Stimulus-frequency-emission group delay: a test of coherent reflection filtering and a window on cochlear tuning

This paper tests and applies a key prediction of the theory of coherent reflection filtering for the generation of reflection-source otoacoustic emissions. The theory predicts that reflection-source-emission group delay is determined by the group delay of the basilar-membrane (BM) transfer function at its peak. This prediction is tested over a seven-octave frequency range in cats and guinea pigs using measurements of stimulus-frequency-emission (SFOAE) group delay. A comparison with group delays calculated from published measurements of BM mechanical transfer functions supports the theory at the basal end of the cochlea. A comparison across the whole frequency range based on variations in the sharpness of neural tuning with characteristic frequency (CF) suggests that the predicted relation holds in the basal-most 60% of the cochlea. At the apical end of the cochlea, however, the measurements disagree with neural and mechanical group delays. This disagreement suggests that there are important differences in cochlear mechanics and/or mechanisms of emission generation between the base and apex of the cochlea. Measurements in humans over a four-octave range indicate that human SFOAE group delays are roughly a factor of 3 longer than their counterparts in cat and guinea pig but manifest similar trends across CF. The measurements thus reveal global deviations from scaling whose form appears quantitatively similar in all three species. Interpreted using the theory of coherent reflection filtering, the group delay measurements indicate that the wavelength at the peak of the traveling wave decreases with increasing CF at a rate of roughly 25% per octave in the base of the cochlea. The measurements and analysis reported here illustrate the rich potential inherent in OAE measurements for obtaining valuable information about basic cochlear properties such as tuning.     

Cochlear reflectivity in transmission-line models and otoacoustic emission characteristic time delays

In transmission-line models of cochlear mechanics, predictions about otoacoustic-emission delays depend on the place- or wave-fixed nature of the emission generation mechanism. In this work, transient evoked otoacoustic emissions (TEOAEs), recorded at different stimulus levels in 10 young subjects, were analyzed using wavelet-based time-frequency analysis to determine the latency of each frequency component of the response. The same wave forms were Fourier analyzed to evaluate the phase-gradient delay as a function of frequency. Interpreting the relation between these two characteristic delays using cochlear models shows that most of the TEOAE response can be attributed to place-fixed reflection mechanisms. The causality principle explains observed correlations between fluctuations of the TEOAE amplitude and phase-gradient delay.     

Distortion-product source unmixing: a test of the two-mechanism model for DPOAE generation

This paper tests key predictions of the "two-mechanism model" for the generation of distortion-product otoacoustic emissions (DPOAEs). The two-mechanism model asserts that lower-sideband DPOAEs constitute a mixture of emissions arising not simply from two distinct cochlear locations (as is now well established) but, more importantly, by two fundamentally different mechanisms: nonlinear distortion induced by the traveling wave and linear coherent reflection off pre-existing micromechanical impedance perturbations. The model predicts that (1) DPOAEs evoked by frequency-scaled stimuli (e.g., at fixed f2/f1) can be unmixed into putative distortion- and reflection-source components with the frequency dependence of their phases consistent with the presumed mechanisms of generation; (2) The putative reflection-source component of the total DPOAE closely matches the reflection-source emission (e.g., low level stimulus-frequency emission) measured at the same frequency under similar conditions. These predictions were tested by unmixing DPOAEs into components using two completely different methods: (a) selective suppression of the putative reflection source using a third tone near the distortion-product frequency and (b) spectral smoothing (or, equivalently, time-domain windowing). Although the two methods unmix in very different ways, they yield similar DPOAE components. The properties of the two DPOAE components are consistent with the predictions of the two-mechanism model.     

Transient evoked otoacoustic emission latency and cochlear tuning at different stimulus levels

Cochlear latency has been evaluated in young adults by time-frequency analysis of transient evoked otoacoustic emissions recorded using the nonlinear acquisition mode at different levels of the click stimulus. Objective, even if model-dependent, estimates of cochlear tuning have been obtained from the otoacoustic latency estimates. Transmission-line cochlear models predict that the transient-evoked otoacoustic emission latency is dependent on the stimulus level, because the bandwidth of the cochlear filter (tuning) depends on the local cochlear excitation level due to nonlinear damping. The results of this study confirm the increase of tuning with increasing frequency and show clearly the decrease of latency and tuning with increasing stimulus level. This decrease is consistent with the expected relation between the slowing down of the traveling wave near the tonotopic place and the cochlear excitation amplitude predicted by cochlear models including nonlinear damping. More specifically, these results support the models in which nonlinear damping consists of a quadratic term and a constant positive term.     

