Graduation Semester and Year
2022
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Benito Chen-Charpentier
Abstract
Wound healing encompasses a group of processes categorized into overlapping stages known as the inflammation, proliferation, and maturation/remodeling stage. The dynamics of these processes are important in studying outcomes of wound care and determining factors that contribute to certain wound outcomes. A system of ordinary differential equations is constructed for the inflammation, proliferation, and remodeling stage. Parameter sets for this model are investigated based on output dynamics according to the literature and based on experimental data. A bifurcation analysis is conducted to determine sudden changes that can occur in the inflammation system. Fourier Amplitude Sensitivity Test (FAST) is implemented to investigate sensitivity in regard to each mechanism considered. Next, the system is turned into a stochastic differential equation to analyze possible realizations that result from biological random fluctuations.
Keywords
Immune system, Ordinary differential equations, Global sensitivity analysis, Inflammation, Proliferation, Stochastic differential equations, Collagen, Macrophages
Disciplines
Mathematics | Physical Sciences and Mathematics
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Patrick, Amanda, "Abrading the enigma of the wound healing process: Modeling the inflammation, proliferation, and maturation stage" (2022). Mathematics Dissertations. 184.
https://mavmatrix.uta.edu/math_dissertations/184
Comments
Degree granted by The University of Texas at Arlington