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To optimize the efficacy of bioheat transfer in capacitive hyperthermia: A physical perspective
Journal of Thermal Biology 38 (2013) 272–279
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To optimize the efficacy of bioheat transfer in capacitive hyperthermia: A physical perspective Muhammad Jamil, E.Y.K. Ng n School of Mechanical and Aerospace Engineering, College of Engineering, Nanyang Technological University, 50 Nanyang Avenue 639798, Singapore
art ic l e i nf o
a b s t r a c t
Article history: Received 15 September 2012 Accepted 20 March 2013 Available online 29 March 2013
This paper presents the capacitive hyperthermia from physical perspective focusing on the geometric dimensions as parameters. For this purpose six parameters having three levels each, including two tunable parameters i.e. applied voltage, frequency together with four geometric parameters i.e. size of the tumor, location of the tumor, electrode size and relative position of the electrodes w.r.t tumor were considered for analysis. Taguchi based design of experiments approach was used for the aforementioned six parameters. Using Taguchi's standard L27 orthogonal array, the required results could be obtained employing least number of experiments. For this study temperature was taken as the quality characteristic to be optimized. Furthermore, analysis of variance (ANOVA) was performed to quantify the effect of each parameter on the response variable and results were presented. To deal with the extent of thermal damage to the healthy tissue and tumor, the fraction of tissue experiencing thermal damage was calculated. For this purpose two indices namely treatment index and damage index were formulated. Finally it was concluded that maximum achieved temperature alone does not depict the effectiveness of the treatment. Rather, the combination of the maximum achieved temperature and accompanied thermal damage to the surrounding healthy tissue which should be considered. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Pennes bioheat equation Treatment objective Treatment index Damage index Thermal treatment planning Taguchi orthogonal arrays
1. Introduction Presently, cancer remains one of the deadly diseases in the world. There are many treatments that are being used to treat cancer that include chemotherapy, radiation therapy, high intensity focussed ultrasound (HIFU), laser ablation, electroporation and surgery (Dewey et al., 1977; Gomonov and Efanov, 2008; Lanzafame, 1995; Neukam and Stelzle, 2010; Rebillard et al., 2003; Saniei, 2009). The aim of a treatment is to inflict lethal damage to the cancer cell while shading the normal cells from the harmful effects. Hyperthermia in cancer treatment is a therapeutic procedure in which the temperature of the biological tissue is raised above 42 1C for certain duration. Biological cells are unable to tolerate such elevated temperatures and the sub-cellular structures that constitute the cell disintegrate and start to shut down. Such elevated temperature hinders the core cell functions imperative for cell survival. Sustained heating at hyperthermic temperatures causes protein denaturation or apoptosis which ultimately leads to cell death. Thermal therapies are the therapeutic modalities which solely utilize heat as the mechanism to cause lethal damage to the tissues. Thermal therapies have been developed for cancer treatment which harness the proven fact that increasing the temperature of the cell above a threshold value causes a cell to
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die (Field and Morris, 1983; Habash et al., 2007; Henriques and Moritz, 1947). Thermal therapy has fewer side effects and is noninvasive in nature which makes it an obvious contender for selection from the large pool of treatments available. Capacitive hyperthermia is a genre of thermal therapy in which heating is attained by applying electric potential across the electrodes. In therapies like HIFU and laser ablation, the energy can be focussed to a particular area with the help of transducers or lenses. But these therapies suffer from focussing issues due to the presence of bones; air filled viscera and large scattering caused by the hydrated environment. In radiofrequency ablation the energy is delivered at the target site using needle type electrodes. Energy is delivered at high frequencies and can result in charring and carbonization which limits the size of the thermal lesion. In microwave ablation an even higher frequency is used and radiative antennas deliver energy to the target site. Owing to high frequencies used, radiofrequency and microwave ablation suffer from limited depth of penetration (Douglas A. Christensen and Durney, 2009). Capacitive hyperthermia relies mainly on the heterogeneity of electrical properties and thermal sensitivity of tumor which can be employed to ones advantage for preferential treatment of tumor. In capacitive hyperthermia lower frequencies are used which also means that higher depth of penetration could be achieved. Simple operation and adjustable position of electrodes favors the heating for various tissues at different angles and sites. Moreover, with different position and customization of electrodes, regional deep heating patterns can be achieved. It can also be used
M. Jamil, E.Y.K. Ng / Journal of Thermal Biology 38 (2013) 272–279
Nomenclature A c cb E ΔE F f hw k N n P Q Q met Qr R T T0 Ta Tw U
Frequency factor (1/s) Specific heat [J/(kg K)] Specific heat of blood [J/(kg K)] Electric field intensity (V/m) Activation energy of tissue (J/mol) Fisher statistic Frequency (Hz) Convection coefficient between tissue and water [W/(m2 K)] Thermal conductivity [W/(m K)] Number of parameter levels Number of parameters Probability value Volumetric heat generation rate (W/m3) Metabolic heat generation rate (W/m3) Spatial heat source (W/m3) Universal gas constant [J/(mol K)] Temperature (K) Body core temperature (K) Arterial blood temperature (K) Temperature of the cooling water (K) Electrode potential (V)
Greek symbols ε
ε0 εr ρ ρb s φ ω ωb Ω
273
Permittivity of the free space (F/m) Relative permittivity of the material Density (kg/m3) Density of blood (kg/m3) Electrical conductivity of the material (S/m) Electric scalar potential (V) Angular frequency (rad/s) Blood perfusion rate (1/s) Numerical domain
Subscripts 1 2 a b met w
Normal tissue domain Tumor domain Artery Blood Metabolic heat Water
Abbreviations ANOVA DF MNE SS Adj MS
Analysis of Variance Degrees of Freedom Minimum Number of Experimental combinations Sum of Squares Adjusted Mean Sum of Squares
Permittivity of the material (F/m)
to treat intracavity tumors like cervix, uterus, oropharyngeal and nasopharyngeal cancers. This research aims to carry out a detailed analysis of the capacitive hyperthermia from a physical perspective. To accomplish this, the geometric dimensions were treated as parameters and were input to the analysis model which subjected these parameters to systematic variation. The primary focus is to quantify the effect of each physical parameter involved which would provide helpful insight for the treatment planning of capacitive hyperthermia. This was accomplished by performing Analysis of Variance (ANOVA) on the data obtained from the experiments. The medical practitioner may need to follow different protocols based on location, orientation or size etc. of the tumor. Moreover, the obtained results were analyzed with respect to achievement of treatment objective and efficiency of inflicting damage to the tumor. Furthermore, the power delivered to the tissue needs to be regulated. Ideally the heating should only occur in the tumor without causing any harm to the peripheral normal tissue. In practice, certain margin of normal tissue is bound to be destroyed. The extent of this margin depends on many parameters like location, type of tissue and size of the tumor etc. For critical organs like liver, brain etc., the margin has to be minimal. The recommendations to localize the heat source were given in the concluding section. The organization of this paper is as follows. The next section outlines the mathematical modeling of capacitive hyperthermia followed by Taguchi experimental design procedure. The results and discussions are presented in the subsequent section and finally conclusions are drawn in the last section.
2. Mathematical modeling of capacitive hyperthermia The setup used for the typical capacitive hyperthermia is shown in Fig. 1. Electric potential is applied across the two electrodes
concomitant by the delivery of electrical energy to the tissue situated in between the electrodes. The delivered electrical energy expresses itself in terms of heat which consequently results in elevated temperature of the tissue. In order to avoid the overheating of the tissue near the electrodes, cooling pads are used. The thickness and size of the cooling pads varies but pads of thickness 5–10 mm have been used (Jacobsen and Stauffer, 2002). They are filled with distilled water and enclosed in a thin sheet of PVC. In the outcome of the thermal therapy, temperature plays a critical role. Elevated temperature has been reported to have lethal effects on the biological cells (Xu and Lu, 2011; Xu and Qian, 1995). So it becomes increasingly important to accurately calculate the temperature field inside the biological tissue. To accomplish this researchers have proposed many bioheat models like Wulff continuum model (Wulff, 1974), Klinger continuum model (Klinger, 1974), continuum model of Chen and Holmes (Holmes and Chen, 1980), Pennes bioheat transfer model
Electrode
Tumor Ω2 Healthy Tissue Ω1
Cooling Pad Fig. 1. Setup used for the analysis (Jamil and Ng, 2013).
