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

A new constitutive model for hydration-dependent mechanical properties in biological soft tissues and hydrogels

It is challenging to noninvasively determine the mechanical properties of biological soft tissues in vivo. In this study, based on the biphasic theory and the transport models, a new constitutive model for hydration-dependent mechanical properties in hydrated soft materials was derived: HA = An(1-fϕ)(fϕ)2-n/2(2-fϕ), where HA(=λ+2 μ) is the aggregate modulus, ϕ(f) is the volume fraction of fluid (i.e., hydration), A and n (>2) are two parameters related to the transport properties of the biphasic materials. A linear model for hydration-dependent shear modulus in the literature was verified for hydrogels. The effects of tissue hydration on mechanical properties (aggregate modulus and Poisson's ratio) were investigated. It was found that the value of Poisson's ratio was very sensitive to the tissue hydration in soft materials with high water content. The predictions of the aggregate modulus and shear modulus for hydrogels by the model compared well with those from experimental results. This study is important for developing new techniques for noninvasively assessing the mechanical properties of biological soft tissues using quantitative MRI methods as well as for designing scaffolds with proper mechanical properties for tissue engineering applications.

Nanocomposite scaffold for chondrocyte growth and cartilage tissue engineering: effects of carbon nanotube surface functionalization

The goal of this study was to assess the long-term biocompatibility of single-wall carbon nanotubes (SWNTs) for tissue engineering of articular cartilage. We hypothesized that SWNT nanocomposite scaffolds in cartilage tissue engineering can provide an improved molecular-sized substrate for stimulation of chondrocyte growth, as well as structural reinforcement of the scaffold's mechanical properties. The effect of SWNT surface functionalization (-COOH or -PEG) on chondrocyte viability and biochemical matrix deposition was examined in two-dimensional cultures, in three-dimensional (3D) pellet cultures, and in a 3D nanocomposite scaffold consisting of hydrogels+SWNTs. Outcome measures included cell viability, histological and SEM evaluation, GAG biochemical content, compressive and tensile biomechanical properties, and gene expression quantification, including extracellular matrix (ECM) markers aggrecan (Agc), collagen-1 (Col1a1), collagen-2 (Col2a1), collagen-10 (Col10a1), surface adhesion proteins fibronectin (Fn), CD44 antigen (CD44), and tumor marker (Tp53). Our findings indicate that chondrocytes tolerate functionalized SWNTs well, with minimal toxicity of cells in 3D culture systems (pellet and nanocomposite constructs). Both SWNT-PEG and SWNT-COOH groups increased the GAG content in nanocomposites relative to control. The compressive biomechanical properties of cell-laden SWNT-COOH nanocomposites were significantly elevated relative to control. Increases in the tensile modulus and ultimate stress were observed, indicative of a tensile reinforcement of the nanocomposite scaffolds. Surface coating of SWNTs with -COOH also resulted in increased Col2a1 and Fn gene expression throughout the culture in nanocomposite constructs, indicative of increased chondrocyte metabolic activity. In contrast, surface coating of SWNTs with a neutral -PEG moiety had no significant effect on Col2a1 or Fn gene expression, suggesting that the charged nature of the -COOH surface functionalization may promote ECM expression in this culture system. The results of this study indicate that SWNTs exhibit a unique potential for cartilage tissue engineering, where functionalization with bioactive molecules may provide an improved substrate for stimulation of cellular growth and repair.

Time and dose-dependent effects of chondroitinase ABC on growth of engineered cartilage

Tissue engineering techniques have been effective in developing cartilage-like tissues in vitro. However, many scaffold-based approaches to cultivating engineered cartilage have been limited by low collagen production, an impediment for attaining native functional load-bearing tensile mechanical properties. Enzymatic digestion of glycosaminoglycans (GAG) with chondroitinase ABC (chABC) temporarily suppresses the construct's GAG content and compressive modulus and increases collagen content. Based on the promising results of these early studies, the aim of this study was to further promote collagen deposition through more frequent chABC treatments. Weekly dosing of chABC at a concentration of 0.15 U/mL resulted in a significant cell death, which impacted the ability of the engineered cartilage to fully recover GAG and compressive mechanical properties. In light of these findings, the influence of lower chABC dosage on engineered tissue (0.004 and 0.015 U/mL) over a longer duration (one week) was investigated. Treatment with 0.004 U/mL reduced cell death, decreased the recovery time needed to achieve native compressive mechanical properties and GAG content, and resulted in a collagen content that was 65 % greater than the control. In conclusion, the results of this study demonstrate that longer chABC treatment (one week) at low concentrations can be used to improve collagen content in developing engineered cartilage more expediently than standard chABC treatments of higher chABC doses administered over brief durations.

The effect of collagen crosslinking on the biphasic poroviscoelastic cartilage properties determined from a semi-automated microindentation protocol for stress relaxation

Given the important role of the collagenous structure in cartilage mechanics, there is considerable interest in the relationship between collagen crosslinking and the mechanical behavior of the cartilage matrix. While crosslink-induced alterations to the elastic modulus of cartilage have been described, changes to time-dependent behavior have not yet been determined. The objective of the study was to quantify changes to cartilage material properties, including viscoelastic coefficients, with crosslinking via indentation. To accomplish this, a semi-autonomous microindentation stress relaxation protocol was first developed, validated and then applied to cartilage specimens before and after crosslinking. The change in mechanical properties with crosslinking was analyzed both in the unloading portions of the test via the Oliver-Pharr method and in the holding portion with an inverse iterative finite element model that represented cartilage as a biphasic poroviscoelastic material. Although both techniques suggested a similar increase in equilibrium modulus in the crosslinked specimens as compared to the controls, distinct differences in the control specimens were apparent, suggesting that the two different techniques may be capturing different aspects of the material behavior. No differences in time-dependent properties were observed between the crosslinked and the control specimens. These results give further insight into the effects of crosslinking in cartilage mechanical behavior. Additionally, the microindentation stress relaxation protocol may enable increased automation for high-throughput testing.

Elastic, permeability and swelling properties of human intervertebral disc tissues: A benchmark for tissue engineering

The aim of functional tissue engineering is to repair and replace tissues that have a biomechanical function, i.e., connective orthopaedic tissues. To do this, it is necessary to have accurate benchmarks for the elastic, permeability, and swelling (i.e., biphasic-swelling) properties of native tissues. However, in the case of the intervertebral disc, the biphasic-swelling properties of individual tissues reported in the literature exhibit great variation and even span several orders of magnitude. This variation is probably caused by differences in the testing protocols and the constitutive models used to analyze the data. Therefore, the objective of this study was to measure the human lumbar disc annulus fibrosus (AF), nucleus pulposus (NP), and cartilaginous endplates (CEP) biphasic-swelling properties using a consistent experimental protocol and analyses. The testing protocol was composed of a swelling period followed by multiple confined compression ramps. To analyze the confined compression data, the tissues were modeled using a biphasic-swelling model, which augments the standard biphasic model through the addition of a deformation-dependent osmotic pressure term. This model allows considering the swelling deformations and the contribution of osmotic pressure in the analysis of the experimental data. The swelling stretch was not different between the disc regions (AF: 1.28±0.16; NP: 1.73±0.74; CEP: 1.29±0.26), with a total average of 1.42. The aggregate modulus (Ha) of the extra-fibrillar matrix was higher in the CEP (390kPa) compared to the NP (100kPa) or AF (30kPa). The permeability was very different across tissue regions, with the AF permeability (64 E(-16)m(4)/Ns) higher than the NP and CEP (~5.5 E(-16)m(4)/Ns). Additionally, a normalized time-constant (3000s) for the stress relaxation was similar for all the disc tissues. The properties measured in this study are important as benchmarks for tissue engineering and for modeling the disc's mechanical behavior and transport.

