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

Electrostatic and non-electrostatic contributions of proteoglycans to the compressive equilibrium modulus of bovine articular cartilage

This study presents direct experimental evidence for assessing the electrostatic and non-electrostatic contributions of proteoglycans to the compressive equilibrium modulus of bovine articular cartilage. Immature and mature bovine cartilage samples were tested in unconfined compression and their depth-dependent equilibrium compressive modulus was determined using strain measurements with digital image correlation analysis. The electrostatic contribution was assessed by testing samples in isotonic and hypertonic saline; the combined contribution was assessed by testing untreated and proteoglycan-depleted samples. Though it is well recognized that proteoglycans contribute significantly to the compressive stiffness of cartilage, results demonstrate that the combined electrostatic and non-electrostatic contributions may add up to more than 98% of the modulus, a magnitude not previously appreciated. Of this contribution, about two thirds arises from electrostatic effects. The compressive modulus of the proteoglycan-depleted cartilage matrix may be as low as 3kPa, representing less than 2% of the normal tissue modulus; experimental evidence also confirms that the collagen matrix in digested cartilage may buckle under compressive strains, resulting in crimping patterns. Thus, it is reasonable to model the collagen as a fibrillar matrix that can sustain only tension. This study also demonstrates that residual stresses in cartilage do not arise exclusively from proteoglycans, since cartilage remains curled relative to its in situ geometry even after proteoglycan depletion. These increased insights on the structure-function relationships of cartilage can lead to improved constitutive models and a better understanding of the response of cartilage to physiological loading conditions.

Zonal chondrocytes seeded in a layered agarose hydrogel create engineered cartilage with depth-dependent cellular and mechanical inhomogeneity

We hypothesized that zonal populations of chondrocytes seeded into a bilayered scaffold with initially prescribed depth-varying, compressive material properties will lead to a biomimetic cartilage tissue construct with depth-dependent cellular and compressive mechanical inhomogeneity similar to that of the native tissue. Superficial zone chondrocytes (SZCs) and middle/deep zone chondrocytes (MDZCs) were isolated and encapsulated with 2% or 3% agarose to form single-layered constructs of 2% SZC, 3% SZC, 2% MDZC; bilayered constructs of 2% SZC/2% MDZC and 3% SZC/2% MDZC; and 2% mixed chondrocyte controls. For SZCs on day 42, increased glycosaminoglycan (GAG) and collagen was found with increased agarose concentration and when layered with MDZCs. Superficial zone protein increased with agarose concentration in bilayered constructs. For MDZCs, increased GAG content and regulation of cell proliferation was observed when layered with SZCs. Bilayered constructs possessed a depth-dependent compressive modulus qualitatively similar to that of native articular cartilage, whereas controls showed a U-shaped profile with stiffer peripheral edges and softer middle region. This study is the first to create an engineered cartilage tissue with depth-varying cellular as well as mechanical inhomogeneity. Future studies will determine if replicating inhomogeneity is advantageous in clinical applications of tissue engineered cartilage.

The Effect of Flash Freezing on Variability in Spinal Cord Compression Behavior

The compression behavior of spinal cord tissue is important for understanding spinal cord injury mechanics but has not yet been established. Characterizing compression behavior assumes precise specimen geometry; however, preparing test specimens of spinal cord tissue is complicated by the extreme compliance of the tissue. The objectives of this study were to determine the effect of flash freezing on both specimen preparation and mechanical response and to quantify the effect of small deviations in specimen geometry on mechanical behavior. Specimens of porcine spinal cord white matter were harvested immediately following sacrifice. The tissue was divided into two groups: partially frozen specimens were flash frozen (60 s at −80°C) prior to cutting, while fresh specimens were kept at room temperature. Specimens were tested in unconfined compression at strain rates of 0.05 s−1 and 5.0 s−1 to 40% strain. Parametric finite element analyses were used to investigate the effect of specimen face angle, cross section, and interface friction on the mechanical response. Flash freezing did not affect the mean mechanical behavior of the tissue but did reduce the variability in the response across specimens (p<0.05). Freezing also reduced variability in the specimen geometry. Variations in specimen face angle (0–10 deg) resulted in a 34% coefficient of variation and a 60% underestimation of peak stress. The effect of geometry on variation and error was greater than that of interface friction. Taken together, these findings demonstrate the advantages of flash freezing in biomechanical studies of spine cord tissue.

Anisotropic mechanical properties of magnetically aligned fibrin gels measured by magnetic resonance elastography

The anisotropic mechanical properties of magnetically aligned fibrin gels were measured by magnetic resonance elastography (MRE) and by a standard mechanical test: unconfined compression. Soft anisotropic biomaterials are notoriously difficult to characterize, especially in vivo. MRE is well-suited for efficient, non-invasive, and non-destructive assessment of shear modulus. Direction-dependent differences in shear modulus were found to be statistically significant for gels polymerized at magnetic fields of 11.7 and 4.7 T compared to control gels. Mechanical anisotropy was greater in the gels polymerized at the higher magnetic field. These observations were consistent with results from unconfined compression tests. Analysis of confocal microscopy images of gels showed measurable alignment of fibrils in gels polymerized at 11.7 T. This study provides direct, quantitative measurements of the anisotropy in mechanical properties that accompanies fibril alignment in fibrin gels.

Unconfined compression properties of a porous poly(vinyl alcohol)-chitosan-based hydrogel after hydration

A poly(vinyl alcohol) (PVA) hydrogel composite scaffold containing N,O-carboxymethylated chitosan (NOCC) was tested to assess its potential as a scaffold for cartilage tissue engineering in a weight-bearing environment. The mechanical properties under unconfined compression for different hydration periods were investigated. The effect of supplementing PVA with NOCC (20wt.% PVA:5vol.% NOCC) produced a porosity of 43.3% and this was compared against a non-porous PVA hydrogel (20g PVA: 100ml of water, control). Under non-hydrated conditions, the porous PVA-NOCC hydrogel behaved in a similar way to the control non-porous PVA hydrogel, with similar non-linear stress-strain response under unconfined compression (0-30% strain). After 7days' hydration, the porous hydrogel demonstrated a reduced stiffness (0.002kPa, at 25% strain), resulting in a more linear stiffness relationship over a range of 0-30% strain. Poisson's ratio for the hydrated non-porous and porous hydrogels ranged between 0.73 and 1.18, and 0.76 and 1.33, respectively, suggesting a greater fluid flow when loaded. The stress relaxation function for the porous hydrogel was affected by the hydration period (from 0 to 600s); however the percentage stress relaxation regained by about 95%, after 1200s for all hydration periods assessed. No significant differences were found between the different hydration periods between the porous hydrogels and control. The calculated aggregate modulus, H(A), for the porous hydrogel reduced drastically from 10.99kPa in its non-hydrated state to about 0.001kPa after 7days' hydration, with the calculated shear modulus reducing from 30.92 to 0.14kPa, respectively. The porous PVA-NOCC hydrogel conformed to a biphasic, viscoelastic model, which has the desired properties required for any scaffold in cartilage tissue engineering.

Influence of decreasing nutrient path length on the development of engineered cartilage

OBJECTIVE

Chondrocyte-seeded agarose constructs of 4mm diameter (2.34 mm thickness) develop spatially inhomogeneous material properties with stiffer outer edges and a softer central core suggesting nutrient diffusion limitations to the central construct region [Guilak F, Sah RL, Setton LA. Physical regulation of cartilage metabolism. In: Mow VC, Hayes WC, Eds. Basic Orthopaedic Biomechanics, Philadelphia 1997;179-207.]. The effects of reducing construct thickness and creating channels running through the depth of the thick constructs were examined.

