#### Poster Title

Using Optimal Control Theory to Treat Chronic Wounds with Oxygen Therapy

#### Grade Level at Time of Presentation

Freshmen

#### 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 non-traumatic 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 differential-equation 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.

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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 non-traumatic 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 differential-equation 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.