تجزیه و تحلیل انتقال حرارت در بافت زنده چند لایه به روش نیمه تحلیلی باقی مانده‌های وزنی گلرکین

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشیار مهندسی مکانیک، دانشکده مهندسی مکانیک، دانشگاه کاشان، کاشان، ایران

2 دانشجوی دکترای مهندسی مکانیک، دانشکده مهندسی مکانیک، دانشگاه کاشان، کاشان، ایران

چکیده

در این تحقیق، رفتار حرارتی بافت زنده در فرایند گرمادرمانی به وسیله منبع گرمایی الکترومغناطیسی مورد مطالعه قرار می‌گیرد. اگرچه معادله انتقال حرارت فوریه و غیرفوریه در بافت زنده تحت شرایط مرزی مختلف مطالعه شده است؛ اما، مطالعه بافت چندلایه با در نظر گرفتن اثرات غیرفوریه‌ای خصوصا به شکل تحلیلی و نیمه تحلیلی کمتر مورد توجه قرار گرفته است. در پژوهش حاضر با استفاده از روش نیمه‌تحلیلی باقی مانده‌های وزنی گلرکین، معادلات انتقال حرارت غیرفوریه‌ای تاخیر فاز دوگانه در بافت زنده چندلایه به همراه تومور حل شده است. نتایج نشان می‌دهد که چندلایه در نظر گرفتن بافت به همراه خواص مختص هر لایه، تاثیر به سزایی در توزیع دمای درون بافت خواهد داشت به طوری‌که این اختلاف دما پس از گذشت 1800 ثانیه به 2 درجه سانتی‌گراد می‌رسد. همچنین، تاثیر عدد ورنوت بر توزیع دمای بافت نشان می‌دهد که با افزایش زمان آسایش شار، سرعت سیگنال دمایی کاهش می‌یابد و در نتیجه آن دمای تومور کاهش خواهد یافت. بررسی پارامترهایی مانند دمای سطح پوست و میزان پرفیوژن خون نشان می‌دهد که خنک‌کاری بیشتر دمای سطح پوست در طول فرایند گرما درمانی موجب انتقال نقطه بیشینه دما به عمق بیشتری از بافت می‌گردد. همچنین کاهش پرفیوژن خون که در تومورهای هیپوکسی اتفاق می‌افتد موجب افزایش دما در تومور حین فرایند گرمادرمانی می‌گردد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Analysis of the Heat Transfer in a Multilayer Living Tissue Using the Galerkin Weighted Residuals Method

نویسندگان [English]

  • Ali Akbar Abbasian Arani 1
  • Ali Arefmanesh 1
  • Armin Emamifar 2
1 Associate Professor of Mechanical Engineering, Mechanical Engineering Department, University of Kashan, Kashan, Iran
2 Ph.D Candidate of Mechanical Enginerring, Mechanical Engineering Department, University of Kashan, Kashan, Iran
چکیده [English]

In this paper, the thermal behavior of living biological tissue during electromagnetic radiation thermal therapy is investigated. While a large number of studies devoted to the Fourier and non-Fourier heat transfer in living tissue are available for different boundary conditions, less analytical and semi-analytical works exist on the heat transfer in the multilayers tissue. In the present study, semi- analytical Galerkin weighted residuals method is used to solve the dual-phase lag non-Fourier heat transfer equation in the multilayer tissue with a tumor placed in. The results show that considering a multilayer tissue with distinct thermophysical properties for each layer has a remarkable effect on the temperature distribution in the tissue, so that 2°C difference in tumor temperature after 1800 s is observed. The effect of the Vernot number on the temperature distribution shows that increasing the flux relaxation time results in reducing the temperature signal velocity and the tumor temperature. Lowering the skin surface temperature, decreases the high values of temperature and forces the maximum temperature region deeper into the tissue. Moreover, the reduction in the blood perfusion rate that occurs in the hypoxic tumors results in the increase of the tumors temperatures during the thermal therapy.

