 20
P P P
P P P
1.6 1.7 1.8
1.4 1.8 2.1
10
433
84
0 2.7 20
P P P
P P P
1.8 2.1 2.4
1.8 2.4 3.1
: 15* * *
:
CC
84
2.7t
5:;t
power level
433
Thoracic .03* * *
Relative
HEP rating
rates
1o*q *, *, :
27
15*-t *, *, :
54
15
433
84
0 2.7 20
P P P
F F P
2.0 2.4 2.9
2.4 3.0 4.2
30*q *, *, :
65
30
433
84
0 2.7 20
F P P
F F P
2.5 3.0 4.7
3.1 3.9 6.5
t
i
Symbols: same as Table L and 2. All perfusion rates given in ml/100
perfusion
values
to
see
whether
gm/min.
higher
values
would
In some of these cases the assumed values were: well outside the normal physiological range, but the objective was to see what blood perfusion values might result in good temperature distributions. For each set of normal tissue blood flow rates, three different tumor perfusion rates were used: result
in better
thermal
1. Necrotic 2. Low 3. High
patterns.
0 ml/100 gm/min 2.7 ml/100 gm/min 20 ml/ 100 gm/min
As a criterion for comparing the temperature distributions produced by each device, the percent of the total tumor area to reach 43°C or greater was computed
and given a hyperthermia equipment performance (HEP) rating as: 1. 2. 3. 4.
Excellent Good Fair Poor
therapeutic therapeutic therapeutic therapeutic
region region region region
= 100% = 7599% = 50-74% < 50%
All electrical and thermal properties used in these calculations are given in Table 4. RESULTS Figures 1 through 6 show a comparison of the power deposition patterns produced by concentric coil applicators and annular phased array devices for each of the
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Table 4. Electrical
conductivity
Tissue
13 MHz
100 MHz
13 MHz
100 MHz
Thermal conductivity (W/m/‘C)
Aorta Bone Fat Heart Kidney Liver Lung Muscle Rectum Spleen Stomach Tumor Viscera Water
1.oo .20 .20 .60 .80 .45 .I1 .60 .35 .51 .41 .60 .41 .oo
.93 .02 .22 .93 1.oo .60 .35 .89 .61 .78 .51 .89 .57 .oo
180 28 28 140 330 150 42 122 106 310 80 122 80 70
73.5 10 10.5 89 89.5 77.5 40 72 52 100 80 72 80 78
.527 .436 .210 .527 .547 ,508 .478 .642 .498 .515 ,527 .642 .550 ,603
Relative permittivity
(W/v2/m)
Specific heat X density (W - sec/m3/“C) (X106) 3.72 2.25 2.12 3.72 3.96 3.81 1.68 3.72 3.35 3.81 3.81 3.72 3.81 4.31
Magnetic permeability of all tissues was taken as equal to that of free space. Other values were assembled from’,4,9-‘4,‘6.26.27.
six body cross-sections. The contour lines in these figures are normalized such that the maximum power deposition is 10. The discontinuity in power deposition contours at the tissue interfaces is because the absorbed power is directly proportional to the electrical conductivity, which is discontinuous at these interfaces. Tables 1, 2, and 3 contain a summary for both devices of the HEP ranking, the total power consumption (in watts/meter), and the overheated normal tissues for each different blood flow case for the different body crosssections investigated. A power value of unity was assigned to the first case in each table and the power values given for all subsequent cases are relative to this quantity.
DISCUSSION
Pelvic models Because both pelvic models have deep centrally located tumors (see Figures 1 and 2 for anatomical location), we would expect a magnetic induction device to produce minimal power deposition in the tumor, and a phased array system to produce significant power deposition in the tumor. Almost the entire tumor area is within the 10% iso-power contour in Figures la and 2a, which show power deposition patterns for a concentric coil device. Figures lb and 2b show that a significantly higher percentage of the maximum power deposition is produced in the tumor by an annular phased array (>40% for pelvic model A, >60% for pelvic model B). This applicator, in fact, produced a higher percentage of power deposition in the tumor in pelvic model B than in any other tumor model whether it or the concentric coil was used. It is interesting to note, however, that neither device produced the maximum power absorption in the tumor in either pelvic model, but that
both systems deposited the maximum power in normal tissue near the muscle-fat interface, which was located in the peripheral portions of these body cross-sections. As would be expected from knowledge of the power deposition, almost every HEP rating (see Table 1) for the concentric coil was poor (therapeutic region < 50%). However, fair temperature distributions (therapeutic region 50-74%) resulted in pelvic model B when basal physiological values were used for the normal tissue blood flow rates, and also for very high normal tissue blood perfusion rates, as long as the tumor was assumed necrotic. This further indicates that this device must heavily rely on thermal conductive effects and/or extensive cooling of normal tissue via highly elevated blood flow rates to produce therapeutic heating in deep-seated tumors. The annular phased array produced good thermal profiles (therapeutic region 75-99%) in almost every case for both pelvic models as long as the tumor remained necrotic. Increasing the tumor perfusion rate to 2.7 ml/100 gm/min reduced the HEP ratings to poor in most cases for pelvic model A, and further increases in tumor blood flow to 20 ml/100 gm/min reduced the HEP ratings to poor in pelvic model B. This suggests that delivering 40-50% of the maximum power deposition to the tumor, as in pelvic model A, may not be enough to heat satisfactory portions of tumors with low blood flow, and more than 60-70% maximum power deposition may be required to heat tumors with blood perfusion rates on the order of 20 ml/100 gm/min. Visceral models Visceral model A has a large tumor, extending from superficial to deep-seated, whereas the tumor site in visceral model B is entirely deep-seated (see Figures 3 and 4 for anatomical sites). A priori we would expect
Comparative theoretical performance 0 K. D. PAULSENet al.
