A Mathematical Approach to the Growth Rate of Solid Breast Cancer Tumors

by Tiffany Miller

Submitted : Spring 2013

The purpose of this project is to utilize Gompertz’s mathematical growth model in order to explore the behavior of breast cancer tumors as it pertains to growth patterns, i.e., whether it be self-limiting or non-self-limiting. While also deriving the tumor cell’s growth rate with some manipulation to the original mathematical model incorporating experimentally found and presented data. To do this we defined a model for the growth of solid breast cancer tumors and then proceeded to manipulated the equation; which then gave us an equation for N(t), the number of cells as a function of time detailed. With this information we were able to determine the cell population at any given time, t. It was found that when the tumor exhibited self-limiting behavior the average growth rate was approximately 2.04 cells per day while on the other hand  the non-self-limiting tumor's average growth rate was found to be approximately 99800 cells per day and it took roughly half a year for the self-limiting tumor to double in size from the initial value of N(t) in comparison to the non-self-limitating tumor; which only took about one month.

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