Date of Award

Summer 6-4-2021

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics


Most tumors are complex ecosystems that emerge and evolve under robust

selective pressure from their microenvironment. Such a pressure promotes the diversification of both tumor cells and the tumor microenvironment, resulting in increased intratumoral heterogeneity (ITH) that enables aggressive disease progression leading to metastasis and resistance to treatment. Metastasis and the emergence of chemo-resistance are the two main reasons for cancer treatment failure. In this work we focus on developing mathematical models to understand cancer evolution leading to metastasis and chemo-resistance with a special focus on the role of ITH. Our central goal is to understand the evolution of phenotypic heterogeneity as tumor cells

adaptation to various environments. We use a multiscale model to systematically study cancer metastasis and make connections to potential clinical implications for optimizing screening and treatment schedules. At the cell level, we use a cell-based model (the Cellular Potts Model or CPM) to simulate the collective cancer invasion. At the population level, we use continuous replicator dynamics to analyze the adaptation strategies of the tumor. This work reveals how the pairwise interactions between phenotypes within the tumor, together with the microenvironments, alter the dynamics of the tumor progression and change their responses to chemotherapy. The study will offer potential clinical prognosis information and treatment strategies for patients.


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