Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

Model Structure

For every solid with a microstructure there is a correlation between its internal structure and its macroscopic mechanical properties. Continuum based constitutive relations describe the overall behaviour that results from this internal structure; and the development of these constitutive relations particularly in the case of soft biological tissues has been an area of active research for several decades.

Soft biological tissue consists primarily of various types of cells, an extracellular matrix, and abundant water. They contain cell types that sense and convert mechanical stimuli into bioelectrical and biochemical signals, which control the homeostatic processes within the tissues and monitors the tissue's homeostatic tendencies in regards to changes in its mechanical environment. It is therefore important to develop realistic constitutive models for these soft biological tissues, in order to quantify changes in their structure and function in response to altered mechanical stimulus.

Over the past few decades, research and modeling of the heart and its associated blood vessels have been a topic of major importance; the paper presented here focuses on hyperelastic modelling of arterial layers with distributed collagen fibre orientation. Collagen fibres are a key component in the structure of arteries, and the structural continuum constitutive models of arterial layers allow the integration of information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading.

Within the media (middle layer) of the artery wall, the collagen fibres are arranged helically and with very little dispersion in their orientation. In contrast to this, in the adventitia (outermost layer) and intima (innermost layer), the orientation of the collagen fibres is dispersed. As a result, continuum models that do not account for this dispersion are not able to capture accurately the stress-strain response of these layers.

In the paper presented here, the authors Gasser, Ogden and Holzapfel focus on the development and introduction of a structural continuum framework that is able to represent the dispersion of the collagen fibres orientation within arterial walls. Thus allowing the development of a new hyperelastic free-energy function that is well suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls.

The model was implemented in a manner that could be used for peforming finite element model simulations on the CMISS software program developed at the Bioengineering Institute, University of Auckland. The model file presented here focuses on the functional form of the fibre dispersion law corresponding to the the combination 2,4,6,8 (FiberDispersion_law_2468), with 2 representing the isotropic component of the functional form, and 4, 6 and 8 representing the anisotropic components of the fucntional form.

For additional information on implementation of cellML files in CMISS, please refer to the following Link.

This file has not been recently checked for compatibility within CMISS, any feedback regarding this and any other issues would be appreciated.

The complete original paper reference is cited below:

Hyperelastic modelling of arterial layers with distributed collagen fibre orientations, T.C. Gasser, R.W. Ogden and G.A. Holzapfel, 2006. Journal of the Royal Society, Interface / the Royal Society , 3(6), 15-35. PubMed ID: 16849214