Altered mechano-chemical environment in hip articular cartilage: effect of obesity

The production of extracellular matrix (ECM) components of articular cartilage is regulated, among other factors, by an intercellular signaling mechanism mediated by the interaction of cell surface receptors (CSR) with insulin-like growth factor-1 (IGF-1). In ECM, the presence of binding proteins (IGFBP) hinders IGF-1 delivery to CSR. It has been reported that levels of IGF-1 and IGFBP in obese population are, respectively, lower and higher than those found in normal population. In this study, an experimental-numerical approach was adopted to quantify the effect of this metabolic alteration found in obese population on the homeostasis of femoral hip cartilage. A new computational model, based on the mechano-electrochemical mixture theory, was developed to describe competitive binding kinetics of IGF-1 with IGFBP and CSR, and associated glycosaminoglycan (GAG) biosynthesis. Moreover, a gait analysis was carried out on obese and normal subjects to experimentally characterize mechanical loads on hip cartilage during walking. This information was deployed into the model to account for effects of physiologically relevant tissue deformation on GAG production in ECM. Numerical simulations were performed to compare GAG biosynthesis in femoral hip cartilage of normal and obese subjects. Results indicated that the lower ratio of IGF-1 to IGFBP found in obese population reduces cartilage GAG concentration up to 18 % when compared to normal population. Moreover, moderate physical activity, such as walking, has a modest beneficial effect on GAG production. The findings of this study suggest that IGF-1/IGFBP metabolic unbalance should be accounted for when considering the association of obesity with hip osteoarthritis.

Poromechanics Parameters of Fluid-Saturated Chemically Active Fibrous Media Derived from a Micromechanical Approach

The authors have derived macroscale poromechanics parameters for chemically active saturated fibrous media by combining microstructure-based homogenization with Hill's volume averaging. The stress-strain relationship of the dry fibrous media is first obtained by considering the fiber behavior. The constitutive relationships applicable to saturated media are then derived in the poromechanics framework using Hill's Lemmas. The advantage of this approach is that the resultant continuum model assumes a form suited to study porous materials, while retaining the effect of discrete fiber deformation. As a result, the model is able to predict the influence of microscale phenomena such as fiber buckling on the overall behavior, and in particular, on the poromechanics constants. The significance of the approach is demonstrated using the effect of drainage and fiber nonlinearity on monotonic compressive stress-strain behavior. The model predictions conform to the experimental observations for articular cartilage. The method can potentially be extended to other porous materials such as bone, clays, foams, and concrete.

Mechanical properties of the extra-fibrillar matrix of human annulus fibrosus are location and age dependent

The mechanical behavior of the annulus fibrosus (AF) of the intervertebral disc can be modeled as a mixture of fibers, extra-fibrillar matrix (EFM), ions, and fluid. However, the properties of the EFM have not been measured directly. We measured mechanical properties of the human EFM at several locations, determined the effect of age and degeneration, and evaluated whether changes in EFM properties correspond to AF compositional changes. EFM mechanical properties were measured using a method that combines osmotic loading and confined compression. AF samples were dissected from several locations, and mechanical properties were correlated with age, degeneration, and composition. EFM modulus was found to range between 10 and 50 kPa, increasing nonlinearly with compression magnitude and being highest in the AF outer-anterior region. EFM properties were not correlated with composition or degeneration. However, the EFM modulus, its relative contribution to tissue modulus, and model parameters were correlated with age. These measurements will result in more accurate predictions of deformations in the intervertebral disc. Additionally, parameters such as permeability and diffusivity used for biotransport analysis of glucose and other solutes depend on EFM deformation. Consequently, the accuracy of biotransport simulations will be greatly improved.

Modeling sample/patient-specific structural and diffusional responses of cartilage using DT-MRI

We propose a new 3D biphasic constitutive model designed to incorporate structural data on the sample/patient-specific collagen fiber network. The finite strain model focuses on the load-bearing morphology, that is, an incompressible, poroelastic solid matrix, reinforced by an inhomogeneous, dispersed fiber fabric, saturated with an incompressible fluid at constant electrolytic conditions residing in strain-dependent pores of the collagen-proteoglycan solid matrix. In addition, the fiber network of the solid influences the fluid permeability and an intrafibrillar portion that cannot be 'squeezed out' from the tissue. We implement the model into a finite element code. To demonstrate the utility of our proposed modeling approach, we test two hypotheses by simulating an indentation experiment for a human tissue sample. The simulations use ultra-high field diffusion tensor magnetic resonance imaging that was performed on the tissue sample. We test the following hypotheses: (i) the through-thickness structural arrangement of the collagen fiber network adjusts fluid permeation to maintain fluid pressure (Biomech. Model. Mechanobiol. 7:367-378, 2008); and (ii) the inhomogeneity of mechanical properties through the cartilage thickness acts to maintain fluid pressure at the articular surface (J. Biomech. Eng. 125:569-577, 2003). For the tissue sample investigated, both through-thickness inhomogeneities of the collagen fiber distribution and of the material properties serve to influence the interstitial fluid pressure distribution and maintain fluid pressure underneath the indenter at the cartilage surface. Tissue inhomogeneity appears to have a larger effect on fluid pressure retention in this tissue sample and on the advantageous pressure distribution.

Tissue-engineered articular cartilage exhibits tension-compression nonlinearity reminiscent of the native cartilage

The tensile modulus of articular cartilage is much larger than its compressive modulus. This tension-compression nonlinearity enhances interstitial fluid pressurization and decreases the frictional coefficient. The current set of studies examines the tensile and compressive properties of cylindrical chondrocyte-seeded agarose constructs over different developmental stages through a novel method that combines osmotic loading, video microscopy, and uniaxial unconfined compression testing. This method was previously used to examine tension-compression nonlinearity in native cartilage. Engineered cartilage, cultured under free-swelling (FS) or dynamically loaded (DL) conditions, was tested in unconfined compression in hypertonic and hypotonic salt solutions. The apparent equilibrium modulus decreased with increasing salt concentration, indicating that increasing the bath solution osmolarity shielded the fixed charges within the tissue, shifting the measured moduli along the tension-compression curve and revealing the intrinsic properties of the tissue. With this method, we were able to measure the tensile (401±83kPa for FS and 678±473kPa for DL) and compressive (161±33kPa for FS and 348±203kPa for DL) moduli of the same engineered cartilage specimens. These moduli are comparable to values obtained from traditional methods, validating this technique for measuring the tensile and compressive properties of hydrogel-based constructs. This study shows that engineered cartilage exhibits tension-compression nonlinearity reminiscent of the native tissue, and that dynamic deformational loading can yield significantly higher tensile properties.

