W. Wilson

Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study

Osteoarthritis (OA) is a multifactorial disease, resulting in diarthrodial joint wear and eventually destruction. Swelling of cartilage, which is proportional to the amount of collagen damage, is an initial event of cartilage degeneration, so damage to the collagen fibril network is likely to be one of the earliest signs of OA cartilage degeneration. We propose that the local stresses and strains in the collagen fibrils, which cause the damage, cannot be determined dependably without taking the local arcade-like collagen-fibril structure into account. We investigate this using a poroviscoelastic fibril-reinforced FEA model. The constitutive fibril properties were determined by fitting numerical data to experimental results of unconfined compression and indentation tests on samples of bovine patellar articular cartilage. It was demonstrated that with this model the stresses and strains in the collagen fibrils can be calculated. It was also exhibited that fibrils with different orientations at the same location can be loaded differently, depending on the local architecture of the collagen network. To the best of our knowledge, the present model is the first that can account for these features. We conclude that the local stresses and strains in the articular cartilage are highly influenced by the local morphology of the collagen-fibril network.

Pathways of load-induced cartilage damage causing cartilage degeneration in the knee after meniscectomy

Results of both clinical and animal studies show that meniscectomy often leads to osteoarthritic degenerative changes in articular cartilage. It is generally assumed that this process of cartilage degeneration is due to changes in mechanical loading after meniscectomy. It is, however, not known why and where this cartilage degeneration starts. Load induced cartilage damage is characterized as either type (1)--damage without disruption of the underlying bone or calcified cartilage layer--or type (2), subchondral fracture with or without damage to the overlying cartilage. We asked the question whether cartilage degeneration after meniscectomy is likely to be initiated by type (1) and/or type (2) cartilage damage. To investigate that we applied an axisymmetric biphasic finite element analysis model of the knee joint. In this model the articular cartilage layers of the tibial and the femoral condyles, the meniscus and the bone underlying the articular cartilage of the tibia plateau were included. The model was validated with data from clinical studies, in which the effects of meniscectomy on contact areas and pressures were measured. It was found that both the maximal values and the distributions of the shear stress in the articular cartilage changed after meniscectomy, and that these changes could lead to both type (1) and type (2) cartilage damage. Hence it likely that the cartilage degeneration seen after meniscectomy is initiated by both type (1) and type (2) cartilage damage.

A Comparison Between Mechano-Electrochemical and Biphasic Swelling Theories for Soft Hydrated Tissues

Biological tissues like intervertebral discs and articular cartilage primarily consist of interstitial fluid, collagen fibrils and negatively charged proteoglycans. Due to the fixed charges of the proteoglycans, the total ion concentration inside the tissue is higher than in the surrounding synovial fluid (cation concentration is higher and the anion concentration is lower). This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. In the last decade several mechano-electrochemical models, which include this mechanism, have been developed. As these models are complex and computationally expensive, it is only possible to analyze geometrically relatively small problems. Furthermore, there is still no commercial finite element tool that includes such a mechano-electrochemical theory. Lanir (Biorheology, 24, pp. 173-187, 1987) hypothesized that electrolyte flux in articular cartilage can be neglected in mechanical studies. Lanirs hypothesis implies that the swelling behavior of cartilage is only determined by deformation of the solid and by fluid flow. Hence, the response could be described by adding a deformation-dependent pressure term to the standard biphasic equations. Based on this theory we developed a biphasic swelling model. The goal of the study was to test Lanirs hypothesis for a range of material properties. We compared the deformation behavior predicted by the biphasic swelling model and a full mechano-electrochemical model for confined compression and 1D swelling. It was shown that, depending on the material properties, the biphasic swelling model behaves largely the same as the mechano-electrochemical model, with regard to stresses and strains in the tissue following either mechanical or chemical perturbations. Hence, the biphasic swelling model could be an alternative for the more complex mechano-electrochemical model, in those cases where the ion flux itself is not the subject of the study. We propose thumbrules to estimate the correlation between the two models for specific problems.

Stress–relaxation of human patellar articular cartilage in unconfined compression: Prediction of mechanical response by tissue composition and structure

