Experimentally validated microstructural 3D constitutive model of coronary arterial media

Abstract

Accurate modeling of arterial response to physiological or pathological loads may shed light on the processes leading to initiation and progression of a number of vascular diseases and may serve as a tool for prediction and diagnosis. In this study, a microstructure based hyperelastic constitutive model is developed for passive media of porcine coronary arteries. The most general model contains 12 independent parameters representing the three-dimensional inner fibrous structure of the media and includes the effects of residual stresses and osmotic swelling. Parameter estimation and model validation were based on mechanical data of porcine left anterior descending (LAD) media under radial inflation, axial extension, and twist tests. The results show that a reduced four parameter model is sufficient to reliably predict the passive mechanical properties. These parameters represent the stiffness and the helical orientation of each lamellae fiber and the stiffness of the interlamellar struts interconnecting these lamellae. Other structural features, such as orientational distribution of helical fibers and anisotropy of the interlamellar network, as well as possible transmural distribution of structural features, were found to have little effect on the global media mechanical response. It is shown that the model provides good predictions of the LAD media twist response based on parameters estimated from only biaxial tests of inflation and extension. In addition, good predictive capabilities are demonstrated for the model behavior at high axial stretch ratio based on data of law stretches.

Fig. 1

A schematic description of the mappings from the open stress-free (SF) sector configuration, through the open sector swollen (SW) and closed unloaded (UL) states, to the loaded (L) configuration.

Fig. 2

Transverse section of the cut open swelled configuration. Distribution of circumferential stress ${\sigma }_{\widehat{ϴ}\widehat{ϴ}}$ is indicated along with its resultant force f and bending moment m.

Fig. 3

A scheme of the vessel wall micro-structure including the lamellae helical elastin-collagen fibers, the inter-lamellar strut networks, and the smooth muscle cells.

Fig. 4

(A) Axial profile of pig RCA media, inflated by luminal pressure of 100mmHg. The vessel radius is constant throughout most of vessel length. A short transition zone, over which the vessel radius decreases from its mid-length level (left) to the cannula radius (right), is seen. (B) Scheme of the loaded vessel axial profile inner diameter.

Fig. 5

Fiber orientation beta distribution functions: (A) The 3D distribution of the inter-lamellar fibers (12); (B) the 2D distribution of the helical fibers (17).

Fig. 6

Model descriptive power: predictions (lines) compared with experimental data (symbols) of (A) outer radius r_o, (B) axial force F, and (C) torsional stiffness μ, vs. inner luminal pressure P_i, under three axial stretch ratios (λ).

Fig. 7

Model descriptive power: predictions (lines) compared with experimental data (symbols) of (A) average circumferential Cauchy stress, and (B) average axial Cauchy stress, vs. inner luminal pressure P_i, under three axial stretch ratios (λ).

Fig. 8

Transmural distribution of (A) radial, (B) circumferential, and (C) axial Cauchy stresses at fix luminal pressure of 12KPa, under three axial stretch ratios (λ).

Fig. 9

Comparative model simulations beyond the range of pressures and axial stretches of the experimental database. In (A), (B), and (C) the influence of helical elastin on the behavior of outer radius, axial force, and torsional stiffness is demonstrated. The influence of orientational distribution on the behavior of axial force in demonstrated in (D). In all subfigures solid and dash lines are the simulations with and without the examined structural feature.

Fig. 10

Model predictive power. (A), (B), and (C) – comparison of data (symbols) with predictions of the model with parameters estimated from partial data of stretch ratios 1.2 and 1.3 (solid lines) and compared to data of 1.4 (dashed line). (D) – predictions of torsional stiffness vs. internal pressure with parameters estimated from inflation-extension data.

Fig. 11

Data structure analysis: predictions (lines) compared with experimental data (symbols) of (A) axial force from inflation extension data, and (B) outer radius from extension torsion estimation, under three axial stretch ratios (λ).

Fig. 12

Transmural distribution of (A) circumferential and (B) axial stresses at fix luminal pressure of 12KPa and axial stretch λ = 1.4 for a model with and without tissue swelling