Anatomic variation of depth-dependent mechanical properties in neonatal bovine articular cartilage

Articular cartilage has well known depth-dependent structure and has recently been shown to have similarly non-uniform depth-dependent mechanical properties. Here, we study anatomic variation of the depth-dependent shear modulus and energy dissipation rate in neonatal bovine knees. The regions we specifically focus on are the patellofemoral groove, trochlea, femoral condyle, and tibial plateau. In every sample, we find a highly compliant region within the first 500 µm of tissue measured from the articular surface, where the local shear modulus is reduced by up to two orders of magnitude. Comparing measurements taken from different anatomic sites, we find statistically significant differences localized within the first 50 µm. Histological images reveal these anatomic variations are associated with differences in collagen density and fiber organization.

Further insight into the depth-dependent microstructural response of cartilage to compression using a channel indentation technique

Stress relaxation and structural analysis were used to investigate the zonally differentiated microstructural response to compression of the integrated cartilage-on-bone tissue system. Fifteen cartilage-on-bone samples were divided into three equal groups and their stress relaxation responses obtained at three different levels of axial compressive strain defined as low (~20%), medium (~40%) and high (~60%). All tests were performed using a channel indenter which included a central relief space designed to capture the response of the matrix adjacent to the directly loaded regions. On completion of each stress relaxation test and while maintaining the imposed axial strain, the samples were formalin fixed, decalcified, and then sectioned for microstructural analysis. Chondron aspect ratios were used to determine the extent of relative strain at different zonal depths. The stress relaxation response of cartilage to all three defined levels of axial strain displayed an initial highly viscous response followed by a significant elastic response. Chondron aspect ratio measurements showed that at the lowest level of compression, axial deformation was confined to the superficial cartilage layer, while in the medium and high axial strain samples the deformation extended into the midzone. The cells in the deep zone remained undeformed for all compression levels.

How the structural integrity of the matrix can influence the microstructural response of articular cartilage to compression

This study investigated how the structural integrity of healthy, surface-removed (healthy), and degenerate matrices can modify the response of cartilage to compression. Six groups of specimens were loaded up to the onset of consolidation or at full consolidation (N = 30, 5 per group, respectively) and then subsequently chemically fixed to capture the deformed state of the tissues. Creep compression was applied through an 8 mm flat-ended indenter containing a 450 μm diameter central pore, providing a region of high stress that also allowed the tissue samples to deform freely around the indenter pore during compression. Differential interference contrast microscopy was used in order to explore the microstructural responses of the tissues. The results demonstrated that superficial layer removal or tissue degeneration can reduce the observed deformation within the tissue region corresponding to the central pore of the loading indenter. Fibril crimping within the central pore matrix and matrix shear at the indenter edge regions are also reduced by both superficial layer removal and by tissue degeneration. These findings suggest that surface removal or tissue degeneration renders the matrix more susceptible to deformation and can also reduce the tissue's ability to transfer forces over a greater surface area and induce stress within the matrix.

Integrating qPLM and biomechanical test data with an anisotropic fiber distribution model and predictions of TGF-β1 and IGF-1 regulation of articular cartilage fiber modulus

A continuum mixture model with distinct collagen (COL) and glycosaminoglycan elastic constituents was developed for the solid matrix of immature bovine articular cartilage. A continuous COL fiber volume fraction distribution function and a true COL fiber elastic modulus ([Formula: see text] were used. Quantitative polarized light microscopy (qPLM) methods were developed to account for the relatively high cell density of immature articular cartilage and used with a novel algorithm that constructs a 3D distribution function from 2D qPLM data. For specimens untreated and cultured in vitro, most model parameters were specified from qPLM analysis and biochemical assay results; consequently, [Formula: see text] was predicted using an optimization to measured mechanical properties in uniaxial tension and unconfined compression. Analysis of qPLM data revealed a highly anisotropic fiber distribution, with principal fiber orientation parallel to the surface layer. For untreated samples, predicted [Formula: see text] values were 175 and 422 MPa for superficial (S) and middle (M) zone layers, respectively. TGF-[Formula: see text]1 treatment was predicted to increase and decrease [Formula: see text] values for the S and M layers to 281 and 309 MPa, respectively. IGF-1 treatment was predicted to decrease [Formula: see text] values for the S and M layers to 22 and 26 MPa, respectively. A novel finding was that distinct native depth-dependent fiber modulus properties were modulated to nearly homogeneous values by TGF-[Formula: see text]1 and IGF-1 treatments, with modulated values strongly dependent on treatment.

The role of the superficial region in determining the dynamic properties of articular cartilage

OBJECTIVE

The objective of this study was to elucidate the role of the superficial region of articular cartilage in determining the dynamic properties of the tissue. It is hypothesised that removal of the superficial region will influence both the flow dependent and independent properties of articular cartilage, leading to a reduction in the dynamic modulus of the tissue.

METHODS

Osteochondral cores from the femoropatellar groove of three porcine knee joints were subjected to static and dynamic loading in confined or unconfined compression at increasing strain increments with and without their superficial regions. Equilibrium moduli and dynamic moduli were measured and the tissue permeability was estimated by fitting experimental data to a biphasic model.

RESULTS

Biochemical analysis confirmed a zonal gradient in the tissue composition and organisation. Histological and PLM analysis demonstrated intense collagen staining in the superficial region of the tissue with alignment of the collagen fibres parallel to the articular surface. Mechanical testing revealed that the superficial region is less stiff than the remainder of the tissue in compression, however removal of this region from intact cores was found to significantly reduce the dynamic modulus of the remaining tissue, suggesting decreased fluid load support within the tissue during transient loading upon removal of the superficial region. Data fits to a biphasic model predict a significantly lower permeability in the superficial region compared to the remainder of the tissue.

CONCLUSIONS

It is postulated that the observed decrease in the dynamic moduli is due at least in part to the superficial region acting as a low permeability barrier, where its removal decreases the tissue's ability to maintain fluid load support. This result emphasises the impact that degeneration of the superficial region has on the functionality of the remaining tissue.

Depth-dependent anisotropy of the micromechanical properties of the extracellular and pericellular matrices of articular cartilage evaluated via atomic force microscopy

The extracellular matrix (ECM) of articular cartilage is structurally and mechanically inhomogeneous and anisotropic, exhibiting variations in composition, collagen fiber architecture, and pericellular matrix (PCM) morphology among the different zones (superficial, middle, and deep). Joint loading exposes chondrocytes to a complex biomechanical environment, as the microscale mechanical environment of the chondrocyte depends on the relative properties of its PCM and local ECM. ECM anisotropy and chondrocyte deformation are influenced by the split-line direction, the preferred collagen fiber orientation parallel to the articular surface. While previous studies have demonstrated that cartilage macroscale properties vary with depth and the direction of loading relative to the split-line direction, the potential anisotropic behavior of the ECM and PCM at the microscale has yet to be examined. The goal of this study was to characterize the depth and directional dependence of the microscale biomechanical properties of porcine cartilage ECM and PCM in situ. Cartilage was cryosectioned to generate samples oriented parallel and perpendicular to the split-line direction and normal to the articular surface. Atomic force microscopy (AFM)-based stiffness mapping was utilized to measure ECM and PCM microscale elastic properties in all three directions within each zone. Distinct anisotropy in ECM elastic moduli was observed in the superficial and deep zones, while the middle zone exhibited subtle anisotropy. PCM elastic moduli exhibited zonal uniformity with depth and directional dependence when pooled across the zones. These findings provide new evidence for mechanical inhomogeneity and anisotropy at the microscale in articular cartilage.

