Cartilage mechanical function relies on a composite structure of a collagen fibrillar network entrapping a proteoglycan matrix. Previous biphasic or poroelastic models of this tissue, which have approximated its composite structure using a homogeneous solid phase, have experienced difficulties in describing measured material responses. Progress to date in resolving these difficulties has demonstrated that a constitutive low that is successful for one test geometry (confined compression) is not necessarily successful for another (unconfined compression). In this study, we hypothesize that an alternative fibril-reinforced composite biphasic representation of cartilage can predict measured material responses and explore this hypothesis by developing and solving analytically a fibril-reinforced biphasic model for the case of uniaxial unconfined compression with frictionless compressing platens. The fibrils were considered to provide stiffness in tension only. The lateral stiffening provided by the fibril network dramatically increased the frequency dependence of disk rigidity in dynamic sinusoidal compression and the magnitude of the stress relaxation transient, in qualitative agreement with previously published data. Fitting newly obtained experimental stress relaxation data to the composite model allowed extraction of mechanical parameters from these tests, such as the rigidity of the fibril network, in addition to the elastic constants and the hydraulic permeability of the remaining matrix. Model calculations further highlight a potentially important difference between homogeneous and fibril-reinforced composite models. In the latter type of model, the stresses carried by different constituents can be dissimilar, even in sign (compression versus tension) even though strains can be identical. Such behavior, resulting only from a structurally physiological description, could have consequences in the efforts to understand the mechanical signals that determine cellular and extracellular biological responses to mechanical loads in cartilage.

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Mechanical behavior of articular cartilage was characterized in unconfined compression to delineate regimes of linear and nonlinear behavior, to investigate the ability of a fibril-reinforced biphasic model to describe measurements, and to test the prediction of biphasic and poroelastic models that tissue dimensions alter tissue stiffness through a specific scaling law for time and frequency. Disks of full-thickness adult articular cartilage from bovine humeral heads were subjected to successive applications of small-amplitude ramp compressions cumulating to a 10 percent compression offset where a series of sinusoidal and ramp compression and ramp release displacements were superposed. We found all equilibrium behavior (up to 10 percent axial compression offset) to be linear, while most nonequilibrium behavior was nonlinear, with the exception of small-amplitude ramp compressions applied from the same compression offset. Observed nonlinear behavior included compression-offset-dependent stiffening of the transient response to ramp compression, nonlinear maintenance of compressive stress during release from a prescribed offset, and a nonlinear reduction in dynamic stiffness with increasing amplitudes of sinusoidal compression. The fibril-reinforced biphasic model was able to describe stress relaxation response to ramp compression, including the high ratio of peak to equilibrium load. However, compression offset-dependent stiffening appeared to suggest strain-dependent parameters involving strain-dependent fibril network stiffness and strain-dependent hydraulic permeability. Finally, testing of disks of different diameters and rescaling of the frequency according to the rule prescribed by current biphasic and poroelastic models (rescaling with respect to the sample's radius squared) reasonably confirmed the validity of that scaling rule. The overall results of this study support several aspects of current theoretical models of articular cartilage mechanical behavior, motivate further experimental characterization, and suggest the inclusion of specific nonlinear behaviors to models.

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Functional mechanical behavior of cartilage can be investigated by testing excised tissue in confined, unconfined or indentation geometries using creep, stress relaxation and dynamic sinusoidal tests. Potential nonlinear behavior of cartilage has been mostly characterized in confined compression [1,2]. The extent to which the nonlinearities are intrinsic to the tissue or depend on the specificities of the testing configuration of confined compression is not known. We have therefore performed experimental and analytical tests of articular cartilage in unconfined compression to reveal linear and nonlinear behavior. We found equilibrium stress responses to behave linearly, but transient or dynamic stress responses to be nonlinear. Transient compressive responses stiffened nonlinearly when increasing the static offset compression present at the beginning of the step. On the contrary, dynamic stiffness decreased (weakened) nonlinearly when the amplitude of sinusoidal displacement, imposed on a static offset, was increased. We also found that the articular cartilage nonlinearly maintained a compressive stress when a release displacement was applied from a 10% static offset compression, suggesting possible physiological roles of these nonlinear behaviors.