Comparison of models for flow induced deformation of soft biological tissue

The behaviour of a deformable porous medium during the flow of fluid under a pressure difference is examined for both infinitesimal and finite deformations. Models for both cases are solved for the problem of steady one-dimensional compression and compared with experimental data from Parker et al. (J. appl. Mech. 54, 794-800, 1987) for a polyurethane sponge. The purpose of this study is to identify a simple model which agrees qualitatively with these published results. To relate the stress relations for biological tissues to the data for polymer sponges (Parker et al., 1987) a translation of 1.1 kPa was introduced. This allows for some structural differences between the two media. It was found that the infinitesimal models were adequate up to 20% strain, but significant divergence occurred for higher strains. A finite deformation model with the permeability depending exponentially on the strain gave the most consistent results and required the fitting of only two parameters.