Intensity-invariance of fine time structure in basilar-membrane click responses: implications for cochlear mechanics

Evaluation of the Decrease in DPOAE Levels After VEMP Testing in Clinical Patients Referred to the Vertigo Outpatient Clinic

Background/Objectives: The objective of this study is to determine whether the strong acoustic stimuli used in vestibular evoked myogenic potential (VEMP) testing contribute to distortion product otoacoustic emission (DPOAE) level reduction due to noise-induced hearing loss. Methods: The DPOAE levels were measured routinely to evaluate vestibular balance disorders with sensorineural hearing loss and to monitor changes in cochlear function before and after VEMP. The changes in DPOAE levels after VEMP testing in 174 patients (80 males and 94 females; median age, 53 years [interquartile range, 39-67 years; range, 15-85 years]) who were examined in the vertigo outpatient clinic between June 2021 and December 2024 were retrospectively analyzed. Results: The DPOAE levels decreased significantly after VEMP testing at 1.4 kHz, 2 kHz, 2.8 kHz, sum all 1/2 octave, and average 1/2 octave (1-6 kHz). The decrease in DPOAE levels at 6 kHz exhibited a significant negative linear correlation with age (the coefficient of determination: 0.0189, p = 0.01), but not sex or side. Conclusions: The strong sound stimulation used in VEMP testing can decrease DPOAE levels. The frequencies at which DPOAE levels decreased significantly were overtones of the stimulus frequency, suggesting a possible effect of acoustic stimulation. VEMP testing can be an invasive test method and should be performed with detailed consideration of the risks and benefits. The age factor can influence the decrease in DPOAE levels in VEMP testing.

Evaluating the Correlation Between Stimulus Frequency Otoacoustic Emission Group Delays and Tuning Sharpness in a Cochlear Model

PURPOSE

A theoretical framework based on coherent reflection and filter theory predicts that the phase-gradient delays of stimulus frequency otoacoustic emissions (SFOAEs) are correlated with tuning sharpness in the mammalian cochlea. In this paper, we use a computational model of the cochlea to test this theory and to evaluate how SFOAE phase-gradient delays may be used to estimate the sharpness of cochlear tuning.

METHODS

This study is based on a physiologically motivated model which has been previously shown to predict key aspects of cochlear micromechanics. Cochlear roughness is introduced to model the reflection mechanism which underlies SFOAE generation. We then examine how varying the values of key model parameters or of the sound pressure level of the stimulus affects the relation between cochlear tuning and SFOAE delays. Finally, we quantify the ability of model simulations of SFOAE phase-gradient delays to provide reliable estimates of the tuning sharpness of the model.

RESULTS

We find that variations of model parameters that cause significant broadening of basilar membrane (BM) tuning typically give rise to a sizeable reduction in SFOAE phase-gradient delays. However, some changes in model parameters may cause a significant broadening of BM tuning with only a moderate decrease in SFOAE delays. SFOAE delays can be used to estimate the tuning sharpness of the model with reasonable accuracy only in cases where broadening of cochlear tuning is associated with a significant reduction in SFOAE delays.

CONCLUSION

The numerical results provide key insights about the correlations between cochlear tuning and SFOAE delays.

Optimal Scale-Invariant Wavelet Representation and Filtering of Human Otoacoustic Emissions

Otoacoustic emissions (OAEs) are generated in the cochlea and recorded in the ear canal either as a time domain waveform or as a collection of complex responses to tones in the frequency domain (Probst et al. J Account Soc Am 89:2027-2067, 1991). They are typically represented either in their original acquisition domain or in its Fourier-conjugated domain. Round-trip excursions to the conjugated domain are often used to perform filtering operations in the computationally simplest way, exploiting the convolution theorem. OAE signals consist of the superposition of backward waves generated in different cochlear regions by different generation mechanisms, over a wide frequency range. The cochlear scaling symmetry (cochlear physics is the same at all frequency scales), which approximately holds in the human cochlea, leaves its fingerprints in the mathematical properties of OAE signals. According to a generally accepted taxonomy (Sher and Guinan Jr, J Acoust Soc Am 105:782-798, 1999), OAEs are generated either by wave-fixed sources, moving with frequency according with the cochlear scaling (as in nonlinear distortion) or by place-fixed sources (as in coherent reflection by roughness). If scaling symmetry holds, the two generation mechanisms yield OAEs with different phase gradient delay: almost null for wave-fixed sources, and long (and scaling as 1/f) for place-fixed sources. Thus, the most effective representation of OAE signals is often that respecting the cochlear scale-invariance, such as the time-frequency domain representation provided by the wavelet transform. In the time-frequency domain, the elaborate spectra or waveforms yielded by the superposition of OAE components from different generation mechanisms assume a much clearer 2-D pattern, with each component localized in a specific and predictable region. The wavelet representation of OAE signals is optimal both for visualization purposes and for designing filters that effectively separate different OAE components, improving both the specificity and the sensitivity of OAE-based applications. Indeed, different OAE components have different physiological meanings, and filtering dramatically improves the signal-to-noise ratio.

Intracochlear overdrive: Characterizing nonlinear wave amplification in the mouse apex

In this study, we explore nonlinear cochlear amplification by analyzing basilar membrane (BM) motion in the mouse apex. Through in vivo, postmortem, and mechanical suppression recordings, we estimate how the cochlear amplifier nonlinearly shapes the wavenumber of the BM traveling wave, specifically within a frequency range where the short-wave approximation holds. Our findings demonstrate that a straightforward mathematical model, depicting the cochlear amplifier as a wavenumber modifier with strength diminishing monotonically as BM displacement increases, effectively accounts for the various experimental observations. This empirically derived model is subsequently incorporated into a physics-based "overturned" framework of cochlear amplification [see Altoè, Dewey, Charaziak, Oghalai, and Shera (2022), J. Acoust. Soc. Am. 152, 2227-2239] and tested against additional experimental data. Our results demonstrate that the relationships established within the short-wave region remain valid over a much broader frequency range. Furthermore, the model, now exclusively calibrated to BM data, predicts the behavior of the opposing side of the cochlear partition, aligning well with recent experimental observations. The success in reproducing key features of the experimental data and the mathematical simplicity of the resulting model provide strong support for the "overturned" theory of cochlear amplification.

