# A Mathematical Model for Biomechanical Evaluation of Micro-motion in Dental Prosthetics using Vibroacoustic RFA

## Abstract

### Purpose

Dental implants are placed in the jaw of a patient to perform the function of a missing tooth. However, before the implant is subjected to masticatory loading, sufficient osseointegration should take place to prevent its failure. Resonance Frequency Analysis is one of the methods to measure the primary stability of an implant system in terms of micromotion. This paper aims to formulate a mathematical model of the dental prosthetic for the vibroacoustic RFA technique.

### Methods

Vibroacoustic RFA is a novel method that excites the implant using either a loudspeaker or a buzzer and captures the subsequent displacement. In this study, a single degree of freedom mathematical model is excited using a sinusoidal force. The subsequent displacement or micro-motion of the implant system is found out by basic equations of vibrations while varying the input frequency between 1 – 50 Hz.

### Results

The resonant frequency corresponding to the maximum micro-motion which lies between 1.2 – 2 µm is plotted using MATLAB. The resonant frequency values lie between 8975 – 8995 Hz with an average value of 8985 Hz. When the input frequency increases beyond 40 Hz, the micromotion shows a percentage increase of 40.62%.

### Conclusion

A higher value of resonance frequency indicates better osseointegration with decrease in micromotion. A Mathematical model and subsequent signal analysis using RFA is advantageous for implant stability measurement. Further research is needed to develop multiple degree of freedom systems to simulate the dental implant model.

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Correspondence to Niharika Karnik.

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Karnik, N., Bhadri, K., Bora, U. et al. A Mathematical Model for Biomechanical Evaluation of Micro-motion in Dental Prosthetics using Vibroacoustic RFA. J. Med. Biol. Eng. (2021). https://doi.org/10.1007/s40846-021-00636-w