Objective estimates of cochlear tuning by otoacoustic emission analysis

A new method is presented for estimating cochlear tuning starting from measurements of either the transient evoked otoacoustic emission latency or the spontaneous otoacoustic emission minimal spacing. This method could be useful in obtaining indirect information about the tuning curve, particularly for subjects that, like neonates, cannot be studied with psycho-acoustical techniques. Theoretical models of the acoustic transmission along the cochlea based on the transmission line formalism predict a relation between the otoacoustic emission latency and the frequency. This relation depends on the tuning curve, i.e., the frequency dependence of the quality factor of the cochlear resonances. On the other hand, models for the generation of spontaneous emissions based on the concept of coherent scattering from cochlear random inhomogeneities imply an independent relation between the tuning curve and the minimal frequency spacing between spontaneous emissions. In this study, experimental measurements of the otoacoustic emission latency and of the minimal spacing between spontaneous emissions are presented. Theoretical relations are derived, which connect these two measured quantities and the tuning curve. The typically longer latency of neonates implies a higher degree of tuning at high levels of stimulation.     

Modeling the temporal behavior of distortion product otoacoustic emissions

The temporal behavior of the 2f1-f2 distortion product otoacoustic emission is theoretically investigated for the case in which the lower frequency (f1) primary tone is on continuously, and the higher frequency (f2) one is pulsed on and off [e.g., Talmadge et al., J. Acoust. Soc. Am. 105, 275-292 (1999)]. On physical grounds, this behavior is expected to be characterized by various group delays associated with the propagation of (1) the f2 cochlear primary wave between the cochlear base and the primary distortion product generation region around x2 (the f2 tonotopic place), and (2) the 2f1-f2 cochlear distortion product (DP) waves between the cochlear base, the primary generation region of the distortion product, and the region around the 2f1-f2 tonotopic place where the generated apical moving DP wave is reflected toward the cochlear base [e.g., Talmadge et al., J. Acoust. Soc. Am. 104, 1517-1543 (1998)]. An approximate analytic expression is obtained for this behavior from the analysis of the Fourier integral representation of the auditory peripheral response to the primary stimuli. This expression also approximately describes the transient build-up of the components of different latencies in terms of the damping properties of the cochlear partition. It is shown that considerable caution must be applied in attempting to relate phase derivatives of the distortion product otoacoustic emissions for steady state stimuli and the physical time delays which are associated with the temporal behavior of a distortion product emission in the case of a pulsed primary.     

Use of stimulus-frequency otoacoustic emission latency and level to investigate cochlear mechanics in human ears

Stimulus frequency otoacoustic emission (SFOAE) sound pressure level (SPL) and latency were measured at probe frequencies from 500 to 4000 Hz and probe levels from 40 to 70 dB SPL in 16 normal-hearing adult ears. The main goal was to use SFOAE latency estimates to better understand possible source mechanisms such as linear coherent reflection, nonlinear distortion, and reverse transmission via the cochlear fluid, and how those sources might change as a function of stimulus level. Another goal was to use SFOAE latencies to noninvasively estimate cochlear tuning. SFOAEs were dominated by the reflection source at low stimulus levels, consistent with previous research, but neither nonlinear distortion nor fluid compression become the dominant source even at the highest stimulus level. At each stimulus level, the SFOAE latency was an approximately constant number of periods from 1000 to 4000 Hz, consistent with cochlear scaling symmetry. SFOAE latency decreased with increasing stimulus level in an approximately frequency-independent manner. Tuning estimates were constant above 1000 Hz, consistent with simultaneous masking data, but in contrast to previous estimates from SFOAEs.     

