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.     

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.     

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.     

Verifying the attenuation of earplugs in situ: method validation using artificial head and numerical simulations

The use of in situ measurements of hearing protectors' (HPD's) attenuation following the microphone in real ear (MIRE) protocol is increasing. The attenuation is hereby calculated from the difference in sound levels outside the ear and inside the ear canal behind the HPD. Custom-made earplugs have been designed with an inner bore that allows inserting a miniature microphone. A thorough understanding of the difference, henceforth called transfer function, between the sound pressure of interest at the eardrum and the one measured at the inner bore of the HPD is indispensable for optimizing the MIRE technique and extending its field of application. This issue was addressed by measurements on a head-and-torso-simulator and finite difference time domain numerical simulations of the outer ear canal occluded by an earplug. Both approaches are in good agreement and reveal a clear distinction between the sound pressure at the MIRE microphone and at eardrum, but the measured transfer functions appear to be stable and reproducible. Moreover, the most striking features of the transfer functions can be traced down to the geometrical and morphological characteristics of the earplug and ear canal.     

Simulating the open-loop transfer function as a means for understanding acoustic feedback in hearing aids

Suppressing unstable acoustic feedback in hearing aids will first require knowledge of the open-loop transfer functions of such systems. Reported herein is a mathematical technique for simulating the open-loop transfer function of an in situ eyeglass-type hearing aid. In particular, a computer program was developed that characterized the hearing aid as a serial connection of two-port blocks, each representing one individual component of a hearing aid. Included, for example, were two-port blocks representing the microphone, amplifier, receiver, sound tubes leading to the eardrum (including the ear canal itself), earmold vent, and external pathway from the vent outlet back to the microphone. The computer program was validated by replicating laboratory data derived from an experiment involving a nonstandard manikin fitted with a nonstandard artificial ear. Next, the open-loop transfer function of an eyeglass-type hearing aid in situ on the manikin was simulated via the computer program. Unfortunately, those computer-generated data were not replicated in the laboratory due to the difficulty encountered in actually measuring the open-loop transfer function. Nevertheless, investigators were able to utilize those data to predict, within +/- 25 Hz, the "squeal" frequency of unstable acoustic feedback.     

Specification of the acoustical input to the ear at high frequencies

The sound fields that arise in the auditory canals of cats have been examined both experimentally and theoretically. Of particular interest was the spatial variation of sound pressure near the eardrum, where reference probes are typically located. Using a computer controlled data acquisition system, sound pressure was measured between 100 Hz and 33 kHz for constant driver input at 14 different locations in the ear canal of a cat, and the standing wave patterns formed. The shape of the patterns could be predicted quite well above 12 kHz using a theory that requires specification of only the geometry of the ear canal. This theory, an extension of the one-dimensional horn equation, applies to three-dimensional, rigid-walled tubes that have both variable cross section and curvature along their lengths. Large variations of sound pressure along the ear canal and over the surface of the eardrum are found above about 10 kHz. As a consequence it is not possible to define the acoustical input to the ear from sound pressure level measured at any single location. Even in comparative experiments, in which only the constancy of the acoustical input is important, any uncertainty in reference probe location would lead to an uncertainty in sound pressure level when different sets of measurements are compared. This error, calculated for various probe locations and frequencies, is especially large when the probe is near a minimum of the sound field. Spatial variations in pressure can also introduce anomalous features into the measured frequency response of other auditory quantities when eardrum sound pressure is used as a reference. This is illustrated with measurements of the round window cochlear microphonic.     

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.     

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.     

A technique for simulating the amplifier-to-eardrum transfer function of an in situ hearing aid

There are numerous articles wherein mathematical models of various parts of an in situ hearing aid have been reported. Such parts include, for example, the microphone, receiver, cylindrical tubes carrying sound to the eardrum and out through the earmold vent, and the external path from the vent back to the microphone. This article extends these earlier works to include the hearing-aid amplifier. In particular, a mathematical technique for characterizing the amplifier in combination with the receiver is reported. Cascade parameters of a two-port model of one particular amplifier/receiver combination are obtained by this method. The cascade-parameter data and the method of obtaining this data are verified by two different experimental procedures. One procedure involves both computing and measuring the input driving-point impedance of the amplifier/receiver combination. In the second procedure, the amplifier-to-eardrum transfer function of a hearing aid incorporating this same amplifier/receiver combination and mounted on an artificial ear is both computed and measured. Experimental and computed values of this transfer function for three different earmold geometries are in reasonably close agreement. The amplifier/receiver model reported herein will be used in future studies of acoustic feedback in hearing aids.     

