In the Periotest, the interfacial damping characteristics between the implant and the surrounding tissue are evaluated. The Periotest and the Osstell Mentor system test are two typical noninvasive methods for the measurement of implant stability in diagnosis. Noninvasive methods are required for the observation and measurement of implant stability. The histological examination is one of the traditional invasive approaches. The quantification of implant stability offers helpful information to keep reliability in the individual treatment. The secondary stability obtains from the bone apposition surrounding the interface of implants and bone. Bone material quality, geometry characteristics of implants, and cortical bone can affect the primary stability. The former is largely associated with osseointegration, while the secondary stability is highly corresponding with the bone formulation and remodeling in the process of healing. Usually, the stability of implantation can be concluded in two categories: the primary and the secondary stability. Fortunately the stability of the implants can be introduced to successfully predict such a failure in most cases by numerical computing or experimental testing. The implantation fails sometimes caused by some complicated reasons in oral environment. The dental implant as a predictable and reliable treatment has been widely applied in the rehabilitation of edentulous patients. The methods developed in this paper provide helpful guidance for designers and researchers in the implantation design and surgical plans. The Latin Hypercube (LH) sampling method as a competent and sophisticated method is applied and combined with the finite element method (FEM). The Kriging surrogate model is proposed to present the numerical relationship between RF and material parameters of dental implants. The model has merits not only in the prediction reliability and accuracy but also in the compatibility and flexibility, in both experimental data and numerical simulation results. In this study, an appropriate mathematical model is proposed to evaluate and predict the implant stability and performance. However, the exact relationship between the design variables of dental implants and RF of the system is correlated, complicated, and dependent. The resonance frequency (RF) can effectively describe the stability of the implant in physical experiments or numerical simulations. The dental implantation in clinical operations often encounters difficulties and challenges of failure in osseointegration, bone formulation, and remodeling.
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