A Rigidity Percolation Framework to Understand How Biologically Induced Changes in Constituent Composition Alter Cartilage Shear Mechanics*

Cartilage can sustain millions of loading cycles over decades of use and outperforms any synthetic substitute. The bulk properties of this tissue primarily reflect the mechanics of an extracellular matrix, comprised of only two components: a collagen network and a reinforcing proteoglycan network. Diseases of cartilage involve loss of extracellular matrix constituents due to mechanical overloading or biochemical processes. A mystery associated with disease is why the same amount of degradation in some cases leads to minor changes in modulus, while in other cases leads to tissue collapse. We present experiments and theory in support of a rigidity percolation framework that explains how the shear properties of cartilage depend on the concentrations of both constituents. This framework predicts a sensitivity to degradation that depends on the collagen concentration. When the collagen network is sparse, changes in aggrecan concentration create dramatic changes in modulus yet deeper into the tissue, similar changes in aggrecan leave properties nearly unchanged. This framework provides a tool for understanding the effect of degradation of cartilage on its shear properties, and its function in vivo.