Ultrasound indentation of bovine knee articular cartilage in situ

We have earlier developed a handheld ultrasound indentation instrument for the diagnosis of articular cartilage degeneration. In ultrasound indentation, cartilage is compressed with the ultrasound transducer. Tissue thickness and deformation are calculated from the A-mode ultrasound signal and the stress applied is registered with the strain gauges. In this study, the applicability of the ultrasound indentation instrument to quantify site-dependent variation in the mechano-acoustic properties of bovine knee cartilage was investigated. Osteochondral blocks (n=6 per site) were prepared from the femoral medial condyle (FMC), the lateral facet of the patello-femoral groove (LPG) and the medial tibial plateau (MTP). Cartilage stiffness (dynamic modulus, E(dyn)), as obtained with the ultrasound indentation instrument in situ, correlated highly linearly (r=0.913, p<0.01) with the values obtained using the reference material-testing device in vitro. Reproducibility (standardized coefficient of variation) of the ultrasound indentation measurements was 5.2%, 1.7% and 3.1% for E(dyn), ultrasound reflection coefficient of articular surface (R) and thickness, respectively. E(dyn) and R were site dependent (p<0.05, Kruskall-Wallis H test). E(dyn) was significantly higher (p<0.05, Kruskall-Wallis Post Hoc test) in LPG (mean+/-SD: 10.1+/-3.1MPa) than in MTP (2.9+/-1.4MPa). In FMC, E(dyn) was 4.6+/-1.3MPa. R was significantly (p<0.05) lower at MTP (2.0+/-0.7%) than at other sites (FMC: 4.2+/-0.9%; LPG: 4.4+/-0.8%). Cartilage glycosaminoglycan concentration, as quantified with the digital densitometry, correlated positively with E(dyn) (r=0.678, p<0.01) and especially with the equilibrium Young's modulus (reference device, r=0.874, p<0.01) but it was not associated with R (r=0.294, p=0.24). We conclude that manual measurements are reproducible and the instrument may be used for detection of cartilage quality in situ. Especially, combined measurement of thickness, E(dyn) and R provides valuable diagnostic information on cartilage status.     

Measuring fixed charge density of goat articular cartilage using indentation methods and biochemical analysis

An important indicator of osteoarthritis (OA) progression is the loss of proteoglycan (PG) aggregates from the cartilage tissue. Using the indentation creep test, two analytical methods, as previously developed by Lu et al. [Lu, X. L., Miller, C., Chen, F. H., Guo, X. E., Mow, V. C., 2007. The generalized triphasic correspondence principle for simultaneous determination of the mechanical properties and proteoglycan content of articular cartilage by indentation. Journal of Biomechanics 40, 2434-2441 (EPub).], for predicting the fixed charge density (FCD) of goat knee articular cartilage in the normal (control) and degenerated states were compared: (1) a "dual-stage" method to calculate FCD from the mechanical properties of the tissue when tested in isotonic and hypertonic solutions; and (2) a "single-stage" method to predict FCD (as in (1)) assuming an intrinsic Poisson's ratio of 0.05 in the hypertonic state. A biochemical analysis using 1,9-dimethylmethylene blue (DMMB) assay was conducted to directly measure PG content, and hence FCD. The association between the FCD and the aggregate modulus of the tissue was also explored. The mean (+/-S.D.) FCD values measured using the dual-stage method were the closest (control: 0.129+/-0.039, degenerated: 0.046+/-029) to the DMMB results (control: 0.125+/-0.034, degenerated: 0.057+/-0.024) as compared to those of the single-stage method (control: 0.147+/-0.035, degenerated: 0.063+/-0.026). The single-stage method was more reliable (r(2)=0.81) when compared to the dual-stage method (r(2)=0.79). A prediction of FCD from the aggregate modulus generated the least reliable FCD prediction (r(2)=0.68). Because both the dual- and single-stage methods provided reliable FCD estimates for normal and degenerated tissue, the less time-consuming single-stage method was concluded to be the ideal technique for predicting FCD and hence PG content of the tissue.     

