Regulation of Blood Vessel Growth

Abstract

Angiogenesis is a complex process where biological signals, such as the activation of signalling pathways by the binding of VEGF to its receptors at the cell membrane, are converted into mechanical forces originating cell movement. The endothelial cells then re-organize spatially into tubular structures that are able to support the flow of blood and that respond to blood pressure and shear stress by changing their number, shape and size. Therefore, a mathematical description of sprouting angiogenesis has to consider biological signals as well as relevant physical processes. In this thesis, we model sprouting events in angiogenesis using a continuum model that takes into account the tissue elasticity and the forces exerted by the cells in the sprout. We demonstrate that the endothelial cell proliferation has to be regulated by the local mechanical stress for a well-formed vascular sprout. The force exerted at the tip cell induces an increase in the stress, which determines the locations with higher endothelial cell proliferation. The model also permits a new look into how anastomosis events are controlled by the local tissue displacements. Our results highlight the ability of mathematical models to suggest relevant hypotheses with respect to the role of forces in sprouting, hence underlining the necessary collaboration between modelling and molecular biology techniques to improve our knowledge of the angiogenesis process.