Implementation of collagen fiber dispersion in a growth and remodeling model of arterial walls

Imaging studies have shown, and more recently quantified, the collagen fiber dispersions within the aortic wall. Simultaneously, experimental and numerical studies highlight a significant influence of the dispersion on the aortic mechanical response. On the other hand, none of the numerical studies describing the adaptation of healthy and diseased aortas in response to different stimuli take fiber dispersion into account. In this study, we present the first implementation of a fiber dispersion model based on the generalized structure tensor approach into a constrained mixture growth and remodeling model of the aortic wall. Additionally, a new definition of the fiber pre-stretch tensor compatible with fiber dispersion is proposed. The new extended model was implemented into a finite element analysis program, and the influence of collagen fiber dispersions and mean fiber angles on aneurysm growth and the distribution of stresses inside the aortic wall were studied on a three-layered axisymmetric model of a fusiform abdominal aortic aneurysm as well as on non-symmetric aneurysm. In the analyses, the dispersion parameters and the mean fiber angles were varied in the range of measured values for healthy abdominal aortas and aneurysms. Results show a reasonable behavior during an extension-inflation test and the expected evolution of residual stresses during adaptation due to hypertension. Moreover, they show that changes in fiber dispersions and mean fiber angles have a significant influence on the aneurysm evolution and the stress distribution. For example, simulations with increased fiber dispersion in the intima or the media showed a slower aneurysm growth, while the opposite was true for the adventitia. Mean fiber direction closer to the circumferential direction resulted in a stiffer response in the aortic inflation analysis, and it also decreased the aneurysm growth rate.