Elliptical contact of thin biphasic cartilage layers: exact solution for monotonic loading

A three-dimensional unilateral contact problem for articular cartilage layers is considered in the framework of the biphasic cartilage model. The articular cartilages bonded to subchondral bones are modeled as biphasic materials consisting of a solid phase and a fluid phase. It is assumed that the subchondral bones are rigid and shaped like elliptic paraboloids. The obtained analytical solution is valid for monotonically increasing loading conditions.     

Measurements of nonhomogeneous, directional mechanical properties of articular cartilage in tension

The purpose of this investigation is to develop an accurate experimental procedure to measure the elastic properties of articular cartilage in uniaxial tension. Standardized, dumbbell shaped specimens, 250–325 μm thick, were taken from the surface, middle, and deep zones of the articular cartilage at 0°, 45°, and 90° from axis of the cleavage line pattern for the study of the zonal and directional properties of articular cartilage. A total of 75 specimens were tested to failure in this study. The use of a video dimensional analyzer system in this study makes accurate monitoring of the deformation of articular cartilage specimens possible. Nonlinear stress-strain relationships of the articular cartilage samples were mathematically approximated by exponential law similar to Fung (1967). Higher stiffness for the 0° specimens in the surface and middle zones was found. The experimental findings are in general agreement with the interpretations of low magnification scanning electron microscopy.     

A numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage

A method for numerical solution of the continuous spectrum linear biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. The method is based on an alternate formulation of the continuous spectrum stress-strain law that is implemented using Gaussian quadrature integration combined with quadratic interpolation of the strain history. For N time steps, the cost of the method is O(N). The method is applied to a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. For a range of relaxation times that are representative of articular cartilage, accuracy of the method is demonstrated by direct comparison to a theoretical Laplace transform solution.     

Experimental determination of the linear biphasic constitutive coefficients of human fetal proximal femoral chondroepiphysis

The mechanical properties of the cartilaginous regions of the proximal femoral epiphysis are an important factor in load transmission through the hip joint of young children. Cylindrical test specimens excised from the chondroepiphysis of human stillborn femoral heads were subjected to uniaxial loading in peripherally-unconfined compression, using a ramp/plateau input strain history. The corresponding load vs time curves were analyzed in terms of a recent analytical solution for a linear biphasic material (the well-known KLM model), allowing calculation of that model's three fundamental constitutive coefficients (permeability, equilibrium modulus and solid-phase Poisson ratio) for this material. The numerical algorithm developed to evaluate the biphasic solution yielded very precise replication of previously published KLM parametric plots. When fitted to experimental load histories, however, the model provided only a rather loose approximation of specimen behavior, due apparently to a substantial underestimation of the transient response component associated with interstitial fluid transport. Averaged over the series, the best-fit values for permeability (2.51 X 10(-15) m4 Ns-1) and equilibrium modulus (0.699 MPa) were in the range of values accepted for human adult articular cartilage. A consequence of the coarseness of the analytical curve fits was that a solid-phase Poisson ratio of 0.0 was inferred for all specimens. The permeability vs equilibrium modulus exhibited a nearly linear (r = 0.74) inverse relationship similar to that reported for adult articular cartilage.     

Biomechanical properties of human articular cartilage under compressive loads

The function of articular cartilage is to support and distribute loads and to provide lubrication in the diarthrodial joints. Cartilage function is described by proper mechanical and rheological properties, strain and depth-dependent, which are not completely assessed. Unconfined and confined compression are commonly used to evaluate the Young's modulus (E) and the aggregate modulus (H(A)), respectively. The Poisson's ratio (nu) can be calculated indirectly from the equilibrium compression data, or using the biphasic indentation technique; it has recently been optically evaluated by using video microscopy during unconfined compression. The transient response of articular cartilage during confined compression depends on its permeability k; a constant value of k can be easily identified by a simple analytical model of confined compression tests, whereas more complex models or direct measurements (permeation tests) are needed to study the permeability dependence on deformation. A poroelastic finite element model of articular cartilage was developed for this purpose. The elastic parameters (E,nu) of the model were evaluated performing unconfined compression creep tests on human articular cartilage disks, whereas k was identified from the confined test response. Our combined experimental and computational method can be used to identify the parameters that define the permeability dependence on deformation, as a function of depth from articular surface.     

Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure.

Failure of articular cartilage has been investigated experimentally and theoretically, but there is only partial agreement between observed failure and predicted regions of peak stresses. Since trauma and repetitive stress are implicated in the etiopathogenesis of osteoarthritis, it is important to develop cartilage models which correctly predict sites of high stresses. Cartilage is anisotropic and inhomogeneous, though it has been difficult to incorporate these complexities into engineering analyses. The objectives of this study are to demonstrate that a transversely isotropic, biphasic model of cartilage can provide agreement between predicted regions of high stresses and observed regions of cartilage failure and that with transverse isotropy cartilage stresses are more sensitive to convexity and concavity of the surfaces than with isotropy. These objectives are achieved by solving problems of diarthrodial joint contact by the finite-element method. Results demonstrate that transversely isotropic models predict peak stresses at the cartilage surface and the cartilage-bone interface, in agreement with sites of fissures following impact loading; isotropic models predict peak stresses only at the cartilage-bone interface. Also, when convex cartilage layers contacted concave layers in this study, the highest tensile stresses occur in the convex layer for transversely isotropic models; no such differences are found with isotropic models. The significance of this study is that it establishes a threshold of modeling complexity for articular cartilage that provides good agreement with experimental observations under impact loading and that surface curvatures significantly affect stress and strain within cartilage when using a biphasic transversely isotropic model.     

The effects of knee joint kinematics on anterior cruciate ligament injury and articular cartilage damage

This study determined which knee joint motions lead to anterior cruciate ligament (ACL) rupture with the knee at 25° of flexion. The knee was subjected to internal and external rotations, as well as varus and valgus motions. A failure locus representing the relationship between these motions and ACL rupture was established using finite element simulations. This study also considered possible concomitant injuries to the tibial articular cartilage prior to ACL injury. The posterolateral bundle of the ACL demonstrated higher rupture susceptibility than the anteromedial bundle. The average varus angular displacement required for ACL failure was 46.6% lower compared to the average valgus angular displacement. Femoral external rotation decreased the frontal plane angle required for ACL failure by 27.5% compared to internal rotation. Tibial articular cartilage damage initiated prior to ACL failure in all valgus simulations. The results from this investigation agreed well with other experimental and analytical investigations. This study provides a greater understanding of the various knee joint motion combinations leading to ACL injury and articular cartilage damage.     

The formation of a stable complex between dissociated proteoglycan and hyaluronic acid in the absence of a link protein.

A proteoglycan fraction prepared from bovine articular cartilage under dissociative conditions was shown to interact with three purified hyaluronic acid preparations to form stable complexes in the analytical ultracentrifuge. It is concluded from these experiments that, although link proteins are associated with hyaluronic acid and proteoglycans in complexes between these macromolecular constituents.     

Construction and identification of a cDNA clone for human type II procollagen mRNA.

Double-stranded cDNA was constructed for poly(A)-containing RNA isolated from foetal human articular cartilage known to contain small amounts of pro alpha 1 (II) collagen mRNA. A 585 base pair PstI-EcoRI cDNA fragment was isolated and cloned into plasmid pBR322. A resulting recombinant plasmid pHCAR1 was shown to hybridize specifically to a 5.4 kilobase mRNA in cartilage but not in calvarial RNA. Definite identification of clone pHCAR1 was based on sequence analysis; marked homology with the corresponding chick gene and complete agreement with the human gene sequences available were observed.     

