Modeling of the human middle ear using the finite-element method

In this study, a three-dimensional finite-element model (FEM) of the human middle ear was established, including features of the middle ear which were not considered in the previous model, i.e., the ligaments, tendons, I-S joint, loading of the cochlea, external auditory meatus (EAM), middle-ear cavities, etc. The unknown mechanical properties of these parts and the boundary conditions were determined so that the impedance obtained from the FEM analysis resembled the measurement values. The validity of this model was confirmed by comparing the motion of the tympanic membrane and ossicles obtained by this model with the measurement data, and the effects of the newly considered features on the numerically obtained results were examined. By taking the ligaments and tendons into account and assuming that the cochlea acts as a damper, with this model it was possible to realistically reproduce complex ossicular chain movement. It was found that the middle-ear cavities did not affect the vibration mode of the tympanic membrane. Although the EAM enhanced the sound pressure applied to the tympanic membrane compared with that at the entrance of the EAM, the pressure distribution on the surface of the tympanic membrane was not affected by the EAM.     

Dynamical behavior of middle ear: theoretical study corresponding to measurement results obtained by a newly developed measuring apparatus

An attempt is made to develop a new measuring apparatus, and the dynamical characteristics of the middle ear of normal subjects and patients are measured with this apparatus. Applying the impedance theory of the tube to the external auditory canal, the aditus, and the tympanic and mastoid cavities, and applying the energy method to the eardrum and the ossicular chain, the equation of the middle ear, corresponding to the output of the apparatus and including the pressure difference effect upon the eardrum, is obtained. The numerical results are compared with the measurement results, and the effects of each part of the middle ear upon its dynamical characteristics are clarified. The great dependence of the dynamical characteristics of the middle ear upon the external auditory canal pressure is mainly caused by the pressure-dependent ossicular chain angular stiffness. The clearly different measurement results of the ossicular chain disorder patients from those of the normal subjects are obtainable by this apparatus, and these characteristics can be explained theoretically.     

Wave model of the cat tympanic membrane

In order to better understand signal propagation in the ear, a time-domain model of the tympanic membrane (TM) and of the ossicular chain (OC) is derived for the cat. Ossicles are represented by a two-port network and the TM is discretized into a series of transmission lines, each one characterized by its own delay and reflection coefficient. Volume velocity samples are distributed along the ear canal, the eardrum, and the middle ear, and are updated periodically to simulate wave propagation. The interest of the study resides in its time-domain implementation--while most previous related works remain in the frequency domain--which provides not only a direct observation of the propagating wave at each location, but also insight about how the wave behaves at the ear canal/TM interface. The model is designed to match a typical impedance behavior and is compared to previously published measurements of the middle ear (the canal, the TM, the ossicles and the annular ligament). The model matches the experimental data up to 15 kHz.     

Finite element modeling of acousto-mechanical coupling in the cat middle ear

The function of the middle ear is to transfer acoustic energy from the ear canal to the cochlea. An essential component of this system is the tympanic membrane. In this paper, a new finite element model of the middle ear of the domestic cat is presented, generated in part from cadaver anatomy via microcomputed tomographic imaging. This model includes a layered composite model of the eardrum, fully coupled with the acoustics in the ear canal and middle-ear cavities. Obtaining the frequency response from 100 Hz to 20 kHz is a computationally challenging task, which has been accomplished by using a new adaptive implementation of the reduced-order matrix Padé-via-Lanczos algorithm. The results are compared to established physiological data. The fully coupled model is applied to study the role of the collagen fiber sublayers of the eardrum and to investigate the relationship between the structure of the middle-ear cavities and its function. Three applications of this model are presented, demonstrating the shift in the middle-ear resonance due to the presence of the septum that divides the middle-ear cavity space, the significance of the radial fiber layer on high frequency transmission, and the importance of the transverse shear modulus in the eardrum microstructure.     

