Using regression models to determine the poroelastic properties of cartilage

The feasibility of determining biphasic material properties using regression models was investigated. A transversely isotropic poroelastic finite element model of stress relaxation was developed and validated against known results. This model was then used to simulate load intensity for a wide range of material properties. Linear regression equations for load intensity as a function of the five independent material properties were then developed for nine time points (131, 205, 304, 390, 500, 619, 700, 800, and 1000 s) during relaxation. These equations illustrate the effect of individual material property on the stress in the time history. The equations at the first four time points, as well as one at a later time (five equations) could be solved for the five unknown material properties given computed values of the load intensity. Results showed that four of the five material properties could be estimated from the regression equations to within 9% of the values used in simulation if time points up to 1000 s are included in the set of equations. However, reasonable estimates of the out of plane Poisson's ratio could not be found. Although all regression equations depended on permeability, suggesting that true equilibrium was not realized at 1000 s of simulation, it was possible to estimate material properties to within 10% of the expected values using equations that included data up to 800 s. This suggests that credible estimates of most material properties can be obtained from tests that are not run to equilibrium, which is typically several thousand seconds.