The method of fundamental solutions and a high order continuation for nonlinear bioheat transfer problems during hyperthermia treatment

Abstract

Hyperthermia involves increasing the temperature of targeted skin tissue during cancer treatment, which can directly destroy cancer cells or enhance the effectiveness of therapies such as radiotherapy or chemotherapy. But can also affect surrounding healthy tissues. This paper examines temperature distribution in a two-dimensional skin model. We present evidence that the High Order Continuation Method (HOCM) combined with the Method of Fundamental Solutions (MFS) can be a robust algorithm for solving the nonlinear bioheat transfer problems. The nonlinearity is due to temperature-dependent blood perfusion. Nonlinear problems are transformed into a sequence of linear problems through Taylor series expansions, applied within a continuation technique to compute the complete solution, branch by branch. MFS is coupled with Radial Basis Functions (RBF) to solve inhomogeneous equations. In the absence of a fundamental solution, particularly for operators with variable coefficients, the MFS-RBF method can be combined with the Analog Equation Method (AEM) to solve the resulting linear systems and compute the complete branch of the solution. The results help to estimate temperature distribution and prevent damage during hyperthermia treatment.

Keywords: High Order Continuation Method (HOCM); Hyperthermia; Method of Fundamental Solutions (MFS); Nonlinear bioheat transfer problems; Radial Basis Functions (RBF).