METHODS

In Study 1, the properties of engineered cartilage of 0.78 mm (thin) or 2.34 mm (thick) thickness were compared. In Study 2, a single nutrient channel (1 mm diameter) was created in the middle of each thick construct. In Study 3, the effects of channels on larger 10 mm diameter, thick constructs were examined.

RESULTS

Thin constructs developed superior mechanical and biochemical properties than thick constructs. The channeled constructs developed significantly higher mechanical properties vs control channel-free constructs while exhibiting similar glycosaminoglycan (GAG) and collagen content. Collagen staining suggested that channels resulted in a more uniform fibrillar network. Improvements in constructs of 10 mm diameter were similarly observed.

CONCLUSIONS

This study demonstrated that more homogeneous tissue-engineered cartilage constructs with improved mechanical properties can be achieved by reducing their thickness or incorporating macroscopic nutrient channels. Our data further suggests that these macroscopic channels remain open long enough to promote this enhanced tissue development while exhibiting the potential to refill with cell elaborated matrix with additional culture time. Together with reports that <3 mm defects in cartilage heal in vivo and that irregular holes are associated with clinically used osteochondral graft procedures, we anticipate that a strategy of incorporating macroscopic channels may aid the development of clinically relevant engineered cartilage with functional properties.

Asymmetrical strain distributions and neutral axis location of cartilage in flexure

Flexural deformation has been used for the biomechanical characterization of native and engineered cartilage and as a mechanical stimulus to induce alteration of cartilage shape during in vitro culture. Flexure is also a physiologically relevant mode of deformation for various cartilaginous structures such as the ears and nose, but a kinematic description of cartilage in flexure is lacking even for simple deformations. The hypothesis of this study was that tension-compression (T-C) nonlinearity of cartilage will result in asymmetrical strain distributions during bending, while a material with similar behavior in tension and compression, such as alginate, will have a more symmetrical distribution of strains. Strips of calf articular cartilage and alginate were tested under uniform circular bending, and strains were determined by a micromechanical analysis of images acquired by epifluorescence microscopy. This experimental analysis was interpreted in the context of a model of small-deflection, pure bending of thin, homogeneous beams of a bimodular elastic material. The results supported the hypothesis and showed that marked asymmetry existed in cartilage flexural strains where the location of the neutral axis was significantly different than the midline and closer to the tensile surface. In contrast, alginate samples had a centrally located neutral axis. These experimental results were supported by the model indicating that the bimodular simplification of cartilage properties is a useful first approximation of T-C nonlinearity in these tests. The neutral axis location in cartilage samples was not influenced by the testing orientation (towards or away from the superficial-most tissue) or magnitude of flexure. These findings characterize the kinematics of cartilage at equilibrium during simple bending and indicate that T-C nonlinearity is an important determinant of the flexural strain distributions in the tested tissue.

Two-dimensional strain fields on the cross-section of the bovine humeral head under contact loading

The objective of this study was to provide a detailed experimental assessment of the two-dimensional cartilage strain distribution on the cross-section of immature and mature bovine humeral heads subjected to contact loading at a relatively rapid physiological loading rate. Six immature and six mature humeral head specimens were loaded against glass and strains were measured at the end of a 5s loading ramp on the textured articular cross-section using digital image correlation analysis. The primary findings indicate that elevated tensile and compressive strains occur near the articular surface, around the center of the contact region. Few qualitative or quantitative differences were observed between mature and immature joints. Under an average contact stress of approximately 1.7 MPa, the peak compressive strains averaged -0.131+/-0.048, which was significantly less than the relative change in cartilage thickness, -0.104+/-0.032 (p<0.05). The peak tensile strains were significantly smaller in magnitude, at 0.0325+/-0.013. These experimental findings differ from a previous finite element analysis of articular contact, which predicted peak strains at the cartilage-bone interface even when accounting for the porous-hydrated nature of the tissue, its depth-dependent inhomogeneity, and the disparity between its tensile and compressive properties. These experimental results yield new insights into the local mechanical environment of the tissue and cells, and suggest that further refinements are needed in the modeling of contacting articular layers.

Interaction between the interstitial fluid and the extracellular matrix in confined indentation

The Movement of the interstitial fluid in extracellular matrices not only affects the mechanical properties of soft tissues, but also facilitates the transport of nutrients and the removal of waste products. In this study, we aim to quantify interstitial fluid movement and fluid-matrix interaction in a new loading configuration-confined tissue indentation, using a poroelastic theory. The tissue sample sits in a cylindrical chamber and loading is applied on the top central surface of the specimen by a porous indenter that is fixed on the specimen. The interaction between the solid and the fluid is examined using a finite element method under ramp and cyclic loads. Typical compression-relaxation responses of the specimen are observed in a ramp load. Under a cyclic load, the system reaches a dynamic equilibrium after a number of loading cycles. Fluid circulation, with opposite directions in the loading and unloading phases in the extracellular matrix, is observed. The most significant variation in the fluid pressure locates just beneath the indenter. Fluid pressurization arrives at equilibrium much faster than the solid matrix deformation. As the loading frequency increases, the location of the peak pressure oscillation moves closer to the indenter and the magnitude of the pressure oscillation increases. Concomitantly, the axial stress variation of the solid matrix is reduced. It is found that interstitial fluid movement helps to alleviate severe strain of the solid matrix beneath the indenter. This study quantifies the interaction between the interstitial fluid and the extracellular matrix by decomposing the loading response of the specimen into the "transient" and "dynamic equilibrium" phases. Confined indentation in this manuscript gives a better representation of some in vitro and in vivo loading configurations where the indenter covers part of the top surface of the tissue.

Mechanical and biochemical characterization of cartilage explants in serum-free culture

Allografts of articular cartilage are both used clinically for tissue-transplantation procedures and experimentally as model systems to study the physiological behavior of chondrocytes in their native extracellular matrix. Long-term maintenance of allograft tissue is challenging. Chemical mediators in poorly defined culture media can stimulate cells to quickly degrade their surrounding extracellular matrix. This is particularly true of juvenile cartilage which is generally more responsive to chemical stimuli than mature tissue. By carefully modulating the culture media, however, it may be possible to preserve allograft tissue over the long-term while maintaining its original mechanical and biochemical properties. In this study juvenile bovine cartilage explants (both chondral and osteochondral) were cultured in both chemically defined medium and serum-supplemented medium for up to 6 weeks. The mechanical properties and biochemical content of explants cultured in chemically defined medium were enhanced after 2 weeks in culture and thereafter remained stable with no loss of cell viability. In contrast, the mechanical properties of explants in serum-supplemented medium were degraded by ( approximately 70%) along with a concurrent loss of biochemical content (30-40% GAG). These results suggest that long-term maintenance of allografts can be extended significantly by the use of a chemically defined medium.

Biomechanical analysis of structural deformation in living cells

Most tissues are subject to some form of physiological mechanical loading which results in deformation of the cells triggering intracellular mechanotransduction pathways. This response to loading is generally essential for the health of the tissue, although more pronounced deformation may result in cell and tissue damage. In order to determine the biological response of cells to loading it is necessary to understand how cells and intracellular structures deform. This paper reviews the various loading systems that have been adopted for studying cell deformation both in situ within tissue explants and in isolated cell culture systems. In particular it describes loading systems which facilitate visualisation and subsequent quantification of cell deformation. The review also describes the associated microscopy and image analysis techniques. The review focuses on deformation of chondrocytes with additional information on a variety of other cell types including neurons, red blood cells, epithelial cells and skin and muscle cells.