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Fig. 1. Absorbed power distribution for Pelvic model A. Contours are normalized to a maximum value of 10 and are separated by increments of 1. Bone is shaded with dots and tumor is shaded with lines. (a) Concentric coil; (b) Annular phased array.
the phased array to deposit more power and subsequently to produce better HEP ratings in visceral model B than the magnetic induction device; however, it is difficult to surmise which system will generate better temperature distributions in visceral model A, because aspects of this tumor location might prove favorable for both devices. As shown in Figures 4a and 4b, most of the deepseated tumor in visceral rnodel B received less than 10% of the maximum absorbed power from magnetic induction and only 40-50% from the phased array system. Surprisingly, the concentric coil deposited less than 20% of the maximum power in the superficial portions of the tumor in visceral model A, and less than 10% in most of the deep-seated regions (see Figure 3a). The annular phased array applicator produced a nonuniform power deposition pattern in this tumor. Figure 3b shows
that iso-power lines ranging from 20-50% of the maximum passed through the tumor region. Again note that for both visceral body cross-sections the phased array produced greater power depositions in the tumor; however, neither device could deliver more than 50-60% of the maximum deposited power density to the tumor. Both systems generated the maximum power absorption in the superficial portions of the body regardless which of the visceral CT slices were used (compare Figures 3 and 4). For the deep-seated tumor in visceral model B, poor temperature distributions resulted in almost every case when a magnetic induction device delivered the hyperthermia. A fair HEP rating could only be obtained when normal tissue blood flow rates were highly elevated and the tumor remained necrotic (see Table 2). The phased
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Fig. 2. Same as Figure
array system did not fair much better for this tumor site. It did not produce acceptable thermal patterns for basal values of blood perfusion rates. However, for elevated values, 5 out of 15 cases resulted in fair HEP ratings. This again suggests that depositing 40-50% of the maximum power in the tumor will produce significant therapeutic heating only under a limited range of physiological conditions. The HEP ratings for visceral mode1 A were similar for the two devices. Fair thermal profiles were obtainable with a concentric coil system for a wide range of normal tissue blood flow rates as long as the tumor remained necrotic and the blood perfusion rates were higher than their basal values. Increasing the tumor perfusion rate to 2.7 ml/100 gm/min reduced fair ratings to poor in every case but one, again demonstrating the critical role of thermal conduction in the potential efficacy of magnetic induction type devices for delivering hyperthermia.
September 1985. Volume 11, Number 9
1 for Pelvic model B.
The annular phased array applicator was able to produce fair HEP ratings in tumors perfused at 2.7 ml/100 gm/ min in some cases; however, tumors with blood flows of 20 ml/ 100 gm/min were poorly heated with this device as well.
Thoracic models
Most of the tumor site for thoracic mode1 A was deeply embedded in normal tissue whereas the majority of the tumor in thoracic model B was located in the superficial portions of the thorax (see Figures 5 and 6 for anatomical location). Based on our previous reasoning, we would expect the annular phased array system to produce superior HEP ratings in the more deepseated tumor in thoracic model A, and the magnetic induction device to do so in the more superficially located tumor in thoracic model B.
Comparative theoretical performance 0 K. D. PAULSENetal.
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Fig. 3. Absorbed power distribution for Visceral Model A. Contours are normalized to a maximum value of 10 and separated by increments of 1. Bone is shaded with dots and tumor is shaded with lines. (a) Concentric coil; (b) Annular phased array.
Figure 5a, which shows the power deposition produced by magnetic induction in thoracic model A is consistent with our expectations and the results from the previous two body sections. The entire tumor in this case is contained within the 10% maximum power deposition contour. The power delivered to the tumor by the phased array applicator, shown in Figure 5b, is, however, only 20% of the maximum. This is several levels lower than in the other deep-seated tumors (compare Figures 1b, 2b, 4b, and 5b). Even. more surprising is the power deposition in the superficial tumor case. Figure 6a and 6b show the power delivery for the concentric coil system and the phased array device, respectively. For the array, most of the tu.mor region received between 20-40% of the maximum power absorption; however, for the concentric coil most of the tumor region absorbed
less than 30% of the power maximum. A closer examination of the anatomy reveals two factors that may explain why the concentric coil was not more successful in its power delivery to this superficial tumor. First, the induced eddy currents are essentially perpendicular to the fat-tumor interface. In these simulations the tumor was assumed to have a larger complex permittivity (see Table 4); hence, the boundary condition governing the behavior of the perpendicular component of the electric field at the tissue interface requires several times as much power to be deposited on the fat side as compared to the tumor side of the interface.5*18 Second, the body anatomy is such that the intensity of the eddy currents is decreasing as they spread apart because of the bulges in the fat region near the tumor site. After examining the respective power deposition pat-
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September 1985, Volume 11, Number 9
Fig. 4. Same as Figure 3 for Visceral
terns, ‘the HEP ratings show no surprises (see Table 3). Poor thermal profiles resulted in every case for thoracic model A when magnetic induction was used as the heat source. Except for the most highly elevated normal tissue perfusion rate case, where a fair rating was achieved, poor thermal ratings occurred in thoracic model B as well. The annular phased array applicator was able to produce fair or better HEP ratings in 8 out of 10 cases for both the necrotic and low perfused (2.7 ml/100 gm min) tumor in thoracic model A; but it still did not produce a good rating for basal perfusion values in normal tissue. However, as in the other body regions, the ratio of power deposited in the tumor to the power
model B.
absorbed by normal tissue was not great enough to heat therapeutically substantial portions of tumors with blood flows as high as 20 ml/ 100 gm/min. Further, like the concentric coil system, the phased array had difficulty in heating the superficial tumor location in thoracic model B. Fair thermal distributions resulted in just 4 out of 15 cases, and then only under conditions of highly elevated normal tissue perfusion rates. SUMMARY
AND CONCLUSIONS
In this study we generated six finite element models of different tumor sites from CT-scans of actual cancer
Comparative theoretical performance 0 K. D. PAULSENet al.
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Fig. 5. Absorbed power distribution for Thoracic Model A. Contours are normalized to a maximum value of 10 and are separated by increments of 1. Bone is shaded with dots and tumor is shaded with lines. (a) Concentric coil; (b) Annular phased array.
patients. We solved the appropriate electromagnetic boundary value problems for two types of regional hyperthermia systems: magnetic induction devices and annular phased array applicators. We then used this information to solve the heat transfer problem for each of these devices under the same physiological conditions. The results we obtained lead to the following conclusions for the models we examined. 1. The maximum power deposition never appeared in the tumor regardless of which device was used as the heat delivery agent or where the tumor was located. The concentric coil type system delivered less than 20% of
the maximum absorbed power to the major portions of the tumor irrespective of location. The annular phased array applicator delivered more power to deep compared to superficial portions of tumors; however, even major regions of deep-seated tumors only received on the order of 50% of the maximum absorbed power. As a result, limiting temperatures often occurred in regions where it is unlikely that they would be monitored. Therefore, these devices clearly present some risk to the patient unless very careful procedures are followed. 2. The maximum absorbed power for both regional systems occurred near the surface of all body sections. Further, for a given body cross-section, regions of high
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September 1985, Volume 11, Number 9
by concentric coil systems regardless of tumor location. To produce fair temperature distributions magnetic induction devices must rely heavily on thermal conduction and/or highly elevated normal tissue perfusion rates. 5. When considering cases with basal values of blood perfusion rates for normal tissue, only the pelvic tumors received HEP ratings of fair or better. This result raises the question of whether either device can be effective for heating tumors in the thorax or abdomen unless blood perfusion rates are altered by some means, e.g., vasodilators. 6. In general, the only tumors that will receive thermal distributions rated as fair or better must have blood perfusion rates of 2.7 ml/ 100 gm/min or less. This raises the question of how often this situation will occur in the clinic, and emphasizes the necessity for much better information on blood perfusion rates in human tumors. 7. While the annular phased array produces better thermal patterns than the concentric coil, the results herein do not indicate that it will be very effective in most situations either. As a result, further study of systems with capability of amplitude and phase control to each applicator is needed.
