Age-Structured Models of Tumor Growth and Evolution of Drug Resistance

Abstract

Spatial heterogeneity plays a critical role in anti-tumor treatment response, influencing how therapies are delivered and interact with tumors. While there have been numerous studies using age-structured models to capture tumor cell behavior in drug response and proliferation that depends on cell cycles, most of these models remain spatially homogeneous. This thesis presents age-structured spatio-temporal tumor cell density models. These models incorporate spatial structure that allows model behaviors such as pressure-driven cell migration and inhibition of proliferation, and delivery of nutrients and drugs.

We develop an age-structured spatio-temporal model of tumor growth, in which cell movement and proliferation is largely driven by pressure. The age of cells is incorporated in the model as a continuous variable, where birth and death mechanisms of tumor cells are allowed to vary by cell age. We demonstrate that the asymptotic behavior of the solutions of our model depends on the presence of cell death. The fronts of model solutions are shown to propagate in finite speed. Additionally, age distributions and the spatial mitotic patterns are investigated. In model simulations, we observe the emergence of a generic structure in early solid tumor, consisting of the non-proliferating tumor core, actively proliferating rim slightly inside the periphery, and 'surfing' cells at the edge of tumor.

We further expand the model by introducing chemotherapy and drug resistance. The proliferation mechanism in this model mainly depends on the nutrient concentration and uptake rate, while proliferation is limited at the homeostatic pressure. Tumor growth and resistance evolution dynamics under varying doses of chemotherapy are observed from several aspects, including the age distribution across tumors. The results demonstrate drug-induced evolution of resistance, where the selection force of drug is greater under higher doses.