Graduation Semester and Year
2014
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Jianzhong Su
Abstract
Implant failure due to fibrotic encapsulation is an ongoing challenge in the bio-medical field. We develop two mathematical models based on partial differential equations in two spatial dimensions, and use them to gain quantitative insights regarding the dynamics of immune cells and proteins following the insertion of a foreign body. We focus heavily on incorporating a distinction between varied phenotypes of macrophage cells and analyzing their effects on healing processes. We extend our research to a new model that incorporates mesenchymal stem cells that influence the chemical reactions of immune regulators. Stability analysis is conducted on a family of equilibria that correspond to "healed states." Additionally, isolated analysis of key components is presented to allow a more comprehensive understanding of the roles that stem cell presence plays on macrophage population trends. For the purposes of temporal dynamic testing, as well as investigations into the model for which mathematical analysis was cumbersome, computational tools such as MatLab and Comsol were implemented. Model simulations are compared against experimental data as validation to each mathematical model's efficacy.
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
Owens, Larrissa, "Differential Equation Models Of Foreign Body Fibrotic Reactions For Assessing Roles Of Macrophage Phenotypes And Mesenchymal Stem Cells" (2014). Mathematics Dissertations. 57.
https://mavmatrix.uta.edu/math_dissertations/57
Comments
Degree granted by The University of Texas at Arlington