Mathematical equations for dental implant stability patterns during the osseointegration period, based on previous resonance frequency analysis studies

Background Total stability of dental implant can be obtained from resonance frequency analysis (RFA) device, but without primary and secondary stability values. Purpose To formulate mathematical equations for dental implant stability patterns during the osseointegration period. Materials and Methods An online systematically search of the literature between January 1996 and December 2017 was performed for all prospective clinical trials that measured implant stability using RFA device during the osseointegration period. Initial mathematical function with adjustable parameters were created. Then curve-fitting was performed using a computerized program to formulate mathematical equations stability patterns. Results Nine publications (24 study groups) were included in the mathematical analysis. Curve fitting with low sum of squared errors could be applied in all studies, except one. The stability has been divided into high, medium, and low stability. The curve fitting showed stability dip areas and intersection point which predict the returning of the stability to reach the primary stability. The study groups with low primary stability showed the poorest results, the high and medium stability group showed the stability pattern following the assumed primary stability pattern according to the mathematic equations. Conclusions The model of primary and secondary stability could be predicted from the proposed equations.