Comparison of bio-heat transfer numerical models based on the Pennes and Cattaneo-Vernotte equations

• Autorzy: Ciesielski M. , Duda M. , Mochnacki B.

Identyfikatory

DOI

10.17512/jamcm.2016.4.04

• Języki publikacji: EN

Abstrakty

EN

The homogeneous soft tissue domain subjected to an external heat source is considered. Thermal processes in this domain are described using the well known Pennes equation and next the Cattaneo-Vernotte one. Within recent years the prevailing view is that the Cattaneo-Vernotte equation better describes the thermal processes proceeding in the biological tissue (it results from the specific internal tissue structure). Appearing in this equation the delay time of heat flux with respect to the temperature gradient (τq) is of the order of several seconds and the different values of τq are taken into account. At the stage of numerical modeling the finite difference method is used. In the final part of the paper, the examples of computations are shown.

Słowa kluczowe

EN

bioheat transfer; Pennes equation; Cattaneo-Vernotte equation; numerical modeling of heating process; finite difference method

PL

przepływ biociepła; równanie Pennesa; równanie Cattaneo-Vernotte; metoda różnic skończonych; modelowanie numeryczne

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 4
• Strony: 33--38
• Opis fizyczny: Bibliogr 12 poz., rys.

Twórcy

autor

Ciesielski M.

• Institute of Computer and Information Sciences, Czestochowa University of Technology Częstochowa, Poland

autor

Duda M.

• University of Occupational Safety Management in Katowice Katowice, Poland

autor

Mochnacki B.

• University of Occupational Safety Management in Katowice Katowice, Poland

Bibliografia

• [1] Pennes H.H., Analysis of tissue and arterial blood temperatures in the resting human forearm, J. Appl. Physiol. 1948, 1, 93-122.
• [2] Majchrzak E., Mochnacki B., Jasinski M., Numerical modelling of bioheat transfer in multilayer skin tissue domain subjected to a flash fire, Computational Fluid and Solid Mechanics 2003, 1-2, 1766-1770.
• [3] Jasinski M., Modelling of tissue thermal injury process with application of direct sensitivity method, Journal of Theoretical and Applied Mechanics 2014, 52, 4, 947-957.
• [4] Majchrzak E., Modelowanie i analiza zjawisk termicznych, Rozdział 4, Biomechanika, Tom XII Mechanika Techniczna, Ed. R. Bedzinski, IPPT PAN, 2011, 223-362.
• [5] Ciesielski M., Mochnacki B., Application of the control volume method using the Voronoi polygons for numerical modeling of bio-heat transfer processes, Journal of Theoretical and Applied Mechanics 2014, 52, 4, 927-935.
• [6] Cattaneo M.C., A form of heat conduction equation which eliminates the paradox of instantaneous propagation, C.R. Acad. Sci. I - Math., 1958, 247, 431-433.
• [7] Antaki P.J., New interpretation of non-Fourier heat conduction in processed meat, ASME J. Heat Transfer 2005, 127, 189-193.
• [8] Majchrzak E., Numerical solution of dual phase lag model of bioheat transfer using the general boundary element method, CMES - Computer Modeling in Engineering & Sciences 2010, 69, 1, 43-60.
• [9] Majchrzak E., Turchan L., The general boundary element method for 3D dual-phase lag model of bioheat transfer, Engineering Analysis with Boundary Elements 2015, 50, 76-82.
• [10] Mochnacki B., Computational simulations and applications. Numerical modeling of solidification process (Chapter 24), Ed. Jianping Zhu, INTECH, 2011, 513-542.
• [11] Tuzikiewicz W., Duda M., Bioheat transfer equation. The problem of FDM explicit scheme stability, Journal of Applied Mathematics and Computational Mechanics 2015, 14(4), 139-144.
• [12] Mochnacki B., Tuzikiewicz W., Cattaneo-Vernotte bioheat transfer equation. Stability conditions of numerical algorithm based on the explicit scheme of finite difference method, Journal of Applied Mathematics and Computational Mechanics 2016, 15(4), 137-144.

Uwagi

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