Mutual suppression in the 6 kHz region of sensitive chinchilla cochleae

Nonlinear reflection as a cause of the short-latency component in stimulus-frequency otoacoustic emissions simulated by the methods of compression and suppression

Stimulus-frequency otoacoustic emissions (SFOAEs) are generated by coherent reflection of forward traveling waves by perturbations along the basilar membrane. The strongest wavelets are backscattered near the place where the traveling wave reaches its maximal amplitude (tonotopic place). Therefore, the SFOAE group delay might be expected to be twice the group delay estimated in the cochlear filters. However, experimental data have yielded steady-state SFOAE components with near-zero latency. A cochlear model is used to show that short-latency SFOAE components can be generated due to nonlinear reflection of the compressor or suppressor tones used in SFOAE measurements. The simulations indicate that suppressors produce more pronounced short-latency components than compressors. The existence of nonlinear reflection components due to suppressors can also explain why SFOAEs can still be detected when suppressors are presented more than half an octave above the probe-tone frequency. Simulations of the SFOAE suppression tuning curves showed that phase changes in the SFOAE residual as the suppressor frequency increases are mostly determined by phase changes of the nonlinear reflection component.

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.

Nonlinearity and amplification in cochlear responses to single and multi-tone stimuli

Mechanical displacements of the basilar membrane (BM) and the electrophysiological responses of the auditory outer hair cells (OHCs) are key components of the frequency tuning and cochlear amplification in the mammalian cochlea. In the work presented here, we measured the responses of (1) the extracellular voltage generated by OHCs (V_OHC) and (2) displacements within the organ of Corti complex (OCC) to a multi-tone stimulus, and to single tones. Using optical coherence tomography (OCT), we were able to measure displacements of different layers in the OCC simultaneously, in the base of the gerbil cochlea. We explored the effect of the two types of sound stimuli to the nonlinear behavior of voltage and displacement in two frequency regions: a frequency region below the BM nonlinearity (sub-BF region: f < ∼0.7 BF), and in the best frequency (BF) region. In the sub-BF region, BM motion (X_BM) had linear growth for both stimulus types, and the motion in the OHC region (X_OHC) was mildly nonlinear for single tones, and relatively strongly nonlinear for multi-tones. Sub-BF, the nonlinear character of V_OHC was similar to that of X_OHC. In the BF region X_BM, V_OHC and X_OHC all possessed the now-classic nonlinearity of the BF peak. Coupling these observations with previous findings on phasing between OHC force and traveling wave motions, we propose the following framework for cochlear nonlinearity: The BF-region nonlinearity is an amplifying nonlinearity, in which OHC forces input power into the traveling wave, allowing it to travel further apical to the region where it peaks. The sub-BF nonlinearity is a non-amplifying nonlinearity; it represents OHC electromotility, and saturates due to OHC current saturation, but the OHC forces do not possess the proper phasing to feed power into the traveling wave.

Probing hair cell's mechano-transduction using two-tone suppression measurements

When two sound tones are delivered to the cochlea simultaneously, they interact with each other in a suppressive way, a phenomenon referred to as two-tone suppression (2TS). This nonlinear response is ascribed to the saturation of the outer hair cell’s mechano-transduction. Thus, 2TS can be used as a non-invasive probe to investigate the fundamental properties of cochlear mechano-transduction. We developed a nonlinear cochlear model in the time domain to interpret 2TS data. The multi-scale model incorporates cochlear fluid dynamics, organ of Corti (OoC) mechanics and outer hair cell electrophysiology. The model simulations of 2TS show that the threshold amplitudes and rates of low-side suppression are dependent on mechano-transduction properties. By comparing model responses to existing 2TS measurement data, we estimate intrinsic characteristics of mechano-transduction such as sensitivity and adaptation. For mechano-transduction sensitivity at the basal location (characteristic frequency of 17 kHz) at 0.06 nm⁻¹, the simulation results agree with 2TS measurements of basilar membrane responses. This estimate is an order of magnitude higher than the values observed in experiments on isolated outer hair cells. The model also demonstrates how the outer hair cell’s adaptation alters the temporal pattern of 2TS by modulating mechano-electrical gain and phase.

