A mathematical approach to estimate micro-displacement of a dental implant using electromagnetic Frequency Response Analysis

The aim of this paper is to formulate a mathematical model of dental prosthetic using single degree of freedom (SDOF) to assess the micro-displacement under electromagnetic excitation. Using Finite Element Analysis (FEA) and values from literature, stiffness and damping values of the mathematical model were estimated. For ensuring the successful implantation of dental implant system, monitoring of primary stability in terms of micro-displacement is crucial. One of the most popular techniques for the measurement of stability is the Frequency Response Analysis (FRA). This technique assesses the resonant frequency of vibration corresponding to the maximum micro-displacement (micro-mobility) of the implant. Among the different FRA techniques, the most common method is the Electromagnetic FRA. The subsequent displacement of the implant in the bone is estimated by equations of vibration. A comparison has been made to observe the variation in resonance frequency and micro-displacement due to varying input frequency ranges of 1–40 Hz. The micro-displacement and corresponding resonance frequency were plotted using MATLAB and the variation in resonance frequency is found to be negligible. The present mathematical model is a preliminary approach to understand the variation of micro-displacement with reference to electromagnetic excitation force and to obtain the resonance frequency. The present study validated the use of input frequency ranges (1–30 Hz) with negligible variation in micro-displacement and corresponding resonance frequency. However, input frequency ranges beyond 31–40 Hz is not recommended due to large variation in micromotion and corresponding resonance frequency.