Deriving the macrocontact condition between cementless hip replacement and bone from the microgeometry of the replacement coating

We consider mature femoral cortical bone which is in contact with a hip implant having a rough coating. The bone is assumed to be separated from the implant by a thin layer of microscopic peaks and valleys formed on the surface of the coating. The size of the peaks and valleys is very small compared with the macrosize of the implant stem and bone. This makes the direct application of the FEM for the calculation of the bone- stem contact problem prohibitively costly. A method is developed that allows deriving a macrocontact condition on the bone-stem interface. The method involves an asymptotic homogenisation procedure that takes into account the microgeometry of the interface layer and the stiffnesses of the bone and the implant material. The macrocontact condition is then used in a FEM model for the bone-stem contact problem on the macrolevel. The averaged contact stiffness obtained allows the replacement of the interface layer in the macromodel by the macrocontact condition. An approximation to the microstresses is found by two-scale homogenization and can be used for the macrostrength estimation. Treatment for hip osteoarthritis focuses on decreasing pain and improving joint move- ment. When conservative methods of treatment fail, it is necessary to replace the affected joint with an artificial replacement called a joint prosthesis. Nowadays there are two types of hip prosthesis: cemented and cementless. The cementless hip prosthesis, the most re- cent type, represents approximately 35% of the European market and is regarded as more promising. The surface of the cementless implant is coated in such a way that the bone is in direct contact with this surface with the idea that the bone grows into the microvalleys and pores of the coating to provide enhanced stability and rapid osseointegration. The aim of the present paper is to investigate the dependence of the bone-implant contact condition on the microgeometry and mechanical properties of the coating.