Amplification and Suppression of Traveling Waves along the Mouse Organ of Corti: Evidence for Spatial Variation in the Longitudinal Coupling of Outer Hair Cell-Generated Forces

Mammalian hearing sensitivity and frequency selectivity depend on a mechanical amplification process mediated by outer hair cells (OHCs). OHCs are situated within the organ of Corti atop the basilar membrane (BM), which supports sound-evoked traveling waves. It is well established that OHCs generate force to selectively amplify BM traveling waves where they peak, and that amplification accumulates from one location to the next over this narrow cochlear region. However, recent measurements demonstrate that traveling waves along the apical surface of the organ of Corti, the reticular lamina (RL), are amplified over a much broader region. Whether OHC forces accumulate along the length of the RL traveling wave to provide a form of "global" cochlear amplification is unclear. Here we examined the spatial accumulation of RL amplification. In mice of either sex, we used tones to suppress amplification from different cochlear regions and examined the effect on RL vibrations near and far from the traveling-wave peak. We found that although OHC forces amplify the entire RL traveling wave, amplification only accumulates near the peak, over the same region where BM motion is amplified. This contradicts the notion that RL motion is involved in a global amplification mechanism and reveals that the mechanical properties of the BM and organ of Corti tune how OHC forces accumulate spatially. Restricting the spatial buildup of amplification enhances frequency selectivity by sharpening the peaks of cochlear traveling waves and constrains the number of OHCs responsible for mechanical sensitivity at each location.SIGNIFICANCE STATEMENT Outer hair cells generate force to amplify traveling waves within the mammalian cochlea. This force generation is critical to the ability to detect and discriminate sounds. Nevertheless, how these forces couple to the motions of the surrounding structures and integrate along the cochlear length remains poorly understood. Here we demonstrate that outer hair cell-generated forces amplify traveling-wave motion on the organ of Corti throughout the wave's extent, but that these forces only accumulate longitudinally over a region near the wave's peak. The longitudinal coupling of outer hair cell-generated forces is therefore spatially tuned, likely by the mechanical properties of the basilar membrane and organ of Corti. Our findings provide new insight into the mechanical processes that underlie sensitive hearing.

Spectral Ripples in Round-Window Cochlear Microphonics: Evidence for Multiple Generation Mechanisms

The cochlear microphonic (CM) results from the vector sum of outer hair cell transduction currents excited by a stimulus. The classical theory of CM generation-that the response measured at the round window is dominated by cellular sources located within the tail region of the basilar membrane (BM) excitation pattern-predicts that CM amplitude and phase vary little with stimulus frequency. Contrary to expectations, CM amplitude and phase-gradient delay measured in response to low-level tones in chinchillas demonstrate a striking, quasiperiodic pattern of spectral ripples, even at frequencies > 5 kHz, where interference with neurophonic potentials is unlikely. The spectral ripples were reduced in the presence of a moderate-level saturating tone at a nearby frequency. When converted to the time domain, only the delayed CM energy was diminished in the presence of the saturator. We hypothesize that the ripples represent an interference pattern produced by CM components with different phase gradients: an early-latency component originating within the tail region of the BM excitation and two delayed components that depend on active cochlear processing near the peak region of the traveling wave. Using time windowing, we show that the early, middle, and late components have delays corresponding to estimated middle-ear transmission, cochlear forward delays, and cochlear round-trip delays, respectively. By extending the classical model of CM generation to include mechanical and electrical irregularities, we propose that middle components are generated through a mechanism of "coherent summation" analogous to the production of reflection-source otoacoustic emissions (OAEs), while the late components arise through a process of internal cochlear reflection related to the generation of stimulus-frequency OAEs. Although early-latency components from the passive tail region typically dominate the round-window CM, at low stimulus levels, substantial contributions from components shaped by active cochlear processing provide a new avenue for improving CM measurements as assays of cochlear health.

