A finite element analysis methodology for representing the articular cartilage functional structure

Recognising that the unique biomechanical properties of articular cartilage are a consequence of its structure, this paper describes a finite element methodology which explicitly represents this structure using a modified overlay element model. The validity of this novel concept was then tested by using it to predict the axial curling forces generated by cartilage matrices subjected to saline solutions of known molality and concentration in a novel experimental protocol. Our results show that the finite element modelling methodology accurately represents the intrinsic biomechanical state of the cartilage matrix and can be used to predict its transient load-carriage behaviour. We conclude that this ability to represent the intrinsic swollen condition of a given cartilage matrix offers a viable avenue for numerical analysis of degenerate articular cartilage and also those matrices affected by disease.     

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.     

Type III collagen is a key regulator of the collagen fibrillar structure and biomechanics of articular cartilage and meniscus

Despite the fact that type III collagen is the second most abundant collagen type in the body, its contribution to the physiologic maintenance and repair of skeletal tissues remains poorly understood. This study queried the role of type III collagen in the structure and biomechanical functions of two structurally distinctive tissues in the knee joint, type II collagen-rich articular cartilage and type I collagen-dominated meniscus. Integrating outcomes from atomic force microscopy-based nanomechanical tests, collagen fibril nanostructural analysis, collagen cross-link analysis and histology, we elucidated the impact of type III collagen haplodeficiency on the morphology, nanostructure and biomechanical properties of articular cartilage and meniscus in Col3a1^+/− mice. Reduction of type III collagen leads to increased heterogeneity and mean thickness of collagen fibril diameter, as well as reduced modulus in both tissues, and these effects became more pronounced with skeletal maturation. These data suggest a crucial role of type III collagen in mediating fibril assembly and biomechanical functions of both articular cartilage and meniscus during post-natal growth. In articular cartilage, type III collagen has a marked contribution to the micromechanics of the pericellular matrix, indicating a potential role in mediating the early stage of type II collagen fibrillogenesis and chondrocyte mechanotransduction. In both tissues, reduction of type III collagen leads to decrease in tissue modulus despite the increase in collagen cross-linking. This suggests that the disruption of matrix structure due to type III collagen deficiency outweighs the stiffening of collagen fibrils by increased cross-linking, leading to a net negative impact on tissue modulus. Collectively, this study is the first to highlight the crucial structural role of type III collagen in both articular cartilage and meniscus extracellular matrices. We expect these results to expand our understanding of type III collagen across various tissue types, and to uncover critical molecular components of the microniche for regenerative strategies targeting articular cartilage and meniscus repair.     

Application of a semi-automatic cartilage segmentation method for biomechanical modeling of the knee joint

Manual segmentation of articular cartilage from knee joint 3D magnetic resonance images (MRI) is a time consuming and laborious task. Thus, automatic methods are needed for faster and reproducible segmentations. In the present study, we developed a semi-automatic segmentation method based on radial intensity profiles to generate 3D geometries of knee joint cartilage which were then used in computational biomechanical models of the knee joint. Six healthy volunteers were imaged with a 3T MRI device and their knee cartilages were segmented both manually and semi-automatically. The values of cartilage thicknesses and volumes produced by these two methods were compared. Furthermore, the influences of possible geometrical differences on cartilage stresses and strains in the knee were evaluated with finite element modeling. The semi-automatic segmentation and 3D geometry construction of one knee joint (menisci, femoral and tibial cartilages) was approximately two times faster than with manual segmentation. Differences in cartilage thicknesses, volumes, contact pressures, stresses, and strains between segmentation methods in femoral and tibial cartilage were mostly insignificant (p > 0.05) and random, i.e. there were no systematic differences between the methods. In conclusion, the devised semi-automatic segmentation method is a quick and accurate way to determine cartilage geometries; it may become a valuable tool for biomechanical modeling applications with large patient groups.     

Load sharing between solid and fluid phases in articular cartilage: II--Comparison of experimental results and u-p finite element predictions.

