A bimodular polyconvex anisotropic strain energy function for articular cartilage

A strain energy function for finite deformations is developed that has the capability to describe the nonlinear, anisotropic, and asymmetric mechanical response that is typical of articular cartilage. In particular, the bimodular feature is employed by including strain energy terms that are only mechanically active when the corresponding fiber directions are in tension. Furthermore, the strain energy function is a polyconvex function of the deformation gradient tensor so that it meets material stability criteria. A novel feature of the model is the use of bimodular and polyconvex "strong interaction terms" for the strain invariants of orthotropic materials. Several regression analyses are performed using a hypothetical experimental dataset that captures the anisotropic and asymmetric behavior of articular cartilage. The results suggest that the main advantage of a model employing the strong interaction terms is to provide the capability for modeling anisotropic and asymmetric Poisson's ratios, as well as axial stress-axial strain responses, in tension and compression for finite deformations.     

Cartilage interstitial fluid load support in unconfined compression

Under physiological conditions of loading, articular cartilage is subjected to both compressive strains, normal to the articular surface, and tensile strains, tangential to the articular surface. Previous studies have shown that articular cartilage exhibits a much higher modulus in tension than in compression, and theoretical analyses have suggested that this tension–compression nonlinearity enhances the magnitude of interstitial fluid pressurization during loading in unconfined compression, above a theoretical threshold of 33% of the average applied stress. The first hypothesis of this experimental study is that the peak fluid load support in unconfined compression is significantly greater than the 33% theoretical limit predicted for porous permeable tissues modeled with equal moduli in tension and compression. The second hypothesis is that the peak fluid load support is higher at the articular surface side of the tissue samples than near the deep zone, because the disparity between the tensile and compressive moduli is greater at the surface zone. Ten human cartilage samples from six patellofemoral joints, and 10 bovine cartilage specimens from three calf patellofemoral joints were tested in unconfined compression. The peak fluid load support was measured at 79±11% and 69±15% at the articular surface and deep zone of human cartilage, respectively, and at 94±4% and 71±8% at the articular surface and deep zone of bovine calf cartilage, respectively. Statistical analyses confirmed both hypotheses of this study. These experimental results suggest that the tension–compression nonlinearity of cartilage is an essential functional property of the tissue which makes interstitial fluid pressurization the dominant mechanism of load support in articular cartilage.     

A Bimodular Theory for Finite Deformations: Comparison of Orthotropic Second-order and Exponential Stress Constitutive Equations for Articular Cartilage

Cartilaginous tissues, such as articular cartilage and the annulus fibrosus, exhibit orthotropic behavior with highly asymmetric tensile–compressive responses. Due to this complex behavior, it is difficult to develop accurate stress constitutive equations that are valid for finite deformations. Therefore, we have developed a bimodular theory for finite deformations of elastic materials that allows the mechanical properties of the tissue to differ in tension and compression. In this paper, we derive an orthotropic stress constitutive equation that is second-order in terms of the Biot strain tensor as an alternative to traditional exponential type equations. Several reduced forms of the bimodular second-order equation, with six to nine parameters, and a bimodular exponential equation, with seven parameters, were fit to an experimental dataset that captures the highly asymmetric and orthotropic mechanical response of cartilage. The results suggest that the bimodular second-order models may be appealing for some applications with cartilaginous tissues.     

Nonlinear mechanical property of tracheal cartilage: a theoretical and experimental study

BACKGROUND: Despite being the stiffest airway of the bronchial tree, the trachea undergoes significant deformation due to intrathoracic pressure during breathing. The mechanical properties of the trachea affect the flow in the airway and may contribute to the biological function of the lung. METHOD: A Fung-type strain energy density function was used to investigate the nonlinear mechanical behavior of tracheal cartilage. A bending test on pig tracheal cartilage was performed and a mathematical model for analyzing the deformation of tracheal cartilage was developed. The constants included in the strain energy density function were determined by fitting the experimental data. RESULT: The experimental data show that tracheal cartilage is a nonlinear material displaying higher strength in compression than in tension. When the compression forces varied from -0.02 to -0.03N and from -0.03 to -0.04N, the deformation ratios were 11.03+/-2.18% and 7.27+/-1.59%, respectively. Both were much smaller than the deformation ratios (20.01+/-4.49%) under tension forces of 0.02 to 0.01N. The Fung-type strain energy density function can capture this nonlinear behavior very well, whilst the linear stress-strain relation cannot. It underestimates the stability of trachea by exaggerating the displacement in compression. This study may improve our understanding of the nonlinear behavior of tracheal cartilage and it may be useful for the future study on tracheal collapse behavior under physiological and pathological conditions.     

Predicting long bone loading from cross-sectional geometry

Long bone loading histories are commonly evaluated using a beam model by calculating cross-sectional second moments of areas (SMAs). Without in vivo strain data, SMA analyses commonly make two explicit or implicit assumptions. First, while it has long been known that axial compression superimposed on bending shifts neutral axes away from cross-sectional area centroids, most analyses assume that cross-sectional properties calculated through the area centroid approximate cross-sectional strength. Second, the orientation of maximum bending rigidity is often assumed to reflect the orientation of peak or habitual bending forces the bone experiences. These assumptions are tested in sheep in which rosette strain gauges mounted at three locations around the tibia and metatarsal midshafts measured in vivo strains during treadmill running at 1.5 m/sec. Calculated normal strain distributions confirm that the neutral axis of bending does not run through the midshaft centroid. In these animals, orientations of the principal centroidal axes around which maximum SMAs (Imax) are calculated are not in the same planes in which the bones experienced bending. Cross-sectional properties calculated using centroidal axes have substantial differences in magnitude (up to 55%) but high correlations in pattern compared to cross-sectional properties calculated around experimentally determined neutral axes. Thus interindividual comparisons of cross-sectional properties calculated from centroidal axes may be useful in terms of pattern, but are subject to high errors in terms of absolute values. In addition, cross-sectional properties do not necessarily provide reliable data on the orientations of loads to which bones are subjected.     

Experimental verification of the roles of intrinsic matrix viscoelasticity and tension-compression nonlinearity in the biphasic response of cartilage

A biphasic-CLE-QLV model proposed in our recent study [2001, J. Biomech. Eng., 123, pp. 410-417] extended the biphasic theory of Mow et al. [1980, J. Biomech. Eng., 102, pp. 73-84] to include both tension-compression nonlinearity and intrinsic viscoelasticity of the cartilage solid matrix by incorporating it with the conewise linear elasticity (CLE) model [1995, J. Elasticity, 37, pp. 1-38] and the quasi-linear viscoelasticity (QLV) model [Biomechanics: Its foundations and objectives, Prentice Hall, Englewood Cliffs, 1972]. This model demonstrates that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelastic effects, as well as tension-compression nonlinearity. The objective of this study is to directly test this biphasic-CLE-QLV model against experimental data from unconfined compression stress-relaxation tests at slow and fast strain rates as well as dynamic loading. Twelve full-thickness cartilage cylindrical plugs were harvested from six bovine glenohumeral joints and multiple confined and unconfined compression stress-relaxation tests were performed on each specimen. The material properties of specimens were determined by curve-fitting the experimental results from the confined and unconfined compression stress relaxation tests. The findings of this study demonstrate that the biphasic-CLE-QLV model is able to describe the strain-rate-dependent mechanical behaviors of articular cartilage in unconfined compression as attested by good agreements between experimental and theoretical curvefits (r2 = 0.966 +/- 0.032 for testing at slow strain rate; r2 = 0.998 +/- 0.002 for testing at fast strain rate) and predictions of the dynamic response (r2 = 0.91 +/- 0.06). This experimental study also provides supporting evidence for the hypothesis that both tension-compression nonlinearity and intrinsic viscoelasticity of the solid matrix of cartilage are necessary for modeling the transient and equilibrium responses of this tissue in tension and compression. Furthermore, the biphasic-CLE-QLV model can produce better predictions of the dynamic modulus of cartilage in unconfined dynamic compression than the biphasic-CLE and biphasic poroviscoelastic models, indicating that intrinsic viscoelasticity and tension-compression nonlinearity of articular cartilage may play important roles in the load-support mechanism of cartilage under physiologic loading.     

Anisotropy, inhomogeneity, and tension-compression nonlinearity of human glenohumeral cartilage in finite deformation

The tensile and compressive properties of human glenohumeral cartilage were determined by testing 120 rectangular strips in uniaxial tension and 70 cylindrical plugs in confined compression, obtained from five human glenohumeral joints. Specimens were harvested from five regions across the articular surface of the humeral head and two regions on the glenoid. Tensile strips were obtained along two orientations, parallel and perpendicular to the split-line directions. Two serial slices through the thickness, corresponding to the superficial and middle zones of the cartilage layers, were prepared from each tensile strip and each compressive plug. The equilibrium tensile modulus and compressive aggregate modulus of cartilage were determined from the uniaxial tensile and confined compression tests, respectively. Significant differences in the tensile moduli were found with depth and orientation relative to the local split-line direction. Articular cartilage of the humeral head was significantly stiffer in tension than that of the glenoid. There were significant differences in the aggregate compressive moduli of articular cartilage between superficial and middle zones in the humeral head. Furthermore, tensile and compressive stress-strain responses exhibited nonlinearity under finite strain, while the tensile modulus differed by up to two orders of magnitude from the compressive aggregate modulus at 0% strain, demonstrating a high degree of tension-compression nonlinearity. The complexity of the mechanical properties of human glenohumeral cartilage was exposed in this study, showing anisotropy, inhomogeneity, and tension-compression nonlinearity within the same joint. The observed differences in the tensile properties of human glenohumeral cartilage suggest that the glenoid may be more susceptible to cartilage degeneration than the humeral head.     

The role of flow-independent viscoelasticity in the biphasic tensile and compressive responses of articular cartilage

A long-standing challenge in the biomechanics of connective tissues (e.g., articular cartilage, ligament, tendon) has been the reported disparities between their tensile and compressive properties. In general, the intrinsic tensile properties of the solid matrices of these tissues are dictated by the collagen content and microstructural architecture, and the intrinsic compressive properties are dictated by their proteoglycan content and molecular organization as well as water content. These distinct materials give rise to a pronounced and experimentally well-documented nonlinear tension-compression stress-strain responses, as well as biphasic or intrinsic extracellular matrix viscoelastic responses. While many constitutive models of articular cartilage have captured one or more of these experimental responses, no single constitutive law has successfully described the uniaxial tensile and compressive responses of cartilage within the same framework. The objective of this study was to combine two previously proposed extensions of the biphasic theory of Mow et al. [1980, ASME J. Biomech. Eng., 102, pp. 73-84] to incorporate tension-compression nonlinearity as well as intrinsic viscoelasticity of the solid matrix of cartilage. The biphasic-conewise linear elastic model proposed by Soltz and Ateshian [2000, ASME J. Biomech. Eng., 122, pp. 576-586] and based on the bimodular stress-strain constitutive law introduced by Curnier et al. [1995, J. Elasticity, 37, pp. 1-38], as well as the biphasic poroviscoelastic model of Mak [1986, ASME J. Biomech. Eng., 108, pp. 123-130], which employs the quasi-linear viscoelastic model of Fung [1981, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York], were combined in a single model to analyze the response of cartilage to standard testing configurations. Results were compared to experimental data from the literature and it was found that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelasticity effects, as well as tension-compression nonlinearity.     

