A Computational Model of Micro-vascular Growth

In order to supply a growing tissue with oxygen and nutrients and to remove its metabolic wastes, blood vessels penetrating the tissue are formed. Multiple mechanisms are involved in this process ranging over many orders of magnitude: chemical signaling on the bio-molecular level (10−9m), genetic program on the protein level (10−7m), microscopic mechanical cell interactions (10−5m) and external forces and stresses reaching macroscopic scales (> 10−3m). Better physiological understanding of this phenomenon could result in many useful medical applications, for example in gene therapy or cancer treatment. We present a simulation framework to study mechanical aspects of the micro-vascular growth using techniques from computational geometry, solid mechanics, computational fluid dynamics and data visualization. Vasculogenesis is modeled as traction driven remodeling of an initially uniform tissue in absence of blood flow. Angiogenesis, the subsequent formation and maturation of blood vessels, is handled as a flow driven remodeling of a porous structure resulting from the preceding stage. The mechanical model of tissue response to the traction forces successfully predicts spontaneous formation of primitive capillary networks. Furthermore, we demonstrate that a shear-stress controlled remodeling of such structures can lead to flow fingering effects observed in real cellular media.