Analysis of biphasic lubrication of articular cartilage loaded by cylindrical indenter

Combination of theoretical biphasic analyses and corresponding experimental measurements for articular cartilage has successfully revealed the fundamental material properties and time-depending mechanical behaviors of articular cartilage containing plenty of water. The insight of load partitioning between solid and fluid phases advanced the prediction of the frictional behavior of articular cartilage. One of the recent concerns about biphasic finite element (FE) analysis seems to be a dynamic and physiological condition in terms of mechanical functionality as a load-bearing for articular joint system beyond material testing, which has mainly focused on time-dependent reaction force and deformation in relatively small and low speed compression. Recently, the biphasic FE model for reciprocating sliding motion was applied to confirm the frictional effect on the migrating contact area. The results indicated that the model of a cylindrical indenter sliding over the cartilage surface remarkably sustained the higher proportion of fluid load support than a condition without migrating contact area, but the effectiveness of constitutive material properties has not been sufficiently evaluated for sliding motion. In our present study, at the first stage, the compressive response of the articular cartilage was examined by high precision testing machine. Material properties for the biphasic FE model, which included inhomogeneous apparent Young's modulus of solid phase along depth, strain-dependent permeability and collagen reinforcement in tensile strain, were estimated in cylindrical indentation tests by the curve fitting between the experimental time-dependent behavior and FE model simulation. Then, the biphasic lubrication mechanism of the articular cartilage including migrating contact area was simulated to elucidate functionality as a load-bearing material. The results showed that the compaction effect on permeability of solid phase was functional particularly in the condition without the migrating contact area, whereas in sliding condition the compaction effect did not clearly show its role in terms of the proportion of fluid load support. The reinforcement of solid phase, which represented the collagen network in the tissue, improved the proportion of fluid load support especially in the sliding condition. Thus, a functional integration of constitutive mechanical properties as a load-bearing was evaluated by FE model simulation in this study.     

Predictive rheological models for the consolidation behaviour of articular cartilage under static loading

This paper evaluates an existing rheological model of articular cartilage and explores the representative capacity of other phenomenological models of the tissue's matrix within the framework of mechanical consolidation. A unique feature is the introduction of a swelling element in tandem with 'fluid-filled' hyperelastic rheological elements to predict the transient load-induced behaviour of the tissue and evaluate the role of swelling in determining its load-carriage mechanism. The rheological models proposed have been used to predict the dependence of the one-dimensional consolidation response of the articular cartilage matrix, and the results obtained have been compared with published experimental results. This comparison demonstrates that the hydrostatic excess pore pressure, especially in the initial stages of deformation cannot be predicted without an adequate representation of swelling and its non-linear interaction with mechanical governing parameters such as permeability and stiffness.     

A finite element model of an idealized diarthrodial joint to investigate the effects of variation in the mechanical properties of the tissues

The stiffness of articular cartilage increases dramatically with increasing rate of loading, and it has been hypothesized that increasing the stiffness of the subchondral bone may result in damaging stresses being generated in the articular cartilage. Despite the interdependence of these tissues in a joint, little is understood of the effect of such changes in one tissue on stresses generated in another. To investigate this, a parametric finite element model of an idealized joint was developed. The model incorporated layers representing articular cartilage, calcified cartilage, the subchondral bone plate and cancellous bone. Taguchi factorial design techniques, employing a two-level full-factorial and a four-level fractional factorial design, were used to vary the material properties and thicknesses of the layers over the wide range of values found in the literature. The effects on the maximum values of von Mises stress in each of the tissues are reported here. The stiffness of the cartilage was the main factor that determined the stress in the articular cartilage. This, and the thickness of the cartilage, also had the largest effect on the stresses in all the other tissues with the exception of the subchondral bone plate, in which stresses were dominated by its own stiffness. The stiffness of the underlying subchondral bone had no effect on the stresses generated in the cartilage. This study shows how stresses in the various tissues are affected by changes in their mechanical properties and thicknesses. It also demonstrates the benefits of a structured, systematic approach to investigating parameter variation in finite element models.     

