Optimized arterial trees supplying hollow organs.

Computer models of arterial trees can be generated from optimization principles using the algorithm of constrained constructive optimization (CCO). Up to now this algorithm could handle only tissue areas of convex shape, without concavities. CCO is now generalized to cope also with non-convex organ shapes, possibly featuring external as well as internal concavities. This allows the modeling of a much larger class of interesting real arterial systems. The concept of a generalized domain-potential was developed to represent arbitrary non-convex shapes mathematically and incorporate them as boundary conditions to optimization. Domain-potentials may be derived from analytical representations as well as from finite element triangulations obtained from organ images. To demonstrate the feasibility of the concept, the optimized growth of an arterial tree model is confined to some part of an elliptical shell, representing the free wall of the left ventricle of the heart.