A comparison of healthy human and swine articular cartilage dynamic indentation mechanics

Articular cartilage is a multicomponent, poroviscoelastic tissue with nonlinear mechanical properties vital to its function. A consequent goal of repair or replacement of injured cartilage is to achieve mechanical properties in the repair tissue similar to healthy native cartilage. Since fresh healthy human articular cartilage (HC) is not readily available, we tested whether swine cartilage (SC) could serve as a suitable substitute for mechanical comparisons. To a first approximation, cartilage tissue and surgical substitutes can be evaluated mechanically as viscoelastic materials. Stiffness measurements (dynamic modulus, loss angle) are vital to function and are also a non-destructive means of evaluation. Since viscoelastic material stiffness is strongly strain rate dependent, stiffness was tested under different loading conditions related to function. Stiffness of healthy HC and SC specimens was determined and compared using two non-destructive, mm-scale indentation test modes: fast impact and slow sinusoidal deformation. Deformation resistance (dynamic modulus) and energy handling (loss angle) were determined. For equivalent anatomic locations, there was no difference in dynamic modulus. However, the HC loss angle was ~35% lower in fast impact and ~12% higher in slow sinusoidal mode. Differences seem attributable to age (young SC, older HC) but also to species anatomy and biology. Test mode-related differences in human-swine loss angle support use of multiple function-related test modes. Keeping loss angle differences in mind, swine specimens could serve as a standard of comparison for mechanical evaluation of e.g. engineered cartilage or synthetic repair materials.     

Direct measurement of the Poisson's ratio of human patella cartilage in tension

Articular cartilage has been shown to exhibit large transverse contractions when loaded in tension, suggesting the existence of large values for the Poisson's ratio. Previous studies have suggested that this effect is dependent on amplitude of applied strain, so that a single Poisson's ratio may not be sufficient to describe cartilage behavior. In this study, the Poisson's ratio (v), toe region modulus (Eo), and linear region modulus (E) of human patellar articular cartilage were calculated in simple tension tests from optical analysis of the two-dimensional strain fields at equilibrium. The Poisson's ratio was found to be independent of strain due to the absence of viscoelastic effects during testing. The Poisson's ratio was found to be significantly higher in the surface zone (1.87 +/- 1.11, p<0.01) than in the middle zone (0.62 +/- 0.23), with no significant correlation of v with age of the cartilage. In general, values for Poisson's ratio were greater than 0.5, suggesting cartilage behavior in tension deviates from isotropy. Reported values for the Poisson's ratio of cartilage in compression have been much lower than values measured here in tension, reflecting a mechanical contribution of the collagen fibers to anisotropy in tension but not compression. The toe-region modulus (Eo) was significantly higher in the surface zone (4.51 +/- 2.78 MPa, n=8) compared to the middle zone (2.51 +/- 1.93 MPa, n=10). In addition, the linear-region modulus (E) in the surface zone, but not middle zone (3.42 +/- 2.17 MPa, n=10), was found to correlate with age (R=0.97, p<0.02) with values of surface zone E equal to 23.92 +/- 12.29 MPa (n=5) for subjects under 70 yr of age, and 4.27 +/- 2.89 MPa (n=3) for subjects over 70 yr. Moduli values and trends with depth were consistent with previous studies of human and animal cartilage. From direct measures of two independent material properties, v and E, we calculated a shear modulus, G, which had not been previously reported for cartilage from tensile testing. Calculated values for surface zone G were 3.64 +/- 1.80 MPa for subjects under 70 yr old and 0.96 +/- 0.69 MPa for subjects over 70 yr old, and were significantly higher in the surface zone than in the middle zone (1.10 +/- 0.78 MPa). This study provides an intrinsic measure for the Poisson's ratio of articular cartilage and its dependence on depth which will be important in understanding the nonlinear tension-compression and anisotropic behaviors of articular cartilage.     

