Drag-induced compression of articular cartilage during a permeation experiment 1

Abstract

Linear and nonlinear theories are used to study the one-dimensional permeation problem of liquids flowing through soft tissues under applied pressure gradients. It is found that the strain field induced by the drag of permeation is nonuniform with respect to depth, causing nonuniform permeability in the tissue sample for which the permeability is to be measured. As a consequence, permeability experiments on soft, porous and permeable tissues can only measure their apparent permeabilities. The concept of “intrinsic” permeability is introduced to define the permeability of the tissue under an imposed, uniform clamping strain and a vanishly small imposed pressure gradient during a flow permeation experiment. Extra-polating from our experimental results for decreasing pressure gradients, we obtained the following intrinsic permeability function: $$\begin{array}{c}{\mathrm{k}}_{\mathrm{intrisic}}={\mathrm{k}}_{\mathrm{o}}exp\mathrm{(}{\mathrm{M}}_{\mathrm{o}}\mathrm{e}\mathrm{)}\end{array}$$ where k_o and M_o are constants and e is the true strain. By using a nonlinear theory which incorporates the above intrinsic permeability function to describe the permeation experiment, we found that the dependence of apparent permeability on pressure gradient observed in our experiments can be predicted reasonably well by the theory. The results thus show that the intrinsic permeability function could be used to provide a better biphasic model whenever fluid flow becomes an important factor during the deformation of a soft, porous, permeable medium such as articular cartilage.