Title: Mathematical model of tumor growth and angiogenesis
Abstract：
Angiogenesis is one of the processes of creation of new blood vessels in the human organism. Understanding tumor induced angiogenesis is a challenging problem with important consequences for diagnosis and treatment of cancer. Here, we present a multi-scale phase-field tumor angiogenesis model that combines the benefits of continuum physics description and the capability of tracking individual cells. The continuous equations of the model rely on the phase-field method to describe the intricate interfaces between the vasculature and the host tissue. The discrete equations are posed on a cellular scale and treat tip endothelial cells and filopodia as mobile agents. We present a simple simulation to study the development of angiogenesis from a preexisting vessel network and a more complicated pre-existing vessel network extracted from actual vessel morphologies in a microfluidic device.