Calculation of theoretical lubrication regimes in two-piece first metatarsophalangeal prostheses

The key joint of the forefoot during gait is the first metatarsophalangeal joint. It plays an important role in propelling the human form but can be subject to a number of diseases which can lead to its replacement with an artificial joint. Some of these designs of prosthesis employ a two-piece ball and socket arrangement and are available with a range of biomaterial couples including ceramic-on-ceramic, metal-on-metal and metal-on-polymer. Calculation of predicted lubrication regimes applicable to these implant designs was undertaken. Modelling the ball and socket implant as an equivalent ball-on-plane model and employing elastohydrodynamic theory allowed the minimum film thickness to be calculated and in turn the lambda ratio to indicate the lubrication regime. The calculations were undertaken for a 50 to 1500 N range of loading values, a 0 to 30 mm/s range of entraining velocities, and a 3 to 15 mm radius range of sizes. Calculations showed that the ceramic-on-ceramic and metal-on-metal implants could operate under fluid film lubrication, whereas the metal-on-polymer combination operated in the boundary lubrication regime. It was also recognized that manufacturing capabilities are critical to the radial clearances and values of surface roughness that can be achieved, and thus the predicted lubrication regime.