Fig. 6. Same as Figure 5 for Thoracic
Model B.
concentrations of deposited power showed a high degree of anatomical correspondence regardless of which device was used. This suggests that the physical anatomy may be as important a factor in causing high concentrations of absorbed power as is the type of device used for heat delivery. 3. As expected, both devices showed increased difficulty in heating tumors as tumor blood flow increased. The percentage of the maximum absorbed power that is delivered to the tumor with these devices is not great enough to heat significant portions of perfused tumors to therapeutic temperatures under a wide range of physiological conditions. 4. In almost every case, annular phased array applicators produced superior HEP ratings to those produced
In closing we acknowledge some of the limitations in our work. Our thermal model does not include the temperature dependency of blood flow and rises in core temperature often found in regional hyperthermia. Implementation of these features in our finite element formulation of the bioheat equation is straightforward; however, the bioheat equation can only be considered a crude approximation of the actual situation, especially when regional effects are of concern. Further, with the lack of good information on these variables during hyperthermia, it is difficult to predict what new information would be gained from such modeling. In the case of the annular array type system, the potential for excessive temperatures to occur in body portions outside the array has been reported. 7,34Clearly, this phenomenon cannot be examined in the two-dimensional, transverse plane analysis performed here. Certainly, the axial dimensions of both of these regional hyperthermia systems are on the order of the cross-sectional ones; hence, one must be concerned with the third dimension. However, it is unlikely that these simulated treatments will perform better when analyzed in 3-D, and we submit the simpler 2-D calculations as a best case analysis. In our twodimensional models we have solved generalized field equations under certain basic assumptions, which we feel are representative of these types of devices. Our conclusions appear to be in general, qualitative agreement with clinical studies recently reported7*8,25; however, detailed comparisons between clinical and numerical results have not been done. How accurately our models represent actual clinical results awaits further investigations.
Comparative theoretical performance 0 K. D. PAULSENet al.
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REFERENCES 1. Bowman, H.F.: Thermodynamics of tissue heating: modeling and measurements for temperature distributions. In Physical Aspects of Hyperthermia, G.H. Nussbaum (Ed.). NY, Amer. Inst. of Physics. pp. 5 1 l-548, 1982. 2. Brezovich, LA., Young, J.H., Atkinson, W.J., Wang, M.T.: Hyperthermia considerations for a conducting cylinder heated by an oscillating electric field applied parallel to the cylinder axis. Med. Phys. 9: 746-748, 1982. 3. Brezovich, LA., Young, J.H., Wang, M.T.: Temperature distributions in hyperthermia by electromagnetic induction: A theoretical model of the thorax. Med. Phys. 10: 57-65, 1983. 4. Burdette, E.C.: Electromagnetic and acoustic properties of tissues. In Physical Aspects of Hyperthermia, G.H. Nussbaum, (Ed.). NY, Amer. Inst. of Physics, pp. 105-150, 1982. 5. Elliott, R.S., Harrison, W.A., Storm, F.K.: Hyperthermia: electromagnetic heating of deep-seated tumors. IEEE Trans. Biomed. Eng. BME-29: 61-64, 1982. 6. Gex-Fabry, M., Landry, J., Marceau, N., Gagne, S.: Prediction of temperature profiles in tumors and surrounding normal tissues during magnetic induction heating. IEEE Trans. Biomed. Engr. BME-30: 271-277, 1983. 7. Gibbs, F.A.: Regional hyperthermia: a clinial appraisal of non-invasive deep-heating methods. Cancer Res. 44(Suppl.): 47653-477OS, 1984. 8. Gibbs, F.A., Sapozink, M.D., Gates, K.S., Stewart, R.J.: Regional hyperthermia with an annular phased array in the experimental treatment of cancer: report of work in progress with a technical emphasis. IEEE Trans. Biomed. Eng. BME31: 115-l 19, 1984. 9. Guy, A.W., Lehmann, J.F., Stonebridge, J.B.: Therapeutic applications of electromagnetic power. Proc. IEEE 62: 55-75, 1974. 10. Hahn, G.M., Kernahan, P., Martinez, A., Pounds, D., Prionas, S., Anderson, T., Justice, G.: Some heat transfer problems associated with heating by ultrasound, microwaves, or radiofrequency. Ann. N. Y. Acad. Sci. 335: 327345, 1980. 11. Halac, S., Roemer, R.13., Cetas, T.C.: Uniform regional heating of the lower trunk: Numerical evaluation of tumor temperature distribution. Int. J. Radiat. Oncol. Biol. Phys. 9: 1833-1890, 1983. 12. Halac, S., Roemer, R.B., Oleson, J.R., Cetas, T.C.: Magnetic induction heating of tissue: numerical evaluation of tumor temperature distributions. Znt. J. Radiat. Oncol. Biol. Phys. 9: 881-891, 1983. 13. Hill, S.C., Christensen, D.A., Durney, C.H.: Power deposition patterns in magnetically induced hyperthermia: a two-dimensional quasistatic numerical analysis. Znt. J. Radiat. Oncol. Biol. Phys. 9: 893-904, 1983. 14. Hill, S.C., Durney, C.H., Christensen, D.A.: Numerical calculations of low-frequency TE fields in arbitrarily shaped inhomogeneous lossy dielectric cylinders. Radio. Sci. 18: 328-336, 1983. 15. Iskander, M.F., Khoshdlel-Milani, 0.: Numerical calculations of the temperature distribution in realistic cross sections of the human body. Int. J. Radiat. Oncol. Biol. Phys. 10: 1907-1912, 1984. 16. Iskander, M.F., Turner, P.F., Dubow, J.B., Kao, J.: Twodimensional technique to calculate the EM power deposition pattern in the human body. J. Microwave Power 17: 175-185, 1982. 17. Jain, R.K.: Bioheat transfer: mathematical models of thermal systems. In Hyperthermia in Cancer Therapy,
18.
19.
20.
2 I.
22.
23.
24.
25.
26.
27.
28.
29.
30.
3 1.
32.
33.
34.
