UC Irvine

Tumor angiogenesis plays a crucial role in cancer progression and metastasis. Mathematical modeling has emerged as a powerful tool to unravel the complex dynamics of tumor angiogenesis and to develop new therapeutic strategies. In this thesis, we focus on a comprehensive study on the mathematical modeling of tumor-induced angiogenesis, spanning from the fundamental concepts to the development of a novel hybrid model that integrates tumor growth and angiogenesis in a complex, realistic vascular network. We begin by investigating a thermodynamically consistent mixture model for avascular solid tumor growth. To simulate tumor growth, we develop a mass-conservative, adaptive, finite difference, nonlinear multigrid method that captures the evolution of tumor morphology accurately and efficiently. Next, we present a hybrid model for angiogenesis growth based on the phase-field theory. The model incorporates the dynamics of capillaries, angiogenic factors, and tip endothelial cells (TECs), along with a discrete conceptualization of filopodia that enables TECs to sense their microenvironment. Finally, we build a mathematical model of tumor-induced angiogenesis that integrates tumor growth and angiogenesis in a complex, realistic vascular network extracted from the vascularized microtumor (VMT) platform. The model combines continuum and discrete modeling approaches to capture the key biological processes involved in tumor angiogenesis, and is simulated by our new developed numerical method.