Computer-optimization of vascular trees

Abstract

Arterial branchings closely fulfill several "bifurcation rules" which are deemed to optimize blood flow. The question is whether these local criteria in conjunction with a general optimization principle can explain the overall structure of an arterial tree. We present a model of an arterial vascular tree which is grown on the computer by successively adding terminal vessel segments. Each new terminal segment is connected to the optimum site within the preexisting tree, and the new bifurcation is optimized geometrically. After each step of adding and optimizing, the whole tree is rescaled to meet invariant boundary conditions of pressure and flow at each terminal site. Thus, local geometric optimization is used to induce simultaneously an optimized global structure. The comparison between the model and real coronary arterial trees shows good agreement regarding structural appearance, morphometric parameters, and pressure profiles.