Transportation of neutral solute in deformable, anisotropic, soft tissue

We present a three-dimensional framework for the transport of neutral solute through soft biological tissue, such as the articular cartilage, under different mechanical loading conditions. The tissue is modelled as a mixture of three phases, a hyperelastic, anisotropic solid matrix, an incompressible inviscid fluid and a solute. The formulation accounts for the anisotropic interaction between the solid and the interstitial water and incorporates the interaction between the solute and the solid matrix. Under the proper circumstances, our model simplifies to biphasic theory and classical convection diffusion.We find that the pressure gradient variation plays an important role in the neutral solute transport when the soft tissue is dynamically loaded, because of the low concentration of solute present in cartilage. A linear function is suggested for the ratio of friction coefficient between the solute and solid to the friction coefficient between the interstitial water and solid matrix. After validating our model with the experiments of Quinn et al. [T.M. Quinn, C. Studer, A.J. Grodzinsky, J.J. Meister, Preservation and analysis of nonequilibrium solute concentration distributions within mechanically compressed cartilage explants, J. Biochem. Biophys. Methods 52 (2) (2002) 83–95], a numerical study of different dynamic loading conditions on solute transport is carried out.