Estimating cochlear impulse responses using frequency sweeps

Cochlear mechanics tends to be studied using single-location measurements of intracochlear vibrations in response to acoustical stimuli. Such measurements, due to their invasiveness and often the instability of the animal preparation, are difficult to accomplish and, thus, ideally require stimulus paradigms that are time efficient, flexible, and result in high resolution transfer functions. Here, a swept-sine method is adapted for recordings of basilar membrane impulse responses in mice. The frequency of the stimulus was exponentially swept from low to high (upward) or high to low (downward) at varying rates (from slow to fast) and intensities. The cochlear response to the swept-sine was then convolved with the time-reversed stimulus waveform to obtain first and higher order impulse responses. Slow sweeps of either direction produce cochlear first to third order transfer functions equivalent to those measured with pure tones. Fast upward sweeps, on the other hand, generate impulse responses that typically ring longer, as observed in responses obtained using clicks. The ringing of impulse response in mice was of relatively small amplitude and did not affect the magnitude spectra. It is concluded that swept-sine methods offer flexible and time-efficient alternatives to other approaches for recording cochlear impulse responses.

Overturning the mechanisms of cochlear amplification via area deformations of the organ of Corti

The mammalian ear embeds a cellular amplifier that boosts sound-induced hydromechanical waves as they propagate along the cochlea. The operation of this amplifier is not fully understood and is difficult to disentangle experimentally. In the prevailing view, cochlear waves are amplified by the piezo-electric action of the outer hair cells (OHCs), whose cycle-by-cycle elongations and contractions inject power into the local motion of the basilar membrane (BM). Concomitant deformations of the opposing (or "top") side of the organ of Corti are assumed to play a minor role and are generally neglected. However, analysis of intracochlear motions obtained using optical coherence tomography calls this prevailing view into question. In particular, the analysis suggests that (i) the net local power transfer from the OHCs to the BM is either negative or highly inefficient; and (ii) vibration of the top side of the organ of Corti plays a primary role in traveling-wave amplification. A phenomenological model derived from these observations manifests realistic cochlear responses and suggests that amplification arises almost entirely from OHC-induced deformations of the top side of the organ of Corti. In effect, the model turns classic assumptions about spatial impedance relations and power-flow direction within the sensory epithelium upside down.

Interplay between traveling wave propagation and amplification at the apex of the mouse cochlea

Sounds entering the mammalian ear produce waves that travel from the base to the apex of the cochlea. An electromechanical active process amplifies traveling wave motions and enables sound processing over a broad range of frequencies and intensities. The cochlear amplifier requires combining the global traveling wave with the local cellular processes that change along the length of the cochlea given the gradual changes in hair cell and supporting cell anatomy and physiology. Thus, we measured basilar membrane (BM) traveling waves in vivo along the apical turn of the mouse cochlea using volumetric optical coherence tomography and vibrometry. We found that there was a gradual reduction in key features of the active process toward the apex. For example, the gain decreased from 23 to 19 dB and tuning sharpness decreased from 2.5 to 1.4. Furthermore, we measured the frequency and intensity dependence of traveling wave properties. The phase velocity was larger than the group velocity, and both quantities gradually decrease from the base to the apex denoting a strong dispersion characteristic near the helicotrema. Moreover, we found that the spatial wavelength along the BM was highly level dependent in vivo, such that increasing the sound intensity from 30 to 90 dB sound pressure level increased the wavelength from 504 to 874 μm, a factor of 1.73. We hypothesize that this wavelength variation with sound intensity gives rise to an increase of the fluid-loaded mass on the BM and tunes its local resonance frequency. Together, these data demonstrate a strong interplay between the traveling wave propagation and amplification along the length of the cochlea.

The Elusive Cochlear Filter: Wave Origin of Cochlear Cross-Frequency Masking

The mammalian cochlea achieves its remarkable sensitivity, frequency selectivity, and dynamic range by spatially segregating the different frequency components of sound via nonlinear processes that remain only partially understood. As a consequence of the wave-based nature of cochlear processing, the different frequency components of complex sounds interact spatially and nonlinearly, mutually suppressing one another as they propagate. Because understanding nonlinear wave interactions and their effects on hearing appears to require mathematically complex or computationally intensive models, theories of hearing that do not deal specifically with cochlear mechanics have often neglected the spatial nature of suppression phenomena. Here we describe a simple framework consisting of a nonlinear traveling-wave model whose spatial response properties can be estimated from basilar-membrane (BM) transfer functions. Without invoking jazzy details of organ-of-Corti mechanics, the model accounts well for the peculiar frequency-dependence of suppression found in two-tone suppression experiments. In particular, our analysis shows that near the peak of the traveling wave, the amplitude of the BM response depends primarily on the nonlinear properties of the traveling wave in more basal (high-frequency) regions. The proposed framework provides perhaps the simplest representation of cochlear signal processing that accounts for the spatially distributed effects of nonlinear wave propagation. Shifting the perspective from local filters to non-local, spatially distributed processes not only elucidates the character of cochlear signal processing, but also has important consequences for interpreting psychophysical experiments.

Denoising click-evoked otoacoustic emission signals by optimal shrinkage

Click-evoked otoacoustic emissions (CEOAEs) are clinically used as an objective way to infer whether cochlear functions are normal. However, because the sound pressure level of CEOAEs is typically much lower than the background noise, it usually takes hundreds, if not thousands, of repetitions to estimate the signal with sufficient accuracy. In this paper, we propose to improve the signal-to-noise ratio (SNR) of CEOAE signals within limited measurement time by optimal shrinkage (OS) in two different settings: covariance-based optimal shrinkage (cOS) and singular value decomposition-based optimal shrinkage (sOS). By simulation, the cOS consistently enhanced the SNR by 1-2 dB from a baseline method that is based on calculating the median. In real data, however, the cOS cannot enhance the SNR over 1 dB. The sOS achieved a SNR enhancement of 2-3 dB in simulation and demonstrated capability to enhance the SNR in real recordings. In addition, the level of enhancement increases as the baseline SNR decreases. An appealing property of OS is that it produces an estimate of all single trials. This property makes it possible to investigate CEOAE dynamics across a longer period of time when the cochlear conditions are not strictly stationary.

