A numerical solution of heat transfer problem of dpl model in living biological tissues amidst hyperthermia treatment

Abstract

Accurate prediction and temperature control are necessary for the successful treatment of cancer during hyperthermia. The main objective of this paper is to solve a highly complex nonlinear dual-phase-lag (DPL) model by a method that uses less computational effort in order to achieve accurate results. This paper also focuses on showing the variation in results due to variation in several factors, which will help improve hyperthermia treatment in the clinical field. For this, a mathematical model has been studied that describes the heat transfer process in living biological tissues as having different values of parameters under different boundary conditions amidst hyperthermia treatment. The finite difference method is used to convert the boundary value problem supervising the process of bioheat transfer into an initial value problem of ordinary differential equations. Then, the Runge–Kutta (4, 5) method is applied to find the dimensionless temperature of the tissue. The whole analysis is presented in nondimensional form. Effects are discussed in detail for different properties of biological tissues such as blood perfusion rate, thermal relaxation time of heat flux, and thermal relaxation time of temperature gradient at the target region during hyperthermia treatment. Effects are also observed for different kinds of boundary conditions. Study of these effects is very useful during the treatment to avoid any harm to neighboring healthy tissues. Thus, this study becomes more useful in clinical fields, especially for oncologists. © 2020 by Begell House, Inc.