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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Daulton, Donna Lynn"],"institution":null,"degree_name":"Master of Science","degree_level":null,"degree_discipline":"Department of Mathematics","degree_department":null,"school":null,"contributors":["Richard Schugart, Director, K. Renee Fister, Thomas Richmond, Di Wu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-05-01T07:00:00Z","date_published":"2013-05-01T07:00:00Z","updated_at":"2026-07-24T06:08:16Z","subjects":["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"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wku.edu/theses/1232","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Richard Schugart, Director, K. Renee Fister, Thomas Richmond, Di Wu"]},{"key":"dc:creator","label":"Author","values":["Daulton, Donna Lynn"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematics"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["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"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wku.edu/theses/1232"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Using Optimal Control Theory to Optimize the Use of Oxygen Therapy in Chronic Wound Healing"]}]}],"canonical_facts":{"dc:contributor":["Richard Schugart, Director, K. Renee Fister, Thomas Richmond, Di Wu"],"dc:creator":["Daulton, Donna Lynn"],"dc:description.abstract":["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.
"],"dc:identifier":["https://digitalcommons.wku.edu/theses/1232"],"dc:subject":["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"],"dc:title":["Using Optimal Control Theory to Optimize the Use of Oxygen Therapy in Chronic Wound Healing"],"dc:type":["Thesis"],"thesis:degree_discipline":["Department of Mathematics"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T06:08:16Z"}