Anatomical Variability and Functional Ability of Vascular Trees Modeled by Constrained Constructive Optimization

The aim of this study was to investigate the extent that functional capability of vascular trees is related to anatomical variability. To these ends we used the method of Constrained Constructive Optimization (CCO) to generate optimized computer models of coronary arterial trees. All these model trees were optimized according to the same principle under equal boundary conditions of pressures and flows. However, by stochastically casting the locations of the terminal segments, different tree structures were generated, each of which conformed to the same boundary conditions. The structural variability of these models was interpreted as the correlate of the anatomical variability found in real arterial trees. The advantage that computer model trees are known in numerical detail was exploited to perform comprehensive and exact classifications of all segments into bifurcation levels, STRAHLER orders and composite vessels, and to compute the area expansion ratio. The unexpected result was that, despite striking visual differences in anatomical structure, the model trees were almost identical with regard to functional performance. We conclude that models optimized on the computer for a given perfusion task show little differences in their morphometric parameters even if they differ considerably regarding the course of the large vessels.