Quantifying undesired parallel components in Thévenin-equivalent acoustic source parameters

Comments on forward pressure and other reflectance-based quantities for delivering stimuli to the ear

The forward pressure has been proposed as an "optimal" reflectance-based quantity for delivering stimuli to the ear during evoked otoacoustic-emission measurements and audiometry. It is motivated by and avoids detrimental stimulus-level errors near standing-wave antiresonance frequencies when levels are adjusted in situ. While enjoying widespread popularity within research, the forward pressure possesses certain undesirable properties, some of which complicate its implementation into commercial otoacoustic-emission instruments conforming to existing international standards. These properties include its inability to approximate the total sound pressure anywhere in the ear canal and its discrepancy from the sound pressure at the tympanic membrane, which depends directly on the reflectance. This paper summarizes and comments on such properties of the forward pressure. Further, based on previous published data, alternative reflectance-based quantities that do not share these properties are investigated. A complex integrated pressure, with magnitude identical to the previously proposed scalar integrated pressure, is suggested as a suitable quantity for avoiding standing-wave errors when delivering stimuli to the ear. This complex integrated pressure approximates the magnitude and phase of the sound pressure at the tympanic membrane and can immediately be implemented into standardized commercial instruments to take advantage of improved stimulus-level accuracy and reproducibility in the clinic.

A reciprocity method for validating acoustic ear-probe source calibrations

Measurements of wideband acoustic immittance (WAI) rely on the calibration of an ear probe to obtain its acoustic source parameters. The clinical use of WAI and instruments offering the functionality are steadily growing, however, no international standard exists to ensure a certain reliability of the hardware and methods underlying such measurements. This paper describes a reciprocity method that can evaluate the accuracy of and identify errors in ear-probe source calibrations. By placing the ear probes of two calibrated WAI instruments face-to-face at opposite ends of a short waveguide, the source parameters of each ear probe can be measured using the opposite calibrated ear probe. The calibrated and measured source parameters of each ear probe can then be compared directly, and the influence of possible calibration errors on WAI measurements may be approximated. In various exemplary ear-probe calibrations presented here, the reciprocity method accurately identifies errors that would otherwise remain undetected and result in measurement errors in real ears. The method is likely unsuitable for routine calibration of WAI instruments but may be considered for conformance testing as part of a potential future WAI standard.

A systematic study on effects of calibration-waveguide geometry and least-squares formulation on ear-probe source calibrations

Measuring ear-canal absorbance and compensating for effects of the ear-canal acoustics on otoacoustic-emission measurements using an ear probe rely on accurately determining its acoustic source parameters. Using pressure measurements made in several rigid waveguides and models of their input impedances, a conventional calibration method estimates the ear-probe Thévenin-equivalent source parameters via a least-squares fit to an over-determined system of equations. Such a calibration procedure involves critical considerations on the geometry and number of utilized calibration waveguides. This paper studies the effects of calibration-waveguide geometry on achieving accurate ear-probe calibrations and measurements by systematically varying the lengths, length ratios, radii, and number of waveguides. For calibration-waveguide lengths in the range of 10-60 mm, accurate calibrations were generally obtained with absorbance measurement errors of approximately 0.02. Longer waveguides resulted in calibration errors, mainly due to coincident resonance frequencies among waveguides in the presence of mismatches between their assumed and actual geometries. The accuracy of calibrations was independent of the calibration-waveguide radius, except for an increased sensitivity of wider waveguides to noise. Finally, it is demonstrated how reformulating the over-determined system of equations to return the least-squares reflectance source parameters substantially reduces calibration and measurement errors.

On causality and aural impulse responses synthesized using the inverse discrete Fourier transform

Causality is a fundamental property of physical systems and dictates that a time impulse response characterizing any causal system must be one-sided. However, when synthesized using the inverse discrete Fourier transform (IDFT) of a corresponding band-limited numerical frequency transfer function, several papers have reported two-sided IDFT impulse responses of ear-canal reflectance and ear-probe source parameters. Judging from the literature on ear-canal reflectance, the significance and source of these seemingly non-physical negative-time components appear largely unclear. This paper summarizes and clarifies different sources of negative-time components through ideal and practical examples and illustrates the implications of constraining aural IDFT impulse responses to be one-sided. Two-sided IDFT impulse responses, derived from frequency-domain measurements of physical systems, normally occur due to the two-sided properties of the discrete Fourier transform. Still, reflectance IDFT impulse responses may serve a number of practical and diagnostic purposes.

