Global Constructive Optimization of Vascular Systems

Abstract

We describe a method for creating realistic vascular systems based on optimality principles of theoretical physiology. Our model is initialized by a complete but simple and suboptimal tree that fills an organ at a given resolution, and subject to local and global optimization techniques, which we provide. The boundary conditions are given by the position and flow distribution for all vascular end points corresponding to the tree leaves, and by the position of the vascular hilum corresponding to the tree root. Optimization is driven by intravascular volume minimization, which is one of the major principles for the design of vascular systems discussed in literature. Our algorithm is novel in that it implements topological changes, which have proven essential to the optimization process. For global optimization, we additionally propose a multi-level strategy, and present initial results. The generated models are shown to be similar to real data acquired from corrosion casts of a human liver. The presented method achieves for the first time global optimization of a complex macroscopic vascular model with respect to a cost functional. We finally conjecture that the phenomenon of interdigitation, which is shown by complementary vascular structures, can be solely explained by optimality principles.