Three-dimensional acoustic waves in the ear canal and their interaction with the tympanic membrane

The long and slender geometry of the ear canal supports an infinite number of cross-sectional acoustic modes. The lower mode(s) travel along the length of the ear canal, while the higher modes are trapped near the ends of the canal. Many of these waves are introduced as a result of the complex vibrational shape of the eardrum. A three-dimensional mathematical model of the ear canal is formulated that includes this acoustic interaction. The coupled system is solved using matched asymptotic expansions that take advantage of the small slenderness ratio. This solution in the ear canal is in the form of a series of modes, the first being the plane-wave solution. As an illustrative example, the analysis is applied to a geometry that partially represents the ear canal and eardrum of a cat. The results indicate that the plane-wave solution is supplemented by multidimensional trapped modes at low frequencies and by a limited number of traveling waves at high frequencies. The magnitude of these higher modes generally increases with frequency and can significantly influence the acoustic coupling of the ear.     

Analysis of dynamic behavior of human middle ear using a finite-element method.

Applying the general-purpose finite-element package program (ISAP), a three-dimensional finite-element method (FEM) model of a human right middle ear, which included ossicles, was made and the mechanical properties and boundary conditions of the middle ear were determined by a comparison between the numerical results obtained from the FEM analysis and the measurement results of the fresh cadavers, normal subjects and patients, which were obtained by our developed sweep frequency middle ear analyzer (MEA). The "Elastic" boundary condition consisting of linear and torsional springs at the eardrum attachments to the annular ligament was more appropriate for the actual condition than "fully clamped" one. Rotational axis of the ossicular chain was assumed to be a fixed straight line from the anterior process of the malleus to the short process of the incus, and a load of the ossicular chain and cochlea was simplified to be expressed by the stiffness of the cochlea. Vibration patterns of the eardrum and ossicles at the first resonance frequency, obtained under these assumptions, were in agreement with the experimental results obtained by means of time-averaged holography and by using a video measuring system, except for the relatively large displacements at the tympanic ring.     

Development of an electroacoustic analogue model of the middle ear and acoustic reflex

Experimental measurements of changes in the acoustic admittance of the eardrum caused by stapedius muscle contractions in human subjects are used to develop and electroacoustic analogue model of the middle ear. In this model the stapedius muscle is included as an explicit functional unit. The acoustical characteristics of the external ear canal are also included. The model is extensively evaluated by comparing its properties with the known characteristics of real ears of humans and other animals. Subsequently, the model is used to predict the effects of the acoustic reflex on middle ear sound transmission, which cannot easily be measured in humans. The model predicts attenuation of potentially hazardous high level sounds at frequencies below 1 kHz of up to about 10 dB, but very little effect at higher frequencies unless the reflex-eliciting stimulus is of sufficient intensity to cause partial disarticulation of the incudo-stapedial joint by stapedius muscle contraction. Overall attenuation for typical industrial noises is unlikely to be greater than approximately 3 dB(A) and will probably be even less in practice, resulting in little effective protection from the harmful effects of high intensity noise. It is considered that the model will be of benefit in the analysis of middle ear function, including the interpretation of audiological measurements of eardrum impedance and acoustic reflex response. This should lead to more versatile diagnosis of peripheral auditory dysfunction than has been possible hitherto.     

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.     

Estimation of eardrum acoustic pressure and of ear canal length from remote points in the canal

Sound pressure distributions in the human ear canal, whether unoccluded or occluded with ear molds, were studied using a probe tube technique. On average, for frequencies below 6 kHz, the measuring probe tube had to be placed within 8 mm of the vertical plane containing the top of the eardrum (TOD), determined optically, in order to obtain sound pressure magnitudes within 6 dB of "eardrum pressure." To obtain that accuracy in all of the eight subjects studied, the probe had to be within 6 mm of the TOD. Since probe location relative to the drum has to be known, a purely acoustic method was developed which can be conveniently used to localize the probe-tip position, utilizing the standing wave property of the sound pressure in the ear canal. The acoustically estimated "drum location" generally lay between the optically determined vertical planes containing the TOD and the umbo. On average, the "drum location" fell 1 mm medial to the TOD. Of the 32 estimates made acoustically in various occluded and unoccluded conditions in 14 subjects, 30 estimates lay within a +/- 2-mm range of this average.     

