Advisor(s) - Committee Chair
Richard Schugart, Director, K. Renee Fister, Thomas Richmond, Di Wu
Department of Mathematics
Master of Science
Approximately 2 to 3 million people in the United States suffer from chronic wounds, which are defined as wounds that do not heal in 30 days time; an estimated $25 billion per year is spent on their treatment in the United States. In our work, we focused on treating chronic wounds with bacterial infections using hyperbaric and topical oxygen therapies.
We used a mathematical model describing the interaction between bacteria, neutrophils and oxygen. Optimal control theory was then employed to study oxygen treatment strategies with the mathematical model. Existence of a solution was shown for both therapies. Uniqueness was also shown for hyperbaric therapy. We then used a forward-backward sweep method to find numerical solutions for the therapies. We concluded by putting forth ideas for how this problem could progress toward finding applicable treatment strategies.
Mathematics | Medicine and Health Sciences | Other Analytical, Diagnostic and Therapeutic Techniques and Equipment
Daulton, Donna Lynn, "Using Optimal Control Theory to Optimize the Use of Oxygen Therapy in Chronic Wound Healing" (2013). Masters Theses & Specialist Projects. Paper 1232.