Non-tip auditory-nerve responses that are suppressed by low-frequency bias tones originate from reticular lamina motion

Recent cochlear mechanical measurements show that active processes increase the motion response of the reticular lamina (RL) at frequencies more than an octave below the local characteristic frequency (CF) for CFs above 5 kHz. A possible correlate is that in high-CF (>5 kHz) auditory-nerve (AN) fibers, responses to frequencies 1-3 octaves below CF ("tail" frequencies) can be inhibited by medial olivocochlear (MOC) efferents. These results indicate that active processes enhance the sensitivity of tail-frequency RL and AN responses. Perhaps related is that some apical low-CF AN fibers have tuning-curve (TC) "side-lobe" response areas at frequencies above and below the TC-tip that are MOC inhibited. We hypothesized that the tail and side-lobe responses are enhanced by the same active mechanisms as CF cochlear amplification. If responses to CF, tail-frequency, and TC-side-lobe tones are all enhanced by prestin motility controlled by outer-hair-cell (OHC) transmembrane voltage, then they should depend on OHC stereocilia position in the same way. To test this, we cyclically changed the OHC-stereocilia mechano-electric-transduction (MET) operating point with low-frequency "bias" tones (BTs) and increased the BT level until the BT caused quasi-static OHC MET saturation that reduced or "suppressed" the gain of OHC active processes. While measuring cat AN-fiber responses, 50 Hz BT level series, 70-120 dB SPL, were run alone and with CF tones, or 2.5 kHz tail-frequency tones, or side-lobe tones. BT-tone-alone responses were used to exclude BT sound levels that produced AN responses that might obscure BT suppression. Data were analyzed to show the BT phase that suppressed the tone responses at the lowest sound level. We found that AN responses to CF, tail-frequency, and side-lobe tones were suppressed at the same BT phase in almost all cases. The data are consistent with the enhancement of responses to CF, tail-frequency, and side-lobe tones all being due to the same OHC-stereocilia MET-dependent active process. Thus, OHC active processes enhance AN responses at frequencies outside of the cochlear-amplified TC-tip region in both high- and low-frequency cochlear regions. The data are consistent with the AN response enhancements being due to enhanced RL motion that drives IHC-stereocilia deflection by traditional RL-TM shear and/or by changing the RL-TM gap. Since tail-frequency basilar membrane (BM) motion is not actively enhanced, the tail-frequency IHC drive is from a vibrational mode little present on the BM, not a "second filter" of BM motion.

Two-Tone Suppression of Simultaneous Electrical and Mechanical Responses in the Cochlea

Cochlear frequency tuning is based on a mildly tuned traveling-wave response that is enhanced in amplitude and sharpness by outer hair cell (OHC)-based forces. The nonlinear and active character of this enhancement is the fundamental manifestation of cochlear amplification. Recently, mechanical (pressure) and electrical (extracellular OHC-generated voltage) responses were simultaneously measured close to the sensory tissue's basilar membrane. Both pressure and voltage were tuned and showed traveling-wave phase accumulation, evidence that they were locally generated responses. Approximately at the frequency where nonlinearity commenced, the phase of extracellular voltage shifted up, to lead pressure by >1/4 cycle. Based on established and fundamental relationships among voltage, force, pressure, displacement, and power, the observed phase shift was identified as the activation of cochlear amplification. In this study, the operation of the cochlear amplifier was further explored, via changes in pressure and voltage responses upon delivery of a second, suppressor tone. Two different suppression paradigms were used, one with a low-frequency suppressor and a swept-frequency probe, the other with two swept-frequency tones, either of which can be considered as probe or suppressor. In the presence of a high-level low-frequency suppressor, extracellular voltage responses at probe-tone frequencies were greatly reduced, and the pressure responses were reduced nearly to their linear, passive level. On the other hand, the amplifier-activating phase shift between pressure and voltage responses was still present in probe-tone responses. These findings are consistent with low-frequency suppression being caused by the saturation of OHC electrical responses and not by a change in the power-enabling phasing of the underlying mechanics. In the two-tone swept-frequency suppression paradigm, mild suppression was apparent in the pressure responses, while deep notches could develop in the voltage responses. A simple analysis, based on a two-wave differencing scheme, was used to explore the observations.

