A novel computational remodelling algorithm for the probabilistic evolution of collagen fibre dispersion in biaxially strained vascular tissue

In this work, we constructed a novel collagen fibre remodelling algorithm that incorporates the complex nature of random evolution acting on single fibres causing macroscopic fibre dispersion. The proposed framework is different from the existing remodelling algorithms, in that the microscopic random force on cellular scales causing a rotational-type Brownian motion alone is considered as an aspect of vascular tissue remodelling. A continuum mechanical framework for the evolution of local dispersion and how it could be used for modeling the evolution of internal radius of biaxially strained artery structures under constant internal blood pressure are presented. A linear evolution form for the statistical fibre dispersion is employed in the model. The random force component of the evolution, which depends on the mechanical stress stimuli, is described by a single parameter. Although the mathematical form of the proposed model is simple, there is a strong link between the microscopic evolution of collagen dispersion on the cellular level and its effects on the macroscopic visible world through mechanical variables. We believe that the proposed algorithm utilizes a better understanding of the relationship between the evolution rates of mean fibre direction and fibre dispersion. The predictive capability of the algorithm is presented using experimental data. The model has been simulated by solving a single-layered axisymmetric artery (adventitia) deformation problem. The algorithm performed well for estimating the quantitative features of experimental anisotropy, the mean fibre direction vector and the dispersion (κ) measurements under strain-dependent evolution assumptions.

A theoretical model of the endothelial cell morphology due to different waveforms

Endothelial cells are key units in the regulatory biological process of blood vessels. They represent an interface to transmit variations on the fluid dynamic changes. They are able to adapt its cytoskeleton, by means of microtubules reorientation and F-actin reorganization, due to new mechanical environments. Moreover, they are responsible for initiating a huge cascade of biological processes, such as the release of endothelins (ET-1), in charge of the constriction of the vessel and growth factors such as TGF-β and PDGF. Although a huge efforts have been made in the experimental characterization and description of these two issues the computational modeling has not gained such an attention. In this work we study the 3D remodeling of endothelial cells based on the main features of blood flow. In particular we study how different oscillatory shear index and the time average wall shear stresses modify the endothelial cell shape. We found our model fitted the experimental works presented before in in vitro studies. We also include our model within a computational fluid dynamics simulation of a carotid artery to evaluate endothelial cell shape index which is a key predictor of atheroma plaque formation. Moreover, our approach can be coupled with models of collagen and smooth muscle cell growth, where remodeling and the associated release of chemical substance are involved.

A quantitative study of the relationship between the distribution of different types of collagen and the mechanical behavior of rabbit medial collateral ligaments

The mechanical properties of ligaments are key contributors to the stability and function of musculoskeletal joints. Ligaments are generally composed of ground substance, collagen (mainly type I and III collagen), and minimal elastin fibers. However, no consensus has been reached about whether the distribution of different types of collagen correlates with the mechanical behaviors of ligaments. The main objective of this study was to determine whether the collagen type distribution is correlated with the mechanical properties of ligaments. Using axial tensile tests and picrosirius red staining-polarization observations, the mechanical behaviors and the ratios of the various types of collagen were investigated for twenty-four rabbit medial collateral ligaments from twenty-four rabbits of different ages, respectively. One-way analysis of variance was used in the comparison of the Young's modulus in the linear region of the stress-strain curves and the ratios of type I and III collagen for the specimens (the mid-substance specimens of the ligaments) with different ages. A multiple linear regression was performed using the collagen contents (the ratios of type I and III collagen) and the Young's modulus of the specimens. During the maturation of the ligaments, the type I collagen content increased, and the type III collagen content decreased. A significant and strong correlation () was identified by multiple linear regression between the collagen contents (i.e., the ratios of type I and type III collagen) and the mechanical properties of the specimens. The collagen content of ligaments might provide a new perspective for evaluating the linear modulus of global stress-strain curves for ligaments and open a new door for studying the mechanical behaviors and functions of connective tissues.