Determining the heat strength required in hyperthermia treatments
☆
Ching-yu Yang
Department of Mold and Die Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung City 807, Taiwan, ROC
a b s t r a c t
a r t i c l e i n f o
Available online 16 August 2014 Keywords:
Hyperthermia treatment Thermal therapy Tumor
Therapeutic temperature
For providing effective hyperthermia treatment, determining the input heat required is critical. In this study, a computational method was developed to predict the heat input that is suitable for various heating durations used during hyperthermia treatment. The unknown heat input was denoted as a variable in an equation that was formulated based on a therapeutic temperature and the calculated temperature, and the equation was then solved using an iterative process. Here, one example that was used to demonstrate the characteristics of the proposed method is presented. The numerical results indicated that the predicted heat input is adequate for the hyperthermia treatment process.
© 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Magnetic hyperthermia is a thermal therapy used to treat tumors. Gilchrist et al.[1]first reported that, in magnetic hyperthermia, fine magnetic particles are localized within tumor tissues; these particles potentially act as a localized heat source when an alternating magnetic field is applied to the target region. The challenge faced in providing effective hyperthermia therapy is in achieving an optimal treatment outcome without damaging healthy tissues. Thus, over the past decades, numerous studies have investigated the distribution of temperature during hyperthermia therapy.
To model small breast carcinomas, Ardra et al.[2]formulated a spherical region containing magnetic particles and used analytically derived equations to calculate the spatial temperature distribution as function of the time of exposure to an alternating magneticfield. Moroz et al.[3]and Maenosono et al.[4]reported that magnetic hyper-thermia produced fewer restrictive side effects than did chemotherapy and radiotherapy, and the treatment exhibited the maximal potential for selective targeting of tumor tissues. Lin and Liu[5]used a transient bioheat equation to predict the rise in temperature within biological tissues during hyperthermia induced using magnetic nanoparticles. Similar studies were conducted by Liu and Lin[6]on hyperbolic heat transfer and by Liu and Chen[7]on dual-phase-lag heat transfer. In addition, studies have proposed methods for achieving an optimal temperature distribution in order to apply hyperthermia treatment in a manner that destroys the entire tumor region without affecting any healthy tissue. To avoid the problem of overdosing, Cheng and Roemer [8]optimized the thermal dose by using the Sapareto–Dewey formu-la[9]after the heating period. Bagaria and Johnson[10]optimized the
concentration of magnetic particles by using a quadratic spatial varia-tion of heat generavaria-tion in a hyperthermia process.
In this paper, the heat input required for a bioheat model is proposed; this model can be used to predict an effective hyperthermia treatment that destroys tumor tissues but does not damage healthy tissues. In the approached described herein, the predicted heat input, the therapeutic temperature, and the intermediate calculated temperature are formulat-ed in an equation, which is solvformulat-ed using an iterative process in order to determine the proper heat input for various heating durations. 2. The proposed method for selecting the heat input suitable for hyperthermia treatment
2.1. Problem statement
A tumor surrounded by normal tissue is modeled herein as two fi-nite concentric spherical regions, with the inner and outer spheres representing the diseased and healthy tissues, respectively. The dis-eased tissue contains the tumor and the magnetic particles that serve as a heat source of constant power density when an alternating magnetic field is applied. The heat is transferred symmetrically along the direction of the radius. The time-dependent distribution of temperature in the tumor and normal tissues varies with the distance r and the power density. This is a bioheat conduction problem and it is described using the following equation[5]:
ρ1c1∂T1 ∂t ¼ k1 1 r2 ∂ ∂r r 2∂T1 ∂r þ ωb1ρbcbðTb−T1Þ þ qm1 þ P u tð Þ−u t−tf h i for 0≤ r ≤ R ð1Þ ρ2c2∂T2∂t ¼ k21 r2 ∂ ∂r r 2∂T2 ∂r þ ωb2ρbcbðTb−T2Þ þ qm2 for R≤ r ≤ a ð2Þ International Communications in Heat and Mass Transfer 57 (2014) 282–285
☆ Communicated by W.J. Minkowycz. E-mail address:cyyang@cc.kuas.edu.tw.
http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.08.014 0735-1933/© 2014 Elsevier Ltd. All rights reserved.