Human cochlear tuning estimates from stimulus-frequency otoacoustic emissions

Two objective measures of human cochlear tuning, using stimulus-frequency otoacoustic emissions (SFOAE), have been proposed. One measure used SFOAE phase-gradient delay and the other two-tone suppression (2TS) tuning curves. Here, it is hypothesized that the two measures lead to different frequency functions in the same listener. Two experiments were conducted in ten young adult normal-hearing listeners in three frequency bands (1-2 kHz, 3-4 kHz and 5-6 kHz). Experiment 1 recorded SFOAE latency as a function of stimulus frequency, and experiment 2 recorded 2TS iso-input tuning curves. In both cases, the output was converted into a sharpness-of-tuning factor based on the equivalent rectangular bandwidth. In both experiments, sharpness-of-tuning curves were shown to be frequency dependent, yielding sharper relative tuning with increasing frequency. Only a weak frequency dependence of the sharpness-of-tuning curves was observed for experiment 2, consistent with objective and behavioural estimates from the literature. Most importantly, the absolute difference between the two tuning estimates was very large and statistically significant. It is argued that the 2TS estimates of cochlear tuning likely represents the underlying properties of the suppression mechanism, and not necessarily cochlear tuning. Thus the phase-gradient delay estimate is the most likely one to reflect cochlear tuning.     

Coherent reflection in a two-dimensional cochlea: Short-wave versus long-wave scattering in the generation of reflection-source otoacoustic emissions

The theory of coherent reflection filtering explains the empirical form of the cochlear reflectance by showing how it emerges from the coherent "backscattering" of forward-traveling waves by impedance perturbations in the mechanics of the cochlear partition. Since the theory was developed using the one-dimensional (1-D) transmission-line model of the cochlea, an obvious logical shortcoming is the failure of the long-wavelength approximation near the peak of the traveling wave, where coherent backscattering is purported to occur. Indeed, existing theory suggests that wave reflection may be strongly suppressed in the short-wave regime. To understand how short-wave behavior near the peak modifies the predictions of the long-wave theory, this paper solves the scattering problem in the 2-D cochlear model. The 2-D problem is reduced to a 1-D wave equation and the solution expressed as an infinite series in which successive terms arise via multiple scattering within the cochlea. The cochlear reflectance is computed in response-matched models constructed by solving the inverse problem to control for variations in mechanical tuning among models of different heights and dimensionality. Reflection from the peak region is significantly enhanced by the short-wave hydrodynamics, but other conclusions of the 1-D analysis--such as the predicted relation between emission group delay and the wavelength of the traveling wave--carry over with only minor modifications. The results illustrate the important role of passive hydromechanical effects in shaping otoacoustic emissions and cochlear tuning.     

Ipsilateral distortion product otoacoustic emission (2f1-f2) suppression in children with sensorineural hearing loss

Distortion product otoacoustic emission (DPOAE) ipsilateral suppression has been applied to study cochlear function and maturation in laboratory animals and humans. Although DPOAE suppression appears to be sensitive to regions of specialized cochlear function and to cochlear immaturity, it is not known whether it reflects permanent cochlear damage, i.e., sensorineural hearing loss (SNHL), in a reliable and systematic manner in humans. Eight school-aged children with mild-moderate SNHL and 20 normal-hearing children served as subjects in this study. DPOAE (2f1-f2) suppression data were collected at four f2 frequencies (1500, 3000, 4000, and 6000 Hz) using moderate-level primary tones. Features of the DPOAE iso-suppression tuning curves and suppression growth were analyzed for both subject groups. Results show that DPOAE suppression tuning curves from hearing-impaired subjects can be reliably recorded. DPOAE suppression tuning curves were generally normal in appearance and shape for six out of eight hearing-impaired subjects but showed subtle abnormalities in at least one feature. There was not one single trend or pattern of abnormality that characterized all hearing-impaired subjects. The most prominent patterns of abnormality included: broadened tuning, elevated tip, and downward shift of tip frequency. The unique patterns of atypical DPOAE suppression in subjects with similar audiograms may suggest different patterns of underlying sensory cell damage. This speculation warrants further investigation.     