A cartilage growth mixture model with collagen remodeling: validation protocols

A cartilage growth mixture (CGM) model is proposed to address limitations of a model used in a previous study. New stress constitutive equations for the solid matrix are derived and collagen (COL) remodeling is incorporated into the CGM model by allowing the intrinsic COL material constants to evolve during growth. An analytical validation protocol based on experimental data from a recent in vitro growth study is developed. Available data included measurements of tissue volume, biochemical composition, and tensile modulus for bovine calf articular cartilage (AC) explants harvested at three depths and incubated for 13 days in 20% fetal borine serum (FBS) and 20% FBS+beta-aminopropionitrile. The proposed CGM model can match tissue biochemical content and volume exactly while predicting theoretical values of tensile moduli that do not significantly differ from experimental values. Also, theoretical values of a scalar COL remodeling factor are positively correlated with COL cross-link content, and mass growth functions are positively correlated with cell density. The results suggest that the CGM model may help us to guide in vitro growth protocols for AC tissue via the a priori prediction of geometric and biomechanical properties.

Characterization of the structure-function relationship at the ligament-to-bone interface

Soft tissues such as ligaments and tendons integrate with bone through a fibrocartilaginous interface divided into noncalcified and calcified regions. This junction between distinct tissue types is frequently injured and not reestablished after surgical repair. Its regeneration is also limited by a lack of understanding of the structure-function relationship inherent at this complex interface. Therefore, focusing on the insertion site between the anterior cruciate ligament (ACL) and bone, the objectives of this study are: (i) to determine interface compressive mechanical properties, (ii) to characterize interface mineral presence and distribution, and (iii) to evaluate insertion site-dependent changes in mechanical properties and matrix mineral content. Interface mechanical properties were determined by coupling microcompression with optimized digital image correlation analysis, whereas mineral presence and distribution were characterized by energy dispersive x-ray analysis and backscattered scanning electron microscopy. Both region- and insertion-dependent changes in mechanical properties were found, with the calcified interface region exhibiting significantly greater compressive mechanical properties than the noncalcified region. Mineral presence was only detectable within the calcified interface and bone regions, and its distribution corresponds to region-dependent mechanical inhomogeneity. Additionally, the compressive mechanical properties of the tibial insertion were greater than those of the femoral. The interface structure-function relationship elucidated in this study provides critical insight for interface regeneration and the formation of complex tissue systems.

Strain field measurements on mouse carotid arteries using microscopic three-dimensional digital image correlation

A stereomicroscope system is adapted to make accurate, quantitative displacement, and strain field measurements with microscale spatial resolution and nanoscale displacement resolution on mouse carotid arteries. To perform accurate and reliable calibration for these systems, a two-step calibration process is proposed and demonstrated using a modification to recently published procedures. Experimental results demonstrate that the microscope system with three-dimensional digital image correlation (3D-DIC) successfully measures the full 3D displacement and surface strain fields at the microscale during pressure cycling of 0.40-mm-diameter mouse arteries, confirming that the technique can be used to quantify changes in local biomechanical response which may result from variations in extracellular matrix composition, with the goal of quantifying properties of the vessel.

On how degeneration influences load-bearing in the cartilage-bone system: a microstructural and micromechanical study

OBJECTIVE

This study investigated the microanatomical response to compression of intact and degenerate cartilage-on-bone samples with the aim of elucidating the functional consequences of articular surface disruption and related matrix changes.

METHOD

Two groups of mature bovine patellae were identified at the time of harvest; those with intact cartilage and those with cartilage exhibiting mild to severe degeneration. Cartilage-on-bone samples were statically compressed (7 MPa) to near-equilibrium using an 8-mm diameter cylindrical indenter, and then formalin-fixed in this deformed state. Following mild decalcification full-depth cartilage-bone sections, incorporating the indentation profile and beyond, were studied in their fully hydrated state using differential interference contrast optical microscopy (DIC).

RESULTS

Differences in matrix texture, degree of disruption of the articular surface layer (or its complete absence), number of tidemarks and absence or presence of vascularization of the calcified cartilage zone were all observable features that provided clear differentiation between the normal and degenerate tissues. Under load a chevron-type shear discontinuity characterized those samples in which the strain-limiting surface layer was still largely intact. The extent to which this shear discontinuity advanced into the adjacent non-directly loaded cartilage continuum was influenced by the integrity of the cartilage general matrix. For those tissues deficient in a strain-limiting articular surface there was no shear discontinuity, the cartilage deformation field was instead shaped primarily by its osteochondral attachment and a laterally-directed compressive collapse of a much weakened matrix. In the degenerate samples the altered matrix textures associated with different regions of the deformation field are interpreted in terms of an intrinsic fibrillar architecture that is weakened by two fundamental processes: (1) a de-structuring resulting from a reduction in connectivity between fibrils and (2) subsequent aggregation of these now disconnected fibrils.

CONCLUSION

DIC microscopy provides a high-resolution description of the integrated osteochondral tissue system across the full continuum of matrices, from normal to severely degenerate. Our study demonstrates the important functional role played by the strain-limiting articular surface, the consequences associated with its disruption, as well as the loss of effective stress transmission associated with a 'de-structured' general matrix. The study also provides new insights into the integration of cartilage with both its subchondral substrate and the wider continuum of non-directly loaded cartilage.

Ultrastructural properties in cortical bone vary greatly in two inbred strains of mice as assessed by synchrotron light based micro- and nano-CT

Nondestructive SR-based microCT and nano-CT methods have been designed for 3D quantification and morphometric analysis of ultrastructural phenotypes within murine cortical bone, namely the canal network and the osteocyte lacunar system. Results in two different mouse strains, C57BL/6J-Ghrhr(lit)/J and C3.B6-Ghrhr(lit)/J, showed that the cannular and lacunar morphometry and their bone mechanics were fundamentally different.

INTRODUCTION

To describe the different aspects of bone quality, we followed a hierarchical approach and assessed bone tissue properties in different regimens of spatial resolution, beginning at the organ level and going down to cellular dimensions. For these purposes, we developed different synchrotron radiation (SR)-based CT methods to assess ultrastructural phenotypes of murine bone.

MATERIALS AND METHODS

The femoral mid-diaphyses of 12 C57BL/6J-Ghrhr(lit)/J (B6-lit/lit) and 12 homozygous mutants C3.B6-Ghrhr(lit)/J (C3.B6-lit/lit) were measured with global SR microCT and local SR nano-CT (nCT) at nominal resolutions ranging from 3.5 microm to 700 nm, respectively. For volumetric quantification, morphometric indices were determined for the cortical bone, the canal network, and the osteocyte lacunar system using negative imaging. Moreover, the biomechanics of B6-lit/lit and C3.B6-lit/lit mice was determined by three-point bending.

RESULTS

The femoral mid-diaphysis of C3.B6-lit/lit was larger compared with B6-lit/lit mice. On an ultrastructural level, the cannular indices for C3.B6-lit/lit were generally bigger in comparison with B6-lit/lit mice. Accordingly, we derived and showed a scaling rule, saying that overall cannular indices scaled with bone size, whereas indices describing basic elements of cannular and lacunar morphometry did not. Although in C3.B6-lit/lit, the mean canal volume was larger than in B6-lit/lit, canal number density was proportionally smaller in C3.B6-lit/lit, so that lacuna volume density was found to be constant and therefore independent of mouse strain and sex. The mechanical properties in C3.B6-lit/lit were generally improved compared with B6-lit/lit specimens. For C3.B6-lit/lit, we observed a sex specificity of the mechanical parameters, which could not be explained by bone morphometry on an organ level. However, there is evidence that for C3.B6-lit/lit, the larger cortical bone mass is counterbalanced or even outweighed by the larger canal network in the female mice.

CONCLUSIONS

We established a strategy to subdivide murine intracortical porosity into ultrastructural phenotypes, namely the canal network and the osteocyte lacunar system. Nondestructive global and local SR-based CT methods have been designed for 3D quantification and subsequent morphometric analysis of these phenotypes. Results in the two different mouse strains C57BL/6J-Ghrhr(lit)/J and C3.B6-Ghrhr(lit)/J showed that the cannular and lacunar morphometry and the biomechanical properties were fundamentally different.

