A non-linear viscoelastic model for the tympanic membrane

Characterization of middle ear soft tissue damping and its role in sound transmission

Damping plays an important role in the middle ear (ME) sound transmission system. However, how to mechanically characterize the damping of ME soft tissues and the role of damping in ME sound transmission have not yet reached a consensus. In this paper, a finite element (FE) model of the partial external and ME of the human ear, considering both Rayleigh damping and viscoelastic damping for different soft tissues, is developed to quantitatively investigate the damping in soft tissues effects on the wide-frequency response of the ME sound transmission system. The model-derived results can capture the high-frequency (above 2 kHz) fluctuations and obtain the 0.9 kHz resonant frequency (RF) of the stapes velocity transfer function (SVTF) response. The results show that the damping of pars tensa (PT), stapedial annular ligament (SAL) and incudostapedial joints (ISJ) can help smooth the broadband response of the umbo and stapes footplate (SFP). It is found that, between 1 and 8 kHz, the damping of the PT increases the magnitude and phase delay of the SVTF above 2 kHz while the damping of the ISJ can avoid excessive phase delay of the SVTF, which is important in maintaining the synchronization in high-frequency vibration but has not been revealed before. Below 1 kHz, the damping of the SAL plays a more important role, and it can decrease the magnitude but increases the phase delay of the SVTF. This study has implications for a better understanding of the mechanism of ME sound transmission.

Mouse middle-ear forward and reverse acoustics

The mouse is an important animal model for hearing science. However, our knowledge of the relationship between mouse middle-ear (ME) anatomy and function is limited. The ME not only transmits sound to the cochlea in the forward direction, it also transmits otoacoustic emissions generated in the cochlea to the ear canal (EC) in the reverse direction. Due to experimental limitations, a complete characterization of the mouse ME has not been possible. A fully coupled finite-element model of the mouse EC, ME, and cochlea was developed and calibrated against experimental measurements. Impedances of the EC, ME, and cochlea were calculated, alongside pressure transfer functions for the forward, reverse, and round-trip directions. The effects on sound transmission of anatomical changes such as removing the ME cavity, pars flaccida, and mallear orbicular apophysis were also calculated. Surprisingly, below 10 kHz, the ME cavity, eardrum, and stapes annular ligament were found to significantly affect the cochlear input impedance, which is a result of acoustic coupling through the round window. The orbicular apophysis increases the delay of the transmission line formed by the flexible malleus, incus, and stapes, and improves the forward sound-transmission characteristics in the frequency region of 7-30 kHz.

Structural stiffening in the human middle ear due to static pressure: Finite-element analysis of combined static and dynamic middle-ear behavior

The vibration response of the middle ear (ME) to sound changes when static pressure gradients are applied across the tympanic membrane (TM). To date, it has not been well understood which mechanisms lead to these changes in ME vibration response. In this study, a 3D finite-element model of the human ME was developed that simulates the sound-induced ME vibration response when positive and negative static pressures of up to 4 kPa are applied to the TM. Hyperelasticity of the soft-tissue components was considered to simulate large deformations under static pressure. Some ME components were treated as viscoelastic materials to capture the difference between their static and dynamic stiffness, which was needed to replicate both static and dynamic ME behavior. The change in dynamic stiffness with static preload was simulated by linearization of the hyperelastic constitutive model around the predeformed state. For the preloaded harmonic response, we found that the statically deformed ME geometry introduced asymmetry in the vibration loss between positive and negative pressure, which was due to the TM cone shape. As opposed to previous assumptions, the prestress in the ME due to static pressure had a substantial impact on the vibration response. We also found that material nonlinearity led to a higher stiffening at the umbo but a less pronounced stiffening at the footplate compared to the linear elastic condition. The results suggest that flexibility of the incudomalleolar joint (IMJ) enhances the decoupling of static umbo and footplate displacements, and that viscosity and viscoelasticity of the IMJ could play a role in the transfer of sound-induced vibrations from the umbo to the footplate. The components of the incudostapedial joint had minimal effect on ME mechanical behavior.

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation of nonlinear viscoelasticity, according to the physical mode of deformation. The theory is consistent with linear viscoelasticity in the small strain limit and makes use of relaxation functions that can be determined from small-strain experiments, given the time/deformation separability assumption. After considering the general constitutive form applicable to compressible materials, attention is restricted to incompressible media. This enables a compact form for the constitutive relation to be derived, which is used to illustrate the behaviour of the model under three key deformations: uniaxial extension, transverse shear and longitudinal shear. Finally, it is demonstrated that the Poynting effect is present in TI, neo-Hookean, modified QLV materials under transverse shear, in contrast to neo-Hookean elastic materials subjected to the same deformation. Its presence is explained by the anisotropic relaxation response of the medium.

Fluid-Structure Finite-Element Modelling and Clinical Measurement of the Wideband Acoustic Input Admittance of the Newborn Ear Canal and Middle Ear

The anatomical differences between the newborn ear and the adult one result in different input admittance responses in newborns than those in adults. Taking into account fluid-structure interactions, we have developed a finite-element model to investigate the wideband admittance responses of the ear canal and middle ear in newborns for frequencies up to 10 kHz. We have also performed admittance measurements on a group of 23 infants with ages between 14 and 28 days, for frequencies from 250 to 8000 Hz with 1/12-octave resolution. Sensitivity analyses of the model were performed to investigate the contributions of the ear canal and middle ear to the overall admittance responses, as well as the effects of the material parameters, measurement location and geometrical variability. The model was validated by comparison with our new data and with data from the literature. The model provides a quantitative understanding of the canal and middle-ear resonances around 500 and 1800 Hz, respectively, and also predicts the effects of the first resonance mode of the middle-ear cavity (around 6 kHz) as well as the first and second standing-wave modes in the ear canal (around 7.2 and 9.6 kHz, respectively), which may explain features seen in our high-frequency-resolution clinical measurements.

