Geometrical and topological optimization and their relation to the bifurcation laws in optimized arterial tree models

Abstract

In generating models of vascular trees, the method of Constrained Constructive Optimization (CCO) draws on the assumption that optimization criterions can be utilized to derive the geometrical and structural features of the tree models, without using informations from topographic anatomy. The boundary conditions imposed describe pressures and flows at the inlet and outlets of the binary branching model tree as well as the ratios of radii at a bifurcation (power-law for bifurcations). During phylogenesis of species, bifurcation laws, tree geometry and tree topology have most likely been simultaneously optimized. In contrast, a supposed optimum form of bifurcation law is prescribed in the CCO-simulation, and geometry together with structure are optimized within that frame. It is shown that CCO trees optimized under different bifurcation laws initially show slightly different geometries but identical topological structures. At a certain stage of development, however, accumulated geometric deviations lead to changes in topology as a result of optimization. From there on we observe different evolutionary paths of tree development.