Transport of neutral solute in articular cartilage: effect of microstructure anisotropy

Due to the avascular nature of articular cartilage, solute transport through its extracellular matrix is critical for the maintenance and the functioning of the tissue. What is more, diffusion of macromolecules may be affected by the microstructure of the extracellular matrix in both undeformed and deformed cartilage and experiments demonstrate diffusion anisotropy in the case of large solute. However, these phenomena have not received sufficient theoretical attention to date. We hypothesize here that the diffusion anisotropy of macromolecules is brought about by the particular microstructure of the cartilage network. Based on this hypothesis, we then propose a mathematical model that correlates the diffusion coefficient tensor with the structural orientation tensor of the network. This model is shown to be successful in describing anisotropic diffusion of macromolecules in undeformed tissue and is capable of clarifying the effects of network reorientation as the tissue deforms under mechanical load. Additionally, our model explains the anomaly that at large strain, in a cylindrical plug under unconfined compression, solute diffusion in the radial direction increases with strain. Our results indicate that in cartilage the degree of diffusion anisotropy is site specific, but depends also on the size of the diffusing molecule. Mechanical loading initiates and/or further exacerbates this anisotropy. At small deformation, solute diffusion is near isotropic in a tissue that is isotropic in its unstressed state, becoming anisotropic as loading progresses. Mechanical loading leads to an attenuation of solute diffusion in all directions when deformation is small. However, loading, if it is high enough, enhances solute transport in the direction perpendicular to the load line, instead of inhibiting it.

A nonlinear finite element model of cartilage growth

The long range objective of this work is to develop a cartilage growth finite element model (CGFEM), based on the theories of growing mixtures that has the capability to depict the evolution of the anisotropic and inhomogeneous mechanical properties, residual stresses, and nonhomogeneities that are attained by native adult cartilage. The CGFEM developed here simulates isotropic in vitro growth of cartilage with and without mechanical stimulation. To accomplish this analysis a commercial finite element code (ABAQUS) is combined with an external program (MATLAB) to solve an incremental equilibrium boundary value problem representing one increment of growth. This procedure is repeated for as many increments as needed to simulate the desired growth protocol. A case study is presented utilizing a growth law dependent on the magnitude of the diffusive fluid velocity to simulate an in vitro dynamic confined compression loading protocol run for 2 weeks. The results include changes in tissue size and shape, nonhomogeneities that develop in the tissue, as well as the variation that occurs in the tissue constitutive behavior from growth.

Material properties in unconfined compression of human nucleus pulposus, injectable hyaluronic acid-based hydrogels and tissue engineering scaffolds

Surgical treatment for lower back pain related to degenerative disc disease commonly includes discectomy and spinal fusion. While surgical intervention may provide short-term pain relief, it results in altered biomechanics of the spine and may lead to further degenerative changes in adjacent segments. One non-fusion technique currently being investigated is nucleus pulposus (NP) support via either an injectable hydrogel or tissue engineered construct. A major challenge for either approach is to mimic the mechanical properties of native NP. Here we adopt an unconfined compression testing configuration to assess toe-region and linear-region modulus and Poisson's ratio, key functional parameters for NP replacement. Human NP, experimental biocompatible hydrogel formulations composed of hyaluronic acid (HA), PEG-g-chitosan, and gelatin, and conventional alginate and agarose gels were investigated as injectable NP replacements or tissue engineering scaffolds. Testing consisted of a stress-relaxation experiment of 5% strain increments followed by 5-min relaxation periods to a total of 25% strain. Human NP had an average linear-region modulus of 5.39 +/- 2.56 kPa and a Poisson's ratio of 0.62 +/- 0.15. The modulus and Poisson's ratio are important parameters for evaluating the design of implant materials and scaffolds. The synthetic HA-based hydrogels approximated NP well and may serve as suitable NP implant materials.

Articular cartilage mechanical and biochemical property relations before and after in vitro growth

The aim of this study was to design in vitro growth protocols that can comprehensively quantify articular cartilage structure-function relations via measurement of mechanical and biochemical properties. Newborn bovine patellofemoral groove articular cartilage explants were tested sequentially in confined compression (CC), unconfined compression (UCC), and torsional shear before (D0, i.e. day zero) and after (D14, i.e. day 14) unstimulated in vitro growth. The contents of collagen (COL), collagen-specific pyridinoline (PYR) crosslinks, glycosaminoglycan, and DNA significantly decreased during in vitro growth; consequently, a wide range of biochemical properties existed for investigating structure-function relations when pooling the D0 and D14 groups. All D0 mechanical properties were independent of compression strain while only Poisson's ratios were dependent on direction (i.e. anisotropic). Select D0 and D14 group mechanical properties were correlated with biochemical measures; including (but not limited to) results that CC/UCC moduli and UCC Poisson's ratios were correlated with COL and PYR. COL network weakening during in vitro growth due to reduced COL and PYR was accompanied by reduced CC/UCC moduli and increased UCC Poisson's ratios.

On the anisotropy and inhomogeneity of permeability in articular cartilage

Articular cartilage is known to be anisotropic and inhomogeneous because of its microstructure. In particular, its elastic properties are influenced by the arrangement of the collagen fibres, which are orthogonal to the bone-cartilage interface in the deep zone, randomly oriented in the middle zone, and parallel to the surface in the superficial zone. In past studies, cartilage permeability has been related directly to the orientation of the glycosaminoglycan chains attached to the proteoglycans which constitute the tissue matrix. These studies predicted permeability to be isotropic in the undeformed configuration, and anisotropic under compression. They neglected tissue anisotropy caused by the collagen network. However, magnetic resonance studies suggest that fluid flow is "directed" by collagen fibres in biological tissues. Therefore, the aim of this study was to express the permeability of cartilage accounting for the microstructural anisotropy and inhomogeneity caused by the collagen fibres. Permeability is predicted to be anisotropic and inhomogeneous, independent of the state of strain, which is consistent with the morphology of the tissue. Looking at the local anisotropy of permeability, we may infer that the arrangement of the collagen fibre network plays an important role in directing fluid flow to optimise tissue functioning.

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.

Efficient collision detection within deforming spherical sliding contact

Handling the evolving permanent contact of deformable objects leads to a collision detection problem of high computing cost. Situations in which this type of contact happens are becoming more and more present with the increasing complexity of virtual human models, especially for the emerging medical applications. In this context, we propose a novel collision detection approach to deal with situations in which soft structures are in constant but dynamic contact, which is typical of 3D biological elements. Our method proceeds in two stages: First, in a preprocessing stage, a mesh is chosen under certain conditions as a reference mesh and is spherically sampled. In the collision detection stage, the resulting table is exploited for each vertex of the other mesh to obtain, in constant time, its signed distance to the fixed mesh. The two working hypotheses for this approach to succeed are typical of the deforming anatomical systems we target: First, the two meshes retain a layered configuration with respect to a central point and, second, the fixed mesh tangential deformation is bounded by the spherical sampling resolution. Within this context, the proposed approach can handle large relative displacements, reorientations, and deformations of the mobile mesh. We illustrate our method in comparison with other techniques on a biomechanical model of the human hip joint.

Analysis of the permeation of cryoprotectants in cartilage

Some tissues, such as cartilage and cornea, carry an internal fixed negative charge, leading to a swelling pressure that is balanced by tensile stress in the tissue matrix. During the addition and removal of cryoprotectants the changes in osmotic pressure will cause the tissue to deform. Because of the fixed charge and osmotic deformation, the permeation process in such tissues differs from ordinary diffusion processes. In this paper a biomechanical multi-solute theory is introduced to describe this process in cartilage tissue. Typical values for the physiological and biomechanical properties are used in the simulation. Several parameters - the aggregate modulus, the fixed charge density and the frictional parameter - are analyzed to show their impact on the process. It is shown that friction between water and cryoprotectant has the greatest influence but the fixed charge density is also important. The aggregate modulus and the frictional parameter between the cryoprotectant and the solid matrix have the least influence. Both the new biomechanical model and the conventional diffusion model were fitted to published experimental data concerning the time course of mean tissue cryoprotectant concentration when cartilage is immersed in solutions of dimethyl sulphoxide or propylene glycol: in all cases and with both models a good fit was obtained only when a substantial amount of non-solvent water was assumed.

