Date of Award

Spring 2006

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computational Analysis and Modeling

First Advisor

Weizhong Dai


The research related to hyperthermia has stimulated a lot of interest in recent years because of its application in cancer treatment. When heating the tumor tissue, the crucial problem is keeping the temperature of the surrounding normal tissue below a certain threshold in order to avoid the damage to the normal tissue. Hence, it is important to obtain the temperature field of the entire region during the treatment. The objective of this dissertation is to develop a numerical method for obtaining an optimal temperature distribution in a 3D triple-layered skin structure embedded with multi-level blood vessels where the surface of the skin is irradiated by laser. The skin structure is composed of epidermis, dermis and subcutaneous, while the dimension and blood flow of the multi-level blood vessels are determined based on the constructal theory of multi-scale tree-shaped heat exchangers. The method determines the optimal laser intensity to obtain prespecified temperatures at the given locations of the skin after a pre-specified laser exposure time under a pre-specified laser irradiation pattern.

The modified Pennes bio-heat transfer model is employed to describe the thermal behavior for tissue coupled with the convective energy balance equations for blood. The finite difference schemes for solving these equations are developed and the least squares method is used to optimize the laser power. As such, we develop an algorithm which can be used to obtain an optimal temperature distribution. Furthermore, the preconditioned Richardson iteration and Thomas algorithm are employed to speed up and simplify the computation. To demonstrate the applicability of the mathematical model and the numerical method, we test on three examples in each of which two cases are considered. The numerical examples show that the method is applicable and efficient.

This research is important since the results will provide the clinician with powerful tools to improve the ability to deliver safe and effective therapy and the means to assess treatment safety, efficacy, and clinical outcome for skin, head, and neck cancer treatments.