Influence of aspect ratios on the creep behaviour of articular cartilage in indentation

Indentation tests are commonly used to determine the mechanical behaviour of articular cartilage with varying properties, thickness, and geometry. This investigation evaluated the effect of changing geometric parameters on the properties determined from creep indentation tests. Finite element analyses simulated the indentation behaviour of two models, an excised cylindrical specimen of cartilage with either normal and repair qualities and an osteochondral defect represented as a cylindrical region of repair cartilage integrated with a surrounding layer of normal tissue. For each model, the ratios of indenter radius to cartilage height (a/h=0.5,1.5) and cartilage radius to indenter radius (r/a=2,5) were varied. The vertical displacement of the cartilage under the indenter obtained through finite element analysis was fitted to a numerical algorithm to determine the aggregate modulus, permeability, and Poisson's ratio. Indentation behaviours of cartilage specimens for either model with a/h=1.5 were not affected by r/a for values of 2 and 5. Aggregate modulus was not greatly affected by the geometric changes studied. Permeability was affected by changes in the ratio of specimen to indenter radii for a/h=0.5. These findings suggest that experimental configurations of excised cylindrical specimens, also representing osteochondral defects with no or unknown degree of integration, where the cartilage layer has a/h=0.5 should not have r/a values on the order of 2 for confidence in the mechanical properties determined. Indentation of osteochondral defects where the repair cartilage is fully integrated to the surrounding cartilage can be performed with confidence for all cases tested.     

Estimation of the Young's modulus of articular cartilage using an arthroscopic indentation instrument and ultrasonic measurement of tissue thickness

We evaluated whether the use of cartilage thickness measurement would improve the ability of the arthroscopic indentation technique to estimate the intrinsic stiffness of articular cartilage. First, cartilage thickness and ultrasound reflection from the surface of bovine humeral head were registered in situ using a high-frequency ultrasound probe. Subsequently, cartilage was indented in situ at the sites of the ultrasound measurements using arthroscopic instruments with plane-ended and spherical-ended indenters. Finally, full-thickness cartilage disks (n=30) were extracted from the indented sites (thickness=799-1654microm) and the equilibrium Young's modulus was determined with a material testing device in unconfined compression geometry. We applied analytical and numerical indentation models for the theoretical correction of experimental indentation measurements. An aspect-ratio (the ratio of indenter radius to cartilage thickness) correction improved the correlation of the indenter force with the equilibrium Young's modulus from r(2)=0.488 to r(2)=0.642-0.648 (n=30) for the plane-ended indenter (diameter=1.000mm, height=0.300mm) and from r(2)=0.654 to r(2)=0.684-0.692 (n=30) for the spherical-ended indenter (diameter=0.500mm, height=0.100mm), depending on the indentation model used for the correction. The linear correlation between the ultrasound reflection and the Young's modulus was r(2)=0.400 (n=30). These results suggest that with large indenters, knowledge of the cartilage thickness improves the reliability of the indentation measurements, especially in pathological situations where cartilage thickness may be significantly lower than normal. Ultrasound measurements also provide diagnostically important information about cartilage thickness as well as knowledge of the integrity of the superficial zone of cartilage.     

Comparison of single-phase isotropic elastic and fibril-reinforced poroelastic models for indentation of rabbit articular cartilage

Classically, single-phase isotropic elastic (IE) model has been used for in situ or in vivo indentation analysis of articular cartilage. The model significantly simplifies cartilage structure and properties. In this study, we apply a fibril-reinforced poroelastic (FRPE) model for indentation to extract more detailed information on cartilage properties. Specifically, we compare the information from short-term (instantaneous) and long-term (equilibrium) indentations, as described here by IE and FRPE models. Femoral and tibial cartilage from rabbit (age 0–18 months) knees (n=14) were tested using a plane-ended indenter (diameter=0.544 mm). Stepwise creep tests were conducted to equilibrium. Single-phase IE solution for indentation was used to derive instantaneous modulus and equilibrium (Young's) modulus for the samples. The classical and modified Hayes’ solutions were used to derive values for the indentation moduli. In the FRPE model, the indentation behavior was sample-specifically described with three material parameters, i.e. fibril network modulus, non-fibrillar matrix modulus and permeability. The instantaneous and fibril network modulus, and the equilibrium Young's modulus and non-fibrillar matrix modulus showed significant (p<0.01) linear correlations of R²=0.516 and 0.940, respectively (Hayes’ solution) and R²=0.531 and 0.960, respectively (the modified Hayes’ solution). No significant correlations were found between the non-fibrillar matrix modulus and instantaneous moduli or between the fibril network modulus and the equilibrium moduli. These results indicate that the instantaneous indentation modulus (IE model) provides information on tensile stiffness of collagen fibrils in cartilage while the equilibrium modulus (IE model) is a significant measure for stiffness of PG matrix. Thereby, this study highlights the feasibility of a simple indentation analysis.     

