Fractal aspects of three-dimensional vascular constructive optimization

We study various properties of constructive optimization in 3D vascular systems. After some remarks on existing approaches to vascular modeling and on the theory of vascular optimality, we briefly describe an algorithm called Global Constructive Optimization (GCO). Twenty-one vascular systems are modeled in three different groups: planar, spherical, and liver shaped. Based on the Strahler ordering scheme, these models are characterized and compared to data from liver corrosion casts. A good correspondence could be observed between modeled and real portal venous systems. The branching characteristics of the hepatic vein still pose open questions. Finally, a concept for the modeling of vascular interdigitation based on optimality principles is suggested.