A model is proposed by which the formation of the vascular network in animals proceeds via progressive penetration of the vessel ramification into a capillary mesh, by means of a laplacian growth mechanism of hydrodynamical origin. In this model, the growth of both arteries and veins follows the directions of high shear stress provoked by the blood flow on the endothelial wall of a pre-existing capillary mesh. This process is shown to be identical to the phenomenon of dendritic growth, which is responsible for the formation of such well-known patterns as dendritic crystals, lightning sparks or branching aggregates of bacteria. A number of straightforward consequences of potentially important medical and physiological interests are deduced. These include the natural and spontaneous organization of the arterial and venal trees, the spontaneous and unavoidable tropism of arteries towards veins and vice-versa, the hierarchical character of the vessels and the possibility of computerized prediction of the vascular pattern from the shape of the capillary bed.
Quadrature Domains and p-Laplacian Growth
