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.     

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.     

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.     

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.     

Comparison of an analytic horn equation approach and a boundary element method for the calculation of sound fields in the human ear canal

The sound field inside a model human ear canal has been computed, to show both longitudinal variations along the canal length and transverse variations through cross-sectional slices. Two methods of computation were used. A modified horn equation approach parametrizes the sound field with a single coordinate, the position along a curved center axis-this approach can accommodate the curvature and varying cross-sectional area of the ear canal but cannot compute transverse variations of the sound field. A boundary element method (BEM) was also implemented to compute the full three-dimensional sound field. Over 2000 triangular mesh elements were used to represent the ear canal geometry. For a plane piston source at the entrance plane, the pressure along the curved center axis predicted by the two methods is in good agreement, for frequencies up to 15 kHz, for four different ear canals. The BEM approach, though, reveals spatial variations of sound pressure within each canal cross section. These variations are small below 4 kHz, but increase with frequency, reaching 1.5 dB at 8 kHz and 4.5 dB at 15 kHz. For source configurations that are more realistic than a simple piston, large transverse variations in sound pressure are anticipated in the vicinity of the source.     

Sound pressure distribution and power flow within the gerbil ear canal from 100 Hz to 80 kHz

Sound pressure was mapped in the bony ear canal of gerbils during closed-field sound stimulation at frequencies from 0.1 to 80 kHz. A 1.27-mm-diam probe-tube microphone or a 0.17-mm-diam fiber-optic miniature microphone was positioned along approximately longitudinal trajectories within the 2.3-mm-diam ear canal. Substantial spatial variations in sound pressure, sharp minima in magnitude, and half-cycle phase changes occurred at frequencies >30 kHz. The sound frequencies of these transitions increased with decreasing distance from the tympanic membrane (TM). Sound pressure measured orthogonally across the surface of the TM showed only small variations at frequencies below 60 kHz. Hence, the ear canal sound field can be described fairly well as a one-dimensional standing wave pattern. Ear-canal power reflectance estimated from longitudinal spatial variations was roughly constant at 0.2-0.5 at frequencies between 30 and 45 kHz. In contrast, reflectance increased at higher frequencies to at least 0.8 above 60 kHz. Sound pressure was also mapped in a microphone-terminated uniform tube-an "artificial ear." Comparison with ear canal sound fields suggests that an artificial ear or "artificial cavity calibration" technique may underestimate the in situ sound pressure by 5-15 dB between 40 and 60 kHz.     

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.     

Frequency characteristics of sound transmission in middle ears from Norwegian cattle, and the effect of static pressure differences across the tympanic membrane and the footplate

For 23 cadaver ears from Norwegian cattle, frequency characteristics for the round-window volume displacement relative to the sound pressure at the eardrum have been measured, and are compared to earlier results for human ears [M. Kringlebotn and T. Gundersen, J. Acoust. Soc. Am. 77(1), 159-164 (1985)]. For human as well as for cattle ears, mean amplitude curves have peaks at about 0.7 kHz. At lower frequencies, the mean amplitude for cattle ears is about 5 dB smaller than for human ears. The amplitude curves cross at about 2 kHz, and toward higher frequencies the amplitude for cattle ears becomes increasingly larger. If amplitude curves are roughly approximated by straight lines above 1 kHz, the slope for cattle ears is about -5 dB/octave as compared to about -15 dB/octave for human ears. The phase of the round-window volume displacement lags behind the phase of the sound pressure at the tympanic membrane. The phase lag is close to zero below 0.2 kHz, but increases to about 3.5 pi at 20 kHz for cattle ears, as compared to less than 2 pi for human ears. Further investigations are needed in order to explain the observed differences. Sound transmission in the ear decreases with an increasing static pressure difference across the tympanic membrane, especially at frequencies below 1 kHz, where pressure differences of 10 and 60 cm water cause mean transmission losses of about 10 and 26 dB, respectively, the losses being somewhat larger for overpressures than for underpressures in the ear canal. At higher frequencies, the transmission losses are smaller. For small overpressures, and in a limited frequency range near 3 kHz, even some transmission enhancement may occur. Static pressure variations in the inner ear have only a minor influence on sound transmission. Static pressures relative to the middle ear in the range 0-60 cm water cause mean sound transmission losses less than 5 dB below 1 kHz, and negligible losses at higher frequencies.     

Specification of absorbed-sound power in the ear canal: application to suppression of stimulus frequency otoacoustic emissions

An insert ear-canal probe including sound source and microphone can deliver a calibrated sound power level to the ear. The aural power absorbed is proportional to the product of mean-squared forward pressure, ear-canal area, and absorbance, in which the sound field is represented using forward (reverse) waves traveling toward (away from) the eardrum. Forward pressure is composed of incident pressure and its multiple internal reflections between eardrum and probe. Based on a database of measurements in normal-hearing adults from 0.22 to 8 kHz, the transfer-function level of forward relative to incident pressure is boosted below 0.7 kHz and within 4 dB above. The level of forward relative to total pressure is maximal close to 4 kHz with wide variability across ears. A spectrally flat incident-pressure level across frequency produces a nearly flat absorbed power level, in contrast to 19 dB changes in pressure level. Calibrating an ear-canal sound source based on absorbed power may be useful in audiological and research applications. Specifying the tip-to-tail level difference of the suppression tuning curve of stimulus frequency otoacoustic emissions in terms of absorbed power reveals increased cochlear gain at 8 kHz relative to the level difference measured using total pressure.     