A transversely isotropic, transversely homogeneous microstructural-statistical model of articular cartilage

Articular cartilage is a multi-phasic, composite, fibre-reinforced material. Therefore, its mechanical properties are determined by the tissue microstructure. The presence of cells (chondrocytes) and collagen fibres within the proteoglycan matrix influences, at a local and a global level, the material symmetries. The volumetric concentration and shape of chondrocytes, and the volumetric concentration and spatial arrangement of collagen fibres have been observed to change as a function of depth in articular cartilage. In particular, collagen fibres are perpendicular to the bone-cartilage interface in the deep zone, their orientation is almost random in the middle zone, and they are parallel to the surface in the superficial zone. The aim of this work is to develop a model of elastic properties of articular cartilage based on its microstructure. In previous work, we addressed this problem based on Piola's notation for fourth-order tensors. Here, mathematical tools initially developed for transversely isotropic composite materials comprised of a statistical orientation of spheroidal inclusions are extended to articular cartilage, while taking into account the dependence of the elastic properties on cartilage depth. The resulting model is transversely isotropic and transversely homogeneous (TITH), the transverse plane being parallel to the bone-cartilage interface and the articular surface. Our results demonstrate that the axial elastic modulus decreases from the deep zone to the articular surface, a result that is in good agreement with experimental findings. Finite element simulations were carried out, in order to explore the TITH model's behaviour in articular cartilage compression tests. The force response, fluid flow and displacement fields obtained with the TITH model were compared with the classical linear elastic, isotropic, homogeneous (IH) model, showing that the IH model is unable to predict the non-uniform behaviour of the tissue. Based on considerations that the mechanical stability of the tissue depends on its topological and microstructural properties, our long-term goal is to clearly understand the stability conditions in topological terms, and the relationship with the growth and remodelling mechanisms in the healthy and diseased tissue.     

A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage

A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss–Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage.     

Lectin-binding in normal and osteoarthrotic articular cartilage from STR/1N-mouse knee joints

Fluorescein-isothiocyanate (FITC) labeled lectins were used to study the distribution pattern of specific binding-sites in histological sections of normal and osteoarthrotic articular cartilage from the mouse knee joint. Male inbred mice of the STR/1N-strain develop spontaneous arthrotic articular cartilage lesions on the medial condyle of tibia and femur. The varus-deformity of the knee joint leads to a recurrent medial patellar luxation with osteoarthrotic defects on the medial part of the facies patellaris femoris. It was demonstrated that the lectin staining pattern of osteoarthrotic articular cartilage, especially on the facies patellaris femoris, was different from that of normal articular cartilage. The differences in lectin staining corresponded to those observed between normal and fibrillated articular cartilage from human patellae. The normal articular cartilage of the mouse knee joint possessed lectin binding-sites for Concanavalin A (ConA) and wheat germ agglutinin (WGA), but not for Ulex europaeus agglutinin (UEA), soy bean agglutinin (SBA) and peanut agglutinin (PNA). In addition to the completely changed distribution pattern of ConA and WGA in osteoarthrotic cartilage, SBA, PNA and UEA developed distinct staining patterns particular to the fibrillated areas of arthrotic cartilage. The increased lectin-binding to arthrotic articular cartilage may be due to unmasking of sugars in the course of bondage breakdown in fibrillated cartilage or the production of pathological glycoproteins. It is evident that lectins can demonstrate minute differences between normal and arthrotic cartilage and it is concluded, therefore, that lectins are sensitive and specific tools for the study of degenerative joint diseases.     

Recent progress of animal transplantation studies for treating articular cartilage damage using pluripotent stem cells

Focal articular cartilage damage can eventually lead to the onset of osteoarthritis with degradation around healthy articular cartilage. Currently, there are no drugs available that effectively repair articular cartilage damage. Several surgical techniques exist and are expected to prevent progression to osteoarthritis, but they do not offer a long‐term clinical solution. Recently, regenerative medicine approaches using human pluripotent stem cells (PSCs) have gained attention as new cell sources for therapeutic products. To translate PSCs to clinical application, appropriate cultures that produce large amounts of chondrocytes and hyaline cartilage are needed. So too are assays for the safety and efficacy of the cellular materials in preclinical studies including animal transplantation models. To confirm safety and efficacy, transplantation into the subcutaneous space and articular cartilage defects have been performed in animal models. All but one study we reviewed that transplanted PSC‐derived cellular products into articular cartilage defects found safe and effective recovery. However, for most of those studies, the quality of the PSCs was not verified, and the evaluations were done with small animals over short observation periods. Large animals and longer observation times are preferred. We will discuss the recent progress and future direction of the animal transplantation studies for the treatment of focal articular cartilage damages using PSCs.     