Low-frequency bias tone suppression of auditory-nerve responses to low-level clicks and tones

We used low-frequency "bias" tones (BT's) to explore whether click and tone responses are affected in the same way by cochlear active processes. In nonlinear systems the responses to clicks are not always simply related to the responses to tones. Cochlear amplifier gain depends on the incremental slope of the outer-hair-cell (OHC) stereocilia mechano-electric transduction (MET) function. BTs transiently change the operating-point of OHC MET channels and can suppress cochlear-amplifier gain by pushing OHC METs into low-slope saturation regions. BT effects on single auditory-nerve (AN) fibers have been studied on tone responses but not on click responses. We recorded from AN fibers in anesthetized cats and compared tone and click responses using 50 Hz BTs at 70-120 dB SPL to manipulate OHC stereocilia position. BTs can also excite and thereby obscure the BT suppression. We measured AN-fiber response synchrony to BTs alone so that we could exclude suppression measurements when the BT synchrony might obscure the suppression. BT suppression of low-level tone and click responses followed the traditional pattern of twice-a-BT-cycle suppression with more suppression at one phase than the other. The major suppression phases of most fibers were tightly grouped with little difference between click and tone suppressions, which is consistent with low-level click and tone responses being amplified in the same way. The data are also consistent with the operating point of the OHC MET function varying smoothly from symmetric in the base to offset in the apex, and, in contrast, with the IHC MET function being offset throughout the cochlea. As previously reported, bias-tones presented alone excited AN fibers at one or more phases, a phenomena termed "peak splitting" with most BT excitation phases ∼¼ cycle before or after the major suppression phase. We explain peak splitting as being due to distortion in multiple fluid drives to inner-hair-cell stereocilia.

Tuning of SFOAEs Evoked by Low-Frequency Tones Is Not Compatible with Localized Emission Generation

Stimulus-frequency otoacoustic emissions (SFOAEs) appear to be well suited for assessing frequency selectivity because, at least on theoretical grounds, they originate over a restricted region of the cochlea near the characteristic place of the evoking tone. In support of this view, we previously found good agreement between SFOAE suppression tuning curves (SF-STCs) and a control measure of frequency selectivity (compound action potential suppression tuning curves (CAP-STC)) for frequencies above 3 kHz in chinchillas. For lower frequencies, however, SF-STCs and were over five times broader than the CAP-STCs and demonstrated more high-pass rather than narrow band-pass filter characteristics. Here, we test the hypothesis that the broad tuning of low-frequency SF-STCs is because emissions originate over a broad region of the cochlea extending basal to the characteristic place of the evoking tone. We removed contributions of the hypothesized basally located SFOAE sources by either pre-suppressing them with a high-frequency interference tone (IT; 4.2, 6.2, or 9.2 kHz at 75 dB sound pressure level (SPL)) or by inducing acoustic trauma at high frequencies (exposures to 8, 5, and lastly 3-kHz tones at 110-115 dB SPL). The 1-kHz SF-STCs and CAP-STCs were measured for baseline, IT present and following the acoustic trauma conditions in anesthetized chinchillas. The IT and acoustic trauma affected SF-STCs in an almost indistinguishable way. The SF-STCs changed progressively from a broad high-pass to narrow band-pass shape as the frequency of the IT was lowered and for subsequent exposures to lower-frequency tones. Both results were in agreement with the "basal sources" hypothesis. In contrast, CAP-STCs were not changed by either manipulation, indicating that neither the IT nor acoustic trauma affected the 1-kHz characteristic place. Thus, unlike CAPs, SFOAEs cannot be considered as a place-specific measure of cochlear function at low frequencies, at least in chinchillas.

