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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.

Optical coherence tomography (OCT) has become a powerful tool for measuring vibrations within the organ of Corti complex (OCC) in cochlear mechanics experiments. However, the one-dimensional nature of OCT measurements, combined with experimental and anatomical constraints, make these data ambiguous: Both the relative positions of measured structures and their orientation relative to the direction of measured vibrations are not known a priori. We present a method by which these measurement features can be determined via the use of a volumetric OCT scan to determine the relationship between the imaging/measurement axes and the canonical anatomical axes. We provide evidence that the method is functional by replicating previously measured radial vibration patterns of the basilar membrane (BM). We used the method to compare outer hair cell and BM vibration phase in the same anatomical cross section (but different optical cross sections), and found that outer hair cell region vibrations lead those of the BM across the entire measured frequency range. In contrast, a phase lead is only present at low frequencies in measurements taken within a single optical cross section. Relative phase is critical to the workings of the cochlea, and these results emphasize the importance of anatomically oriented measurement and analysis.

This paper discusses the role of two-dimensional (2-D)/three-dimensional (3-D) cochlear fluid hydrodynamics in the generation of the large nonlinear dynamical range of the basilar membrane (BM) and pressure response, in the decoupling between cochlear gain and tuning, and in the dynamic stabilization of the high-gain BM response in the peak region. The large and closely correlated dependence on stimulus level of the BM velocity and fluid pressure gain [Dong, W., and Olson, E. S. (2013). Biophys. J. 105(4), 1067-1078] is consistent with a physiologically oriented schematization of the outer hair cell (OHC) mechanism if two hydrodynamic effects are accounted for: amplification of the differential pressure associated with a focusing phenomenon, and viscous damping at the BM-fluid interface. The predictions of the analytical 2-D Wentzel-Kramers-Brillouin (WKB) approach are compared to solutions of a 3-D finite element model, showing that these hydrodynamic phenomena yield stable high-gain response in the peak region and a smooth transition among models with different effectiveness of the active mechanism, mimicking the cochlear nonlinear response over a wide stimulus level range. This study explains how an effectively anti-damping nonlinear outer hair cells (OHC) force may yield large BM and pressure dynamical ranges along with an almost level-independent admittance.

The basilar membrane in the cochlea can be modeled as an array of fluid coupled segments driven by stapes vibration and by the undamping nonlinear force simulating cochlear amplification. If stimulated with two tones, the model generates additional tones due to nonlinear distortion. These distortion products (DPs) can be transmitted into the ear canal and produce distortion-product otoacoustic emissions (DPOAEs) known to be generated in the healthy ear of various vertebrates. This study presents a solution for DPs in a two-dimensional nonlinear cochlear model with cochlear roughness—small irregularities in the impedance along the basilar membrane, which may produce additional DPs due to coherent reflection. The solution allows for decomposition of various sources of DPs in the model. In addition to the already described nonlinear-distortion and coherent-reflection mechanisms of DP generation, this study identifies a long-latency DPOAE component due to perturbation of nonlinear force. DP wavelets that are coherently reflected due to impedance irregularities travel toward the stapes across the primary generation region of DPs and there evoke perturbation of the nonlinear undamping force. The ensuing DP wavelets have opposite phase to the wavelets arising from coherent reflection, which results in partial cancellation of the coherent-reflection DP wavelets.

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.

Acoustic energy can be transmitted into the cochlea by two modes: one mode is the forward stimulation where acoustic waves are normally transmitted from the tympanic membrane (TM) to the cochlea via the ossicular chain, another mode is the reverse stimulation where a transducer is coupled to the round window (RW) and it provides a direct mechanical stimulation to the cochlea via the RW membrane. Due to the difference of the energy transmission pathway, the acoustic waves encounter different impedances and the basilar membrane (BM) vibrates with different forms during the acoustic transmission processes. To understand the dynamic characteristics of human cochlea during forward and reverse stimulations, a finite element model of human ear is developed in this study. And the cochlear input impedance, the cochlear reverse impedance, and the BM displacement responses are derived. The results show that the cochlea input impedance keeps stable in a certain frequency range, while the RW impedance and middle ear impedance vary obviously with frequency. And the middle ear impedance is higher than the cochlear input impedance at lower frequencies. Furthermore, the BM motions in response to two stimulations not only have the phase difference, but also have the efficiency difference. The vibration efficiency of the BM in response to forward stimulation is about 13 dB higher than that to reverse stimulation. But under the impulsive stimulus, the maximum displacement of the BM occurs in the middle cochlea for both of stimulations.

