A validated 3D microstructure-based constitutive model of coronary artery adventitia

Abstract

A structure-based model that accurately predicts micro- or macromechanical behavior of blood vessels is necessary to understand vascular physiology. Based on recently measured microstructural data, we propose a three-dimensional microstructural model of coronary adventitia that incorporates the elastin and collagen distributions throughout the wall. The role of ground substance was found to be negligible under physiological axial stretch λz = 1.3, based on enzyme degradation of glycosaminoglycans in swine coronary adventitia (n = 5). The thick collagen bundles of outer adventitia (n = 4) were found to be undulated and unengaged at physiological loads, whereas the inner adventitia consisted of multiple sublayers of entangled fibers that bear the majority of load at higher pressures. The microstructural model was validated against biaxial (inflation and extension) experiments of coronary adventitia (n = 5). The model accurately predicted the nonlinear responses of the adventitia, even at high axial force (axial stretch ratio λz = 1.5). The model also enabled a reliable estimation of material parameters of individual fibers that were physically reasonable. A sensitivity analysis was performed to assess the effect of using mean values of the distributions for fiber orientation and waviness as opposed to the full distributions. The simplified mean analysis affects the fiber stress-strain relation, resulting in incorrect estimation of mechanical parameters, which underscores the need for measurements of fiber distribution for a rigorous analysis of fiber mechanics. The validated structure-based model of coronary adventitia provides a deeper understanding of vascular mechanics in health and can be extended to disease conditions.

Keywords: adventitia; collagen; constitutive model; elastin; material parameters; microstructure.

Fig. 1.

A: outer adventitia (OA) consists of thicker collagen bundles and few elastin fibers. B: inner adventitia (IA) is a layered structure with entangled elastin and collagen fibers in each sublayer. C: the cross section of a coronary artery at no-load state. D: a schematic diagram demonstrates the cross section and lateral section of a vessel segment. E and F: OA and IA deformed under elevated pressures, 100 and 200 mmHg, respectively, showing that fibers in IA were stretched to take up loads, whereas most of the collagen bundles in OA were still undulated and unengaged. Lateral sections (A and B); cross sections (C, E, and F). Original scale bars, 100 μ.

Fig. 2.

A–C: immunohistochemical images of control and GAG-digested vessels. A: Control group (purple); B: vessel labeled with antibody CS-56 (brown specifying GAGs); C: GAG-digested vessel labeled with antibody CS-56 (purple confirming GAG removal). D: mechanical testing of coronary adventitia, with or without GAGs under physiological axial stretch λ_z = 1.3. There was no significant difference between these 2 groups (P = 0.384).

Fig. 3.

Comparison of model predictions (solid lines) with experimental measurements (dashed lines: sample mean, error bar denotes SD of experimental data). Outer radius (top) and axial force (bottom) at 3 axial stretch ratios λ_z = 1.0, 1.3, and 1.5.

Fig. 4.

Model predictions of Cauchy stress components of adventitia (Sample #1) under 3 axial stretch ratios. Top: transmural stress distribution at a fixed luminal pressure 0.013 MPa (100 mmHg); bottom: stress components as a function of circumferential strain in the middle wall of the adventitia.

Fig. 5.

The stress-strain curves of individual elastin and collagen fibers using mean material parameters estimated by various models. Straightening strain e₀ was set to 0.345 for collagen fiber. E and C denote the stress-strain curves of elastin and collagen fibers, respectively. E1 and C1 are the curves estimated by a full distribution model with full data sets; E2 and C2 are the curves estimated by full distribution model with partial data sets of λ_z = 1.3 and 1.5; and E3 and C3 are the curves estimated by the simplified mean-values model with full data sets. σ_θθ denotes the circumferential stress-strain relation of the adventitia at the middle wall under the axial stretch ratio λ_z = 1.3.