Attenuating the ear canal feedback pressure of a laser-driven hearing aid

Microphone placement behind the pinna, which minimizes feedback but also reduces perception of the high-frequency pinna cues needed for sound localization, is one reason why hearing-aid users often complain of poor sound quality and difficulty understanding speech in noisy situations. In this paper, two strategies are investigated for minimizing the feedback pressure (thereby increasing the maximum stable gain, MSG) of a wide-bandwidth light-activated contact hearing aid (CHA) to facilitate microphone placement in the ear canal (EC): (1) changing the location of the drive force and its direction at the umbo, and (2) placing an acoustic damper within the EC to reduce the feedback pressure at the microphone location. The MSG and equivalent pressure output (EPO) are calculated in a 3D finite element model of a human middle ear based on micro computed tomography (micro-CT) images. The model calculations indicate that changing the umbo-force direction can decrease feedback pressure, but at the expense of decreased EPO. However the model shows improvements in MSG without sacrificing EPO when an acoustic damper is placed in the EC. This was verified through benchtop experimentation and in human cadaver temporal bones. The results pave the path towards a wide-bandwidth hearing aid that incorporates an EC-microphone design.

Finite-Element Modelling of the Acoustic Input Admittance of the Newborn Ear Canal and Middle Ear

Admittance measurement is a promising tool for evaluating the status of the middle ear in newborns. However, the newborn ear is anatomically very different from the adult one, and the acoustic input admittance is different than in adults. To aid in understanding the differences, a finite-element model of the newborn ear canal and middle ear was developed and its behaviour was studied for frequencies up to 2000 Hz. Material properties were taken from previous measurements and estimates. The simulation results were within the range of clinical admittance measurements made in newborns. Sensitivity analyses of the material properties show that in the canal model, the maximum admittance and the frequency at which that maximum admittance occurs are affected mainly by the stiffness parameter; in the middle-ear model, the damping is as important as the stiffness in influencing the maximum admittance magnitude but its effect on the corresponding frequency is negligible. Scaling up the geometries increases the admittance magnitude and shifts the resonances to lower frequencies. The results suggest that admittance measurements can provide more information about the condition of the middle ear when made at multiple frequencies around its resonance.

Finite-Element Modelling of the Response of the Gerbil Middle Ear to Sound

We present a finite-element model of the gerbil middle ear that, using a set of baseline parameters based primarily on a priori estimates from the literature, generates responses that are comparable with responses we measured in vivo using multi-point vibrometry and with those measured by other groups. We investigated the similarity of numerous features (umbo, pars-flaccida and pars-tensa displacement magnitudes, the resonance frequency and break-up frequency, etc.) in the experimental responses with corresponding ones in the model responses, as opposed to simply computing frequency-by-frequency differences between experimental and model responses. The umbo response of the model is within the range of variability seen in the experimental data in terms of the low-frequency (i.e., well below the middle-ear resonance) magnitude and phase, the main resonance frequency and magnitude, and the roll-off slope and irregularities in the response above the resonance frequency, but is somewhat high for frequencies above the resonance frequency. At low frequencies, the ossicular axis of rotation of the model appears to correspond to the anatomical axis but the behaviour is more complex at high frequencies (i.e., above the pars-tensa break-up). The behaviour of the pars tensa in the model is similar to what is observed experimentally in terms of magnitudes, phases, the break-up frequency of the spatial vibration pattern, and the bandwidths of the high-frequency response features. A sensitivity analysis showed that the parameters that have the strongest effects on the model results are the Young's modulus, thickness and density of the pars tensa; the Young's modulus of the stapedial annular ligament; and the Young's modulus and density of the malleus. Displacements of the tympanic membrane and manubrium and the low-frequency displacement of the stapes did not show large changes when the material properties of the incus, stapes, incudomallear joint, incudostapedial joint, and posterior incudal ligament were changed by ±10 % from their values in the baseline parameter set.

Simultaneous full-field 3-D vibrometry of the human eardrum using spatial-bandwidth multiplexed holography

Holographic interferometric methods typically require the use of three sensitivity vectors in order to obtain three-dimensional (3-D) information. Methods based on multiple directions of illumination have limited applications when studying biological tissues that have temporally varying responses such as the tympanic membrane (TM). Therefore, to measure 3-D displacements in such applications, the measurements along all the sensitivity vectors have to be done simultaneously. We propose a multiple-illumination directions approach to measure 3-D displacements from a single-shot hologram that contains displacement information from three sensitivity vectors. The hologram of an object of interest is simultaneously recorded with three incoherently superimposed pairs of reference and object beams. The incident off-axis angles of the reference beams are adjusted such that the frequency components of the multiplexed hologram are completely separate. Because of the differences in the directions and wavelengths of the reference beams, the positions of each reconstructed image corresponding to each sensitivity vector are different. We implemented a registration algorithm to accurately translate individual components of the hologram into a single global coordinate system to calculate 3-D displacements. The results include magnitudes and phases of 3-D sound-induced motions of a human cadaveric TM at several excitation frequencies showing modal and traveling wave motions on its surface.