Rheological effects of synovial fluid on nutritional transport

Synovial fluid is an excellent source of nutrients for the cells of the cartilage, through which water and other solutes like glucose are permeable. It has long been established that the tissue imbibes and exudes fluid when deformed, metabolities are believed to move to and from the cells through the ground substance by mechanical effects and by diffusion. Local variation of the permeability within the articular cartilage plays an important role in nutritional transport. To account for the effects of structural configuration of tissue, rate, depth and amount of solute penetration, we have modelled the cartilage by mixture of two distinct constituents, i.e., an incompressible fluid phase and an incompressible porous solid phase. It is observed that when local permeability decreases, the concentration decreases. When fluid flows into the cartilage due to metabolism, the solid portion of the porous matrix increases. Due to the increased solidity of the cartilage matrix, less fluid enters into the cartilage and nutritional transport decreases. In the case of diseased joints the nutritional transport is very difficult, owing to increased rigidity or local variation of permeability within the cartilage. The concentration distribution at the same depth in articular cartilage for low-molecular-weight solutes is less than that for high-molecular-weight solutes. Thus, for low-molecular-weight solutes, the phenomenon of nutrition transport is diffusion dominated whereas for high-molecular-weight solutes, it is dominated by mechanical pumping action. The paper further concludes that in the process of imbibition and exudation, the cells of the middle area of the cartilage surface get more nutrition as compared to the cells at the periphery, so the earliest signs of cartilage degeneration appear in the unstressed areas. Therefore joint motion is assumed necessary for cartilage nutrition. It also concludes that as the viscoelastic parameter increases, the concentration decreases in the articular cartilage so that the cells of the cartilage get less nutrition and can deteriorate.     

温度对橡胶隔振器刚度阻尼特性的影响

在不同温度( 20~80 ℃ )下对橡胶材料进行了单轴静态拉伸试验与动态频率扫描试验,分析了应力应变关系、储能模量及损耗模量随温度的变化规律,拟合获得了不同温度下表征橡胶力学性能的超弹性和粘弹性本构模型参数。对某倒 V 形橡胶隔振器进行了不同温度本构参数下的静态与动态仿真,结果表明,温度对橡胶隔振器力学性能有较大影响,研究结果可为橡胶隔振器的工程应用提供参考。     

Design characteristics for temporomandibular joint disc tissue engineering: learning from tendon and articular cartilage

Tissue engineering of chondrocytic or fibroblastic musculoskeletal tissues has been relatively well studied compared with that of the temporomandibular joint (TMJ) disc. Early attempts at tissue engineering the disc have been misguided owing to a lack of understanding of the composition and function of the TMJ disc. The objective of this review is to compare the TMJ disc with a chondrocytic tissue (hyaline articular cartilage) and a fibroblastic tissue (tendon) to understand better the properties of this fibrocartilaginous tissue. The TMJ disc has 25 times more glycosaminoglycan (GAG) per dry weight than tendon but half that of articular cartilage. The disc's tensile modulus is six times more than cartilage but orders less than tendon. The GAG content and tensile modulus suggest that the TMJ disc is characterized as a tissue between hyaline cartilage and tendon, but the disc appears more tendon like when considering its collagen make-up and cell content. Like tendon, the TMJ disc contains primarily collagen type I at 85 per cent per dry weight, while articular cartilage has 30 per cent less collagen, which is type II. Knowledge of quantitative comparisons between joint tissues can give extensive insight into how to improve tissue engineering of the TMJ disc.     

