Western Kentucky University

Poster Title

Formulating Mathematical Models to Analyze the Treatment of Chronic Wounds

Institution

Western Kentucky University

Abstract

Chronic wounds plague approximately 1.3-3 million Americans. The treatment of these wounds requires knowledge of the complex healing process of typical wounds. With mathematical modeling, we can simulate this intricate process. Researchers can potentially use the models to understand the effects of various therapies, and thus modify their treatments to maximize healing capabilities. In this work, two mathematical models using differential equations have been developed. The first model describes the interaction within the wound site among oxygen, bacteria, and neutrophils, which kill the bacteria. The model was analyzed and computationally simulated to determine whether it accurately described the biological processes that occur during wound healing. Analytical techniques were used to determine that the model provided biological solutions during the first hours of wound healing. Numerical solutions provided a visualization of the modeled healing response and can be used to analyze various oxygen treatment strategies. The second mathematical model describes the interactions of the proteins and their change over time and are based upon the data from Muller, et al., 2007, a research outcome that provided patient measurements of the proteins and the percent of which the wounds had healed. Matlab, a high-level technical computing language, was used to minimize the error between our model solutions and the data. The best model was established by choosing the results with the least error. A sensitivity analysis was then conducted to measure to what degree the equations were affected by slight changes in the model. The sensitivity analysis aided in identifying the effect of a particular treatment on each of the considered protein levels.

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Formulating Mathematical Models to Analyze the Treatment of Chronic Wounds

Chronic wounds plague approximately 1.3-3 million Americans. The treatment of these wounds requires knowledge of the complex healing process of typical wounds. With mathematical modeling, we can simulate this intricate process. Researchers can potentially use the models to understand the effects of various therapies, and thus modify their treatments to maximize healing capabilities. In this work, two mathematical models using differential equations have been developed. The first model describes the interaction within the wound site among oxygen, bacteria, and neutrophils, which kill the bacteria. The model was analyzed and computationally simulated to determine whether it accurately described the biological processes that occur during wound healing. Analytical techniques were used to determine that the model provided biological solutions during the first hours of wound healing. Numerical solutions provided a visualization of the modeled healing response and can be used to analyze various oxygen treatment strategies. The second mathematical model describes the interactions of the proteins and their change over time and are based upon the data from Muller, et al., 2007, a research outcome that provided patient measurements of the proteins and the percent of which the wounds had healed. Matlab, a high-level technical computing language, was used to minimize the error between our model solutions and the data. The best model was established by choosing the results with the least error. A sensitivity analysis was then conducted to measure to what degree the equations were affected by slight changes in the model. The sensitivity analysis aided in identifying the effect of a particular treatment on each of the considered protein levels.