A fibril-network-reinforced biphasic model of cartilage in unconfined compression

Cartilage mechanical function relies on a composite structure of a collagen fibrillar network entrapping a proteoglycan matrix. Previous biphasic or p oroelastic models of this tissue, which have approximated its composite str ucture using a homogeneous solid phase, have experienced difficulties in de scribing measured material responses. Progress to date in resolving these d ifficulties has demonstrated that a constitutive law that is successful for one test geometry (confined compression) is not necessarily successful for another (unconfined compression). In this study, we hypothesize that an al ternative fibril-reinforced composite biphasic representation of cartilage can predict measured material responses and explore this hypothesis by deve loping and solving analytically a fibril-reinforced biphasic model for the case of uniaxial unconfined compression with frictionless compressing plate ns. The fibrils were considered to provide stiffness in tension only. The l ateral stiffening provided by the fibril network dramatically increased the frequency dependence of disk rigidity in dynamic sinusoidal compression an d the magnitude of the stress relaxation transient, in qualitative agreemen t with previously published data. Fitting newly obtained experimental stres s relaxation data to the composite model allowed extraction of mechanical p arameters from these tests, such as the rigidity of the fibril network, in addition to the elastic constants and the hydraulic permeability of the rem aining matrix. Model calculations further highlight a potentially important difference between homogeneous and fibril-reinforced composite models. In the latter type of model, the stresses carried by different constituents ca n be dissimilar, even in sign (compression versus tension) even though stra ins can be identical. Such behavior, resulting only from a structurally phy siological description, could have consequences in the efforts to understan d the mechanical signals that determine cellular and extracellular biologic al responses to mechanical loads in cartilage.