Using Optimal Control Theory to Treat Chronic Wounds with Oxygen Therapy
Grade Level at Time of Presentation
Freshmen
Major

Minor

Institution
Western Kentucky University
KY House District #
86
KY Senate District #
25
Faculty Advisor/ Mentor
Dr. Richard Schugart
Department
Department of Mathematics
Abstract
Using Optimal Control Theory to Treat Chronic Wounds with Oxygen Therapy
Nikhil Krishna, Arjun Kanthawar, Stefan Stryker
Dr. Richard Schugart
Department of Mathematics
Chronic wounds such as diabetic foot ulcers are the leading cause of nontraumatic amputation in developed countries. In order for researchers to better understand the physiology of these wounds, a mathematical model describing oxygen levels at the wound site can help predict healing responses. Daulton (2013) used optimal control theory to formulate a differentialequation model to optimize hyperbaric oxygen treatment strategies. The model consisted of three variables  oxygen, bacteria, and neutrophils  and a control variable for supplemental oxygen. Using a similar approach, we formulated a differential equation model with four variables adding a chemoattractant to better describe the healing response of the wound. We then numerically solved these differential equations using a finite volume approach. The solutions to these equations will later be incorporated into a mathematical model to find the optimal amount of supplemental oxygen that would result in the most rapid rate of healing in a chronic wound.
Using Optimal Control Theory to Treat Chronic Wounds with Oxygen Therapy
Using Optimal Control Theory to Treat Chronic Wounds with Oxygen Therapy
Nikhil Krishna, Arjun Kanthawar, Stefan Stryker
Dr. Richard Schugart
Department of Mathematics
Chronic wounds such as diabetic foot ulcers are the leading cause of nontraumatic amputation in developed countries. In order for researchers to better understand the physiology of these wounds, a mathematical model describing oxygen levels at the wound site can help predict healing responses. Daulton (2013) used optimal control theory to formulate a differentialequation model to optimize hyperbaric oxygen treatment strategies. The model consisted of three variables  oxygen, bacteria, and neutrophils  and a control variable for supplemental oxygen. Using a similar approach, we formulated a differential equation model with four variables adding a chemoattractant to better describe the healing response of the wound. We then numerically solved these differential equations using a finite volume approach. The solutions to these equations will later be incorporated into a mathematical model to find the optimal amount of supplemental oxygen that would result in the most rapid rate of healing in a chronic wound.