Suppression tuning curves in a two-degrees-of-freedom nonlinear cochlear model

A two-degrees-of-freedom nonlinear cochlear model [Sisto, Shera, Altoè, and Moleti (2019). J. Acoust. Soc. Am. 146, 1685-1695] correctly predicts that the reticular lamina response is nonlinear over a wide basal region. Numerical simulations of suppression tuning curves agree with a recent experiment [Dewey, Applegate, and Oghalai (2019). J. Neurosci. 39, 1805-1816], supporting the idea that the strong susceptibility of the reticular lamina response to suppression by high-frequency tones does not imply that the total traveling wave energy builds-up in correspondingly basal regions. This happens because the reticular lamina is the lightest element of a coupled-oscillators system, only indirectly coupled to the differential pressure.

Asymmetry and Microstructure of Temporal-Suppression Patterns in Basilar-Membrane Responses to Clicks: Relation to Tonal Suppression and Traveling-Wave Dispersion

The cochlea's wave-based signal processing allows it to efficiently decompose a complex acoustic waveform into frequency components. Because cochlear responses are nonlinear, the waves arising from one frequency component of a complex sound can be altered by the presence of others that overlap with it in time and space (e.g., two-tone suppression). Here, we investigate the suppression of basilar-membrane (BM) velocity responses to a transient signal (a test click) by another click or tone. We show that the BM response to the click can be reduced when the stimulus is shortly preceded or followed by another (suppressor) click. More surprisingly, the data reveal two curious dependencies on the interclick interval, Δt. First, the temporal suppression curve (amount of suppression vs. Δt) manifests a pronounced and nearly periodic microstructure. Second, temporal suppression is generally strongest not when the two clicks are presented simultaneously (Δt = 0), but when the suppressor click precedes the test click by a time interval corresponding to one to two periods of the best frequency (BF) at the measurement location. By systematically varying the phase of the suppressor click, we demonstrate that the suppression microstructure arises from alternating constructive and destructive interference between the BM responses to the two clicks. And by comparing temporal and tonal suppression in the same animals, we test the hypothesis that the asymmetry of the temporal-suppression curve around Δt = 0 stems from cochlear dispersion and the well-known asymmetry of tonal suppression around the BF. Just as for two-tone suppression, BM responses to clicks are most suppressed by tones at frequencies just above the BF of the measurement location. On average, the frequency place of maximal suppressibility of the click response predicted from temporal-suppression data agrees with the frequency at which tonal suppression peaks, consistent with our hypothesis.

Nonlinear cochlear mechanics without direct vibration-amplification feedback

Recent in vivo recordings from the mammalian cochlea indicate that although the motion of the basilar membrane appears actively amplified and nonlinear only at frequencies relatively close to the peak of the response, the internal motions of the organ of Corti display these same features over a much wider range of frequencies. These experimental findings are not easily explained by the textbook view of cochlear mechanics, in which cochlear amplification is controlled by the motion of the basilar membrane (BM) in a tight, closed-loop feedback configuration. This study shows that a simple phenomenological model of the cochlea inspired by the work of Zweig [J. Acoust. Soc. Am. 138, 1102 (2015)] can account for recent data in mouse and gerbil. In this model, the active forces are regulated indirectly, through the effect of BM motion on the pressure field across the cochlear partition, rather than via direct coupling between active-force generation and BM vibration. The absence of strong vibration-amplification feedback in the cochlea also provides a compelling explanation for the observed intensity invariance of fine time structure in the BM response to acoustic clicks.

Constraints imposed by zero-crossing invariance on cochlear models with two mechanical degrees of freedom

The zero crossings of basilar-membrane (BM) responses to clicks are nearly independent of stimulus intensity. This work explores the constraints that this invariance imposes on one-dimensional nonlinear cochlear models with two degrees of freedom (2DoF). The locations of the poles and zeros of the BM admittance, calculated for a set of linear models in which the strength of the active force is progressively decreased, provides a playground for evaluating the behavior of a corresponding nonlinear model at increasing stimulus levels. Mathematical constraints on the model parameters are derived by requiring that the poles of the admittance move horizontally in the s-plane as the active force is varied. These constraints ensure approximate zero-crossing invariance over a wide stimulus level range in a nonlinear model in which the active force varies as a function of the local instantaneous BM displacement and velocity. Two different 2DoF models are explored, each capable of reproducing the main qualitative characteristics of the BM response to tones (i.e., the tall and broad activity pattern at low stimulus levels, the large gain dynamics, and the partial decoupling between gain and phase). In each model, the motions of the two masses are compared with response data from animal experiments.

Cochlear impulse responses resolved into sets of gammatones: the case for beating of closely spaced local resonances

Gammatones have had a long history in auditory studies, and recent theoretical work suggests they may play an important role in cochlear mechanics as well. Following this lead, the present paper takes five examples of basilar membrane impulse responses and uses a curve-fitting algorithm to decompose them into a number of discrete gammatones. The limits of this ‘sum of gammatones’ (SOG) method to accurately represent the impulse response waveforms were tested and it was found that at least two and up to six gammatones could be isolated from each example. Their frequencies were stable and largely independent of stimulus parameters. The gammatones typically formed a regular series in which the frequency ratio between successive members was about 1.1. Adding together the first few gammatones in a set produced beating-like waveforms which mimicked waxing and waning, and the instantaneous frequencies of the waveforms were also well reproduced, providing an explanation for frequency glides. Consideration was also given to the impulse response of a pair of elastically coupled masses—the basis of two-degree-of-freedom models comprised of coupled basilar and tectorial membranes—and the resulting waveform was similar to a pair of beating gammatones, perhaps explaining why the SOG method seems to work well in describing cochlear impulse responses. A major limitation of the SOG method is that it cannot distinguish a waveform resulting from an actual physical resonance from one derived from overfitting, but taken together the method points to the presence of a series of closely spaced local resonances in the cochlea.

Physiologically motivated individual loudness model for normal hearing and hearing impaired listeners

A loudness model with a central gain is suggested to improve individualized predictions of loudness scaling data from normal hearing and hearing impaired listeners. The current approach is based on the loudness model of Pieper et al. [(2016). J. Acoust. Soc. Am. 139, 2896], which simulated the nonlinear inner ear mechanics as transmission-line model in a physical and physiological plausible way. Individual hearing thresholds were simulated by a cochlear gain reduction in the transmission-line model and linear attenuation (damage of inner hair cells) prior to an internal threshold. This and similar approaches of current loudness models that characterize the individual hearing loss were shown to be insufficient to account for individual loudness perception, in particular at high stimulus levels close to the uncomfortable level. An additional parameter, termed "post gain," was introduced to improve upon the previous models. The post gain parameter amplifies the signal parts above the internal threshold and can better account for individual variations in the overall steepness of loudness functions and for variations in the uncomfortable level which are independent of the hearing loss. The post gain can be interpreted as a central gain occurring at higher stages as a result of peripheral deafferentation.