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(Pennes, 1948), and Weinbaum-Jiji bioheat model (Weinbaum and Jiji, 1985) but Pennes bioheat model has been used most often because of accuracy and ease of implementation. Pennes model is based on the classical Fourier law which assumes that thermal disturbance travels at an infinite speed and small disturbance is felt instantaneously in the body. To incorporate this, non-Fourier models which assume finite propagation speed of thermal disturbance were also presented (Tzou, 1997; Xu and Lu, 2011). Non-Fourier phenomenon has been observed in processes involving very low temperatures, or processes where large amount of energy is deposited in short time scales like laser heating and materials with large heterogeneities. Neither of these is relevant for the current research, so Pennes bioheat model based on the classical Fourier law is sufficient for this research. The heat transfer inside the tissue can be represented by the Pennes equation (Pennes, 1948): ρc
∂TðX; tÞ ¼ ∇: kðXÞ∇TðX; tÞ þ ρb ωb cb ½T a −TðX; tÞ ∂t þQ ðX; tÞ X∈Ω
ð1Þ
where Q ðX; tÞ includes the heat generated by external electromagnetic field Q r ðX; tÞ and metabolic heat Q met ðX; tÞ generated by natural mechanisms of the body. As shown in Fig. 1, subscripts 1 and 2 are used for tissue and tumor respectively while Γ c represents the interface boundary between the tissue and tumor. In flat plate electrodes there is a tendency of concentration of electric field near the edges of the electrodes. As a result the tissue near the edges tends to heat up more. To overcome this problem, cooling pads are used between the electrodes and the tissue. They are useful in preventing the overheating and also help in enhancing the electromagnetic coupling. In this study the electrodes were not explicitly modeled rather their effect was quantified by using the proper boundary condition. The effect of cooling pads can be incorporated by using either convective boundary condition (Lv et al., 2005) between the surface and cooling pad or applying Dirichlet boundary condition (Majchrzak et al., 2008; Thiebaut and Lemonnier, 2002). In this study convective boundary condition was applied on the upper and lower surface of the domain to quantify the effect of cooling pads. i.e., −k1
∂T 1 ðx; yÞ ¼ hw ½T 1 ðx; yÞ−T w ∂n
ð2Þ
where hw represents the convection coefficient between tissue and water and Tw is the temperature of the cooling water. Respective values for hw and Tw were taken from Ref Lv et al. (2005). Thermal insulation boundary condition is used on all other boundaries based on the assumption that the side boundaries are far enough so that they are not affected by the temperature field in the middle of the domain (Lv et al., 2005). Furthermore, it has been reported that in some situations imposing Dirichlet boundary condition at the distant boundaries may cause numerical simulations to diverge (Barauskas et al., 2008). Owing to heterogeneity of tissue and tumor properties, Eq. (1) needs to be solved separately in tumor and normal tissue domains. Solution of the system of bioheat equations would provide us with temperature field in each domain. The interaction of electromagnetic field with the biological tissue depends on size and frequency of the field. For the configuration used in the current research as shown in Fig. 1, Quasi-static approximation can be used which essentially means that electromagnetic field behaves as static field and the field inside the biological tissue can be calculated by solving the following equation (Andreuccetti and Zoppetti, 2006; Dimbylow, 1988): −∇:½ðs þ jωεÞ∇φðx; yÞ ¼ 0
ð3Þ
where s and ε represent electrical conductivity and dielectric permittivity of the material whereas ω is the angular frequency.
Electric field strength E can be found using the following equation: Eðx; yÞ ¼ −∇φðx; yÞ
ð4Þ
Electrical potential U is applied across the electrode surfaces. ðx; yÞ∈Γ 1 : φ1 ðx; yÞ ¼ U ðx; yÞ∈Γ 2 : φ2 ðx; yÞ ¼ −U
ð5Þ
where Γ 1 and Γ 2 represent the upper and lower electrode boundary respectively as shown in Fig. 1. Electrical insulation is assumed on all other boundaries. i.e., −ε1
∂φ1 ðx; yÞ ¼0 ∂n
ð6Þ
This assumption is valid for the surface of the tissue since conductivity of the air or that of the cooling pad filled with distilled water is very low and normal component of electric field at the surface will indeed be negligible. It is also assumed that the side boundaries are far enough and electric field does not penetrate the side boundaries. It is a relevant assumption because the electric field lines start and end at the electrodes. Furthermore, continuity boundary conditions were imposed at the interface between tissue and tumor. The volumetric heat generation as a result of electric field inside the biological tissue can be calculated using sjEðx; yÞj2 2 s½jEx j2 þ jEy j2 ¼ 2
Q r ðx; y; tÞ ¼
ð7Þ
where s represents the electrical conductivity of the tissue which is measured in S/m. Table 1 shows the conductivity and permittivity values for tissue and tumor. For further details of the capacitive hyperthermia readers are referred to Ref Jamil and Ng (2013). For the current research following values of the variables were used: k1 ¼ 0:5 W=m K; k2 ¼ 0:6 W=m K;
ωb1 ¼ 0:0005 s−1 ; −1
ωb2 ¼ 0:002 s ;
Q met2 ¼ 42000 W=m3 ;
ρb ¼ 1000 kg=m ;
cb ¼ 4200 J=kg K;
T a ¼ 37 1 C;
hw ¼ 100 W=m2 1 C;
3
Q met1 ¼ 4200 W=m3 ;
T w ¼ 10 1 C:
3. Taguchi design of experiments In order to quantify the effect of each parameter considered, a systematic experimental design is needed. The concept of experimental design was introduced by Fisher et al. (Fisher, 1925, 1926). The primitive method to find the effect of parameters is to vary the level of each variable one by one while keeping the other variables constant. Following the primitive method, the number of experimental combinations needed to establish the effect of each parameter would be prohibitively large. Consequently this method Table 1 Electromagnetic properties used for tissue and tumor domain (Jamil and Ng, 2013). S.No. Frequency f [MHz] Dielectric permittivity [F/m]
1 2 3
0.1 1 10
Electrical conductivity [S/m]
ε1
ε2
s1
s2
20000ε0 2000ε0 100ε0
1.2ε1 1.2ε1 1.2ε1
0.192 0.4 0.625
1.2s1 1.2s1 1.2s1
where the dielectric constant of the vacuum ε0 is 0.8538 10−12 F/m.
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has been proved to be inefficient owing to extensive effort and time required (Montgomery, 1985). The minimum number of experimental combinations (MNE) required is given by N∧n where N is the number of levels and n is the number of variables. For current setup 36 ¼ 729 experimental combinations are required. These can be reduced if fractional factorial design is used instead of full factorial design (Montgomery and Runger, 1994; Ng and Ng, 2006) but the number of experiments still remains large. Taguchi improved the experimental design concept [6] and put forth the concept of orthogonal arrays (Kacker et al., 1991a, 1991b; Taguchi, 2004). By utilizing orthogonal arrays, the number of experiments could be drastically reduced. For 6 factors having 3 levels each, the effect of each parameter can be quantified by utilizing Taguchi's standard L27 array (Table A1). By using L27 orthogonal array, only 27 experiments will be required to obtain the desired results. For the current research, the maximum obtained temperature in the domain was considered as the quality characteristic to be optimized. As a number of experiments needed to be performed, a 2-D geometry was selected for analysis as was also done in Ref. Jamil and Ng (2013) in which the parameters in bioheat equation were ranked using Taguchi design. In Jamil and Ng (2013) maximum achieved temperature was regarded as the sole response variable and thermal damage to the tumor and tissue were not considered explicitly. In the current paper the physical parameters are scrutinized with respect to their effect on the maximum achievable temperature and thermal damage to the tissue and tumor domain is considered explicitly. Thermal damage is coupled to the respective damage to the tissue or tumor and a detailed two pronged strategy was formulated. Two indices namely treatment index and damage index were defined, which were used to analyze the results from the treatment objective point of view and efficiency of tumor killing. This simplified approach would allow easy acquisition of results owing to less computational resources requirement. The parameters considered for current analysis are shown in Table 2 and Fig. 2 out of which four are geometric parameters (X1– X4) and two are tunable parameters (X5–X6). The six parameters have three levels each. The physical parameters have been varied progressively whereas levels for tunable parameters were taken from Ref. Jamil and Ng (2013). Fig. 2 labels the parameters considered for analysis.
