Influence of Fiber Dispersion Representation on the Accuracy of the Mechanical Response of Healthy and Aneurysmal Aortic Wall Tissue

Abstract

This study investigates the influence of fiber dispersion representation on the accuracy of the mechanical response of anisotropic hyperelastic material models for healthy and aneurysmal human aortic wall tissue under planar biaxial loading. Five fitting strategies were compared: (i) detailed integration of fiber orientation and dispersion data across the thickness; (ii) a single, thickness-averaged fiber distribution; (iii) two representative layers (media and adventitia); (iv) multiple layers discretized in the radial direction; and (v) a single layer with a symmetrical in-plane distribution of collagen fibers. The goodness of fit was calculated using the coefficient of determination averaged over all experimental tests. The most accurate fits were achieved with strategy (i), with a goodness of fit $R_{\mathrm{avg}}^2\approx 0.96\pm 0.02$ for the combined cohort of aneurysm patients and the healthy cohort; comparable accuracy was achieved by the two-layer model (iii), $R_{\mathrm{avg}}^2\approx 0.91\pm 0.06$, but with significantly less complexity in model implementation. As a secondary objective of this study, regional parameters that correlate with the two-layer model (iii) and are intended for finite element analyses are presented. The method using a symmetrical single layer in model (v) yielded the lowest accuracy, $R_{\mathrm{avg}}^2\approx 0.73\pm 0.14$, and highlighted the need to capture non-symmetric fiber families. The modeling of elastin as a separate anisotropic material was also investigated by comparing two different constitutive modeling approaches. While the healthy cohort showed the best fit by including elastin in model (i) ($R_{\mathrm{avg}}^2\approx 0.99\pm 0.01$), separate treatment of elastin in the combined cohorts resulted in only a slight increase of $R_{\mathrm{avg}}^2$ of $\approx 0.02$. This marginal improvement is offset by the risk of overfitting due to additional parameters, which supports the inclusion of elastin in the ground matrix.