Tissue Growth and the Pólya Distribution

Abstract

In tissue growth, cells divide and so increase in number. This produces tissue elongation. We describe a discrete model for proliferative tissue growth. This model produces an interesting distribution for the displacement of the original cells in the tissue. We take the reader on our journey to determine this distribution—it turns out to be the well-known Pólya distribution associated with drawing coloured balls from bags. Connections between this model and a simple differential equation model are also investigated. The exercises outlined in this paper can be incorporated into undergraduate courses on probability and differential equations, and the unanswered research problems investigated i..