A finite element analysis of the indentation stress-relaxation response of linear biphasic articular cartilage.

The indentation problem of a thin layer of hydrated soft tissue such as cartilage or meniscus by a circular plane-ended indenter is investigated. The tissue is represented by a biphasic continuum model consisting of a solid phase (collagen and proteoglycan) and a fluid phase (interstitial water). A finite element formulation of the linear biphasic continuum equations is used to solve an axisymmetric approximation of the indentation problem. We consider stress-relaxation problems for which analytic solution is intractable; where the indenter is impermeable (solid) and/or when the interface between the indenter and tissue is perfectly adhesive. Thicknesses corresponding to a thin and thick specimen are considered to examine the effects of tissue thickness. The different flow, pressure, stress and strain fields which are predicted within the tissue, over time periods typically used in the mechanical testing of soft tissues, will be presented. Results are compared with the case of a porous free-draining indenter with a perfectly lubricated tissue-indenter interface, for which an analytic solution is available, to show the effects of friction at the tissue-indenter interface, and the effects of an impermeable indenter. While these effects are present for both thin and thick tissues, they are shown to be more significant for the thin tissue. We also examine the effects of the stiffness of the subchondral bone on the response of the soft tissue and demonstrate that the subchondral bone substrate can be modeled as a rigid, impermeable boundary. The effects of a curved tissue-subchondral bone interface, and the early time response are also studied. For physiologically reasonable levels of curvature, we will show that the curved tissue-subchrondal bone interface has negligible influence on the tissue response away from the interface. In addition, the short-time stress-relaxation responses of the tissue (e.g., at times less than 1s) demonstrate the essential role of the fluid phase in supporting the load applied to the tissue, and by extrapolation to shorter times characteristics of normal joint motion, suggest the essential role of a biphasic model in representing soft tissue behavior in joint response.     

Comparison of the equilibrium response of articular cartilage in unconfined compression,confined compression and indentation

At mechanical equilibrium, articular cartilage is usually characterized as an isotropic elastic material with no interstitial fluid flow. In this study, the equilibrium properties (Young's modulus, aggregate modulus and Poisson's ratio) of bovine humeral, patellar and femoral cartilage specimens (n=26) were investigated using unconfined compression, confined compression, and indentation tests. Optical measurements of the Poisson's ratio of cartilage were also carried out. Mean values of the Young's modulus (assessed from the unconfined compression test) were 0.80+/-0.33, 0.57+/-0.17 and 0.31+/-0.18MPa and of the Poisson's ratio (assessed from the optical test) 0.15+/-0.06, 0.16+/-0.05 and 0.21+/-0.05 for humeral, patellar, and femoral cartilages, respectively. The indentation tests showed 30-79% (p<0.01) higher Young's modulus values than the unconfined compression tests. In indentation, values of the Young's modulus were independent of the indenter diameter only in the humeral cartilage. The mean values of the Poisson's ratio, obtained indirectly using the mathematical relation between the Young's modulus and the aggregate modulus in isotropic material, were 0.16+/-0.06, 0.21+/-0.05, and 0.26+/-0.08 for humeral, patellar, and femoral cartilages, respectively. We conclude that the values of the elastic parameters of the cartilage are dependent on the measurement technique in use. Based on the similar values of Poisson's ratios, as determined directly or indirectly, the equilibrium response of articular cartilage under unconfined and confined compression is satisfactorily described by the isotropic elastic model. However, values of the isotropic Young's modulus obtained from the in situ indentation tests are higher than those obtained from the in vitro unconfined or confined compression tests and may depend on the indenter size in use.     

