On the descriptive and predictive capabilities of two model approaches considering the collagen fiber dispersion in healthy and aneurysmal arteries

Abstract

Most constitutive models aim to describe the arterial macroscopic mechanical behavior via an elastin-rich ground substance reinforced by spatially dispersed collagen fibers. Two approaches are frequently considered for modeling collagen fiber dispersion, one is based on the generalized structure tensor (GST), and the other uses the angular integration (AI) method. Recently, both approaches have been reviewed for non-symmetric fiber distributions. It was concluded that both model ‘predictions’ fit very well with experimental data, solely based on the ability to ‘describe’ the same uniaxial or equibiaxial data set used for parameter estimation by not addressing any ‘predictive’ aspects. Therefore, this study systematically analyzes the ‘descriptive’ and ‘predictive’ capabilities of the GST and AI approaches by fitting their parameters to multiratio biaxial tensile test data of healthy and aneurysmal abdominal arteries. Subsequently, both model responses are investigated under realistic in vivo loading conditions, considering residual stresses, an axial in vivo stretch, and physiological blood pressure levels. In summary, no statistically significant difference in the ‘descriptive’ features of the two modeling approaches was identified. The pressure-radius relationship, the transmural stress distributions, and the axial force predicted by both models were analyzed for the healthy and diseased arterial ring, showing minor deviations based on fitting limitations.