Modeling the dependence of the distortion product otoacoustic emission response on primary frequency ratio

When measured as a function of primary frequency ratio r = f₂/f₁, using a constant f₂, distortion product otoacoustic emission (DPOAE) response demonstrates a bandpass shape, previously interpreted as the evidence for a cochlear "second filter." In this study, an alternate, interference-based explanation, previously advanced in variants, is forwarded on the basis of experimental data along with numerical and analytical solutions of nonlinear and linear cochlear models. The decrease of the DPOAE response with increasing and decreasing ratios is explained by a diminishing "overlap" generation region and the onset of negative interference among wavelets of different phase, respectively. In this paper, the additional quantitative hypothesis is made that negative interference becomes the dominant effect when the spatial width of the generation (overlap) region exceeds half a wavelength of the DPOAE wavelets. Therefore, r is predicted to be optimal when this condition is matched. Additionally, the minimum on the low-ratio side of the DPOAE curve is predicted to occur as the overlap region width equals one wavelength. As the width of the overlap region depends on both tuning and ratio, while wavelength depends on tuning only, an experimental method for estimating tuning from either the width of the pass band or the optimal ratio of the DPOAE vs. ratio curve has been theoretically formulated and evaluated using numerical simulations. A linear model without the possibility of nonlinear suppression is shown to reasonably approximate data from human subjects at low ratios reinforcing the relevance of the proposed negative interference effect. The different dependence of the distortion and reflection DPOAE components on r as well as the nonmonotonic behavior of the distortion component observed at very low ratios are also in agreement with this interpretation.

The 1.06 frequency ratio in the cochlea: evidence and outlook for a natural musical semitone

A frequency ratio of about 1.06 often appears in cochlear mechanics, and the question naturally arises, why? The ratio is close to that of the semitone (1.059) in music, giving reason to think that this aspect of musical perception might have a cochlear basis. Here, data on synchronised spontaneous otoacoustic emissions is presented, and a clustering of ratios between 1.05 and 1.07 is found with a peak at 1.063 ± 0.005. These findings reinforce what has been found from previous sources, which are reviewed and placed alongside the present work. The review establishes that a peak in the vicinity of 1.06 has often been found in human cochlear data. Several possible cochlear models for explaining the findings are described. Irrespective of which model is selected, the fact remains that the cochlea itself appears to be the origin of a ratio remarkably close to an equal-tempered musical semitone, and this close coincidence leads to the suggestion that the inner ear may play a role in constructing a natural theory of music. The outlook for such an enterprise is surveyed.

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

Fitting pole-zero micromechanical models to cochlear response measurements

An efficient way of describing the linear micromechanical response of the cochlea is in terms of its poles and zeros. Pole-zero models with local scaling symmetry are derived for both one and two degree-of-freedom micromechanical systems. These elements are then used in a model of the coupled cochlea, which is optimised to minimise the mean square difference between its frequency response and that measured on the basilar membrane inside the mouse cochlea by Lee, Raphael, Xia, Kim, Grillet, Applegate, Ellerbee Bowden, and Oghalai [(2016) J. Neurosci. 36, 8160-8173] and Oghalai Lab [(2015). https://oghalailab.stanford.edu], at different excitation levels. A model with two degree-of-freedom micromechanics generally fits the measurements better than a model with single degree-of-freedom micromechanics, particularly at low excitations where the cochlea is active, except post-mortem conditions, when the cochlea is passive. The model with the best overall fit to the data is found to be one with two degree-of-freedom micromechanics and 3D fluid coupling. Although a unique lumped parameter network cannot be inferred from such a pole-zero description, these fitted results help indicate what properties such a network should have.

Evidence for apical-basal transition in the delay of the reflection components of otoacoustic emissions

Stimulus-frequency, transient-evoked, and distortion product otoacoustic emissions (OAEs) have been measured in eight normal-hearing human ears over a wide stimulus level range, with high spectral resolution. The single-reflection component of the response was isolated using time-frequency filtering, and its average delay was measured as a function of frequency and stimulus level. The apical-basal transition was studied by fitting the average delay of the filtered single-reflection OAEs, expressed in number of cycles, to a three-slope power-law function with two knot frequencies. The results show that the scale-invariant prediction of constant dimensionless delay approximately holds only over a narrow intermediate frequency range (1-2.5 kHz). Below 1 kHz, and, to some extent, above 2.5 kHz, the dimensionless delay increases with frequency, at all stimulus levels. Comparison with the numerical simulations of a delayed-stiffness active cochlear model show that the increase of tuning with frequency reported by behavioral experiments only partly explains this result. The low-frequency scaling symmetry breaking associated with the deviation of the Greenwood tonotopic map from a pure exponential function is also insufficient to explain the steep low-frequency increase of the OAE delay. Other sources of symmetry breaking, not included in the model, could therefore play a role.

Comparisons of transient evoked otoacoustic emissions using chirp and click stimuli

Transient-evoked otoacoustic emission (TEOAE) responses (0.7-8 kHz) were measured in normal-hearing adult ears using click stimuli and chirps whose local frequency increased or decreased linearly with time over the stimulus duration. Chirp stimuli were created by allpass filtering a click with relatively constant incident pressure level over frequency. Chirp TEOAEs were analyzed as a nonlinear residual signal by inverse allpass filtering each chirp response into an equivalent click response. Multi-window spectral and temporal averaging reduced noise levels compared to a single-window average. Mean TEOAE levels using click and chirp stimuli were similar with respect to their standard errors in adult ears. TEOAE group delay, group spread, instantaneous frequency, and instantaneous bandwidth were similar overall for chirp and click conditions, except for small differences showing nonlinear interactions differing across stimulus conditions. These results support the theory of a similar generation mechanism on the basilar membrane for both click and chirp conditions based on coherent reflection within the tonotopic region. TEOAE temporal fine structure was invariant across changes in stimulus level, which is analogous to the intensity invariance of click-evoked basilar-membrane displacement data.