Medial olivocochlear reflex effects on amplitude growth functions of long- and short-latency components of click-evoked otoacoustic emissions in humans

Functional outcomes of medial olivocochlear reflex (MOCR) activation, such as improved hearing in background noise and protection from noise damage, involve moderate to high sound levels. Previous noninvasive measurements of MOCR in humans focused primarily on otoacoustic emissions (OAEs) evoked at low sound levels. Interpreting MOCR effects on OAEs at higher levels is complicated by the possibility of the middle-ear muscle reflex and by components of OAEs arising from different locations along the length of the cochlear spiral. We overcame these issues by presenting click stimuli at a very slow rate and by time-frequency windowing the resulting click-evoked (CE)OAEs into short-latency (SL) and long-latency (LL) components. We characterized the effects of MOCR on CEOAE components using multiple measures to more comprehensively assess these effects throughout much of the dynamic range of hearing. These measures included CEOAE amplitude attenuation, equivalent input attenuation, phase, and slope of growth functions. Results show that MOCR effects are smaller on SL components than LL components, consistent with SL components being generated slightly basal of the characteristic frequency region. Amplitude attenuation measures showed the largest effects at the lowest stimulus levels, but slope change and equivalent input attenuation measures did not decrease at higher stimulus levels. These latter measures are less commonly reported and may provide insight into the variability in listening performance and noise susceptibility seen across individuals.NEW & NOTEWORTHY The auditory efferent system, operating at moderate to high sound levels, may improve hearing in background noise and provide protection from noise damage. We used otoacoustic emissions to measure these efferent effects across a wide range of sound levels and identified level-dependent and independent effects. Previous reports have focused on level-dependent measures. The level-independent effects identified here may provide new insights into the functional relevance of auditory efferent activity in humans.

Effects of Forward- and Emitted-Pressure Calibrations on the Variability of Otoacoustic Emission Measurements Across Repeated Probe Fits

OBJECTIVE

The stimuli used to evoke otoacoustic emissions (OAEs) are typically calibrated based on the total SPL measured at the probe microphone. However, due to the acoustics of the ear-canal space (i.e., standing-wave interference), this method can underestimate the stimulus pressure reaching the tympanic membrane at certain frequencies. To mitigate this effect, stimulus calibrations based on forward pressure level (FPL) can be applied. Furthermore, the influence of ear-canal acoustics on measured OAE levels can be compensated by expressing them in emitted pressure level (EPL). To date, studies have used artificial shallow versus deep probe fits to assess the effects of calibration method on changes in probe insertion. In an attempt to better simulate a clinical setting, the combined effects of FPL calibration of stimulus level and EPL compensation of OAE level on response variability during routine (noncontrived) probe fittings were examined.

DESIGN

The distortion component of the distortion-product OAE (DPOAE) and the stimulus-frequency OAE (SFOAE) were recorded at low and moderate stimulus levels in 20 normal-hearing young-adult subjects across a five-octave range. In each subject, three different calibration approaches were compared: (1) the conventional SPL-based stimulus calibration with OAE levels expressed in SPL; (2) FPL stimulus calibration with OAEs expressed in SPL; and (3) FPL stimulus calibration with OAEs expressed in EPL. Test and retest measurements were obtained during the same session and, in a subset of subjects, several months after the initial test. The effects of these different procedures on the inter- and intra-subject variability of OAE levels were assessed across frequency and level.

RESULTS

There were no significant differences in the inter-subject variability of OAE levels across the three calibration approaches. However, there was a significant effect on OAE intra-subject variability. The FPL/EPL approach resulted in the overall lowest test-rest differences in DPOAE level for frequencies above 4 kHz, where standing-wave interference is strongest. The benefit was modest, ranging on average from 0.5 to 2 dB and was strongest at the lower stimulus level. SFOAE level variability did not show significant differences among the three procedures, perhaps due to insufficient signal-to-noise ratio and nonoptimized stimulus levels. Correlations were found between the short-term replicability of DPOAEs and the benefit derived from the FPL/EPL procedure: the more variable the DPOAE, the stronger the benefit conferred by the advanced calibration methods.