Zonal changes in the three-dimensional morphology of the chondron under compression: the relationship among cellular, pericellular, and extracellular deformation in articular cartilage

The pericellular matrix (PCM) is a narrow region of tissue that completely surrounds chondrocytes in articular cartilage. Previous theoretical models of the "chondron" (the PCM with enclosed cells) suggest that the structure and properties of the PCM may significantly influence the mechanical environment of the chondrocyte. The objective of this study was to quantify changes in the three-dimensional (3D) morphology of the chondron in situ at different magnitudes of compression applied to the cartilage extracellular matrix. Fluorescence immunolabeling for type-VI collagen was used to identify the boundaries of the cell and PCM, and confocal microscopy was used to form 3D images of chondrons from superficial, middle, and deep zone cartilage in explants compressed to 0%, 10%, 30%, and 50% surface-to-surface strain. Lagrangian tissue strain, determined locally using texture correlation, was highly inhomogeneous and revealed depth-dependent compressive stiffness and Poisson's ratio of the extracellular matrix. Compression significantly decreased cell and chondron height and volume, depending on the zone and magnitude of compression. In the superficial zone, cellular-level strains were always lower than tissue-level strains. In the middle and deep zones, however, tissue strains below 25% were amplified at the cellular level, while tissue strains above 25% were decreased at the cellular level. These findings are consistent with previous theoretical models of the chondron, suggesting that the PCM can serve as either a protective layer for the chondrocyte or a transducer that amplifies strain, such that cellular-level strains are more homogenous throughout the tissue depth despite large inhomogeneities in local ECM strains.

Depth-dependent biomechanical and biochemical properties of fetal, newborn, and tissue-engineered articular cartilage

Adult articular cartilage has depth-dependent mechanical and biochemical properties which contribute to zone-specific functions. The compressive moduli of immature cartilage and tissue-engineered cartilage are known to be lower than those of adult cartilage. The objective of this study was to determine if such tissues exhibit depth-dependent compressive properties, and how these depth-varying properties were correlated with cell and matrix composition of the tissue. The compressive moduli of fetal and newborn bovine articular cartilage increased with depth (p<0.05) by a factor of 4-5 from the top 0.1 mm (28+/-13 kPa, 141+/-10 kPa, respectively) to 1 mm deep into the tissue. Likewise, the glycosaminoglycan and collagen content increased with depth (both p<0.001), and correlated with the modulus (both p<0.01). In contrast, tissue-engineered cartilage formed by either layering or mixing cells from the superficial and middle zone of articular cartilage exhibited similarly soft regions at both construct surfaces, as exemplified by large equilibrium strains. The properties of immature cartilage may provide a template for developing tissue-engineered cartilage which aims to repair cartilage defects by recapitulating the natural development and growth processes. These results suggest that while depth-dependent properties may be important to engineer into cartilage constructs, issues other than cell heterogeneity must be addressed to generate such tissues.

Mechanical strains induced in osteoblasts by use of point femtosecond laser targeting

A study demonstrating how ultrafast laser radiation stimulates osteoblasts is presented. The study employed a custom made optical system that allowed for simultaneous confocal cell imaging and targeted femtosecond pulse laser irradiation. When femtosecond laser light was focused onto a single cell, a rise in intracellular Ca²⁺ levels was observed followed by contraction of the targeted cell. This contraction caused deformation of neighbouring cells leading to a heterogeneous strain field throughout the monolayer. Quantification of the strain fields in the monolayer using digital image correlation revealed local strains much higher than threshold values typically reported to stimulate extracellular bone matrix production in vitro. This use of point targeting with femtosecond pulse lasers could provide a new method for stimulating cell activity in orthopaedic tissue engineering.

Mitochondrial dynamics in chondrocytes and their connection to the mechanical properties of the cytoplasm

BACKGROUND

The motion and redistribution of intracellular organelles is a fundamental process in cells. Organelle motion is a complex phenomenon that depends on a large number of variables including the shape of the organelle, the type of motors with which the organelles are associated, and the mechanical properties of the cytoplasm. This paper presents a study that characterizes the diffusive motion of mitochondria in chondrocytes seeded in agarose constructs and what this implies about the mechanical properties of the cytoplasm.

METHOD OF APPROACH

Images showing mitochondrial motion in individual cells at 30 s intervals for 15 min were captured with a confocal microscope. Digital image correlation was used to quantify the motion of the mitochondria, and the mean square displacement (MSD) was calculated. Statistical tools for testing whether the characteristic motion of mitochondria varied throughout the cell were developed. Calculations based on statistical mechanics were used to establish connections between the measured MSDs and the mechanical nature of the cytoplasm.

RESULTS

The average MSD of the mitochondria varied with time according to a power law with the power term greater than 1, indicating that mitochondrial motion can be viewed as a combination of diffusion and directional motion. Statistical analysis revealed that the motion of the mitochondria was not uniform throughout the cell, and that the diffusion coefficient may vary by over 50%, indicating intracellular heterogeneity. High correlations were found between movements of mitochondria when they were less than 2 microm apart. The correlation is probably due to viscoelastic properties of the cytoplasm. Theoretical analysis based on statistical mechanics suggests that directed diffusion can only occur in a material that behaves like a fluid on large time scales.

CONCLUSIONS

The study shows that mitochondria in different regions of the cell experience different characteristic motions. This suggests that the cytoplasm is a heterogeneous viscoelastic material. The study provides new insight into the motion of mitochondria in chondrocytes and its connection with the mechanical properties of the cytoplasm.

Zonal variations in the three-dimensional morphology of the chondron measured in situ using confocal microscopy

OBJECTIVE

Chondrocytes in articular cartilage are surrounded by a narrow pericellular matrix (PCM), which together with the enclosed cell(s) are termed the "chondron". Although the precise function of this tissue region is unknown, previous studies provide indirect evidence that the PCM plays an important role in governing the local mechanical environment of chondrocytes. In particular, theoretical models of the chondron under mechanical loading suggest that the shape, size, and biomechanical properties of the PCM significantly influence the stress-strain and fluid flow environment of the cell. The goal of this study was to quantify the three-dimensional morphology of chondron in situ using en bloc immunolabeling of type VI collagen coupled with fluorescence confocal microscopy.

METHODS

Three-dimensional reconstructions of intact, fluorescently labeled chondrons were made from stacks of confocal images recorded in situ from the superficial, middle, and deep zones of porcine articular cartilage of the medial femoral condyle.

RESULTS

Significant variations in the shape, size, and orientation of chondrocytes and chondrons were observed with depth from the tissue surface, revealing flattened discoidal chondrons in the superficial zone, rounded chondrons in the middle zone, and elongated, multicellular chondrons in the deep zone.

CONCLUSIONS

The shape and orientation of the chondron appear to reflect the local collagen architecture of the interterritorial matrix, which varies significantly with depth. Quantitative measurements of morphology of the chondron and its variation with site, disease, or aging may provide new insights into the influence of this structure on physiology and the pathology of articular cartilage.

