title: Structure-function relations and rigidity percolation in the shear properties of articular cartilage.
abstract: Among mammalian soft tissues, articular cartilage is particularly interesting because it can endure a lifetime of daily mechanical loading despite having minimal regenerative capacity. This remarkable resilience may be due to the depth-dependent mechanical properties, which have been shown to localize strain and energy dissipation. This paradigm proposes that these properties arise from the depth-dependent collagen fiber orientation. Nevertheless, this structure-function relationship has not yet been quantified. Here, we use confocal elastography, quantitative polarized light microscopy, and Fourier-transform infrared imaging to make same-sample measurements of the depth-dependent shear modulus, collagen fiber organization, and extracellular matrix concentration in neonatal bovine articular cartilage. We find weak correlations between the shear modulus |G(∗)| and both the collagen fiber orientation and polarization. We find a much stronger correlation between |G(∗)| and the concentration of collagen fibers. Interestingly, very small changes in collagen volume fraction vc lead to orders-of-magnitude changes in the modulus with |G(∗)| scaling as (vc - v0)(ξ). Such dependencies are observed in the rheology of other biopolymer networks whose structure exhibits rigidity percolation phase transitions. Along these lines, we propose that the collagen network in articular cartilage is near a percolation threshold that gives rise to these large mechanical variations and localization of strain at the tissue's surface.
authors.affiliation: Physics Department, Cornell University, Ithaca, New York. Electronic address: jls533@cornell.edu.
authors.forename: Jesse L
authors.initials: JL
authors.lastname: Silverberg
authors.affiliation: Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York.
authors.forename: Aliyah R
authors.initials: AR
authors.lastname: Barrett
authors.affiliation: School of Physics & Astronomy, Rochester Institute of Technology, Rochester, New York.
authors.forename: Moumita
authors.initials: M
authors.lastname: Das
authors.affiliation: Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York.
authors.forename: Poul B
authors.initials: PB
authors.lastname: Petersen
authors.affiliation: Biomedical Engineering, Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York.
authors.forename: Lawrence J
authors.initials: LJ
authors.lastname: Bonassar
authors.affiliation: Physics Department, Cornell University, Ithaca, New York.
authors.forename: Itai
authors.initials: I
authors.lastname: Cohen
mesh_terms: D000818:Animals; D000831:Animals, Newborn; D001696:Biomechanical Phenomena; D002358:Cartilage, Articular / Q000737:chemistry* / Q000378:metabolism*; D002417:Cattle; D003094:Collagen / Q000737:chemistry / Q000378:metabolism; D054459:Elasticity Imaging Techniques; D008954:Models, Biological; D033081:Shear Strength; D013329:Structure-Activity Relationship
chemical_list: D003094:Collagen