F.K. Storm (Ed.). Boston, MA, G.K. Hall Medical Publishers. 1983, pp. 9-46. Joines, W.T.: Frequency-dependent absorption of electromagnetic energy in biological tissue. IEEE. Trans. Biomed. Eng. BME31: 17-20, 1984. Lynch, D.R., Paulsen, K.D., Strohbehn, J.W.: Finite element solution of Maxwell’s equations for hyperthermia treatment planning. J. Comp. Phys. 58: 246-269, 1985. Oleson, J.R.: Hyperthermia by magnetic induction: I. Physical characteristics of the technique. Int. J. Radiat. Oncol. Biol. Phys. 8: 1747-1756, 1982. Oleson, J.R.: A review of magnetic induction methods for hyperthermia treatment of cancer. IEEE Trans. Biomed. Eng. BME31: 91-97, 1984. Paulsen, K.D., Strohbehn, J.W., Hill, S.C., Lynch, D.R., Kennedy, F.E.: Theoretical temperature profiles for concentric coil induction heating devices in a twodimensional, axi-asymmetric, inhomogeneous patient model. Int. J. Radiat. Oncol. Biol. Phys. 10: 1095-l 107, 1984. Paulsen, K.D., Strohbehn, J.W., Lynch, D.R.: Theoretical temperature distributions produced by an annular phased array type system in CT-based patient models. Radiat. Res. 100: 536-552, 1984. Roemer, R.B., Cetas, T.C., Oleson, J.R., Halac, S., Matloubieh, A.Y.: Comparative evaluation of hyperthermia heating modalities: II. application of the acceptable power range technique. Radiat. Res. 100: 473-486, 1984. Sapozink, M.D., Gibbs, F.A., Gates, K.S., Stewart, J.R.: Regional hyperthermia in the treatment of clinically advanced, deep-seated malignancy. Results of a pilot study employing an annular array applicator. Int. J. Radiat. Oncol. Biol. Phys. 10: 775-786, 1984. Schawn, H.P.: Interaction of microwave and radio frequency radiation with biological systems. IEEE Trans. Microwave Theory Tech. M’IT-19: 146-152, 1971. Schawn, H.P., Foster, K.R.: RF-field interactions with biological systems: electrical properties and biophysical mechanisms. Proc. IEEE 68: 104-l 13, 1980. Storm, F.K., Elliott, R.S., Harrison, W.H., Morton, D.L.: CLinical RF hyperthermia by magnetic-loop induction: A new approach to human cancer therapy. IEEE Trans. Microwave Theory Tech. M1T-30: 1149-I 158, 1982. Storm, F.K., Harrison, W.H., Elliott, R.S., Kaiser, L.R., Silberman, A.W., Morton, D.L.: Clinical radiofrequency hyperthermia by magnetic-loop induction. J. Microwave Power 16: 179-184, 1981. Storm, F.K., Harrison, W.H., Elliott, R.S., Silberman, A.W., Morton, D.L.: Thermal distribution of magneticloop induction hyperthermia in phantoms and animals: Effect of living state and velocity of heating. Znt. J. Radiat. Oncol. Biol. Phys. 8: 865-871, 1982. Strohbehn, J.W.: Theoretical temperature distributions for solenoidal-type hyperthermia systems. Med. Phys. 9: 673682, 1982. Strohbehn, J.W., Roemer, R.B.: A survey of computer simulations of hyperthermia treatments. IEEE Trans. Biomed. Engr. BME31: 136-149, 1984. Turner, P.F.: Deep heating of cylindrical or elliptical tissue masses. NCZ Monograph 61, U.S. Health and Human Services, pp. 493-495; presented at the 3rd Int. Symp. Cancer Therapy by Hyperthermia, Drugs, and Radiation, Fort Collins, CO, June 22-26, 1980. Turner, P.F.: Regional hyperthermia with an annular phased array. IEEE Trans. Biomed. Engr. BME31: 106114, 1984.
I I, pp.1659-1671 Copyright
0360-3016/85 $03.00 + .OO 0 1985 Pergamon Press Ltd.
??Original Contribution
COMPARATIVE THEORETICAL PERFORMANCE FOR TWO TYPES OF REGIONAL HYPERTHERMIA SYSTEMS
KEITH D. PAULSEN,M.S.,JOHN W. STROHBEHN, PH.D.AND DANIEL R. LYNCH, PH.D. Thayer School of Engineering, Dartmouth
College, Hanover, NH 03755
Regional hyperthermia systems have drawn attention because of their potential for depositing power noninvasively in deep-seated tumors. Two such systems that have received clinical attention because of their ability to deposit significant amounts of power in tissue are magnetic induction devices and annular phased array applicators. In this paper, theoretical calculations for the specific absorption rate (SAR) and the resulting temperature distributions for these systems are compared. The finite element method is used in the formulation of both the electromagnetic and thermal boundary value problems. Six detailed patient models based on CT-scan data from the pelvic, viscera& and thoracic regions are generated to simulate a variety of tumor locations. In general, the annular phased array deposited more power within the tumor and produced better temperature distributions than the magnetic induction device. However, the ratio of the maximum power absorbed by the tumor to the maximum power absorbed in normal tissue does not appear to be high enough for either device to heat significant portions of perfused tumors to therapeutic temperatures under a wide range of physiological conditions. The results contained herein slhould aid the physician in comparative treatment planning with existing regional hyperthermia systems. Comparative thermal dosimetry, Regional hyperthermia.
been published, and the analysis that has been done has generally been carried out on idealized patient configurations. 2,3,6S1 1-14,22,24,31 Generally, reported results suggest difficulty in deep-seated heating in the torso, but satisfactory temperature rises in superficial tumors when magnetic induction devices are used.12,20-22,31 Annular phased array applicators have been reported to produce a nearly uniform electric field across the body, and have been modeled as such, suggesting that they should heat deep centrally located tumors the best.“3’5*16.33*34 The question of which of these two types of regional hyperthermia systems will produce the superior thermal dosimetry given the same tumor location heated under the same physiological conditions has been addressed by Roemer et. a1.24In this study, idealized power deposition and patient geometry were used with a wide range of physiological and anatomical variables. Quantitative results from these simulations agree with the qualitative statements made above for each type of device. These studies have been useful in setting some general guidelines for evaluating the potential efficacy of magnetic induction devices and annular phased array applicators. In this paper we compare two-dimensional theoretical
INTRODUCIION
the resurgent interest in hyperthermia as a cancer therapy, a number of different hyperthermia systems have emerged in the clinic. External devices that produce regional hyperthermia are particularly popular because of their noninvasive approach to heating deep-seated tumors. Two such systems that have been proposed as capable of depositing significant amounts of power in tissue are magnetic induction devices and annular phased array applicators.5,28-30,33,34 In the case of magnetic induction, tissue is heated by power deposited from eddy currents induced by magnetic fields. In one configuration these magnetic fields are generated inside the patient by a concentric conducting coil which wraps around the body section to be heated. Annular phased array devices are also large external applicators that fit around the diseased body section. Power is deposited in tissue by electric fields produced from concentric rings of inphase apertures. Although these two types of hyperthermia systems have received much clinical attention, only a modest amount of analysis on their theoretical performance has With
Presented in part at The: 4th International Symposium on Hyperthermic Oncology, Aarhus, Denmark, July 2-6, 1984. Supported in part by NIIH/NCI Grants CA23594, and NSF Grant EC%0258 18.
