Biomechanical response of soft tissues during passage of synovial fluid in compression

Abstract The present study provides a novelty approach for the computational biological model based on continuum mixture theory in combination with power-law model for incorporating an accurate governing model for the synovial fluids. We investigated the biomechanical response of a soft tissue while passage of non-Newtonian fluid during act of loading at the rigid bony interface. A special kind of multiphasic deformation has been reported in these types of problems that justify nonlinear coupling between the fluid and solid. In modeling these types of problems, general assumption of mixture constituents incompressibility is often provoked. The mixture components are considered intrinsically incompressible; however, in the derivation of governing equations, viscoelastic behavior of the solid along with interstitial fluid was developed. The nonlinear interaction between the fluid–solid is modeled using strain-dependent permeability and is experimentally determined. This manipulation of linear model with nonlinear permeability required attention for the computational point of view. A system of nonlinear coupled partial differential equations is derived for the local fluid pressure along with an equation for solid deformation. The governing system of equations is solved numerically for the case of permeability dependent flow, whereas an exact solution is given for constant permeability case. Various interesting features, such as, pressure changes within the tissue, swelling behavior of the solid matrix, and effects of power law index on the tissue deformation have been presented graphically. A good qualitative agreement has been noticed between the exact and numerical solutions for constant permeability case.