کلیدواژه‌ها [English]

  • Non-Fourier heat transfer
  • Galerkin weighted residuals
  • Multilayer tissue
  • Thermal therapy

مراجع

[1] R.W. Habash, R. Bansal, D. Krewski, H.T. Alhafid, Thermal therapy, part 1: an introduction to thermal therapy, Critical reviews in biomedical engineering, 34(6) (2006) 459-489.
[2]   M.H. Seegenschmiedt, C.C. Vernon, A Historical Perspective on Hyperthermia in Oncology, in: M.H. Seegenschmiedt, P. Fessenden, C.C. Vernon (Eds.) Thermoradiotherapy and Thermochemotherapy: Biology, Physiology, Physics, Springer Berlin Heidelberg, Berlin, Heidelberg, 1995, pp. 3-44.
[3] D. Kumar, S. Singh, K.N. Rai, Analysis of classical Fourier, SPL and DPL heat transfer model in biological tissues in presence of metabolic and external heat source, Heat and Mass Transfer, 52(6) (2016) 1089-1107.
[4] K. Shchors, G. Evan, Tumor Angiogenesis: Cause or Consequence of Cancer?, Cancer Research, 67(15) (2007) 7059.
[5]  H.H. Pennes, Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm, Journal of Applied Physiology, 1(2) (1948) 93-122.
[6] C. Cattaneo, J. Kampé de Fériet,  s.  Académie  des, Sur une forme de l'équation de la chaleur éliminant le paradoxe d'une propagation instantanée, [Gauthier- Villars], [Paris], 1958.
[7] J.P. Hartnett, Luikov, A. V., CHAPTER 1 - PHYSICAL FUNDAMENTALS OF HEAT TRANSFER, in:Analytical Heat Diffusion Theory, Academic Press, 1968, pp. 1-34.
[8] D.Y. Tzou, A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales, Journal of Heat Transfer, 117(1) (1995) 8-16.
[9]    J. Zhou, Y. Zhang, J.K. Chen, Non-Fourier Heat Conduction Effect on Laser-Induced Thermal Damage in Biological Tissues, Numerical Heat Transfer, Part A: Applications, 54(1) (2008) 1-19.
[10]  B. Kundu, Exact analysis for propagation of heat in a biological tissue subject to different surface conditions for therapeutic applications, Applied Mathematics and Computation, 285 (2016) 204-216.
[11]  H. Askarizadeh, H. Ahmadikia, Analytical study on the transient heating of a two-dimensional skin tissue using parabolic and hyperbolic bioheat transfer equations, Applied Mathematical Modelling, 39(13) (2015) 3704- 3720.
[12]   H. Ziaeipoor, H. Moosavi, a. morad, Analysis of the DPL Bio- Heat Transfer Equation with Constant and Time- Dependent Heat Flux Conditions on Skin Surface, 2015.
[13]  B. Kundu, D. Dewanjee, A new method for non-Fourier thermal response in a single layer skin tissue, Case Studies in Thermal Engineering, 5 (2015) 79-88.
[14]  K.-C. Liu, H.-T. Chen, Analysis for the dual-phase-lag bio-heat transfer during magnetic hyperthermia treatment, International Journal of Heat and Mass Transfer, 52(5) (2009) 1185-1192.
[15]  Z.-S. Deng, J. Liu, Analytical Study on Bioheat Transfer Problems with Spatial or  Transient  Heating on Skin Surface or Inside BiologicalBodies, Journal of Biomechanical Engineering, 124(6) (2002) 638-649.
 