A comparative study of seven human cochlear filter models

Auditory models have been developed for decades to simulate characteristics of the human auditory system, but it is often unknown how well auditory models compare to each other or perform in tasks they were not primarily designed for. This study systematically analyzes predictions of seven publicly-available cochlear filter models in response to a fixed set of stimuli to assess their capabilities of reproducing key aspects of human cochlear mechanics. The following features were assessed at frequencies of 0.5, 1, 2, 4, and 8 kHz: cochlear excitation patterns, nonlinear response growth, frequency selectivity, group delays, signal-in-noise processing, and amplitude modulation representation. For each task, the simulations were compared to available physiological data recorded in guinea pigs and gerbils as well as to human psychoacoustics data. The presented results provide application-oriented users with comprehensive information on the advantages, limitations and computation costs of these seven mainstream cochlear filter models.

Estimating cochlear tuning dependence on stimulus level and frequency from the delay of otoacoustic emissions

An objective technique based on the time-frequency analysis of otoacoustic emissions is proposed to get fast and stable estimates of cochlear tuning. Time-frequency analysis allows one to get stable measurements of the delay/frequency function, which is theoretically expected to be a function of cochlear tuning. Theoretical considerations and numerical solutions of a nonlinear cochlear model suggest that the average phase-gradient delay of the otoacoustic emission single-reflection components, weighted, for each frequency, by the amplitude of the corresponding wavelet coefficients, approximately scales as the square root of the cochlear quality factor. The application of the method to human stimulus-frequency and transient-evoked otoacoustic emissions shows that tuning decreases approximately by a factor of 2, as the stimulus level increases by 30 dB in a moderate stimulus level range. The results also show a steady increase of tuning with increasing frequency, by a factor of 2 between 1 and 5 kHz. This last result is model-dependent, because it relies on the assumption that cochlear scale-invariance breaking is only due to the frequency dependence of tuning. The application of the method to the reflection component of distortion product otoacoustic emissions, separated using time-frequency filtering, is complicated by the necessity of effectively canceling the distortion component.

Physiological motivated transmission-lines as front end for loudness models

The perception of loudness is strongly influenced by peripheral auditory processing, which calls for a physiologically correct peripheral auditory processing stage when constructing advanced loudness models. Most loudness models, however, rather follow a functional approach: a parallel auditory filter bank combined with a compression stage, followed by spectral and temporal integration. Such classical loudness models do not allow to directly link physiological measurements like otoacoustic emissions to properties of their auditory filterbank. However, this can be achieved with physiologically motivated transmission-line models (TLMs) of the cochlea. Here two active and nonlinear TLMs were tested as the peripheral front end of a loudness model. The TLMs are followed by a simple generic back end which performs integration of basilar-membrane "excitation" across place and time to yield a loudness estimate. The proposed model approach reaches similar performance as other state-of-the-art loudness models regarding the prediction of loudness in sones, equal-loudness contours (including spectral fine structure), and loudness as a function of bandwidth. The suggested model provides a powerful tool to directly connect objective measures of basilar membrane compression, such as distortion product otoacoustic emissions, and loudness in future studies.

Nonlinear cochlear mechanics

An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.

Functional modeling of the human auditory brainstem response to broadband stimulation

Population responses such as the auditory brainstem response (ABR) are commonly used for hearing screening, but the relationship between single-unit physiology and scalp-recorded population responses are not well understood. Computational models that integrate physiologically realistic models of single-unit auditory-nerve (AN), cochlear nucleus (CN) and inferior colliculus (IC) cells with models of broadband peripheral excitation can be used to simulate ABRs and thereby link detailed knowledge of animal physiology to human applications. Existing functional ABR models fail to capture the empirically observed 1.2-2 ms ABR wave-V latency-vs-intensity decrease that is thought to arise from level-dependent changes in cochlear excitation and firing synchrony across different tonotopic sections. This paper proposes an approach where level-dependent cochlear excitation patterns, which reflect human cochlear filter tuning parameters, drive AN fibers to yield realistic level-dependent properties of the ABR wave-V. The number of free model parameters is minimal, producing a model in which various sources of hearing-impairment can easily be simulated on an individualized and frequency-dependent basis. The model fits latency-vs-intensity functions observed in human ABRs and otoacoustic emissions while maintaining rate-level and threshold characteristics of single-unit AN fibers. The simulations help to reveal which tonotopic regions dominate ABR waveform peaks at different stimulus intensities.

Decoupling the level dependence of the basilar membrane gain and phase in nonlinear cochlea models

In animal experiments, the strong dependence on stimulus level of the basilar membrane gain and tuning is not matched by a corresponding change in the phase slope in the resonant region. Linear models, in which the gain dependence on the stimulus level has to be schematized by explicitly changing the tuning parameters of the resonant model, do not easily match this feature of the experimental data. Nonlinear models predict a phase slope that is relatively decoupled from tuning. In addition, delayed-stiffness and feed-forward models also show a significant intrinsic decoupling between gain and tuning, which helps in matching the experimental data.

Nonlinear response to a click in a time-domain model of the mammalian ear

In this paper, a state-space implementation of a previously developed frequency-domain model of the cochlea is coupled to a lumped parameter model of the middle ear. After validation of the time-domain model by comparison of its steady-state response to results obtained with a frequency-domain formulation, the nonlinear response of the cochlea to clicks is investigated. As observed experimentally, a compressive nonlinearity progressively develops within the first few cycles of the response of the basilar membrane (BM). Furthermore, a time-frequency analysis shows that the instantaneous frequency of the BM response to a click progressively approaches the characteristic frequency. This phenomenon, called glide, is predicted at all stimulus intensities, as in experiments. In typical experiments with sensitive animals, the click response is characterized by a long ringing and the response envelope includes several lobes. In order to achieve similar results, inhomogeneities are introduced in the cochlear model. Simulations demonstrate the strong link between characteristics of the frequency response, such as dispersion and frequency-dependent nonlinearity, and characteristics of the time-domain response, such as the glide and a time-dependent nonlinearity. The progressive buildup of cochlear nonlinearity in response to a click is shown to be a consequence of the glide and of frequency-dependent nonlinearity.

The spiral staircase: tonotopic microstructure and cochlear tuning

Although usually assumed to be smooth and continuous, mammalian cochlear frequency-position maps are predicted to manifest a staircase-like structure comprising plateaus of nearly constant characteristic frequency separated by abrupt discontinuities. The height and width of the stair steps are determined by parameters of cochlear frequency tuning and vary with location in the cochlea. The step height is approximately equal to the bandwidth of the auditory filter (critical band), and the step width matches that of the spatial excitation pattern produced by a low-level pure tone. Stepwise tonotopy is an emergent property arising from wave reflection and interference within the cochlea, the same mechanisms responsible for the microstructure of the hearing threshold. Possible relationships between the microstructure of the cochlear map and the tiered tonotopy observed in the inferior colliculus are explored.

