How Constitutive Model Complexity can Affect the Capability to Fit Experimental Data: a Focus on Human Carotid Arteries and Extension/Inflation Data

To perform realistic finite element simulations of cardiovascular surgical procedures (such as balloon angioplasty, stenting or bypass), it is necessary to use appropriate constitutive models able to describe the mechanical behavior of the human arterial wall (in healthy and diseased conditions) as well as to properly calibrate the material parameters involved in such constitutive models. Moving from these considerations, the goal of the present study is to compare the reliability of two isotropic phenomenological models and of four structural invariant-based constitutive models, commonly used to describe the passive mechanical behavior of arteries. The arterial wall is modeled as a thick-wall tube with one- and two- layer structure. Residual stresses inclusion is also considered, to evaluate informations on the stress distribution through the wall thickness. The predictive capability of the investigated models is tested using extension/inflation data on human carotid arteries related by two different experimental works available in the literature. The material parameters involved in the investigated models are computed in the least-square sense thought a best fitting procedure, relying on a multi-start optimization algorithm. The good quality of the optimal solution is validated quantitatively computing proper error measures and comparing the model prediction curves. The final outcome of the paper is a critical review of the six considered constitutive models, comparing their formulation and evidencing the more or less capability of such models to fit the considered experimental data.