Depletion of chondrocyte primary cilia reduces the compressive modulus of articular cartilage

Primary cilia are slender, microtubule based structures found in the majority of cell types with one cilium per cell. In articular cartilage, primary cilia are required for chondrocyte mechanotransduction and the development of healthy tissue. Loss of primary cilia in Col2aCre;ift88^fl/fl transgenic mice results in up-regulation of osteoarthritic (OA) markers and development of OA like cartilage with greater thickness and reduced mechanical stiffness. However no previous studies have examined whether loss of primary cilia influences the intrinsic mechanical properties of articular cartilage matrix in the form of the modulus or just the structural properties of the tissue. The present study describes a modified analytical model to derive the viscoelastic moduli based on previous experimental indentation data. Results show that the increased thickness of the articular cartilage in the Col2aCre;ift88^fl/fl transgenic mice is associated with a reduction in both the instantaneous and equilibrium moduli at indentation strains of greater than 20%. This reveals that the loss of primary cilia causes a significant reduction in the mechanical properties of cartilage particularly in the deeper zones and possibly the underlying bone. This is consistent with histological analysis and confirms the importance of primary cilia in the development of a mechanically functional articular cartilage.     

Small animal models to understand pathogenesis of osteoarthritis and use of stem cell in cartilage regeneration

Osteoarthritis (OA) is one of the most common diseases, which affect the correct functionality of synovial joints and is characterized by articular cartilage degradation. Limitation in the treatment of OA is mostly due to the very limited regenerative characteristic of articular cartilage once is damaged. Small animal models are of particular importance for mechanistic analysis to understand the processes that affect cartilage degradation. Combination of joint injury techniques with the use of stem cells has been shown to be an important tool for understanding the processes of cartilage degradation and regeneration. Implementation of stem cells and small animal models are important tools to help researchers to find a solution that could ameliorate and prevent the symptoms of OA.     

Relaxation and creep quasilinear viscoelastic models for normal articular cartilage

A quasilinear viscoelastic model was used to develop relaxation and creep forms for a constitutive law for soft tissues. Combined relaxation and cyclic test data as well as preconditioned and nonpreconditioned creep data were used to demonstrate the approach for normal bovine articular cartilage. Values for mechanical parameters in the analytical models were determined using a generalized least squares method.     

Direct measurement of osmotic pressure of glycosaminoglycan solutions by membrane osmometry at room temperature

Articular cartilage is a hydrated soft tissue composed of negatively charged proteoglycans fixed within a collagen matrix. This charge gradient causes the tissue to imbibe water and swell, creating a net osmotic pressure that enhances the tissue's ability to bear load. In this study we designed and utilized an apparatus for directly measuring the osmotic pressure of chondroitin sulfate, the primary glycosaminoglycan found in articular cartilage, in solution with varying bathing ionic strength (0.015 M, 0.15 M, 0.5 M, 1 M, and 2 M NaCl) at room temperature. The osmotic pressure (pi) was found to increase nonlinearly with increasing chondroitin sulfate concentration and decreasing NaCl ionic bath environment. Above 1 M NaCl, pi changes negligibly with further increases in salt concentration, suggesting that Donnan osmotic pressure is negligible above this threshold, and the resulting pressure is attributed to configurational entropy. Results of the current study were also used to estimate the contribution of osmotic pressure to the stiffness of cartilage based on theoretical and experimental considerations. Our findings indicate that the osmotic pressure resulting from configurational entropy is much smaller in cartilage (based on an earlier study on bovine articular cartilage) than in free solution. The rate of change of osmotic pressure with compressive strain is found to contribute approximately one-third of the compressive modulus (H(A)(eff)) of cartilage (Pi approximately H(A)(eff)/3), with the balance contributed by the intrinsic structural modulus of the solid matrix (i.e., H(A) approximately 2H(A)(eff)/3). A strong dependence of this intrinsic modulus on salt concentration was found; therefore, it appears that proteoglycans contribute structurally to the magnitude of H(A), in a manner independent of osmotic pressure.     

