A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations

David M Pierce, Michael Johannes Unterberger, Werner Trobin, Tim Ricken, Gerhard Holzapfel

Research output: Contribution to journalArticleResearchpeer-review

Abstract

The remarkable mechanical properties of cartilage derive from an interplay of isotropically distributed, densely packed and negatively charged proteoglycans; a highly anisotropic and inhomogeneously oriented fiber network of collagens; and an interstitial electrolytic fluid. We propose a new 3D finite strain constitutive model capable of simultaneously addressing both solid (reinforcement) and fluid (permeability) dependence of the tissue's mechanical response on the patient-specific collagen fiber network. To represent fiber reinforcement, we integrate the strain energies of single collagen fibers-weighted by an orientation distribution function (ODF) defined over a unit sphere-over the distributed fiber orientations in 3D. We define the anisotropic intrinsic permeability of the tissue with a structure tensor based again on the integration of the local ODF over all spatial fiber orientations. By design, our modeling formulation accepts structural data on patient-specific collagen fiber networks as determined via diffusion tensor MRI. We implement our new model in 3D large strain finite elements and study the distributions of interstitial fluid pressure, fluid pressure load support and shear stress within a cartilage sample under indentation. Results show that the fiber network dramatically increases interstitial fluid pressure and focuses it near the surface. Inhomogeneity in the tissue's composition also increases fluid pressure and reduces shear stress in the solid. Finally, a biphasic neo-Hookean material model, as is available in commercial finite element codes, does not capture important features of the intra-tissue response, e.g., distributions of interstitial fluid pressure and principal shear stress.

LanguageEnglish
Pages229-44
Number of pages16
JournalBiomechanics and Modeling in Mechanobiology
Volume15
Issue number1
DOIs
StatusPublished - Feb 2016

Fingerprint

Fiber Orientation
Cartilage
Viscoelasticity
Continuum Model
Fiber reinforced materials
Permeability
Extracellular Fluid
Collagen
Pressure
Fluid
Fiber
Fluids
Shear Stress
Fibers
Tissue
Shear stress
Reinforcement
Distribution functions
Tensors
Diffusion Magnetic Resonance Imaging

Keywords

  • Cartilage, Articular
  • Collagen
  • Computer Simulation
  • Diffusion Tensor Imaging
  • Elasticity
  • Finite Element Analysis
  • Models, Biological
  • Models, Statistical
  • Permeability
  • Stress, Mechanical
  • Viscosity
  • Journal Article

Cite this

A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations. / Pierce, David M; Unterberger, Michael Johannes; Trobin, Werner; Ricken, Tim; Holzapfel, Gerhard.

In: Biomechanics and Modeling in Mechanobiology, Vol. 15, No. 1, 02.2016, p. 229-44.

Research output: Contribution to journalArticleResearchpeer-review

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