Comparison between otoacoustic and auditory brainstem response latencies supports slow backward propagation of otoacoustic emissions

Experimental measurements of the latency of transient evoked otoacoustic emission and auditory brainstem responses are compared, to discriminate between different cochlear models for the backward acoustic propagation of otoacoustic emissions. In most transmission-line cochlear models otoacoustic emissions propagate towards the base as a slow transverse traveling wave, whereas other models assume fast backward propagation via longitudinal compression waves in the fluid. Recently, sensitive measurements of the basilar membrane motion have cast serious doubts on the existence of slow backward traveling waves associated with distortion product otoacoustic emissions [He et al., Hear. Res. 228, 112-122 (2007)]. On the other hand, recent analyses of "Allen-Fahey" experiments suggest instead that the slow mechanism transports most of the otoacoustic energy [Shera et al., J. Acoust. Soc. Am. 122, 1564-1575 (2007)]. The two models can also be discriminated by comparing accurate estimates of the otoacoustic emission latency and of the auditory brainstem response latency. In this study, this comparison is done using human data, partly original, and partly from the literature. The results are inconsistent with fast otoacoustic propagation, and suggest that slow traveling waves on the basilar membrane are indeed the main mechanism for the backward propagation of the otoacoustic energy.     

Transient-evoked otoacoustic emission generators in a nonlinear cochlea

This study focuses on the theoretical prediction and experimental evaluation of the latency of transient-evoked otoacoustic emissions. Response components with different delay have been identified in several studies. The main generator of the transient response is assumed to be coherent reflection from cochlear roughness near the resonant place. Additional components of different latency can be generated by different mechanisms. Experimental data are re-analyzed in this study to evaluate the dependence of the latency on stimulus level, for each component of the response, showing that previous estimates of the otoacoustic emission latency were affected by systematic errors. The latency of the emission from each generator changes very little with stimulus level, whereas their different growth rate causes sharp changes of the single-valued latency, estimated as the time of the absolute maximum of the bandpass filtered response. Results of passive linear models, in which gain and bandwidth of the cochlear amplifier are strictly related, are incompatible with the observations. Although active linear models including delayed stiffness terms do predict much slower dependence of latency on the stimulus level, a suitable nonlinear model should be designed, capable of decoupling more effectively the dependence on stimulus level of amplitude and phase of the otoacoustic response.     

Delay dependence for the origin of the nonlinear derived transient evoked otoacoustic emission

In the guinea pig it has been shown that the nonlinear derived transient evoked otoacoustic emission (TEOAEnl) is comprised of significant amounts of intermodulation distortion energy. It is expected that intermodulation distortion arising from a nonlinear distortion mechanism will contribute to the overall TEOAE in a stimulus-level-dependent manner, being greatest when basilar-membrane vibration in response to a click stimulus is greatest; with decay of vibration of the basilar membrane subsequent to stimulation by a click, nonlinear interaction along the cochlear partition should reduce and so provide for a linear mechanism to dominate TEOAEnl generation, i.e., the contributions of each of these mechanisms should be delay dependent. To examine this delay dependence, TEOAEnl evoked by acoustic clicks of varying bandwidth were time-domain windowed using a recursive exponential filter in an attempt to separate two components with amplitude and phase properties consistent with different mechanisms of OAE generation. It was found that the part of the TEOAEnl occurring first in time can have a relatively constant amplitude and shallow phase slope, consistent with a nonlinear distortion mechanism. The latter part of the TEOAEnl has an amplitude microstructure and a phase response more consistent with a place-fixed mechanism.     

Modeling the combined effects of basilar membrane nonlinearity and roughness on stimulus frequency otoacoustic emission fine structure

A theoretical framework for describing the effects of nonlinear reflection on otoacoustic emission fine structure is presented. The following models of cochlear reflection are analyzed: weak nonlinearity, distributed roughness, and a combination of weak nonlinearity and distributed roughness. In particular, these models are examined in the context of stimulus frequency otoacoustic emissions (SFOAEs). In agreement with previous studies, it is concluded that only linear cochlear reflection can explain the underlying properties of cochlear fine structures. However, it is shown that nonlinearity can unexpectedly, in some cases, significantly modify the level and phase behaviors of the otoacoustic emission fine structure, and actually enhance the pattern of fine structures observed. The implications of these results on the stimulus level dependence of SFOAE fine structure are also explored.     

