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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.

1D generalized dual-phase lag equation. Sensitivity analysis with respect to the porosity

Kałuża G., Majchrzak E., Turchan Ł.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 1

49--58

Thermal processes occurring in the heated tissue are described by the 1D generalized dual-phase lag equation supplemented by appropriate boundary and initial conditions. Using the sensitivity analysis method, the additional problem connected with the porosity is formulated. Both problems are solved by means of the explicit scheme of the finite difference method. In this way it is possible to estimate the temperature changes due to the perturbation of porosity. In the final part of the paper, the example of computation is shown and the conclusions are formulated.