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

Author (s): Saez, P.; Peña, E.; Martinez, M.A.
Journal: Annals of biomedical engineering

Volume: 42, Issue 6
Pages: 1158 – 1169
Date: 2014

The objective of this work is to develop a remodeling model for biological matter coupling two different processes in a 3D framework: reorientation of the preferential direction of a given fibered structure and reorientation of the fibrils or filaments that make up such a structure. This work uses the microsphere-based approach to take into account the micro mechanics involved in biological fibered structures regarding both their passive behavior and the reorientation of their micro constituents. Moreover, the macro behavior of the material as a whole is obtained by means of homogenizing the underlying micro response. We associate the orientation space of the integration directions to the physical space of micro-fibrils. To approximate the directional distribution of the fibrils within each fiber bundle, a Bingham probability orientation density function is introduced into the Helmholtz energy function. With all these assumptions, the problem is studied from an energetic point of view, describing the dissipation inherent to remodeling processes, and the evolution equations for both reorientations (change in preferential direction of the network and change in shape of the fibril distribution) re obtained. The model is included in a finite element code which allows computing different geometries and boundary value problems. This results in a complete methodology for characterizing the reorientation evolution of different fibered biological structures, such as cells. Our results show remodeling of fibered structures in two different scales, presenting a qualitatively good agreement with experimental findings in cell mechanics. Hierarchical structures align in the direction of the maximum principal direction of the considered stimulus and narrow in the perpendicular direction. The dissipation rates follows predictable trends although there are no experimental findings to date for comparison. The incorporation of metabolic processes and an insight into cell-oriented mechano-sensing processes can help to overcome the limitations involved.



author="S{\'a}ez, P.
and Pe{\~{n}}a, E.
and Mart{\'i}nez, M. A.",
title="A Structural Approach Including the Behavior of Collagen Cross-Links to Model Patient-Specific Human Carotid Arteries",
journal="Annals of Biomedical Engineering",
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 introduced 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 patient-specific carotid artery geometry is reconstructed and simulated in a finite element framework, providing a microstructural description of the arterial wall. Our results qualitatively and quantitatively describe the experimental findings given in the literature fitting macroscopic mechanical tests and improving the features of previously developed models.",