Effect of the attachment of the tectorial membrane on cochlear micromechanics and two-tone suppression

The mechanical stimulation of the outer hair cell hair bundle (HB) is a key step in nonlinear cochlear amplification. We show how two-tone suppression (TTS), a hallmark of cochlear nonlinearity, can be used as an indirect measure of HB stimulation. Using two different nonlinear computational models of the cochlea, we investigate the effect of altering the mechanical load applied by the tectorial membrane (TM) on the outer hair cell HB. In the first model (TM-A model), the TM is attached to the spiral limbus (as in wild-type animals); in the second model (TM-D model), the TM is detached from the spiral limbus (mimicking the cochlea of Otoa(EGFP/EGFP) mutant mice). As in recent experiments, model simulations demonstrate that the absence of the TM attachment does not preclude cochlear amplification. However, detaching the TM alters the mechanical load applied by the TM on the HB at low frequencies and therefore affects TTS by low-frequency suppressors. For low-frequency suppressors, the suppression threshold obtained with the TM-A model corresponds to a constant suppressor displacement on the basilar membrane (as in experiments with wild-type animals), whereas it corresponds to a constant suppressor velocity with the TM-D model. The predictions with the TM-D model could be tested by measuring TTS on the basilar membrane of the Otoa(EGFP/EGFP) mice to improve our understanding of the fundamental workings of the cochlea.

Estimating cochlear frequency selectivity with stimulus-frequency otoacoustic emissions in chinchillas

It has been suggested that the tuning of the cochlear filters can be derived from measures of otoacoustic emissions (OAEs). Two approaches have been proposed to estimate cochlear frequency selectivity using OAEs evoked with a single tone (stimulus-frequency (SF)) OAEs: based on SFOAE group delays (SF-GDs) and on SFOAE suppression tuning curves (SF-STCs). The aim of this study was to evaluate whether either SF-GDs or SF-STCs obtained with low probe levels (30 dB SPL) correlate with more direct measures of cochlear tuning (compound action potential suppression tuning curves (CAP-STCs)) in chinchillas. The SFOAE-based estimates of tuning covaried with CAP-STCs tuning for >3 kHz probe frequencies, indicating that these measures are related to cochlear frequency selectivity. However, the relationship may be too weak to predict tuning with either SFOAE method in an individual. The SF-GD prediction of tuning was sharper than CAP-STC tuning. On the other hand, SF-STCs were consistently broader than CAP-STCs implying that SFOAEs may have less restricted region of generation in the cochlea than CAPs. Inclusion of <3 kHz data in a statistical model resulted in no significant or borderline significant covariation among the three methods: neither SFOAE test appears to reliably estimate an individual's CAP-STC tuning at low-frequencies. At the group level, SF-GDs and CAP-STCs showed similar tuning at low frequencies, while SF-STCs were over five times broader than the CAP-STCs indicating that low-frequency SFOAE may originate over a very broad region of the cochlea extending ≥5 mm basal to the tonotopic place of the probe.

Stimulus-frequency otoacoustic emission suppression tuning in humans: comparison to behavioral tuning

As shown by the work of Kemp and Chum in 1980, stimulus-frequency otoacoustic emission suppression tuning curves (SFOAE STCs) have potential to objectively estimate behaviorally measured tuning curves. To date, this potential has not been tested. This study aims to do so by comparing SFOAE STCs and behavioral measures of tuning (simultaneous masking psychophysical tuning curves, PTCs) in 10 normal-hearing listeners for frequency ranges centered around 1,000 and 4,000 Hz at low probe levels. Additionally, SFOAE STCs were collected for varying conditions (probe level and suppression criterion) to identify the optimal parameters for comparison with behavioral data and to evaluate how these conditions affect the features of SFOAE STCs. SFOAE STCs qualitatively resembled PTCs: they demonstrated band-pass characteristics and asymmetric shapes with steeper high-frequency sides than low, but unlike PTCs they were consistently tuned to frequencies just above the probe frequency. When averaged across subjects the shapes of SFOAE STCs and PTCs showed agreement for most recording conditions, suggesting that PTCs are predominantly shaped by the frequency-selective filtering and suppressive effects of the cochlea. Individual SFOAE STCs often demonstrated irregular shapes (e.g., "double-tips"), particularly for the 1,000-Hz probe, which were not observed for the same subject's PTC. These results show the limited utility of SFOAE STCs to assess tuning in an individual. The irregularly shaped SFOAE STCs may be attributed to contributions from SFOAE sources distributed over a region of the basilar membrane extending beyond the probe characteristic place, as suggested by a repeatable pattern of SFOAE residual phase shifts observed in individual data.

