Delays of stimulus-frequency otoacoustic emissions and cochlear vibrations contradict the theory of coherent reflection filtering

When stimulated by tones, the ear appears to emit tones of its own, stimulus-frequency otoacoustic emissions (SFOAEs). SFOAEs were measured in 17 chinchillas and their group delays were compared with a place map of basilar-membrane vibration group delays measured at the characteristic frequency. The map is based on Wiener-kernel analysis of responses to noise of auditory-nerve fibers corroborated by measurements of vibrations at several basilar-membrane sites. SFOAE group delays were similar to, or shorter than, basilar-membrane group delays for frequencies >4 kHz and <4 kHz, respectively. Such short delays contradict the generally accepted "theory of coherent reflection filtering" [Zweig and Shera, J. Acoust. Soc. Am. 98, 2018-2047 (1995)], which predicts that the group delays of SFOAEs evoked by low-level tones approximately equal twice the basilar-membrane group delays. The results for frequencies higher than 4 kHz are compatible with hypotheses of SFOAE propagation to the stapes via acoustic waves or fluid coupling, or via reverse basilar membrane traveling waves with speeds corresponding to the signal-front delays, rather than the group delays, of the forward waves. The results for frequencies lower than 4 kHz cannot be explained by hypotheses based on waves propagating to and from their characteristic places in the cochlea.     

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.     

Stimulus-frequency otoacoustic emission: measurements in humans and simulations with an active cochlear model

An efficient method for measuring stimulus-frequency otoacoustic emissions (SFOAEs) was developed incorporating (1) stimulus with swept frequency or level and (2) the digital heterodyne analysis. SFOAEs were measured for 550-1450 Hz and stimulus levels of 32-62 dB sound pressure level in eight normal human adults. The mean level, number of peaks, frequency spacing between peaks, phase change, and energy-weighted group delays of SFOAEs were determined. Salient features of the human SFOAEs were stimulated with an active cochlear model containing spatially low-pass filtered irregularity in the impedance. An objective fitting procedure yielded an optimal set of model parameters where, with decreasing stimulus level, the amount of cochlear amplification and the base amplitude of the irregularity increased while the spatial low-pass cutoff and the slope of the spatial low-pass filter decreased. The characteristics of the human cochlea were inferred with the model. In the model, an SFOAE consisted of a long-delay component originating from irregularity in a traveling-wave peak region and a short-delay component originating from irregularity in regions remote from the peak. The results of this study should be useful both for understanding cochlear function and for developing a clinical method of assessing cochlear status.     

Transient-evoked stimulus-frequency and distortion-product otoacoustic emissions in normal and impaired ears

Transient-evoked stimulus-frequency otoacoustic emissions (SFOAEs), recorded using a nonlinear differential technique, and distortion-product otoacoustic emissions (DPOAEs) were measured in 17 normal-hearing and 10 hearing-impaired subjects using pairs of tone pips (pp), gated tones (gg), and for DPOAEs, continuous and gated tones (cg). Temporal envelopes of stimulus and OAE waveforms were obtained by narrow-band filtering at the stimulus or DP frequency. Mean SFOAE latencies in normal ears at 2.7 and 4.0 kHz decreased with increasing stimulus level and were larger at 4.0 kHz than latencies in impaired ears. Equivalent auditory filter bandwidths were calculated as a function of stimulus level from SFOAE latencies by assuming that cochlear transmission is minimum phase. DPOAE latencies varied less with level than SFOAE latencies. The ppDPOAEs often had two (or more) peaks separated in time with latencies consistent with model predictions for distortion and reflection components. Changes in ppDPOAE latency with level were sometimes explained by a shift in relative amplitudes of distortion and reflection components. The pp SFOAE SPL within the main spectral lobe of the pip stimulus was higher for normal ears in the higher-frequency half of the pip than the lower-frequency half, which is likely an effect of basilar membrane two-tone suppression.     

A parametric model of the spectral periodicity of stimulus frequency otoacoustic emissions

A model for estimating the spectral period of stimulus frequency otoacoustic emissions (SFOAEs) is presented. The model characterizes the frequency spectrum of an SFOAE in terms of four parameters which can be directly related to cochlear mechanical quantities featuring in the theory of SFOAE generation proposed by Zweig and Shera [J. Acoust. Soc. Am. 98, 2018-2047 (1995)]. The results of applying the parametric model to SFOAEs generated by cochlear models suggest that it gives a sensitive measure of spectral period. It is concluded that the parametric model may be a useful tool for detecting small changes in cochlear function using SFOAE measurements.     

