Toward a constitutive law of cartilage: A polymer physics perspective

To describe load bearing and lubrication of cartilage requires treating its collagen network and proteoglycan (PG) phases separately in a constitutive law of the tissue. We propose a framework for developing such an empirical constitutive law that treats the cartilage extracellular matrix (ECM) as a composite medium, with a PG phase that exerts a swelling pressure, and a collagen network phase that restrains it. We compare and contrast this model to a biornechanical constitutive law that aggregates the collagen and PG phases into a single "solid-like" elastic tissue matrix, and show that aggregation obscures essential differences in the physical-chemical properties of the collagen and PG constituents as well as their distinct biological roles within cartilage's ECM. We also relate moduli in the aggregate constitutive model to quantities measured in an osmotic stress titration experiment.