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Full-Text Articles in Physical Sciences and Mathematics
Application Of A Numerical Method And Optimal Control Theory To A Partial Differential Equation Model For A Bacterial Infection In A Chronic Wound, Stephen Guffey
Masters Theses & Specialist Projects
In this work, we study the application both of optimal control techniques and a numerical method to a system of partial differential equations arising from a problem in wound healing. Optimal control theory is a generalization of calculus of variations, as well as the method of Lagrange Multipliers. Both of these techniques have seen prevalent use in the modern theories of Physics, Economics, as well as in the study of Partial Differential Equations. The numerical method we consider is the method of lines, a prominent method for solving partial differential equations. This method uses finite difference schemes to discretize the …
Using Partial Differential Equations To Model And Analyze The Treatment Of A Chronic Wound With Oxygen Therapy Techniques, Brandon C. Russell
Using Partial Differential Equations To Model And Analyze The Treatment Of A Chronic Wound With Oxygen Therapy Techniques, Brandon C. Russell
Mahurin Honors College Capstone Experience/Thesis Projects
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 a system of partial differential equations, this project attempts to model the intricate biological process and to describe oxygen levels, neutrophil and bacteria concentrations, and other biological parameters with respect to time and space. Analytical solutions for the model will be derived for various frames of time in the wound-healing process. The system of equations will be numerically solved using Matlab. Numerical simulations are performed to determine optimal treatment strategies for a chronic wound.