Dynamics of a viscoelastic rotor shaft using augmenting thermodynamic fields—A finite element approach

Modelling viscoelastic materials is always difficult since such materials store energy as well as dissipate it to the thermal domain. Whereas modelling the elastic behaviour is easy, modelling the energy dissipation mechanism poses difficulty. This paper presents a theoretical study of the dynamics of a viscoelastic rotor-shaft system, where the internal material damping in the rotor-shaft introduces a rotary force well known to cause instability of the rotor-shaft system. An efficient modelling technique that assumes coupled (thermo-mechanical) augmenting thermodynamic field (ATF) to derive the constitutive relationships is found more suitable in comparison with the viscous and hysteric damping models, and is used to model the viscoelastic rotor material. Dynamic behaviour of an aluminium rotor is predicted through viscoelastic modelling of the continuum to take into account the effect of internal material damping. Stability limit speed (SLS) and unbalance response (UBR) amplitude are used as two indices to study the dynamics. It is observed that, the ATF approach predicts more reliable SLS and UBR amplitude in comparison with the viscous and hysteretic model of rotor-internal damping. Composite rotor-shaft assumed by reinforcing the aluminium matrix with carbon fibre is found to postpone the critical speeds and thus make available, higher speed of rotor operation and lower UBR amplitude in comparison with pure aluminium rotor-shaft. Finite element method is used for modelling and analysis.     

Comparison of human and animal femoral head chondral properties and geometries

Investigations into tissue-preserving orthopaedic treatments should consider the tribology of articular cartilage; where simulations using animal joints are a predominant choice. However, very few studies have investigated the differences between human and animal cartilage. The aim of the present study was to characterise the differences in geometry and mechanical properties of human, porcine, bovine and ovine articular cartilage. Creep indentation was performed on osteochondral plugs taken from the superior region of femoral heads of all these species. Cartilage thickness was measured via the resistive force change of a needle descending through cartilage and bone. A biphasic finite element model was used to derive equilibrium elastic modulus and permeability. Results showed that human cartilage was significantly thicker than all other species tested. A positive correlation was found between femoral head diameter and cartilage thickness when comparing between species of quadrupeds. Human cartilage had the largest equilibrium elastic modulus, which was significant when comparing against porcine and bovine. However, porcine cartilage had significantly lower permeability. Significant differences in geometry and mechanical properties of articular cartilage were found between all species tested. It is necessary to consider these variations when choosing animal tissue to represent human.     

Axisymmetric squeezing of a Phan‐Thien and Tanner lubricant film under imposed constant load in the presence of a poroelastic medium

In this paper, a modified Reynolds equation in polar coordinates using the Phan‐Thien and Tanner rheological model is combined with a modified Darcy law describing a poroelastic confining surface. The Phan‐Thien and Tanner model is commonly used to describe the viscoelastic behaviour of synovial fluid, while the poroelastic model can portray articular cartilage. Together, they may provide a simulation basis for lubrication of the tribology of the knee contact under squeezing. The results obtained for the axisymmetric case are analysed and compared for certain non‐Newtonian shear phenomena on the basis of works from the literature. Copyright © 2015 John Wiley & Sons, Ltd.     

Design, validation, and utilization of an articular cartilage impact instrument

This paper describes the development and use of an instrument mechanically to impact bovine articular cartilage and record the event using a piezoelectric accelerometer, as well as to carry out post-impact characterization of the tissue. Two levels of impact (low: 6 cm drop height, 18.4 N tup; high: 10 cm drop height, 27.8 N tup) were chosen such that the former did not show gross damage upon inspection, while the latter showed substantial gross damage. Peak stress, time to peak stress, and impact duration were taken from data recorded by the instrument. Three cartilage biomechanical properties (aggregate modulus, Poisson's ratio, and permeability) were acquired by creep indentation, and tissue morphology rated on a standardized scale was also determined. When subjected to the high level of impact, articular cartilage showed statistically significant (p < 0.05) differences in all three impact metrics and morphology. This high level of impact also resulted in a 37 per cent decrease in the aggregate modulus of the tissue. Lower drop heights resulted in more consistent impact curves, demonstrated less standard deviation, and did not change the biomechanical properties of the tissues. With the instrument and techniques described in this study, articular cartilage can be subjected to specific levels of impact in order to study injury biomechanics of the tissue at specific levels of mechanical damage.     

