Modeling Heat Transfer Using an Integral Equation Approach via Green's Function: Application to Cancerous Tumor Undergoing Hyperthermia Treatment

Abstract

In recent years, studies have been performed in which cancer tissues are exposed to high temperatures in order to damage/kill cancer cells. This treatment is referred to as hyperthermia, and the goal of this work is to develop a model that describes the heat transfer and temperature profile throughout a cancerous tumor undergoing hyperthermia. The model consists of two portions: linear and nonlinear aspects. The linear aspects of this transient model involve the accumulation and conductive transport terms of the model, while the nonlinear aspect of the model involves the heat sources term resulting from applied hyperthermia treatment. The resulting model equation is a second-order, non-homogeneous partial differential equation and is challenging to solve using standard methods such as separation of variables, etc. Instead, a Green's function approach is employed which allows the problem to become decoupled and solved through the use of integral equations and associated eigenvalue problems.