Immunofluorescence-guided atomic force microscopy to measure the micromechanical properties of the pericellular matrix of porcine articular cartilage

The pericellular matrix (PCM) is a narrow region that is rich in type VI collagen that surrounds each chondrocyte within the extracellular matrix (ECM) of articular cartilage. Previous studies have demonstrated that the chondrocyte micromechanical environment depends on the relative properties of the chondrocyte, its PCM and the ECM. The objective of this study was to measure the influence of type VI collagen on site-specific micromechanical properties of cartilage in situ by combining atomic force microscopy stiffness mapping with immunofluorescence imaging of PCM and ECM regions in cryo-sectioned tissue samples. This method was used to test the hypotheses that PCM biomechanical properties correlate with the presence of type VI collagen and are uniform with depth from the articular surface. Control experiments verified that immunolabelling did not affect the properties of the ECM or PCM. PCM biomechanical properties correlated with the presence of type VI collagen, and matrix regions lacking type VI collagen immediately adjacent to the PCM exhibited higher elastic moduli than regions positive for type VI collagen. PCM elastic moduli were similar in all three zones. Our findings provide further support for type VI collagen in defining the chondrocyte PCM and contributing to its biological and biomechanical properties.

The effect of calcification on the structural mechanics of the costal cartilage

The costal cartilage often undergoes progressive calcification with age. This study sought to investigate the effects of calcification on the structural mechanics of whole costal cartilage segments. Models were developed for five costal cartilage specimens, including representations of the cartilage, the perichondrium, calcification, and segments of the rib and sternum. The material properties of the cartilage were determined through indentation testing; the properties of the perichondrium were determined through optimisation against structural experiments. The calcified regions were then expanded or shrunk to develop five different sensitivity analysis models for each. Increasing the relative volume of calcification from 0% to 24% of the cartilage volume increased the stiffness of the costal cartilage segments by a factor of 2.3-3.8. These results suggest that calcification may have a substantial effect on the stiffness of the costal cartilage which should be considered when modelling the chest, especially if age is a factor.

Contribution of proteoglycan osmotic swelling pressure to the compressive properties of articular cartilage

The negatively charged proteoglycans (PG) provide compressive resistance to articular cartilage by means of their fixed charge density (FCD) and high osmotic pressure (π(PG)), and the collagen network (CN) provides the restraining forces to counterbalance π(PG). Our objectives in this work were to: 1), account for collagen intrafibrillar water when transforming biochemical measurements into a FCD-π(PG) relationship; 2), compute π(PG) and CN contributions to the compressive behavior of full-thickness cartilage during bovine growth (fetal, calf, and adult) and human adult aging (young and old); and 3), predict the effect of depth from the articular surface on π(PG) in human aging. Extrafibrillar FCD (FCD(EF)) and π(PG) increased with bovine growth due to an increase in CN concentration, whereas PG concentration was steady. This maturation-related increase was amplified by compression. With normal human aging, FCD(EF) and π(PG) decreased. The π(PG)-values were close to equilibrium stress (σ(EQ)) in all bovine and young human cartilage, but were only approximately half of σ(EQ) in old human cartilage. Depth-related variations in the strain, FCD(EF), π(PG), and CN stress profiles in human cartilage suggested a functional deterioration of the superficial layer with aging. These results suggest the utility of the FCD-π(PG) relationship for elucidating the contribution of matrix macromolecules to the biomechanical properties of cartilage.

Extra-fibrillar matrix mechanics of annulus fibrosus in tension and compression

The annulus fibrosus (AF) of the disk is a highly nonlinear and anisotropic material that undergoes a complex combination of loads in multiple orientations. The tensile mechanical behavior of AF in the lamellar plane is dominated by collagen fibers and has been accurately modeled using exponential functions. On the other hand, AF mechanics perpendicular to the lamella, in the radial direction, depend on the properties of the ground matrix with little to no fiber contribution. The ground matrix is mainly composed of proteoglycans (PG), which are negatively charged macromolecules that maintain the tissue hydration via osmotic pressure. The mechanical response of the ground matrix can be divided in the contribution of osmotic pressure and an elastic solid part known as extra-fibrillar matrix (EFM). Mechanical properties of the ground matrix have been measured using tensile and confined compression tests. However, EFM mechanics have not been measured directly. The objective of this study was to measure AF nonlinear mechanics of the EFM in tension and compression. To accomplish this, a combination of osmotic swelling and confined compression in disk radial direction, perpendicular to the lamella, was used. For this type of analysis, it was necessary to define a stress-free reference configuration. Thus, a brief analysis on residual stress in the disk and a procedure to estimate the reference configuration are presented. The proposed method was able to predict similar swelling deformations when using different loading protocols and models for the EFM, demonstrating its robustness. The stress-stretch curve of the EFM was linear in the range 0.9 < λ₃ < 1.3 with an aggregate modulus of 10.18±3.32 kPa; however, a significant nonlinearity was observed for compression below 0.8. The contribution of the EFM to the total aggregate modulus of the AF decreased from 70 to 30% for an applied compression of 50% of the initial thickness. The properties obtained in this study are essential for constitutive and finite element models of the AF and disk and can be applied to differentiate between functional degeneration effects such as PG loss and stiffening due to cross-linking.

Mechanically induced structural changes during dynamic compression of engineered cartilaginous constructs can potentially explain increases in bulk mechanical properties

Several studies on chondrocyte-seeded hydrogels in bioreactor culture report increased mechanical properties of mechanically loaded constructs compared with unloaded free swelling controls despite no significant differences in biochemical composition. One possible explanation is that changes in the collagen architecture of dynamically compressed constructs lead to improved mechanical properties. Collagen molecules are incorporated locally into the extracellular matrix with individual stress-free configurations and orientations. In this study, we computationally investigated possible influences of loading on the collagen architecture in chondrocyte-seeded hydrogels and their resulting mechanical properties. Both the collagen orientation and its stress-free configuration were hypothesized to depend on the local mechanical environment. Reorientation of the collagen network alone in response to dynamic compression leads to a prediction of constructs with lower compressive properties. In contrast, remodelling of the stress-free configuration of the collagen fibres was predicted to result in a more compacted tissue with higher swelling pressures and an altered pre-stressed state within the collagen network. Combining both mechanisms resulted in predictions of construct geometry and mechanical properties in agreement with experimental observations. This study provides support for the hypothesis that structural changes to the collagen network contribute to the enhanced mechanical properties of cartilaginous tissues engineered in bioreactors.

