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Even though 'healthy' heart transplants without CAD exhibit normal ejection fraction, deformation indices are reduced in this population when compared with control subjects. Our findings suggests that strain analysis is more sensitive than assessment of ejection fraction for the detection of abnormalities of systolic function.

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.

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.

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Models of coronary arterial trees are generated by the algorithm of constrained constructive optimization (CCO). In a given perfusion area a binary branching network of straight cylindrical tubes is generated by successively adding terminal segments to the growing structure. In each step the site of connection is chosen according to an optimization target function (total intravascular volume), and in any stage of development the tree fulfills physiologic boundary conditions (constraints involving pressures, flows and bifurcation rules). CCO generates structures which in many aspects resemble real coronary arterial trees, except for very asymmetric bifurcations, occurring when a large branch gives off a tiny terminal segment. In the present work we evaluate an additional constraint within CCO, namely imposing a limit on the asymmetry of bifurcations during the construction process. Model trees are grown with different limits imposed, and the effects on structure are studied both phenomenologically and via statistical descriptors. As the limit to asymmetry is tightened, blood is conveyed to the perfusion sites via detours rather than directly and the comparison with measured data shows the structure to change from a conveying to a delivering type of function. Simultaneously total intravascular volume, surface and sum of segments' lengths increase. It is shown why and how local bifurcation asymmetry is able to determine the global structure of the optimized arterial tree model. Surprisingly, the pressure profile from inlet to terminals, being a functional characteristic, remains unaffected.