Document Type

Thesis - University Access Only

Award Date

2010

Degree Name

Master of Science (MS)

Department / School

Mathematics and Statistics

Abstract

A model was developed to simulate the growth of a tumor during an avascular state. The amount of nutrients available to the cell and the local cell density affect a cell's ability to grow. The nutrients are supplied to the tissue by a distant blood vessel. The nutrient's flow through the tissue is represented by a diffusion-absorption partial differential equation. A stable and efficient numerical method for solving the partial differential equation was developed. A cell has three possible actions it can perform: division, movement, or death. The likelihood of any of the actions depends on the nutrient concentration and cell density. For all simulations which produce tumor cell growth, the cell population will reach a carrying capacity. This occurs when the nutrient concentration and cell density have reached a steady state. Low cell density at the center of the tumor represents a necrotic core that is expected for actual tumors. A search for model parameters that would match the predicted cell population to hypothetical experimental data was performed. Variations between successive simulations and the large amount of computational time required for one simulation limit the ability to fit the parameters. The variations in simulation results can be reduced by averaging repeated simulations. To do so in practical computing time, the simulations would have to be performed in parallel. More advanced models would increase the computing time required, due to an increase in model complexity and the number of model parameters.

Library of Congress Subject Headings

Tumors -- Growth -- Mathematical models

Format

application/pdf

Number of Pages

44

Publisher

South Dakota State University

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