Effects of hypertonic (NaCl) two-dimensional and three-dimensional culture conditions on the properties of cartilage tissue engineered from an expanded mature bovine chondrocyte source

Clinically relevant mature cartilage cells (chondrocytes) present challenges for use in cartilage tissue engineering applications, given their low capacity for cell division and tissue production. Since the in situ environment of chondrocytes is hypertonic relative to standard culture medium conditions, in this study we tested the hypothesis that using culture medium of a hypertonic, more physiologic osmolarity during both two-dimensional (2D) expansion of mature bovine chondrocytes (MBCs) and their subsequent encapsulation culture in three-dimensional (3D) agarose hydrogel constructs produces improved engineered tissue construct mechanical and biochemical properties. Results demonstrate that 2D expansion of MBCs in hypertonic (NaCl) medium before encapsulation yielded improved construct mechanical properties. However, 3D encapsulation culture of cells in hypertonic (NaCl) medium yielded poorer construct mechanical properties. Osmolarity-related differences in construct biochemical content and organization may have contributed to differences in mechanical properties, as construct glycosaminoglycan content correlated moderately with construct mechanical properties, and construct collagen distribution varied between 3D osmotic culture groups. Results of this study suggest that application of hypertonic (NaCl) medium during 2D mature chondrocyte expansion, but not 3D encapsulated chondrocyte culture, may serve as a convenient and inexpensive method for improving mechanical properties of expanded cell-seeded constructs.

The influence of fiber orientation on the equilibrium properties of neutral and charged biphasic tissues

Constitutive models facilitate investigation into load bearing mechanisms of biological tissues and may aid attempts to engineer tissue replacements. In soft tissue models, a commonly made assumption is that collagen fibers can only bear tensile loads. Previous computational studies have demonstrated that radially aligned fibers stiffen a material in unconfined compression most by limiting lateral expansion while vertically aligned fibers buckle under the compressive loads. In this short communication, we show that in conjunction with swelling, these intuitive statements can be violated at small strains. Under such conditions, a tissue with fibers aligned parallel to the direction of load initially provides the greatest resistance to compression. The results are further put into the context of a Benninghoff architecture for articular cartilage. The predictions of this computational study demonstrate the effects of varying fiber orientations and an initial tare strain on the apparent material parameters obtained from unconfined compression tests of charged tissues.

Response of engineered cartilage to mechanical insult depends on construct maturity

Injury to articular cartilage leads to degenerative changes resulting in a loss of mechanical and biochemical properties. In engineered cartilage, the injury response of developing constructs is unclear.

OBJECTIVE

To characterize the cellular response of tissue-engineered constructs cultured in chemically-defined medium after mechanical insult, either by compression-induced cracking, or by cutting, as a function of construct maturity.

METHODS

Primary immature bovine articular chondrocytes (4-6 weeks) were encapsulated in agarose hydrogel (2%, 30 millioncells/mL) and cultured in chemically-defined medium supplemented with Transforming growth factor (TGF)-β3 (10ng/mL, first 2 weeks). At early (5 days) and late (35 days) times in culture, subsets of constructs were exposed to mechanical overload to produce a crack in the tissue or were exposed to a sharp wound with a perpendicular cut. Constructs were returned to culture and allowed to recover in static conditions. Mechanical and biochemical properties were evaluated at 2-week intervals to day 70, and cellular viability was assessed at 2-week intervals to day 85.

RESULTS

Constructs injured early in culture recovered their mechanical stiffness back to control values, regardless of the mode of injury. Later in culture, when constructs exhibited properties similar to those of native cartilage, compression-induced cracking catastrophically damaged the bulk matrix of the tissue and resulted in permanent mechanical failure with persistent cell death. No such detrimental outcomes were observed with cutting. Biochemical content was similar across all groups irrespective of mode or time of injury.

CONCLUSIONS

Unlike native cartilage, engineered cartilage constructs exhibit a reparative capacity when the bulk integrity of the developing tissue is preserved after injury.

New insights into the role of the superficial tangential zone in influencing the microstructural response of articular cartilage to compression

OBJECTIVE

The purpose of this study was to characterize the microstructural response of healthy cartilage in a perturbed physical environment to compressive loading with a novel channel indentation device. Manipulation of the cartilage physical environment was achieved through (1) removal of the superficial tangential zone (STZ) and (2) varying the saline bathing solution concentration.

DESIGN

Cartilage-on-bone blocks were subjected to creep loading under a nominal stress of 4.5 MPa via an indenter consisting of two rectangular platens separated by a narrow channel relief space to create a specific region where cartilage would not be directly loaded. Each sample was fixed in its near-equilibrium deformed state, after which the cartilage microstructure was examined using differential interference contrast (DIC) optical microscopy and scanning electron microscopy (SEM). The cartilage bulge in the channel relief space was studied in detail.

RESULTS

STZ removal altered the indentation response at the macro- and microstructural levels. Specifically, the strain in the directly compressed regions was reduced (P=0.012) and the bulge height in the channel relief space was greater (P<0.0001) in the STZ-removed compared with the surface-intact samples. The bulge height in the STZ-removed group was always less than the preloaded cartilage thickness. There was intense shear in the non-directly-loaded regions of intact-cartilage but not in STZ-removed cartilage. Bathing solution concentration influenced only the STZ-removed group, where lower concentrations produced significantly abrupt transitions in matrix continuity between the directly compressed and adjacent non-directly-loaded cartilage (P=0.012).

CONCLUSIONS

This study showed that while the surface layer was important in distributing loads away from directly-loaded regions, so were other factors such as the matrix fibrillar interconnectivity, swelling potential, and tissue anisotropy.

Spatial mapping of the biomechanical properties of the pericellular matrix of articular cartilage measured in situ via atomic force microscopy

In articular cartilage, chondrocytes are surrounded by a narrow region called the pericellular matrix (PCM), which is biochemically, structurally, and mechanically distinct from the bulk extracellular matrix (ECM). Although multiple techniques have been used to measure the mechanical properties of the PCM using isolated chondrons (the PCM with enclosed cells), few studies have measured the biomechanical properties of the PCM in situ. The objective of this study was to quantify the in situ mechanical properties of the PCM and ECM of human, porcine, and murine articular cartilage using atomic force microscopy (AFM). Microscale elastic moduli were quantitatively measured for a region of interest using stiffness mapping, or force-volume mapping, via AFM. This technique was first validated by means of elastomeric models (polyacrylamide or polydimethylsiloxane) of a soft inclusion surrounded by a stiff medium. The elastic properties of the PCM were evaluated for regions surrounding cell voids in the middle/deep zone of sectioned articular cartilage samples. ECM elastic properties were evaluated in regions visually devoid of PCM. Stiffness mapping successfully depicted the spatial arrangement of moduli in both model and cartilage surfaces. The modulus of the PCM was significantly lower than that of the ECM in human, porcine, and murine articular cartilage, with a ratio of PCM to ECM properties of approximately 0.35 for all species. These findings are consistent with previous studies of mechanically isolated chondrons, and suggest that stiffness mapping via AFM can provide a means of determining microscale inhomogeneities in the mechanical properties of articular cartilage in situ.

