A Structural Approach Including the Behavior of Collagen Cross-Links to Model Patient-Specific Human Carotid Arteries

Abstract

In this work the mechanical response of the carotid arterial wall is studied. Some limitations of previous models of the arterial wall are overcomed and variability of the fitting problem is reduced. We review some experimental data from the literature and provide a constitutive model to characterize such data. A strain energy function is intoduced including the behavior of cross-links between the main collagen fibers. With this function we are able to fit experimental data including information about the microstructure that previous models were not able to do. To demonstrate the applicability of the proposed model a patientspecific carotid artery geometry is reconstruted and simulated in a finite element framework, providing a microstructural description of the arterial wall. Our results qualitatively and 1 Micro-structural modeling of patient specific human carotid artery 2 quantitatively describe the experimental findings given in the literature fitting macroscopic mechanical tests including information of the microstructure distribution.

Microstructural quantification of collagen fiber orientations and its integration in constitutive modeling of the porcine carotid artery

“…Finally, we mentioned that considering cross-linking among the collagen fibers (α > 0) was essential for the constitutive model to capture the experimental data. As described previously by [30], the cross-links between the main collagen fibers contribute to the compliance of the tissue. Based on previous models, the mechanical contribution in the longitudinal direction could not be observed in cases where the main fibers are preferentially aligned in circumferential behavior, as in the present study.…”

“…Interestingly, these finer structures seem to cross-bridge thicker fibers in a mesh-like network without a clear preferred fiber orientation. In the present study such a coupling amongst thicker collagen fibers it is thought to be captured by the previously suggested coupling parameter α [30]. However, since the level of mechanical coupling can not be histologically identified, α was considered as an unknown in the parameter estimation procedure, i.e.…”

“…is an effective orientation density that accounts for cross-links between the main collagen fibers, see Figure 3.ρ takes into account the space covered by the collagen cross-links appearing in the physical space where main collagen fibers do not exist, as reported by a previous model [30]. Specifically,…”

Patient-Specific Airway Wall Remodeling in Chronic Lung Disease

“…To create volume meshes from the initial surface representation, we offset the geometry outward to generate the mucosal and submucosal layers with dimensions according to Table 1 [64]. For each geometric parameter set, we create a new Y-branch model.…”

Towards the modelling of ageing and atherosclerosis effects in ApoE-/- mice aortic tissue

“…Later, and using the value of the elastin as seed c, we fit the rest of the parameters related with the collagen fibers, so k 1 and k 2 are identified with c = const using all experimental data points [27]. This non-standard sequential optimization technique is applied, as it may occur that a single optimization including every experimental data point for all of the three material parameters results in unphysical material parameters, e.g.…”