Reprint requests to: John W. Strohbehn. Accepted for publication 3 April 1985.
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1660
calculations for the specific absorption rate (SAR) and the resulting steady-state temperature distributions produced by magnetic induction devices and annular phased array applicators in anatomical models based on CT scans of typical cancer patients. A number of detailed patient models from the pelvic, visceral, and thoracic regions were generated to simulate a variety of tumor locations and surrounding normal tissues that are representative of clinical situations. The methods and results contained herein are useful for both comparative thermal dosimetry, where the objective is to compare different types of hyperthermia systems for their ability to heat typical tumors, and for prospective thermal dosimetry, where the goal is to plan the treatment for a specific patient.32 METHODS
AND MATERIALS
Predicting temperature profiles is a two-fold problem; first, to predict the power deposition in tissues; and second, to predict the resultant temperatures. The second problem is common to all hyperthermia devices and has been formulated as a heat diffusion equation with a first order decay term that represents the crucial role of blood circulation in temperature regulation. We used a standard form of the bioheat transfer equation’.” whose finite element formulation we have previously employed.22,23 The first problem, the heat source calculation, tends to be device-specific. Our finite element formulation for this problem is explained in detail in Ref. 19, where we demonstrated its ability to conserve energy exactly, to faithfully reproduce the analytic dispersion relationship, and to accurately predict analytic solutions under representative conditions; hence, only the governing equations for each device will be reviewed here. Assuming a time variation of the form exp(-iwt), Maxwell’s curl equations in differential form become:
September 1985, Volume I I, Number 9
where k is the complex wavenumber: k2 = o*pP = w2pc + iups.
For magnetic induction devices, it is assumed that the magnetic field is directed down the long axis of the patient; thus, the electric field is confined to the transverse or CT-scan plane. In this plane, & in eqn (2) is a vector quantity in which continuity in its parallel component and discontinuity in its perpendicular component must exist at all tissue interfaces where the electrical properties change abruptly. We have successfully solved eqn (2) on finite elements incorporating the appropriate boundary conditions at each tissue interface [ 191; however, because of the large number of different tissue regions in a typical CT-scan, we also adopted a second numerically simpler but less elegant approach: calculate @ via finite elements; then differentiate to find &. Because CL is effectively constant in tissue, @ is continuous across all tissue interfaces-hence the added numerical simplicity. We can isolate @ in the same fashion as & above by combining eqns (la) and (1 b) giving:
px($yxy)-H-0
(3)
Because the magnetic field is assumed unidirectional and perpendicular to the plane of analysis (@ = H,(x, y)~), eqn (3) reduces to a scalar equation in Hz:
8 can be isolated by taking the curl of eqn (la) and substituting (lb) which results in (assuming CLconstant)
At the device boundary, Hz = .I,, the amplitude of the current per unit length in the coil, which we assumed known and constant. Operationally, we solve eqn (3a) for @ on finite elements, then take the curl of this solution to obtain &, the desired quantity, via eqn (lb). The drawback in this simpler approach is the loss of accuracy in & as a result of the necessary differentiation of @. An additional consequence is that & will be discontinuous across all element boundaries on the simple elements we employ. Nonetheless, we have found essentially the same accuracy between the two approaches when compared to analytic solutions under representative conditions.” Further, we have found that virtually identical temperature profiles were produced in a four region, CT-based patient model regardless of which method was used to compute the SAR distribution. For annular phased array applicators, the electric field is assumed to be polarized down the long axis of the patient and we solve directly for E,. The double curl in eqn (2) reduces to V2 and the electromagnetic problem is one of solving a scalar Helmholtz equation in Ez:
V x (0 x @ - k2& = 0
V’E, + k2Ez = 0
0 X & = iwp@
(la)
0 X fl=
(lb)
-it.&&
&
is the time-invariant complex amplitude electric field E-1: is the time-invariant complex amplitude magnetic field is the magnetic permeability p t* = t + is/o is the complex permittivity u is the electrical conductivity is the permittivity t frequency w E tr
of the of the
i
(2)
(4)
1661
Comparative theoretical performance 0 K. D. PAULSEN etal.
At the device boundary, we assume that the electric field distribution is known and can be represented across each aperture by a half-wavelength cosine function: E, = E. cos (ra/L)
(5)
where L a
the length of a segment is the distance from .the center of a segment. is
Because of the unidirectional nature of & in this problem, E, is continuous across tissue interfaces; hence the finite element formulation for eqn (4) becomes the analog of that for eqn (3a).19
Table Perfusion Fat
Muscle
Bone
Both of these heat source problems and their subsequent heat diffusion problems were solved on six finite element models that were generated from CT-scans of actual cancer patients. The finite element discretization of each patient’s anatomy has been published previously. 23Two-dimensional power deposition patterns were calculated for each of the six body cross-sections for each of the two types of regional hyperthermia systems. The concentric coil device was assumed to operate at 13 MHz, whereas the annular phased array applicator was assumed to operate at 100 MHz with all apertures driven inphase. The numerically calculated SAR distributions were then used as the source input for the
1. HEP rating
rates Rectum
Tumor
cc
Relative
power level
AA
cc
AA
1 = 245 W/m 1.0 1.0
1 = 266 W/m 1.5 1.6
Pelvic model A .03*q * *
2.1
0
1.8-f
0 2.7 20
P P P
G P P
lot
0 2.1 20
P P P
G P P
2.3 2.3 2.3
3.3 3.3 3.3
0 2.7 20
P P P
F P P
3.6 3.6 3.6
4.7 4.7 4.7
:
5**t *. *. :
15
5
10*-t *. *, :
21
10
15*,t *. *, :
54
15
W
0 2.7 20
P P P
F P P
4.1 4.1 4.1
6.2 6.2 6.2
30* *, *, :
65
30
45
0t 2.1 20
P P P
G F P
7.8 7.8 7.8
9.5 11.3 11.3
t
Pelvic model B 2.7*q *, *. :
0
1.8
0 2.1 20
F P P
G G P
5* * *
15*q *, *, :
5
10
0 2.1 20
P P P
G G P
3.1 3.1 3.1
2.8 6.0 7.8
lo* * *, t
27* *. t *
10
18
ot 2.1 20
P P P
G G P
5.0 5.0 5.0
3.8 8.0 10.4
15* * *.
