Poroviscoelastic Properties of Mouse Cartilage From Inverse Finite Elements and Indentation

Transgenic mice offer a novel way to probe structure function relationships in healthy and osteoarthritic cartilage. Indentation is a convenient method to measure mechanical properties of cartilage in the mouse. In order to reduce test data to material properties, test model geometry along with a material model needs to be assumed. Most recent developments support the use of a poroviscoelastic (PVE) model for cartilage. However, using this model makes separation of the flow-dependent and flow-independent viscoelastic parameters challenging. For cartilage from larger animals, Huang [1] showed that tensile tests have negligible flow-dependent response and hence can identify the flow-independent material parameters. A compression experiment can then be used to find only the flow-dependent parameters. However, limited cartilage volumes in mouse do not allow for tension tests, so mouse cartilage is primarily tested by indentation. Mak [2] has shown that fluid flow occurs mainly for times comparable to the gel diffusion time T = a²/Hκ where a is the tip size, H is the aggregate modulus and κ is permeability. Consequently, we propose use of two different sized indenters to separate flow-independent and dependent effects in mouse cartilage. One tip is small enough to make T negligible (say <0.1 s), then relaxation data will probe only the flow-independent response, whereas a second considerably larger tip will probe both flow-dependent and fluid flow effects. The data from the small indenter can be used to fit the flow-independent parameters; the data from the large indenter, in conjunction with parameters from the first fit, can be used to fit the flow-dependent parameters.