Testing coherent reflection in chinchilla: Auditory-nerve responses predict stimulus-frequency emissions

Coherent-reflection theory explains the generation of stimulus-frequency and transient-evoked otoacoustic emissions by showing how they emerge from the coherent "backscattering" of forward-traveling waves by mechanical irregularities in the cochlear partition. Recent published measurements of stimulus-frequency otoacoustic emissions (SFOAEs) and estimates of near-threshold basilar-membrane (BM) responses derived from Wiener-kernel analysis of auditory-nerve responses allow for comprehensive tests of the theory in chinchilla. Model predictions are based on (1) an approximate analytic expression for the SFOAE signal in terms of the BM traveling wave and its complex wave number, (2) an inversion procedure that derives the wave number from BM traveling waves, and (3) estimates of BM traveling waves obtained from the Wiener-kernel data and local scaling assumptions. At frequencies above 4 kHz, predicted median SFOAE phase-gradient delays and the general shapes of SFOAE magnitude-versus-frequency curves are in excellent agreement with the measurements. At frequencies below 4 kHz, both the magnitude and the phase of chinchilla SFOAEs show strong evidence of interference between short- and long-latency components. Approximate unmixing of these components, and association of the long-latency component with the predicted SFOAE, yields close agreement throughout the cochlea. Possible candidates for the short-latency SFOAE component, including wave-fixed distortion, are considered. Both empirical and predicted delay ratios (long-latency SFOAE delay/BM delay) are significantly less than 2 but greater than 1. Although these delay ratios contradict models in which SFOAE generators couple primarily into cochlear compression waves, they are consistent with the notion that forward and reverse energy propagation in the cochlea occurs predominantly by means of traveling pressure-difference waves. The compelling overall agreement between measured and predicted delays suggests that the coherent-reflection model captures the dominant mechanisms responsible for the generation of reflection-source otoacoustic emissions.     

Bias due to noise in otoacoustic emission measurements

Measurements of otoacoustic emission (OAE) magnitude are often made at low signal/noise ratios (SNRs) where measurement noise generates bias and variability errors that have led to the misinterpretation of OAE data. To gain an understanding for these errors and their effects, a two part investigation was carried out. First, the nature of OAE measurement noise was investigated using human data from 50 stimulus-frequency OAE experiments involving medial olivocochlear reflex (MOCR) activation. The noise was found to be reasonably approximated by circular Gaussian noise. Furthermore, when bias errors were taken into account, measurement variability was not found to be affected by MOCR activation as had been previously reported. Second, to quantify the errors circular Gaussian noise produces for different methods of OAE magnitude estimation for distortion-product, stimulus-frequency, and spontaneous OAEs, simulated OAE measurements were analyzed via four different magnitude estimation methods and compared. At low SNRs (below -6 dB), estimators involving Rice probability density functions produced less biased estimates of OAE magnitudes than conventional estimation methods, and less total rms error-particularly for spontaneous OAEs. They also enabled the calculation of probability density functions for OAE magnitudes from experimental data.     

Interrelations among distortion-product phase-gradient delays: their connection to scaling symmetry and its breaking

Distortion-product-otoacoustic-emission (DPOAE) phase-versus-frequency functions and corresponding phase-gradient delays have received considerable attention because of their potential for providing information about mechanisms of emission generation, cochlear wave latencies, and characteristics of cochlear tuning. The three measurement paradigms in common use (fixed-f1, fixed-f2, and fixed-f2/f1) yield significantly different delays, suggesting that they depend on qualitatively different aspects of cochlear mechanics. In this paper, theory and experiment are combined to demonstrate that simple phenomenological arguments, which make no detailed mechanistic assumptions concerning the underlying cochlear mechanics, predict relationships among the delays that are in good quantitative agreement with experimental data obtained in guinea pigs. To understand deviations between the simple theory and experiment, a general equation is found that relates the three delays for any deterministic model of DPOAE generation. Both model-independent and exact, the general relation provides a powerful consistency check on the measurements and a useful tool for organizing and understanding the structure in DPOAE phase data (e.g., for interpreting the relative magnitudes and intensity-dependencies of the three delays). Analysis of the general relation demonstrates that the success of the simple, phenomenological approach can be understood as a consequence of the mechanisms of emission generation and the approximate local scaling symmetry of cochlear mechanics. The general relation is used to quantify deviations from scaling manifest in the measured phase-gradient delays; the results indicate that deviations from scaling are typically small and that both linear and nonlinear mechanisms contribute significantly to these deviations. Intensity-dependent mechanisms contributing to deviations from scaling include cochlear-reflection and wave-interference effects associated with the mixing of distortion- and reflection-source emissions (as in DPOAE fine structure). Finally, the ratio of the fixed-f1 and fixed-f2 phase-gradient delays is shown to follow from the choice of experimental paradigm and, in the scaling limit, contains no information about cochlear physiology whatsoever. These results cast considerable doubt on the theoretical basis of recent attempts to use relative DPOAE phase-gradient delays to estimate the bandwidths of peripheral auditory filters.     

