Faculty Advisor

Olson, Sarah D

Abstract

In this project, we develop study the behavior of a collagen network around fixed cells in a two-dimensional model. A mathematical distribution is used to determine a random direction theta which the collagen molecules can use to move via a random walk. We show the versatility of using both discrete and continuous mathematics to create a working collagen model. We create a discrete model which is used to locate and plot cells, as well as determine if conditions are appropriate for collagen to form and move. To study the variability of different distributions, we plot the number of collagen able to be produced. Results are discussed in connection with the diffusion equation in order to extrapolate further adaptations to existing code.

Publisher

Worcester Polytechnic Institute

Date Accepted

April 2017

Major

Mathematical Sciences

Project Type

Major Qualifying Project

Accessibility

Unrestricted

Advisor Department

Mathematical Sciences

Advisor Program

Mathematical Sciences

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