Constitutive Modeling of Cartilaginous Tissues: A Review

An important and longstanding field of research in orthopedic biomechanics is the elucidation and mathematical modeling of the mechanical response of cartilaginous tissues. Traditional approaches have treated such tissues as continua and have described their mechanical response in terms of macroscopic models borrowed from solid mechanics. The most important of such models are the biphasic and single-phase viscoelastic models, and the many variations thereof. These models have reached a high level of maturity and have been successful in describing a wide range of phenomena. An alternative approach that has received considerable recent interest, both in orthopedic biomechanics and in other fields, is the description of mechanical response based on consideration of a tissue's structure—so-called microstructural modeling. Examples of microstructurally based approaches include fibril-reinforced biphasic models and homogenization approaches. A review of both macroscopic and microstructural constitutive models is given in the present work.

The effect of finite compressive strain on chondrocyte viability in statically loaded bovine articular cartilage

Recent studies have reported that certain regimes of compressive loading of articular cartilage result in increased cell death in the superficial tangential zone (STZ). The objectives of this study were (1) to test the prevalent hypothesis that preferential cell death in the STZ results from excessive compressive strain in that zone, relative to the middle and deep zones, by determining whether cell death correlates with the magnitude of compressive strain and (2) to test the corollary hypothesis that the viability response of cells is uniform through the thickness of the articular layer when exposed to the same loading environment. Live cartilage explants were statically compressed by approximately 65% of their original thickness, either normal to the articular surface (axial loading) or parallel to it (transverse loading). Cell viability after 12 h was compared to the local strain distribution measured by digital image correlation. Results showed that the strain distribution in the axially loaded samples was highest in the STZ (77%) and lowest in the deep zone (55%), whereas the strain was uniformly distributed in the transversely loaded samples (64%). In contrast, axially and transversely loaded samples exhibited very similar profiles of cell death through the depth, with a preferential distribution in the STZ. Unloaded control samples showed negligible cell death. Thus, under prolonged static loading, depth-dependent variations in chondrocyte death did not correlate with the local depth-dependent compressive strain, and the prevalent hypothesis must be rejected. An alternative hypothesis, suggested by these results, is that superficial zone chondrocytes are more vulnerable to prolonged static loading than chondrocytes in the middle and deep zones.

Viscoelastic properties of zonal articular chondrocytes measured by atomic force microscopy

OBJECTIVE

Articular chondrocytes respond to chemical and mechanical signals depending on their zone of origin with respect to distance from the tissue surface. However, little is known of the zonal variations in cellular mechanical properties in cartilage. The goal of this study was to determine the zonal variations in the elastic and viscoelastic properties of porcine chondrocytes using atomic force microscopy (AFM), and to validate this method against micropipette aspiration.

METHODS

A theoretical solution for stress relaxation of a viscoelastic, incompressible, isotropic surface indented with a hard, spherical indenter (5 microm diameter) was derived and fit to experimental stress-relaxation data for AFM indentation of chondrocytes isolated from the superficial or middle/deep zones of cartilage.

RESULTS

The instantaneous moduli of chondrocytes were 0.55+/-0.23 kPa for superficial cells (S) and 0.29+/-0.14 kPa for middle/deep cells (M/D) (P<0.0001), and the relaxed moduli were 0.31+/-0.15 kPa (S) and 0.17+/-0.09 kPa (M/D) (P<0.0001). The apparent viscosities were 1.15+/-0.66 kPas (S) and 0.61+/-0.69 kPa-s (M/D) (P<0.0001). Results from the micropipette aspiration test showed similar cell moduli but higher apparent viscosities, indicating that mechanical properties measured by these two techniques are similar.

CONCLUSION

Our findings suggest that chondrocyte biomechanical properties differ significantly with the zone of origin, consistent with previous studies showing zonal differences in chondrocyte biosynthetic activity and gene expression. Given the versatility and dynamic testing capabilities of AFM, the ability to conduct stress-relaxation measurements using this technique may provide further insight into the viscoelastic properties of isolated cells.

The influence of fibril organization on the mechanical behaviour of articular cartilage

The paper presents a three-dimensional microstructural model that was developed to study both equilibrium and time-dependent mechanical behaviour of articular cartilage. The model is based on consolidation theory and makes use of the structure and the mechanical properties of tissue components. Fibrils provide tensile stiffness in this model, whose geometric orientation is described by distribution functions that can be changed freely, making the model applicable to any particular fibril configuration. The model is capable of quantitatively predicting equilibrium properties of the different tests using a single set of model parameters, and explains the anomaly that small compressive modulus and small Poisson's ratio are observed in unconfined compression while tension is governed by large tensile modulus and large Poisson's ratio.

Measurement of intracellular strain on deformable substrates with texture correlation

Mechanical stimuli are important factors that regulate cell proliferation, survival, metabolism and motility in a variety of cell types. The relationship between mechanical deformation of the extracellular matrix and intracellular deformation of cellular sub-regions and organelles has not been fully elucidated, but may provide new insight into the mechanisms involved in transducing mechanical stimuli to biological responses. In this study, a novel fluorescence microscopy and image analysis method was applied to examine the hypothesis that mechanical strains are fully transferred from a planar, deformable substrate to cytoplasmic and intranuclear regions within attached cells. Intracellular strains were measured in cells derived from the anulus fibrosus of the intervertebral disc when attached to an elastic silicone membrane that was subjected to tensile stretch. Measurements indicated cytoplasmic strains were similar to those of the underlying substrate, with a strain transfer ratio (STR) of 0.79. In contrast, nuclear strains were much smaller than those of the substrate, with an STR of 0.17. These findings are consistent with previous studies indicating nuclear stiffness is significantly greater than cytoplasmic stiffness, as measured using other methods. This study provides a novel method for the study of cellular mechanics, including a new technique for measuring intranuclear deformations, with evidence of differential magnitudes and patterns of strain transferred from the substrate to cell cytoplasm and nucleus.

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.

Considerations on Joint and Articular Cartilage Mechanics

When studying joint degeneration leading to osteoarthritis (OA), it seems imperative that local joint tissue loading is known during normal everyday movement and that the adaptive/degenerative effects of this loading are quantified systematically. Philosophically, we believe the best way to approach this problem is by studying joint degeneration and osteoarthritis in long-term experimental models and by representing diarthrodial joints and the associated tissues with accurate, geometric and structural, theoretical models. Here, we present selected examples of our work representing this approach. Experimentally, we demonstrate that the local loading of joints changes continuously in experimental models of OA, not only because of the changing external and internal loading, but also because of the continuous alterations in joint contact geometry and tissue mechanical properties. Furthermore, we show that single bouts of joint loading affect gene expression, and that gene expression, as well as subsequent joint degeneration is site-specific. In fact, opposing articular surfaces that are exposed to the same loading may degenerate at completely different rates. Finally, we propose a series of theoretical models of articular cartilage and contact mechanics, demonstrating that many of the anisotropic and inhomogeneous properties can be explained by structural elements and their orientation and volumetric concentration across the tissue.

Chondrocyte deformation induces mitochondrial distortion and heterogeneous intracellular strain fields

Chondrocyte mechanotransduction is poorly understood but may involve cell deformation and associated distortion of intracellular structures and organelles. This study quantifies the intracellular displacement and strain fields associated with chondrocyte deformation and in particular the distortion of the mitochondria network, which may have a role in mechanotransduction. Isolated articular chondrocytes were compressed in agarose constructs and simultaneously visualised using confocal microscopy. An optimised digital image correlation technique was developed to calculate the local intracellular displacement and strain fields using confocal images of fluorescently labelled mitochondria. The mitochondria formed a dynamic fibrous network or reticulum, which co-localised with microtubules and vimentin intermediate filaments. Cell deformation induced distortion of the mitochondria, which collapsed in the axis of compression with a resulting loss of volume. Compression generated heterogeneous intracellular strain fields indicating mechanical heterogeneity within the cytoplasm. The study provides evidence supporting the potential involvement of mitochondrial deformation in chondrocyte mechanotransduction, possibly involving strain-mediated release of reactive oxygen species. Furthermore the heterogeneous strain fields, which appear to be influenced by intracellular structure and organisation, may generate significant heterogeneity in mechanotransduction behaviour for cells subjected to identical levels of deformation.

