Studying the genealogy of cancer cells using the Biased Voter Model (2015)
Undergraduates: Samir Patel, Dongzhi Zheng Lili Chen, Samir Patel
Faculty Advisor: Louis (Wai-Tong) Fan
Department: Mathematics
Our project explores the genealogies of cancer tumors by both mathematical modeling and computer simulations. As a first step, we modeled the random growth of a solid tumor by a stochastic spatial model, the biased voter model. In this model, cancer cells and healthy cells change the cells around them with different rates, where cancer cells invade other cells faster. Our simulations statistically verify the shape theorem proved by Bramson and Griffeath (1980, 1981). We also find that if we mark the initial cancer cells with different colors and run the simulation for a long time, there will be color segregation within the tumor, where some colors coexist in asymptotic sectors and the other colors die out. Through the colors of cells, we can trace back the ancestors of the newly appeared cancer cells. Studying this genealogical phenomenon in two dimensions is very difficult, so to simplify our study, we again ran simulations in just one spatial dimension. Our results suggest that the growth occurred in a wave-like fashion, similar to the theoretical prediction by the stochastic FKPP (Fisher-Kolmogorov-Petrovsky-Piscunov) equation. ¿¿¿