Attenuation and protection provided by ossicular removal

Behavioral studies of hearing loss produced by exposure to ototraumatic agents in experimental animals, combined with the anatomical evaluation of end-organ pathology, have provided useful information about the relation between dysfunction and pathology. However, in order to attribute a given hearing loss to some pattern of cochlear damage, it is necessary to test each ear independently. The objective of the present study was to evaluate attenuation measured behaviorally and protection to the cochlea provided by removal of the malleus and incus in noise-exposed chinchillas. Results from one behaviorally trained chinchilla with ossicular removal indicated a conductive hearing loss that varied from 41 dB at 0.125 kHz to 81 dB at 4.8 kHz and averaged 60 dB. Counts of missing sensory cells in ears of seven chinchillas with unilateral ossicular removal and exposure to noise (octave band centered at 0.5 kHz, 95 dB SPL, for durations up to 216 days, or centered at 4.0 kHz, 108 dB SPL, for 1.75 h) showed no more cell loss on the protected side than in age-matched control ears. From these data it is concluded that ossicular removal provides enough attenuation to protect the chinchilla cochlea from damage during these noise exposures, and that it will insure monaural responses behaviorally as long as the hearing loss in the test ear does not exceed that in the ear with ossicular removal by approximately 50 dB at any frequency.     

Acoustics of ear canal measurement of eardrum SPL in simulators

The effect of standing waves on the ear canal measurement of eardrum sound pressure level (SPL) was determined by both calculation and measurement. Transmission line calculations of the standing wave were made using the dimensions of the ANSI S3.25-1979 ear simulator and three different eardrum impedances. Standing wave curves have been obtained for the standard eardrum impedance at 1-kHz intervals in the range of 1-8 kHz. The changes in standing wave position due to each of the three eardrum impedances and their effects on ear canal measurements of SPL were computed for each of the eardrum impedances. Ear canal SPL measurements conducted on simulators modified to correspond to the eardrum impedances used in the calculations were compared to the computed values. Differences between eardrum SPLs and those measured at different locations in the ear canal approached a standing wave ratio (SWR) of 10-12 dB as the position of the measuring probe approached the standing wave minimum at each frequency. These maximum differences compared favorably with data developed by other investigators from real ears. Differences due to the eardrum impedance were found to be significant only in the frequency region of 2-5 kHz. Calibration of probes in a standard or modified ANSI simulator at the same distance from the eardrum as in the real ear reduces the eardrum SPL measurement errors to those resulting from differences in eardrum impedance.     

High-frequency hearing in phocid and otariid pinnipeds: an interpretation based on inertial and cochlear constraints (L)

Audiograms in air and underwater, determined by previous workers for four pinniped species, two eared seals (Otariidae) and two phocids (Phocidae), are supplemented here by measurements on their middle ear ossicular mass, enabling mechanistic interpretations of high-frequency hearing and audiogram differences. Otariid hearing is not largely affected by the medium (air/water). This indicates that cochlear constraints limit high-frequency hearing in otariids. Phocids, however, have massive middle ear ossicles, and underwater hearing has radically shifted towards higher frequencies. This suggests that the high-frequency hearing of phocids in air is constrained by ossicle inertia.     

Frequency domain finite-element and spectral-element acoustic wave modeling using absorbing boundaries and perfectly matched layer

Wave propagation modeling as a vital tool in seismology can be done via several different numerical methods among them are finite-difference, finite-element, and spectral-element methods (FDM, FEM and SEM). Some advanced applications in seismic exploration benefit the frequency domain modeling. Regarding flexibility in complex geological models and dealing with the free surface boundary condition, we studied the frequency domain acoustic wave equation using FEM and SEM. The results demonstrated that the frequency domain FEM and SEM have a good accuracy and numerical efficiency with the second order interpolation polynomials. Furthermore, we developed the second order Clayton and Engquist absorbing boundary condition (CE-ABC2) and compared it with the perfectly matched layer (PML) for the frequency domain FEM and SEM. In spite of PML method, CE-ABC2 does not add any additional computational cost to the modeling except assembling boundary matrices. As a result, considering CE-ABC2 is more efficient than PML for the frequency domain acoustic wave propagation modeling especially when computational cost is high and high-level absorbing performance is unnecessary.     

On the damped frequency response of a finite-element model of the cat eardrum

This article presents frequency responses calculated using a three-dimensional finite-element model of the cat eardrum that includes damping. The damping is represented by both mass-proportional and stiffness-proportional terms. With light damping, the frequency responses of points on the eardrum away from the manubrium display numerous narrow minima and maxima, the frequencies and amplitudes of which are different for different positions on the eardrum. The frequency response on the manubrium is smoother than that on the eardrum away from the manubrium. Increasing the degree of damping smooths the frequency responses both on the manubrium and on the eardrum away from the manubrium. The overall displacement magnitudes are not significantly reduced even when the damping is heavy enough to smooth out all but the largest variations. Experimentally observed frequency responses of the cat eardrum are presented for comparison with the model results.     