Mechanical properties of articular cartilage are controlled by tissue composition and structure. Cartilage function is sensitively altered during tissue degeneration, in osteoarthritis (OA). However, mechanical properties of the tissue cannot be determined non-invasively. In the present study, we evaluate the feasibility to predict, without mechanical testing, the stress-relaxation response of human articular cartilage under unconfined compression. This is carried out by combining microscopic and biochemical analyses with composition-based mathematical modeling. Cartilage samples from five cadaver patellae were mechanically tested under unconfined compression. Depth-dependent collagen content and fibril orientation, as well as proteoglycan and water content were derived by combining Fourier transform infrared imaging, biochemical analyses and polarized light microscopy. Finite element models were constructed for each sample in unconfined compression geometry. First, composition-based fibril-reinforced poroviscoelastic swelling models, including composition and structure obtained from microscopical and biochemical analyses were fitted to experimental stress-relaxation responses of three samples. Subsequently, optimized values of model constants, as well as compositional and structural parameters were implemented in the models of two additional samples to validate the optimization. Theoretical stress-relaxation curves agreed with the experimental tests (R=0.95-0.99). Using the optimized values of mechanical parameters, as well as composition and structure of additional samples, we were able to predict their mechanical behavior in unconfined compression, without mechanical testing (R=0.98). Our results suggest that specific information on tissue composition and structure might enable assessment of cartilage mechanics without mechanical testing.

Importance of collagen orientation and depth-dependent fixed charge densities of cartilage on mechanical behavior of chondrocytes.

The collagen network and proteoglycan matrix of articular cartilage are thought to play an important role in controlling the stresses and strains in and around chondrocytes, in regulating the biosynthesis of the solid matrix, and consequently in maintaining the health of diarthrodial joints. Understanding the detailed effects of the mechanical environment of chondrocytes on cell behavior is therefore essential for the study of the development, adaptation, and degeneration of articular cartilage. Recent progress in macroscopic models has improved our understanding of depth-dependent properties of cartilage. However, none of the previous works considered the effect of realistic collagen orientation or depth-dependent negative charges in microscopic models of chondrocyte mechanics. The aim of this study was to investigate the effects of the collagen network and fixed charge densities of cartilage on the mechanical environment of the chondrocytes in a depth-dependent manner. We developed an anisotropic, inhomogeneous, microstructural fibril-reinforced finite element model of articular cartilage for application in unconfined compression. The model consisted of the extracellular matrix and chondrocytes located in the superficial, middle, and deep zones. Chondrocytes were surrounded by a pericellular matrix and were assumed spherical prior to tissue swelling and load application. Material properties of the chondrocytes, pericellular matrix, and extracellular matrix were obtained from the literature. The loading protocol included a free swelling step followed by a stress-relaxation step. Results from traditional isotropic and transversely isotropic biphasic models were used for comparison with predictions from the current model. In the superficial zone, cell shapes changed from rounded to elliptic after free swelling. The stresses and strains as well as fluid flow in cells were greatly affected by the modulus of the collagen network. The fixed charge density of the chondrocytes, pericellular matrix, and extracellular matrix primarily affected the aspect ratios (height/width) and the solid matrix stresses of cells. The mechanical responses of the cells were strongly location and time dependent. The current model highlights that the collagen orientation and the depth-dependent negative fixed charge densities of articular cartilage have a great effect in modulating the mechanical environment in the vicinity of chondrocytes, and it provides an important improvement over earlier models in describing the possible pathways from loading of articular cartilage to the mechanical and biological responses of chondrocytes.

Remodeling of fracture callus in mice is consistent with mechanical loading and bone remodeling theory

During the remodeling phase of fracture healing in mice, the callus gradually transforms into a double cortex, which thereafter merges into one cortex. In large animals, a double cortex normally does not form. We investigated whether these patterns of remodeling of the fracture callus in mice can be explained by mechanical loading. Morphologies of fractures after 21, 28, and 42 days of healing were determined from an in vivo mid‐diaphyseal femoral osteotomy healing experiment in mice. Bone density distributions from microCT at 21 days were converted into adaptive finite element models. To assess the effect of loading mode on bone remodeling, a well‐established remodeling algorithm was used to examine the effect of axial force or bending moment on bone structure. All simulations predicted that under axial loading, the callus remodeled to form a single cortex. When a bending moment was applied, dual concentric cortices developed in all simulations, corresponding well to the progression of remodeling observed experimentally and resulting in quantitatively comparable callus areas of woven and lamellar bone. Effects of biological differences between species or other reasons cannot be excluded, but this study demonstrates how a difference in loading mode could explain the differences between the remodeling phase in small rodents and larger mammals.