4. Results and discussion As stated earlier that the experimental design was carried out using the Taguchi L27 orthogonal array. Experimental matrix was produced and the required data was obtained using the COMSOL multiphysics software. (Comsol Multiphysics, 2012)
Table 2 The six independent variables with corresponding levels used for analysis. Factor
Units
Level 1 (low)
Size of the tumor (X1) Relative position of electrodes (X2) Depth of tumor (X3) Size of the electrodes (X4) Frequency (X5) Voltage (X6)
(m) (m)
0.01 −0.02
(m) 0.025 (m) 0.01 (MHz) 0.1 (V) 10
Level 2 (medium)
Level 3 (high)
0.015 0
0.02 0.04
0.03 0.015 1 15
0.035 0.02 10 20
275
Fig. 2. Pictorial representation of variables considered for analysis.
Table 3 ANOVA table for the selected parameters and interactions. Factors
DF
SS
Adj MS
F
P
% Contribution
Ranking
X1 X2 X3 X4 X5 X6 Error Total
2 2 2 2 2 2 14 26
80.84 158.74 11.50 32.60 690.87 975.42 218.12 2102.38
40.42 79.37 5.75 16.30 345.44 487.71 15.58
2.59 5.09 0.37 1.05 22.17 31.30
0.110 0.022 0.698 0.377 0.000 0.000
4.139 8.135 0.591 1.678 35.432 50.024
4 3 6 5 2 1
The results obtained from the experimental matrix are shown in Table 3. Analysis of Variance (ANOVA) was carried out to categorize each parameter with respect to its effect on the maximum achieved temperature. Table 3 shows that as expected, tunable parameters i.e., frequency and voltage parameters have substantial impact on the achieved temperature. This is because of the fact that applied voltage (X6) is indirectly an indicator of the amount of energy supplied to the target area and frequency (X5) dictates how this supplied energy would interact with the biological matter. It is also noteworthy that relative position of the electrodes (X2) also affects the response variable considerably followed by the tumor size (X1). Main effects plot for the variables selected is shown in Fig. 3. Voltage and frequency affect the achieved temperature the most as can be seen by their highest gradients. Mean temperature increases by 14 1C and 12 1C respectively when voltage and frequency change levels from low to high. From the analysis, it can also be concluded that for the six variables each having three levels as shown in Table 2, the best arrangement would be to keep X4, X5 and X6 at high levels and X1, X2 at low levels whereas X3 should be at the medium level. In subsequent sections the result obtained from Taguchi's analysis are used for further analysis. It is well a known fact that thermal damage to the biological material is a combination of temperature and exposure time. Tissue damage can be evaluated using the Arrhenius function. Thermal damage Ω can be described as Z Ω¼A
t 0
e−ΔE=Ru T dt
ð8Þ
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Fig. 3. Main effects plot for temperature.
or dΩ ¼ Ae−ΔE=Ru T dt
ð9Þ
where e is constant having value 2.718, A is the frequency factor, ΔE is the tissue activation energy (J/mol), Ru is the universal gas constant [8.31 J/(mol K)], T is the absolute temperature (K) and t is the thermal treatment time (s). Ω¼1 corresponds to a point at which the tissue coagulation first occurs (Agah et al., 1994). For the capacitive hyperthermia arrangement, heat generated as a consequence of delivered electromagnetic energy is not uniform and produces a heterogeneous temperature field instead of homogeneous temperature. It can be seen from Eqs. (8) and (9) that same exposure will lead to different thermal damage for a varying temperature field. Moreover, it is also evident from Eq. (9) that for fixed temperature, the slope of thermal damage is constant w.r.t time i.e., dΩ ¼ Ae−ΔE=Ru T ¼ constant dt
ðfor constant TÞ
This means that if the temperature is fixed or steady state has been achieved, thermal damage is linearly related to the exposure time. It has also been observed that at elevated temperatures around 40–41 1C cells are inactivated. However, this inactivation is temporary and after some time the cells become resistant to heat. This phenomenon is known as thermotolerance (Habash et al., 2006). Prolonged exposure at temperatures above 41 1C overcomes the thermotolerance and required biological rationale can be achieved. So for current research, threshold value of 42 1C has been used. Once the steady state temperature of at least 42 1C has been achieved, thermal damage becomes a linear function of exposure time only. Similarly, for tissue at temperature above the threshold limit, the slope of thermal damage will be even higher which translates to more swift thermal damage. Fig. 4 shows the plot of thermal damage against exposure time for a fixed temperature of 42 1C. Moreover, in clinical practice typical exposure time at 42 1C is around 60 min (Stauffer, 2005). For hyperthermia treatment, the temperature of the tumor needs to be raised to at least 42 1C. The maximum achieved temperature indicates the efficiency of the energy delivered but
Fig. 4. Plot of thermal damage against exposure time for fixed temperature at 42 1C, A ¼ 7.39e39 1/s, ΔE¼ 2.577e5 J/mol.
it alone does not quantify the efficacy of the treatment. For the setup shown in Fig. 2, the aim of the treatment is to raise the temperature of the tumor above 42 1C while causing minimum damage to the surrounding normal tissue. An ideal treatment would be one in which the whole tumor is above 42 1C while all of the normal tissue should preferably be at body temperature. The ideal temperature profile is obviously impossible to achieve but attempt should be made to replicate it as closely as possible. The next section will analyze the results from two perspectives. 1. From the treatment objective (complete tumor regression) 2. From the efficiency of tumor killing When a therapy is performed, its main objective is to achieve complete tumor regression. There should be no tumor cells left unharmed, otherwise it would result in recurrence of cancer. For the current research this objective can be accomplished by calculating the percentage of tumor damaged. To quantify the efficacy of therapy with respect to tumor destruction, a treatment
M. Jamil, E.Y.K. Ng / Journal of Thermal Biology 38 (2013) 272–279
Fig. 5. Plot of treatment index for Taguchi L27 array.
277
Fig. 6. Percentage damage to the tissue and tumor for Taguchi L27 array.
index is defined which is given by Treatment index ¼ Fraction of tumor at or above hyperthermic temperature The value of treatment index can vary from 0 to 1. A value of 1 would guarantee complete regression of the tumor while a value of 0 would mean no effect whatsoever. In simple words treatment index only focuses on whether the treatment objective has been achieved or not. Fig. 5 shows the graph for treatment index against experiment no. The graph reveals that treatment index is 1 for observation number 6, 9 and 24 suggesting that treatment goal has been achieved and is highlighted by circles. Complete tumor regression can be achieved if arrangements in experiments where treatment index of 1 are used. From Fig. 5 it is evident although treatment objective will be achieved for experiments number 6, 9 and 24 but the information contained in Fig. 5 above is not sufficiently comprehensive because treatment index alone does not contain information about the damage caused to the normal tissue. A treatment index value of 1 does not necessarily mean best experimental arrangement or optimum treatment output. Fig. 6 further elaborates this point in which the percentage thermal damage to the tissue and tumor is plotted. It is evident that for experiments 6 and 9 the treatment index is 1 but the accompanying thermal damage to the normal tissue is also very high. Another perspective of analysis can be as to how effectively the tumor damage is achieved. Effectiveness here means incurring maximal damage to the tumor and minimum damage to the normal tissue. To accomplish this, damage index is defined which takes into account the thermal damage to the normal tissue as well as thermal damage to the tumor. Damage index is defined as Damage index ¼ Fractional thermal damage to the tumor −fractional thermal damage to the normal tissue Fractional thermal damage for the tissue is the fraction of tissue above hyperthermic temperature of 42 1C. Similarly fractional thermal damage for tumor is defined as the fraction of tumor above hyperthermic temperature of 42 1C. The value of damage index varies from 1 to −1. Ideally the value of damage index should be 1 which would mean complete damage to the tumor with no damage to the peripheral normal tissue. A value of −1 means that damage is only incurred by the normal tissue which is the worst
Fig. 7. Damage index for Taguchi L27 array.
case scenario. An attempt should be made to achieve a value of damage index which is close to 1. The damage index describes the protocol which is able to cause maximum damage to the tumor while rendering minimal damage to the normal tissue. In other words it is a measure of how efficiently the tumor is destroyed. Fig. 7 shows the damage index for all the 27 experimental combinations which underlines different ranking for damage index than the ranking for treatment index. It can be seen that the damage index is highest for experiment number 14 and 24 whereas it is least for experiment 21. The results suggest that highest killing efficiency for tumor is achieved for experiments 14 and 24. It is also evident that for experiments 17 and 21 damage is more to the normal tissue than to the tumor which is highly undesirable. Although the best tumor killing efficiency is achieved for experiment number 14 as shown in Fig. 7 by its highest value of damage index, but this may not be the best option from treatment objective point of view. This can be explained further if we compare Figs. 5 and 7. From Fig. 5 it is evident that for experiment number 14, treatment objective is not achieved as its treatment index value is less than 1. As stated earlier, treatment objective is achieved for the experiments 6, 9 and 24 but not all of these have highest damage index. Out of these experiments, experiment 24 has the highest damage index whereas experiments 6 and 9 have lower damage indices. This suggests that experiments with lower
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Table A1 Data matrix for Taguchi's L27 orthogonal array. Exp. No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Side of tumor
Position of electrodes
Depth of tumor
Size of electrodes
Freq.
