Unconfined compression of articular cartilage: nonlinear behavior and comparison with a fibril-reinforced biphasic model

Nonlinear tensile properties of bovine articular cartilage and their variation with age and depth

Tensile stiffness of articular cartilage is much greater than its compressive stiffness and plays an essential role even in compressive properties by increasing transient fluid pressures during physiological loading. Recent studies of nonlinear properties of articular cartilage in compression revealed several physiologically pertinent nonlinear behaviors, all of which required that cartilage tensile stiffness increase significantly with stretch. We therefore performed sequences of uniaxial tension tests on fresh bovine articular cartilage slices using a protocol that allowed several hours to attain equilibrium and measured longitudinal and transverse tissue strain. By testing bovine cartilage from different ages (6 months to 6 years) we found that equilibrium and transient tensile modulus increased significantly with maturation and age, from 0 to 15 MPa at equilibrium and from 10 to 28 MPa transiently. Our results indicate that cartilage stiffens with age in a manner similar to other highly hydrated connective tissues, possibly due to age-dependent content of enzymatic and nonenzymatic collagen cross links. The long relaxation period used in our tests (5-10 hours) was necessary in order to attain equilibrium and avoid a very significant overestimation of equilibrium modulus that occurs when much shorter times are used (15-30 minutes). We also found that equilibrium and transient tensile modulus increased nonlinearly when cartilage is stretched from 0 to 10% strain without any previous tare load. Although our results estimate a nonlinear increase in tensile stiffness with stretch that is an order of magnitude lower than that required to predict nonlinear properties in compression, they are in agreement with previous results from other uniaxial tension tests of collagenous materials. We therefore speculate that biaxial tensile moduli may be much higher and thereby more compatible with observed nonlinear compressive properties.

Methods for quasi-linear viscoelastic modeling of soft tissue: application to incremental stress-relaxation experiments

The quasi-linear viscoelastic (QLV) model was applied to incremental stress-relaxation tests and an expression for the stress was derived for each step. This expression was used to compare two methods for normalizing stress data prior to estimating QLV parameters. The first and commonly used normalization method was shown to be strain-dependent. Thus, a second normalization method was proposed and shown to be strain-independent and more sensitive to QLV time constants. These analytical results agreed with representative tendon data. Therefore, this method for normalizing stress data was proposed for future studies of incremental stress-relaxation, or whenever comparing stress-relaxation at different strains.

Effect of fiber orientation and strain rate on the nonlinear uniaxial tensile material properties of tendon

Tendons are exposed to complex loading scenarios that can only be quantified by mathematical models, requiring a full knowledge of tendon mechanical properties. This study measured the anisotropic, nonlinear, elastic material properties of tendon. Previous studies have primarily used constant strain-rate tensile tests to determine elastic modulus in the fiber direction. Data for Poisson's ratio aligned with the fiber direction and all material properties transverse to the fiber direction are sparse. Additionally, it is not known whether quasi-static constant strain-rate tests represent equilibrium elastic tissue behavior. Incremental stress-relaxation and constant strain-rate tensile tests were performed on sheep flexor tendon samples aligned with the tendon fiber direction or transverse to the fiber direction to determine the anisotropic properties of toe-region modulus (E0), linear-region modulus (E), and Poisson's ratio (v). Among the modulus values calculated, only fiber-aligned linear-region modulus (E1) was found to be strain-rate dependent. The E1 calculated from the constant strain-rate tests were significantly greater than the value calculated from incremental stress-relaxation testing. Fiber-aligned toe-region modulus (E(1)0 = 10.5 +/- 4.7 MPa) and linear-region modulus (E1 = 34.0 +/- 15.5 MPa) were consistently 2 orders of magnitude greater than transverse moduli (E(2)0 = 0.055 +/- 0.044 MPa, E2 = 0.157 +/- 0.154 MPa). Poisson's ratio values were not found to be rate-dependent in either the fiber-aligned (v12 = 2.98 +/- 2.59, n = 24) or transverse (v21 = 0.488 +/- 0.653, n = 22) directions, and average Poisson's ratio values in the fiber-aligned direction were six times greater than in the transverse direction. The lack of strain-rate dependence of transverse properties demonstrates that slow constant strain-rate tests represent elastic properties in the transverse direction. However, the strain-rate dependence demonstrated by the fiber-aligned linear-region modulus suggests that incremental stress-relaxation tests are necessary to determine the equilibrium elastic properties of tendon, and may be more appropriate for determining the properties to be used in elastic mathematical models.