Experimental and model determination of human intervertebral disc osmoviscoelasticity

Finite element (FE) models have become an important tool to study load distribution in the healthy and degenerated disc. However, model predictions require accurate constitutive laws and material properties. As the mechanical properties of the intervertebral disc are regulated by its biochemical composition and fiber‐reinforced structure, the relationship between the constitutive behavior of the tissue and its composition requires careful consideration. While numerous studies have investigated the annulus fibrosus compressive and tensile properties, specific conditions required to determine model parameters for the osmoviscoelastic model are unavailable. Therefore, the objectives of this study were (1) to complement the existing material testing in the literature with confined compression and tensile tests on human annulus fibrosus and (2) to use these data, together with existing nucleus pulposus compression data to tune a composition‐based, osmoviscoelastic material constitutive law. The osmoviscoelastic material constitutive law and the experimental data were used to describe the fiber and nonfiber properties of the human disc. The compressive material properties of normal disc tissue were Gm = 1.23 MPa, M = 1.57, and α = 1.964 × 10−16 m4/Ns; the tensile fiber material parameters were E0 = 77.0 MPa; Eε = 500 MPa, and η = 1.8 × 103 MPa−s. The goodness of fit ranged from 0.88 to 0.96 for the four experimental conditions evaluated. The constitutive law emphasized the interdependency of the strong swelling ability of the tissue and the viscoelastic nature of the collagen fibers. This is especially important for numerical models to further study the load sharing behavior with regard to disc degeneration and regeneration.

Composition of the pericellular matrix modulates the deformation behaviour of chondrocytes in articular cartilage under static loading

The aim was to assess the role of the composition changes in the pericellular matrix (PCM) for the chondrocyte deformation. For that, a three-dimensional finite element model with depth-dependent collagen density, fluid fraction, fixed charge density and collagen architecture, including parallel planes representing the split-lines, was created to model the extracellular matrix (ECM). The PCM was constructed similarly as the ECM, but the collagen fibrils were oriented parallel to the chondrocyte surfaces. The chondrocytes were modelled as poroelastic with swelling properties. Deformation behaviour of the cells was studied under 15% static compression. Due to the depth-dependent structure and composition of cartilage, axial cell strains were highly depth-dependent. An increase in the collagen content and fluid fraction in the PCMs increased the lateral cell strains, while an increase in the fixed charge density induced an inverse behaviour. Axial cell strains were only slightly affected by the changes in PCM composition. We conclude that the PCM composition plays a significant role in the deformation behaviour of chondrocytes, possibly modulating cartilage development, adaptation and degeneration. The development of cartilage repair materials could benefit from this information.

A numerical model to study mechanically induced initiation and progression of damage in articular cartilage

OBJECTIVE Proteoglycan (PG) loss and surface roughening, early signs of osteoarthritis (OA), are likely preceded by softening of the ground substance and the collagen network. Insight in their relative importance to progression of OA may assist the development of treatment strategies for early OA. To support interpretation of experimental data, a numerical model is proposed that can predict damage progression in cartilage over time, as a consequence of excessive mechanical loading. The objective is to assess the interaction between ground substance softening and collagen fiber damage using this model. DESIGN An established cartilage mechanics model is extended with the assumption that excessive strains may damage the ground substance or the collagen network, resulting in softening of the overstrained constituent. During subsequent loading cycles the strain may or may not cross a threshold, resulting in damage to stabilize or to progress. To evaluate how softening of the ground substance and collagen may interact, damage progression is computed when either one of them, or both together are allowed to occur during stepwise increased loading. RESULTS Softening in the ground substance was predicted to localize in the superficial and transitional zone and resulted in cartilage softening. Collagen damage was most prominent in the superficial zone, with more diffuse damage penetrating deeper into the tissue, resulting in adverse strain gradients. Effects were more pronounced if both constituents developed damage in parallel. CONCLUSION Ground substance softening and collagen damage have distinct effects on cartilage mechanopathology, and damage in either one of them may promote each other.

Mechanics of chondrocyte hypertrophy

Chondrocyte hypertrophy is a characteristic of osteoarthritis and dominates bone growth. Intra- and extracellular changes that are known to be induced by metabolically active hypertrophic chondrocytes are known to contribute to hypertrophy. However, it is unknown to which extent these mechanical conditions together can be held responsible for the total magnitude of hypertrophy. The present paper aims to provide a quantitative, mechanically sound answer to that question. To address this aim requires a quantitative tool that captures the mechanical effects of collagen and proteoglycans, allows temporal changes in tissue composition, and can compute cell and tissue deformations. These requirements are met in our numerical model that is validated for articular cartilage mechanics, which we apply to quantitatively explain a range of experimental observations related to hypertrophy. After validating the numerical approach for studying hypertrophy, the model is applied to evaluate the direct mechanical effects of axial tension and compression on hypertrophy (Hueter-Volkmann principle) and to explore why hypertrophy is reduced in case of partially or fully compromised proteoglycan expression. Finally, a mechanical explanation is provided for the observation that chondrocytes do not hypertrophy when enzymatical collagen degradation is prohibited (S1Pcko knock-out mouse model). This paper shows that matrix turnover by metabolically active chondrocytes, together with externally applied mechanical conditions, can explain quantitatively the volumetric change of chondrocytes during hypertrophy. It provides a mechanistic explanation for the observation that collagen degradation results in chondrocyte hypertrophy, both under physiological and pathological conditions.