Volt.
%age of area damaged
X1
X2
X3
X4
X5
X6
Tissue
Tumor
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
−0.02 −0.02 −0.02 0 0 0 0.04 0.04 0.04 −0.02 −0.02 −0.02 0 0 0 0.04 0.04 0.04 −0.02 −0.02 −0.02 0 0 0 0.04 0.04 0.04
0.025 0.025 0.025 0.03 0.03 0.03 0.035 0.035 0.035 0.03 0.03 0.03 0.035 0.035 0.035 0.025 0.025 0.025 0.035 0.035 0.035 0.025 0.025 0.025 0.03 0.03 0.03
0.01 0.01 0.01 0.015 0.015 0.015 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.015 0.015 0.015 0.015 0.015 0.015 0.02 0.02 0.02 0.01 0.01 0.01
0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10
10 15 20 10 15 20 10 15 20 15 20 10 15 20 10 15 20 10 20 10 15 20 10 15 20 10 15
0.00 0.00 42.59 0.00 0.00 51.87 0.00 0.00 57.54 0.00 38.73 0.00 0.00 15.79 0.00 0.00 4.61 0.00 0.00 0.00 32.56 0.00 0.00 20.56 0.00 0.00 0.00
0.00 0.00 56.33 0.00 0.00 100.00 0.00 0.00 100.00 0.00 42.24 0.00 0.00 95.39 0.00 0.00 0.14 0.00 0.00 0.00 12.14 0.00 0.00 100.00 0.00 0.00 0.00
damage index do not kill the tumor efficiently as can be seen from Fig. 7. It can be seen that experiment number 24 is the best protocol. Firstly, it achieves the treatment objective of incurring complete damage to the tumor as it has a treatment index of 1 (Fig. 5). Secondly, the treatment objective is achieved with high tumor killing efficiency as well which is signified by high damage index (Fig. 7). It can be concluded that achievement of treatment objective does not necessarily mean optimum killing efficiency. The best treatment protocol would be the one which has highest treatment index as well as the highest damage index. An important indicator that needs to be taken into consideration is the location of the maximum temperature. Table A1 in appendix lists the domain in which the maximum temperature is located. To achieve optimum results, maximum temperature should preferably lie inside the tumor region. This arrangement is likely to inflict more damage to the tumor and would shield the normal tissue from the thermal damage. For selective killing of tumor, ideally the hyperthermic condition should only be achieved inside the tumor while normal tissue should be protected from the concomitant thermal damage.
5. Conclusion In this research the capacitive hyperthermia was analyzed from the physical perspective. Physical dimensions were treated as parameters and total of six parameters were selected including two tunable parameters namely frequency and applied voltage. Maximum achieved temperature inside the domain was treated as the relevant quality characteristic. Following a systematic analysis underlined by Taguchi's L27 orthogonal array, the effect of each selected parameter was quantified. Moreover, under the framework of capacitive hyperthermia it was concluded that for reliable treatment promising optimum results, thermal damage to the tissue as well as to the tumor needs to be taken into account. Results were analyzed from two perspectives, from treatment
Tmax
Location of Tmax
32.10 41.09 62.04 33.03 41.07 63.68 32.15 38.69 55.79 37.56 59.45 41.16 35.13 47.56 36.70 34.61 42.99 35.70 41.86 36.12 51.90 39.79 36.56 47.25 36.00 34.55 39.54
Tumor Normal Normal Tumor Normal Normal Tumor Normal Normal Normal Normal Normal Tumor Normal Normal Tumor Normal Tumor Normal Normal Normal Tumor Tumor Normal Tumor tumor Normal
objective point of view and from the point of view of tumor killing efficiency. In this context two indices namely treatment index and damage index were defined which highlight the respective perspective quantitatively. It was concluded that treatment objective may be achieved but it may not represent the most efficient treatment protocol. Higher values of both, treatment and damage indices, would qualify a treatment protocol to be the optimum one.
Appendix A Also see Table A1. References Comsol Multiphysics. 3.5a Ed. 〈http://www.math.nju.edu.cn/help/mathhpc/doc/ comsol/modeling.pdf〉 (last access: Sept. 2012). Agah, R., Pearce, J.A., Welch, A.J., Motamedi, M., 1994. Rate process model for arterial tissue thermal damage implications on vessel photocoagulation. Lasers Surg. Med. 15, 176–184. Andreuccetti, D., Zoppetti, N., 2006. Quasi-static electromagnetic dosimetry: from basic principles to examples of applications. Int. J. Occup. Saf. Ergon. 12, 201–215. Barauskas, R., Gulbinas, A., Vanagas, T., Barauskas, G., 2008. Finite element modeling of cooled-tip probe radiofrequency ablation processes in liver tissue. Comput. Biol. Med. 38, 694–708. Dewey, W.C., Hopwood, L.E., Sapareto, S.A., Gerweck, L.E., 1977. Cellular responses to combinations of hyperthermia and radiation. Radiology 123, 463–474. Dimbylow, P.J., 1988. The calculation of induced currents and absorbed power in a realistic, heterogeneous model of the lower leg for applied electric field from 60 Hz to 30 MHz. Phys. Med. Biol. 33, 1453–1468. Douglas A. Christensen, C.F., Durney, Carl H., 2009. Electromagnetics in Medicine, Basic Introduction to Bioelectromagnetics, second ed. CRC Press, pp. 229–251. Field, S.B., Morris, C.C., 1983. The relationship between heating time and temperature: its relevance to clinical hyperthermia. Radiother. Oncol. 1, 179–186. Fisher, R.A.S., 1925. Statistical Methods for Research Workers/by R.A. Fisher. Oliver & Boyd, London, UK. Fisher, R.A.S., 1926. The arrangement of field experiments. J. Minist. Agric. G. B. 33, 503–513. Gomonov, S.V., Efanov, V.M., 2008. Theoretical Model of Irreversible Intracellular Electroporation (Supra-Electroporation) in a Single Cell, in: Proceedings of the
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2008 IEEE International Power Modulators and High Voltage Conference, pp. 330–333. Habash, R.W.Y., Bansal, R., Krewski, D., Alhafid, H.T., 2006. Thermal therapy. Part 2: Hyperthermia Techniques 34, 491–542. Habash, R.W.Y., Bansal, R., Krewski, D., Alhafid, H.T., 2007. Thermal therapy. Part IV: Electromagnetic and Thermal Dosimetry 35, 123–182. Henriques, F.C., Moritz, A.R., 1947. Studies of thermal injury. I. The conduction of heat to and through skin and the temperatures attained therein—A theoretical and experimental investigation. Am. J. Pathol. 23, 530–549. Holmes, K.R., Chen, M.M., 1980. Microvascular contributions in tissue heat transfer. Annals N.Y. Acad. Sci. 335, 137–150. Jacobsen, S., Stauffer, P.R., 2002. Multifrequency radiometric determination of temperature profiles in a lossy homogeneous phantom using a dual-mode antenna with integral water bolus. IEEE Trans. Microwave Theory Tech. 50, 1737–1746. Jamil, M., Ng, E.Y.K., 2013. Ranking of parameters in bioheat transfer using Taguchi analysis. Int. J. Therm. Sci. 63, 15–21. Kacker, R.N., Lagergren, E.S., Filliben, J.J., 1991a. Taguchi based orthogonal arrays are classical designs of experiments. J. Res. Natl. Inst. Stand. Technol. 96, 577–591. Kacker, R.N., Lagergren, E.S., Filliben, J.J., 1991b. Taguchi fixed-element arrays are fractional factorials. J. Qual. Technol. 23, 107–116. Klinger, H., 1974. Heat transfer in perfused biological tissue—I: General theory. Bull. Math. Biol. 36, 403–415. Lanzafame, R.J., 1995. Applications of laser technology in breast cancer therapy. Semin. Surg. Oncol. 11, 328–332. Lv, Y.G., Deng, Z.S., Liu, J., 2005. 3-D numerical study on the induced heating effects of embedded micro/nanoparticles on human body subject to external medical electromagnetic field. IEEE Trans. Nanobiosci. 4, 284–294. Majchrzak, E., Dziatkiewicz, G., Paruch, M., 2008. The modeling of heating a tissue subjected to external electromagnetic field. Acta Bioeng. Biomech. 10, 29–37. Montgomery, D.C., 1985. Introduction to Statistical Quality Control. Wiley, Canada. Montgomery, D.C., Runger, G.C., 1994. Applied Statistics and Probability for Engineers. Wiley, New York.