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.

Environmental infrasound is usually accompanied by low-frequency (LF) sounds. Considering that inner hair cell transduction equals half-wave rectification, activity of low-frequency auditory nerve fibres may be indistinguishable whether elicited by LF sound that is amplitude-modulated at an infrasonic rate, or LF sound that is superimposed onto infrasound that "biases" the basilar membrane position. We tested whether listeners are able to distinguish a 63-Hz carrier tone, amplitude modulated at 8 Hz, from a 63-Hz pure tone that was perceptually loudness-modulated by an 8-Hz biasing tone. Using a maximum-likelihood procedure, 12 participants first adjusted the intensity of the 8-Hz tone so that the perceived modulation of the pure tone matched a reference amplitude-modulated tone. Both stimuli types were then presented in random order, and participants had to identify presentations which contained the infrasound tone. About half the participants performed close to chance. The best had 81% correct. Experiments with a 125-Hz carrier tone gave similar results. Although performance may improve in a 2-interval discrimination task, this would not be representative of real listening conditions. Results suggest that slowly amplitude-modulated LF sounds may underlie complaints about environmental infrasound, where measured infrasound levels are well below sensation threshold.

This study tests the hypothesis that amplitude modulation (AM) detection will be better under conditions where basilar membrane (BM) response growth is expected to be linear rather than compressive. This hypothesis was tested by (1) comparing AM detection for a tonal carrier as a function of carrier level for subjects with and without cochlear hearing impairment (HI), and by (2) comparing AM detection for carriers presented with and without an ipsilateral notched-noise precursor, under the assumption that the precursor linearizes BM responses. Average AM detection thresholds were approximately 5 dB better for subjects with HI than for subjects with normal hearing (NH) at moderate-level carriers. Average AM detection for low-to-moderate level carriers was approximately 2 dB better with the precursor than without the precursor for subjects with NH, whereas precursor effects were absent or smaller for subjects with HI. Although effect sizes were small and individual differences were noted, group differences are consistent with better AM detection for conditions where BM responses are less compressive due to cochlear hearing loss or due to a reduction in cochlear gain. These findings suggest the auditory system may quickly adjust to the local soundscape to increase effective AM depth and improve signal-to-noise ratios.

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.

The origin of ripples in distortion product otoacoustic emission (DPOAE) amplitude which appear at specific DPOAE frequencies during f1 tone sweeps using fixed high frequency f2 (>20 kHz) in guinea pigs is investigated. The peaks of the ripples, or local DPOAE amplitude maxima, are separated by approximately half octave intervals and are accompanied by phase oscillations. The local maxima appear at the same frequencies in DPOAEs of different order and velocity responses of the stapes and do not shift with increasing levels of the primaries. A suppressor tone had little effect on the frequencies of the maxima, but partially suppressed DPOAE amplitude when it was placed close to the f2 frequencies. These findings agree with earlier observations that the maxima occur at the same DPOAE frequencies, which are independent of the f2 and the primary ratio, and thus are likely to be associated with DPOAE propagation mechanisms. Furthermore, the separation of the local maxima by approximately half an octave may suggest that the maxima are due to interference of the travelling waves along the basilar membrane at the frequency of the DPOAE. It is suggested that the rippling pattern appears because of interaction between DPOAE reverse travelling waves with standing waves formed in the cochlea.

Hearing relies on a series of coupled electrical, acoustical, and mechanical interactions inside the cochlea that enable sound processing. The local structural and electrical properties of the organ of Corti (OoC) and basilar membrane give rise to the global, coupled behavior of the cochlea. However, it is difficult to determine the root causes of important behavior, such as the mediator of active processes, in the fully coupled in vivo setting. An alternative experimental approach is to use an excised segment of the cochlea under controlled electrical and mechanical conditions. Using the excised cochlear segment experiment conducted by Chan and Hudspeth [Nat. Neurosci. 8, 149–155 (2005); Biophys. J. 89, 4382–4395 (2005)] as the model problem, a quasilinear computational model for studying the active in vitro response of the OoC to acoustical stimulation was developed. The model of the electrical, mechanical, and acoustical conditions of the experimental configuration is able to replicate some of the experiment results, such as the shape of the frequency response of the sensory epithelium and the variation of the resonance frequency with the added fluid mass. As in the experiment, the model predicts a phase accumulation along the segment. However, it was found that the contribution of this phase accumulation to the dynamics is insignificant. Taking advantage of the relative simplicity of the fluid loading, the three-dimensional fluid dynamics was reduced into an added mass loading on the OoC thereby reducing the overall complexity of the model.

