Date of Award

Summer 2004

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Weizhong Dai

Abstract

Investigations on instantaneous skin burns are useful for an accurate assessment of burn-evaluation and for establishing thermal protections for various purposes. Meanwhile, hyperthermia with radiation is important in the treatment of cancer, and it is essential for developers and users of hyperthermia systems to predict, and interpret correctly the biomass thermal and vascular response to heating. In this dissertation, we employ the well-known Pennes' bioheat transfer equation to predict the degree of skin burn and the temperature distribution in hyperthermia cancer treatment.

A fourth-order compact finite difference scheme is developed to solve Pennes' bioheat transfer equation in a three-dimensional single vessel embedded triple-layered skin structure, with two different boundary conditions (constant heating and insulation) on the top surface. To this end, we employ the fourth-order compact finite difference method to discretize the Pennes' bioheat equation, where the second-order derivatives of temperature at boundaries and interfaces are calculated using a combined compact finite difference method incorporating the boundary conditions and interfacial conditions. As such, the solution system becomes a diagonal-dominated tridiagonal linear system.

To demonstrate the applicability of the scheme, we investigate four physical models. Numerical results show that this compact finite difference scheme is unconditionally stable for a one-dimensional uniform-layered skin structure and more accurate than the Crank-Nicholson scheme. The comparison of the numerical results in the three-dimensional triple-layered skin structures shows that the blood vessel has a significant influence on the thermal response of the biomass. Thus, the outcomes described above provide a reliable, flexible and efficient numerical method for solving Pennes' bioheat model in a comparatively realistic skin structure.

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