Boundary element modeling of the external human auditory system

In this paper the response of the external auditory system to acoustical waves of varying frequencies and angles of incidence is computed using a boundary element method. The resonance patterns of both the ear canal and the concha are computed and compared with experimental data. Specialized numerical algorithms are developed that allow for the efficient computation of the eardrum pressures. In contrast to previous results in the literature that consider only the "blocked meatus" configuration, in this work the simulations are conducted on a boundary element mesh that includes both the external head/ear geometry, as well as the ear canal and eardrum. The simulation technology developed in this work is intended to demonstrate the utility of numerical analysis in studying physical phenomena related to the external auditory system. Later work could extend this towards simulating in situ hearing aids, and possibly using the simulations as a tool for optimizing hearing aid technologies for particular individuals.     

A hierarchy of examples illustrating the acoustic coupling of the eardrum

Basic principles underlying the acoustic coupling of the eardrum are illustrated in the form of a hierarchy of examples ranging from a simple piston coupled to a semi-infinite acoustic duct, to a flexible partition coupled to a variable cross-section duct, and to a closed cavity. The hierarchy illuminates some of the limitations of various simplified elements commonly used to model the middle ear and demonstrates the necessity of treating the acoustics and the eardrum as an integrated subsystem. Results show that the tympanic cavity and the secondary middle-ear air chambers contribute fundamental features to the acoustic coupling of the ear. The nature of the acoustic coupling limits the passive energy absorption and transmission properties of the eardrum. The magnitude and frequency dependence of the energy dissipation within the ultrastructure of the partition, due to bending and transverse deflection, is discussed in analogy to possible dissipation mechanisms within the eardrum itself. Examples are provided for several simple systems reproducing some of the gross anatomical characteristics of the cat eardrum.     

An empirical bound on the compressibility of the cochlea.

Effects of a possible inner-ear compressibility on middle-ear transfer functions are explored and a small upper bound on the magnitude of that compressibility established. Consequently. the traditional two-port representation of middle-ear mechanics remains valid to within a few percent. If the compressibility of the cochlea is small but finite, a simple phenomenological model of that compressibility correctly predicts hearing thresholds in the "middleless" ear at low frequencies. Experiments to establish the value of cochlear compressibility and to explore further its possible contributions to residual hearing in patients with missing or disarticulated middle-ear ossicles are suggested.     

Factors contributing to bone conduction: the middle ear

Measurement of the motion of the malleus umbo and stapes footplate during bone conduction (BC) stimulation was conducted in vitro in 26 temporal bones using a laser Doppler vibrometer over the frequency range 0.1 to 10 kHz. For lower frequencies, both ossicular sites followed the motion of the temporal bone. The differential motion between the malleus and the surrounding bone was greater than the differential motion of the stapes footplate; both resonated near 1.5 kHz. Different lesions were shown to affect the response: (1) a mass attached to the umbo lowered the resonance frequency of the ossicular vibration; (2) fixation of either the malleus or stapes increased the stiffness and shifted the resonance frequency upward; and (3) dislocation of the incudo-stapedial joint did not significantly affect the ossicular vibration. The sound radiated from the tympanic membrane was approximately 85 dB SPL at an umbo differential velocity of 1 mm/s for low frequencies in an open ear canal and about 10 dB higher for an occluded one; at higher frequencies (above 2 kHz) resonances of the canal determine the response. It was also found that the motion between the footplate and promontory was within 5 dB when the specimen was stimulated orthogonal to the vibration direction of the ossicles than in line with the same. Measurement of the differential motion of the umbo in one live human skull gave similar response as the average result from the temporal bone specimens.     

The spatial distribution of sound pressure within scaled replicas of the human ear canal

A theoretical model for calculating the variation of sound pressure within the ear canal is presented. The theory is an extension of the horn equation approach, and accounts for the variation of cross-sectional area and curvature of the ear canal along its length. Absorption of acoustic energy at the eardrum is included empirically through an effective eardrum impedance that acts at a single location in the canal. For comparison, measurements of the distribution of sound pressure have been made in two replica ear canals. Both replicas have geometries that duplicate, as nearly as possible, that of a real human ear canal, except that they have been scaled up in size to increase the precision of measurements. One of the replicas explicitly contains a load impedance to provide acoustical absorption at a single eardrum position. Agreement between theory and experiment was good. It is clear that at higher frequencies (above about 6 kHz in human ear canals), this theoretical approach is preferable to the more usual "uniform cylinder" approximation for the ear canal. At higher frequencies, there is no unique eardrum pressure; rather, very large variations of sound pressure are found over the tympanic membrane surface.     