Experimental measurements in conjunction with theoretical predictions were used to determine the extent of load supported by the fluid phase of cartilage at the articular surface. The u-p finite element model was used to simulate the loading of six separate porcine knee joints and to predict surface deformations of the cartilage layer on the lateral femoral condyle. Representative geometry for the condyle, contact pressures, and intrinsic material properties of the cartilage layer were supplied from experimental measures (see Part I). The u-p finite element predictions for surface deformations of the cartilage layer were obtained for several load partitioning states between the solid and fluid phases of cartilage at the articular surface. These were then compared to actual surface deformations obtained experimentally. It appeared from the comparison that approximately 75 percent of the applied load was borne by the fluid phase at the articular surface under this loading regime. This was qualitatively in agreement with the hypothesis that an applied load to articular joints is partitioned at the surface to the two phases according to the surface area ratios of the solid and fluid phases. It appeared that the solid phase was shielded from the total applied stress on the articular surface by the fluid and could be a reason for the excellent durability of the tissue under the demanding conditions in a diarthrodial joint.     

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

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

Investigating the relationship between proteomic,compositional, and histologic biomarkers and cartilage biomechanics using artificial neural networks

A thorough understanding of the relationship between the biological and mechanical functions of articular cartilage is necessary to develop diagnostics and treatments for arthritic diseases. A key step in developing this understanding is the establishment of models which utilize large numbers of biomarkers to create comprehensive models of the interplay between cartilage biology and biomechanics, which will more accurately demonstrate the complex etiology and progression of tissue adaptation and degradation. It is the goal of this study to demonstrate the ability of artificial neural networks (ANNs) to utilize biomarkers to create predictive models of articular cartilage biomechanics, which will provide a basis for more sophisticated research in the future. Osteochondral plugs were collected from patients undergoing total knee arthroplasty, cultured, then analyzed to collect proteomic, compositional, and histologic biomarker data. Samples were subjected to stress relaxation testing as well as computational simulations using finite element analysis (FEA) modeling and optimization to determine key mechanical properties. The acquired data was fed into an ANN to generate a model which predicts the biomechanical properties of cartilage from given biomarkers. Using all significant inputs, the developed neural network predicted the ground substance modulus with a moderate degree of accuracy, but had difficulty predicting the collagen fiber modulus and cartilage permeability. Using only clinically attainable biomarkers, the best-performing model produced comparably accurate and more consistent predictions of all three mechanical properties. These models demonstrate the potential for ANNs to be included in clinical studies of articular cartilage.     

A nonlinear biphasic fiber-reinforced porohyperviscoelastic model of articular cartilage incorporating fiber reorientation and dispersion

A nonlinear biphasic fiber-reinforced porohyperviscoelastic (BFPHVE) model of articular cartilage incorporating fiber reorientation effects during applied load was used to predict the response of ovine articular cartilage at relatively high strains (20%). The constitutive material parameters were determined using a coupled finite element-optimization algorithm that utilized stress relaxation indentation tests at relatively high strains. The proposed model incorporates the strain-hardening, tension-compression, permeability, and finite deformation nonlinearities that inherently exist in cartilage, and accounts for effects associated with fiber dispersion and reorientation and intrinsic viscoelasticity at relatively high strains. A new optimization cost function was used to overcome problems associated with large peak-to-peak differences between the predicted finite element and experimental loads that were due to the large strain levels utilized in the experiments. The optimized material parameters were found to be insensitive to the initial guesses. Using experimental data from the literature, the model was also able to predict both the lateral displacement and reaction force in unconfined compression, and the reaction force in an indentation test with a single set of material parameters. Finally, it was demonstrated that neglecting the effects of fiber reorientation and dispersion resulted in poorer agreement with experiments than when they were considered. There was an indication that the proposed BFPHVE model, which includes the intrinsic viscoelasticity of the nonfibrillar matrix (proteoglycan), might be used to model the behavior of cartilage up to relatively high strains (20%). The maximum percentage error between the indentation force predicted by the FE model using the optimized material parameters and that measured experimentally was 3%.     