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Neukam, F.W., Stelzle, F., 2010. Laser Tumor Treatment in Oral and Maxillofacial Surgery. In: Schmidt, M., Vollertsen, F., Geiger, M. (Eds.), Laser Assisted Net Shape Engineering 6, Proceedings of the Lane, 2010. Elsevier Science Bv, Amsterdam, pp. 91–100. Ng, E., Ng, W., 2006. Parametric study of the biopotential equation for breast tumour identification using ANOVA and Taguchi method. Med. Biol. Eng. Comput. 44, 131–139. Pennes, H.H., 1948. Analysis of tissue and arterial blood temperature in the resting human forearm. J. Appl. Physiol. 1, 93–122. Rebillard, X., Davin, J.L., Soulie, M., Ccafu, 2003. Treatment by HIFU of prostate cancer: survey of literature and treatment indications. Prog. Urol. 13, 1428–1456. Saniei, N., 2009. Hyperthermia and cancer treatment. Heat Transfer Eng. 30, 915–917. Stauffer, P.R., 2005. Evolving technology for thermal therapy of cancer. Int. J. Hyperthermia 21, 731–744. Taguchi, G., 2004. Computer Based Robust Engineering: Essentials for DFSS. ASQ Quality Press, Milwoukee, WI. Thiebaut, C., Lemonnier, D., 2002. Three-dimensional modeling and optimisation of thermal fields induced in a human body during hyperthermia. Int. J. Therm. Sci. 41, 500–508. Tzou, D.Y., 1997. Macro- to Microscale Heat Transfer: The Lagging Behavior. Weinbaum, S., Jiji, L.M., 1985. A new simplified bioheat equation for the effect of blood flow on local average tissue temperature. J. Biomech. Eng.—Trans. ASME 107, 131–139. Wulff, W., 1974. The energy conservation equation for living tissue. IEEE Trans. Biomed. Eng. 21, 494–495. Xu, F., Lu, T., 2011. Skin Bioheat Transfer and Skin Thermal Damage, Introduction to Skin Biothermomechanics and Thermal Pain. Springer, Berlin Heidelberg, pp. 23–68. Xu, Y.S., Qian, R.Z., 1995. Analysis of thermal injury process based on enzyme deactivation mechanisms. J. Biomech. Eng.Trans. ASME 117, 462–465.
Contents lists available at SciVerse ScienceDirect
Journal of Thermal Biology journal homepage: www.elsevier.com/locate/jtherbio
To optimize the efficacy of bioheat transfer in capacitive hyperthermia: A physical perspective Muhammad Jamil, E.Y.K. Ng n School of Mechanical and Aerospace Engineering, College of Engineering, Nanyang Technological University, 50 Nanyang Avenue 639798, Singapore
art ic l e i nf o
a b s t r a c t
Article history: Received 15 September 2012 Accepted 20 March 2013 Available online 29 March 2013
This paper presents the capacitive hyperthermia from physical perspective focusing on the geometric dimensions as parameters. For this purpose six parameters having three levels each, including two tunable parameters i.e. applied voltage, frequency together with four geometric parameters i.e. size of the tumor, location of the tumor, electrode size and relative position of the electrodes w.r.t tumor were considered for analysis. Taguchi based design of experiments approach was used for the aforementioned six parameters. Using Taguchi's standard L27 orthogonal array, the required results could be obtained employing least number of experiments. For this study temperature was taken as the quality characteristic to be optimized. Furthermore, analysis of variance (ANOVA) was performed to quantify the effect of each parameter on the response variable and results were presented. To deal with the extent of thermal damage to the healthy tissue and tumor, the fraction of tissue experiencing thermal damage was calculated. For this purpose two indices namely treatment index and damage index were formulated. Finally it was concluded that maximum achieved temperature alone does not depict the effectiveness of the treatment. Rather, the combination of the maximum achieved temperature and accompanied thermal damage to the surrounding healthy tissue which should be considered. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Pennes bioheat equation Treatment objective Treatment index Damage index Thermal treatment planning Taguchi orthogonal arrays
1. Introduction Presently, cancer remains one of the deadly diseases in the world. There are many treatments that are being used to treat cancer that include chemotherapy, radiation therapy, high intensity focussed ultrasound (HIFU), laser ablation, electroporation and surgery (Dewey et al., 1977; Gomonov and Efanov, 2008; Lanzafame, 1995; Neukam and Stelzle, 2010; Rebillard et al., 2003; Saniei, 2009). The aim of a treatment is to inflict lethal damage to the cancer cell while shading the normal cells from the harmful effects. Hyperthermia in cancer treatment is a therapeutic procedure in which the temperature of the biological tissue is raised above 42 1C for certain duration. Biological cells are unable to tolerate such elevated temperatures and the sub-cellular structures that constitute the cell disintegrate and start to shut down. Such elevated temperature hinders the core cell functions imperative for cell survival. Sustained heating at hyperthermic temperatures causes protein denaturation or apoptosis which ultimately leads to cell death. Thermal therapies are the therapeutic modalities which solely utilize heat as the mechanism to cause lethal damage to the tissues. Thermal therapies have been developed for cancer treatment which harness the proven fact that increasing the temperature of the cell above a threshold value causes a cell to
n
Corresponding author. Tel.: +65 6790 4455. E-mail address: [email protected] (E.Y.K. Ng).
