Modeling and Estimating Intratumoral Heterogeneity in Cancer
Heterogeneity in biological populations, from cancer to ecological systems, is ubiquitous. Despite this knowledge, current mathematical models in population biology often do not account for inter- or intra-individual heterogeneity. In systems such as cancer, this means assuming cellular homogeneity and deterministic phenotypes, despite the fact that heterogeneity is thought to play a crucial role in therapy resistance. In this talk, I will discuss several approaches I have developed towards incorporating and estimating cellular heterogeneity in partial differential equation (PDE) models of GBM growth. In particular, I will use random differential equations for modeling heterogeneity and the Prohorov metric framework for estimating parameter distributions from aggregate data. Although the phenotypic heterogeneity I examine in this talk is specifically directed towards growth and diffusion rates of cells, the framework is broadly applicable to any model parameters, including those relevant to the tumor microenvironment.