[16] T.C. Shih, P. Yuan, W.L. Lin, H.S. Kou, Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface, Medical engineering & physics, 29(9) (2007) 946-953.
[17] K.-C. Liu, Thermal propagation analysis for living tissue with surface heating, International Journal of Thermal Sciences, 47(5) (2008) 507-513.
[18] H. Askarizadeh, H. Ahmadikia, Analytical Solution of the classical and generalized dual phase lag heat transfer equations in skin tissue under transient heating, Modares Mechanical Engineering, 13(Special issue 13) (2014) 14- 25. (in Persian).
[19] F. Xu, K.A. Seffen, T.J. Lu, Non-Fourier analysis of skin biothermomechanics, International Journal of Heat and Mass Transfer, 51(9) (2008) 2237-2259.
[20] M.M. Tung, M. Trujillo, J.A. López Molina, M.J. Rivera, E.J. Berjano, Modeling the heating of biological tissue based on the hyperbolic heat transfer equation,  Mathematical and Computer Modelling, 50(5) (2009) 665-672.
[21] R.M. Cotta, B.P. Cotta, C.P. Naveira-Cotta, G. Cotta- Pereira, Hybrid integral transforms analysis of the bioheat equation with variable properties, International Journal of Thermal Sciences, 49(9) (2010) 1510-1516.
[22] P.K. Gupta, J. Singh, K.N. Rai, Numerical simulation for heat transfer in tissues during thermal therapy, Journal of Thermal Biology, 35(6) (2010) 295-301.
[23] D. Kumar, K.N. Rai, A study on thermal damage during hyperthermia treatment based on DPL model for multilayer tissues using finite element Legendre wavelet Galerkin approach, Journal of Thermal Biology, 62 (2016) 170-180.
[24]  P. Kumar, D. Kumar, K.N. Rai, Non-linear dual-phase- lag model for analyzing heat transfer phenomena in living tissues during thermal ablation, Journal of Thermal Biology, 60 (2016) 204-212.
[25]   P. Kumar, D. Kumar, K.N. Rai, Numerical simulation of dual-phase-lag bioheat transfer model during thermal therapy, Mathematical Biosciences, 281 (2016) 82-91.
[26]   P.K. Gupta, J. Singh, K.N. Rai, S.K. Rai, Solution of the heat transfer problem in tissues during hyperthermia by finite difference–decomposition method, Applied Mathematics and Computation, 219(12) (2013) 6882- 6892.
[27]  Y. Zhang, B. Chen, D. Li, Non-Fourier effect of laser- mediated thermal behaviors in bio-tissues: A numerical study by the dual-phase-lag model, International Journal of Heat and Mass Transfer, 108 (2017) 1428-1438.
[28]   J. Zhou, Y. Zhang, J.K. Chen, An axisymmetric dual- phase-lag bioheat model for laser heating of living tissues, International Journal of Thermal Sciences, 48(8) (2009) 1477-1485.
[29]  A.K. Verma, P. Rath, S.K. Mahapatra, Assessment of Thermal Damage During Skin Tumor Treatment Using Thermal Wave Model: A Realistic Approach, Journal of Heat Transfer, 139(5) (2017) 051102-051102-051109.
[30]  S. Nóbrega, P.J. Coelho, A parametric study of thermal therapy of skin tissue, Journal of Thermal Biology, 63 (2017) 92-103.
[31]  G.R. Ströher, G.L. Ströher, Numerical thermal analysis of skin tissue using parabolic and hyperbolic approaches, International Communications in Heat and Mass Transfer, 57 (2014) 193-199.
[32]  M. Mital, H.V. Tafreshi, A methodology for determining optimal thermal damage in magnetic nanoparticle hyperthermia cancer treatment, International  Journal  for numerical methods in biomedical engineering, 28(2) (2012) 205-213.
[33]   M. M. Heidar, M.R., M. Nasiri, Analytical Solution  of Heat Transfer in LaserIrradiated Skin Tissue with Surface Heat Convection Using Dual Phase Lag Model, Amirkabir Journal of Mechanical Engineering, 50 (2018) 285-294. (in Persian)
[34]   A. Zolfaghari, H. Bijari, A new index for evaluating thermal sensation based on the principles of non- Fourier heat transfer, Amirkabir Journal of Mechanical Engineering 2018, 10.22060/mej.2018.14472.5866. (in Persian)
[35]   A. Welch, The thermal response of laser irradiated tissue, IEEE Journal of Quantum Electronics, 20(12) (1984) 1471-1481.
[36]   P. Bogacki, L.F. Shampine, An efficient Runge-Kutta (4,5) pair, Computers & Mathematics with Applications, 32(6) (1996) 15-28.
[37]   D. Kumar, K.N. Rai, Numerical simulation of time fractional dual-phase-lag model of heat transfer within skin tissue during thermal therapy, Journal of Thermal Biology, 67 (2017) 49-58.
[38]   S. Kumar, A. Srivastava, Thermal analysis of laser- irradiated tissue phantoms using dual phase lag model coupled with transient radiative transfer equation, International Journal of Heat and Mass Transfer, 90 (2015) 466-479.
نشریه مهندسی مکانیک امیرکبیر
دوره 52، شماره 9
آذر 1399
صفحه 2609-2626

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