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.     

How the cross-sectional discontinuity between ear canal and probe affects the ear canal length estimation

Many ear canal probes both deliver and measure sound via narrow tubes. This study investigates the effect of the cross-sectional discontinuity at the interface between ear canal models and the connecting tubes of a commercially available otoacoustic emission probe on the "acoustically" estimated cavity lengths. Rigid cavities having the same length but different diameters were produced, and modeled by the finite element method. Cavities with a diameter larger than 8 mm had acoustic lengths that considerably overestimated the real geometry. A length correction was derived, which, in most applications, compensates for the measurement errors emerging from the discontinuity effects.     

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.     

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.     

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.     

Eartip modifications for more accurate acoustic length estimations of ear canal models or calibration cavities

The cross-sectional discontinuity between a probe eartip and an ear canal (EC) causes the latter to “acoustically” appear longer than it is “geometrically”. In this study, the idea of whether modifications within the eartip geometry can reduce this length overestimation was investigated: (i) upon extending one of the connecting (sound or microphone) tubes and (ii) upon sinking the entire probe tube assembly into the eartip. Finite element models of the eartip modifications were created, and validated by measurements on rigid EC models using eartip prototypes. Whereas extending the sound tube yielded no considerable effect, extending the microphone tube by 2 mm counterbalanced the discontinuity effect for a 12 mm diameter EC model. Alternatively, sinking the tube assembly 2 mm into the eartip allowed for radially symmetric sound radiation at the discontinuity, which was then described by a series inductance in the lumped-element equivalent circuit. Whereas this elaborate modification with the recess is more appropriate for calibration purposes (where the exact geometry of a calibration cavity or EC simulator is known), a microphone extension is more practical when a rough length estimate of large-diameter ECs is required. In most practical applications, discontinuity effects can be accounted for by using modified eartips.     

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.     

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.     

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.     

Ear canal cross-sectional pressure distributions: mathematical analysis and computation.

Cross-sectional pressure distributions, natural acoustic modes, and associated cutoff frequencies are determined for real ear-canal geometries using an asymptotic theory in combination with a numerical method. The technique is particularly well suited to obtain the higher modes, which are trapped near both ends of the ear canal. Results detail the influence of the canal geometry and frequency on the spatial distribution of the pressure. Adult ear-canal geometries are determined near the concha from ear-mold sections using a light microscope interfaced to a video-data-acquisition system. Computed results compare favorably to the exact solutions for circular and square acoustic waveguides. The cutoff frequency of the two adult ear canals studied averaged 20% less than the cutoff frequency of a circular tube of identical cross-sectional area. Inserting a probe microphone into the canal decreases the rate of decay of circumferential nonplanar modes while increasing the rate of decay of radial modes. Relative to the pressure beyond the tube, insertion increases the plane-wave component of the pressure around the tube by a multiplicative factor approximately equal to the square root of the original area divided by the occluded area. Eccentric placement of the probe tube has a relatively small influence on the cutoff frequency. The transition of the pressure distribution at the entrance to a simple plane wave in the core region of the canal is calculated and shown graphically for the actual geometry of two adult subjects.     

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.     

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.     

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.     

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.     

Impact of unilateral hearing loss on sound localization

The impact of unilateral hearing loss on the localization of horizontal plane sound sources ipsilateral and contralateral to the side of the unimpaired ear was examined. Normal-hearing listeners judged the direction of six loudspeakers, separated by 30° and arrayed frontally or laterally on the right side with the right or left ear occluded. The benefit of massed practice over three sequential days was assessed. For the frontal loudspeaker array, azimuthal discrimination on the occluded side was poor but only 30% of sounds were perceived to come from the unoccluded side. For the right lateral array, when the ipsilateral ear was unoccluded, front and back were rarely confused. Accuracy mainly decreased for speakers close to the midline axis, front and back. When the contralateral ear was unoccluded responses were biased toward the rearmost speaker. Practice did not improve performance. The findings were discussed within the context of military operations. They support the need for job-specific hearing standards.     

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.     

High-frequency plane waves in the ear canal: application of a simple asymptotic theory

An asymptotic theory describing the propagation of plane waves in a variable cross-section ear canal is combined with pressure measurements in order to determine the energy reflection coefficient at the eardrum and the standing wave patterns along the length of the canal. The relative phase of the reflected wave, and the cross-sectional area function of the ear canal, are also determined from the noninvasive pressure measurements. The theory is based on a high-frequency multiscale solution of the one-dimensional horn equation and is shown to agree well with the phase and amplitude of experimental measurements in human replica ear canals.     

Standing wave patterns in the human ear canal used for estimation of acoustic energy reflectance at the eardrum

Standing wave patterns were measured in the unoccluded ear canals of 13 human subjects, for applied pure tones of 3 to 13 kHz. Measurements were made, using a probe microphone technique, over a region which could be approximated as a duct of constant cross-sectional area. Analysis of the patterns allowed the reflective properties of the middle ear to be determined in terms of an acoustic energy reflection coefficient, or reflectance, at the eardrum. Over all subjects the trend of the results was for the energy reflection coefficient to rise from about 0.3 at 4 kHz up to 0.8 at 8 kHz, and continue at this value to 13 kHz. There was, however, significant intersubject variation, especially at frequencies greater than 7 kHz.