J. Gen. Physiol.
© The Rockefeller University Press
0022-1295/97/02/129/12 $2.00
Volume 109, Number 2, February 1997 129-140

Limited Bifurcation Asymmetry in Coronary Arterial Tree Models Generated by Constrained Constructive Optimization

Wolfgang Schreiner,^* Friederike Neumann, Martin Neumann,^§ Rudolf Karch,^* Adelheid End, and Susanne M. Roedler^||

From the ^* Department of Medical Computer Sciences,  Department of Cardiothoracic Surgery, ^§ Institute for Experimental Physics, Division of Computational Physics, and ^|| Department of Cardiology, University of Vienna, A-1090 Vienna, Austria

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.

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