0160 - the Asymmetry of Compression vs. Release for Articular Cartilage in Unconfined Compression Can Be Described by a Nonlinear Poroelastic Model

نویسنده

  • LePing Li
چکیده

Introduction: Mechanical behavior of articular cartilage is a consequence of its collagen fibrillar network entrapping a proteoglycan dominant matrix swollen by electrolyte. Fibril reinforced poroelastic models which distinguish the two major solid components (fibrillar and nonfibrillar) have been able to account for several previously difficult to describe behaviors, such as the large transient to equilibrium load ratios in unconfined compression stress relaxation [1] and the compression-offset dependent stiffening of the transient response [2]. Another interesting experimentally observed nonlinear behavior of articular cartilage has been the asymmetry of compression vs. release from a pre-imposed compression offset. In confined and unconfined compression, the transient amplitude in release is smaller than in compression [3, 4]. The goal of this study was to theoretically investigate potential sources of this compression/release asymmetry for the transient response of articular cartilage in unconfined uniaxial geometry, including nonlinear tensile strain stiffening of the collagenous fibrillar network. Theory and Method: Intrinsic property nonlinearities were incorporated into a previously developed fibril reinforced biphasic model. Three material properties are required to define the elastic porous: the Young’s modulus and Poisson’s ratio of the drained matrix and the permeability which varies exponentially with the dilatation [5]. The fibrillar network is considered as a distinct constituent whose Young’s modulus is taken to vary linearly with the tensile strain (while nil for compressive strain). The model is employed here to simulate an experimentally observed nonlinear compression-release phenomenon (Fig.A). A 100 microns compression offset was applied to a cartilage disk (with thickness 1 mm and radius 1.4 mm) in unconfined compression using a sequence of 20 compression/relaxation steps. After the disk had reached equilibrium (i.e. pore pressure vanished; for convenience time was set to zero at this time), a sequence of compression/relaxation and release/relaxation (5 or 10 microns amplitude was applied at 1 micron/s) was then applied as shown in the inset of Fig.A. Solutions were extracted from a finite element procedure by using the commercial code ABAQUS. Results: For the same increment of displacement, release produces a smaller load transient than compression (Fig.A). Furthermore the larger the displacement increment, the larger the difference between the compression and release transient amplitudes; doubling compression amplitude approximately doubles the force transient while doubling release amplitude generates much less than doubling of its force transient. These phenomena correspond to what has been experimentally observed [3, 4]. The dependence of permeability on dilatation and the effect of finite deformation were found not to account for the asymmetric nonlinear compression-release transient if fibril nonlinearity is not considered simultaneously, although their presence produces a stronger compression-release nonlinearity when the fibril nonlinearity is involved. Thus, for clarity, here we present typical results for which the only nonlinear factor considered is fibril stiffening with its strain (Fig.B; note that removal of permeability dependence on dilatation reduces relaxation times compared to Fig.A) to explore the potential mechanism of this nonlinear behavior. Compression or release in the axial direction, results in a rise or reduction of tensile strain in the radial direction (Fig.C). This would also be the case even if fibril stiffness was taken to be constant. However, since the Young’s modulus of the fibrils is linear with its tensile strain, it has the same form as the radial strain, and thus the fibrils soften in a release situation. Furthermore the pore pressure scales with the modulus of the material (i.e. the stiffer the fibrils, the higher the pore pressure) and thus has a lower amplitude in release than in compression (Fig.D). The reduced pore pressure results in reduced load (Fig.B). It is also seen that the transient increment in the radial strain is larger in a release situation as compared with the same displacement increment in compression. This aspect of the fibril nonlinear feature makes the fibrils soften further in a release situation, resulting in an even stronger asymmetry in the compression-release transient. Discussion: This investigation has proposed one theoretical explanation of the experimentally observed asymmetrical nonlinear compression vs. release transient. This result has moreover demonstrated the advantages of distinguishing fibrils as nonlinear constituents in the modeling of mechanical behavior of articular cartilage. Since most physiological loads involve repeated application of both compression and release phases, this behavior and its model description are of practical importance for cartilage biomechanical function, evaluation and physiological response to loads.

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تاریخ انتشار 1999