Input-output functions for stimulus-frequency otoacoustic emissions in normal-hearing adult ears

Input-output (I/O) functions for stimulus-frequency (SFOAE) and distortion-product (DPOAE) otoacoustic emissions were recorded in 30 normal-hearing adult ears using a nonlinear residual method. SFOAEs were recorded at half octaves from 500-8000 Hz in an L1=L2 paradigm with L2=0 to 85 dB SPL, and in a paradigm with L1 fixed and L2 varied. DPOAEs were elicited with primary levels of Kummer et al. [J. Acoust. Soc. Am. 103, 3431-3444 (1998)] at f2 frequencies of 2000 and 4000 Hz. Interpretable SFOAE responses were obtained from 1000-6000 Hz in the equal-level paradigm. SFOAE levels were larger than DPOAEs levels, signal-to-noise ratios were smaller, and I/O functions were less compressive. A two-slope model of SFOAE I/O functions predicted the low-level round-trip attenuation, the breakpoint between linearity and compression, and compressive slope. In ear but not coupler recordings, the noise at the SFOAE frequency increased with increasing level (above 60 dB SPL), whereas noise at adjacent frequencies did not. This suggests the existence of a source of signal-dependent noise producing cochlear variability, which is predicted to influence basilar-membrane motion and neural responses. A repeatable pattern of notched SFOAE I/O functions was present in some ears, and explained using a two-source mechanism of SFOAE generation.     

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.     

Near equivalence of human click-evoked and stimulus-frequency otoacoustic emissions

Otoacoustic emissions (OAEs) evoked by broadband clicks and by single tones are widely regarded as originating via different mechanisms within the cochlea. Whereas the properties of stimulus-frequency OAEs (SFOAEs) evoked by tones are consistent with an origin via linear mechanisms involving coherent wave scattering by preexisting perturbations in the mechanics, OAEs evoked by broadband clicks (CEOAEs) have been suggested to originate via nonlinear interactions among the different frequency components of the stimulus (e.g., intermodulation distortion). The experiments reported here test for bandwidth-dependent differences in mechanisms of OAE generation. Click-evoked and stimulus-frequency OAE input/output transfer functions were obtained and compared as a function of stimulus frequency and intensity. At low and moderate intensities human CEOAE and SFOAE transfer functions are nearly identical. When stimulus intensity is measured in "bandwidth-compensated" sound-pressure level (cSPL), CEOAE and SFOAE transfer functions have equivalent growth functions at fixed frequency and equivalent spectral characteristics at fixed intensity. This equivalence suggests that CEOAEs and SFOAEs are generated by the same mechanism. Although CEOAEs and SFOAEs are known by different names because of the different stimuli used to evoke them, the two OAE "types" are evidently best understood as members of the same emission family.     

Modeling the effect of suppression on the periodicity of stimulus frequency otoacoustic emissions

The distributed roughness theory of the origins of spectral periodicity in stimulus frequency otoacoustic emissions (SFOAEs) predicts that the spectral period will be altered by suppression of the traveling wave (TW) [Zweig and Shera, J. Acoust. Soc. Am. 98, 2018-2047 (1995)]. In order to investigate this effect in more detail, simulations of the variation of the spectral period under conditions of self-suppression and two-tone suppression are obtained from nonlinear cochlear models based on this theory. The results show that during self-suppression the spectral period is increased, while during high-side two-tone suppression, the period is reduced, indicating that the detailed pattern of disruption of the cochlear amplifier must be examined if the nonlinear behavior of SFOAEs is to be understood. The model results suggest that the SFOAE spectral period may be sensitive to changes in the state of the cochlear amplifier. A companion paper [Lineton and Lutman, J. Acoust. Soc. Am. 114, 871-882 (2003)] presents experimental data which are compared with the results of the above models with a view to testing the underlying theory of Zweig and Shera.     

The effect of suppression on the periodicity of stimulus frequency otoacoustic emissions: experimental data

In a companion paper [Lineton and Lutman, J. Acoust. Soc. Am. 114, 859-870 (2003)], changes in the spectral period of stimulus frequency otoacoustic emissions (SFOAEs) during self-suppression and two-tone suppression were simulated using a nonlinear cochlear model based on the distributed roughness theory of otoacoustic emission generation [Zweig and Shera, J. Acoust. Soc. Am. 98, 2018-2047 (1995)1. The current paper presents the results of an experimental investigation of SFOAE suppression obtained from 20 human subjects. It was found that, in most subjects, the spectral period increased during self-suppression, but reduced during high-side two-tone suppression. This pattern of results is in close agreement with the predictions of the cochlear model, and therefore strongly supports the distributed roughness theory of Zweig and Shera. In addition, the results suggest that the SFOAE spectral period is sensitive to changes in the state of the cochlear amplifier.     

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.     

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.     

Two-tone suppression of stimulus frequency otoacoustic emissions

Stimulus frequency otoacoustic emissions (SFOAEs) measured using a suppressor tone in human ears are analogous to two-tone suppression responses measured mechanically and neurally in mammalian cochleae. SFOAE suppression was measured in 24 normal-hearing adults at octave frequencies (f(p)=0.5-8.0 kHz) over a 40 dB range of probe levels (L(p)). Suppressor frequencies (f(s)) ranged from -2.0 to 0.7 octaves re: f(p), and suppressor levels ranged from just detectable suppression to full suppression. The lowest suppression thresholds occurred for "best" f(s) slightly higher than f(p). SFOAE growth of suppression (GOS) had slopes close to one at frequencies much lower than best f(s), and shallow slopes near best f(s), which indicated compressive growth close to 0.3 dBdB. Suppression tuning curves constructed from GOS functions were well defined at 1, 2, and 4 kHz, but less so at 0.5 and 8.0 kHz. Tuning was sharper at lower L(p) with an equivalent rectangular bandwidth similar to that reported behaviorally for simultaneous masking. The tip-to-tail difference assessed cochlear gain, increasing with decreasing L(p) and increasing f(p) at the lowest L(p) from 32 to 45 dB for f(p) from 1 to 4 kHz. SFOAE suppression provides a noninvasive measure of the saturating nonlinearities associated with cochlear amplification on the basilar membrane.     

