Theoretical Determination of Lubrication Regimes in Two-Piece First Metatarsophalangeal Prostheses

Abstract

The key joint of the forefoot during gait is the first metatarsophalangeal joint. It is subject to high loads and plays an important role in propelling the human form. Unfortunately the first metatarsophalangeal joint can be subject to a number of diseases, such as rheumatoid arthritis, hallux rigidus and hallux valgus, all of which can lead to replacement of the natural joint with a prosthesis. Most commonly, a silicone spacer might be implanted but other designs are available which more closely try to match the natural joint by employing a two-piece ball and socket arrangement. Such designs 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. Modeling 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. Boundary lubrication is indicated for lambda less than 1, mixed lubrication for lambda between 1 and 3, and fluid film lubrication for lambda greater than 3. The calculations were undertaken for a 10 to 1500N range of loading values, a 0 to 30mm/s range of entraining velocities, and a 3 to 15mm radius ranger of sizes. Calculations showed that, for the range of loads, sizes and entraining velocities considered, 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. Inevitably, a range of factors need to be considered when designing or choosing an implant for the first metatarsophalangeal joint.Keywordsmetatarsophalangeallubrication regimesmetal-on-metalceramic-on-ceramicmetal-on-polymer