Date of Award

Summer 2016

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Weizhong Dai

Abstract

In hyperthermia skin cancer treatment, the objective is to control laser heating of the tumor (target temperatures of 42-46 °C) so that the temperatures of the normal tissue surrounding the tumor remains low enough not to damage the normal tissue. However, obtaining accurate temperature distributions in living tissue related to hyperthermia skin cancer treatment without using an intruding sensor is a challenge. The objective of this dissertation research is to develop a mathematical model that can accurately predict the temperature distribution in the tumor region and surrounding normal tissue induced by laser irradiation. The model is based on a modified Pennes' equation for the bioheat transfer in a 3-D triple-layered skin structure embedded with a vascular countercurrent network and a tumor appearing in the subcutaneous region. The vascular network is designed based on the constructal theory of multi-scale tree-shaped heat exchangers. The tumor is injected with gold nanoshells in order to be heated quickly. The proposed model is implemented numerically using a stable finite-difference scheme. To determine the laser intensity so that an optimal temperature distribution can be obtained, we pre-specify the temperature elevations to be obtained at the center of the tumor and on some locations on the perimeter of the skin's surface. Using the least squares method, we obtain the optimal laser power and develop a computational procedure to obtain the temperature distribution.

The method was tested in a 3-D triple-layered skin structure embedded with a vascular countercurrent network and a tumor appearing in the subcutaneous region. Gold nanoshells are assumed to have been injected into the central region of the tumor. The tumor region that has the gold nanoshells has ? x 109 particles/cm3 for each voxel of 0.01 cm x 0.01 cm x 0.001 cm. The tempeature is elevated by means of laser irradiation. The results show that the nanoshells have an effect on the tumor by heating the entire tumor to above 42 °C while not overheating the surrounding tissue. In comparison, results show that without nanoshells in the tumor region the tumor does heat up along its central axis; however, the perimeter of the tumor fails to reach 42 °C while the top of the skin reaches undesirable temperature levels due to the laser intensity required to heat the tumor. Such research may provide a useful tool for optimizing laser irradiation to kill the tumor while keeping the damage to the surrounding healthy tissue to a minimum (≤ 42 °C) during the hyperthermia cancer treatment.

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