Estimating head-related transfer functions of human subjects from pressure-velocity measurements

Direct measurements of individual head-related transfer functions (HRTFs) with a probe microphone at the eardrum are unpleasant, risky, and unreliable and therefore have not been widely used. Instead, the HRTFs are commonly measured from the blocked ear canal entrance, which excludes the effects of the individual ear canals and eardrums. This paper presents a method that allows obtaining individually correct magnitude frequency responses of HRTFs at the eardrum from pressure-velocity (PU) measurements at the ear canal entrance with a miniature PU sensor. The HRTFs of 25 test subjects with nine directions of sound incidence were estimated using real anechoic measurements and an energy-based estimation method. To validate the approach, measurements were also conducted with probe microphones near the eardrums as well as at blocked ear canal entrances. Comparisons between the different methods show that the method presented is a valid and reliable technique for obtaining magnitude frequency responses of HRTFs. The HRTF filters designed using the PU measurements are also shown to yield more correct frequency responses at the eardrum than the filters designed using measurements from the blocked ear canal entrance.     

Development of form and function in peripheral auditory structures of the zebrafish (Danio rerio)

Investigations of the development of auditory form and function have, with a few exceptions, thus far been largely restricted to birds and mammals, making it difficult to postulate evolutionary hypotheses. Teleost fishes represent useful models for developmental investigations of the auditory system due to their often extensive period of posthatching development and the diversity of auditory specializations in this group. Using the auditory brainstem response and morphological techniques we investigated the development of auditory form and function in zebrafish (Danio rerio) ranging in size from 10 to 45 mm total length. We found no difference in auditory sensitivity, response latency, or response amplitude with development, but we did find an expansion of maximum detectable frequency from 200 Hz at 10 mm to 4000 Hz at 45 mm TL. The expansion of frequency range coincided with the development of Weberian ossicles in zebrafish, suggesting that changes in hearing ability in this species are driven more by development of auxiliary specializations than by the ear itself. We propose a model for the development of zebrafish hearing wherein the Weberian ossicles gradually increase the range of frequencies available to the inner ear, much as middle ear development increases frequency range in mammals.     

A computer simulation of hearing aid response and the effects of ear canal size

The response of a hearing aid is affected by many factors which include the head and outer ear, the microphone, amplifier, and receiver used in the hearing aid, the properties of the ear canal and the eardrum, and acoustic feedback through the vent. This article presents a computer simulation of an in-the-ear (ITE) hearing aid that includes all of the above factors. The simulation predicts the pressure at the eardrum for a frontal free-field sound source. The computer model was then used to determine the effects on the hearing aid response due to variations in the size of the ear canal. The simulation indicates that, for an unvented hearing aid, changes in the size of the ear canal shift the overall sound-pressure level at the eardrum but have only small effects on the shape of the frequency response. The situation is more complicated when a vent is present, however, since changes in the size of the ear canal that cause apparently small perturbations in the acoustic feedback signal may, nonetheless, have large effects on the overall system response.     

Occluded-ear simulator with variable acoustic properties.

Ear simulators were designed to replicate acoustical characteristics of the average adult ear. Due to variability of ear-canal geometry and eardrum impedance among individuals, the possibility of any one person exhibiting such "average" characteristics--especially if that person is a child and/or has a conductive pathology--is remote. Thus, ear simulators have been of only peripheral value when prescribing a hearing aid (a high output impedance device) to fit the acoustical requirements of a particular patient. Reported herein is development of a programmable artificial ear (PAE) that can account for individual differences in ear-canal geometry and eardrum impedance. It consists of a 2.0-cc coupler, microphone, amplifier, computer, PAE code, and a computer card and/or software for digitization and Fourier transformation. Required input data includes ear-canal dimensions, eardrum impedance, and output impedance of the hearing aid being tested. Sound-pressure recordings produced in the 2.0-cc coupler by the hearing aid are adjusted by the computer to what they would have been had the recordings been made at the eardrum of a particular patient wearing the same hearing aid. Good agreement was observed between experiment and theory for one test case involving a totally occluding miniature earphone.