54
15
2?5t 20
P P P
G G P
7.1 7.1 7.1
4.2 10.0 12.9
0t 2.7t 20
F P P
G G F
11.1 11.1 11.1
4.3 10.1 19.5
.03
36
t
30* * *, t
65
30
45
CC = Concentric coil; AA = Annular array; G = Good, F = Fair; P = Poor. *-t Indicate tissue reaching limiting temperatures for the concentric coil and the annular on two tissues usually means the limiting temperature was at an interface. All perfusion rates given in ml/l00 gm/min.
1 = 528 W/m 1.0 1.0
1 = 240 W/m 2.4 2.5
phased array cases, respectively.
A symbol
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September 1985, Volume 11, Number 9
Radiation Oncology 0 Biology 0 Physics
bioheat transfer equation to calculate the temperature profiles. As a thermal boundary condition, we assumed the patient was surrounded by water bolus, which was maintained at 20°C. We adopted the same protocol we used in a previous work23 for scaling the input power, varying normal and malignant tissue blood flow rates, and ranking the resulting temperature distributions. Only the essential points of our procedure will be reviewed. The input power was increased until either: 1. Tumor temperature > 60°C 2. Fat, muscle, or bone temperature 3. Visceral organs > 42°C
The required input power for each case was computed and reported, but no simulation was restricted on the basis of this value alone. It is difficult to relate our calculated values to any practical power requirements since our model is two-dimensional and our calculated values represent power absorbed by the body. Any physical device will have losses from reflected power and power radiated but not absorbed by the patient. We leave extrapolation of any practical power requirements from our two-dimensional data to those more familiar with the efficiency of existing physical systems. For normal tissue we first assumed basal blood perfusion values typical for the various tissue types (see the first case in Tables 1, 2, and 3). We then increased these
> 44°C
Table 2.
Perfusion Fat
Muscle
Bone
Viscera
Liver
HEP rating
rates
Kidney
Spleen
Aorta
Stomach
Relative
power level
Tumor
CC
AA
cc
AA
1 = 376 W/m 1.5 1.6
Visceral model A 2.F1_ *, t *, i
.03
15* * *,t
5
10
15
27
54
t 30
65 t
* *, * * * *
o*q * *.t
27
420
0 2.7 20
P P P
P P P
1 = 305 W/m 1.0 1.0
5*-t * *
27t t
420
0 2.7 20
F P P
F P P
2.7 2.8 3.8
2.1 3.2 4.4
10*,t *,
54
420
0 2.7 20
F P P
F F P
3.8 4.0 4.0
3.3 4.9 6.7
70
420
0 2.7 20
F P P
F F P
4.8 6.0 6.0
3.5 6.2 8.9
100
420
0t 2.1 20
F P P
F F P
6.2 8.0 8.0
3.8 7.8 14.8
1 = 340 W/m 1.4 1.4
*
t
t
15*-f *,
*
t
30* *, t *
Visceral model B 2.7* * *
0* * *
57
420
60
84
40
0 2.7 20
P P P
P P P
1 = 561 W/m 1.0 1.0
5*-/ *. *, :
15
5
57
420
60
84
40
0 2.1 20
P P P
F F P
2.5 2.8 2.8
2.1 3.6 7.4
1O*,f
27
10
57
420
60
84
40
0 2.7 20
P P P
F P P
3.6 4.3 4.3
2.4 4.0 10.2
15
57
420
60
84
40
0 2.7 20
P P P
P P P
4.4 6.3 6.6
2.6 4.2 12.6
30
57
420
60
84
40
0 2.7 20
F P P
P F F
6.4 8.4 8.4
3.2 5.0 15.0
.03t :
: 15*-t *, t *
54
30*q *, t *
65
* * * *
* *
Symbols: same as Table 1. All perfusion rates given in ml/100
gm/min.
Comparative theoretical performance 0 K. D. PAULSENet al.
1663
Table 3. Perfusion Fat
Bane
Muscle
Lung
Heart
Tumor Thoracic
.03
5
2.7*%1 *, *. ;
0* *. *,
15*q *, *, :
10* * *
27t
15* * *
34.t
30* * *
65t
:
:
:
*,
AA
cc
AA
model A
0 2.7 20
P P P
P P P
L = 678 W/m 1.0 1.0
1 = 768 W/m 1.2 1.3
5* * *
433
84
0 2.7 20
P P P
F F P
2.4 2.4 2.4
1.8 2.6 3.0
10* * *
433
84
0 2.7 20
P P P
F F P
3.1 3.1 3.1
2.3 3.2 4.0
15* * *
433
84
0 2.7 20
P P P
F F P
3.6 3.6 3.6
5.1 4.3 6.1
30* * *
433
84
0 2.7 20
P P P
G F P
5.3 5.3 5.3
3.5 4.7 7.4
5
model B
0
433
84
0 2.7 20
P P P
P P P
1 = 660 W/m 1.0 1.0
1 = 746 W/m 1.0 1.0
51
433
84
0 2.7 20
P P P
P P P
1.6 1.7 1.8
1.4 1.8 2.1
10
433
84
0 2.7 20
P P P
P P P
1.8 2.1 2.4
1.8 2.4 3.1
: 15* * *
:
CC
84
2.7t
5:;t
power level
433
Thoracic .03* * *
Relative
HEP rating
rates
1o*q *, *, :
27
15*-t *, *, :
54
15
433
84
0 2.7 20
P P P
F F P
2.0 2.4 2.9
2.4 3.0 4.2
30*q *, *, :
65
30
433
84
0 2.7 20
F P P
F F P
2.5 3.0 4.7
3.1 3.9 6.5
t
i
Symbols: same as Table L and 2. All perfusion rates given in ml/100
perfusion
values
to
see
whether
gm/min.
higher
values
would
In some of these cases the assumed values were: well outside the normal physiological range, but the objective was to see what blood perfusion values might result in good temperature distributions. For each set of normal tissue blood flow rates, three different tumor perfusion rates were used: result
in better
thermal
1. Necrotic 2. Low 3. High
patterns.
0 ml/100 gm/min 2.7 ml/100 gm/min 20 ml/ 100 gm/min
As a criterion for comparing the temperature distributions produced by each device, the percent of the total tumor area to reach 43°C or greater was computed
and given a hyperthermia equipment performance (HEP) rating as: 1. 2. 3. 4.