0306-4565/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jtherbio.2013.03.007
die (Field and Morris, 1983; Habash et al., 2007; Henriques and Moritz, 1947). Thermal therapy has fewer side effects and is noninvasive in nature which makes it an obvious contender for selection from the large pool of treatments available. Capacitive hyperthermia is a genre of thermal therapy in which heating is attained by applying electric potential across the electrodes. In therapies like HIFU and laser ablation, the energy can be focussed to a particular area with the help of transducers or lenses. But these therapies suffer from focussing issues due to the presence of bones; air filled viscera and large scattering caused by the hydrated environment. In radiofrequency ablation the energy is delivered at the target site using needle type electrodes. Energy is delivered at high frequencies and can result in charring and carbonization which limits the size of the thermal lesion. In microwave ablation an even higher frequency is used and radiative antennas deliver energy to the target site. Owing to high frequencies used, radiofrequency and microwave ablation suffer from limited depth of penetration (Douglas A. Christensen and Durney, 2009). Capacitive hyperthermia relies mainly on the heterogeneity of electrical properties and thermal sensitivity of tumor which can be employed to ones advantage for preferential treatment of tumor. In capacitive hyperthermia lower frequencies are used which also means that higher depth of penetration could be achieved. Simple operation and adjustable position of electrodes favors the heating for various tissues at different angles and sites. Moreover, with different position and customization of electrodes, regional deep heating patterns can be achieved. It can also be used
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Nomenclature A c cb E ΔE F f hw k N n P Q Q met Qr R T T0 Ta Tw U
Frequency factor (1/s) Specific heat [J/(kg K)] Specific heat of blood [J/(kg K)] Electric field intensity (V/m) Activation energy of tissue (J/mol) Fisher statistic Frequency (Hz) Convection coefficient between tissue and water [W/(m2 K)] Thermal conductivity [W/(m K)] Number of parameter levels Number of parameters Probability value Volumetric heat generation rate (W/m3) Metabolic heat generation rate (W/m3) Spatial heat source (W/m3) Universal gas constant [J/(mol K)] Temperature (K) Body core temperature (K) Arterial blood temperature (K) Temperature of the cooling water (K) Electrode potential (V)
Greek symbols ε
ε0 εr ρ ρb s φ ω ωb Ω
273
Permittivity of the free space (F/m) Relative permittivity of the material Density (kg/m3) Density of blood (kg/m3) Electrical conductivity of the material (S/m) Electric scalar potential (V) Angular frequency (rad/s) Blood perfusion rate (1/s) Numerical domain
Subscripts 1 2 a b met w
Normal tissue domain Tumor domain Artery Blood Metabolic heat Water
Abbreviations ANOVA DF MNE SS Adj MS
Analysis of Variance Degrees of Freedom Minimum Number of Experimental combinations Sum of Squares Adjusted Mean Sum of Squares
Permittivity of the material (F/m)
to treat intracavity tumors like cervix, uterus, oropharyngeal and nasopharyngeal cancers. This research aims to carry out a detailed analysis of the capacitive hyperthermia from a physical perspective. To accomplish this, the geometric dimensions were treated as parameters and were input to the analysis model which subjected these parameters to systematic variation. The primary focus is to quantify the effect of each physical parameter involved which would provide helpful insight for the treatment planning of capacitive hyperthermia. This was accomplished by performing Analysis of Variance (ANOVA) on the data obtained from the experiments. The medical practitioner may need to follow different protocols based on location, orientation or size etc. of the tumor. Moreover, the obtained results were analyzed with respect to achievement of treatment objective and efficiency of inflicting damage to the tumor. Furthermore, the power delivered to the tissue needs to be regulated. Ideally the heating should only occur in the tumor without causing any harm to the peripheral normal tissue. In practice, certain margin of normal tissue is bound to be destroyed. The extent of this margin depends on many parameters like location, type of tissue and size of the tumor etc. For critical organs like liver, brain etc., the margin has to be minimal. The recommendations to localize the heat source were given in the concluding section. The organization of this paper is as follows. The next section outlines the mathematical modeling of capacitive hyperthermia followed by Taguchi experimental design procedure. The results and discussions are presented in the subsequent section and finally conclusions are drawn in the last section.
2. Mathematical modeling of capacitive hyperthermia The setup used for the typical capacitive hyperthermia is shown in Fig. 1. Electric potential is applied across the two electrodes
concomitant by the delivery of electrical energy to the tissue situated in between the electrodes. The delivered electrical energy expresses itself in terms of heat which consequently results in elevated temperature of the tissue. In order to avoid the overheating of the tissue near the electrodes, cooling pads are used. The thickness and size of the cooling pads varies but pads of thickness 5–10 mm have been used (Jacobsen and Stauffer, 2002). They are filled with distilled water and enclosed in a thin sheet of PVC. In the outcome of the thermal therapy, temperature plays a critical role. Elevated temperature has been reported to have lethal effects on the biological cells (Xu and Lu, 2011; Xu and Qian, 1995). So it becomes increasingly important to accurately calculate the temperature field inside the biological tissue. To accomplish this researchers have proposed many bioheat models like Wulff continuum model (Wulff, 1974), Klinger continuum model (Klinger, 1974), continuum model of Chen and Holmes (Holmes and Chen, 1980), Pennes bioheat transfer model
Electrode
Tumor Ω2 Healthy Tissue Ω1
Cooling Pad Fig. 1. Setup used for the analysis (Jamil and Ng, 2013).
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(Pennes, 1948), and Weinbaum-Jiji bioheat model (Weinbaum and Jiji, 1985) but Pennes bioheat model has been used most often because of accuracy and ease of implementation. Pennes model is based on the classical Fourier law which assumes that thermal disturbance travels at an infinite speed and small disturbance is felt instantaneously in the body. To incorporate this, non-Fourier models which assume finite propagation speed of thermal disturbance were also presented (Tzou, 1997; Xu and Lu, 2011). Non-Fourier phenomenon has been observed in processes involving very low temperatures, or processes where large amount of energy is deposited in short time scales like laser heating and materials with large heterogeneities. Neither of these is relevant for the current research, so Pennes bioheat model based on the classical Fourier law is sufficient for this research. The heat transfer inside the tissue can be represented by the Pennes equation (Pennes, 1948): ρc
∂TðX; tÞ ¼ ∇: kðXÞ∇TðX; tÞ þ ρb ωb cb ½T a −TðX; tÞ ∂t þQ ðX; tÞ X∈Ω
ð1Þ
where Q ðX; tÞ includes the heat generated by external electromagnetic field Q r ðX; tÞ and metabolic heat Q met ðX; tÞ generated by natural mechanisms of the body. As shown in Fig. 1, subscripts 1 and 2 are used for tissue and tumor respectively while Γ c represents the interface boundary between the tissue and tumor. In flat plate electrodes there is a tendency of concentration of electric field near the edges of the electrodes. As a result the tissue near the edges tends to heat up more. To overcome this problem, cooling pads are used between the electrodes and the tissue. They are useful in preventing the overheating and also help in enhancing the electromagnetic coupling. In this study the electrodes were not explicitly modeled rather their effect was quantified by using the proper boundary condition. The effect of cooling pads can be incorporated by using either convective boundary condition (Lv et al., 2005) between the surface and cooling pad or applying Dirichlet boundary condition (Majchrzak et al., 2008; Thiebaut and Lemonnier, 2002). In this study convective boundary condition was applied on the upper and lower surface of the domain to quantify the effect of cooling pads. i.e., −k1
∂T 1 ðx; yÞ ¼ hw ½T 1 ðx; yÞ−T w ∂n
ð2Þ
where hw represents the convection coefficient between tissue and water and Tw is the temperature of the cooling water. Respective values for hw and Tw were taken from Ref Lv et al. (2005). Thermal insulation boundary condition is used on all other boundaries based on the assumption that the side boundaries are far enough so that they are not affected by the temperature field in the middle of the domain (Lv et al., 2005). Furthermore, it has been reported that in some situations imposing Dirichlet boundary condition at the distant boundaries may cause numerical simulations to diverge (Barauskas et al., 2008). Owing to heterogeneity of tissue and tumor properties, Eq. (1) needs to be solved separately in tumor and normal tissue domains. Solution of the system of bioheat equations would provide us with temperature field in each domain. The interaction of electromagnetic field with the biological tissue depends on size and frequency of the field. For the configuration used in the current research as shown in Fig. 1, Quasi-static approximation can be used which essentially means that electromagnetic field behaves as static field and the field inside the biological tissue can be calculated by solving the following equation (Andreuccetti and Zoppetti, 2006; Dimbylow, 1988): −∇:½ðs þ jωεÞ∇φðx; yÞ ¼ 0
ð3Þ
where s and ε represent electrical conductivity and dielectric permittivity of the material whereas ω is the angular frequency.