On the spatial distribution of the reflection sources of different latency components of otoacoustic emissions

The experimental observation of long- and short-latency components in both stimulus-frequency and transient-evoked otoacoustic emissions admits a comprehensive explanation within the coherent reflection mechanism, in a linear active transmission-line cochlear model. A local complex reflectivity function associated with roughness was defined and analyzed by varying the tuning factor of the model, systematically showing, for each frequency, a multiple-peak spatial structure, compatible with the observed multiple-latency structure of otoacoustic emissions. Although this spatial pattern and the peak relative intensity changes with the chosen random roughness function, the multiple-peak structure is a reproducible feature of different "digital ears," in good agreement with experimental data. If one computes the predicted transmission delays as a function of frequency and position for each source, one gets a good match to the latency-frequency patterns that are directly computed from synthesized otoacoustic spectra using time-frequency analysis. This result clarifies the role of the spatial distribution of the otoacoustic emission sources, further supporting the interpretation of different-latency otoacoustic components as due to reflection sources localized at different places along the basilar membrane.

Transmission line cochlear models: improved accuracy and efficiency

This paper presents an efficient method to compute the numerical solutions of transmission-line (TL) cochlear models, and its application on the model of Verhulst et al. The stability region of the model is extended by adopting a variable step numerical method to solve the system of ordinary differential equations that describes it, and by adopting an adaptive scheme to take in account variations in the system status within each numerical step. The presented method leads to improve simulations numerical accuracy and large computational savings, leading to employ TL models for more extensive simulations than currently possible.

Stationary noise responses in a nonlinear model of cochlear mechanics: iterative solutions in the frequency domain

To examine quasilinear filtering properties in cochlear mechanics, Liu and Neely [(2012). What Fire is in Mine Ears: Progress in Auditory Biomechanics, edited by C. A. Shera and E. S. Olson (AIP, Melville, NY), pp. 218-223] calculated Wiener kernels of a nonlinear cochlear model; it was verified that the model's responses to noise could be accurately predicted by treating the kernels as the impulse responses of an equivalent linear system. However, this previous work fell short of showing that the quasilinear filters could be realized under the same structure of the model, a property predicted by de Boer [(1997). Aud. Neurosci. 3, 377-388]. To address the issue of realizability, this paper presents a method that computes the cochlear model's responses to noise iteratively in the frequency domain. First, cochlear transfer functions are calculated as if the system is linear; then, the efficiency of the outer hair cell electromechanical transduction is adjusted. The two steps repeat until the transfer functions converge. Simulation shows that, as the stimulus level increases, the magnitude response of the cochlea decreases and the latency shortens. The corresponding impulse responses are approximately equal to the Wiener kernels obtained in time-domain simulation; as the stimulus varies, the approximation error is <5% in terms of energy. Thus, the Wiener kernels are effectively computed via the present method, which guarantees that the structure of the model is preserved.

Experimental evidence for the basal generation place of the short-latency transient-evoked otoacoustic emissions

Time-frequency analysis of the transient-evoked otoacoustic emission response was performed on a population of subjects affected by sensory-neural hearing loss characterized by a sharp audiometric profile, caused by firearm noise exposure (42 ears), and on a control population of normal-hearing subjects (84 ears). Time-frequency filtering permitted a careful evaluation of the relation between the audiometric profile and the spectral shape of the long- and short-latency otoacoustic components. Both filtered spectra closely follow the shape of the audiometric profile, with a frequency shift between them. The typical frequency shift was evaluated by averaging the otoacoustic spectra and the audiograms among groups of ears with the same cutoff frequency. Assuming that the otoacoustic emission source function depends on the local effectiveness of the cochlear amplifier, this experimental evidence suggests that the short-latency response is generated at a cochlear place displaced towards the base by about 0.5-1 mm with respect to the generation place of the long-latency component. The analysis of the control group demonstrates that, below 4 kHz, the observed effect is not dependent on the data acquisition and analysis procedure. These results confirm previous theoretical estimates and independent experimental evidence based on the measured latency difference between the two components.

Detection of cochlear amplification and its activation

The operation of the mammalian cochlea relies on a mechanical traveling wave that is actively boosted by electromechanical forces in sensory outer hair cells (OHCs). This active cochlear amplifier produces the impressive sensitivity and frequency resolution of mammalian hearing. The cochlear amplifier has inspired scientists since its discovery in the 1970s, and is still not well understood. To explore cochlear electromechanics at the sensory cell/tissue interface, sound-evoked intracochlear pressure and extracellular voltage were measured using a recently developed dual-sensor with a microelectrode attached to a micro-pressure sensor. The resulting coincident in vivo observations of OHC electrical activity, pressure at the basilar membrane and basilar membrane displacement gave direct evidence for power amplification in the cochlea. Moreover, the results showed a phase shift of voltage relative to mechanical responses at frequencies slightly below the peak, near the onset of amplification. Based on the voltage-force relationship of isolated OHCs, the shift would give rise to effective OHC pumping forces within the traveling wave peak. Thus, the shift activates the cochlear amplifier, serving to localize and thus sharpen the frequency region of amplification. These results are the most concrete evidence for cochlear power amplification to date and support OHC somatic forces as its source.

Basilar-membrane interference patterns from multiple internal reflection of cochlear traveling waves

At low stimulus levels, basilar-membrane (BM) mechanical transfer functions in sensitive cochleae manifest a quasiperiodic rippling pattern in both amplitude and phase. Analysis of the responses of active cochlear models suggests that the rippling is a mechanical interference pattern created by multiple internal reflection within the cochlea. In models, the interference arises when reverse-traveling waves responsible for stimulus-frequency otoacoustic emissions (SFOAEs) reflect off the stapes on their way to the ear canal, launching a secondary forward-traveling wave that combines with the primary wave produced by the stimulus. Frequency-dependent phase differences between the two waves then create the rippling pattern measurable on the BM. Measurements of BM ripples and SFOAEs in individual chinchilla ears demonstrate that the ripples are strongly correlated with the acoustic interference pattern measured in ear-canal pressure, consistent with a common origin involving the generation of SFOAEs. In BM responses to clicks, the ripples appear as temporal fine structure in the response envelope (multiple lobes, waxing and waning). Analysis of the ripple spacing and response phase gradients provides a test for the role of fast- and slow-wave modes of reverse energy propagation within the cochlea. The data indicate that SFOAE delays are consistent with reverse slow-wave propagation but much too long to be explained by fast waves.

