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.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Berube, Timothy Joseph

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-042717-152853

Advisor

• Olson, Sarah D

Year

• 2017

Date created

• 2017-04-27

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright