Elastic deformation of mineralized collagen fibrils: an equivalent inclusion based composite model

Mineralized collagen fibrils are the basic building blocks of bone tissue at the supramolecular level. Several disease states, manipulation of the expression of specific proteins involved in biomineralization, and treatment with different agents alter the extent of mineralization as well as the morphology of mineral crystals which in turn affect the mechanical function of bone tissue. An experimental assessment of mineralized fibers' mechanical properties is challenged by their small size, leaving analytical and computational models as a viable alternative for investigation of the fibril-level mechanical properties. In the current study the variation of the elastic stiffness tensor of mineralized collagen fibrils with changing mineral volume fraction and mineral aspect ratios was predicted via a micromechanical model. The partitioning of applied stresses between mineral and collagen phases is also predicted for normal and shear loading of fibrils. Model predictions resulted in transversely isotropic collagen fibrils in which the modulus along the longer axis of the fibril was the greatest. All the elastic moduli increased with increasing mineral volume fraction whereas Poisson's ratios decreased with the exception of v12 (=v21). The partitioning of applied stresses were such that the stresses acting on mineral crystals were about 1.5, 15, and 3 times greater than collagen stresses when fibrils were loaded transversely, longitudinally, and in shear, respectively. In the overall the predictions were such that: (a) greatest modulus along longer axis; (b) the greatest mineral/collagen stress ratio along the longer axis of collagen fibers (i.e., greatest relief of stresses acting on collagen); and (c) minimal lateral contraction when fibers are loaded along the longer axis. Overall, the pattern of mineralization as put forth in this model predicts a superior mechanical function along the longer axis of collagen fibers, the direction which is more likely to experience greater stresses.     

Simple shear testing of parallel-fibered planar soft tissues

The simple shear test may provide unique information regarding the material response of parallel-fibered soft tissues because it allows the elimination of the dominant fiber material response from the overall stresses. However, inhomogeneities in the strain field due to clamping and free edge effects have not been documented. The finite element method was used to study finite simple shear of simulated ligament material parallel to the fiber direction. The effects of aspect ratio, clamping prestrain, and bulk modulus were assessed using a transversely isotropic, hyperelastic material model. For certain geometries, there was a central area of uniform strain. An aspect ratio of 1:2 for the fiber to cross-fiber directions provided the largest region of uniform strain. The deformation was nearly isochoric for all bulk moduli indicating this test may be useful for isolating solid viscoelasticity from interstitial flow effects. Results suggest this test can be used to characterize the matrix properties for the type of materials examined in this study, and that planar measurements will suffice to characterize the strain. The test configuration may be useful for the study of matrix, fiber-matrix, and fiber-fiber material response in other types of parallel-fibered transversely isotropic soft tissues.     

Effects of damage on the orthotropic material symmetry of bovine tibial trabecular bone

The macroscopic mechanical properties of trabecular bone can be predicted by its architecture using theoretical relationships between the elastic and architectural properties. Microdamage caused by overloading or fatigue decreases the apparent elastic moduli of trabecular bone requiring these relationships to be modified to predict the damaged elastic properties. In the case of isotropic damage, the apparent level elastic properties could be determined by multiplying all of the elastic constants by a single scalar factor. If the damage is anisotropic, the elastic constants may change by differing factors and the material coordinate system could become misaligned with the fabric coordinate system. High-resolution finite element models were used to simulate damage overloading on seven trabecular bone specimens subjected to pure shear strain in two planes. Comparison of the apparent elastic moduli of the specimens before and after damage showed that the reduction of the elastic moduli was anisotropic. This suggests that the microdamage within the specimens was inhomogeneous. However, after damage the specimens exhibited nearly orthotropic material symmetry as they did before damage. Changes in the orientation of the orthotropic material coordinate system were also small and occurred primarily in the transverse plane. Thus, while damage in trabecular bone is anisotropic, the material coordinate system remains aligned with the fabric tensor.     

A homogenization model of the annulus fibrosus

The objective of this study was to use a homogenization model of the anisotropic mechanical behavior of annulus fibrosus (AF) to address some of the issues raised in structural finite element and fiber-reinforced strain energy models. Homogenization theory describes the effect of microstructure on macroscopic material properties by assuming the material is composed of repeating representative volume elements. We first developed the general homogenization model and then specifically prescribed the model to in-plane single lamella and multi-lamellae AF properties. We compared model predictions to experimentally measured AF properties and performed parametric studies. The predicted tensile moduli (E theta and E z) and their dependence on fiber volume fraction and fiber angle were consistent with measured values. However, the model prediction for shear modulus (G thetaz) was two orders of magnitude larger than directly measured values. The values of E theta and E z were strongly dependent on the model input for matrix modulus, much more so than the fiber modulus. These parametric analyses demonstrated the contribution of the matrix in AF load support, which may play a role when protoeglycans are decreased in disc degeneration, and will also be an important design factor in tissue engineering. We next compared the homogenization model to a 3-D structural finite element model and fiber-reinforced energy models. Similarities between the three model types provided confidence in the ability of these models to predict AF tissue mechanics. This study provides a direct comparison between the several types of AF models and will be useful for interpreting previous studies and elucidating AF structure-function relationships in disc degeneration and for functional tissue engineering.     

Evaluation of affine fiber kinematics in human supraspinatus tendon using quantitative projection plot analysis

Structural constitutive modeling approaches are often based on the assumption of affine fiber kinematics, even though this assumption has rarely been evaluated experimentally. We are interested in applying mathematical models to understand the mechanisms responsible for the inhomogeneous, anisotropic, and non-linear properties of human supraspinatus tendon (SST); however, the relationship between macroscopic and fiber-level deformation in this tendon remains unknown and current methods for making this assessment are inadequate. Therefore, the purpose of this study was to develop an improved method for quantitatively assessing agreement between two distributions and to examine the affine assumption in SST by comparing experimental fiber alignment to affine model predictions using this analysis approach. Measured fiber angle values of SST samples in uniaxial tensile tests were compared with predictions of affine fiber deformation using modified projection plots, which provide a method for qualitative and quantitative comparisons of two distributions. The projection plot metrics of offset and range, which were developed in this study, are of particular benefit by providing a quantitative representation of agreement that can be subjected to statistical comparisons. For SST, offset and range values varied by tendon location and test orientation, with more affine deformation evidenced for tendon regions of higher alignment. Results suggest that non-affine fiber behavior is dependent on specific tissue, orientation of the applied stretch relative to the fiber organization, and length scale of the observation. In addition, this study has established a method for evaluating the affine assumption in other tissues.     

Continuum description of the Poisson׳s ratio of ligament and tendon under finite deformation

Ligaments and tendons undergo volume loss when stretched along the primary fiber axis, which is evident by the large, strain-dependent Poisson?s ratios measured during quasi-static tensile tests. Continuum constitutive models that have been used to describe ligament material behavior generally assume incompressibility, which does not reflect the volumetric material behavior seen experimentally. We developed a strain energy equation that describes large, strain dependent Poisson?s ratios and nonlinear, transversely isotropic behavior using a novel method to numerically enforce the desired volumetric behavior. The Cauchy stress and spatial elasticity tensors for this strain energy equation were derived and implemented in the FEBio finite element software (www.febio.org). As part of this objective, we derived the Cauchy stress and spatial elasticity tensors for a compressible transversely isotropic material, which to our knowledge have not appeared previously in the literature. Elastic simulations demonstrated that the model predicted the nonlinear, upwardly concave uniaxial stress–strain behavior while also predicting a strain-dependent Poisson?s ratio. Biphasic simulations of stress relaxation predicted a large outward fluid flux and substantial relaxation of the peak stress. Thus, the results of this study demonstrate that the viscoelastic behavior of ligaments and tendons can be predicted by modeling fluid movement when combined with a large Poisson?s ratio. Further, the constitutive framework provides the means for accurate simulations of ligament volumetric material behavior without the need to resort to micromechanical or homogenization methods, thus facilitating its use in large scale, whole joint models.     

A computational study of invariant I5 in a nearly incompressible transversely isotropic model for white matter

The aligned axonal fiber bundles in white matter make it suitable to be modeled as a transversely isotropic material. Recent experimental studies have shown that a minimal form, nearly incompressible transversely isotropic (MITI) material model, is capable of describing mechanical anisotropy of white matter. Here, we used a finite element (FE) computational approach to demonstrate the significance of the fifth invariant (I₅) when modeling the anisotropic behavior of white matter in the large-strain regime. We first implemented and validated the MITI model in an FE simulation framework for large deformations. Next, we applied the model to a plate-hole structural problem to highlight the significance of the invariant I₅ by comparing with the standard fiber reinforcement (SFR) model. We also compared the two models by fitting the experiment data of asymmetric indentation, shear test, and uniaxial stretch of white matter. Our results demonstrated the significance of I₅ in describing shear deformation/anisotropy, and illustrated the potential of the MITI model to characterize transversely isotropic white matter tissues in the large-strain regime.     

Prediction of cortical bone elastic constants by a two-level micromechanical model using a generalized self-consistent method

A two-level micromechanical model of cortical bone based on a generalized self-consistent method was developed to take into consideration the transversely isotropic elasticity of many microstructural features in cortical bone, including Haversian canals, resorption cavities, and osteonal and interstitial lamellae. In the first level, a single osteon was modeled as a two-phase composite such that Haversian canals were represented by elongated pores while the surrounding osteonal lamellae were considered as matrix. In the second level, osteons and resorption cavities were modeled as multiple inclusions while interstitial lamellae were regarded as matrix. The predictions of cortical bone elasticity from this two-level micromechanical model were mostly in agreement with experimental data for the dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. However, variation in cortical bone elastic constants was greater in experimental data than in model predictions. This could be attributed to variations in the elastic properties of microstructural features in cortical bone. The present micromechanical model of cortical bone will be useful in understanding the contribution of cortical bone porosity to femoral neck fractures.     

The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone.

Conceptually, the elastic characteristics of cancellous bone could be predicted directly from the trabecular morphology--or architecture--and by the elastic properties of the tissue itself. Although hardly any experimental evidence exists, it is often implicitly assumed that tissue anisotropy has a negligible effect on the apparent elastic properties of cancellous bone. The question addressed in this paper is whether this is actually true. If it is, then micromechanical finite element analysis (micro-FEA) models, representing trabecular architecture, using an 'effective isotropic tissue modulus' should be able to predict apparent elastic properties of cancellous bone. To test this, accurate multi-axial compressive mechanical tests of 29 whale bone specimens were simulated with specimen-specific micro-FEA computer models built from true three-dimensional reconstructions. By scaling the micro-FEA predictions by a constant tissue modulus, 92% of the variation of Young's moduli determined experimentally could be explained. The correlation even increased to 95% when the micro-FEA moduli were scaled to the isotropic tissue moduli of individual specimens. Excellent agreement was also found in the elastic symmetry axes and anisotropy ratios. The prediction of Poisson's ratios was somewhat less precise at 85% correlation. The results support the hypothesis; for practical purposes, the concept of an 'effective isotropic tissue modulus' concept is a viable one. They also suggest that the value of such a modulus for individual cases might be inferred from the average tissue density, hence the degree of mineralization. Future studies must clarify how specific the tissue modulus should be for different types of bone if adequate predictions of elastic behavior are to be made in this way.     

Elastic characterization of transversely isotropic soft materials by dynamic shear and asymmetric indentation

The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isotropic soft material. A soft gel with controlled anisotropy was obtained by polymerizing a mixture of fibrinogen and thrombin solutions in a high field magnet (B?=?11.7 T); fibrils in the resulting gel were predominantly aligned parallel to the magnetic field. Aligned fibrin gels were subject to dynamic (20-40 Hz) shear deformation in two orthogonal directions. The shear storage modulus was 1.08?±?0. 42 kPa (mean?±?std. dev.) for shear in a plane parallel to the dominant fiber direction, and 0.58?±?0.21 kPa for shear in the plane of isotropy. Gels were indented by a rectangular tip of a large aspect ratio, aligned either parallel or perpendicular to the normal to the plane of transverse isotropy. Aligned fibrin gels appeared stiffer when indented with the long axis of a rectangular tip perpendicular to the dominant fiber direction. Three-dimensional numerical simulations of asymmetric indentation were used to determine the relationship between direction-dependent differences in indentation stiffness and material parameters. This approach enables the estimation of a complete set of parameters for an incompressible, transversely isotropic, linear elastic material.     

Multiscale mechanics of the cervical facet capsular ligament,with particular emphasis on anomalous fiber realignment prior to tissue failure

The facet capsular ligaments encapsulate the bilateral spinal facet joints and are common sources of painful injury due to afferent innervation. These ligaments exhibit architectural complexity, which is suspected to contribute to the experimentally observed lack of co-localization between macroscopic strain and microstructural tissue damage. The heterogeneous and multiscale nature of this ligament, combined with challenges in experimentally measuring its microscale mechanics, hinders the ability to understand sensory mechanisms under normal or injurious loading. Therefore, image-based, subject-specific, multiscale finite-element models were constructed to predict the mechanical responses of the human cervical facet capsular ligament under uniaxial tensile stretch. The models precisely simulated the force–displacement responses for all samples (\(\textit{R}^{2}=0.99\pm 0.01\)) and showed promise in predicting the magnitude and location of peak regional strains at two different displacements. Yet, there was a loss of agreement between the model and experiment in terms of fiber organization at large tissue stretch, possibly due to a lack of accounting for tissue failure. The mean fiber stretch ratio predicted by the models was found to be significantly higher in regions that exhibited anomalous fiber realignment experimentally than in regions with normal realignment (\(\textit{p}<0.002\)). The development of microstructural abnormalities was associated with the predicted fiber-level stretch (\(\textit{p}<0.009\)), but not with the elemental maximum principal stress or maximum principal strain by logistic regression. The multiscale models elucidate a potential mechanical basis for predicting injury-prone tissue domains and for defining the relationships between macroscopic ligament stretch and microscale pathophysiology in the subfailure regime.     

An inverse modeling approach for stress estimation in mitral valve anterior leaflet valvuloplasty for in-vivo valvular biomaterial assessment

Estimation of regional tissue stresses in the functioning heart valve remains an important goal in our understanding of normal valve function and in developing novel engineered tissue strategies for valvular repair and replacement. Methods to accurately estimate regional tissue stresses are thus needed for this purpose, and in particular to develop accurate, statistically informed means to validate computational models of valve function. Moreover, there exists no currently accepted method to evaluate engineered heart valve tissues and replacement heart valve biomaterials undergoing valvular stresses in blood contact. While we have utilized mitral valve anterior leaflet valvuloplasty as an experimental approach to address this limitation, robust computational techniques to estimate implant stresses are required. In the present study, we developed a novel numerical analysis approach for estimation of the in-vivo stresses of the central region of the mitral valve anterior leaflet (MVAL) delimited by a sonocrystal transducer array. The in-vivo material properties of the MVAL were simulated using an inverse FE modeling approach based on three pseudo-hyperelastic constitutive models: the neo-Hookean, exponential-type isotropic, and full collagen–fiber mapped transversely isotropic models. A series of numerical replications with varying structural configurations were developed by incorporating measured statistical variations in MVAL local preferred fiber directions and fiber splay. These model replications were then used to investigate how known variations in the valve tissue microstructure influence the estimated ROI stresses and its variation at each time point during a cardiac cycle. Simulations were also able to include estimates of the variation in tissue stresses for an individual specimen dataset over the cardiac cycle. Of the three material models, the transversely anisotropic model produced the most accurate results, with ROI averaged stresses at the fully-loaded state of  432.6±46.5 kPa and 241.4±40.5 kPa in the radial and circumferential directions, respectively. We conclude that the present approach can provide robust instantaneous mean and variation estimates of tissue stresses of the central regions of the MVAL.     

Epicardial suction: a new approach to mechanical testing of the passive ventricular wall

The lack of an appropriate three-dimensional constitutive relation for stress in passive ventricular myocardium currently limits the utility of existing mathematical models for experimental and clinical applications. Previous experiments used to estimate parameters in three-dimensional constitutive relations, such as biaxial testing of excised myocardial sheets or passive inflation of the isolated arrested heart, have not included significant transverse shear deformation or in-plane compression. Therefore, a new approach has been developed in which suction is applied locally to the ventricular epicardium to introduce a complex deformation in the region of interest, with transmural variations in the magnitude and sign of nearly all six strain components. The resulting deformation is measured throughout the region of interest using magnetic resonance tagging. A nonlinear, three-dimensional, finite element model is used to predict these measurements at several suction pressures. Parameters defining the material properties of this model are optimized by comparing the measured and predicted myocardial deformations. We used this technique to estimate material parameters of the intact passive canine left ventricular free wall using an exponential, transversely isotropic constitutive relation. We tested two possible models of the heart wall: first, that it was homogeneous myocardium, and second, that the myocardium was covered with a thin epicardium with different material properties. For both models, in agreement with previous studies, we found that myocardium was nonlinear and anisotropic with greater stiffness in the fiber direction. We obtained closer agreement to previously published strain data from passive filling when the ventricular wall was modeled as having a separate, isotropic epicardium. These results suggest that epicardium may play a significant role in passive ventricular mechanics.     

The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity

The objective of this study was to examine the dependence of the elastic properties of cortical bone as a transversely isotropic material on its porosity. The longitudinal Young's modulus, transverse Young's modulus, longitudinal shear modulus, transverse shear modulus, and longitudinal Poisson's ratio of cortical bone were determined from eighteen groups of longitudinal and transverse specimens using tensile and torsional tests on a servo-hydraulic material testing system. These cylindrical waisted specimens of cortical bone were harvested from the middle diaphysis of three pairs of human femora. The porosity of these specimens was assessed by means of histology. Our study demonstrated that the longitudinal Young's and shear moduli of human femoral cortical bone were significantly (p<0.01) negatively correlated with the porosity of cortical bone. Conversely, the elastic properties in the transverse direction did not have statistically significant correlations with the porosity of cortical bone. As a result, the transverse elastic properties of cortical bone were less sensitive to changes in porosity than those in the longitudinal direction. Additionally, the anisotropic ratios of cortical bone elasticity were found to be significantly (p<0.01) negatively correlated with its porosity, indicating that cortical bone tended to become more isotropic when its porosity increased. These results may help a number of researchers develop more accurate micromechanics models of cortical bone.     

Tensile properties of the mandibular condylar cartilage

Mandibular condylar cartilage plays a crucial role in temporomandibular joint (TMJ) function, which includes facilitating articulation with the temporomandibular joint disc and reducing loads on the underlying bone. The cartilage experiences considerable tensile forces due to direct compression and shear. However, only scarce information is available about its tensile properties. The present study aims to quantify the biomechanical characteristics of the mandibular condylar cartilage to aid future three-dimensional finite element modeling and tissue engineering studies. Porcine condylar cartilage was tested under uniaxial tension in two directions, anteroposterior and mediolateral, with three regions per direction. Stress relaxation behavior was modeled using the Kelvin model and a second-order generalized Kelvin model, and collagen fiber orientation was determined by polarized light microscopy. The stress relaxation behavior of the tissue was biexponential in nature. The tissue exhibited greater stiffness in the anteroposterior direction than in the mediolateral direction as reflected by higher Young's (2.4 times), instantaneous (1.9 times), and relaxed (1.9 times) moduli. No significant differences were observed among the regional properties in either direction. The predominantly anteroposterior macroscopic fiber orientation in the fibrous zone of condylar cartilage correlated well with the biomechanical findings. The condylar cartilage appears to be less stiff and less anisotropic under tension than the anatomically and functionally related TMJ disc. The anisotropy of the condylar cartilage, as evidenced by tensile behavior and collagen fiber orientation, suggests that the shear environment of the TMJ exposes the condylar cartilage to predominantly but not exclusively anteroposterior loading.     

Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone consists of mineral platelet with nanometer size embedded in a protein matrix, it is similar to the microstructure of soft matrix nanocomposites reinforced with hard nanostructures. Considering a representative volume element (RVE) of the microstructure of bone as the microscale problem in our hierarchical multiscale modeling scheme, the global behavior of bone is obtained under various macroscopic loading conditions. This scheme may be suitable for modeling arbitrary bone geometries subjected to a variety of loading conditions. Using the presented method, mechanical properties of cortical bone including elastic moduli and Poisson's ratios in two major directions and shear modulus is obtained for different mineral volume fractions.     

Estimation of cat medial gastrocnemius fascicle lengths during dynamic contractions

In typical muscle models, it is often assumed that the contractile element (fascicle) length depends exclusively on the instantaneous muscle-tendon length and the instantaneous muscle force. In order to test whether the instantaneous fascicle length during dynamic contractions can be predicted from muscle-tendon length and force, fascicle lengths, muscle-tendon lengths, and muscle forces were directly measured in cat medial gastrocnemii during isometric and dynamic contractions. Two theoretical muscle models were developed: model A was based on force-time data obtained during the activation phase and model D on force-time data obtained during the deactivation phase of isometric contractions. To test the models, instantaneous fascicle lengths were predicted from muscle-tendon lengths and forces during dynamic contractions that simulated cat locomotion for speeds ranging from 0.4 to 1.6m/s. The theoretically predicted fascicle lengths were compared with the experimentally measured fascicle lengths. It was found that fascicle lengths were not uniquely associated with muscle-tendon lengths and forces; that is, for a given muscle-tendon length and force, fascicle lengths varied depending on the contractile history. Consequently, models A and D differed in fascicle length predictions; model D (maximum average error=8.5%) was considerably better than model A (maximum average error=22.3%). We conclude from this study that it is not possible to predict the exact fascicle lengths from muscle-tendon lengths and forces alone, however, adequate predictions seem possible based on such a model. The relationship between fascicle length and muscle force and muscle-tendon length is complex and highly non-linear, thus, it appears unlikely that accurate fascicle length predictions can be made without some reference contractions in which fascicle length, muscle-tendon length, and force are measured simultaneously.     

A transversely isotropic viscoelastic constitutive equation for brainstem undergoing finite deformation

The objective of this study was to define the constitutive response of brainstem undergoing finite shear deformation. Brainstem was characterized as a transversely isotropic viscoelastic material and the material model was formulated for numerical implementation. Model parameters were fit to shear data obtained in porcine brainstem specimens undergoing finite shear deformation in three directions: parallel, perpendicular, and cross sectional to axonal fiber orientation and determined using a combined approach of finite element analysis (FEA) and a genetic algorithm (GA) optimizing method. The average initial shear modulus of brainstem matrix of 4-week old pigs was 12.7 Pa, and therefore the brainstem offers little resistance to large shear deformations in the parallel or perpendicular directions, due to the dominant contribution of the matrix in these directions. The fiber reinforcement stiffness was 121.2 Pa, indicating that brainstem is anisotropic and that axonal fibers have an important role in the cross-sectional direction. The first two leading relative shear relaxation moduli were 0.8973 and 0.0741, respectively, with corresponding characteristic times of 0.0047 and 1.4538 s, respectively, implying rapid relaxation of shear stresses. The developed material model and parameter estimation technique are likely to find broad applications in neural and orthopaedic tissues.     

The mechanics of surface expansion anisotropy in Medicago truncatula root hairs

Wall expansion in tip-growing cells shows variations according to position and direction. In Medicago truncatula root hairs, wall expansion exhibits a strong meridional gradient with a maximum near the pole of the cell. Root hair cells also show a striking expansion anisotropy, i.e. over most of the dome surface the rate of circumferential wall expansion exceeds the rate of meridional expansion. Concomitant measurements of expansion rates and wall stresses reveal that the extensibility of the cell wall must vary abruptly along the meridian of the cell to maintain the gradient of wall expansion. To determine the mechanical basis of expansion anisotropy, we compared measurements of wall expansion with expansion patterns predicted from wall structural models that were either fully isotropic, transversely isotropic, or fully anisotropic. Our results indicate that a model based on a transversely isotropic wall structure can provide a good fit of the data although a fully anisotropic model offers the best fit overall. We discuss how such mechanical properties could be controlled at the microstructural level.     

An approach for the stress analysis of transversely isotropic biphasic cartilage under impact load.

Stress analysis of contact models for isotropic articular cartilage under impacting loads shows high shear stresses at the interface with the subchondral bone and normal compressive stresses near the surface of the cartilage. These stress distributions are not consistent, with lesions observed on the cartilage surface of rabbit patellae from blunt impact, for example, to the patello-femoral joint. The purpose of the present study was to analyze, using the elastic capabilities of a finite element code, the stress distribution in more morphologically realistic transversely isotropic biphasic contact models of cartilage. The elastic properties of an incompressible material, equivalent to those of the transversely isotropic biphasic material at time zero, were derived algebraically using stress-strain relations. Results of the stress analysis showed the highest shear stresses on the surface of the solid skeleton of the cartilage and tensile stresses in the zone of contact. These results can help explain the mechanisms responsible for surface injuries observed during blunt insult experiments.