Stepien, Tracy L.
(2013)
Collective cell migration in single and dual cell layers.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Collective cell migration plays a substantial role in maintaining the cohesion of epithelial cell layers, in wound healing, and in embryonic development. We extend a previously developed one-dimensional continuum mechanical model of cell layer migration based on an assumption of elastic deformation of the cell layer to incorporate stretch-dependent proliferation, which leads to a generalized Stefan problem for the density of the layer. The resulting partial differential equation system is solved numerically using an adaptive finite difference method and similarity solutions are studied analytically. We show the existence of traveling wave solutions with constant wave speed for a large class of constitutive equations for the dependence of proliferation on stretch.
We then extend the corresponding two-dimensional model of cell migration to incorporate two adhering cell layers. A numerical method to solve the model equations is based on a level set method for free boundary problems with a domain decomposition method to account for where the migrating cells in each layer are located. We apply the model to experimental migration of epithelial and mesenchymal cell layers during gastrulation, an early phase of development, in animal cap explants of Xenopus laevis embryos to analyze the mechanical properties of each cell layer. Understanding the mechanics of collective cell migration during embryonic development will aid in developing tools to perturb pathological cases such as during wound healing and to aid in the prediction and early detection of birth defects.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
30 September 2013 |
| Date Type: |
Publication |
| Defense Date: |
24 May 2013 |
| Approval Date: |
30 September 2013 |
| Submission Date: |
6 May 2013 |
| Access Restriction: |
1 year -- Restrict access to University of Pittsburgh for a period of 1 year. |
| Number of Pages: |
140 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
cell migration, wound healing, embryology, mathematical modeling, elastic continuum, free boundary problem, traveling wave solutions |
| Date Deposited: |
30 Sep 2013 17:44 |
| Last Modified: |
15 Nov 2016 14:12 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/18675 |
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