The spatial buildup of compression and suppression in the mammalian cochlea

We recorded responses of the gerbil basilar membrane (BM) to wideband tone complexes. The intensity of one component was varied and the effects on the amplitude and phase of the others were assessed. This suppression paradigm enabled us to vary probe frequency and suppressor frequency independently, allowing the use of simple scaling arguments to analyze the spatial buildup of the nonlinear interaction between traveling waves. Most suppressors had the same effects on probe amplitude and phase as did wideband intensity increments. The main exception were suppressors above the characteristic frequency (CF) of the recording location, for which the frequency range of most affected probes was not constant, but shifted upward with suppressor frequency. BM displacement reliably predicted the effectiveness of low-side suppressors, but not high-side suppressors. We found “anti-suppression” of probes well below CF, i.e., suppressor-induced enhancement of probe response amplitude. Large (>1 cycle) phase effects occurred for above-CF probes. Phase shifts varied nonmonotonically, but systematically, with suppressor level, probe frequency, and suppressor frequency, reconciling apparent discrepancies in the literature. The analysis of spatial buildup revealed an accumulation of local effects on the propagation of the traveling wave, with larger BM displacement reducing the local forward gain. The propagation speed of the wave was also affected. With larger BM displacement, the basal portion of the wave slowed down, while the apical part sped up. This framework of spatial buildup of local effects unifies the widely different effects of overall intensity, low-side suppressors, and high-side suppressors on BM responses.

Masking of sounds by a background noise--cochlear mechanical correlates

In the search for cochlear correlates of auditory masking by noise stimuli, we recorded basilar membrane (BM) vibrations evoked by either tone or click signals in the presence of varying levels of background noise. The BM vibrations were recorded from basal regions in healthy cochleae of anaesthetized chinchilla and gerbil. Non-linear interactions that could underpin various aspects of psychophysical masking data, including both compression and suppression at the BM level, were observed. The suppression effects, whereby the amplitude of the responses to each stimulus component could be reduced, depended on the relative intensities of the noise and the tones or clicks. Only stimulus components whose frequencies fell inside the non-linear region of the recording site, i.e. around its characteristic frequency (CF), were affected by presentation of the 'suppressing' stimulus (which could be either the tone or the noise). Mutual suppression, the simultaneous reduction of the responses to both tones and noise components, was observed under some conditions, but overall reductions of BM vibration were rarely observed. Moderate- to high-intensity tones suppressed BM responses to low-intensity Gaussian stimuli, including both broadband and narrowband noise. Suppression effects were larger for spectral components of the noise response that were closer to the CF. In this regime, the tone and noise stimuli became the suppressor and probe signals, respectively. This study provides the first detailed observations of cochlear mechanical correlates of the masking effects of noise. Mechanical detection thresholds for tone signals, which were arbitrarily defined using three criteria, are shown to increase in almost direct proportion to the noise level for low and moderately high noise levels, in a manner that resembles the findings of numerous psychophysical observations.

Comparison of nonlinear mammalian cochlear-partition models

Various simple mathematical models of the dynamics of the organ of Corti in the mammalian cochlea are analyzed and their dynamics compared. The specific models considered are phenomenological Hopf and cusp normal forms, a recently proposed description combining active hair-bundle motility and somatic motility, a reduction thereof, and finally a model highlighting the importance of the coupling between the nonlinear transduction current and somatic motility. It is found that for certain models precise tuning to any bifurcation is not necessary and that a compressively nonlinear response over a range similar to experimental observations and that the normal form of the Hopf bifurcation is not the only description that reproduces compression and tuning similar to experiment.

