Mathematical Modeling of Angiogenesis - Flow, Elasticity and Experiments -

Understanding angiogenesis in a pathological setting is a challenging problem with important consequences for diagnosis and treatment of severe diseases such as cancer. We present a multi-scale phase-field model that combines the benefits of continuum physics description and the capability of tracking individual cells. The model allows us to discuss the role of the endothelial cells’ chemotactic response and proliferation rate as key factors that tailor the neovascular network. We include in the phase-field model the effect of the vessels’ mechanical properties in vascular patterning by considering blood flow and the elastic properties of the different tissues. We also run a set of experiments with the aim of measuring directly the parameters of the model, such as the dependences of endothelial cell proliferation and chemotaxis on the concentration and gradients of growth factors. We test the predictions of our theoretical model against relevant experimental approaches in mice that displayed distinctive vascular patterns. Our results highlight the ability of mathematical models to suggest relevant hypotheses with respect to the role of different parameters in this process, hence underlining the necessary collaboration between modeling, in vivo imaging and molecular biology techniques to improve current diagnostic and therapeutic tools.