Using Optimal Control Theory to Optimize the Use of Oxygen Therapy in Chronic Wound Healing

<p>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.</p> <p>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.</p>

Name thesis:degree_name

Master of Science

Discipline thesis:degree_discipline

Department of Mathematics

Year

2013

Author dc:creator

• Daulton, Donna Lynn

Contributors dc:contributor

• Richard Schugart, Director, K. Renee Fister, Thomas Richmond, Di Wu

• Hamiltonian Systems
• Pontryagin's Maximum Principle
• Mathematical Modeling
• Mathematical Analysis
• Wounds and Injuries-Treatment
• Wound Healing
• Mathematics
• Medicine and Health Sciences
• Other Analytical, Diagnostic and Therapeutic Techniques and Equipment

Repository record dc:identifier

https://digitalcommons.wku.edu/theses/1232

OAI identifier oai:identifier

oai:digitalcommons.wku.edu:theses-2235