Basilar membrane responses to tones and tone complexes: nonlinear effects of stimulus intensity

The mammalian inner ear combines spectral analysis of sound with multiband dynamic compression. Cochlear mechanics has mainly been studied using single-tone and tone-pair stimulation. Most natural sounds, however, have wideband spectra. Because the cochlea is strongly nonlinear, wideband responses cannot be predicted by simply adding single-tone responses. We measured responses of the gerbil basilar membrane to single-tone and wideband stimuli and compared them, while focusing on nonlinear aspects of the response. In agreement with previous work, we found that frequency selectivity and its dependence on stimulus intensity were very similar between single-tone and wideband responses. The main difference was a constant shift in effective sound intensity, which was well predicted by a simple gain control scheme. We found expansive nonlinearities in low-frequency responses, which, with increasing frequency, gradually turned into the more familiar compressive nonlinearities. The overall power of distortion products was at least 13 dB below the overall power of the linear response, but in a limited band above the characteristic frequency, the power of distortion products often exceeded the linear response. Our results explain the partial success of a "quasilinear" description of wideband basilar membrane responses, but also indicate its limitations.

Perception of across-frequency asynchrony and the role of cochlear delays

Cochlear filtering results in earlier responses to high than to low frequencies. This study examined potential perceptual correlates of cochlear delays by measuring the perception of relative timing between tones of different frequencies. A brief 250-Hz tone was combined with a brief 1-, 2-, 4-, or 6-kHz tone. Two experiments were performed, one involving subjective judgments of perceived synchrony, the other involving asynchrony detection and discrimination. The functions relating the proportion of "synchronous" responses to the delay between the tones were similar for all tone pairs. Perceived synchrony was maximal when the tones in a pair were gated synchronously. The perceived-synchrony function slopes were asymmetric, being steeper on the low-frequency-leading side. In the second experiment, asynchrony-detection thresholds were lower for low-frequency rather than for high-frequency leading pairs. In contrast with previous studies, but consistent with the first experiment, thresholds did not depend on frequency separation between the tones, perhaps because of the elimination of within-channel cues. The results of the two experiments were related quantitatively using a decision-theoretic model, and were found to be highly correlated. Overall the results suggest that frequency-dependent cochlear group delays are compensated for at higher processing stages, resulting in veridical perception of timing relationships across frequency.

Nonlinear models of development, amplification and compression in the mammalian cochlea

This paper reviews current understanding and presents new results on some of the nonlinear processes that underlie the function of the mammalian cochlea. These processes occur within mechano-sensory hair cells that form part of the organ of Corti. After a general overview of cochlear physiology, mathematical modelling results are presented in three parts. First, the dynamic interplay between ion channels within the sensory inner hair cells is used to explain some new electrophysiological recordings from early development. Next, the state of the art is reviewed in modelling the electro-motility present within the outer hair cells (OHCs), including the current debate concerning the role of cell body motility versus active hair bundle dynamics. A simplified model is introduced that combines both effects in order to explain observed amplification and compression in experiments. Finally, new modelling evidence is presented that structural longitudinal coupling between OHCs may be necessary in order to capture all features of the observed mechanical responses.

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.

Threshold tuning curves of chinchilla auditory-nerve fibers. I. Dependence on characteristic frequency and relation to the magnitudes of cochlear vibrations

