Multi-scale mathematical modeling of brain tumor growth

Abstract

Mathematical modeling of tumor growth has been an active area of research for the past several decades. One of the holy grails of the field is to develop a simulation tool that can be utilized in the clinic to predict tumor progression and propose individualized treatment strategies. In this talk, I will discuss the work we have done with this long-term goal in mind. In particular, I will focus on both the implementation of, and the results drawn from, several of the models we have developed. Questions we have addressed through our modeling efforts include: 1. How do the geometry and topology of the environment in which a tumor grows impact the shape, size and spread of a tumor? What are the consequences for patient prognosis? 2. Under what conditions can a tumor overcome its limited blood supply and grow to a macroscopic size? 3. What is the likelihood that advantageous or deleterious genetic mutations arise within a tumor and how do these mutations impact growth dynamics? After looking at a set of model variants that allows each of these questions to be addressed, I talk about recent efforts to merge these models into one comprehensive cancer simulation tool. I use the merged model to highlight biological features that must be considered in a clinically-relevant tumor growth algorithm, and to test the impact of vascular-targeting treatment strategies.