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.     

Modeling cochlear dynamics: interrelation between cochlea mechanics and psychoacoustics

A model of the cochlea was used to bridge the gap between model approaches commonly used to investigate phenomena related to otoacoustic emissions and more filter-based model approaches often used in psychoacoustics. In the present study, a nonlinear and active one-dimensional transmission line model was developed that accounts for several aspects of physiological data with a single fixed parameter set. The model shows plausible excitation patterns and an input-output function similar to the linear-compressive-linear function as hypothesized in psychoacoustics. The model shows realistic results in a two-tone suppression paradigm and a plausible growth function of the 2f(1)-f(2) component of distortion product otoacoustic emissions. Finestructure was found in simulated stimulus-frequency otoacoustic emissions (SFOAE) with realistic levels and rapid phase rotation. A plausible "threshold in quiet" including finestructure and spontaneous otoacoustic emissions (SOAE) could be simulated. It is further shown that psychoacoustical data of modulation detection near threshold can be explained by the mechanical dynamics of the modeled healthy cochlea. It is discussed that such a model can be used to investigate the representation of acoustic signals in healthy and impaired cochleae at this early stage of the auditory pathway for both, physiological as well as psychoacoustical paradigms.     

Dual traveling waves in an inner ear model with two degrees of freedom

We calculate traveling waves in the mammalian cochlea, which transduces acoustic vibrations into neural signals. We use a WKB-based mechanical model with both the tectorial membrane (TM) and basilar membrane (BM) coupled to the fluid to calculate motions along the length of the cochlea. This approach generates two wave numbers that manifest as traveling waves with different modes of motion between the BM and TM. The waves add differently on each mass, producing distinct tuning curves and different characteristic frequencies (CFs) for the TM and the BM. We discuss the effect of TM stiffness and coupling on the waves and tuning curves. We also consider how the differential motions between the masses could influence the cochlear amplifier and how mode conversion could take place in the cochlea.     

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.     

Medial olivocochlear efferent inhibition of basilar-membrane responses to clicks: evidence for two modes of cochlear mechanical excitation

Conceptualizations of mammalian cochlear mechanics are based on basilar-membrane (BM) traveling waves that scale with frequency along the length of the cochlea, are amplified by outer hair cells (OHCs), and excite inner hair cells and auditory-nerve (AN) fibers in a simple way. However, recent experimental work has shown medial-olivocochlear (MOC) inhibition of AN responses to clicks that do not fit with this picture. To test whether this AN-initial-peak (ANIP) inhibition might result from hitherto unrecognized aspects of the traveling-wave or MOC-evoked inhibition, MOC effects on BM responses to clicks in the basal turns of guinea pig and chinchilla cochleae were measured. MOC stimulation inhibited BM click responses in a time and level dependent manner. Inhibition was not seen during the first half-cycle of the responses, but built up gradually, and ultimately increased the responses' decay rates. MOC stimulation also produced small phase leads in the response wave forms, but had little effect on the instantaneous frequency or the waxing and waning of the responses. These data, plus recent AN data, support the hypothesis that the MOC-evoked inhibitions of the traveling wave and of the ANIP response are separate phenomena, and indicate that the OHCs can affect at least two separate modes of excitation in the mammalian cochlea.     

Laser amplification with a twist: traveling-wave propagation and gain functions from throughout the cochlea

Except at the handful of sites explored by the inverse method, the characteristics-indeed, the very existence-of traveling-wave amplification in the mammalian cochlea remain largely unknown. Uncertainties are especially pronounced in the apex, where mechanical and electrical measurements lack the independent controls necessary for assessing damage to the preparation. At a functional level, the form and amplification of cochlear traveling waves are described by quantities known as propagation and gain functions. A method for deriving propagation and gain functions from basilar-membrane mechanical transfer functions is presented and validated by response reconstruction. Empirical propagation and gain functions from locations throughout the cochlea are obtained in mechanically undamaged preparations by applying the method to published estimates of near-threshold basilar membrane responses derived from Wiener-kernel (chinchilla) and zwuis analysis (cat) of auditory-nerve responses to broadband stimuli. The properties of these functions, and their variation along the length of the cochlea, are described. In both species, and at all locations examined, the gain functions reveal a region of positive power gain basal to the wave peak. The results establish the existence of traveling-wave amplification throughout the cochlea, including the apex. The derived propagation and gain functions resemble those characteristic of an active optical medium but rotated by 90 degrees in the complex plane. Rotation of the propagation and gain functions enables the mammalian cochlea to operate as a wideband, hydromechanical laser analyzer.     

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.