Excellent Good Fair Poor
therapeutic therapeutic therapeutic therapeutic
region region region region
= 100% = 7599% = 50-74% < 50%
All electrical and thermal properties used in these calculations are given in Table 4. RESULTS Figures 1 through 6 show a comparison of the power deposition patterns produced by concentric coil applicators and annular phased array devices for each of the
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Radiation Oncology 0 Biology 0 Physics
September 1985, Volume 11, Number 9
Table 4. Electrical
conductivity
Tissue
13 MHz
100 MHz
13 MHz
100 MHz
Thermal conductivity (W/m/‘C)
Aorta Bone Fat Heart Kidney Liver Lung Muscle Rectum Spleen Stomach Tumor Viscera Water
1.oo .20 .20 .60 .80 .45 .I1 .60 .35 .51 .41 .60 .41 .oo
.93 .02 .22 .93 1.oo .60 .35 .89 .61 .78 .51 .89 .57 .oo
180 28 28 140 330 150 42 122 106 310 80 122 80 70
73.5 10 10.5 89 89.5 77.5 40 72 52 100 80 72 80 78
.527 .436 .210 .527 .547 ,508 .478 .642 .498 .515 ,527 .642 .550 ,603
Relative permittivity
(W/v2/m)
Specific heat X density (W - sec/m3/“C) (X106) 3.72 2.25 2.12 3.72 3.96 3.81 1.68 3.72 3.35 3.81 3.81 3.72 3.81 4.31
Magnetic permeability of all tissues was taken as equal to that of free space. Other values were assembled from’,4,9-‘4,‘6.26.27.
six body cross-sections. The contour lines in these figures are normalized such that the maximum power deposition is 10. The discontinuity in power deposition contours at the tissue interfaces is because the absorbed power is directly proportional to the electrical conductivity, which is discontinuous at these interfaces. Tables 1, 2, and 3 contain a summary for both devices of the HEP ranking, the total power consumption (in watts/meter), and the overheated normal tissues for each different blood flow case for the different body crosssections investigated. A power value of unity was assigned to the first case in each table and the power values given for all subsequent cases are relative to this quantity.
DISCUSSION
Pelvic models Because both pelvic models have deep centrally located tumors (see Figures 1 and 2 for anatomical location), we would expect a magnetic induction device to produce minimal power deposition in the tumor, and a phased array system to produce significant power deposition in the tumor. Almost the entire tumor area is within the 10% iso-power contour in Figures la and 2a, which show power deposition patterns for a concentric coil device. Figures lb and 2b show that a significantly higher percentage of the maximum power deposition is produced in the tumor by an annular phased array (>40% for pelvic model A, >60% for pelvic model B). This applicator, in fact, produced a higher percentage of power deposition in the tumor in pelvic model B than in any other tumor model whether it or the concentric coil was used. It is interesting to note, however, that neither device produced the maximum power absorption in the tumor in either pelvic model, but that
both systems deposited the maximum power in normal tissue near the muscle-fat interface, which was located in the peripheral portions of these body cross-sections. As would be expected from knowledge of the power deposition, almost every HEP rating (see Table 1) for the concentric coil was poor (therapeutic region < 50%). However, fair temperature distributions (therapeutic region 50-74%) resulted in pelvic model B when basal physiological values were used for the normal tissue blood flow rates, and also for very high normal tissue blood perfusion rates, as long as the tumor was assumed necrotic. This further indicates that this device must heavily rely on thermal conductive effects and/or extensive cooling of normal tissue via highly elevated blood flow rates to produce therapeutic heating in deep-seated tumors. The annular phased array produced good thermal profiles (therapeutic region 75-99%) in almost every case for both pelvic models as long as the tumor remained necrotic. Increasing the tumor perfusion rate to 2.7 ml/100 gm/min reduced the HEP ratings to poor in most cases for pelvic model A, and further increases in tumor blood flow to 20 ml/100 gm/min reduced the HEP ratings to poor in pelvic model B. This suggests that delivering 40-50% of the maximum power deposition to the tumor, as in pelvic model A, may not be enough to heat satisfactory portions of tumors with low blood flow, and more than 60-70% maximum power deposition may be required to heat tumors with blood perfusion rates on the order of 20 ml/100 gm/min. Visceral models Visceral model A has a large tumor, extending from superficial to deep-seated, whereas the tumor site in visceral model B is entirely deep-seated (see Figures 3 and 4 for anatomical sites). A priori we would expect
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Fig. 1. Absorbed power distribution for Pelvic model A. Contours are normalized to a maximum value of 10 and are separated by increments of 1. Bone is shaded with dots and tumor is shaded with lines. (a) Concentric coil; (b) Annular phased array.
the phased array to deposit more power and subsequently to produce better HEP ratings in visceral model B than the magnetic induction device; however, it is difficult to surmise which system will generate better temperature distributions in visceral model A, because aspects of this tumor location might prove favorable for both devices. As shown in Figures 4a and 4b, most of the deepseated tumor in visceral rnodel B received less than 10% of the maximum absorbed power from magnetic induction and only 40-50% from the phased array system. Surprisingly, the concentric coil deposited less than 20% of the maximum power in the superficial portions of the tumor in visceral model A, and less than 10% in most of the deep-seated regions (see Figure 3a). The annular phased array applicator produced a nonuniform power deposition pattern in this tumor. Figure 3b shows
that iso-power lines ranging from 20-50% of the maximum passed through the tumor region. Again note that for both visceral body cross-sections the phased array produced greater power depositions in the tumor; however, neither device could deliver more than 50-60% of the maximum deposited power density to the tumor. Both systems generated the maximum power absorption in the superficial portions of the body regardless which of the visceral CT slices were used (compare Figures 3 and 4). For the deep-seated tumor in visceral model B, poor temperature distributions resulted in almost every case when a magnetic induction device delivered the hyperthermia. A fair HEP rating could only be obtained when normal tissue blood flow rates were highly elevated and the tumor remained necrotic (see Table 2). The phased
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Fig. 2. Same as Figure
array system did not fair much better for this tumor site. It did not produce acceptable thermal patterns for basal values of blood perfusion rates. However, for elevated values, 5 out of 15 cases resulted in fair HEP ratings. This again suggests that depositing 40-50% of the maximum power in the tumor will produce significant therapeutic heating only under a limited range of physiological conditions. The HEP ratings for visceral mode1 A were similar for the two devices. Fair thermal profiles were obtainable with a concentric coil system for a wide range of normal tissue blood flow rates as long as the tumor remained necrotic and the blood perfusion rates were higher than their basal values. Increasing the tumor perfusion rate to 2.7 ml/100 gm/min reduced fair ratings to poor in every case but one, again demonstrating the critical role of thermal conduction in the potential efficacy of magnetic induction type devices for delivering hyperthermia.
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1 for Pelvic model B.
The annular phased array applicator was able to produce fair HEP ratings in tumors perfused at 2.7 ml/100 gm/ min in some cases; however, tumors with blood flows of 20 ml/ 100 gm/min were poorly heated with this device as well.
Thoracic models
Most of the tumor site for thoracic mode1 A was deeply embedded in normal tissue whereas the majority of the tumor in thoracic model B was located in the superficial portions of the thorax (see Figures 5 and 6 for anatomical location). Based on our previous reasoning, we would expect the annular phased array system to produce superior HEP ratings in the more deepseated tumor in thoracic model A, and the magnetic induction device to do so in the more superficially located tumor in thoracic model B.
