Modeling the Matrix of Articular Cartilage Using a Continuous Fiber Angular Distribution Predicts Many Observed Phenomena

Abstract

Background Cartilage is a hydrated soft tissue whose solid matrix consists of negatively charged proteoglycans enmeshed within a fibrillar collagen network. Though many aspects of cartilage mechanics are well understood today, most notably in the context of porous media mechanics, there remain a number of responses observed experimentally whose prediction from theory has been challenging. Method of approach In this study the solid matrix of cartilage is modeled with a continuous fiber angular distribution, where fibers can only sustain tension, swelled by the osmotic pressure of a proteoglycan ground matrix. Results It is shown that this representation of cartilage can predict a number of observed phenomena in relation to the tissue’s equilibrium response to mechanical and osmotic loading, when flow-dependent and flow-independent viscoelastic effects have subsided. In particular, this model can predict the transition of Poisson’s ratio from very low values in compression (~0.02) to very high values in tension (~2.0). Most of these phenomena cannot be explained when using only three orthogonal fiber bundles to describe the tissue matrix, a common modeling assumption used to date. Conclusions The main picture emerging from this analysis is that the anisotropy of the fibrillar matrix of articular cartilage is intimately dependent on the mechanism of tensed fiber recruitment, in the manner suggested by our recent theoretical study (G. A. Ateshian. J Biomech Eng, 129(2):240-9, 2007).

Constitutive modelling of arteries

“…The recent study by Cortes et al (in press) uses the formulation based on the generalized structure tensor (4.3) for quantitative comparisons with an angular integration formulation in which the strain energy and stresses are calculated by integrating the energy and stresses of the individual fibres, as in, for example, connective tissues (Lanir 1983), aortic valve cusps (Billiar & Sacks 2000), corneal stroma (Nguyen et al 2008), articular cartilage (Ateshian et al 2009) or the posterior sclera (Girard et al 2009). Cortes et al (in press) derived analytically the differences between the general structure tensor and angular integration formulations.…”

Multiscale cartilage biomechanics: technical challenges in realizing a high-throughput modelling and simulation workflow

“…for the hip [35] rsfs.royalsocietypublishing.org Interface Focus 5: 20140081 II), water content (75-80% wet weight), dissolved ions and aggregating proteoglycans [2]. The material properties are depth-dependent [36], and as a result of varying fibre alignment in each zone, they also exhibit anisotropy [37]. All these influence how the mechanical deformations and loads distribute within the tissue.…”

Microsphere-Based Gradient Implants for Osteochondral Regeneration: a Long-Term Study in Sheep

“…Our previous report on TGF-β3-chondroitin sulfate combination encapsulated in PLGA microspheres was found to favor chondrogenic differentiation of stem cells [20]. The rationale for these pilot Joints retrieved 1 year post-implantation were subjected to uniaxial compressive indentation and modeled with the biphasic theory, with the solid phase consisting of a biphasic material with a 'neo-Hookean' ground matrix and a spherical fiber distribution to model the collagen fibrillar matrix [33]. Note that the LFC of the microfracture group had the only permeability to be statistically significantly larger than the untreated control, whereas the gradient LFC group had the only aggregate modulus statistically significantly below that of the untreated control.…”

“…The porous extracellular matrix was described by a solid mixture of a neo-Hookean ground matrix reinforced by a continuous, random distribution of fibril bundles sustaining tension only; the hydraulic permeability was assumed constant [26][27][28]. The model had a total of five material constants: Aggregate modulus (E) and Poisson's ratio (ν) for the neo-Hookean solid, the fibril modulus (k si ) and the power-law exponent β for the spherical fiber distribution, and the constant hydraulic permeability k. It was assumed a priori that ν = 0 (for the porous ground matrix due to the compressibility of the pore space) and β = 2 (to produce a linear tensile response in the range of small strains, consistent with the known behavior of cartilage) so that the parameter optimization was only performed on E, k si and k [27].…”