Tensile mechanical properties of bovine articular cartilage: variations with growth and relationships to collagen network components

One approach to repairing articular defects is to regenerate cartilage by recapitulating the changes that occur during fetal and postnatal growth into adulthood, and to thereby restore functional biomechanical properties, especially those of the normally strong superficial region. The objectives of this study were (1) to characterize and compare tensile biomechanical properties of the superficial region of articular cartilage of the patellofemoral groove (PFG) and femoral condyle (FC) from bovine animals over a range of growth stages (third-trimester fetal, 1-3 week-old calf, and adult), and (2) to determine if these properties were correlated with collagen network components. With growth from the fetus to the adult, the equilibrium and dynamic tensile moduli and strength of cartilage samples increased by an average of 391-1060%, while the strain at the failure decreased by 43%. The collagen concentration (per wet weight) increased by 98%, and the pyridinoline cross-link concentration increased by 730%, while the glycosaminoglycan concentration remained unchanged or decreased slightly. Some growth-associated changes were location-specific, with tensile moduli and strength attaining higher values in the PFG than the FC. The growth-associated variation in tensile moduli and strength were associated strongly with variation in the contents of collagen and pyridinoline cross-link, but not sulfated glycosaminoglycan. The marked changes in the tensile properties and collagen network components of articular cartilage with growth suggest that such parameters may be used to evaluate the degrees to which regenerated cartilage recapitulates normal development and growth.

Increasing strain and strain rate strengthen transient stiffness but weaken the response to subsequent compression for articular cartilage in unconfined compression

Strain amplitude and strain rate dependent nonlinear behavior and load-induced mechanical property alterations of full-thickness bovine articular cartilage attached to bone were investigated in unconfined compression. A sequence of test compressions of finite deformation (ranging from 0.9% to 34.5% nominal strain) was performed at strain rates ranging from approximately 0.053%/s to 5.8%/s. Peak and equilibrium loads were analyzed to determine strain amplitude and strain rate dependence of linear versus nonlinear responses. The test protocol was designed to reveal changes in mechanical properties due to these finite deformations by interspersing small-amplitude witness ramps of approximately 1.1% deformation and approximately 0.44%/s strain rate between the test ramps ("witness" meaning to assess any mechanical property changes). We found that peak loads displayed high nonlinearity, stiffening with both increasing compression amplitude and more so with increasing strain rate. The response to witness ramps suggested that mechanical weakening occurred when compression amplitude reached 1.9-2.9% strain and beyond, and that weakening was much more significant at higher strain rate. These findings delineate regimes of linear versus nonlinear behavior of cartilage, and indicate the types of loads which can cause mechanical property alterations. Biological implications of this study are that strain amplitude and strain rate dependent stiffening may be essential to bear physiological loads and to protect cells and matrix from mechanical damage. Structural changes reflected by mechanical weakening at small compression could also initiate remodeling or disease processes.

Experimental verification of the roles of intrinsic matrix viscoelasticity and tension-compression nonlinearity in the biphasic response of cartilage

A biphasic-CLE-QLV model proposed in our recent study [2001, J. Biomech. Eng., 123, pp. 410-417] extended the biphasic theory of Mow et al. [1980, J. Biomech. Eng., 102, pp. 73-84] to include both tension-compression nonlinearity and intrinsic viscoelasticity of the cartilage solid matrix by incorporating it with the conewise linear elasticity (CLE) model [1995, J. Elasticity, 37, pp. 1-38] and the quasi-linear viscoelasticity (QLV) model [Biomechanics: Its foundations and objectives, Prentice Hall, Englewood Cliffs, 1972]. This model demonstrates that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelastic effects, as well as tension-compression nonlinearity. The objective of this study is to directly test this biphasic-CLE-QLV model against experimental data from unconfined compression stress-relaxation tests at slow and fast strain rates as well as dynamic loading. Twelve full-thickness cartilage cylindrical plugs were harvested from six bovine glenohumeral joints and multiple confined and unconfined compression stress-relaxation tests were performed on each specimen. The material properties of specimens were determined by curve-fitting the experimental results from the confined and unconfined compression stress relaxation tests. The findings of this study demonstrate that the biphasic-CLE-QLV model is able to describe the strain-rate-dependent mechanical behaviors of articular cartilage in unconfined compression as attested by good agreements between experimental and theoretical curvefits (r2 = 0.966 +/- 0.032 for testing at slow strain rate; r2 = 0.998 +/- 0.002 for testing at fast strain rate) and predictions of the dynamic response (r2 = 0.91 +/- 0.06). This experimental study also provides supporting evidence for the hypothesis that both tension-compression nonlinearity and intrinsic viscoelasticity of the solid matrix of cartilage are necessary for modeling the transient and equilibrium responses of this tissue in tension and compression. Furthermore, the biphasic-CLE-QLV model can produce better predictions of the dynamic modulus of cartilage in unconfined dynamic compression than the biphasic-CLE and biphasic poroviscoelastic models, indicating that intrinsic viscoelasticity and tension-compression nonlinearity of articular cartilage may play important roles in the load-support mechanism of cartilage under physiologic loading.