A study of the anisotropy and tension/compression behavior of human cervical tissue

The cervix plays a crucial role in maintaining a healthy pregnancy, acting as a mechanical barrier to hold the fetus in utero during gestation. Altered mechanical properties of the cervical tissue are suspected to play a critical role in spontaneous preterm birth. Both MRI and X-ray data in the literature indicate that cervical stroma contains regions of preferentially aligned collagen fibers along anatomical directions (circumferential/longitudinal/radial). In this study, a mechanical testing protocol is developed to investigate the large-strain response of cervical tissue in uniaxial tension and compression along its three orthogonal anatomical directions. The stress response of the tissue along the different orthogonal directions is captured using a minimal set of model parameters generated by fitting a one-dimensional time-dependent rheological model to the experimental data. Using model parameters, mechanical responses can be compared between samples from patients with different obstetric backgrounds, between samples from different anatomical sites, and between the different loading directions for a single specimen. The results presented in this study suggest that cervical tissue is mechanically anisotropic with a uniaxial response dependent on the direction of loading, the anatomical site of the specimen, and the obstetric history of the patient. We hypothesize that the directionality of the tissue mechanical response is primarily due to collagen orientation in the cervical stroma, and provides an interpretation of our mechanical findings consistent with the literature data on preferential collagen alignment.

Differential regulation of immature articular cartilage compressive moduli and Poisson's ratios by in vitro stimulation with IGF-1 and TGF-beta1

Mechanisms of articular cartilage growth and maturation have been elucidated by studying composition-function dynamics during in vivo development and in vitro culture with stimuli such as insulin-like growth factor-1 (IGF-1) and transforming growth factor-beta 1 (TGF-beta1). This study tested the hypothesis that IGF-1 and TGF-beta1 regulate immature cartilage compressive moduli and Poisson's ratios in a manner consistent with known effects on tensile properties. Bovine calf articular cartilage from superficial-articular (S) and middle-growth (M) regions were analyzed fresh or following culture in medium with IGF-1 or TGF-beta1. Mechanical properties in confined (CC) and unconfined (UCC) compression, cartilage matrix composition, and explant size were assessed. Culture with IGF-1 resulted in softening in CC and UCC, increased Poisson's ratios, substantially increased tissue volume, and accumulation of glycosaminoglycan (GAG) and collagen (COL). Culture with TGF-beta1 promoted maturational changes in the S layer, including stiffening in CC and UCC and increased concentrations of GAG, COL, and pyridinoline crosslinks (PYR), but little growth. Culture of M layer explants with TGF-beta1 was nearly homeostatic. Across treatment groups, compressive moduli in CC and UCC were positively related to GAG, COL, and PYR concentrations, while Poisson's ratios were negatively related to concentrations of these matrix components. Thus, IGF-1 and TGF-beta1 differentially regulate the compressive mechanical properties and size of immature articular cartilage in vitro. Prescribing tissue growth, maturation, or homeostasis by controlling the in vitro biochemical environment with such growth factors may have applications in cartilage repair and tissue engineering.

Mechanical asymmetry during articulation of tibial and femoral cartilages: local and overall compressive and shear deformation and properties

During knee movement, femoral cartilage articulates against cartilage from the tibial plateau, and the resulting mechanical behavior is yet to be fully characterized. The objectives of this study were to determine (1) the overall and depth-varying axial and shear strains and (2) the associated moduli, of femoral and tibial cartilages during the compression and shearing of apposing tibial and femoral samples. Osteochondral blocks from human femoral condyles (FCs) characterized as normal and donor-matched lateral tibial plateau (TP) were apposed, compressed 13%, and subjected to relative lateral motion. When surfaces began to slide, axial (-E(zz)) and shear (E(xz)) strains and compressive (E) and shear (G) moduli, overall and as a function of depth, were determined for femoral and tibial cartilages. Tibial -E(zz) was approximately 2-fold greater than FC -E(zz) near the surface (0.38 versus 0.22) and overall (0.16 versus 0.07). Near the surface, E(xz) of TP was 8-fold higher than that of FC (0.41 versus 0.05), while overall E(xz) was 4-fold higher (0.09 versus 0.02). For TP and FC, -E(zz) and E(xz) were greatest near the surface and decreased monotonically with depth. E for FC was 1.7-fold greater than TP, both near the surface (0.40 versus 0.24MPa) and overall (0.76 versus 0.47MPa). Similarly, G was 7-fold greater for FC (0.22MPa) than TP near the surface (0.03MPa) and 3-fold higher for FC (0.38MPa) than TP (0.13MPa) overall. These results indicate that tibial cartilage deforms and strains more axially and in shear than the apposing femoral cartilage during tibial-femoral articulation, reflecting their respective moduli.

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.

Chondroitinase ABC treatment results in greater tensile properties of self-assembled tissue-engineered articular cartilage

Collagen content and tensile properties of engineered articular cartilage have remained inferior to glycosaminoglycan (GAG) content and compressive properties. Based on a cartilage explant study showing greater tensile properties after chondroitinase ABC (C-ABC) treatment, C-ABC as a strategy for cartilage tissue engineering was investigated. A scaffold-less approach was employed, wherein chondrocytes were seeded into non-adherent agarose molds. C-ABC was used to deplete GAG from constructs 2 weeks after initiating culture, followed by 2 weeks culture post-treatment. Staining for GAG and type I, II, and VI collagen and transmission electron microscopy were performed. Additionally, quantitative total collagen, type I and II collagen, and sulfated GAG content were measured, and compressive and tensile mechanical properties were evaluated. At 4 wks, C-ABC treated construct ultimate tensile strength and tensile modulus increased 121% and 80% compared to untreated controls, reaching 0.5 and 1.3 MPa, respectively. These increases were accompanied by increased type II collagen concentration, without type I collagen. As GAG returned, compressive stiffness of C-ABC treated constructs recovered to be greater than 2 wk controls. C-ABC represents a novel method for engineering functional articular cartilage by departing from conventional anabolic approaches. These results may be applicable to other GAG-producing tissues functioning in a tensile capacity, such as the musculoskeletal fibrocartilages.

High-resolution spatial mapping of shear properties in cartilage

Structural properties of articular cartilage such as proteoglycan content, collagen content and collagen alignment are known to vary over length scales as small as a few microns (Bullough and Goodfellow, 1968; Bi et al., 2006). Characterizing the resulting variation in mechanical properties is critical for understanding how the inhomogeneous architecture of this tissue gives rise to its function. Previous studies have measured the depth-dependent shear modulus of articular cartilage using methods such as particle image velocimetry (PIV) that rely on cells and cell nuclei as fiducial markers to track tissue deformation (Buckley et al., 2008; Wong et al., 2008a). However, such techniques are limited by the density of trackable markers, which may be too low to take full advantage of optical microscopy. This limitation leads to noise in the acquired data, which is often exacerbated when the data is manipulated. In this study, we report on two techniques for increasing the accuracy of tissue deformation measurements. In the first technique, deformations were tracked in a grid that was photobleached on each tissue sample (Bruehlmann et al., 2004). In the second, a numerical technique was implemented that allowed for accurate differentiation of optical displacement measurements by minimizing the propagated experimental error while ensuring that truncation error associated with local averaging of the data remained small. To test their efficacy, we employed these techniques to compare the depth-dependent shear moduli of neonatal bovine and adult human articular cartilage. Using a photobleached grid and numerical optimization to gather and analyze data led to results consistent with those reported previously (Buckley et al., 2008; Wong et al., 2008a), but with increased spatial resolution and characteristic coefficients of variation that were reduced up to a factor of 3. This increased resolution allowed us to determine that the shear modulus of neonatal bovine and adult human tissue both exhibit a global minimum at a depth z of around 100 microm and plateau at large depths. The consistency of the depth dependence of |G*|(Z) for adult human and neonatal bovine tissue suggests a functional advantage resulting from this behavior.

