Simulating the swelling and deformation behaviour in soft tissues using a convective thermal analogy

It is generally accepted that cartilage adaptation and degeneration are mechanically mediated. Investigating the swelling behaviour of cartilage is important because the stress and strain state of cartilage is associated with the swelling and deformation behaviour. It is well accepted that the swelling of soft tissues is associated with mechanical, chemical, and electrical events.

The purpose of the present study was to implement the triphasic theory into a commercial finite element tool (ABAQUS) to solve practical problems in cartilage mechanics. Because of the mathematical identity between thermal and mass diffusion processes, the triphasic model was transferred into a convective thermal diffusion process in the commercial finite element software. The problem was solved using an iterative procedure.

The proposed approach was validated using the one-dimensional numerical solutions and the experimental results of confined compression of articular cartilage described in the literature. The time-history of the force response of a cartilage specimen in confined compression, which was subjected to swelling caused by a sudden change of saline concentration, was predicted using the proposed approach and compared with the published experimental data.

The advantage of the proposed thermal analogy technique over previous studies is that it accounts for the convective diffusion of ion concentrations and the Donnan osmotic pressure in the interstitial fluid.