Nonlinear time-domain cochlear model for transient stimulation and human otoacoustic emission

This paper describes the implementation and performance of a nonlinear time-domain model of the cochlea for transient stimulation and human otoacoustic emission generation. The nonlinearity simulates compressive growth of measured basilar-membrane impulse responses. The model accounts for reflection and distortion-source otoacoustic emissions (OAEs) and simulates spontaneous OAEs through manipulation of the middle-ear reflectance. The model was calibrated using human psychoacoustical and otoacoustic tuning parameters. It can be used to investigate time-dependent properties of cochlear mechanics and the generator mechanisms of otoacoustic emissions. Furthermore, the model provides a suitable preprocessor for human auditory perception models where realistic cochlear excitation patterns are desired.

Cascades of two-pole-two-zero asymmetric resonators are good models of peripheral auditory function

A cascade of two-pole-two-zero filter stages is a good model of the auditory periphery in two distinct ways. First, in the form of the pole-zero filter cascade, it acts as an auditory filter model that provides an excellent fit to data on human detection of tones in masking noise, with fewer fitting parameters than previously reported filter models such as the roex and gammachirp models. Second, when extended to the form of the cascade of asymmetric resonators with fast-acting compression, it serves as an efficient front-end filterbank for machine-hearing applications, including dynamic nonlinear effects such as fast wide-dynamic-range compression. In their underlying linear approximations, these filters are described by their poles and zeros, that is, by rational transfer functions, which makes them simple to implement in analog or digital domains. Other advantages in these models derive from the close connection of the filter-cascade architecture to wave propagation in the cochlea. These models also reflect the automatic-gain-control function of the auditory system and can maintain approximately constant impulse-response zero-crossing times as the level-dependent parameters change.

Signal processing in the cochlea: the structure equations

BACKGROUND

Physical and physiological invariance laws, in particular time invariance and local symmetry, are at the outset of an abstract model. Harmonic analysis and Lie theory are the mathematical prerequisites for its deduction.

RESULTS

The main result is a linear system of partial differential equations (referred to as the structure equations) that describe the result of signal processing in the cochlea. It is formulated for phase and for the logarithm of the amplitude. The changes of these quantities are the essential physiological observables in the description of signal processing in the auditory pathway.

CONCLUSIONS

The structure equations display in a quantitative way the subtle balance for processing information on the basis of phase versus amplitude. From a mathematical point of view, the linear system of equations is classified as an inhomogeneous ∂¯-equation. In suitable variables the solutions can be represented as the superposition of a particular solution (determined by the system) and a holomorphic function (determined by the incoming signal). In this way, a global picture of signal processing in the cochlea emerges.

Temporal suppression of the click-evoked otoacoustic emission level-curve

The click-evoked otoacoustic emission (CEOAE) level-curve grows linearly for clicks below 40-60 dB and saturates for higher inputs. This study investigates dynamic (i.e., time-dependent) features of the CEOAE level-curve by presenting a suppressor-click less than 8 ms before the test-click. An alteration of the CEOAE level-curve, designated here as temporal suppression, was observed within this time period, and was shown to depend on the levels and the temporal separation of the two clicks. Temporal suppression occurred for all four subjects tested, and resulted in a vertical offset from the unsuppressed level-curve for test-click levels greater than 50 dB peak-equivalent level (peSPL). Temporal suppression was greatest for suppressors presented 1-4 ms before the test click, and the magnitude and time scale of the effect were subject dependent. Temporal suppression was furthermore observed for the short- (i.e., 6-18 ms) and long-latency (i.e., 24-36 ms) regions of the CEOAE, indicating that temporal suppression similarly affects synchronized spontaneous otoacoustic emissions (SSOAEs) and purely evoked CEOAE components. Overall, this study demonstrates that temporal suppression of the CEOAE level-curve reflects a dynamic process in human cochlear processing that works on a time scale of 0-10 ms.

The remarkable cochlear amplifier

This composite article is intended to give the experts in the field of cochlear mechanics an opportunity to voice their personal opinion on the one mechanism they believe dominates cochlear amplification in mammals. A collection of these ideas are presented here for the auditory community and others interested in the cochlear amplifier. Each expert has given their own personal view on the topic and at the end of their commentary they have suggested several experiments that would be required for the decisive mechanism underlying the cochlear amplifier. These experiments are presently lacking but if successfully performed would have an enormous impact on our understanding of the cochlear amplifier.

In vivo impedance of the gerbil cochlear partition at auditory frequencies

The specific acoustic impedance of the cochlear partition was measured from 4 to 20 kHz in the basal turn of the gerbil cochlea, where the best frequency is approximately 40 kHz. The acoustic impedance was found as the ratio of driving pressure to velocity response. It is the physical attribute that governs cochlear mechanics and has never before been directly measured, to our knowledge. The basilar membrane velocity was measured through the transparent round window membrane. Simultaneously, the intracochlear pressure was measured close to the stapes and quite close to the cochlear partition. The impedance phase was close to -90 degrees and the magnitude decreased with frequency, consistent with stiffness-dominated impedance. The resistive component of the impedance was relatively small. Usually the resistance was negative at frequencies below 8 kHz; this unexpected finding might be due to other vibration modes within the cochlear partition.

Basilar membrane responses to noise at a basal site of the chinchilla cochlea: quasi-linear filtering

Basilar membrane responses to clicks and to white noise were recorded using laser velocimetry at basal sites of the chinchilla cochlea with characteristic frequencies near 10 kHz. Responses to noise grew at compressive rates and their instantaneous frequencies decreased with increasing stimulus level. First-order Wiener kernels were computed by cross-correlation of the noise stimuli and the responses. For linear systems, first-order Wiener kernels are identical to unit impulse responses. In the case of basilar membrane responses, first-order Wiener kernels and responses to clicks measured at the same sites were similar but not identical. Both consisted of transient oscillations with onset frequencies which increased rapidly, over about 0.5 ms, from 4-5 kHz to the characteristic frequency. Both first-order Wiener kernels and responses to clicks were more highly damped, exhibited slower frequency modulation, and grew at compressive rates with increasing stimulus levels. Responses to clicks had longer durations than the Wiener kernels. The statistical distribution of basilar membrane responses to Gaussian white noise is also Gaussian and the envelopes of the responses are Rayleigh distributed, as they should be for Gaussian noise passing through a linear band-pass filter. Accordingly, basilar membrane responses were accurately predicted by linear filters specified by the first-order Wiener kernels of responses to noise presented at the same level. Overall, the results indicate that cochlear nonlinearity is not instantaneous and resembles automatic gain control.

