A contact mechanics model for ankle implants with inclusion of surface roughness effects

Abstract

Total ankle replacement is recognized as one of the best procedures to treat painful arthritic ankles. Even though this method can relieve patients from pain and reproduce the physiological functions of the ankle, an improper design can cause an excessive amount of metal debris due to wear, causing toxicity in implant recipient. This paper develops a contact model to treat the interaction of tibia and talus implants in an ankle joint. The contact model describes the interaction of implant rough surfaces including both elastic and plastic deformations. In the model, the tibia and the talus surfaces are viewed as macroscopically conforming cylinders or conforming multi-cylinders containing micrometre-scale roughness. The derived equations relate contact force on the implant and the minimum mean surface separation of the rough surfaces. The force is expressed as a statistical integral function of asperity heights over the possible region of interaction of the roughness of the tibia and the talus implant surfaces. A closed-form approximate equation relating contact force and minimum separation is used to obtain energy loss per cycle in a load–unload sequence applied to the implant. In this way implant surface statistics are related to energy loss in the implant that is responsible for internal void formation and subsequent wear and its harmful toxicity to the implant recipient.