Coronary Arterial Branching Structure is Highly Variable

Abstract

The coronary arterial branching structure forms an important determinant for flow distribution and its heterogeneity. We analyzed this structure in two steps: (A) performing morphometric measurements on coronary casts; (B) using these measurements for the computer generation of arterial networks, in order to determine global parameters. Two porcine coronary casts were made after maximal dilation, diastolic arrest, and glutaraldehyde fixation. Unbranched lengths and diameters (L and d, μm) of successive vascular segments were measured. The length (L) was related to d: ¹⁰log (L) = 1.01 + 0.72* ¹⁰log (d) (n = 2366, r² = 0.45). For any d, L varied 100-fold. The relation between diameters of proximal (do) and distal segments (d_L, d_s, with d_L > d_s) at a node was quantified using the polar variables growth (G) and symmetry (S): G = sqrt [(d_L/d₀)² + (d_s/d₀)²]; S = arctan [(d_s — 5)/(d_L — 5)]. G was slightly dependent on d₀: G = 1.131 — 0.042* ¹⁰log (d₀) (r² = 0.02, n = 1663, P < 0.0001). Deviations of G were normally distributed with SD = 0.13. Observed values of S covered the possible range of 0 to pi/4 radians (rad). Larger vessels branched less symmetrically (P < 0.0001): d₀ < 40: S = 0.49 ± 0.20 rad (mean + SD, n = 579); 40 < d₀ < 200: S = 0.45 ± 0.19 (n = 817); d₀ > 200: S = 0.38 ± 0.19 (n 267). The above relations, including the variability, were used to construct 30 stochastic models of arterial networks, starting at 500 μm and ending with arterioles between 5 and 10 μm. Strahler ordering was applied to these generated trees.