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Numerical analysis of biological tissue heating using the dual-phase lag equation with temperature - dependent parameters

Majchrzak Ewa, Stryczyński Mikołaj

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 3

85--98

The dual-phase lag equation is formulated for the case when the thermophysical parameters occurring in this equation are temperature-dependent. The axial-symmetrical domain of biological tissue heated by an external heat source is considered. The problem is solved using the implicit scheme of the finite difference method. At the stage of numerical computations, the analytical relationships taken from the literature describing changes in parameters are taken into account.

Identification of boundary heat flux assuring the destruction of target region of biological tissue application of the generalized dual-phase lag model and gradient method

Turchan Łukasz, Majchrzak Ewa

Computer Assisted Methods in Engineering and Science

2019

Vol. 26, no. 1

21--34

In this paper, an axially symmetrical biological tissue domain subjected to an external heat source is analyzed. The thermal processes occurring in the domain considered are described using the generalized dual-phase lag model supplemented by the Neumann boundary conditions and the appropriate initial conditions. The problem of tissue heating is solved using the implicit scheme of the finite difference method. The obtained solution allows one to determine the local and temporary values of the Arrhenius integral. Next, the inverse problem related to the identification of the boundary heat flux assuring the postulated destruction of the tissue target region is considered. The problem is solved using the gradient method. In the final part of the paper, the results of computations and the conclusions are presented.