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Numerical implementation of fiber dispersion in growth and remodeling model

Human aortas can be viewed as fibrous composite with three layers (intima, media, and adventitia) and three main load-bearing constituents (elastin, collagen fibers, and smooth muscle cells). Collagen fibers are grouped into several families with different mean direction and dispersion in tangential plane and out-of-plane that vary from layer to layer. Furthermore, diseased aortas (e.g., abdominal aortic aneurysms) are characterized with local loss of elastin and increased dispersion compared to the healthy aortas [1]. Numerical studies that focus on the modeling of healthy arterial wall and aortic aneurysms often use constrained mixture models of growth and remodeling (G&R) that can describe processes within the aortic wall and responses of the aorta to different mechanical (e.g. stress) and chemical (e.g. diffusion of vasoconstrictors and vasodilators) stimuli. Some G&R models have four collagen fiber families (e.g. [2]) whereas some model only two fiber families (e.g. [3]). Nevertheless, none of the studies so far has incorporated fiber dispersion in G&R model. Our aim in this work is to extend the current G&R model by integrating fiber dispersion and to study influence of fiber dispersion on abdominal aortic aneurysm (AAA) evolution. For modeling AAA growth, we use constrained mixture G&R model slightly adapted from [2] and fiber dispersion model presented in [4]. The dispersion model is based on generalized structure tensor approach and can capture non-symmetric fiber dispersion (i.e. different dispersion in and out-of-plane). Numerical models were implemented in finite element software FEAP using subroutines for user defined material model. Augmented Lagrange method was used for achieving incompressibility. The aortic wall was modeled as three-layer structure. Each layer was defined by different mass ratios of main constituents, mean fiber angles of the two collagen fiber families, and dispersion parameters. Fiber angles and dispersion parameters were taken from [1] whereas other model parameters were defined similar to the work in [5]. Influence of fiber dispersion was analyzed on an arterial cylindrical model, as well as on an axisymmetric model of a fusiform aneurysm. In order to initiate the formation of an aneurysm, elastin was degraded locally with a time-depended degradation function. Results have shown that collagen fiber dispersion has a significant influence on aortic wall behavior and outcome of an aneurysm growth. Increased fiber dispersion (i.e. more isotropic material) led to faster growth rate and higher risk of rupture, whereas model with perfectly aligned fibers showed slowest growth rate. Therefore, we suggest that fiber should be taken into account in future G&R studies.

collagen fiber dispersion, growth and remodeling, abdominal aortic aneurysm

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