Osteoarthritic changes in the biphasic mechanical properties of the chondrocyte pericellular matrix in articular cartilage

The pericellular matrix (PCM) is a narrow region of cartilaginous tissue that surrounds chondrocytes in articular cartilage. Previous modeling studies indicate that the mechanical properties of the PCM relative to those of the extracellular matrix (ECM) can significantly affect the stress-strain, fluid flow, and physicochemical environments of the chondrocyte, suggesting that the PCM plays a biomechanical role in articular cartilage. The goals of this study were to measure the mechanical properties of the PCM using micropipette aspiration coupled with a linear biphasic finite element model, and to determine the alterations in the mechanical properties of the PCM with osteoarthritis (OA). Using a recently developed isolation technique, chondrons (the chondrocyte and its PCM) were mechanically extracted from non-degenerate and osteoarthritic human cartilage. The transient mechanical behavior of the PCM was well-described by a biphasic model, suggesting that the viscoelastic response of the PCM is attributable to flow-dependent effects, similar to that of the ECM. With OA, the mean Young's modulus of the PCM was significantly decreased (38.7+/-16.2 kPa vs. 23.5+/-12.9 kPa, p < 0.001), and the permeability was significantly elevated (4.19+/-3.78 x10(-17) m(4)/Ns vs. 10.2+/-9.38 x 10(-17) m(4)/Ns, p < 0.01). The Poisson's ratio was similar for both non-degenerate and OA PCM (0.044+/-0.063 vs. 0.030+/-0.068, p > 0.6). These findings suggest that the PCM may undergo degenerative processes with OA, similar to those occurring in the ECM. In combination with previous theoretical models of cell-matrix interactions in cartilage, our findings suggest that changes in the properties of the PCM with OA may have an important influence on the biomechanical environment of the chondrocyte.     

Hip chondrolabral mechanics during activities of daily living: Role of the labrum and interstitial fluid pressurization

Osteoarthritis of the hip can result from mechanical factors, which can be studied using finite element (FE) analysis. FE studies of the hip often assume there is no significant loss of fluid pressurization in the articular cartilage during simulated activities and approximate the material as incompressible and elastic. This study examined the conditions under which interstitial fluid load support remains sustained during physiological motions, as well as the role of the labrum in maintaining fluid load support and the effect of its presence on the solid phase of the surrounding cartilage. We found that dynamic motions of gait and squatting maintained consistent fluid load support between cycles, while static single-leg stance experienced slight fluid depressurization with significant reduction of solid phase stress and strain. Presence of the labrum did not significantly influence fluid load support within the articular cartilage, but prevented deformation at the cartilage edge, leading to lower stress and strain conditions in the cartilage. A morphologically accurate representation of collagen fibril orientation through the thickness of the articular cartilage was not necessary to predict fluid load support. However, comparison with simplified fibril reinforcement underscored the physiological importance. The results of this study demonstrate that an elastic incompressible material approximation is reasonable for modeling a limited number of cyclic motions of gait and squatting without significant loss of accuracy, but is not appropriate for static motions or numerous repeated motions. Additionally, effects seen from removal of the labrum motivate evaluation of labral reattachment strategies in the context of labral repair.     

A Finite Element Formulation and Program to Study Transient Swelling and Load-carriage in Healthy and Degenerate Articular Cartilage

The theory of poroelasticity is extended to include physico-chemical swelling and used to predict the transient responses of normal and degenerate articular cartilage to both chemical and mechanical loading; with emphasis on isolating the influence of the major parameters which govern its deformation. Using a new hybrid element, our mathematical relationships were implemented in a purpose-built poroelastic finite element analysis algorithm (u–π–c fortran program) which was used to resolve the nature of the coupling between the mechanical and chemical responses of cartilage when subjected to ionic transport across its membranous skeleton. Our results demonstrate that one of the roles of the strain-dependent matrix permeability is to limit the rate of transmission of stresses from the fluid to the collagen-proteoglycan solid skeleton in the incipient stages of loading, and that the major contribution of the swelling pressure is that of preventing any excessive deformation of the matrix.     

Transport phenomena in articular cartilage cryopreservation as predicted by the modified triphasic model and the effect of natural inhomogeneities

