Diameter-dependent axial prestretch of porcine coronary arteries and veins

Abstract

The pressure-diameter relation (PDR) and the wall strain of coronary blood vessels have important implications for coronary blood flow and arthrosclerosis, respectively. Previous studies have shown that these mechanical quantities are significantly affected by the axial stretch of the vessels. The objective of this study was to measure the physiological axial stretch in the coronary vasculature; i.e., from left anterior descending (LAD) artery tree to coronary sinus vein and to determine its effect on the PDR and hence wall stiffness. Silicone elastomer was perfused through the LAD artery and coronary sinus trees to cast the vessels at the physiologic pressure. The results show that the physiological axial stretch exists for orders 4 to 11 (> 24 μm in diameter) arteries and orders -4 to -12 (>38 μm in diameter) veins but vanishes for the smaller vessels. Statistically, the axial stretch is higher for larger vessels and is higher for arteries than veins. The axial stretch λ(z) shows a linear variation with the order number (n) as: λ(z) = 0.062n + 0.75 (R(2) = 0.99) for artery and λ(z) = -0.029n + 0.89 (R(2) = 0.99) for vein. The mechanical analysis shows that the axial stretch significantly affects the PDR of the larger vessels. The circumferential stretch/strain was found to be significantly higher for the epicardial arteries (orders 9-11), which are free of myocardium constraint, than the intramyocardial arteries (orders 4-8). These findings have fundamental implications for coronary blood vessel mechanics.

Fig. 1.

Morphological measurements of coronary vessels at physiological state and zero-stress state. A: vessel segment dissected from myocardium, with hardened elastomer in the lumen. Water-resistant carbon particles were used to mark the vessel segments to measure axial changes before and after removal of the elastomer. B: cross section of a left anterior descending (LAD) arterial vessel segment at physiological state, with hardened elastomer in the lumen. Inner and outer dimension and wall thickness were measured. C: cross section of a vein segment with hardened elastomer in the lumen. D: cut-open vein segment at zero-stress state. Opening angle ϕ and midwall circumferential length were measured.

Fig. 2.

A: correlation between the logarithm wall thickness (WT, μm) and the logarithm of inner diameter (D_in, μm) along LAD arterial and coronary venous tree. B: variation of WT of the LAD artery and vein with order number (n). Solid line, least-square fit of the following form: LAD, WT = 0.71e^−0.38n (R² = 0.99); vein, WT = 1.04e^−0.38n (R² = 0.99). Statistical data are given in Supplemental Tables S1A (LAD) and S1B (coronary vein).

Fig. 3.

A: correlation between wall thickness-to-radius ratio (WTRR) and the logarithm of inner diameter (D_in, μm) along LAD arterial and coronary venous tree. B: variation of WTRR of the LAD artery and vein with order number (n). Solid line, least-square fit of the following form: LAD: WTRR = 0.0038n² − 0.0774n + 0.48 (R² = 0.98); vein, WTRR = 0.0017n² + 0.039n + 0.29 (R² = 0.95).

Fig. 4.

A: correlation between axial stretch ratio λ_z and the logarithm of inner diameter D_in (μm) along LAD arterial and coronary venous tree. B: variation of λ_z of the LAD artery and vein with order number, n. Solid line, least-square fit of the following form: LAD, λ_z = 0.062n + 0.75 (R² = 0.99); Vein, λ_z = −0.029n + 0.89 (R² = 0.99). Statistical values of λ_z are given in Supplemental Tables S1A (LAD) and S1B (coronary vein).

Fig. 5.

A: correlation between axial stretch ratio λ_z and WTRR along LAD arterial and coronary venous tree. B: data were classified into order numbers throughout the LAD and venous tree. Solid line, least-square fit of the following form: LAD, λ_z = 24.67WTRR² − 10.71WTRR + 2.17 (R² = 0.98); vein, λ_z = 22.44WTRR² − 7.06WTRR + 1.56 (R² = 0.97).

Fig. 6.

Variation of the opening angle (ϕ) of the coronary venous tree with order number (n). Solid line, linear least-square fit ϕ = −11.67n − 10.57 (R² = 0.98).

Fig. 7.

Representative pressure-diameter curves of LAD arteries. Solid line: λ_z = measured physiological axial stretch; dashed line: λ_z = 1.0 (vessel is free of axial stretch); ♦: calculated physiological state (see Supplemental Table S3 for the values). A: order 11 epicardial vessels. B: order 7 intramyocardial vessels. C: order 5 intramyocardial vessels. D: diameter distensibility (×100% × mmHg⁻²) of LAD arteries at physiological pressure with and without consideration of physiological axial stretch.