Solving the dual-phase lag bioheat transfer equation by the generalized finite difference method

• Autorzy: Turchan Ł.
• Języki publikacji: EN

Abstrakty

EN

The modeling of bioheat transfer process described by the dual-phase lag equation is considered. The basic equation is supplemented by the appropriate boundary-initial conditions. In the central part of the cylindrical domain the heated sub-domain is located. In this region the additional component determining the capacity of an internal heat source is taken into account. At the stage of numerical computations the generalized finite difference method (GFDM) is used. The GFDM nodes distribution is generated in a random way (with some limitations). The examples of computations for different nodes distribution and comparison with the classical finite difference method are presented. In the final part of the paper the conclusions are formulated.

Słowa kluczowe

EN

bioheat transfer; dual-phase lag model; generalized finite difference method

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2017
• Tom: Vol. 69, nr 4-5
• Strony: 389--407
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Turchan Ł.

• Institute of Computational Mechanics and Engineering Silesian University of Technology Konarskiego 18A 44-100 Gliwice, Poland

Bibliografia

• 1. H.H. Pennes, Analysis of tissue and arterial blood temperatures in the resting human forearm, Journal of Applied Physiology, 1, 2, 93–122, 1948.
• 2. M. Stańczyk, J. Telega, Modelling of heat transfer in biomechanics, a review. Part 1. Soft tissues, Acta of Bioengineering and Biomechanics, 1, 4, 31–61, 2002.
• 3. K.N. Rai, S.K. Rai, Heat transfer inside the tissues with a supplying vessel for the case when metabolic heat generation and blood perfusion are temperature dependent, Heat and Mass Transfer, 35, 4, 345–350, 1999.
• 4. M.C. Cattaneo, A form of heat conduction equation which eliminates the paradox of instantaneous propagation, Compte Rendus, 247, 431–433, 1958.
• 5. W. Roetzel, N. Putra, Nandy, S.K. Das, Experiment and analysis for non-Fourier conduction in materials with non-homogeneous inner structure, International Journal of Thermal Sciences, 42, 6, 541–552, 2003.
• 6. K. Mitra, S. Kumar, A. Vedevarz, M.K. Moallemi, Experimental evidence of hyperbolic heat conduction in processed meat, Journal of Heat Transfer, 117, 3, 568–573, 1995.
• 7. M.N. Özisik, D.Y. Tzou, On the wave theory in heat conduction, Journal of Heat Transfer, 116, 3, 526–535, 1994.
• 8. K.C. Liu, Y.N. Wang, Y.S. Chen, Investigation on the bio-heat transfer with the dual-phase-lag effect, International Journal of Thermal Sciences, 58, 29–35, 2012.
• 9. K.C. Liu, Thermal propagation analysis for living tissue with surface heating, International Journal of Thermal Sciences, 47, 5, 507–513, 2008.
• 10. 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, 5–6, 1185–1192, 2009.
• 11. P. Kumar, D. Kumar, K.N. Rai, A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment, Journal of Thermal Biology, 49–50, 98–105, 2015.
• 12. J. Zhou, J.K. Chen, Y. Zhang, Dual-phase lag effects on thermal damage to biological tissues caused by laser irradiation, Computers in Biology and Medicine, 39, 3, 286–293, 2009.
• 13. 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, 1477–1485, 2009.
• 14. M.A. Castro, J.A. Martin, F. Rodriguez, Unconditional stability of a numerical method for the dual-phase-lag equation, Mathematical Problems in Engineering, 2017, 5, 2017.
• 15. S. Singh, S. Kumar, Numerical study on triple layer skin tissue freezing using dual phase lag bio-heat model, International Journal of Thermal Sciences, 86, 12–20, 2014.
• 16. E. Majchrzak, L. Turchan, J. Dziatkiewicz, Modeling of skin tissue heating using the generalized dual phase-lag equation, Archives of Mechanics, 67, 6, 417–437, 2015.
• 17. H. Wang, W. Dai, R. Melnik, A finite difference method for studying thermal deformation in a double-layered thin film exposed to ultrashort pulsed lasers, International Journal of Thermal Sciences, 45, 12, 1179–1196, 2006.
• 18. J. McDonough, I. Kunadian, R. Kumar, T. Yang, An alternative discretization and solution procedure for the dual phase-lag equation, Journal of Computational Physics, 219, 1, 163–171, 2006.
• 19. E. Majchrzak, B. Mochnacki, Sensitivity analysis of transient temperature field in microdomains with respect to the dual-phase-lag model parameters, International Journal for Multiscale Computational Engineering, 12, 1, 65–77, 2014.
• 20. M. Ciesielski, B. Mochnacki, Application of the control volume method using the Voronoi polygons for numerical modeling of bio-heat transfer processes, Journal of Theoretical and Applied Mechanics, 52, 4, 927–935, 2014.
• 21. E. Majchrzak, Numerical solution of dual phase lag model of bioheat transfer using the general boundary element method, CMES: Computer Modeling in Engineering and Sciences, 69, 1, 43–60, 2010.
• 22. E. Majchrzak, L. Turchan, The general boundary element method for 3D dual-phase lag model of bioheat transfer, Engineering Analysis with Boundary Elements, 50, 76–82, 2015.
• 23. B. Yu, W.A. Yao, H.L. Zhou, H.L. Chen, Precise time-domain expanding BEM for solving non-Fourier heat conduction problems, Numerical Heat Transfer, Part B: Fundamentals, 68, 6, 511–532, 2015.
• 24. T. Liszka, J. Orkisz, The finite difference method at arbitrary irregular grids and its application in applied mechanics, Computers and Structures, 11, 1–2, 83–95, 1980.
• 25. L. Gavete, J.J. Benito, F. Ureña, Generalized finite differences for solving 3D elliptic and parabolic equations, Applied Mathematical Modelling, 40, 2, 955–965, 2016.
• 26. L. Gavete, F. Ureña, J.J. Benito, A. García, M. Ureña, E. Salete, Solving second order non-linear elliptic partial differential equations using generalized finite difference method, Journal of Computational and Applied Mathematics, 318, 378–387, 2017.
• 27. B. Mochnacki, E. Pawlak, Numerical modelling of non-steady thermal diffusion on the basis of generalized FDM, [in:] Advanced Computational Methods in Heat Transfer V, Computational Studies, 33–42, 1998.
• 28. B. Mochnacki, E. Majchrzak, Numerical modeling of casting solidification using generalized finite difference method, [in:] THERMEC 2009, Materials Science Forum, 638, 2676–2681, Trans Tech Publications, 2010.
• 29. E. Majchrzak, L. Turchan, G. Kałuża, Sensitivity analysis of temperature field in the heated tissue with respect to the dual-phase-lag model parameters, [in:] Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues, M. Kleiber, T. Burczyński, K. Wilde, J. Górski, K. Winkelmann, L. Smakosz (Eds.), CRC Press/Balkema, 371–375, 2016.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).