The Mechanical Behaviour of Chondrocytes Predicted with a Micro-structural Model of Articular Cartilage

The integrity of articular cartilage depends on the proper functioning and mechanical stimulation of chondrocytes, the cells that synthesize extracellular matrix and maintain tissue health. The biosynthetic activity of chondrocytes is influenced by genetic factors, environmental influences, extracellular matrix composition, and mechanical factors. The mechanical environment of chondrocytes is believed to be an important determinant for joint health, and chondrocyte deformation in response to mechanical loading is speculated to be an important regulator of metabolic activity. In previous studies of chondrocyte deformation, articular cartilage was described as a biphasic material consisting of a homogeneous, isotropic, linearly elastic solid phase, and an inviscid fluid phase. However, articular cartilage is known to be anisotropic and inhomogeneous across its depth. Therefore, isotropic and homogeneous models cannot make appropriate predictions for tissue and cell stresses and strains. Here, we modelled articular cartilage as a transversely isotropic, inhomogeneous (TI) material in which the anisotropy and inhomogeneity arose naturally from the microstructure of the depth-dependent collagen fibril orientation and volumetric fraction, as well as the chondrocyte shape and volumetric fraction. The purpose of this study was to analyse the deformation behaviour of chondrocytes using the TI model of articular cartilage. In order to evaluate our model against experimental results, we simulated indentation and unconfined compression tests for nominal compressions of 15%. Chondrocyte deformations were analysed as a function of location within the tissue. The TI model predicted a non-uniform behaviour across tissue depth: in indentation testing, cell height decreased by 43% in the superficial zone and between 11 and 29% in the deep zone. In unconfined compression testing, cell height decreased by 32% in the superficial zone, 25% in the middle, and 18% in the deep zones. This predicted non-uniformity is in agreement with experimental studies. The novelty of this study is the use of a cartilage material model accounting for the intrinsic inhomogeneity and anisotropy of cartilage caused by its microstructure.     

Elastic anisotropy of articular cartilage is associated with the microstructures of collagen fibers and chondrocytes

Chondrocyte shape and volumetric concentration change as a function of depth in articular cartilage. A given chondrocyte shape produces different effects on the global material properties depending on the structure of the collagen fiber network. The shape and volumetric concentration of chondrocytes in articular cartilage appear to be related to the mechanical stability of the matrix. The present study was aimed to investigate, theoretically, the effects of the structural arrangement of the collagen fiber network, and the shape and distribution of chondrocytes, on the global material behavior of articular cartilage. Articular cartilage was assumed to be a four-phasic composite comprised of a matrix (associated with the properties of the proteoglycan structure), vertically and horizontally distributed collagen fibers, and spheroidal inclusions representing chondrocytes. A solution for composite materials was used to estimate the global, effective material properties of cartilage. Only the elasticity of the solid phase was investigated in the present study. Our simulations suggest that a soft, spheroidal cell inclusion in a fiber-reinforced proteoglycan matrix affects the material properties differently depending on the shape of the spheroidal inclusions. If the long axis of the inclusions is parallel to the collagen fibers, as in the deep zone, the soft inclusions increase the stiffness of the composite in the fiber direction, and reduce the stiffness of the composite in the direction normal to the fibers. Furthermore, we found that Young's modulus normal to the contact surface increases from the superficial to the deep zone in articular cartilage by a factor of 10-50, a finding that agrees well with experimental observations. Our analysis suggests that the combination of proteoglycan matrix, fiber orientation, and shape of chondrocytes are intimately related and are likely adapted to optimize the mechanical stability and load carrying capacity of the structure.