Graduation Semester and Year

2012

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Hristo Kojouharov

Abstract

Mathematical modeling of cell movement is needed to aid in the deeper understanding of vital processes such as embryogenesis, angiogenesis, tumor metastasis, and immune reactions to foreign bodies. In this work, cell movement and growth in response to external stimulus and the interactions between cells and the stimulus are considered. In order to model the random nature of the movement, a discrete model is created to simulate cells moving in the presence of a growing and moving stimulus distribution. The model also includes the depletion of the stimulus under the presence of cells. The discrete model is then upscaled, based on transition probabilities of the individuals at each site, to obtain a corresponding continuous differential equation model. Under traditional modeling assumptions the proposed continuous model reduces to previously developed models in the literature. Next, a set of numerical experiments are presented showing very good agreement between the continuous and discrete models for a variety of different values of the parameters. Furthermore, applications of the new mathematical models to infection control on medical implants are also discussed.

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

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Mathematics Commons

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