Optical method for measurement of ear canal length

A noninvasive optical method using an operating microscope was developed to measure the length of an ear canal under both open and occluded conditions. The method is based on the optical measurement of the distance between a reference point at the eardrum and a second point on the lateral aspect of an earmold-occluded ear canal. To estimate the occluded canal length, the length of the earmold is then subtracted from results of the previous measurement. The method was also used to determine the open ear canal length (the lateral reference point was the ear canal entrance), and averaged results agreed closely with previously reported data.     

Transverse pressure distributions in a simple model ear canal occluded by a hearing aid test fixture

The sound field in a model ear canal with a hearing aid test fixture has been investigated experimentally and theoretically. Large transverse variations of sound pressure level, as much as 20 dB at 8 kHz, were found across the inner face of the hearing aid. Variations are greatest near the outlet port of the receiver and the vent port. Deeper into the canal, the transverse variations are less significant and, at depths greater than 4 mm, only a longitudinal variation remains. The model canal was cylindrical, 7.5 mm diameter, and terminated with a Zwislocki coupler to represent absorption by the human middle ear. The outer end of the canal was driven by the receiver in the hearing aid test fixture, with the acoustic output entering the canal through a 1 mm port. The hearing aid was provided with a 20-mm-long vent, either 1 or 2 mm in diameter. The sound field inside the canal was measured using a specially designed 0.2-mm-diam probe microphone [Daigle and Stinson, J. Acoust. Soc. Am. 116, 2618 (2004)]. In parallel, calculations of the interior sound field were performed using a boundary element technique and found to agree well with measurements.     

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.     

Sound propagation in the ear canal and coupling to the eardrum, with measurements on model systems

A theoretical model of sound propagation in the ear canal is described, which takes into account both the complicated geometry of real ear canals and the distributed acoustical load presented by the eardrum. The geometry of the ear canal enters the theory in the form of a cross-sectional area function relative to a curved axis that follows the center of the ear canal. The tympanic membrane forms part of the ear canal wall and absorbs acoustical energy over its surface. Its motion leads to a driving term that must be added to the horn equation describing the pressure distribution in the ear canal. The sound field within the canal is assumed to be effectively one dimensional, depending only on longitudinal position along the canal. Experiments using model ear canals of uniform cross section were performed to test the ability of the theory to handle distributed loads. Sound-pressure distributions within each model canal were measured using a probe microphone. The behavior of the eardrum was simulated using either a distributed, locally reacting impedance or a mechanically driven piston. The agreement between theory and experiment is good up to a nominal upper frequency limit at which the ratio of canal width to wavelength is 0.25. It is estimated that the theory is applicable in ear canals of cats for frequencies at least as high as 25 kHz and in human ear canals to at least 15 kHz.     

Experimental analysis of considering the sound pressure distribution pattern at the ear canal entrance as an unrevealed head-related localization clue

By analyzing the differences between binaural recording and real listening, it was deduced that there were some unrevealed auditory localization clues, and the sound pressure distribution pattern at the entrance of ear canal was probably a clue. It was proved through the listening test that the unrevealed auditory localization clues really exist with the reduction to absurdity. And the effective frequency bands of the unrevealed localization clues were induced and summed. The result of finite element based simulations showed that the pressure distribution at the entrance of ear canal was non-uniform, and the pattern was related to the direction of sound source. And it was proved that the sound pressure distribution pattern at the entrance of the ear canal carried the sound source direction information and could be used as an unrevealed localization clue. The frequency bands in which the sound pressure distribution patterns had significant differences between front and back sound source directions were roughly matched with the effective frequency bands of unrevealed localization clues obtained from the listening tests. To some extent, it supports the hypothesis that the sound pressure distribution pattern could be a kind of unrevealed auditory localization clues.     

A mechano-acoustic model of the effect of superior canal dehiscence on hearing in chinchilla

Superior canal dehiscence (SCD) is a pathological condition of the ear that can cause a conductive hearing loss. The effect of SCD (a hole in the bony wall of the superior semicircular canal) on chinchilla middle- and inner-ear mechanics is analyzed with a circuit model of the dehiscence. The model is used to predict the effect of dehiscence on auditory sensitivity and mechanics. These predictions are compared to previously published measurements of dehiscence related changes in chinchilla cochlear potential, middle-ear input admittance and stapes velocity. The comparisons show that the model predictions are both qualitatively and quantitatively similar to the physiological results for frequencies where physiologic data are available. The similarity supports the third-window hypothesis of the effect of superior canal dehiscence on auditory sensitivity and mechanics and provides the groundwork for the development of a model that predicts the effect of superior canal dehiscence syndrome on auditory sensitivity and mechanics in humans.