A New Three-Dimensional Exponential Material Model of the Coronary Arterial Wall to Include Shear Stress Due to Torsion

The biomechanical milieu of the coronary arteries is unique in that they experience mechanical deformations of twisting, bending, and stretching due to their tethering to the epicardial surface. Spatial variations in stresses caused by these deformations could account for the heterogeneity of atherosclerotic plaques within the coronary tree. The goal of this work was to utilize previously reported shear moduli to calculate a shear strain parameter for a Fung-type exponential model of the arterial wall and determine if this single constant can account for the observed behavior of arterial segments under torsion. A Fung-type exponential strain-energy function was adapted to include a torsional shear strain term. The material parameter for this term was determined from previously published data describing the relationship between shear modulus and circumferential stress and longitudinal stretch ratio. Values for the shear strain parameter were determined for three geometries representing the mean porcine left anterior descending coronary artery dimensions plus or minus one standard deviation. Finite element simulation of triaxial biomechanical testing was then used to validate the model. The mean value calculated for the shear strain parameter was $0.0759±0.0009$ (⁠$N=3$ geometries). In silico triaxial experiments demonstrated that the shear modulus is directly proportional to the applied pressure at a constant longitudinal stretch ratio and to the stretch ratio at a constant pressure. Shear moduli determined from these simulations showed excellent agreement to shear moduli reported in literature. Previously published models describing the torsional shear behavior of porcine coronary arteries require a total of six independent constants. We have reduced that description into a single parameter in a Fung-type exponential strain-energy model. This model will aid in the estimation of wall stress distributions of vascular segments undergoing torsion, as such information could provide insight into the role of mechanical stimuli in the localization of atherosclerotic plaque formation.