Branching patterns in the porcine coronary arterial tree. Estimation of flow heterogeneity.

Abstract

The aim of this study is to quantify the porcine coronary arterial branching pattern and to use this quantification for the interpretation of flow heterogeneity. Two casts of the coronary arterial tree were made at diastolic arrest and maximal dilation. The relation between length and diameter of arterial segments was quantified, as well as the area expansion ratio and diameter symmetry of vascular nodes. These relations were used to construct computer models of the coronary arterial tree, covering diameters between 10 and 500 microns. Topology of these simulated trees was analyzed using Strahler ordering: Bifurcation ratio, diameter ratio, and length ratio were constant along orders 2-8 and equal to 3.30, 1.51, and 1.63, respectively. In each order, the number of segments per Strahler vessel was almost geometrically distributed. For the lowest orders, these predictions were confirmed by direct observations. From the network model, local pressure and flow were also predicted: Pressure fell from 90 to 32 mm Hg at the 10-microns level. The coefficient of variation (CV) of flow in individual segments was dependent on the number of perfused terminal segments (Nt) according to the fractal relation CV(Nt) approximately Nt(1-D), where D is the fractal dimension (1.20). CV of flow in 1-g tissue units was predicted to be 18%. This study shows that the structure of the coronary arterial bed is an important determinant of the fractal nature of local flow heterogeneity.

Relation between branching patterns and perfusion in stochastic generated coronary arterial trees

“…To quantify and to reconstruct the arterial tree, the morphometric data of VanBavel and Spaan [15] were used. In summary, in that study two male pig hearts have been dilated by 10 lM adenosine and before supplying the casting material, the vascular bed was perfused with fixation solution at 90 mmHg [15].…”

“…In summary, in that study two male pig hearts have been dilated by 10 lM adenosine and before supplying the casting material, the vascular bed was perfused with fixation solution at 90 mmHg [15]. After removal of the surrounding tissue, diameter and length of 2,366 smaller vessels were measured.…”

“…During vascular development, vascular networks remodel into complex networks through dilatation, sprouting, and bridging [5,6,13,15,17]. The large variability in myocardial flow per 100 g tissue that is found indicates variation in anatomical characteristics of the coronary arterial tree [7,16].…”

“…Kassab et al [6] and VanBavel and Spaan [15] quantified coronary arterial branching patterns. Kassab et al measured more segments than VanBavel and Spaan, however, Kassab's classification method, based on a modification of Strahler ordering based on diameter (diameter defined Strahler ordering) and a connectivity matrix, was difficult to use for generating trees in our simulation structure.…”

“…Kassab et al measured more segments than VanBavel and Spaan, however, Kassab's classification method, based on a modification of Strahler ordering based on diameter (diameter defined Strahler ordering) and a connectivity matrix, was difficult to use for generating trees in our simulation structure. Therefore, in this study vascular trees were generated applying VanBavel's model [15] based on measured heterogeneously branching patterns of the coronary vascular bed. Stochastic relations for length of segments, area ratio and symmetry of nodes along the bed were used to reconstruct stochastic asymmetrical branching arterial trees.…”