Morphometry of human coronary arterial trees

Abstract

Background: Some groups, including ours, have been generating arterial tree models using constrained constructive optimization (CCO). Arterial trees have been grown to arbitrary resolution without input of anatomical data. We performed this study to learn about the shortcomings that might have resulted from neglecting the anatomical data in CCO models.

Methods: In a total of 450 segments obtained from 4 human cast hearts, the ratio ofbifurcating daughter segment radii (O < Sbif = r(2)/r(1) < 1) was examined, which corresponds to the split of the total flow of the mother segment. For any complete bifurcation, where the radii of the parent segments and the radii of daughters were known, the area expansion ratio was computed (Aexp = [r(1)2 + r(2)2]/r(parent)2).

Results: The bifurcating ratio was found to be distributed in a nonnormal fashion, with a median of 0.76. The average area expansion ratio Aexp, characterizing the change of cross-sectional area of the vasculature from proximal to distal, was 0.93+/-0.26. The 'rate of branching' (d(i)/(d(0)) was defined by the segment diameter relative to the diameter of the root segment. Averaging the rate of branching over segments within each bifurcation level resulted in a decreasing function of bifurcation level.

Conclusions: This article provides new experimental data on branching geometry of coronary arteries (i.e., the trees evaluated in this study are purely delivering rather than conveying). Based on these facts, we suggest that the analytical bifurcation law in CCO might be replaced by the bifurcation rule obeyed on a stochastic basis only.