Effect of structural distortions on articular cartilage permeability under large deformations
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The permeability of articular cartilage has a key role in load support and lubrication in diarthrodial joints. The microstructural rearrangement and consequent alteration in permeability caused by the large deformations undergone by cartilage have been previously modelled with a multi-scale approach. At the microscopic scale, the tissue is regarded as a homogeneous fluid-filled proteoglycan matrix reinforced by collagen fibres. A material point is described by a representative element of volume (REV), comprising a collagen fibre surrounded by a jacket of fluid-saturated proteoglycan matrix. At the macroscopic scale, the statistical orientation of the fibres is accounted for via averaging of the REV over all possible directions. The previous models accounted for volumetric deformation and fibre reorientation, but did not consider the cross-sectional distortion of the REV, which changes the widths of the fluid channels in different directions. We account for REV cross-sectional distortion and demonstrate its effects by simulating confined compression tests for the superficial, middle and deep zones of articular cartilage. The proposed model captures published experimental results that were not reproduced correctly by the previous models, and shows that each factor (volumetric deformation, fibre reorientation, REV cross-sectional distortion) can be dominant, depending on fibre orientation and amount of compression, implying that all three factors should be accounted for when modelling cartilage permeability.
KeywordsArticular cartilage Distortion Permeability Large deformations Collagen fibre Proteoglycans Statistical orientation
This work was supported in part by Alberta Innovates - Technology Futures (Canada), through the AITF New Faculty Programme [SF], Alberta Innovates - Health Solutions (Canada), through the Postgraduate Fellowship Programme [MM] and the Sustainability Programme [SF], the Natural Sciences and Engineering Research Council of Canada, through the NSERC Discovery Programme [WH,SF] the NSERC CREATE Programme [MM], the Canadian Institutes of Health Research (CIHR) [WH], the Canada Research Chair Programme [WH], the Killam Foundation [WH], the Biomedical Engineering Graduate Programme of the University of Calgary (Canada), through the BME GP Academic Award [KH] and the BME Research Scholarship Award [KH]. We acknowledge the useful discussions with Dr. Alfio Grillo (Politecnico di Torino, Italy), Dr. Robert J. Martinuzzi (The University of Calgary, Canada), and Dr. Gerhard A. Holzapfel (Technische Universität Graz, Austria). Part of this research was initially presented at the European Society of Biomechanics Annual Congress (Lyon, France, 10–13 July 2016). Finally, we would like to thank two anonymous Referees for their crucial comments on the description of the problem.
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