DPOAE group delays versus electrophysiological measures of cochlear delay in normal human ears

Group delays of 2 f1-f2 distortion product otoacoustic emissions (DPOAEs) were determined using both f1- and f2-sweep paradigms in 24 normal-hearing subjects. These DPOAE group delays were studied in comparison with cochlear delays estimated from derived band VIIIth nerve compound action potentials (CAPs) and auditory brainstem responses (ABRs) in the same subjects. The center frequencies of the derived bands in the electrophysiological experiment were matched with the f2-frequencies in the DPOAE recording to ensure that DPOAEs and derived CAPs and ABRs were generated at the same places along the cochlear partition, thus allowing for a direct comparison. The degree to which DPOAE group delays are larger in the f2- than in the f1-sweep paradigm is consistent with a theoretical analysis of the so-called wave-fixed model. Both DPOAE group delays are highly correlated with CAP- and ABR-derived measures of cochlear delay. The principal result of this study is that "roundtrip" DPOAE group delay in the f1-sweep paradigm is exactly twice as large as the neural estimate of the "forward" cochlear delay. The interpretation of this notion in the context of cochlear wave propagation properties and DPOAE-generating mechanisms is discussed.     

Frequency specificity of distortion-product otoacoustic emissions produced by high-level tones despite inefficient cochlear electromechanical feedback

Distortion product otoacoustic emissions (DPOAEs) are thought to stem from the outer hair cells (OHCs) around the normally narrow place tuned to the primary tone stimuli. They are thus said to be frequency-specific: their local absence should accurately pinpoint local OHC damage. Yet the influence of impaired tuning on DPOAE frequency specificity is poorly documented. Mice with local damage to OHCs were examined. Their DPOAEs were frequency-specific in that audiometric notches were accurately tracked. The same cochleae were further impaired by ischemia or furosemide injection inducing strial dysfunction with flat loss of sensitivity and tuning, while the preexisting pattern of damaged OHCs remained unaltered. Despite the loss of cochlear activity, DPOAEs produced by high-level (> or =70 dB SPL) primaries remained large in about the same interval where they had been initially normal, i.e., that with nondamaged OHCs, albeit with a slight frequency shift, of -1.1 kHz on average. Thus, the ability of DPOAEs to map structurally intact OHCs cannot be a mere consequence of cochlear tuning as it largely persists in its absence. The key element for this correct mapping is likely part of intact OHC structures (e.g., stereocilia bundles) and must have some tuning of its own.     

Comparing stimulus-frequency otoacoustic emissions measured by compression, suppression, and spectral smoothing

Stimulus-frequency otoacoustic emissions (SFOAEs) have been measured in several different ways, including (1) nonlinear compression, (2) two-tone suppression, and (3) spectral smoothing. Each of the three methods exploits a different cochlear phenomenon or signal-processing technique to extract the emission. The compression method makes use of the compressive growth of emission amplitude relative to the linear growth of the stimulus. The emission is defined as the complex difference between ear-canal pressure measured at one intensity and the rescaled pressure measured at a higher intensity for which the emission is presumed negligible. The suppression method defines the SFOAE as the complex difference between the ear-canal pressure measured with and without a suppressor tone at a nearby frequency. The suppressor tone is presumed to substantially reduce or eliminate the emission. The spectral smoothing method involves convolving the complex ear-canal pressure spectrum with a smoothing function. The analysis exploits the differing latencies of stimulus and emission and is equivalent to windowing in the corresponding latency domain. Although the three methods are generally assumed to yield identical emissions, no equivalence has ever been established. This paper compares human SFOAEs measured with the three methods using procedures that control for temporal drifts, contamination of the calibration by evoked emissions, and other potential confounds. At low stimulus intensities, SFOAEs measured using all three methods are nearly identical. At higher intensities, limitations of the procedures contribute to small differences, although the general spectral shape and phase of the three SFOAEs remain similar. The near equivalence of SFOAEs measured by compression, suppression, and spectral smoothing indicates that SFOAE characteristics are not mere artifacts of measurement methodology.