Approximate closed-form solution of the synovial fluid film force in the human ankle joint with non-Newtonian lubricant

The aim of this paper is to propose an approximate closed form lubrication model of the human ankle joint by taking into account the porosity of the cartilage matrix and the non-Newtonian behaviour of the synovial fluid. The model is based on the theory of squeeze lubrication and introduce an original modified Reynolds equation obtained modelling the synovial fluid as a couple-stress fluid and the synovial fluid transport across the articular cartilage by using a modified Darcy's equation. This approach gives the advantage to obtain an analytical expression of the synovial pressure field and of the non-stationary fluid film force acting in the synovial joint during the squeeze motion in terms of couple-stress parameter, film thickness, and porosity parameter.     

Mechanical anisotropy of the human knee articular cartilage in compression

Articular cartilage exhibits anisotropic mechanical properties when subjected to tension. However, mechanical anisotropy of mature cartilage in compression is poorly known. In this study, both confined and unconfined compression tests of cylindrical cartilage discs, taken from the adult human patello-femoral groove and cut either perpendicular (normal disc) or parallel (tangential disc) to the articular surface, were utilized to determine possible anisotropy in Young's modulus, E, aggregate modulus, Ha, Poisson's ratio, v and hydraulic permeability, k, of articular cartilage. The results indicated that Ha was significantly higher in the direction parallel to the articular surface as compared with the direction perpendicular to the surface (Ha = 1.237 +/- 0.486 MPa versus Ha = 0.845 +/- 0.383 MPa, p = 0.017, n = 10). The values of Poisson's ratio were similar, 0.158 +/- 0.148 for normal discs compared with 0.180 +/- 0.046 for tangential discs. Analysis using the linear biphasic model revealed that the decrease of permeability during the offset compression of 0-20 per cent was higher (p = 0.015, n = 10) in normal (from 25.5 x 10(-15) to 1.8 x 10(-15) m4/N s) than in tangential (from 12.3 x 10(-15) to 1.3 x 10(-15) m4/N s) discs. Based on the results, it is concluded that the mechanical characteristics of adult femoral groove articular cartilage are anisotropic also during compression. Anisotropy during compression may be essential for normal cartilage function. This property has to be considered when developing advanced theoretical models for cartilage biomechanics.     

Boundary Lubrication in Natural Articular Joints

This review concentrates on studies into the behaviour of natural articular cartilage under boundary lubrication. This includes investigations into the chemical composition at the surface of cartilage, carried out as a means of identifying the boundary lubricant. Studies on the friction of cartilage sliding against cartilage and cartilage sliding steel or glass under conditions expected to be in the boundary regime are described. Additionally, model studies on the possible mechanisms of boundary lubrication using well-defined artificial surfaces are also discussed. Although there appears to be some contradiction between the results of friction measurements, an explanation can, at least in part, be given in terms of the layer of cartilage that is being measured. The different chemical nature and lubricating behaviour of the layers found at or near the surface are discussed in relation to the various results given in the literature.     

Mechanical and tribological properties of poly(hydroxyethyl methacrylate) hydrogels as articular cartilage substitutes

Poly(hydroxyethyl methacrylate) (p(HEMA)) hydrogels have been proposed as promising biomaterials to replace damaged articular cartilage. A major obstacle to their use as replacement bearing tissue is their poor mechanical properties in comparison with healthy articular cartilage. The purpose of this study was to obtain p(HEMA) hydrogels with physicochemical and mechanical properties close to healthy articular cartilage, by introducing a hydrophilic monomer, namely acrylic acid (AA). Formulations of hydrogels with different amounts of hydrophilic monomer (acrylic acid, AA) were synthesized and tested: p(HEMA), p(HEMA-co-5%AA), p(HEMA-co-25%AA). The macro-mechanical tests were reproduced at nanoscale in order to verify if the superficial properties of the hydrogels are similar to the bulk ones.     