CONCLUSIONS

Stimulus and response calibration procedures designed to mitigate the effects of standing-wave interference on both the stimulus and the OAE enhance the repeatability of OAE measurements and reduce their dependence on probe position, even when probe shifts are small. Modest but significant improvements in short-term test-retest repeatability were observed in the mid- to high-frequency region when using combined FPL/EPL procedures. The authors posit that the benefit will be greater in a more heterogeneous group of subjects and when different testers participate in the fitting and refitting of subjects, which is a common practice in the audiology clinic. The impact of calibration approach on OAE inter-subject variability was not significant, possibly due to a homogeneous subject population and because factors other than probe position are at play.

Causality-constrained measurements of aural acoustic reflectance and reflection functions

Causality-constrained procedures are described to measure acoustic pressure reflectance and reflection function (RF) in the ear canal or unknown waveguide, in which reflectance is the Fourier transform of the RF. Reflectance calibration is reformulated to generate causal outputs, with results described for a calibration based on a reflectance waveguide equation to calculate incident pressure and source reflectance in the frequency domain or source RF in the time domain. The viscothermal model RF of each tube is band-limited to the stimulus bandwidth. Results are described in which incident pressure is either known from long-tube measurements or calculated as a calibration output. Calibrations based on constrained nonlinear optimizations are simpler and more accurate when incident pressure is known. Outputs measured by causality-constrained procedures differ at higher frequencies from those using standard procedures with non-causal outputs. Evanescent-mode effects formulated in the time domain and incorporated into frequency-domain calibrations are negligible for long-tube calibrations. Causal reflectance and RFs are evaluated in an adult ear canal and time- and frequency-domain results are contrasted using forward and inverse Fourier transforms. These results contribute to the long-term goals of improving applications to calibrate sound stimuli in the ear canal at high frequencies and diagnose conductive hearing impairments.

On the calculation of reflectance in non-uniform ear canals

Ear-canal reflectance is useful for quantifying the conductive status of the middle ear because it can be measured non-invasively at a distance from the tympanic membrane. Deriving the ear-canal reflectance requires decomposing the total acoustic pressure into its forward- and reverse-propagating components. This decomposition is conveniently achieved using formulas that involve the input and characteristic impedances of the ear canal. The characteristic impedance is defined as the ratio of sound pressure to volume flow of a propagating wave and, for uniform waveguides, the plane-wave characteristic impedance is a real-valued constant. However, in non-uniform waveguides, the characteristic impedances are complex-valued quantities, depend on the direction of propagation, and more accurately characterize a propagating wave in a non-uniform ear canal. In this paper, relevant properties of the plane-wave and spherical-wave characteristic impedances are reviewed. In addition, the utility of the plane-wave and spherical-wave reflectances in representing the reflection occurring due to the middle ear, calibrating stimulus levels, and characterizing the emitted pressure in simulated non-uniform ear canals is investigated and compared.

A comparison of ear-canal-reflectance measurement methods in an ear simulator

Ear-canal reflectance has been researched extensively for diagnosing conductive hearing disorders and compensating for the ear-canal acoustics in non-invasive measurements of the auditory system. Little emphasis, however, has been placed on assessing measurement accuracy and variability. In this paper, a number of ear-canal-reflectance measurement methods reported in the literature are utilized and compared. Measurement variation seems to arise chiefly from three factors: the residual ear-canal length, the ear-probe insertion angle, and the measurement frequency bandwidth. Calculation of the ear-canal reflectance from the measured ear-canal impedance requires estimating the ear-canal characteristic impedance in situ. The variability in ear-canal estimated characteristic impedance and reflectance due to these principal factors is assessed in an idealized controlled setup using a uniform occluded-ear simulator. In addition, the influence of this measurement variability on reflectance-based methods for calibrating stimulus levels is evaluated and, by operating the condenser microphone of the occluded-ear simulator as an electro-static speaker, the variability in estimating the emitted pressure from the ear is determined. The various measurement methods differ widely in their robustness to variations in the three principal factors influencing the accuracy and variability of ear-canal reflectance.