Immunochemical and mechanical characterization of cartilage subtypes in rabbit

Cartilage is categorized into three general subgroups, hyaline, elastic, and fibrocartilage, based primarily on morphologic criteria and secondarily on collagen (Types I and II) and elastin content. To more precisely define the different cartilage subtypes, rabbit cartilage isolated from joint, nose, auricle, epiglottis, and meniscus was characterized by immunohistochemical (IHC) localization of elastin and of collagen Types I, II, V, VI, and X, by biochemical analysis of total glycosaminoglycan (GAG) content, and by biomechanical indentation assay. Toluidine blue staining and safranin-O staining were used for morphological assessment of the cartilage subtypes. IHC staining of the cartilage samples showed a characteristic pattern of staining for the collagen antibodies that varied in both location and intensity. Auricular cartilage is discriminated from other subtypes by interterritorial elastin staining and no staining for Type VI collagen. Epiglottal cartilage is characterized by positive elastin staining and intense staining for Type VI collagen. The unique pattern for nasal cartilage is intense staining for Type V collagen and collagen X, whereas articular cartilage is negative for elastin (interterritorially) and only weakly positive for collagen Types V and VI. Meniscal cartilage shows the greatest intensity of staining for Type I collagen, weak staining for collagens V and VI, and no staining with antibody to collagen Type X. Matching cartilage samples were categorized by total GAG content, which showed increasing total GAG content from elastic cartilage (auricle, epiglottis) to fibrocartilage (meniscus) to hyaline cartilage (nose, knee joint). Analysis of aggregate modulus showed nasal and auricular cartilage to have the greatest stiffness, epiglottal and meniscal tissue the lowest, and articular cartilage intermediate. This study illustrates the differences and identifies unique characteristics of the different cartilage subtypes in rabbits. The results provide a baseline of data for generating and evaluating engineered repair cartilage tissue synthesized in vitro or for post-implantation analysis.

Detection and analysis of cartilage degeneration by spatially resolved streaming potentials

Cartilage molecular changes in osteoarthritis are most commonly related to the degradation and loss of proteoglycan and collagen fibrils of the extracellular matrix, which directly influence tissue stiffness and compression-generated streaming potentials. In this study, we evaluated the potential of a new technique, spatially resolved mapping of streaming potentials, to non-destructively indicate cartilage health or degeneration. Matched pairs of bovine cartilage/bone explant disks were cultured for 11 days in a serum free medium with and without interleukin-lalpha (IL-1alpha). The electromechanical properties (static stiffness, dynamic stiffness and streaming potentials) of cartilage disks were measured during unconfined compression using a mechanical tester coupled with a linear array of eight 50 microm diameter platinum-iridium microelectrodes. After 11 days of culture, the proteoglycan content of IL-1alpha treated disks was significantly reduced and the denatured and cleaved collagen content was increased compared to control disks. These biochemical alterations were concomitant with the reductions in the amplitudes of the static stiffness, the dynamic stiffness and the streaming potential profile as well as changes in the shape of the streaming potential profile. We found that spatial mapping of streaming potentials presents several advantages for the development of a clinical instrument to evaluate the degeneration of articular cartilage.

Experimental and biphasic FEM determinations of the material properties and hydraulic permeability of the meniscus in tension

Tensile tests and biphasic finite element modeling were used to determine a set of transversely isotropic properties for the meniscus, including the hydraulic permeability coefficients and solid matrix properties. Stress-relaxation tests were conducted on planar samples of canine meniscus samples of different orientations, and the solid matrix properties were determined from equilibrium data. A 3-D linear biphasic and tranversely isotropic finite element model was developed to model the stress-relaxation behavior of the samples in tension, and optimization was used to determine the permeability coefficients, k1 and k2, governing fluid flow parallel and perpendicular to the collagen fibers, respectively. The collagen fibrillar orientation was observed to have an effect on the Young's moduli (E1=67.8 MPa, E2=11.1 MPa) and Poisson's ratios (v12=2.13, v21 =1.50, v23=1.02). However, a significant effect of anisotropy on permeability was not detected (k1 =0.09x10(-16) m4/Ns, k2=0.10x10(-16) m4/Ns). The low permeability values determined in this study provide insight into the extent of fluid pressurization in the meniscus and will impact modeling predictions of load support in the meniscus.

