Instability Mechanisms and Wavelength Selection during Vasculogenesis and Angiogenesis

Abbas Shirinifard, Biocomplexity Institute, Indiana University,

The initial organization of randomly-distributed capillary endothelial cells to form a primary vascular network is a striking and counterintuitive process during early vertebrate development. The network rapidly reorganizes into a pattern of quasi-polygonal domains whose length-scale increases in time due to domain disappearance. This organization presents several fundamental biological and mathematical problems. Biologically, by what mechanisms do the endothelial cells signal to each other to form the network: mechanically or by secretion of diffusible chemicals? If the latter, what chemicals? Do the same mechanisms also direct sprouting angiogenesis (which is important in wound healing and cancer in adults)? Mathematically, what determines the thickness of the vascular cords and the much longer scale of the quasi-polygonal network? I will present a number of results on the mathematics and simulation of chemotaxis-driven vasculogenesis and angiogenesis, including a discussion of a novel instability mechanism which leads to the wavelength selection which determines the cord width.