The generalized triphasic correspondence principle for simultaneous determination of the mechanical properties and proteoglycan content of articular cartilage by indentation

The triphasic mixture theory has been used to describe the mechanical and physicochemical behaviors of articular cartilage under some specialized loading conditions. However, the mathematical complexities of this theory have limited its applications for theoretical analyses of experimental studies and models for predicting cartilage and other biological tissues' deformational behaviors. A generalized correspondence principle has been established in the present study, and this principle shows that the equilibrium deformational behavior of a charged-hydrated material under loading is identical to that of an elastic medium without charge. A set of explicit formulas has been derived to correlate the mechanical properties of an equivalent material with the intrinsic elastic moduli, fixed charge density and free-ion concentration within the cartilage tissue. The validity of these formulas is independent of the deformation state of the elastic solid matrix under an infinitesimal strain. Therefore they can be employed for any loading conditions, such as confined or unconfined compression, tension, and indentation tests, etc. In the current study, the fixed charge density of bovine cartilage is determined from the indentation creep data using this generalized correspondence principle. The proteoglycan content results were then compared with those from biochemical assay, yielding a linear regression slope of 1.034. Additionally a correspondence principle within a framework of cubic symmetry and a bilinear response in tension-compression (the conewise linear elasticity model) has also been developed to demonstrate the potential application of current methodology for inhomogeneous, anisotropic and nonlinear situations.     

Lubrication mode analysis of articular cartilage using Stribeck surfaces

Lubrication of articular cartilage occurs in distinct modes with various structural and biomolecular mechanisms contributing to the low-friction properties of natural joints. In order to elucidate relative contributions of these factors in normal and diseased tissues, determination and control of lubrication mode must occur. The objectives of these studies were (1) to develop an in vitro cartilage on glass test system to measure friction coefficient, mu; (2) to implement and extend a framework for the determination of cartilage lubrication modes; and (3) to determine the effects of synovial fluid on mu and lubrication mode transitions. Patellofemoral groove cartilage was linearly oscillated against glass under varying magnitudes of compressive strain utilizing phosphate buffered saline (PBS) and equine and bovine synovial fluid as lubricants. The time-dependent frictional properties were measured to determine the lubricant type and strain magnitude dependence for the initial friction coefficient (mu(0)=mu(t-->0)) and equilibrium friction coefficient (mu(eq)=mu(t-->infinity)). Parameters including tissue-glass co-planarity, normal strain, and surface speed were altered to determine the effect of the parameters on lubrication mode via a 'Stribeck surface'. Using this testing apparatus, cartilage exhibited biphasic lubrication with significant influence of strain magnitude on mu(0) and minimal influence on mu(eq), consistent with hydrostatic pressurization as reported by others. Lubrication analysis using 'Stribeck surfaces' demonstrated clear regions of boundary and mixed modes, but hydrodynamic or full film lubrication was not observed even at the highest speed (50mm/s) and lowest strain (5%).     

A linearized formulation of triphasic mixture theory for articular cartilage,and its application to indentation analysis

The negative charges on proteoglycans significantly affect the mechanical behaviors of articular cartilage. Mixture theories, such as the triphasic theory, can describe quantitatively how this charged nature contributes to the mechano-electrochemical behaviors of such tissue. However, the mathematical complexity of the theory has hindered its application to complicated loading profiles, e.g., indentation or other multi-dimensional configurations. In this study, the governing equations of triphasic mixture theory for soft tissue were linearized and dramatically simplified by using a regular perturbation method and the use of two potential functions. We showed that this new formulation can be used for any axisymmetric problem, such as confined or unconfined compressions, hydraulic perfusion, and indentation. A finite difference numerical program was further developed to calculate the deformational, electrical, and flow behaviors inside the articular cartilage under indentation. The calculated tissue response was highly consistent with the data from indentation experiments (our own and those reported in the literature). It was found that the charged nature of proteoglycans can increase the apparent stiffness of the solid matrix and lessen the viscous effect introduced by fluid flow. The effects of geometric and physical properties of indenter tip, cartilage thickness, and that of the electro-chemical properties of cartilage on the resulting deformation and fluid pressure fields across the tissue were also investigated and presented. These results have implications for studying chondrocyte mechanotransduction in different cartilage zones and for tissue engineering designs or in vivo cartilage repair.     

