An analytical calculation of the fluid load support fraction in a biphasic material: an alternative technique.

Background: The fluid load support fraction (W(F)/W(T)) can be used to define the mechanical contribution of the interstitial fluid (W(F)) to the total force (W(T)) in the deformation of cartilage. Traditionally, W(F)/W(T) is calculated using complex experimental setups or time-consuming micromechanical poroelastic Finite Element (FE) simulations.

Aim: To define and validate a fast and efficient technique to predict W(F)/W(T) using an analytical approach that can be applied without micromechanical detail or experimental measurement.

Methodology: Poroelastic FE simulations defined accurate values of W(F)/W(T) for a range of loading configurations and were used to validate subsequent predictions. The analytical prediction of W(F)/W(T) used elastic contact mechanics to calculate W(F), and viscoelastic FE representation to calculate W(T). Subsequently, these independent calculations of W(F) and W(T) provided values of W(F)/W(T) that were compared with the poroelastic FE calculations.

Results And Discussion: The analytical prediction of W(F)/W(T) proved effective and suitably accurate (mean difference S<0.05). This technique demonstrated how W(F) and W(T) can be determined independently, without a biphasic constitutive model. Here we used viscoelasticity to calculate W(T) as an example, however, W(T) could be measured experimentally or predicted computationally.