The effect of glycosaminoglycan depletion on the friction and deformation of articular cartilage

Glycosaminoglycans (GAGs) have been shown to be responsible for the interstitial fluid pressurization of articular cartilage and hence its compressive stiffness and load-bearing properties. Contradictory evidence has been presented in the literature on the effect of depleting GAGs on the friction properties of articular cartilage. The aim of this study was to investigate the effect of depleting GAGs on the friction and deformation characteristics of articular cartilage under different tribological conditions. A pin-on-plate machine was utilized to measure the coefficient of friction of native and chondroitinase ABC (CaseABC)-treated articular cartilage under two different models: static (4 mm/s start-up velocity) and dynamic (4 mm/s sliding velocity; 4 mm stroke length) under a load of 25 N (0.4 MPa contact stress) and with phosphate-buffered saline as the lubricant. Indentation tests were carried out at 1 N and 2 N loads (0.14 MPa and 0.28 MPa contact stress levels) to study the deformation characteristics of both native and GAG-depleted cartilage samples. CaseABC treatment rendered the cartilage tissue soft owing to the loss of compressive stiffness and a sulphated-sugar assay confirmed the loss of GAGs from the cartilage samples. CaseABC treatment significantly increased (by more than 50 per cent) the friction levels in the dynamic model (p < 0.05) at higher loading times owing to the loss of biphasic lubrication. CaseABC treatment had no effect on friction in the static model in which the cartilage surfaces did not have an opportunity to recover fluid because of static loading unlike the cartilage tissue in the dynamic model, in which translation of the cartilage surfaces was involved, ensuring effective biphasic lubrication. Therefore the depletion of GAGs had a smaller effect on the coefficient of friction for the static model. Indentation tests showed that GAG-depleted cartilage samples had a lower elastic modulus and higher permeability than native tissue. These results corroborate the role of GAGs in the compressive and friction properties of articular cartilage and emphasize the need for developing strategies to control GAG loss from diseased articular cartilage tissue.     

The effect of cartilage deformation on the laxity of the knee joint

In this paper, deformation of the articular cartilage layers is incorporated into an existing two-dimensional quasi-static model of the knee joint. The new model relates the applied force and the joint displacement, as measured in the Lachmann drawer test, and allows the effect of cartilage deformation on the knee joint laxity to be determined. The new model augments the previous knee model by calculating the tibio-femoral contact force subject to an approximate 'thin-layer' constitutive equation, and a method is described for finding the configuration of the knee under a specified load, in terms of a displacement from a zero-load reference configuration. The results show that inclusion of deformable cartilage layers can cause a reduction of between 10 and 35 per cent in the force required to produce a given tibial displacement, over the range of flexion angles considered. The presence of cartilage deformation was found to be an important modifier of the loading response but is secondary to the effect of ligamentous extension. The flexion angle dependence of passive joint laxity is much more strongly influenced by fibre recruitment in the ligaments than by cartilage deformation.     

Application of autofluorescence robotic histology for quantitative evaluation of the 3‐dimensional morphology of murine articular cartilage

