A Stochastic Spatial Model for Tumor Growth

Dheeraj, Aashiq

2014-04-29T17:54:08Z

2014-04-29T17:54:08Z

2014-04-29

Mathematics

Evolutionary game theory can be used to study the interactions of different cell phenotypes and describe tumor population dynamics. Instead of killing tumor cells, clinical treatment could aim to change the nature of the evolutionary game-- enabling healthy cells to outcompete malignant cells. Most applications of evolutionary game theory to tumor growth have considered the tumor as a homogeneously mixing population that is governed by the replicator equation. We model the tumor population as an interacting particle system (IPS), with discrete individuals, stochastic local interactions, and explicit spatial consideration. Using this model, we see how predictions are changed when space is taken into account. In particular, we consider Basanta's work on glioma progression, the analysis of multiple myeloma proposed by Dingli et al., and Tomlinson's model for tumors containing cytotoxin-producing cells. Our model agrees with Basanta's in that we should have coexistence between the three tumor phenotypes, but the spatial model allows coexistence in a significantly wider region of parameter space. Dingli's tumor population exhibits bistability in a certain parameter regime. Our spatial model predicts a transition between the two stable states at a critical parameter value, so there is no bistability. In Tomlinson's game, the IPS does not allow for coexistence between cell types.

https://hdl.handle.net/10161/8605

en_US

stochastic spatial model

Cancer

interacting particle system

evolutionary game theory

A Stochastic Spatial Model for Tumor Growth

Honors thesis