Verified non-linear DPL model with experimental data for analyzing heat transfer in tissue during thermal therapy

Abstract

In this paper, mathematical modeling and simulation of heat transfer in tissue using non-linear dual-phase-lag bioheat transfer (DPLBHT) model under Dirichlet boundary condition has been studied for therapeutic treatment of cancerous or tumorous cells. The components of volumetric heat source in non-linear DPLBHT model such as blood perfusion and metabolism are assumed experimentally validated temperature-dependent function which results in non-linear DPLBHT model in order to predict more accurate. A hybrid numerical method which is based on finite difference and Runge-Kutta (4, 5) schemes, is used to solve the present non-linear problem. The exact solution has been obtained in a particular case and compared with the present numerical scheme, and we found that those are in good agreement. A comparison of models has been made when the variation of blood perfusion rate and metabolism is realistic function of temperature, is of non-linear DPLBHT model, non-linear single-phase-lag bioheat transfer (SPLBHT) model and non-linear Pennes bioheat transfer (PBHT) model with experimental data in same situation and it has been found that non-linear DPL model is closest to the experimental data. The whole paper is analyzed and presented in dimensionless form. The effect of coefficient of blood perfusion rate, dimensionless heating source parameters, relaxation and thermalisation time on dimensionless temperature distribution has been analyzed in treatment process.