Honors College Capstone Experience/Thesis Projects

Department

Mathematics

Document Type

Thesis

Abstract

The purpose of this project is to use Bayesian statistics to analyze values of parameters for a previously developed system of differential equations which describes the healing process of diabetic foot ulcers. The model describes the relationships between matrix metalloproteinases (MMPs), their inhibitors (TIMPs), and extracellular matrix (ECM). A Bayesian approach is used when the availability of data is sparse, as it is in this case. Delayed Rejection Adaptive Metropolis (DRAM), a MATLAB implementation of a Metropolis-Hastings algorithm, is used to estimate parameters. This approach with the individual patient data allows us to estimate and compare parameters and their pairwise plots. This will help improve the wound-healing model in order to better predict wound-healing outcomes for individual patients. iv

Advisor(s) or Committee Chair

Dr. Richard Schugart, Dr. Melanie Autin, Dr. Thomas Richmond

Disciplines

Biology | Mathematics | Statistics and Probability

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