Purpose: The purpose of this study was to show the full evolution of bone anchorage caused by the growth of secondary stability and to determine which empirical model would provide the best quantitative description of this growth.

Materials and methods: The retention and anchorage of machined (M), grit-blasted and dual acid etched (BAE), and BAE implants with discrete crystals of calcium phosphate (+DCD) were evaluated with both ex vivo and in vivo methods. Ex vivo evaluation of implant retention was tested by measuring the force required to pull implants out of blood-filled osteotomies formed in bovine bone for up to 1 hour. In vivo measurements of bone anchorage were evaluated by reverse torque testing of implants placed in the proximal metaphysis of rat tibiae up to 28 days after initial placement. Four models were fit to the reverse torque results, and fits were evaluated by Bayesian and Akaike information criteria (BIC and AIC) and analysis of variance (ANOVA).

Results: AIC and BIC were 655.53 and 684.78, 472.53 and 512.74, 477.40 and 513.96, and 470.60 and 507.16 for the monomolecular, Richards, Gompertz, and logistic curves, respectively. Comparison of the Richards and logistic curves by analysis of variance (ANOVA) resulted in a P value of .78. A comparison of the three implant types using the logistic curve found that M implants had an earlier inflection point compared with BAE implants (P = .038), and the BAE+DCD implants had the greatest peak anchorage and were significantly greater than both M (P < .0001) and BAE implants (P = .005).

Conclusion: Bone anchorage was found to follow sigmoidal growth, which was best described by the logistic function. Further comparison of the fit values for the logistic curve shows that both overall anchorage and timing of bone anchorage are influenced by implant surface topography.