  In this paper, we introduce a new framework for generating synthetic vascular
trees, based on rigorous model-based mathematical optimization. Our main
contribution is the reformulation of finding the optimal global tree geometry
into a nonlinear optimization problem (NLP). This rigorous mathematical
formulation accommodates efficient solution algorithms such as the interior
point method and allows us to easily change boundary conditions and constraints
applied to the tree. Moreover, it creates trifurcations in addition to
bifurcations. A second contribution is the addition of an optimization stage
for the tree topology. Here, we combine constrained constructive optimization
(CCO) with a heuristic approach to search among possible tree topologies. We
combine the NLP formulation and the topology optimization into a single
algorithmic approach. Finally, we attempt the validation of our new model-based
optimization framework using a detailed corrosion cast of a human liver, which
allows a quantitative comparison of the synthetic tree structure to the tree
structure determined experimentally down to the fifth generation. The results
show that our new framework is capable of generating asymmetric synthetic trees
that match the available physiological corrosion cast data better than trees
generated by the standard CCO approach.
