Numerical study of a dual-phase-lag bioheat transfer model via finite element Runge-Kutta (4,5) in spherical tissue with temperature-dependent blood perfusion during magnetic hyperthermia

Abstract

The present article involves a dual-phase-lag nonlinear bioheat model for living spherical tissue during magnetic hyperthermia. In this study, we considered temperature-dependent blood perfusion to forecast accurate hyperthermia temperature for the treatment of tumor cells. Due to the nonlinearity, this problem is handled by a finite element Runge-Kutta (4,5) technique, which is a combination of Runge-Kutta (4,5) and finite difference approaches. In this technique, we discretize the partial derivatives of space variables by using the central difference scheme. After the discretization, the current problem turns out as a system of second-order ODEs with initial conditions. Again, we convert the system of second-order ODEs into the system of first-order coupled ODEs. Then, we employed the RK (4,5) scheme to resolve the problem completely for time interval. The result obtained by the present numerical scheme is validated through an exact analytical result in a special situation, and it is noticed that both results are very close to each other. After analyzing the results, we found that when tumor cells are treated by magnetic hyperthermia, temperature-dependent blood perfusion significantly affects the hyperthermia temperature. It is seen that the impact of quadratically temperature-dependent blood perfusion is more effective than the linearly temperature-dependent types of blood perfusion. The convection effect due to the quadratically temperature-dependent term in the blood perfusion is greater than the other terms. The magnetic heat source is crucial in regulating the temperature inside the living tissue for determining hyperthermia temperature. By rising the ratio of lagging time due to heat flux ((Formula presented.)) and temperature gradient ((Formula presented.)), the temperature profile drops, and these effects are observed initially for a few seconds. © 2025 Taylor & Francis Group, LLC.