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.