(182p) Modeling Heat Transfer Using an Integral Equation Approach Via Green’s Function: Application to Cancerous Tumor Undergoing Hyperthermia Treatment

Allred, A. N., Tennessee Technological University
Liu, Y. W., Tennessee Technological University
Sanders, J. R., Tennessee Technological University
Arce, P. E., Tennessee Technological University
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 used in engineering. 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. This approach also allows for a certain “flexibility” through which the generation function can be manipulated without altering the Green’s function, thus allowing for multiple scenarios to be modeled efficiently. Another possible implication of this work is utilizing the information provided by the temperature profile in order to predict the killing rate of cancerous tissues (and possibly even the killing/healing rate of healthy tissues) which can be described using an F-kill ratio described by Pascal, et al. 2013. Fundamental aspects and illustration will be described in the contribution.


  1. Pascal, Jennifer, et al. “Mechanistic Patient-Specific Predictive Correlation of Tumor Drug Response with Microenvironment and Perfusion Measurements.” Proceedings of the National Academy of Sciences, vol. 110, no. 35, Aug. 2013, p. 14266, doi:10.1073/pnas.1300619110.