Age-Structured Tumor Growth Models

Abstract

Mathematical models of tumor growth are essential for complementing experimental findings and furthering the understanding of cancer development and spread, as well as creating treatment plans. This dissertation focuses on an age-structured partial differential equation (PDE) model. The underlying process for tumor growth is similar to classical models, where growth is driven by pressure-limited cell division, and Darcy's law, describing cell movement away from regions of high internal pressure. By introducing an age-structure, the model accounts for the life-cycle of tumor cells. This allows for more accurate medical predictions and optimal therapy design.

There are three main results in this dissertation. The first is the existence of weak solutions. The second is a proof of the convergence of solutions to an incompressible limit satisfying a Hele-Shaw free boundary problem, describing the geometric growth of the tumor. The third is a proof of the existence of traveling wave solutions of the model, providing insight into the tumor spreading speed.