Local Symmetry And Global Structure OfCoronary Arterial Tree Models Generated ByConstrained Constructive Optimization

Abstract

The procedure of Constrained Constructive Optimization (CCO) generates a binary branching model of vascular segments, represented as straight cylindrical tubes through which resistance to blood flow follows Poiseuille's Law. While several constraints regarding pressures, flows and branching radii are fulfilled throughout the optimization process, the branching structure is generated so as to convey blood to each site of a perfusion area, where it is delivered into the microcirculation. As every real arterial tree CCO-models also comprise a mixture of conveying and delivering elements of function. Since no anatomical information is plugged into CCO-models, the local and global structure solely results from the numerical optimization process. Different target functions as well as additional constraints can be examined regarding their impact on structural features. Likewise changes in constraints induce different structures of the model trees. In the present work we illustrate the impact of an additional local criterion applied to each new bifurcation generated, namely setting a lower limit to the ratio between the radii of smaller and larger daughter. Thus, precluding very asymmetric bifurcations was found to convert a CCO-model from a conveying to a delivering type of function, as reflected in the respective numerical indices. Transactions on Biomedicine and Health vol 4, © 1997 WIT Press, www.witpress.com, ISSN 1743-3525