Collagen of articular cartilage

The extracellular framework and two-thirds of the dry mass of adult articular cartilage are polymeric collagen. Type II collagen is the principal molecular component in mammals, but collagens III, VI, IX, X, XI, XII and XIV all contribute to the mature matrix. In developing cartilage, the core fibrillar network is a cross-linked copolymer of collagens II, IX and XI. The functions of collagens IX and XI in this heteropolymer are not yet fully defined but, evidently, they are critically important since mutations in COLIX and COLXI genes result in chondrodysplasia phenotypes that feature precocious osteoarthritis. Collagens XII and XIV are thought also to be bound to fibril surfaces but not covalently attached. Collagen VI polymerizes into its own type of filamentous network that has multiple adhesion domains for cells and other matrix components. Collagen X is normally restricted to the thin layer of calcified cartilage that interfaces articular cartilage with bone.     

Indentation testing of human articular cartilage: effects of probe tip geometry and indentation depth on intra-tissue strain

Experimental determination of intra-tissue deformation during clinically applicable rapid indentation testing would be useful for understanding indentation biomechanics and for designing safe indentation probes and protocols. The objectives of this study were to perform two-dimensional (2-D) indentation tests, using indenters and protocols that are analogous to those in clinically oriented probes, of normal adult-human articular cartilage in order to determine: (1) intra-tissue strain maps and regions of high strain magnitude, and (2) the effects on strain of indenter geometry (rectangular prismatic and cylindrical) and indentation depth (40-190 microm). Epifluorescence microscopy of samples undergoing indentation and subsequent video image correlation analysis allowed determination of strain maps. Regions of peak strain were near the "edges" of indenter contact with the cartilage surface, and the strain magnitude in these regions ranged from approximately 0.05 to approximately 0.30 in compression and shear, a range with known biological consequences. With increasing indentation displacement, strain magnitudes generally increased in all regions of the tissue. Compared to indentation using a rectangular prismatic tip, indentation with a cylindrical tip resulted in slightly higher peak strain magnitudes while influencing a smaller region of cartilage. These results may be used to refine clinical indenters and indentation protocols.     

Measurement of diffusion in articular cartilage using fluorescence correlation spectroscopy

Background  

Fluorescence correlation spectroscopy (FCS) provides information about translational diffusion of fluorescent molecules in tiny detection volumes at the single-molecule level. In normal states, cartilage tissue lacks vascularity, so chondrocyte metabolism depends on diffusion for molecular exchanges. The abundant extracellular matrix (ECM) of cartilage is maintained by a limited number of chondrocytes. ECM plays an important role in the regulation of chondrocyte functions. In this study, FCS was used to measure diffusion behaviors of albumin, the major protein of the intra-articular space, using normal and degenerated cartilage. Preliminary investigation of fluorescence dyes including Alexa 488, Rhodamine 6G and Rhodamine 123 was conducted to evaluate their properties in cartilage.     

Thrombospondin is present in articular cartilage and is synthesized by articular chondrocytes

Thrombospondin, a multifunctional adhesive glycoprotein originally identified in platelets, was isolated and identified from an extract of ovine articular cartilage. Immunoreactive material from a cartilage extract comigrated on gel electrophoresis with purified human platelet thrombospondin. When articular chondrocytes were cultured in the presence of 35S-methionine, metabolically labeled thrombospondin was immunoprecipitated from the culture medium and cell layer extract. These results demonstrate that thrombospondin is present in articular cartilage and is synthesized by articular chondrocytes.