Compensating for oblique ear-probe insertions in ear-canal reflectance measurements

Measurements of the ear-canal reflectance using an ear probe require estimating the characteristic impedance of the ear canal in situ. However, an oblique insertion of the ear probe into a uniform waveguide prevents accurately estimating its characteristic impedance using existing time-domain methods. This is caused by the non-uniformity immediately in front of the ear probe when inserted at an oblique angle, resembling a short horn loading, and introduces errors into the ear-canal reflectance. This paper gives an overview of the influence of oblique ear-probe insertions and shows how they can be detected and quantified by estimating the characteristic impedance using multiple truncation frequencies, i.e., limiting the utilized frequency range. Additionally, a method is proposed to compensate for the effects on reflectance of an oblique ear-probe insertion into a uniform waveguide. The incident impedance of the horn loading is estimated, i.e., were the uniform waveguide anechoic, which replaces the characteristic impedance when calculating reflectance. The method can compensate for an oblique ear-probe insertion into a uniform occluded-ear simulator and decrease the dependency of reflectance on insertion depth in an ear canal. However, more research is required to further assess the method in ear canals.

Sound pressure distribution within human ear canals: II. Reverse mechanical stimulation

This work is part of a study of the interactions of ear canal (EC) sound with tympanic membrane (TM) surface displacements. In human temporal bones, the ossicles were stimulated mechanically "in reverse" to mimic otoacoustic emissions (OAEs), and the sound field within the ear canal was sampled with 0.5-2 mm spacing near the TM surface and at more distal locations within the EC, including along the longitudinal EC axis. Sound fields were measured with the EC open or occluded. The reverse-driven sound field near the TM had larger and more irregular spatial variations below 10 kHz than with forward sound stimulation, consistent with a significant contribution of nonuniform sound modes. These variations generally did not propagate more than ∼4 mm laterally from the TM. Longitudinal sound field variations with the EC open or blocked were consistent with standing-wave patterns in tubes with open or closed ends. Relative contributions of the nonuniform components to the total sound pressure near the TM were largest at EC natural frequencies where the longitudinal component was small. Transverse variations in EC sound pressure can be reduced by reducing longitudinal EC sound pressure variations, e.g., via reducing reflections from occluding earplugs.

A coupler-based calibration method for ear-probe microphones

The calibration of ear-probe microphones can increase the precision of calibrating stimulus levels in situ and of measuring acoustic responses from the ear. This paper proposes a methodology to measure the sensitivity of an ear-probe microphone, requiring only an acoustic coupler and a calibrated reference microphone. The input impedance of the coupler is measured, enabled by a preliminary acoustic Thévenin calibration of the ear probe, and the plane-wave transfer impedance of the coupler is calculated analytically. Using these two quantities, the pressure transfer function between the reference microphone and the ear-probe microphone is estimated. This enables estimating the sensitivity of the ear-probe microphone. The proposed and an existing method were compared, resulting in substantially similar ear-probe microphone sensitivities. The proposed method is practically feasible in producing reliable measurements of sound pressure in the ear canal and calibrating stimulus levels in a clinical setting.

Evanescent waves in simulated ear canals: Experimental demonstration and method for compensation

Evanescent waves emerge from a small sound source that radiates into a waveguide with a larger cross-sectional area, but unlike planar waves, do not propagate far from the source. Evanescent waves thus contaminate in-ear calibration of acoustic stimuli. Measurements with an otoacoustic-emission (OAE) probe inserted at the entrance of long tubes of various diameters show a decline in the evanescent wave with distance from the source when advancing a probe tube through the OAE probe and into the long tube. The amplitude of the evanescent pressure increases with frequency and depends strongly on the diameter of the long tube. Modifying the shape of the aperture of the probe's sound source, thus effectively enlarging its diameter and redirecting acoustic flow, greatly reduced evanescent waves. The reduction in evanescent-wave pressure was observed in calibration cavities used to determine the Thévenin-equivalent source pressure and impedance of the probe. Errors in source calibrations were considerably larger in the unmodified configuration. An alternative method is proposed for calculation of acoustic source parameters that models the evanescent-wave pressure and reduces its influence on the calculation. This reduction greatly improves the quality of source calibrations, which should improve the accuracy of ear-canal impedance measurements and related quantities.