Date Thesis Awarded

7-2012

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Jianjun Paul Tian

Committee Member

Paul D. Heideman

Committee Member

Robert Michael Lewis

Committee Member

Junping Shi

Abstract

Colorectal cancer is one of the most common forms of cancer, and it is widely accepted that it is initiated in the colon crypts. Consequently, a lot of work has been put into understanding the cell dynamics of intestinal crypts. In rodents, circadian oscillations have been observed in the three different cell populations at whole gut level. The goal of this thesis is to capture this phenomenon and draw biological conclusions. First, we look at previous models of a single intestinal crypt. The first two lay the groundwork by introducing a compartmental approach, and the second two introduce methods for maintaining homeostasis. We capture the circadian phenomenon by introducing time delays to these older models. The time delays represent the time it takes the cell populations to send, receive, and respond to signals. In our models we observe that longer delays for the stem cell population lead to periodic solutions for all three cell populations. We conclude that the response of the stem cell population is delayed, and that this is related to the circadian oscillations.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Public Domain Dedication 1.0 License.

Comments

Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.

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