An improved solution for the contact of two biphasic cartilage layers

The purpose of this study was to present a solution for the contact of two biphasic cartilage layers which can be used for dynamic loading, is not restricted to predictions over small time periods, and predicts biologically meaningful changes in contact areas over time. The proposed solution was based on the work of Ateshian et al. (1994, J. Biomechanics27, 1347–1360) who retained the first term of an asymptotic expansion and used an approximate integration which is valid for short time periods. The solution proposed here uses an exact integration, is valid over long time periods, and can be used for increasing loading. The new solution corrects a limitation of the work by Ateshian et al., which manifests itself immediately (i.e. at time t = 0±s): the rate of change in the contact radius (and therefore, the contact area) is increasing in Ateshian et al.ʹs solution for a constant force, whereas it is decreasing in the new solution. An increasing rate of change in the contact radius suggests that the contact radius (area) is unbounded, and a steady-state solution cannot be reached, which is physically not correct for the contact of two joint surfaces. In the new solution, the contact radius reaches a steady-state value given sufficient time.