Electric field strength E can be found using the following equation: Eðx; yÞ ¼ −∇φðx; yÞ
ð4Þ
Electrical potential U is applied across the electrode surfaces. ðx; yÞ∈Γ 1 : φ1 ðx; yÞ ¼ U ðx; yÞ∈Γ 2 : φ2 ðx; yÞ ¼ −U
ð5Þ
where Γ 1 and Γ 2 represent the upper and lower electrode boundary respectively as shown in Fig. 1. Electrical insulation is assumed on all other boundaries. i.e., −ε1
∂φ1 ðx; yÞ ¼0 ∂n
ð6Þ
This assumption is valid for the surface of the tissue since conductivity of the air or that of the cooling pad filled with distilled water is very low and normal component of electric field at the surface will indeed be negligible. It is also assumed that the side boundaries are far enough and electric field does not penetrate the side boundaries. It is a relevant assumption because the electric field lines start and end at the electrodes. Furthermore, continuity boundary conditions were imposed at the interface between tissue and tumor. The volumetric heat generation as a result of electric field inside the biological tissue can be calculated using sjEðx; yÞj2 2 s½jEx j2 þ jEy j2 ¼ 2
Q r ðx; y; tÞ ¼
ð7Þ
where s represents the electrical conductivity of the tissue which is measured in S/m. Table 1 shows the conductivity and permittivity values for tissue and tumor. For further details of the capacitive hyperthermia readers are referred to Ref Jamil and Ng (2013). For the current research following values of the variables were used: k1 ¼ 0:5 W=m K; k2 ¼ 0:6 W=m K;
ωb1 ¼ 0:0005 s−1 ; −1
ωb2 ¼ 0:002 s ;
Q met2 ¼ 42000 W=m3 ;
ρb ¼ 1000 kg=m ;
cb ¼ 4200 J=kg K;
T a ¼ 37 1 C;
hw ¼ 100 W=m2 1 C;
3
Q met1 ¼ 4200 W=m3 ;
T w ¼ 10 1 C:
3. Taguchi design of experiments In order to quantify the effect of each parameter considered, a systematic experimental design is needed. The concept of experimental design was introduced by Fisher et al. (Fisher, 1925, 1926). The primitive method to find the effect of parameters is to vary the level of each variable one by one while keeping the other variables constant. Following the primitive method, the number of experimental combinations needed to establish the effect of each parameter would be prohibitively large. Consequently this method Table 1 Electromagnetic properties used for tissue and tumor domain (Jamil and Ng, 2013). S.No. Frequency f [MHz] Dielectric permittivity [F/m]
1 2 3
0.1 1 10
Electrical conductivity [S/m]
ε1
ε2
s1
s2
20000ε0 2000ε0 100ε0
1.2ε1 1.2ε1 1.2ε1
0.192 0.4 0.625
1.2s1 1.2s1 1.2s1
where the dielectric constant of the vacuum ε0 is 0.8538 10−12 F/m.
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has been proved to be inefficient owing to extensive effort and time required (Montgomery, 1985). The minimum number of experimental combinations (MNE) required is given by N∧n where N is the number of levels and n is the number of variables. For current setup 36 ¼ 729 experimental combinations are required. These can be reduced if fractional factorial design is used instead of full factorial design (Montgomery and Runger, 1994; Ng and Ng, 2006) but the number of experiments still remains large. Taguchi improved the experimental design concept [6] and put forth the concept of orthogonal arrays (Kacker et al., 1991a, 1991b; Taguchi, 2004). By utilizing orthogonal arrays, the number of experiments could be drastically reduced. For 6 factors having 3 levels each, the effect of each parameter can be quantified by utilizing Taguchi's standard L27 array (Table A1). By using L27 orthogonal array, only 27 experiments will be required to obtain the desired results. For the current research, the maximum obtained temperature in the domain was considered as the quality characteristic to be optimized. As a number of experiments needed to be performed, a 2-D geometry was selected for analysis as was also done in Ref. Jamil and Ng (2013) in which the parameters in bioheat equation were ranked using Taguchi design. In Jamil and Ng (2013) maximum achieved temperature was regarded as the sole response variable and thermal damage to the tumor and tissue were not considered explicitly. In the current paper the physical parameters are scrutinized with respect to their effect on the maximum achievable temperature and thermal damage to the tissue and tumor domain is considered explicitly. Thermal damage is coupled to the respective damage to the tissue or tumor and a detailed two pronged strategy was formulated. Two indices namely treatment index and damage index were defined, which were used to analyze the results from the treatment objective point of view and efficiency of tumor killing. This simplified approach would allow easy acquisition of results owing to less computational resources requirement. The parameters considered for current analysis are shown in Table 2 and Fig. 2 out of which four are geometric parameters (X1– X4) and two are tunable parameters (X5–X6). The six parameters have three levels each. The physical parameters have been varied progressively whereas levels for tunable parameters were taken from Ref. Jamil and Ng (2013). Fig. 2 labels the parameters considered for analysis.
4. Results and discussion As stated earlier that the experimental design was carried out using the Taguchi L27 orthogonal array. Experimental matrix was produced and the required data was obtained using the COMSOL multiphysics software. (Comsol Multiphysics, 2012)
Table 2 The six independent variables with corresponding levels used for analysis. Factor
Units
Level 1 (low)
Size of the tumor (X1) Relative position of electrodes (X2) Depth of tumor (X3) Size of the electrodes (X4) Frequency (X5) Voltage (X6)
(m) (m)
0.01 −0.02
(m) 0.025 (m) 0.01 (MHz) 0.1 (V) 10
Level 2 (medium)
Level 3 (high)
0.015 0
0.02 0.04
0.03 0.015 1 15
0.035 0.02 10 20
275
Fig. 2. Pictorial representation of variables considered for analysis.
Table 3 ANOVA table for the selected parameters and interactions. Factors
DF
SS
Adj MS
F
P
% Contribution
Ranking
X1 X2 X3 X4 X5 X6 Error Total
2 2 2 2 2 2 14 26
80.84 158.74 11.50 32.60 690.87 975.42 218.12 2102.38
40.42 79.37 5.75 16.30 345.44 487.71 15.58
2.59 5.09 0.37 1.05 22.17 31.30
0.110 0.022 0.698 0.377 0.000 0.000
4.139 8.135 0.591 1.678 35.432 50.024
4 3 6 5 2 1
The results obtained from the experimental matrix are shown in Table 3. Analysis of Variance (ANOVA) was carried out to categorize each parameter with respect to its effect on the maximum achieved temperature. Table 3 shows that as expected, tunable parameters i.e., frequency and voltage parameters have substantial impact on the achieved temperature. This is because of the fact that applied voltage (X6) is indirectly an indicator of the amount of energy supplied to the target area and frequency (X5) dictates how this supplied energy would interact with the biological matter. It is also noteworthy that relative position of the electrodes (X2) also affects the response variable considerably followed by the tumor size (X1). Main effects plot for the variables selected is shown in Fig. 3. Voltage and frequency affect the achieved temperature the most as can be seen by their highest gradients. Mean temperature increases by 14 1C and 12 1C respectively when voltage and frequency change levels from low to high. From the analysis, it can also be concluded that for the six variables each having three levels as shown in Table 2, the best arrangement would be to keep X4, X5 and X6 at high levels and X1, X2 at low levels whereas X3 should be at the medium level. In subsequent sections the result obtained from Taguchi's analysis are used for further analysis. It is well a known fact that thermal damage to the biological material is a combination of temperature and exposure time. Tissue damage can be evaluated using the Arrhenius function. Thermal damage Ω can be described as Z Ω¼A
t 0
e−ΔE=Ru T dt
ð8Þ
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Fig. 3. Main effects plot for temperature.
or dΩ ¼ Ae−ΔE=Ru T dt
ð9Þ
where e is constant having value 2.718, A is the frequency factor, ΔE is the tissue activation energy (J/mol), Ru is the universal gas constant [8.31 J/(mol K)], T is the absolute temperature (K) and t is the thermal treatment time (s). Ω¼1 corresponds to a point at which the tissue coagulation first occurs (Agah et al., 1994). For the capacitive hyperthermia arrangement, heat generated as a consequence of delivered electromagnetic energy is not uniform and produces a heterogeneous temperature field instead of homogeneous temperature. It can be seen from Eqs. (8) and (9) that same exposure will lead to different thermal damage for a varying temperature field. Moreover, it is also evident from Eq. (9) that for fixed temperature, the slope of thermal damage is constant w.r.t time i.e., dΩ ¼ Ae−ΔE=Ru T ¼ constant dt
ðfor constant TÞ
This means that if the temperature is fixed or steady state has been achieved, thermal damage is linearly related to the exposure time. It has also been observed that at elevated temperatures around 40–41 1C cells are inactivated. However, this inactivation is temporary and after some time the cells become resistant to heat. This phenomenon is known as thermotolerance (Habash et al., 2006). Prolonged exposure at temperatures above 41 1C overcomes the thermotolerance and required biological rationale can be achieved. So for current research, threshold value of 42 1C has been used. Once the steady state temperature of at least 42 1C has been achieved, thermal damage becomes a linear function of exposure time only. Similarly, for tissue at temperature above the threshold limit, the slope of thermal damage will be even higher which translates to more swift thermal damage. Fig. 4 shows the plot of thermal damage against exposure time for a fixed temperature of 42 1C. Moreover, in clinical practice typical exposure time at 42 1C is around 60 min (Stauffer, 2005). For hyperthermia treatment, the temperature of the tumor needs to be raised to at least 42 1C. The maximum achieved temperature indicates the efficiency of the energy delivered but
Fig. 4. Plot of thermal damage against exposure time for fixed temperature at 42 1C, A ¼ 7.39e39 1/s, ΔE¼ 2.577e5 J/mol.
it alone does not quantify the efficacy of the treatment. For the setup shown in Fig. 2, the aim of the treatment is to raise the temperature of the tumor above 42 1C while causing minimum damage to the surrounding normal tissue. An ideal treatment would be one in which the whole tumor is above 42 1C while all of the normal tissue should preferably be at body temperature. The ideal temperature profile is obviously impossible to achieve but attempt should be made to replicate it as closely as possible. The next section will analyze the results from two perspectives. 1. From the treatment objective (complete tumor regression) 2. From the efficiency of tumor killing When a therapy is performed, its main objective is to achieve complete tumor regression. There should be no tumor cells left unharmed, otherwise it would result in recurrence of cancer. For the current research this objective can be accomplished by calculating the percentage of tumor damaged. To quantify the efficacy of therapy with respect to tumor destruction, a treatment
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Fig. 5. Plot of treatment index for Taguchi L27 array.