Deformation of nasal septal cartilage during mastication

The cartilaginous nasal septum plays a major role in structural integrity and growth of the face, but its internal location has made physiologic study difficult. By surgically implanting transducers in 10 miniature pigs (Sus scrofa), we recorded in vivo strains generated in the nasal septum during mastication and masseter stimulation. The goals were (1) to determine whether the cartilage should be considered as a vertical strut supporting the nasal cavity and preventing its collapse, or as a damper of stresses generated during mastication and (2) to shed light on the overall pattern of snout deformation during mastication. Strains were recorded simultaneously at the septo‐ethmoid junction and nasofrontal suture during mastication. A third location in the anterior part of the cartilage was added during masseter stimulation and manipulation. Contraction of jaw closing muscles during mastication was accompanied by anteroposterior compressive strains (around ?1,000 με) in the septo‐ethmoid junction. Both the orientation and the magnitude of the strain suggest that the septum does not act as a vertical strut but may act in absorbing loads generated during mastication. The results from masseter stimulation and manipulation further suggest that the masticatory strain pattern arises from a combination of dorsal bending and/or shearing and anteroposterior compression of the snout. J. Morphol., 2009. © 2009 Wiley‐Liss, Inc.     

Patterns of strain in the macaque tibia during functional activity.

The strain environment of the tibial midshaft of two female macaques was evaluated through in vivo bone strain experiments using three rosette gauges around the circumference of the bones. Strains were collected for a total of 123 walking and galloping steps as well as several climbing cycles. Principal strains and the angle of the maximum (tensile) principal strain with the long axis of the bone were calculated for each gauge site. In addition, the normal strain distribution throughout the cross section was determined from the longitudinal normal strains (strains in the direction of the long axis of the bone) at each of the three gauge sites, and at the corresponding cross-sectional geometry of the bone. This strain distribution was compared with the cross-sectional properties (area moments) of the midshaft. For both animals, the predominant loading regime was found to be bending about an oblique axis running from anterolateral to posteromedial. The anterior and part of the medial cortex are in tension; the posterior and part of the lateral cortex are in compression. The axis of bending does not coincide with the maximum principal axis of the cross section, which runs mediolaterally. The bones are not especially buttressed in the plane of bending, but offer the greatest strength anteroposteriorly. The cross-sectional geometry therefore does not minimize strain or bone tissue. Peak tibial strains are slightly higher than the peak ulnar strains reported earlier for the same animals (Demes et al. [1998] Am J Phys Anthropol 106:87-100). Peak strains for both the tibia and the ulna are moderate in comparison to strains recorded during walking and galloping activities in nonprimate mammals.     

Relationships of loading history and structural and material characteristics of bone: development of the mule deer calcaneus

If a bone's morphologic organization exhibits the accumulated effects of its strain history, then the relative contributions of a given strain stimulus to a bone's development may be inferred from a bone's hierarchical organization. The artiodactyl calcaneus is a short cantilever, loaded habitually in bending, with prevalent compression in the cranial (Cr) cortex, tension in the caudal (Cd) cortex, and shear in the medial and lateral cortices (i.e., neutral axis). Artiodactyl calcanei demonstrate unusually heterogeneous structural and material organization between these cortices. This study examines potential relationships between developmental morphologic variations and the functional strain distribution of the deer calcaneus. One calcaneus was obtained from each of 36 (fetus to adult) wild deer. Predominant collagen fiber orientation (CFO), microstructural characteristics, mineral content (% ash), and geometric parameters were determined from transversely cut segments. Radiographs were examined for arched trabeculae, which may reflect tension/compression stress trajectories. Results showed that cross-sectional shape changes with age from quasi-circular to quasi-elliptical, with the long axis in the cranial-caudal direction of habitual bending. Cranial ("compression") cortical thickness increased at a greater rate than the Cd ("tension") cortex. Fetal bones exhibited arched trabeculae. Percent ash was not uniform (Cr > Cd), and this disparity increased with age (absolute differences: 2.5% fetuses, 4.3% adults). Subadult bones showed progressively more secondary osteons and osteocyte lacunae in the Cr cortex, but the Cd cortex tended to have more active remodeling in the subadult and adult bones. Nonuniform Cr:Cd CFO patterns first consistently appear in the subadults, and are correlated with secondary bone formation and habitual strain mode. Medial and lateral cortices in these groups exhibited elongated secondary osteons. These variations may represent "strain-mode-specific" (i.e., tension, compression, shear) adaptations. The heterogeneous organization may also be influenced by variations in longitudinal strain magnitude (highest in the Cr cortex) and principal strain direction-oblique in medial-lateral cortices (where shear strains also predominate). Other factors such as local reductions in longitudinal strain may influence the increased remodeling activity of the Cd cortex. Some structural variations, such as arched trabeculae, that are established early in ontogeny may be strongly influenced by genetic- or epigenetic-derived processes. Material variations, such as secondary osteon population densities and CFO, which appear later, may be products of extragenetic factors, including microdamage.     

Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach

Trabecular bone tissue failure can be considered as consisting of two stages: damage and fracture; however, most failure analyses of 3D high-resolution trabecular bone samples are confined to damage mechanisms only, that is, without fracture. This study aims to develop a computational model of trabecular bone consisting of an explicit representation of complete failure, incorporating damage criteria, fracture criteria, cohesive forces, asymmetry and large deformation capabilities. Following parameter studies on a test specimen, and experimental testing of bone sample to complete failure, the asymmetric critical tissue damage and fracture strains of ovine vertebral trabecular bone were calibrated and validated to be compression damage ?1.16 %, tension damage 0.69 %, compression fracture ?2.91 % and tension fracture 1.98 %. Ultimate strength and post–ultimate strength softening were captured by the computational model, and the failure of individual struts in bending and shear was also predicted. This modelling approach incorporated a cohesive parameter that provided a facility to calibrate ductile–brittle behaviour of bone tissue in this non-linear geometric and non-linear constitutive property analyses tool. Finally, the full accumulation of tissue damage and tissue fracture has been monitored from range of small magnitude (normal daily loading) through to specimen yielding, ultimate strength and post–ultimate strength softening.     

Biomechanical properties of knee articular cartilage

Structure and properties of knee articular cartilage are adapted to stresses exposed on it during physiological activities. In this study, we describe site- and depth-dependence of the biomechanical properties of bovine knee articular cartilage. We also investigate the effects of tissue structure and composition on the biomechanical parameters as well as characterize experimentally and numerically the compression-tension nonlinearity of the cartilage matrix. In vitro mechano-optical measurements of articular cartilage in unconfined compression geometry are conducted to obtain material parameters, such as thickness, Young's and aggregate modulus or Poisson's ratio of the tissue. The experimental results revealed significant site- and depth-dependent variations in recorded parameters. After enzymatic modification of matrix collagen or proteoglycans our results show that collagen primarily controls the dynamic tissue response while proteoglycans affect more the static properties. Experimental measurements in compression and tension suggest a nonlinear compression-tension behavior of articular cartilage in the direction perpendicular to articular surface. Fibril reinforced poroelastic finite element model was used to capture the experimentally found compression-tension nonlinearity of articular cartilage.     

Polymer-based composite hip prostheses

A composite hip prosthesis (CHP) made from poly(ether-imide) reinforced with carbon and glass fibres was manufactured and characterized. The main objective of the study was to evaluate the effect of fibre organization on the mechanical properties of the composite femoral implant and compare with the bone. A stacking sequence of drop-off plies of carbon/glass fibres reinforcing poly(ether-imide) (PEI) constitutes a symmetrical and balanced CHP. The hip was manufactured according to the finite element modelling (FEM) design and using the compression moulding and water-jet technologies. The measured stress-strain data according to tensile, flexural and torsional tests showed agreement with the numerical calculation. Young's modulus and the strength in tension are uniform along the stem axis (40 GPa and 600 MPa, respectively) while the elastic modulus in bending varies from 10 to 60 GPa in the tip-head direction. The composite stem showed a linear load-displacement relation up to 4500 N without breaking. Mechanical behaviour of the CHP is compared to that of a canine femur. Comparison with metal prostheses has also been undertaken. CHPs control stress-strain distributions, and hence the mechanical signals to bone, through a material-structure design.     

Collagen fiber orientation and geometry effects on the mechanical properties of secondary osteons.