WITHDRAWN: Membrane-based amplification in hearing

This article has been withdrawn at the request of the author(s) and/or editor. The Publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy.

On- and off-frequency forward masking by Schroeder-phase complexes

Forward masking by harmonic tone complexes was measured for on- and off-frequency maskers as a function of masker phase curvature for two masker durations (30 and 200 ms). For the lowest signal frequency (1 kHz), the results matched predictions based on the expected interactions between the phase curvature and amplitude compression of peripheral auditory filtering. For the higher signal frequencies (2 and 6 kHz), the data increasingly departed from predictions in two respects. First, the effects of the masker phase curvature became stronger with increasing masker duration, inconsistent with the expected effects of the fast-acting compression and time-invariant phase response of basilar membrane filtering. Second, significant effects of masker phase curvature were observed for the off-frequency masker using a 6-kHz signal, inconsistent with predictions based on linear processing of stimuli well below the signal frequency. New predictions were generated assuming an additional effect with a longer time constant, consistent with the influence of medial olivocochlear efferent activation on otoacoustic emissions in humans. Reasonable agreement between the predicted and the measured effects suggests that efferent activation is a potential candidate mechanism to explain certain spectro-temporal masking effects in human hearing.

Detection without deflection? A hypothesis for direct sensing of sound pressure by hair cells

It is widely thought that organisms detect sound by sensing the deflection of hair-like projections, the stereocilia, at the apex of hair cells. In the case of mammals, the standard interpretation is that hair cells in the cochlea respond to deflection of stereocilia induced by motion generated by a hydrodynamic travelling wave. But in the light of persistent anomalies, an alternative hypothesis seems to have some merit: that sensing cells (in particular the outer hair cells) may, at least at low intensities, be reacting to a different stimulus - the rapid pressure wave that sweeps through the cochlear fluids at the speed of sound in water. This would explain why fast responses are sometimes seen before the peak of the travelling wave. Yet how could cells directly sense fluid pressure? Here, a model is constructed of the outer hair cell as a pressure vessel able to sense pressure variations across its cuticular pore, and this 'fontanelle' model, based on the sensing action of the basal body at this compliant spot, could explain the observed anomalies. Moreover, the fontanelle model can be applied to a wide range of other organisms, suggesting that direct pressure detection is a general mode of sensing complementary to stereociliar displacement.

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.

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.

Temporary hearing loss influences post-stimulus time histogram and single neuron action potential estimates from human compound action potentials

An analytic compound action potential (CAP) obtained by convolving functional representations of the post-stimulus time histogram summed across auditory nerve neurons [P(t)] and a single neuron action potential [U(t)] was fit to human CAPs. The analytic CAP fit to pre- and postnoise-induced temporary hearing threshold shift (TTS) estimated in vivo P(t) and U(t) and the number of neurons contributing to the CAPs (N). The width of P(t) decreased with increasing signal level and was wider at the lowest signal level following noise exposure. P(t) latency decreased with increasing signal level and was shorter at all signal levels following noise exposure. The damping and oscillatory frequency of U(t) increased with signal level. For subjects with large amounts of TTS, U(t) had greater damping than before noise exposure particularly at low signal levels. Additionally, U(t) oscillation was lower in frequency at all click intensities following noise exposure. N increased with signal level and was smaller after noise exposure at the lowest signal level. Collectively these findings indicate that neurons contributing to the CAP during TTS are fewer in number, shorter in latency, and poorer in synchrony than before noise exposure. Moreover, estimates of single neuron action potentials may decay more rapidly and have a lower oscillatory frequency during TTS.

The role of organ of Corti mass in passive cochlear tuning

The mechanism for passive cochlear tuning remains unsettled. Early models considered the organ of Corti complex (OCC) as a succession of spring-mass resonators. Later, traveling wave models showed that passive tuning could arise through the interaction of cochlear fluid mass and OCC stiffness without local resonators. However, including enough OCC mass to produce local resonance enhanced the tuning by slowing and thereby growing the traveling wave as it approached its resonant segment. To decide whether the OCC mass plays a role in tuning, the frequency variation of the wavenumber of the cochlear traveling wave was measured (in vivo, passive cochleae) and compared to theoretical predictions. The experimental wavenumber was found by taking the phase difference of basilar membrane motion between two longitudinally spaced locations and dividing by the distance between them. The theoretical wavenumber was a solution of the dispersion relation of a three-dimensional cochlear model with OCC mass and stiffness as the free parameters. The experimental data were only well fit by a model that included OCC mass. However, as the measurement position moved from a best-frequency place of 40 to 12 kHz, the role of mass was diminished. The notion of local resonance seems to only apply in the very high-frequency region of the cochlea.

Intracochlear pressure and derived quantities from a three-dimensional model

Intracochlear pressure is calculated from a physiologically based, three-dimensional gerbil cochlea model. Olson [J. Acoust. Soc. Am. 103, 3445-3463 (1998); 110, 349-367 (2001)] measured gerbil intracochlear pressure and provided approximations for the following derived quantities: (1) basilar membrane velocity, (2) pressure across the organ of Corti, and (3) partition impedance. The objective of this work is to compare the calculations and measurements for the pressure at points and the derived quantities. The model includes the three-dimensional viscous fluid and the pectinate zone of the elastic orthotropic basilar membrane with dimensional and material property variation along its length. The arrangement of outer hair cell forces within the organ of Corti cytoarchitecture is incorporated by adding the feed-forward approximation to the passive model as done previously. The intracochlear pressure consists of both the compressive fast wave and the slow traveling wave. A Wentzel-Kramers-Brillowin asymptotic and numerical method combined with Fourier series expansions is used to provide an efficient procedure that requires about 1 s to compute the response for a given frequency. Results show reasonably good agreement for the direct pressure and the derived quantities. This confirms the importance of the three-dimensional motion of the fluid for an accurate cochlear model.