Evaluating the dynamic behaviour of bone anchored hearing aids using a finite element model and its applications to implant stability assessment

Abstract

The dynamic behavior of osseointegrated implants can be used for the non-invasive evaluation of the condition of the bone-implant-interface (BII). The Advanced System for Implant Stability Testing (ASIST) is a vibration measurement system that relies on an impact technique and an analytical model to compute the interface stiffness and the ASIST stability coefficient ($ASC$). The objective of this work is to develop a finite element (FE) model capable of capturing the dynamic behaviour of the bone-anchored hearing aid under the ASIST loading condition. The model was validated with previously collected in vitro and in vivo data which were compared to the model’s acceleration responses and $ASC$ scores. Similar acceleration responses were obtained, and the maximum absolute differences in $ASC$ scores between the FE model and the in vitro and in vivo data were 1.15% and 5.48% respectively. The model was then used to show the existence of a relationship between the rod’s acceleration response and the BII stress field. Finally, the model was used to interpret the factors that affect the stiffness parameters of the ASIST analytical model. The interface stiffness and the system’s dynamic properties were more influenced ($p<0.05$) by the BII material and friction coefficient compared to the implant geometry.

Graphical abstract

In this work, a finite element model of the bone anchored hearing aid was used to simulate the dynamic behaviour of the bone-implant system under the ASIST’s loading conditions. The model was first validated with previously collected experimental and clinical results. The validated model was then used to study the relationship between the impact rod’s acceleration response and the response at the bone implant interface. Finally, the model was used to formulate a better understanding on the influencing factors on the interface stiffness.

Appendices

Appendix 1 Mesh independence

Tables 4, 5 and 6

Table 4 Mesh 1 settings

Table 5 Mesh 2 settings (this mesh was used for all of the simulations in the results section)

Table 6 Mesh 3 settings

Figures 10 and 11

Fig. 10

Acceleration response for the Oticon 4 mm/wide FRB model

Fig. 11

Acceleration response for the Oticon 4 mm/wide PLA model

Appendix 2 Complete ANOVA analysis

Tables 7, 8, 9, 10, 11, 12 and 13

Table 7 ${2}^{3}$ ANOVA un-replicated factorial design: The analysis relies on three factors: implant type ($\mathrm{I}$), base material (M), and interface friction coefficient (F), and each factor has two levels. There are three response parameters of interest the first mode frequency (${f}_{1}$), second mode frequency (${f}_{2}$), and ASIST stability coefficient (ASC). The analysis is carried out independently for each response parameter of interest

Table 8 Computing the contrast, effect, and sum squared (SS) values for ${f}_{1}$. All of the effects are positive which indicated that there is a positive correlation between the factors’ levels and an increase in the natural frequency

Table 9 ANOVA analysis indicates that f and m are statistically significant factors ($p<0.05)$ on the response ${f}_{1}$

Table 10 Computing the contrasts, Effects and Sum Squared (SS) values for ${\mathrm{f}}_{2}$

Table 11 ANOVA analysis indicates that m is the only statistically significant factors ($p<0.05)$ on the response ${f}_{2}$

Table 12 Computing the contrasts, effects, and sum squared (SS) values for $\mathrm{ASC}$

Table 13 ANOVA analysis indicates that m and f are statistically significant factors ($p<0.05)$ on the response $\mathrm{ASC}$

Figures 12, 13 and 14

Fig. 12

Pareto analysis for the effects on ${f}_{1}$; the analysis indicates that the f, m, and their interaction mf are the primary factors that affect on the response

Fig. 13

Pareto Analysis for the effects on ${\mathrm{f}}_{2}$, the analysis indicates that the m, f,i,im and imf are the primary factors that affect on the response

Fig. 14

Pareto Analysis for the effects on ASC; the analysis indicates that the m, f, mf, and i are the primary factors that affect on the response