Analysis of the oxygen supply to porous implants in bone

A mathematical model of cylindrical porous surgical implant for orthopaedic prosthesis is presented. The model allows calculation of the net oxygen consumption as a function of porosity and pore diameter from 0 to 500 microM. In addition, limitations on implant size and pore diameter due to the length of the arteriole 'tree' have been considered. Literature data have been used to evaluate the model of the implant when infiltrated with bone in the steady-state. The model suggests that minimum pore diameter of 75 microM is necessary for bone ingrowth. Further, the limiting relationship between pellet diameter and pore diameter due to arterial tree length has been found to be a nearly linear function, with slope dependent on the tortuosity of the pores of the implant.