A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis, computational aspects and applications

Abstract

Cartilage is a multi-phase material composed of fluid and electrolytes (68–85% by wet weight), proteoglycans (5–10% by wet weight), chondrocytes, collagen fibres and other glycoproteins. The solid phase constitutes an isotropic proteoglycan gel and a fibre network of predominantly type II collagen, which provides tensile strength and mechanical stiffness. The same two components control diffusion of the fluid phase, e.g. as visualised by diffusion tensor MRI: (i) the proteoglycan gel (giving a baseline isotropic diffusivity) and (ii) the highly anisotropic collagenous fibre network. We propose a new constitutive model and finite element implementation that focus on the essential load-bearing morphology: an incompressible, poroelastic solid matrix reinforced by an inhomogeneous, dispersed fibre fabric, which is saturated with an incompressible fluid residing in strain-dependent pores of the collagen–proteoglycan solid matrix. The inhomogeneous, dispersed fibre fabric of the solid further influences the fluid permeability, as well as an intrafibrillar portion that cannot be ‘squeezed out’ from the tissue. Using representative numerical examples on the mechanical response of cartilage, we reproduce several features that have been demonstrated experimentally in the cartilage mechanics literature.

Keywords::

• cartilage
• constitutive modelling
• finite element simulation
• collagen fibre
• biphasic
• homogenisation

Acknowledgements

We thank Magnus B. Lilledahl from Norwegian University of Science and Technology (NTNU), Department of Physics, for part of the inspiration for developing this modelling approach, and Thomas S.E. Eriksson from Graz University of Technology, Institute of Biomechanics, for many discussions on this subject matter.

Notes

^1. Email: [email protected]

^2. Email: [email protected]