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Fig. 3. Absorbed power distribution for Visceral Model A. Contours are normalized to a maximum value of 10 and separated by increments of 1. Bone is shaded with dots and tumor is shaded with lines. (a) Concentric coil; (b) Annular phased array.
Figure 5a, which shows the power deposition produced by magnetic induction in thoracic model A is consistent with our expectations and the results from the previous two body sections. The entire tumor in this case is contained within the 10% maximum power deposition contour. The power delivered to the tumor by the phased array applicator, shown in Figure 5b, is, however, only 20% of the maximum. This is several levels lower than in the other deep-seated tumors (compare Figures 1b, 2b, 4b, and 5b). Even. more surprising is the power deposition in the superficial tumor case. Figure 6a and 6b show the power delivery for the concentric coil system and the phased array device, respectively. For the array, most of the tu.mor region received between 20-40% of the maximum power absorption; however, for the concentric coil most of the tumor region absorbed
less than 30% of the power maximum. A closer examination of the anatomy reveals two factors that may explain why the concentric coil was not more successful in its power delivery to this superficial tumor. First, the induced eddy currents are essentially perpendicular to the fat-tumor interface. In these simulations the tumor was assumed to have a larger complex permittivity (see Table 4); hence, the boundary condition governing the behavior of the perpendicular component of the electric field at the tissue interface requires several times as much power to be deposited on the fat side as compared to the tumor side of the interface.5*18 Second, the body anatomy is such that the intensity of the eddy currents is decreasing as they spread apart because of the bulges in the fat region near the tumor site. After examining the respective power deposition pat-
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Fig. 4. Same as Figure 3 for Visceral
terns, ‘the HEP ratings show no surprises (see Table 3). Poor thermal profiles resulted in every case for thoracic model A when magnetic induction was used as the heat source. Except for the most highly elevated normal tissue perfusion rate case, where a fair rating was achieved, poor thermal ratings occurred in thoracic model B as well. The annular phased array applicator was able to produce fair or better HEP ratings in 8 out of 10 cases for both the necrotic and low perfused (2.7 ml/100 gm min) tumor in thoracic model A; but it still did not produce a good rating for basal perfusion values in normal tissue. However, as in the other body regions, the ratio of power deposited in the tumor to the power
model B.
absorbed by normal tissue was not great enough to heat therapeutically substantial portions of tumors with blood flows as high as 20 ml/ 100 gm/min. Further, like the concentric coil system, the phased array had difficulty in heating the superficial tumor location in thoracic model B. Fair thermal distributions resulted in just 4 out of 15 cases, and then only under conditions of highly elevated normal tissue perfusion rates. SUMMARY
AND CONCLUSIONS
In this study we generated six finite element models of different tumor sites from CT-scans of actual cancer
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Fig. 5. Absorbed power distribution for Thoracic Model A. Contours are normalized to a maximum value of 10 and are separated by increments of 1. Bone is shaded with dots and tumor is shaded with lines. (a) Concentric coil; (b) Annular phased array.
patients. We solved the appropriate electromagnetic boundary value problems for two types of regional hyperthermia systems: magnetic induction devices and annular phased array applicators. We then used this information to solve the heat transfer problem for each of these devices under the same physiological conditions. The results we obtained lead to the following conclusions for the models we examined. 1. The maximum power deposition never appeared in the tumor regardless of which device was used as the heat delivery agent or where the tumor was located. The concentric coil type system delivered less than 20% of
the maximum absorbed power to the major portions of the tumor irrespective of location. The annular phased array applicator delivered more power to deep compared to superficial portions of tumors; however, even major regions of deep-seated tumors only received on the order of 50% of the maximum absorbed power. As a result, limiting temperatures often occurred in regions where it is unlikely that they would be monitored. Therefore, these devices clearly present some risk to the patient unless very careful procedures are followed. 2. The maximum absorbed power for both regional systems occurred near the surface of all body sections. Further, for a given body cross-section, regions of high
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by concentric coil systems regardless of tumor location. To produce fair temperature distributions magnetic induction devices must rely heavily on thermal conduction and/or highly elevated normal tissue perfusion rates. 5. When considering cases with basal values of blood perfusion rates for normal tissue, only the pelvic tumors received HEP ratings of fair or better. This result raises the question of whether either device can be effective for heating tumors in the thorax or abdomen unless blood perfusion rates are altered by some means, e.g., vasodilators. 6. In general, the only tumors that will receive thermal distributions rated as fair or better must have blood perfusion rates of 2.7 ml/ 100 gm/min or less. This raises the question of how often this situation will occur in the clinic, and emphasizes the necessity for much better information on blood perfusion rates in human tumors. 7. While the annular phased array produces better thermal patterns than the concentric coil, the results herein do not indicate that it will be very effective in most situations either. As a result, further study of systems with capability of amplitude and phase control to each applicator is needed.
Fig. 6. Same as Figure 5 for Thoracic
Model B.
concentrations of deposited power showed a high degree of anatomical correspondence regardless of which device was used. This suggests that the physical anatomy may be as important a factor in causing high concentrations of absorbed power as is the type of device used for heat delivery. 3. As expected, both devices showed increased difficulty in heating tumors as tumor blood flow increased. The percentage of the maximum absorbed power that is delivered to the tumor with these devices is not great enough to heat significant portions of perfused tumors to therapeutic temperatures under a wide range of physiological conditions. 4. In almost every case, annular phased array applicators produced superior HEP ratings to those produced
In closing we acknowledge some of the limitations in our work. Our thermal model does not include the temperature dependency of blood flow and rises in core temperature often found in regional hyperthermia. Implementation of these features in our finite element formulation of the bioheat equation is straightforward; however, the bioheat equation can only be considered a crude approximation of the actual situation, especially when regional effects are of concern. Further, with the lack of good information on these variables during hyperthermia, it is difficult to predict what new information would be gained from such modeling. In the case of the annular array type system, the potential for excessive temperatures to occur in body portions outside the array has been reported. 7,34Clearly, this phenomenon cannot be examined in the two-dimensional, transverse plane analysis performed here. Certainly, the axial dimensions of both of these regional hyperthermia systems are on the order of the cross-sectional ones; hence, one must be concerned with the third dimension. However, it is unlikely that these simulated treatments will perform better when analyzed in 3-D, and we submit the simpler 2-D calculations as a best case analysis. In our twodimensional models we have solved generalized field equations under certain basic assumptions, which we feel are representative of these types of devices. Our conclusions appear to be in general, qualitative agreement with clinical studies recently reported7*8,25; however, detailed comparisons between clinical and numerical results have not been done. How accurately our models represent actual clinical results awaits further investigations.
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