Alterations in mechanical behaviour of articular cartilage due to changes in depth varying material properties--a nonhomogeneous poroelastic model study

The depth dependence of the material properties is present in normal adult cartilage and is believed to have significant implications in its normal mechanical function. Cartilage pathology may alter the depth dependence, e.g. a reduced depth dependence of the fibril stiffness has been observed in osteoarthritic cartilage. The objective of the present study is to investigate the alterations in the mechanical response of articular cartilage when the depth dependence of the material properties is varied to simulate healthy and pathological situations. This study is made possible by a recently developed nonhomogeneous poroelastic model. Depth variations of the strains and stresses for individual material phases (collagen, proteoglycan and fluid) are obtained for cartilage disks in unconfined compression using the finite element method. The mean nominal axial strain considered is up to 15%, while the axial strain at the articular surface can reach 33%. This paper demonstrates how the mechanical behaviours of cartilage are affected by individual depth dependent cartilage properties, while such observations are not fully available in experimental investigations. This study suggests the possibility of diagnosing cartilage health by analysing its mechanical behaviours.

Streaming potentials maps are spatially resolved indicators of amplitude, frequency and ionic strength dependant responses of articular cartilage to load

Streaming potential distributions were measured on the surface of articular cartilage in uniaxial unconfined compression using a linear array of microelectrodes. Potential profiles were obtained for sinusoidal and ramp/stress-relaxation displacements and exhibited dependencies on radial position, sinusoidal amplitude and frequency, time during stress relaxation, and on ionic strength. The measurements agreed with trends predicted by biphasic and related models. In particular, the absolute potential amplitude was maximal at the disk center, as was the predicted fluid pressure and the potential gradient (the electric field) was seen to be maximal at the disk periphery, as was the predicted fluid velocity. We also observed a similarity between non-linear behavior of streaming potential amplitude and load amplitude with respect to sinusoidal displacement amplitude. Taken together, these results support many of the phenomena concerning relative fluid-solid movement and fluid pressurization predicted by biphasic and related models, and they indicate the general utility of spatially resolved measurements of streaming potentials for the investigation of electromechanical phenomena in tissues. For example, these streaming potential maps could be used to non-destructively diagnose cartilage extracellular matrix composition and function, as well as to quantify spatially and temporally varying physical signals in cartilage that can induce cellular and extracellular biological responses to load.

Surface fissures in articular cartilage: new concepts, hypotheses and modeling

OBJECTIVE

Clarification and mesomechanical modeling of the inception of fissures at the surface of articular cartilage.

DESIGN

Articular cartilage is described as a macroscopically heterogeneous medium consisting of zones - layers - with different orientation of collagen fibers.

BACKGROUND

Degradation of mechanical properties of cartilage is a serious, still not fully clarified problem that deserves attention.

METHODS

Theoretical analysis based on a survey of known experimental findings related to the subject. The general author's mesomechanical concept of modeling heterogeneous media is applied to the elucidation and description of the formation of fissures at the surface of articular cartilage.

RESULTS

Our model clarifies how the high tensile stresses in the collagen fibers of the superficial tangential zone depend on the rate of loading.

CONCLUSIONS

The superficial cracks are caused predominantly by a very quick loading. This explains among others the high incidence of post-traumatic osteoarthritis of the lower extremity after accidents and injuries in sports.

RELEVANCE

Superficial fissures in articular cartilage are observed in joints with primary osteoarthritis. The current study specifies the kinds of loading that lead to their inception.

The asymmetry of transient response in compression versus release for cartilage in unconfined compression

Observations in compression tests of articular cartilage have revealed unequal load increments for compression and release of the same amplitude applied to a disk with an identical previously imposed compression (in equilibrium). The mechanism of this asymmetric transient response is investigated here using a nonlinear fibril-reinforced model. It is found that the asymmetry is predominantly produced by the fibril stiffening with its tensile strain. In addition, allowing the hydraulic permeability to decrease significantly with compressive dilatation of cartilage increases the transient fibril strain, resulting in a stronger asymmetry. Large deformation also enhances the asymmetry as a consequence of stronger fibril stiffening.