Mathematical and Experimental Modelling of the Dynamic Response of the Transfemoral Bone Implant System and Bone Anchored Hearing Aids and its Potential Application to the Non-invasive Evaluation of Implant Stability
Creators: Mohamed, Mostafa
Publisher: name: University of Alberta Library
Year: 2023

<p>Osseointegrated implants rely on the direct structural and functional attachment of an implant to the surrounding bone tissues. These implants are used in various fields including dentistry, bone conduction hearing and lower-limb amputations. Determining the quality of the bond between the implant and the surrounding bone (implant stability) is important in evaluating the surgical outcomes, early failure-detection and optimising rehabilitation. Vibration analysis can non-invasively quantify the bone-implant-interface (BII) properties. The Advanced System for Implant Stability Testing (ASIST) is a vibration-based stability measurement system that has been used with Bone Anchored Hearing Aids (BAHA). It evaluates the BII stiffness by matching the measured acceleration to the prediction of a mathematical model. This work focuses on the mathematical and experimental analysis of the dynamic behavior of the implant for Transfemoral lower-limb Amputations (TFA) and BAHA systems. The analysis extends the ASIST approach to TFA systems and builds on the existing knowledge of BAHA systems using novel modelling approaches. <br>
The TFA bone-implant system was first analysed using 3D Finite Element (FE) modal analysis and benchtop experiments under different BII, loading, boundary and implant-adapter conditions. The analysis indicated that a measurement system based on the axial modes is: 1) more sensitive to the BII condition, 2) more immune to the femoral boundary condition and 3) more characterizable for different implant-adapter configurations compared to the transverse modes. Therefore, a 1D FE model of the TFA system was developed using axial bar elements. The model was validated by: 1) testing the 1D FE formulation using a uniform cylinder, 2) comparing the 1D FE modal behavior with a 3D FE model for the actual implant geometry and 3) using the 1D FE model to analyse signals generated from 3D FE implicit and benchtop models. The 1D FE formulation converged to the analytical and 3D FE solutions for the uniform cylinder. The 1D model was representative of the TFA system and predicted similar axial modes (maximum frequency difference of 2.07%) compared to the 3D FE model. The 1D FE model was then incorporated into a custom-built MATLAB® application that extracts the BII stiffness by matching the input signal to the model’s prediction using an optimization routine. The approach was highly sensitive to the BII condition and predicted interface stiffness values of  4.75×106, 1.43×108 and 2.21×109 N/m for the experimental LOW, INTERMEDIATE and HIGH conditions respectively. The model also predicted similar damping ratios compared to the 3D FE simulations. The optimization routine successfully matched the signals, with frequency domain similarity scores of 94-100%.<br>
1D and 3D FE models of the BAHA systems were developed. Although the previous work involved modelling BAHA implants using an analytical 4 Degree of Freedom (DOF) and benchtop setups, the developed FE models tested the implant system under a wider range of conditions. The 3D FE signals were analysed with the ASIST utility, the ASIST Stability Coefficient (ASC; directly computed from the BII stiffness) was more sensitive to the BII condition and less sensitive to the abutment geometry compared to the natural frequencies. The 3D models were also validated with benchtop and clinical signals that represented extreme BII cases and were then used to study the nature of the BII and its influencing parameters. Finally, a 1D FE model was developed for BAHA systems using Timoshenko beam elements. The 1D FE model behaved similarly to the previously developed 4 DOF model, where they both predicted similar natural frequencies with differences of -0.77 to 4.40% and -1.07 to -2.76% for the 1st and 2nd modes respectively. The consistently lower 2nd mode frequencies of the 1D FE model (due the larger number of DOF) resulted in lower ASC scores but the trends between both models were preserved. <br>
The mathematical analysis performed in this work offers a comprehensive understanding of the dynamic behavior of both implant systems. This is the first attempt to model the Osseointegrated Prosthetic Limb (OPL) TFA system and the first one to propose a vibration-based implant stability measurement method for it. The 1D FE models for both bone-implant systems (TFA and BAHA)  show high promise in modelling them and evaluating the BII stiffness. This approach paves the way for the non-invasive evaluation of the BII properties in clinical settings.</p>