Knowledge of the spatial and temporal distribution of cryoprotective agent (CPA) is necessary for the cryopreservation of articular cartilage. Cartilage dehydration and shrinkage, as well as the change in extracellular osmolality, may have a significant impact on chondrocyte survival during and after CPA loading, freezing, and thawing, and during CPA unloading. In the literature, Fick's law of diffusion is commonly used to predict the spatial distribution and overall concentration of the CPA in the cartilage matrix, and the shrinkage and stress-strain in the cartilage matrix during CPA loading are neglected. In this study, we used a previously described biomechanical model to predict the spatial and temporal distributions of CPA during loading. We measured the intrinsic inhomogeneities in initial water and fixed charge densities in the cartilage using magnetic resonance imaging and introduced them into the model as initial conditions. We then compared the prediction results with the results obtained using uniform initial conditions. The simulation results in this study demonstrate the presence of a significant mechanical strain in the matrix of the cartilage, within all layers, during CPA loading. The osmotic response of the chondrocytes to the cartilage dehydration during CPA loading was also simulated. The results reveal that a transient shrinking occurs to different levels, and the chondrocytes experience a significant decrease in volume, particularly in the middle and deep zones of articular cartilage, during CPA loading.     

Effect of the anisotropic permeability in the frequency dependent properties of the superficial layer of articular cartilage

Abstract

Articular cartilage is a tissue of fundamental importance for the mechanics of joints, since it provides a smooth and lubricated surface for the proper transfer of loads. From a mechanical point of view, this tissue is an anisotropic poroviscoelastic material: its characteristics at the macroscopic level depend on the complex microscopic architecture. With the ability to probe the local microscopic features, dynamic nanoindentation test is a powerful tool to investigate cartilage mechanics. In this work we focus on a length scale where the time dependent behaviour is regulated by poroelasticity more than viscoelasticity and we aim to understand the effect of the anisotropic permeability on the mechanics of the superficial layer of the articular cartilage. In a previous work, a finite element model for the dynamic nanoindentation test has been presented. In this work, we improve the model by considering the presence of an anisotropic permeability tensor that depends on the collagen fibers distribution. Our sensitivity analysis highlights that the permeability decreases with increasing indentation, thus making the tissue stiffer than the case of isotropic permeability, when solicited at the same frequency. With this improved model, a revised identification of the mechanical and physical parameters for articular cartilage is provided. To this purpose the model was used to simulate experimental data from tests performed on bovine tissue, giving a better estimation of the anisotropy in the elastic properties. A relation between the identified macroscopic anisotropic permeability properties and the microscopic rearrangement of the fiber/matrix structure during indentation is also provided.     

A biphasic multiscale study of the mechanical microenvironment of chondrocytes within articular cartilage under unconfined compression

Computational analyses have been used to study the biomechanical microenvironment of the chondrocyte that cannot be assessed by in vitro experimental studies; yet all computational studies thus far have focused on the effect of zonal location (superficial, middle, and deep) on the mechanical microenvironment of chondrocytes. The aim of this paper was to study the effect of both zonal and radial locations on the biomechanical microenvironment of chondrocytes in inhomogeneous cartilage under unconfined stress relaxation. A biphasic multiscale approach was employed and nine chondrocytes in different locations were studied. Hyperelastic biphasic theory and depth-dependent aggregate modulus and permeability of articular cartilage were included in the models. It was found that both zonal and radial locations affected the biomechanical stresses and strains of the chondrocytes. Chondrocytes in the mid-radial location had increased volume during the early stage of the loading process. Maximum principal shear stress at the interface between the chondrocyte and the extracellular matrix (ECM) increased with depth, yet that at the ECM–pericellular matrix (PCM) interface had an inverse trend. Fluid pressure decreased with depth, while the fluid pressure difference between the top and bottom boundaries of the microscale model increased with depth. Regardless of location, fluid was exchanged between the chondrocyte, PCM, and ECM. These findings suggested that even under simple compressive loading conditions, the biomechanical microenvironment of the chondrocytes, PCM and ECM was spatially dependent. The current study provides new insight on chondrocyte biomechanics.     

Quantitative ultrasonic assessment for detecting microscopic cartilage damage in osteoarthritis