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Fig. 6. Percentage damage to the tissue and tumor for Taguchi L27 array.
index is defined which is given by Treatment index ¼ Fraction of tumor at or above hyperthermic temperature The value of treatment index can vary from 0 to 1. A value of 1 would guarantee complete regression of the tumor while a value of 0 would mean no effect whatsoever. In simple words treatment index only focuses on whether the treatment objective has been achieved or not. Fig. 5 shows the graph for treatment index against experiment no. The graph reveals that treatment index is 1 for observation number 6, 9 and 24 suggesting that treatment goal has been achieved and is highlighted by circles. Complete tumor regression can be achieved if arrangements in experiments where treatment index of 1 are used. From Fig. 5 it is evident although treatment objective will be achieved for experiments number 6, 9 and 24 but the information contained in Fig. 5 above is not sufficiently comprehensive because treatment index alone does not contain information about the damage caused to the normal tissue. A treatment index value of 1 does not necessarily mean best experimental arrangement or optimum treatment output. Fig. 6 further elaborates this point in which the percentage thermal damage to the tissue and tumor is plotted. It is evident that for experiments 6 and 9 the treatment index is 1 but the accompanying thermal damage to the normal tissue is also very high. Another perspective of analysis can be as to how effectively the tumor damage is achieved. Effectiveness here means incurring maximal damage to the tumor and minimum damage to the normal tissue. To accomplish this, damage index is defined which takes into account the thermal damage to the normal tissue as well as thermal damage to the tumor. Damage index is defined as Damage index ¼ Fractional thermal damage to the tumor −fractional thermal damage to the normal tissue Fractional thermal damage for the tissue is the fraction of tissue above hyperthermic temperature of 42 1C. Similarly fractional thermal damage for tumor is defined as the fraction of tumor above hyperthermic temperature of 42 1C. The value of damage index varies from 1 to −1. Ideally the value of damage index should be 1 which would mean complete damage to the tumor with no damage to the peripheral normal tissue. A value of −1 means that damage is only incurred by the normal tissue which is the worst
Fig. 7. Damage index for Taguchi L27 array.
case scenario. An attempt should be made to achieve a value of damage index which is close to 1. The damage index describes the protocol which is able to cause maximum damage to the tumor while rendering minimal damage to the normal tissue. In other words it is a measure of how efficiently the tumor is destroyed. Fig. 7 shows the damage index for all the 27 experimental combinations which underlines different ranking for damage index than the ranking for treatment index. It can be seen that the damage index is highest for experiment number 14 and 24 whereas it is least for experiment 21. The results suggest that highest killing efficiency for tumor is achieved for experiments 14 and 24. It is also evident that for experiments 17 and 21 damage is more to the normal tissue than to the tumor which is highly undesirable. Although the best tumor killing efficiency is achieved for experiment number 14 as shown in Fig. 7 by its highest value of damage index, but this may not be the best option from treatment objective point of view. This can be explained further if we compare Figs. 5 and 7. From Fig. 5 it is evident that for experiment number 14, treatment objective is not achieved as its treatment index value is less than 1. As stated earlier, treatment objective is achieved for the experiments 6, 9 and 24 but not all of these have highest damage index. Out of these experiments, experiment 24 has the highest damage index whereas experiments 6 and 9 have lower damage indices. This suggests that experiments with lower
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Table A1 Data matrix for Taguchi's L27 orthogonal array. Exp. No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Side of tumor
Position of electrodes
Depth of tumor
Size of electrodes
Freq.
Volt.
%age of area damaged
X1
X2
X3
X4
X5
X6
Tissue
Tumor
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
−0.02 −0.02 −0.02 0 0 0 0.04 0.04 0.04 −0.02 −0.02 −0.02 0 0 0 0.04 0.04 0.04 −0.02 −0.02 −0.02 0 0 0 0.04 0.04 0.04
0.025 0.025 0.025 0.03 0.03 0.03 0.035 0.035 0.035 0.03 0.03 0.03 0.035 0.035 0.035 0.025 0.025 0.025 0.035 0.035 0.035 0.025 0.025 0.025 0.03 0.03 0.03
0.01 0.01 0.01 0.015 0.015 0.015 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.015 0.015 0.015 0.015 0.015 0.015 0.02 0.02 0.02 0.01 0.01 0.01
0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10
10 15 20 10 15 20 10 15 20 15 20 10 15 20 10 15 20 10 20 10 15 20 10 15 20 10 15
0.00 0.00 42.59 0.00 0.00 51.87 0.00 0.00 57.54 0.00 38.73 0.00 0.00 15.79 0.00 0.00 4.61 0.00 0.00 0.00 32.56 0.00 0.00 20.56 0.00 0.00 0.00
0.00 0.00 56.33 0.00 0.00 100.00 0.00 0.00 100.00 0.00 42.24 0.00 0.00 95.39 0.00 0.00 0.14 0.00 0.00 0.00 12.14 0.00 0.00 100.00 0.00 0.00 0.00
damage index do not kill the tumor efficiently as can be seen from Fig. 7. It can be seen that experiment number 24 is the best protocol. Firstly, it achieves the treatment objective of incurring complete damage to the tumor as it has a treatment index of 1 (Fig. 5). Secondly, the treatment objective is achieved with high tumor killing efficiency as well which is signified by high damage index (Fig. 7). It can be concluded that achievement of treatment objective does not necessarily mean optimum killing efficiency. The best treatment protocol would be the one which has highest treatment index as well as the highest damage index. An important indicator that needs to be taken into consideration is the location of the maximum temperature. Table A1 in appendix lists the domain in which the maximum temperature is located. To achieve optimum results, maximum temperature should preferably lie inside the tumor region. This arrangement is likely to inflict more damage to the tumor and would shield the normal tissue from the thermal damage. For selective killing of tumor, ideally the hyperthermic condition should only be achieved inside the tumor while normal tissue should be protected from the concomitant thermal damage.
5. Conclusion In this research the capacitive hyperthermia was analyzed from the physical perspective. Physical dimensions were treated as parameters and total of six parameters were selected including two tunable parameters namely frequency and applied voltage. Maximum achieved temperature inside the domain was treated as the relevant quality characteristic. Following a systematic analysis underlined by Taguchi's L27 orthogonal array, the effect of each selected parameter was quantified. Moreover, under the framework of capacitive hyperthermia it was concluded that for reliable treatment promising optimum results, thermal damage to the tissue as well as to the tumor needs to be taken into account. Results were analyzed from two perspectives, from treatment
Tmax
Location of Tmax
32.10 41.09 62.04 33.03 41.07 63.68 32.15 38.69 55.79 37.56 59.45 41.16 35.13 47.56 36.70 34.61 42.99 35.70 41.86 36.12 51.90 39.79 36.56 47.25 36.00 34.55 39.54
Tumor Normal Normal Tumor Normal Normal Tumor Normal Normal Normal Normal Normal Tumor Normal Normal Tumor Normal Tumor Normal Normal Normal Tumor Tumor Normal Tumor tumor Normal
objective point of view and from the point of view of tumor killing efficiency. In this context two indices namely treatment index and damage index were defined which highlight the respective perspective quantitatively. It was concluded that treatment objective may be achieved but it may not represent the most efficient treatment protocol. Higher values of both, treatment and damage indices, would qualify a treatment protocol to be the optimum one.
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