Modeling Cancer Evolution as an Interacting Particle System

Abstract

Tumor growth is a somatic evolutionary process. Each time that a cell divides, there is a chance that the daughter cells acquire mutations in their genome. Occasionally a mutation confers a selective advantage to the cell, allowing it to replicate uncontrollably and invade the surrounding tissue. By the time a tumor reaches a clinically detectable size, it will comprise many genetically distinct subpopulations known as subclones. This phenomenon, which is known as intratumor heterogeneity, is a significant roadblock to the development of effective cancer therapies since it is unlikely that all subclones will respond uniformly to a treatment. This thesis develops a stochastic spatial model of tumor growth and uses it to investigate aspects of intratumor heterogeneity. Mathematically, the model is an example of an interacting particle system and can be analyzed using percolation theory. This theoretical framework allows us to prove basic results about the model dynamics. For example, we show that the tumor has an asymptotic shape and a polynomial growth rate. To answer more complex questions, we design and implement a simulation algorithm that can generate tumors with millions of cells in under a minute. Using our open-source software package, we show that cells near the tumor boundary have higher mutation burdens and that subclones with more aggressively growing cells exhibit a higher degree of spatial autocorrelation. Finally, we compare our simulations to publicly available cancer data and find that standard sampling procedures may lead to significantly biased estimates of tumor heterogeneity.