Honors College Capstone Experience/Thesis Projects

Department

Mathematics

Additional Departmental Affiliation

Economics

Document Type

Thesis

Abstract

When diabetes progresses, many patients suffer from chronic foot ulcers. In a study described in Matrix Metalloproteinases and Diabetic Foot Ulcers (Muller et al., 2008), sixteen patients with diabetic foot ulcers were examined throughout a twelve week healing period. During this period, levels of matrix metalloproteinases (MMP-1), their inhibitors (TIMP-1), and the extracellular matrix in a wound area were measured at distinct time intervals for each patient. The ratios of these healing components are vital in determining whether a wound will heal or become chronic and never properly heal. Connecting Local and Global Sensitivities in a Mathematical Model for Wound Healing (Krishna et al., 2015) mathematically describes the healing interactions between the MMP-1, TIMP-1, the extracellular matrix, and fibroblasts to highlight key differences between those patients categorized as ‘good’ healers or as ‘poor’ healers in the Matrix Metalloproteinases and Diabetic Foot Ulcers (Muller et al., 2008) study. The goal of this research is to utilize the individual patient data obtained from Matrix Metalloproteinases and Diabetic Foot Ulcers (Muller et al., 2008) to identify key parameters, through the use of nonlinear mixed effects modeling, a technique that allows for each parameter estimate to be split into a fixed and random effect. The fixed effect is assumed to remain the same across every data collection. Random effects vary from collection to collection and patient to patient. Through this split, information from the population trends, using the fixed effect estimates, can be utilized to help inform the individual patient estimates for patients with fewer data points. The identification of key parameters in the healing process can provide valuable insight about which parameters should be taken into special consideration during the diagnosis and treatment process.

Advisor(s) or Committee Chair

Dr. Richard Schugart, Dr. Ferhan Atici, Dr. Christopher Keller

Disciplines

Biology | Mathematics | Statistics and Probability

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