The effects of collagen fiber orientation and osteon geometry on the mechanical properties of secondary osteons under axial compression/tension and combined loadings (compression, bending and torsion) were investigated using a composite-beam finite-element model. Three cross-sectional shapes of secondary osteons were studied to show the effect of geometry. The results of stiffness are presented using the tension and compression properties for each lamella. The model shows that the mechanical properties of osteons are enhanced in bending and torsion when collagen fibers are oriented within 30 degrees of the loading axis. Osteons with alternating lamellar orientation are not well adapted to resist torsional moments, but alternate collagen fiber orientation has virtually no effect on the bending stiffness of osteons. Fiber orientation affects the mechanical properties less significantly when osteons are non-circular. Collagen fiber orientation and osteon geometry interact to determine the mechanical behavior of the osteon, and may act in a compensatory manner in the adaptive process.     

Patterns of strain in the macaque ulna during functional activity

In vivo bone strain experiments were performed on the ulnae of three female rhesus macaques to test how the bone deforms during locomotion. The null hypothesis was that, in an animal moving its limbs predominantly in sagittal planes, the ulna experiences anteroposterior bending. Three rosette strain gauges were attached around the circumference of the bone slightly distal to midshaft. They permit a complete characterization of the ulna's loading environment. Strains were recorded during walking and galloping activities. Principal strains and strain directions relative to the long axis of the bone were calculated for each gauge site. In all three animals, the lateral cortex experienced higher tensile than compressive principal strains during the stance phase of walking. Compressive strains predominated at the medial cortex of two animals (the gauge on this cortex of the third animal did not function). The posterior cortex was subject to lower strains; the nature of the strain was highly dependent on precise gauge position. The greater principal strains were aligned closely with the long axis of the bone in two animals, whereas they deviated up to 45° from the long axis in the third animal. A gait change from walk to gallop was recorded for one animal. It was not accompanied by an incremental change in strain magnitudes. Strains are at the low end of the range of strain magnitudes recorded for walking gaits of nonprimate mammals. The measured distribution of strains in the rhesus monkey ulna indicates that mediolateral bending, rather than anteroposterior bending, is the predominant loading regime, with the neutral axis of bending running from anterior and slightly medial to posterior and slightly lateral. A variable degree of torsion was superimposed over this bending regime. Ulnar mediolateral bending is apparently caused by a ground reaction force vector that passes medial to the forearm. The macaque ulna is not reinforced in the plane of bending. The lack of buttressing in the loaded plane and the somewhat counterintuitive bending direction recommend caution with regard to conventional interpretations of long bone cross-sectional geometry. Am J Phys Anthropol 106:87–100, 1998. © 1998 Wiley-Liss, Inc.     

Nonlinear behavior of trabecular bone at small strains

Study of the behavior of trabecular bone at strains below 0.40 percent is of clinical and biomechanical importance. The goal of this work was to characterize, with respect to anatomic site, loading mode, and apparent density, the subtle concave downward stress-strain nonlinearity, that has been observed recently for trabecular bone at these strains. Using protocols designed to minimize end-artifacts, 155 cylindrical cores from human vertebrae, proximal tibiae, proximal femora, and bovine proximal tibiae were mechanically tested to yield at 0.50 percent strain per second in tension or compression. The nonlinearity was quantified by the reduction in tangent modulus at 0.20 percent and 0.40 percent strain as compared to the initial modulus. For the pooled data, the mean +/- SD percentage reduction in tangent modulus at 0.20 percent strain was 9.07+/- 3.24 percent in compression and 13.8 +/- 4.79 percent in tension. At 0.40 percent strain, these values were 23.5 +/- 5.71 and 35.7+/- 7.10 percent, respectively. The magnitude of the nonlineari't depended on both anatomic site (p < 0.001) and loading mode (p < 0.001), and in tension was positively correlated with density. Calculated values of elastic modulus and yield properties depended on the strain range chosen to define modulus via a linear curve fit (p < 0.005). Mean percent differences in 0.20 percent offset yield strains were as large as 10.65 percent for some human sites. These results establish that trabecular bone exhibits nonlinearity at low strains, and that this behavior can confound intersite comparisons of mechanical properties. A nonlinear characterization of the small strain behavior of trabecular bone was introduced to characterize the initial stress-strain behavior more thoroughly.     