Effect of Compressive Strain on Cell Viability in Statically Loaded Articular Cartilage

Physiological loading of articulating joints is necessary for normal cartilage function. However, conditions of excessive overloading or trauma can cause cartilage injury resulting in matrix damage and cell death. The objective of this study was to evaluate chondrocyte viability within mechanically compressed articular cartilage removed from immature and mature bovine knees. Twenty-three mature and 68 immature cartilage specimens were subjected to static uniaxial confined-creep compressions of 0-70% and the extent of cell death was measured using fluorescent microscopic imaging. In both age groups, cell death was always initiated at the articular surface and increased linearly in depth with increasing strain magnitude. However, most of the cell death was localized within the superficial zone (SZ) of the cartilage matrix with the depth never greater than approximately 500 microm or 25% of the thickness of the test specimen. The immature cartilage was found to have a significantly greater (> 2 times) amount (depth) of cell death compared to the mature cartilage, especially at the higher strains. This finding was attributed to the lower compressive modulus of the immature cartilage in the SZ compared to that of the mature cartilage, resulting in a greater local matrix strain and concomitant cell surface membrane strain in this zone when the matrix was compressed. These results provide further insight into the capacity of articular cartilage in different age groups to resist the severity of traumatic injury from compressive loads.

Analysis of articular cartilage as a composite using nonlinear membrane elements for collagen fibrils

To develop a composite fibre-reinforced model of the cartilage, membrane shell elements were introduced to represent collagen fibrils reinforcing the isotropic porous solid matrix filled with fluid. Nonlinear stress-strain curve of pure collagen fibres and collagen volume fraction were explicitly presented in the formulation of these membrane elements. In this composite model, in accordance with tissue structure, the matrix and fibril membrane network experienced dissimilar stresses despite identical strains in the fibre directions. Different unconfined compression and indentation case studies were performed to determine the distinct role of membrane collagen fibrils in nonlinear poroelastic mechanics of articular cartilage. The importance of nonlinear fibril membrane elements in the tissue relaxation response as well as in temporal and spatial variations of pore pressure and solid matrix stresses was demonstrated. By individual adjustments of the collagen volume fraction and collagen mechanical properties, the model allows for the simulation of alterations in the fibril network structure of the tissue towards modelling damage processes or repair attempts. The current model, which is based on a physiological description of the tissue structure, is promising in improvement of our understanding of the cartilage pathomechanics.

Heterogeneous three-dimensional strain fields during unconfined cyclic compression in bovine articular cartilage explants

Articular cartilage provides critical load-bearing and tribological properties to the normal function of diarthrodial joints. The unique properties of cartilage, as well as heterogeneous deformations during mechanical compression, are due to the nonuniform microstructural organization of tissue components such as collagens and proteoglycans. A new cartilage deformation by tag registration (CDTR) technique has been developed by the authors to determine heterogeneous deformations in articular cartilage explants. The technique uses a combination of specialized MRI methods, a custom cyclic loading apparatus, and image processing software. The objective of this study was to use the CDTR technique to document strain patterns throughout the volume of normal bovine articular cartilage explants during cyclic unconfined compression at two physiologically-relevant applied normal stress levels (1.29 and 2.57 MPa). Despite simple uniaxial cyclic compressive loading with a flat, nonporous indenter, strain patterns were heterogeneous. Strains in the thickness direction (E(yy)) were compressive, varied nonlinearly with depth from the articular surface from a maximum magnitude of 11% at the articular surface, and were comparable despite a 2-fold increase in applied normal stress. Strains perpendicular to the thickness direction (E(xx) and E(zz)) were tensile, decreased linearly with depth from the articular surface from a maximum of 7%, and increased in magnitude 2.5-fold with a 2-fold increase in applied normal stress. Shear strains in the transverse plane (E(xz)) were approximately zero while shear strains in the other two planes were much larger and increased in magnitude with depth from the articular surface, reaching maximum magnitudes of 2% at the articular cartilage-subchondral bone interface. In general, strain patterns indicated that cartilage osteochondral explants exhibited depth-dependent nonisotropic behavior during uniaxial cyclic loading. These results are useful in verifying constitutive formulations of articular cartilage during cyclic unconfined compression and in characterizing the micromechanical environment likely experienced by individual chondrocytes throughout the tissue volume.

Mechanical effects of ionic replacements in articular cartilage. Part II: Simulations of successive substitutions of NaCl and CaCl2

A three-phase multi-species electro-chemo-mechanical model of articular cartilage was developed in a companion paper, Loret and Simões (in Biomech Model Mechanobiol, in press, DOI 10.1007/s10237-004-0062-7). The model can handle mechanical and chemical loadings and unloadings involving the two salts, NaCl and CaCl(2). In order to reproduce experimental data, the shielding effects are made cation-dependent. In a tensile experiment, at constant axial strain, refreshment of the bath in contact with the cartilage is observed, and simulated, to induce a much different increase in tension depending on the order of the chemical sequence to which the cartilage is exposed. For example, the sequence dw (distilled water)-NaCl-dw-CaCl(2)-dw results in a decrease in tension. But the initial tension is recovered if the chemical sequence is pursued by NaCl-dw. Therefore, ionic replacements are essentially reversible, as evidenced when the chemical loading events respect a certain symmetry. Distinct shielding effects by cations sodium and calcium stem from two main features: (1) different free enthalpies of formation that represent different affinities of the proteoglycans for these ions and that result in an equilibrium constant not equal to 1; (2) distinct valences but approximately the same diameter, which results in a more efficient shielding by cations calcium. The model accounts also: (1) for the anisotropy of the mechanical properties that are due to the strong orientation of collagen fibers; (2) for large deformations that occur during uniaxial traction with deionized water.

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.

Depth-dependent strain of patellofemoral articular cartilage in unconfined compression

This biomechanical study reports strain gradients in patellofemoral joint cross-sections of seven porcine specimens in response to 1% unconfined axial compression subsequent to specific amounts of off-set strain. Strain distributions were quantified with a customized laser-based electronic speckle pattern interferometry (ESPI) system in a non-contact manner, delivering high-resolution, high-sensitivity strain maps over entire patellofemoral cartilage cross-sections. Strain reports were evaluated to determine differences in strain magnitudes between the superficial, middle, and deep cartilage layers in femoral and patellar cartilage. In addition, the effect of 5%, 10%, 15%, and 20% off-set strain on depth-dependent strain gradients was quantified. Regardless of the amount of off-set strain, the superficial layer of femoral cartilage absorbed the most strain, and the deep layer absorbed the least strain. These depth-dependent strain gradients were most pronounced for 5% off-set strain, at which the superficial layer absorbed on average 5.7 and 23.7 times more strain as compared to the middle and deep layers, respectively. For increased off-set strain levels, strain gradients became less pronounced. At 20% off-set strain, differences in layer-specific strain were not statistically significant, with the superficial layer showing a 1.4 fold higher strain as the deep layer. Patellar cartilage exhibited similar strain gradients and effects of off-set strain, although the patellar strain was on average 19% larger as compared to corresponding femoral strain reports. This study quantified for the first time continuous strain gradients over patellofemoral cartilage cross-sections. Next to provision of a detailed functional characterization of normal diarthrodial joints, this novel experimental approach holds considerable attraction to investigate joint degenerative processes.