Osteoarthritis (OA) is one of the most prevalent chronic conditions. The histological cartilage changes in OA include surface erosion and irregularities, deep fissures, and alterations in the staining of the matrix. The reversibility of these chondral alterations is still under debate. It is expected that clinical and basic science studies will provide the clinician with new scientific information about the natural history and optimal treatment of OA at an early stage. However, a reliable method for detecting microscopic changes in early OA has not yet been established. We have developed a novel system for evaluating articular cartilage, in which the acoustic properties of the articular cartilage are measured by introducing an ultrasonic probe into the knee joint under arthroscopy. The purpose of this study was to assess microscopic cartilage damage in OA by using this cartilage evaluation system on collagenase-treated articular cartilage in vivo and in vitro. Ultrasonic echoes from articular cartilage were converted into a wavelet map by wavelet transformation. On the wavelet map, the maximum magnitude and echo duration were selected as quantitative indices. Using these indices, the articular cartilage was examined to elucidate the relationships of the ultrasonic analysis with biochemical, biomechanical and histological analyses. In the in vitro study, the maximum magnitude decreased as the duration of collagenase digestion increased. Correlations were observed between the maximum magnitude and the proteoglycan content from biochemical findings, and the maximum magnitude and the aggregate modulus from biomechanical findings. From the histological findings, matrix staining of the surface layer to a depth of 500 μm was closely related to the maximum magnitude. In the in vivo study, the maximum magnitude decreased with increasing duration of the collagenase injection. There was a significant correlation between the maximum magnitude and the aggregate modulus. The evaluation system therefore successfully detected microscopic changes in degenerated cartilage with the use of collagen-induced OA.     

Articular cartilage tensile integrity: modulation by matrix depletion is maturation-dependent

Articular cartilage function depends on the molecular composition and structure of its extracellular matrix (ECM). The collagen network (CN) provides cartilage with tensile integrity, but must also remodel during growth. Such remodeling may depend on matrix molecules interacting with the CN to modulate the tensile behavior of cartilage. The objective of this study was to determine the effects of increasingly selective matrix depletion on tensile properties of immature and mature articular cartilage, and thereby establish a framework for identifying molecules involved in CN remodeling. Depletion of immature cartilage with guanidine, chondroitinase ABC, chondroitinase AC, and Streptomyces hyaluronidase markedly increased tensile integrity, while the integrity of mature cartilage remained unaltered after depletion with guanidine. The enhanced tensile integrity after matrix depletion suggests that certain ECM components of immature matrix serve to inhibit CN interactions and may act as modulators of physiological alterations of cartilage geometry and tensile properties during growth/maturation.     

Dielectric characterization of costal cartilage chondrocytes

Background

Chondrocytes respond to biomechanical and bioelectrochemical stimuli by secreting appropriate extracellular matrix proteins that enable the tissue to withstand the large forces it experiences. Although biomechanical aspects of cartilage are well described, little is known of the bioelectrochemical responses. The focus of this study is to identify bioelectrical characteristics of human costal cartilage cells using dielectric spectroscopy.

Methods

Dielectric spectroscopy allows non-invasive probing of biological cells. An in house computer program is developed to extract dielectric properties of human costal cartilage cells from raw cell suspension impedance data measured by a microfluidic device. The dielectric properties of chondrocytes are compared with other cell types in order to comparatively assess the electrical nature of chondrocytes.

Results

The results suggest that electrical cell membrane characteristics of chondrocyte cells are close to cardiomyoblast cells, cells known to possess an array of active ion channels. The blocking effect of the non-specific ion channel blocker gadolinium is tested on chondrocytes with a significant reduction in both membrane capacitance and conductance.

Conclusions

We have utilized a microfluidic chamber to mimic biomechanical events through changes in bioelectrochemistry and described the dielectric properties of chondrocytes to be closer to cells derived from electrically excitably tissues.

General significance

The study describes dielectric characterization of human costal chondrocyte cells using physical tools, where results and methodology can be used to identify potential anomalies in bioelectrochemical responses that may lead to cartilage disorders.     

A finite element formulation and program to study transient swelling and load-carriage in healthy and degenerate articular cartilage

The theory of poroelasticity is extended to include physico-chemical swelling and used to predict the transient responses of normal and degenerate articular cartilage to both chemical and mechanical loading; with emphasis on isolating the influence of the major parameters which govern its deformation. Using a new hybrid element, our mathematical relationships were implemented in a purpose-built poroelastic finite element analysis algorithm (u-pi-c program) which was used to resolve the nature of the coupling between the mechanical and chemical responses of cartilage when subjected to ionic transport across its membranous skeleton. Our results demonstrate that one of the roles of the strain-dependent matrix permeability is to limit the rate of transmission of stresses from the fluid to the collagen-proteoglycan solid skeleton in the incipient stages of loading, and that the major contribution of the swelling pressure is that of preventing any excessive deformation of the matrix.