Characterizing bone strain distributions in vivo using three triple rosette strain gages.

Three triple-element rosette strain gages were attached to the equine third metacarpal midshaft to record site-specific strains engendered by locomotion. The distribution of strains acting upon the midshaft cross section were characterized using a combined beam theory and finite element model analysis that did not presume the manner by which the bone was inertially loaded. A medium-speed trot (3.6 ms-1) was chosen as a representative speed and gait, with normal and shear strains, and strain energy density (SED) distributions determined throughout the stance and subsequent swing phase. Importantly, the sites of maximum compression (-2400 mu epsilon), tension (810 mu epsilon), shear (1500 mu epsilon), and SED (54 kPa) were not located at any of the gage attachment sites, emphasizing that a minimum of three rosette gages are necessary to resolve the peaks and locations of functionally induced normal and shear strains. Considering the nonuniform strain distributions across the cortex, we conclude that the third metacarpal is subject to a complex loading milieu comprised of bending, axial compression, end shear, and torsion. As this complex manner of loading was consistent through the entire stance phase, it would appear that, at least during the trot, specific sites within the same cross section are subject to vastly different magnitudes of strain stimulus.     

Role of cartilage collagen fibrils networks in knee joint biomechanics under compression

Collagen fibrils networks in knee cartilage and menisci change in content and structure from a region to another. While resisting tension, they influence global joint response as well as local strains particularly at short-term periods. To investigate the role of fibrils networks in knee joint mechanics and in particular cartilage response, a novel model of the knee joint is developed that incorporates the cartilage and meniscus fibrils networks as well as depth-dependent properties in cartilage. The joint response under up to 2000 N compression is investigated for conditions simulating the absence in cartilage of deep fibrils normal to subchondral bone or superficial fibrils parallel to surface as well as localized split of cartilage at subchondral junction or localized damage to superficial fibrils at loaded areas. Deep vertical fibrils network in cartilage play a crucial role in stiffening (by 10%) global response and protecting cartilage by reducing large strains (from maximum of 102% to 38%), in particular at subchondral junction. Superficial horizontal fibrils protect the tissue mainly from excessive strains at superficial layers (from 27% to 8%). Local cartilage split at base disrupts the normal function of vertical fibrils at the affected areas resulting in higher strains.Deep fibrils, and to a lesser extent superficial fibrils, play dominant mechanical roles in cartilage response under transient compression. Any treatment modality attempting to repair or regenerate cartilage defects involving partial or full thickness osteochondral grafts should account for the crucial role of collagen fibrils networks and the demanding mechanical environment of the tissue.     

Optical determination of anisotropic material properties of bovine articular cartilage in compression

The precise nature of the material symmetry of articular cartilage in compression remains to be elucidated. The primary objective of this study was to determine the equilibrium compressive Young's moduli and Poisson's ratios of bovine cartilage along multiple directions (parallel and perpendicular to the split line direction, and normal to the articular surface) by loading small cubic specimens (0.9 x 0.9 x 0.8 mm, n =15) in unconfined compression, with the expectation that the material symmetry of cartilage could be determined more accurately with the help of a more complete set of material properties. The second objective was to investigate how the tension-compression nonlinearity of cartilage might alter the interpretation of material symmetry. Optimized digital image correlation was used to accurately determine the resultant strain fields within the specimens under loading. Experimental results demonstrated that neither the Young's moduli nor the Poisson's ratios exhibit the same values when measured along the three loading directions. The main findings of this study are that the framework of linear orthotropic elasticity (as well as higher symmetries of linear elasticity) is not suitable to describe the equilibrium response of articular cartilage nor characterize its material symmetry; a framework which accounts for the distinctly different responses of cartilage in tension and compression is more suitable for describing the equilibrium response of cartilage; within this framework, cartilage exhibits no lower than orthotropic symmetry.