Frequency-threshold tuning curves were recorded in thousands of auditory-nerve fibers (ANFs) in chinchilla. Synthetic tuning curves with 21 characteristic frequencies (187 Hz to 19.04 kHz, spaced every 1/3 octave) were constructed by averaging individual tuning curves within 2/3-octave frequency bands. Tuning curves undergo a gradual transition in symmetry at characteristic frequencies (CFs) of 1 kHz and an abrupt change in shape at CFs of 3-4 kHz. For CFs < or = 3 kHz, the lower limbs of tuning curves have similar slopes, about -18 dB/octave, but the upper limbs have slopes that become increasingly steep with increasing frequency and CF. For CFs >4 kHz, tuning curves normalized to the CF are nearly identical and consist of three segments. A tip segment, within 30-40 dB of CF threshold, has lower- and upper-limb slopes of -60 and +120 dB/octave, respectively, and is flanked by a low-frequency ("tail") segment, with shallow slope, and a terminal high-frequency segment with very steep slope (several hundreds of dB/octave). The tuning curves of fibers innervating basal cochlear sites closely resemble basilar-membrane tuning curves computed with low isovelocity criteria. At the apex of the chinchilla cochlea, frequency tuning is substantially sharper for ANFs than for available recordings of organ of Corti vibrations.

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.

Comment on "Mutual suppression in the 6 kHz region of sensitive chinchilla cochleae" [J. Acoust. Soc. Am. 121, 2805-2818 (2007)]

Rhode [J. Acoust. Soc. Am. 121, 2805-2818 (2007)] acknowledges that two-tone neural rate responses for low-side suppression differ from those measured in basilar membrane mechanics, making one question whether this aspect of suppression has a mechanical correlate. It is suggested here that signal coding between mechanical and neural processing stages may be responsible for the fact that the total rate response (but not the basilar membrane response) for low-frequency suppressors is smaller than that for the probe-alone condition. For example, the velocity dependence of inner hair cell (IHC) transduction, membrane/synaptic filtering and the sensitivity difference between ac and dc components of the IHC receptor potential all serve to reduce excitability for low-side suppressors at the single-unit level. Hence, basilar membrane mechanics may well be the source of low-side suppression measured in the auditory nerve.

Distortion product otoacoustic emissions and basilar membrane vibration in the 6-9 kHz region of sensitive chinchilla cochleae

Distortion product otoacoustic emissions (DPOAEs) and basilar membrane (BM) vibration were measured simultaneously in the 6-9 kHz region of chinchilla cochleae. BM-Input-Output functions in a two-tone paradigm behaved similarly to DPOAEs for the 2f1-f2 component, nonmonotonic growth with the intensity of the lower frequency primary and a notch in the functions around 60 dB SPL. Ripples in frequency functions occur in both BM and OAE curves as a function of the distortion frequency. Optimum f2/f1 ratios for DPOAE generation are near 1.2. The slope of phase curves indicates that for low f2f1(<1.1) the emission source is the place location while for f2f1>1.1 the relative constancy of the phase function suggests that the place is the nonlinear region of f2, i.e., the wave location. Magnitudes of the DPOAEs increase rapidly above 60 dB SPL suggesting a different source or mechanism at high levels. This is supported by the observation that the high level DPOAE and BM-DP responses remain for a considerable period postmortem.

Low-frequency modulation of distortion product otoacoustic emissions in humans

Low-frequency modulation of distortion product otoacoustic emissions (DPOAEs) was measured from the human ears. In the frequency domain, increasing the bias tone level resulted in a suppression of the cubic difference tone (CDT) and an increase in the magnitudes of the modulation sidebands. Higher-frequency bias tones were more efficient in producing the suppression and modulation. Quasi-static modulation patterns were derived from measuring the CDT amplitude at the peaks and troughs of bias tones with various amplitudes. The asymmetric bell-shaped pattern resembled the absolute value of the third derivative of a nonlinear cochlear transducer function. Temporal modulation patterns were obtained from inverse FFT of the spectral contents around the DPOAE. The period modulation pattern, averaged over multiple bias tone cycles, showed two CDT peaks each correlated with the zero-crossings of the bias tone. The typical period modulation pattern varied and the two CDT peaks emerged with the reduction in bias tone level. The present study replicated the previous experimental results in gerbils. This noninvasive technique is capable of revealing the static position and dynamic motion of the cochlear partition. Moreover, the results of the present study suggest that this technique could potentially be applied in the differential diagnosis of cochlear pathologies.