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International Communications in Heat and Mass Transfer
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i c h m tconstant when tfwasN400 s. For example, the determined value of P was
2,960,714.000 W/m3at t
f= 20 s and 1,808,231.265 W/m3at tf= 40 s, but
the P value approached a constant near 930,000.000 W/m3 when
tf≥ 400 s. To further illustrate the temperature response under various
conditions, the temperature responses obtained when the duration tf
wasb400 s are shown inFigs. 2–4, and the responses obtained when tf
wasN400 s are shown inFigs. 5–6. In the case of tfb 400 s, to investigate
the status of tissue heating, the temperature responses calculated for a heating duration tf= 80 s are shown inFig. 2. InFig. 2, the temperature
responses shown are 49.327, 47.735 and 42.5 °C at r = 0, 0.0025, and 0.005 m, respectively. Thus, the therapeutic temperature in the tumor re-gion wasN42.5 °C; at this temperature, the tumor tissue can be potential-ly destroyed. InFig. 3, the temperature distribution across the medium is shown for tf= 40, 80, and 120 s; the slope at r = 0.005 m is negative, and
the temperature wasb42.5 °C when r N 0.005 m, indicating that healthy tissue was not damaged.Fig. 4shows the temperature responses at various heating durations when r = 0.005 m, and the results indicated that the hyperthermia treatment was effective when various heating durations were used. In the case of tf≥ 400 s, the temperature responses
exhibited a similar trend at tf= 400, 600 and 800 s (Fig. 5), implying
that the input heat energy was balanced by the dispersion of the heat caused by blood perfusion. The results inFig. 6show that the slope at
r = 0.005 m is negative, indicating that this temperature response was lower than the therapeutic temperature when rN 0.005 m. Thus, the healthy tissue was not damaged even when the heating duration was increased.
The numerical results presented in this section were obtained by using the proposed method together with a model of the hyperthermia treatment process. First, the results indicated that a comprehensive hyperthermia treatment was achieved because the tumor tissue could be destroyed without damaging the healthy tissue. Second, the input power density approached a stable value and the temperature responses exhibited similar trends when the selected heat duration was increased. These results support the conclusion that the proposed method can be used to determine the heat input that is appropriate for hyperthermia treatment.
4. Conclusions
This preliminary study was conducted to predict the heat input required during hyperthermia treatment and to establish a method for treating tumor tissues without damaging healthy tissues. In the pro-posed approach, the magnitude of the input heat is determined based on the expected heating duration that is selected. The numerical results indicated that the estimated heat input is sufficient for destroying dis-eased tissues without affecting healthy tissues. Moreover, this method can be used to develop long-term therapy because the input heat and the temperature are stabilized when the selected heating duration is extended. The results revealed that the proposed algorithm can be used effectively in predicting the heat input in hyperthermia-treatment prob-lems. In conclusion, in the proposed method, a validated numerical pro-cess is used to determine the treatment parameters employed in thermal therapy and to evaluate heating in multidimensional problems. References
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of thermal wave, Numer. Heat Transfer, Part A 58 (2010) 819–833. 37 38 39 40 41 42 43 0 200 400 600 800 1000 tf= 40 s tf= 80 s tf = 120 s tf= 160 s tf= 240 s tf = 320 s tf= 400 s Te m pe ra tu re ( 0C ) Temporial-coordinate (s)
Fig. 4. Temperature response at r = 0.005 m when the heating duration tf= 40, 80, 120,
160, 240, 320 and 400 s. 37 38 39 40 41 42 43 0 200 400 600 800 1000 tf= 400 s tf = 600 s tf= 800 s Temporial-coordinate (s) Te m pe ra tu re ( 0C )
Fig. 5. Temperature response at r = 0.005 m when the heating duration tf= 400, 600 and
800 s. 36 38 40 42 44 46 48 50 0 0.005 0.01 0.015 t = 400 s when tf = 400 s t = 600 s when tf = 600 s t = 800 s when tf = 800 s Spatial-coordinate (m) Tem pe rat ur e ( 0C )
Fig. 6. Temperature response along the spatial-coordinate r when the heating duration tf= 400, 600 and 800 s.
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