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.

Relationships between mechanical properties and extracellular matrix constituents of the cervical stroma during pregnancy

In normal pregnancy, the cervix maintains its shape during a period of substantial fetal and uterine growth. Hence, maintenance of biomechanical integrity is an important aspect of cervical function. It is known that cervical mechanical properties arise from extracellular matrix (ECM). The most important constituent of the cervical ECM is fibrillar collagen-it is collagen protein that the cervix derives its "strength" from. Other matrix molecules known to affect the collagen network include water, proteoglycans, hyaluronan, and elastin. The objective of this review is to discuss relationships between biochemical constituents and macroscopic mechanical properties. The individual constituents of the ECM will be discussed, especially in regard to collagen remodeling during pregnancy. In addition, the macroscopic mechanical properties of cervical tissue will be reviewed. An improved understanding of the biochemistry of cervical "strength" will shed light on how the cervix maintains its shape in normal pregnancy and shortens in preterm birth.

Modeling the matrix of articular cartilage using a continuous fiber angular distribution predicts many observed phenomena

Cartilage is a hydrated soft tissue whose solid matrix consists of negatively charged proteoglycans enmeshed within a fibrillar collagen network. Though many aspects of cartilage mechanics are well understood today, most notably in the context of porous media mechanics, there remain a number of responses observed experimentally whose prediction from theory has been challenging. In this study the solid matrix of cartilage is modeled with a continuous fiber angular distribution, where fibers can only sustain tension, swelled by the osmotic pressure of a proteoglycan ground matrix. It is shown that this representation of cartilage can predict a number of observed phenomena in relation to the tissue's equilibrium response to mechanical and osmotic loading, when flow-dependent and flow-independent viscoelastic effects have subsided. In particular, this model can predict the transition of Poisson's ratio from very low values in compression (approximately 0.02) to very high values in tension (approximately 2.0). Most of these phenomena cannot be explained when using only three orthogonal fiber bundles to describe the tissue matrix, a common modeling assumption used to date. The main picture emerging from this analysis is that the anisotropy of the fibrillar matrix of articular cartilage is intimately dependent on the mechanism of tensed fiber recruitment, in the manner suggested by our recent theoretical study (Ateshian, 2007, ASME J. Biomech. Eng., 129(2), pp. 240-249).

A Phenomenological Approach Toward Patient-Specific Computational Modeling of Articular Cartilage Including Collagen Fiber Tracking

To model the cartilage morphology and the material response, a phenomenological and patient-specific simulation approach incorporating the collagen fiber fabric is proposed. Cartilage tissue response is nearly isochoric and time-dependent under physiological pressure levels. Hence, a viscoelastic constitutive model capable of reproducing finite strains is employed, while the time-dependent deformation change is purely isochoric. The model incorporates seven material parameters, which all have a physical interpretation. To calibrate the model and facilitate further analysis, five human cartilage specimens underwent a number of tests. A series of magnetic resonance imaging (MRI) sequences is taken, next the cartilage surface is imaged, then mechanical indentation tests are completed at 2–7 different locations per sample, resulting in force/displacement data over time, and finally, the underlying bone surface is imaged. Imaging and mechanical testing are performed with a custom-built robotics-based testing device. Stereo reconstruction of the cartilage and subchondral bone surface is employed, which, together with the proposed constitutive model, led to specimen-specific finite element simulations of the mechanical indentation tests. The force-time response of 23 such indentation experiment simulations is optimized to estimate the mean material parameters and corresponding standard deviations. The model is capable of reproducing the deformation behavior of human articular cartilage in the physiological loading domain, as demonstrated by the good agreement between the experiment and numerical results (R2=0.95±0.03, mean±standard deviation of force-time response for 23 indentation tests). To address validation, a sevenfold cross-validation experiment is performed on the 21 experiments representing healthy cartilage. To quantify the predictive error, the mean of the absolute force differences and Pearson’s correlation coefficient are both calculated. Deviations in the mean absolute difference, normalized by the peak force, range from 4% to 90%, with 40±25%(M±SD). The correlation coefficients across all predictions have a minimum of 0.939, and a maximum of 0.993 with 0.975±0.013(M±SD), which demonstrates an excellent match of the decay characteristics. A novel feature of the proposed method is 3D sample-specific numerical tracking of the fiber fabric deformation under general loading. This feature is demonstrated by comparing the estimated fiber fabric deformation with recently published experimental data determined by diffusion tensor MRI. The proposed approach is efficient enough to enable large-scale 3D contact simulations of knee joint loading in simulations with accurate joint geometries.

Simulating the growth of articular cartilage explants in a permeation bioreactor to aid in experimental protocol design

Recently a cartilage growth finite element model (CGFEM) was developed to solve nonhomogeneous and time-dependent growth boundary-value problems (Davol et al., 2008, "A Nonlinear Finite Element Model of Cartilage Growth," Biomech. Model. Mechanobiol., 7, pp. 295-307). The CGFEM allows distinct stress constitutive equations and growth laws for the major components of the solid matrix, collagens and proteoglycans. The objective of the current work was to simulate in vitro growth of articular cartilage explants in a steady-state permeation bioreactor in order to obtain results that aid experimental design. The steady-state permeation protocol induces different types of mechanical stimuli. When the specimen is initially homogeneous, it directly induces homogeneous permeation velocities and indirectly induces nonhomogeneous solid matrix shear stresses; consequently, the steady-state permeation protocol is a good candidate for exploring two competing hypotheses for the growth laws. The analysis protocols were implemented through the alternating interaction of the two CGFEM components: poroelastic finite element analysis (FEA) using ABAQUS and a finite element growth routine using MATLAB. The CGFEM simulated 12 days of growth for immature bovine articular cartilage explants subjected to two competing hypotheses for the growth laws: one that is triggered by permeation velocity and the other by maximum shear stress. The results provide predictions for geometric, biomechanical, and biochemical parameters of grown tissue specimens that may be experimentally measured and, consequently, suggest key biomechanical measures to analyze as pilot experiments are performed. The combined approach of CGFEM analysis and pilot experiments may lead to the refinement of actual experimental protocols and a better understanding of in vitro growth of articular cartilage.

The role of interstitial fluid pressurization in articular cartilage lubrication

Over the last two decades, considerable progress has been reported in the field of cartilage mechanics that impacts our understanding of the role of interstitial fluid pressurization on cartilage lubrication. Theoretical and experimental studies have demonstrated that the interstitial fluid of cartilage pressurizes considerably under loading, potentially supporting most of the applied load under various transient or steady-state conditions. The fraction of the total load supported by fluid pressurization has been called the fluid load support. Experimental studies have demonstrated that the friction coefficient of cartilage correlates negatively with this variable, achieving remarkably low values when the fluid load support is greatest. A theoretical framework that embodies this relationship has been validated against experiments, predicting and explaining various outcomes, and demonstrating that a low friction coefficient can be maintained for prolonged loading durations under normal physiological function. This paper reviews salient aspects of this topic, as well as its implications for improving our understanding of boundary lubrication by molecular species in synovial fluid and the cartilage superficial zone. Effects of cartilage degeneration on its frictional response are also reviewed.

