A B S T RA C T The computational method of constrained constructive optimization was used to generate complex arterial model trees by optimization with respect to a target function. Changing the target function also changes the tree structure obtained. For a parameterized family of target functions a series of trees was created, showing visually striking differences in structure that can also be quantified by appropriately chosen numerical indexes. Blood transport path length, pressure profile, and an index for relative segment orientation show clear dependencies on the optimization target, and the nature of changes can be explained on theoretical grounds. The main goal was to display, quantify, and explain the structural changes induced by different optimization target functions.
The structure of a complex arterial tree model is generated on the computer using the newly developed method of "constrained constructive optimization." The model tree is grown step by step, at each stage of development fulfilling invariant boundary conditions for pressures and flows. The development of structure is governed by adopting minimum volume inside the vessels as target function. The resulting model tree is analyzed regarding the relations between branching angles and segment radii. Results show good agreement with morphometric measurements on corrosion casts of human coronary arteries reported in the literature.
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