Constitutive Modeling of Coronary Arterial Media—Comparison of Three Model Classes

Planar schematics of vessel mappings. Left: In the true reference state the vessel is open, unswollen, and stress-free (SF) with inner and outer radii, Ri and Ro, length L, and an opening angle Θ0. In the swollen state (SW) it is open but not stress free, with corresponding dimensions R̂i, R̂o, Λ0L, with Λ0 as the SF-SW transformation stretch ratio, and an opening angle Θ1. The closed unloaded (UL) configuration is not subjected to further swelling, and with dimensions ρi, ρo, and Λ0Λ1L, with Λ1 as the SW-UL stretch ratio. The closed loaded (L) configuration has dimensions: inner and outer radii ri and ro, length λΛ0Λ1L, with λ as the UL-L stretch ratio, and twist per unit length γ (not shown in figure). Right: Force and bending moment resultants of circumferential stress acting on the swollen open sector free edges; both vanish, yielding a boundary constraint on the circumferential stress distribution.

Fung-type phenomenological model (1) descriptive power (sample No. 1). Predictions (lines) and experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, versus inner luminal pressure Pi, under three axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+).

Structure-motivated Invariant-based model (2) descriptive power (sample No. 1). Predictions (lines) and experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, all versus inner luminal pressure Pi, under three axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+).

Fully structural model (4) descriptive power (sample No. 1). Predictions (lines) and experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, all versus inner luminal pressure Pi, under three axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+).

Fung-type model (1) stretch predictive power (sample No. 1): predictions (lines) compared with experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, all versus inner luminal pressure Pi, under three axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+). Parameters are estimated from data at stretch ratios 1.2 and 1.3, and predictions are then simulated for stretch ratio 1.4 (bold dashed-dotted lines).

Invariant-based model (2) stretch predictive power (sample No. 1). Predictions (lines) compared with experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, all versus inner luminal pressure Pi, under three axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+). Parameters are estimated from data at stretch ratios 1.2 and 1.3, and predictions are then simulated for stretch ratio 1.4 (bold dashed-dotted lines).

Structural model (4) stretch predictive power (sample No. 1). Predictions (lines) compared with experimental data (symbols) of (a) outer radius ro, (b) axial force F, and (c) torsional apparent stiffness μ, all versus inner luminal pressure Pi, under 3 axial stretch ratios (λ) of 1.2 (○), 1.3 (□), and 1.4 (+). Parameters are estimated from data at stretch ratios 1.2 and 1.3, and predictions are then simulated for stretch ratio 1.4 (bold dashed-dotted lines).

2D-to-3D predictive power (sample No. 1). Comparison between predicted twist apparent stiffness (lines) and measured data (symbols) at three axial stretch ratios (λ) 1.2 (○), 1.3 (□), and 1.4 (+) for (a) the invariant-based and (b) the structural models.