Validation of finite element predictions of cartilage contact pressure in the human hip joint

Methods to predict contact stresses in the hip can provide an improved understanding of load distribution in the normal and pathologic joint. The objectives of this study were to develop and validate a three-dimensional finite element (FE) model for predicting cartilage contact stresses in the human hip using subject-specific geometry from computed tomography image data, and to assess the sensitivity of model predictions to boundary conditions, cartilage geometry, and cartilage material properties. Loads based on in vivo data were applied to a cadaveric hip joint to simulate walking, descending stairs, and stair-climbing. Contact pressures and areas were measured using pressure sensitive film. CT image data were segmented and discretized into FE meshes of bone and cartilage. FE boundary and loading conditions mimicked the experimental testing. Fair to good qualitative correspondence was obtained between FE predictions and experimental measurements for simulated walking and descending stairs, while excellent agreement was obtained for stair-climbing. Experimental peak pressures, average pressures, and contact areas were 10.0 MPa (limit of film detection), 4.4-5.0 MPa, and 321.9-425.1 mm(2), respectively, while FE-predicted peak pressures, average pressures, and contact areas were 10.8-12.7 MPa, 5.1-6.2 MPa, and 304.2-366.1 mm(2), respectively. Misalignment errors, determined as the difference in root mean squared error before and after alignment of FE results, were less than 10%. Magnitude errors, determined as the residual error following alignment, were approximately 30% but decreased to 10-15% when the regions of highest pressure were compared. Alterations to the cartilage shear modulus, bulk modulus, or thickness resulted in +/-25% change in peak pressures, while changes in average pressures and contact areas were minor (+/-10%). When the pelvis and proximal femur were represented as rigid, there were large changes, but the effect depended on the particular loading scenario. Overall, the subject-specific FE predictions compared favorably with pressure film measurements and were in good agreement with published experimental data. The validated modeling framework provides a foundation for development of patient-specific FE models to investigate the mechanics of normal and pathological hips.

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.

Tensile properties of engineered cartilage formed from chondrocyte- and MSC-laden hydrogels

OBJECTIVE

The objective of this study was to determine the capacity of chondrocyte- and mesenchymal stem cell (MSC)-laden hydrogel constructs to achieve native tissue tensile properties when cultured in a chemically defined medium supplemented with transforming growth factor-beta3 (TGF-beta3).

DESIGN

Cell-laden agarose hydrogel constructs (seeded with bovine chondrocytes or MSCs) were formed as prismatic strips and cultured in a chemically defined serum-free medium in the presence or absence of TGF-beta3. The effects of seeding density (10 vs 30 million cells/mL) and cell type (chondrocyte vs MSC) were evaluated over a 56-day period. Biochemical content, collagenous matrix deposition and localization, and tensile properties (ramp modulus, ultimate strain, and toughness) were assessed biweekly.

RESULTS

Results show that the tensile properties of cell-seeded agarose constructs increase with time in culture. However, tensile properties (modulus, ultimate strain, and toughness) achieved on day 56 were not dependent on either the initial seeding density or the cell type employed. When cultured in medium supplemented with TGF-beta3, tensile modulus increased and plateaued at a level of 300-400 kPa for each cell type and starting cell concentration. Ultimate strain and toughness also increased relative to starting values. Collagen deposition increased in constructs seeded with both cell types and at both seeding densities, with exposure to TGF-beta3 resulting in a clear shift toward type II collagen deposition as determined by immunohistochemical staining.

CONCLUSIONS

These findings demonstrate that the tensile properties, an important and often overlooked metric of cartilage development, increase with time in culture in engineered hydrogel-based cartilage constructs. Under the free-swelling conditions employed in the present study, tensile moduli and toughness did not match that of the native tissue, though significant time-dependent increases were observed with the inclusion of TGF-beta3. Of note, MSC-seeded constructs achieved tensile properties that were comparable to chondrocyte-seeded constructs, confirming the utility of this alternative cell source in cartilage tissue engineering. Further work, including both modulation of the chemical and mechanical culture environment, is required to optimize the deposition of collagen and its remodeling to achieve tensile properties in engineered constructs matching the native tissue.

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.

Importance of collagen orientation and depth-dependent fixed charge densities of cartilage on mechanical behavior of chondrocytes

The collagen network and proteoglycan matrix of articular cartilage are thought to play an important role in controlling the stresses and strains in and around chondrocytes, in regulating the biosynthesis of the solid matrix, and consequently in maintaining the health of diarthrodial joints. Understanding the detailed effects of the mechanical environment of chondrocytes on cell behavior is therefore essential for the study of the development, adaptation, and degeneration of articular cartilage. Recent progress in macroscopic models has improved our understanding of depth-dependent properties of cartilage. However, none of the previous works considered the effect of realistic collagen orientation or depth-dependent negative charges in microscopic models of chondrocyte mechanics. The aim of this study was to investigate the effects of the collagen network and fixed charge densities of cartilage on the mechanical environment of the chondrocytes in a depth-dependent manner. We developed an anisotropic, inhomogeneous, microstructural fibril-reinforced finite element model of articular cartilage for application in unconfined compression. The model consisted of the extracellular matrix and chondrocytes located in the superficial, middle, and deep zones. Chondrocytes were surrounded by a pericellular matrix and were assumed spherical prior to tissue swelling and load application. Material properties of the chondrocytes, pericellular matrix, and extracellular matrix were obtained from the literature. The loading protocol included a free swelling step followed by a stress-relaxation step. Results from traditional isotropic and transversely isotropic biphasic models were used for comparison with predictions from the current model. In the superficial zone, cell shapes changed from rounded to elliptic after free swelling. The stresses and strains as well as fluid flow in cells were greatly affected by the modulus of the collagen network. The fixed charge density of the chondrocytes, pericellular matrix, and extracellular matrix primarily affected the aspect ratios (height/width) and the solid matrix stresses of cells. The mechanical responses of the cells were strongly location and time dependent. The current model highlights that the collagen orientation and the depth-dependent negative fixed charge densities of articular cartilage have a great effect in modulating the mechanical environment in the vicinity of chondrocytes, and it provides an important improvement over earlier models in describing the possible pathways from loading of articular cartilage to the mechanical and biological responses of chondrocytes.

Remodeling of engineered tissue anisotropy in response to altered loading conditions

Structural and mechanical anisotropy are critical to the function of many engineered tissues. This study examined the ability of anisotropic tissue constructs to overcome contact guidance cues and remodel in response to altered mechanical loading conditions. Square tissues engineered from dermal fibroblasts and type-I collagen were uniaxially loaded to induce cell and matrix alignment. After an initial time, t*, of 5-72 h, loading was switched from the x-axis to the y-axis. Cell alignment was examined throughout the experiment until a steady state was reached. Before t*, cells spontaneously aligned in the x-direction. After t*, the strength of alignment transiently decreased then increased, and mean cell orientation transitioned from the x- to the y-direction following an exponential time course with a time constant that increased with t*. Collagen fiber orientation exhibited similar trends that could not be explained by passive kinematics alone. Structural realignment resulted in concomitant changes in biaxial tissue mechanical properties. The findings suggest that even highly aligned engineered tissue constructs retain the capacity to remodel in response to altered mechanical stimuli. This may have important functional consequences when an anisotropic engineered tissue designed in vitro is surgically implanted into a mechanically complex graft site.