Murine models of osteoarthritis (OA) are increasingly important for understating pathogenesis and for testing new therapeutic approaches. Their translational potential is, however, limited by the reduced size of mouse limbs which requires a much higher resolution to evaluate their articular cartilage compared to clinical imaging tools. In experimental models, this tissue has been predominantly assessed by time‐consuming histopathology using standardized semi‐quantitative scoring systems. This study aimed to develop a novel imaging method for 3‐dimensional (3D) histology of mouse articular cartilage, using a robotic system—termed here “3D histocutter”—which automatically sections tissue samples and serially acquires fluorescence microscopy images of each section. Tibiae dissected from C57Bl/6 mice, either naïve or OA‐induced by surgical destabilization of the medial meniscus (DMM), were imaged using the 3D histocutter by exploiting tissue autofluorescence. Accuracy of 3D imaging was validated by ex vivo contrast‐enhanced micro‐CT and sensitivity to lesion detection compared with conventional histology. Reconstructions of tibiae obtained from 3D histocutter serial sections showed an excellent agreement with contrast‐enhanced micro‐CT reconstructions. Furthermore, osteoarthritic features, including articular cartilage loss and osteophytes, were also visualized. An in‐house developed software allowed to automatically evaluate articular cartilage morphology, eliminating the subjectivity associated to semi‐quantitative scoring and considerably increasing analysis throughput. The novelty of this methodology is, not only the increased throughput in imaging and evaluating mouse articular cartilage morphology starting from conventionally embedded samples, but also the ability to add the third dimension to conventional histomorphometry which might be useful to improve disease assessment in the model.     

Nonlinear viscoelastic analysis of thick-walled cylindrical composite pipes

This paper analyzes the effect of the polymer matrix non-viscoelastic behaviour in the mechanical behaviour of thick multilayered cylinders. The original contribution of this work is to provide novel approximate analytical solutions to compute the time-dependent internal stress state through the pipe thickness within the framework of nonlinear viscoelasticity theory. The structures considered are thick, multilayered anisotropic infinitive long cylinders subjected to axisymmetric mechanical loading. Under such conditions there is an exact elastic solution which naturally satisfies equilibrium, strain-displacement, compatibility and boundary conditions for the stated constitutive equations and loading. Due to the continuous stress variations through the cylinder thickness, the proposed nonlinear viscoelastic solution assumes the averaged stress state to calculate the nonlinear elastic and viscoelastic factors in each layer. Furthermore, the solution is obtained assuming that the creep strains, within each layer, are constant through the thickness. The proposed algorithm converges to the exact solution when the number of layers is artificially increased. For the linear viscoelastic case, the proposed solution proved to match the exact known solution for isotropic viscoelastic materials. Finally several invented cases are run to illustrate the importance of the viscoelasticity phenomenon on the internal stress field in thick-laminated cylinders.     

CrMnFeCoNi高熵合金拉伸断裂的晶体塑性有限元模拟

CrMnFeCoNi高熵合金的优异力学性能使其具有广阔的工程应用前景。材料力学行为的本构描述对其工程服役行为的安全评估至关重要,但是描述CrMnFeCoNi高熵合金拉伸断裂行为的本构模型少见报道。基于晶体塑性本构模型,利用Cohesive单元在多晶代表性体积单元内部植入含损伤破坏机制的晶界,模拟了CrMnFeCoNi高熵合金在单轴拉伸下的晶间断裂过程。模拟结果与试验所得的应力-应变曲线吻合较好,且能准确描述断裂发生时的应力下降过程,说明采用晶体塑性本构模型与Cohesive本构模型可以有效描述材料的宏观响应行为和断裂失效行为。进一步分析表明：裂纹从应力集中处开始萌生;随着应变的持续增加,裂纹沿着晶界扩展,最终造成断裂;晶粒随机取向对裂纹萌生位置与扩展路径有显著影响,但对宏观拉伸应力-应变曲线几乎没有影响。     

Experimental and numerical investigation of the behaviour of articular cartilage under shear loading—Interstitial fluid pressurisation and lubrication mechanisms

In this paper, the mechanical and frictional responses of articular cartilage when subjected to alternating shearing forces under a constant load were investigated. Shear testing was performed at physiological contact pressures to ascertain the influence of interstitial fluid support on the evolution of frictional forces during cyclic loading.Numerical studies were also performed using the finite element software Abaqus. The tissue was modelled as a biphasic material with strain dependent permeability. The influence of the material characteristics on the lubrication mechanisms occurring when cartilage is subject to compression and shear was studied to corroborate the experimental findings.