Three-dimensional optimization of arterial tree models

The computational method of Constrained Constructive Optimization has been generalized to grow arterial model trees within a three-dimensional perfusion volume, representing a piece of tissue to be supplied with blood. Starting from an inlet at the surface of the perfusion volume, a binary branching tree of cylindrical tubes is generated so as to fulfill several physiologic boundary conditions and constraints. The model tree is grown by successively adding terminal segments while optimizing the geometric location and topological site of each new connection according to minimum total intravasal volume. Introducing additional ''post-optimization'' steps into the optimization algorithm improves the degree of optimality (measured in terms of the target function) of the trees generated. While the structure of the resulting trees changes considerably, the pressure profile from inlet to terminals, representing a functional characteristic, remains practically unaffected.