Abstract

Collagen is an important structural protein in the body, which plays a role in wound healing, particularly the contraction process. Collagen lattices have been studied for nearly 50 years to provide insight into wound contraction. In some cases, collagen interacts with surfaces that have fixed shapes, such as medical implants. Our model focuses on the interactions of a collagen lattice with such a fixed surface. We mathematically model a collagen lattice as a network of nodes connected by springs. We also model fixed surfaces that have various topographies. Our model includes fibroblast cells that connect to both surfaces and remodel the collagen lattice via integrin based adhesion sites. We introduce a novel algorithm for the movement of the fibroblasts, particularly the reattachment process for integrins. We find that this model leads to highly local collagen remodeling by the cells, which move very little. Increasing the number of cells leads to more remodeling of the collagen lattice. Different fixed surfaces lead to slightly different results.

Degree

MS

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2026-06-24

Document Type

Thesis

Keywords

collagen lattices, cell motion, mathematical modeling

Language

english

Download

Share

COinS