Spatial and temporal development of chondrocyte-seeded agarose constructs in free-swelling and dynamically loaded cultures

Dynamic deformational loading has been shown to significantly increase the development of material properties of chondrocyte-seeded agarose hydrogels, however little is known about the spatial development of the material properties within these constructs. In this study, a technique that combines video microscopy and optimized digital image correlation, was applied to assess the spatial development of material properties in tissue-engineered cartilage constructs cultured in free-swelling and dynamically-loaded conditions (3h/day, 5 days/week, and maintained in free-swelling conditions when not being loaded) over a 6-week period. Although homogeneous at day 0, both free-swelling and dynamically loaded samples progressively developed stiffer outer edges and a softer central region. The distribution of GAGs and collagens were shown to mimic this profile. These results indicate that although dynamic loading augments the development of bulk properties in these samples, possibly by overcoming some of the diffusion limitation and nutrient transport issues, the overall profile of construct properties in the axial direction remains qualitatively the same as in free-swelling culture conditions. Poisson's ratio of these constructs increased over time in culture with increased fixed charged density contributed by the GAGs, but this increase was significantly less in dynamically loaded samples by day 42. Polarized light microscopy of Picrosirius Red labeled samples, at an angle perpendicular to the direction of loading, suggests that these differences in Poisson's ratio may be due to improved organization of collagen network in the dynamically loaded samples.

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.

The biomechanical role of the chondrocyte pericellular matrix in articular cartilage

The pericellular matrix (PCM) is a narrow tissue region that surrounds chondrocytes in articular cartilage. Previous parametric studies of cell-matrix interactions suggest that the mechanical properties of the PCM relative to those of the extracellular matrix (ECM) can significantly affect the micromechanical environment of the chondrocyte. The goal of this study was to use recently quantified mechanical properties of the PCM in a biphasic finite element model of the cell-PCM-ECM structure to determine the potential influence of the PCM on the mechanical environment of the chondrocyte under normal and osteoarthritic conditions. Our findings suggest that the mismatch between the Young's moduli of PCM and ECM amplifies chondrocyte compressive strains and exhibits a significant stress shielding effect in a zone-dependent manner. Furthermore, the lower permeability of PCM relative to the ECM inhibits fluid flux near the cell by a factor of 30, and thus may have a significant effect on convective transport to and from the chondrocyte. Osteoarthritic changes in the PCM and ECM properties significantly altered the mechanical environment of the chondrocyte, leading to approximately 66% higher compressive strains and higher fluid flux near the cell. These findings provide further support for a potential biomechanical role for the chondrocyte PCM, and suggest that changes in the properties of the PCM with osteoarthritis may alter the stress-strain and fluid flow environment of the chondrocytes.

Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression

Articular cartilage exhibits complex mechanical properties such as anisotropy, inhomogeneity and tension-compression nonlinearity. This study proposes and demonstrates that the application of compressive loading in the presence of osmotic swelling can be used to acquire a spectrum of incremental cartilage moduli (EYi) and Poisson's ratios (upsilon ij) from tension to compression. Furthermore, the anisotropy of the tissue can be characterized in both tension and compression by conducting these experiments along three mutually perpendicular loading directions: parallel to split-line (1-direction), perpendicular to split-line (2-direction) and along the depth direction (3-direction, perpendicular to articular surface), accounting for tissue inhomogeneity between the surface and deep layers in the latter direction. Tensile moduli were found to be strain-dependent while compressive moduli were nearly constant. The peak tensile (+) Young's moduli in 0.15M NaCl were E+Y1=3.1+/-2.3, E+Y2=1.3+/-0.3, E+Y3(Surface)=0.65+/-0.29 and E+Y3(Deep)=2.1+/-1.2 MPa. The corresponding compressive (-) Young's moduli were E-Y1=0.23+/-0.07, E-Y2=0.22+/-0.07, E-Y3(Surface)=0.18+/-0.07 and E-Y3(Deep)=0.35+/-0.11 MPa. Peak tensile Poisson's ratios were upsilon+12=0.22+/-0.06, upsilon+21=0.13+/-0.07, upsilon+31(Surface)=0.10+/-0.03 and upsilon+31(Deep)=0.20+/-0.05 while compressive Poisson's ratios were upsilon-12=0.027+/-0.012, upsilon-21=0.017+/-0.07, upsilon-31(Surface)=0.034+/-0.009 and upsilon-31(Deep)=0.065+/-0.024. Similar measurements were also performed at 0.015 M and 2 M NaCl, showing strong variations with ionic strength. Results indicate that (a) a smooth transition occurs in the stress-strain and modulus-strain responses between the tensile and compressive regimes, and (b) cartilage exhibits orthotropic symmetry within the framework of tension-compression nonlinearity. The strain-softening behavior of cartilage (the initial decrease in EYi with increasing compressive strain) can be interpreted in the context of osmotic swelling and tension-compression nonlinearity.

The role of viscoelasticity of collagen fibers in articular cartilage: axial tension versus compression

The role of viscoelasticity of collagen fibers in bovine articular cartilage was examined in compression and tension using stress relaxation measurements in the axial direction (normal to the articular surface). Experimentally, for a given axial strain, both peak and equilibrium loads were higher in tension than in compression, whereas stress relaxation was stronger in compression, as indicated by the higher peak-to-equilibrium ratios. A viscoelastic fibril-reinforced model including fluid flow was used for analysis of the experimental data. The collagen fibrillar matrix was assumed to be viscoelastic with a strain-dependent tensile modulus, and the nonfibrillar matrix was modeled as linearly elastic. For axial tension, collagen viscoelasticity was found to account for most of the stress relaxation, while the effects of fluid pressurization on the tensile stress were negligible. In contrast, for axial compression, the dominant mechanism for stress relaxation arose from fluid pressurization, while the associated relaxation in collagen fibers mainly resulted in an increase in radial strain. The effective Poisson's ratio, defined as the ratio of the radial and axial strains, was generally smaller in compression than in tension, and deviated from the true Poisson's ratio in tensile tests because of the frictional contacts between the specimen and the loading platens. Furthermore, lower collagen elasticity in the axial direction was observed than in the radial direction. This study illustrates the essential role of collagen viscoelasticity and interstitial fluid pressurization in the mechanical response of articular cartilage.

A transversely isotropic, transversely homogeneous microstructural-statistical model of articular cartilage

Articular cartilage is a multi-phasic, composite, fibre-reinforced material. Therefore, its mechanical properties are determined by the tissue microstructure. The presence of cells (chondrocytes) and collagen fibres within the proteoglycan matrix influences, at a local and a global level, the material symmetries. The volumetric concentration and shape of chondrocytes, and the volumetric concentration and spatial arrangement of collagen fibres have been observed to change as a function of depth in articular cartilage. In particular, collagen fibres are perpendicular to the bone-cartilage interface in the deep zone, their orientation is almost random in the middle zone, and they are parallel to the surface in the superficial zone. The aim of this work is to develop a model of elastic properties of articular cartilage based on its microstructure. In previous work, we addressed this problem based on Piola's notation for fourth-order tensors. Here, mathematical tools initially developed for transversely isotropic composite materials comprised of a statistical orientation of spheroidal inclusions are extended to articular cartilage, while taking into account the dependence of the elastic properties on cartilage depth. The resulting model is transversely isotropic and transversely homogeneous (TITH), the transverse plane being parallel to the bone-cartilage interface and the articular surface. Our results demonstrate that the axial elastic modulus decreases from the deep zone to the articular surface, a result that is in good agreement with experimental findings. Finite element simulations were carried out, in order to explore the TITH model's behaviour in articular cartilage compression tests. The force response, fluid flow and displacement fields obtained with the TITH model were compared with the classical linear elastic, isotropic, homogeneous (IH) model, showing that the IH model is unable to predict the non-uniform behaviour of the tissue. Based on considerations that the mechanical stability of the tissue depends on its topological and microstructural properties, our long-term goal is to clearly understand the stability conditions in topological terms, and the relationship with the growth and remodelling mechanisms in the healthy and diseased tissue.