Human Middle Ear: Material Characterization, Analysis of Effects of Uncertainties, and Investigation of Impacts of Medical-Device Attachment

Abstract

The middle ear is a complex organ that plays a vital role in the hearing process. This thesis attempts to investigate different aspects of the biomechanics of the middle ear for diagnosis and treatment. This thesis can be divided into three broad categories which are, analysis of the effects of uncertainties of the middle-ear model parameters and finding the most influential parameters on the vibrations of middle-ear structures, estimation of the material properties of the structures in the middle ear for diagnostic purposes, and investigation of the effects of attachment of medical devices to the tympanic membrane on the middle-ear vibrations.

The inter-individual variabilities in the material properties and geometrical features of the middle ear lead to uncertainties in the middle-ear responses and the models of the middle ear. To be able to develop realistic models of the middle ear, we need to have a clear understanding of the effects of these uncertainties on the middle ear vibrations. However, these effects and especially the interactions of uncertainties with one another have not been well addressed in the literature. We used stochastic finite-element method to study the effects of these uncertainties on the sound conduction in the middle ear. Our results suggest that the uncertainties in the model parameters can be magnified by up to more than three times in the umbo and stapes footplate responses. Additionally, we used our stochastic finite-element model results to perform a global sensitivity analysis of middle-ear parameters. For this aim, we used the Sobol′ sensitivity analysis method that can evaluate the global impact of model parameters as well as the interactions among them. To reduce the computational cost of evaluating Sobol′ indices, we first created surrogate models of the middle ear using the polynomial chaos expansion method. We then estimated the values of Sobol′ indices from these surrogate models. Our results suggest that Young’s modulus and thickness of the tympanic membrane, Young’s modulus and damping of the stapedial annular ligament, and the Young’s modulus of the ossicles are the parameters with the greatest impacts on the amplitudes of the umbo and stapes footplate and the phase of the stapes footplate. The greatest interactions in the parameters were observed between the thickness and Young’s modulus of the tympanic membrane.

In this thesis, we also proposed a novel method for material characterization of the middle ear. In the first step, the method was used to estimate the Young’s modulus of 2D thin planar structures using single frequency full-field harmonic vibration data of the structure. Our proposed method uses Bayesian optimization for parameter estimation and we found that the estimated values of the Young’s modulus had errors of less than 5% even with very low values of signal-to-noise ratio. In the next step, we made some changes to the method to make it suitable to apply to the tympanic membrane. In order to increase the speed of the parameter estimation of the middle-ear structures and make the proposed estimation method suitable for future real-time applications, we combined our parameter estimation method with machine-learning-based surrogate models created using the eXtreme gradient boosting (XGBoost) method. The results show that the created surrogate models can fairly represent the behaviours of the middle ear. Also, the proposed machine-learning-based parameter estimation method can estimate the Young’s modulus of the tympanic membrane and the Young’s modulus of the stapedial annular ligament (with mean absolute percentage errors of less than 7%) which are among the most influential mechanical parameters in the middle ear as was demonstrated using our global sensitivity analysis.

Another objective of this study was to identify the mechanical and acoustical effects of medical devices attached to the tympanic membrane on middle-ear vibrations. The outcomes of this section can lead to optimizing current and future medical devices that are designed to be attached to the tympanic membrane. We used finite-element modelling to systematically study the effects of changes of middle-ear responses as a result of the attachment of the device. We first investigated the mechanical effects of the attachment of the device (due to changes in the mass and stiffness of the middle ear) on the sound conduction in the middle ear. We found that variations of the material properties of the device have significant effects on the umbo and stapes footplate motions at frequencies below 5 kHz. We also observed that the variations of geometrical properties of the device and its location on the tympanic membrane can have significant effects on the middle-ear vibrations at several frequencies in the frequency range of 100 Hz to 10 kHz. In the next step, we studied the acoustical effects of the medical device and its combination with the mechanical effects of the device. The acoustical effects of the device are significant if the desired treatment method requires perforating the tympanic membrane in addition to attaching a medical device to it. We observed that when both the mechanical effects (due to the mass and stiffness of the device) and the acoustical effects (due to perforations of the tympanic membrane) are present, the acoustical effects are dominant at low frequencies (below about 1 kHz) while the mechanical effects are dominant at frequencies above 1 kHz.