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A continuum mechanics framework and a constitutive model for remodelling of collagen gels and collagenous tissues

Authors
Journal
Journal of the Mechanics and Physics of Solids
0022-5096
Publisher
Elsevier
Publication Date
Volume
58
Issue
6
Identifiers
DOI: 10.1016/j.jmps.2010.03.005
Keywords
  • Collagen
  • Remodelling
  • Constitutive
  • Anisotropy
  • Hyperelasticity
Disciplines
  • Biology
  • Physics

Abstract

Abstract Collagen is a very important protein of the human body and is responsible for the structural stability of many body components. Furthermore, collagen fibre networks are able to grow and remodel themselves, which enables them to adjust to varying physiological conditions. This remodelling is accomplished by fibre-producing cells, such as fibroblasts. The ability to adjust to new physiological conditions is very important, for example in wound healing. In the present paper, a theoretical framework for modelling collagenous tissues and collagen gels is proposed. Continuum mechanics is employed to describe the kinematics of the collagen, and affine deformations of fibres are assumed. Biological soft tissues can be approximated as being hyperelastic, and the constitutive model for the collagen fabric is therefore formulated in terms of a strain energy function. This strain energy function includes a density function that describes the distribution of the collagen fibre orientation. The density function evolves according to an evolution law, where fibres tend to reorient towards the direction of maximum Cauchy stress. The remodelling of the collagen network is also assumed to include a pre-stretching of collagen fibres, accomplished by fibroblasts. The theoretical framework is applied to experiments performed on collagen gels, where gels were exposed to remodelling under both biaxial and uniaxial constraints. The proposed model was able to predict both the resulting collagen distribution and the resulting stress–strain relationships obtained for the remodelled collagen gels. The influence of the most important model parameters is demonstrated, and it appears that there is a fairly unique set of model parameters that gives an optimal fit to the experimental data.

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