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.     

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.     

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.     

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.     

Factors contributing to bone conduction: the outer ear

The ear canal sound pressure and the malleus umbo velocity with bone conduction (BC) stimulation were measured in nine ears from five cadaver heads in the frequency range 0.1 to 10 kHz. The measurements were conducted with both open and occluded ear canals, before and after resection of the lower jaw, in a canal with the cartilage and soft tissues removed, and with the tympanic membrane (TM) removed. The sound pressure was about 10 dB greater in an intact ear canal than when the cartilage part of the canal had been removed. The occlusion effect was close to 20 dB for the low frequencies in an intact ear canal; this effect diminished with sectioning of the canal. At higher frequencies, the resonance properties of the ear canal determined the effect of occluding the ear canal. Sectioning of the lower jaw did not significantly alter the sound pressure in the ear canal. The sound radiated from the TM into the ear canal was investigated in four temporal bone specimens; this sound is significantly lower than the sound pressure in an intact ear canal with BC stimulation. The malleus umbo velocity with air conduction stimulation was investigated in nine temporal bone specimens and compared with the umbo velocity obtained with BC stimulation in the cadaver heads. The results show that for a normal open ear canal, the sound pressure in the ear canal with BC stimulation is not significant for BC hearing. At threshold levels and for frequencies below 2 kHz, the sound in the ear canal caused by BC stimulation is about 10 dB lower than air conduction hearing thresholds; this difference increases at higher frequencies. However, with the ear canal occluded, BC hearing is dominated by the sound pressure in the outer ear canal for frequencies between 0.4 and 1.2 kHz.     

Calibration of ear canals for audiometry at high frequencies

A procedure is described for determining the absolute sound pressure at the inner end of the ear canal when a sound source is coupled to the ear, for frequencies in the range 8-20 kHz. The transducer that generates the sound is coupled to the ear canal through a lossy tube, yielding a source impedance that is approximately matched to the characteristic impedance of the ear canal. A small microphone is located in the coupling tube close to the entrance to the ear canal. Calibration is carried out by measuring the response at this microphone when an impulse is applied at the transducer. To estimate the sound pressure at the medial end of the ear canal, the Fourier transform of this impulse response is corrected by an all-pole function in which the poles are estimated from the minima in this Fourier transform. Data on individual ear canals are presented in terms of gain functions relating the sound pressure at the medial end of the ear canal to the sound pressure when the coupling tube is blocked. The average gain function for a group of adult ears increases from 2 to 12 dB over the frequency range 8-20 kHz, in rough agreement with data from ear-canal models. Possible sources of error in the calibration procedure are discussed.     

Frequency characteristics of the middle ear

For 68 temporal bones, frequency curves for the round window volume displacement have been measured for a constant sound pressure at the eardrum. Phase curves were measured for 33 of the specimens. The levels averaged amplitude curve is approximately flat below 1 kHz, where the round window volume displacement per unit sound pressure at the eardrum is 6.8 X 10(-5) mm3/Pa, and falls off by about 15 dB/oct at higher frequencies. For the 20 ears having the largest sound transmission magnitude at low frequencies, the corresponding amplitude curve is displaced about 5 dB towards higher levels. The phase of the round window volume displacement lags the eardrum sound pressure phase. In average for 33 temporal bones, the phase lag increases from zero at the lowest frequencies to pi near 2 kHz and to about 1.5 pi at 10 kHz.     

Inverse solution of ear-canal area function from reflectance

A number of acoustical applications require the transformation of acoustical quantities, such as impedance and pressure that are measured at the entrance of the ear canal, to quantities at the eardrum. This transformation often requires knowledge of the shape of the ear canal. Previous attempts to measure ear-canal area functions were either invasive, non-reproducible, or could only measure the area function up to a point mid-way along the canal. A method to determine the area function of the ear canal from measurements of acoustic impedance at the entrance of the ear canal is described. The method is based on a solution to the inverse problem in which measurements of impedance are used to calculate reflectance, which is then used to determine the area function of the canal. The mean ear-canal area function determined using this method is similar to mean ear-canal area functions measured by other researchers using different techniques. The advantage of the proposed method over previous methods is that it is non- invasive, fast, and reproducible.     

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.     

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.     

Coupling of earphones to human ears and to standard coupler

A standardized acoustical coupler should enable the calibration of audiometric earphones which ensures that the hearing thresholds determined in the audiometric measurement are independent of the earphone type. This requires that the coupler approximates the average human ear closely. Nevertheless, the differences among earphones as well as between human ears and the coupler affect the results of the audiometric measurements inducing uncertainty. As the mentioned differences are related to the coupling of different earphones to human ears and to a standardized coupler, the effects of this coupling are investigated by measuring the transfer functions from input voltage of the earphone terminals to the pressure at the ear canal entrance in two situations: open and blocked canals. Since the "ear canal entrance" is not well-defined for the coupler, transfer function measurements in the coupler were carried out in a similar way but at different depths. In order to describe and compare the earphone couplings, the pressure divisions at the entrance of the ear canal are calculated from the measured transfer functions. The results indicate that significant difference appears among sound pressures generated in different individuals' ears. Also, the earphone couplings to human ears and to the coupler differ considerably.