Noise induced hearing loss (NIHL) remains a severe health problem worldwide. Current noise metrics and models have assessment limitations on gradually developing NIHL (GDNIHL). In this study, we apply a complex velocity level (CVL) auditory fatigue model to quantitatively assess the impact of basilar membrane (BM) movement on GDNIHL. The transfer functions of chinchilla and human auditory systems, including the triple-path nonlinear (TRNL) filters to simulate the inner ear responses, are applied to obtain BM velocity distribution. Chinchilla and human experimental hearing loss data are used to validate the proposed CVL model’s effectiveness. The results reveal that the developed CVL model demonstrates high correlations with both chinchilla and human hearing loss data. The linear regression based correlation study indicates the proposed CVL model may accurately predict NIHL in both human and chinchilla.

Little research exists describing how the human auditory and vestibular systems respond to higher intensity pressure at ultrasonic frequencies. In large part, this literature gap arises from the well-known attenuation of frequencies higher than 20 kHz by the air-conduction hearing path. Most studies of bone-conducted sound also avoid characterization of ultrasonic sound transmission, in part because the basilar membrane of the cochlea is seen as a physical Fourier analyzer which does not have sensitivity above 20 kHz. We used finite-element modeling of human and macaque intracranial structures to investigate transmission of modulated airborne ultrasound signals in the skull base, middle ear, and inner ear. Even in the presence of soft tissue damping, a family of resonant structural features could locally amplify sound within ultrasonic frequency range. High-amplitude, air-propagated ultrasound carrier signals, heterodyned with audio-band signals, may be able to use these resonant features to deliver perceptible signals to the cochlea without activation of the vestibular sensors. These principles offer the potential to develop new, less obtrusive, noncontact equipment enabling personal communication. [Work supported by ONR Grant N00014-18-1-2157.]

Distortion product otoacoustic emissions (DPOAEs) are evoked by two stimulus tones with frequency f 1 and f 2 of ratio f 2 / f 1 in the range between approximately 1.05 and 1.4. This study theoretically and experimentally analyzes the cubic 2 f 1 − f 2 DPOAE for different stimulus levels of one of the tones while the other is constant. Simulations for f 2 / f 1 of 1.2 and moderate stimulus levels (30–70 dB sound pressure level) indicate that cubic distortion products are generated along a relatively large length of the basilar membrane, the extent of which increases with stimulus level. However, apical from the place of maximum nonlinear force, the wavelets generated by these distributed sources mutually cancel. Therefore, although the spatial extent of the primary DPOAE sources broadens with increasing stimulus level (up to 1.5 oct), the basilar-membrane region contributing to the DPOAE signal is relatively narrow (0.6 oct) and level independent. The observed dependence of DPOAE amplitude on stimulus level can be well-approximated by a point source at the basilar-membrane place where the largest distortion product (maximum of the nonlinear force) is generated. Onset and offset of the DPOAE signal may contain amplitude overshoots (complexities), which are in most cases asymmetrical. Two-tone suppression was identified as the main cause of these onset and offset complexities. DPOAE measurements in two normal-hearing subjects support the level dependence of the steady-state DPOAE amplitude and the asymmetry in the onset and offset responses predicted by the theoretical analysis.

The instability derived from the cochlear model is a phenomenon used to characterize its active processing, which is one of the fundamentals of hearing. This processing relates to the activities of outer hair cells (OHCs) lining in the cochlea. The decline of this processing function is accounted for by the spatially irregular activities of OHCs. Current cochlear models show excessive instability when cochlea containing the irregular activity of the OHCs is simulated. To explain this phenomenon, there are two possibilities. First, excessive instability may be essential to the model. Second, discretized errors may affect the instability of the model in numerical calculation. To investigate these possibilities, a state space model of two-dimensional cochlear mechanics is developed and applied to a high-accuracy scheme of numerical calculation. As a result of this simulation, the basilar membrane responses include the discretization error, which depends on the modeling accuracy. Furthermore, the transfer function and the temporal response show more instability with higher modeling accuracy, with the irregularity of the feedback gain corresponding to the activities of the OHCs. Therefore, when the discretization error is large, the instability is weakened. Consequently, this paper concludes that excessive instability is an essential feature of the cochlear model.

The paper proposes a new method for objective sound quality evaluation for the vehicle interior noise based on the displacement of the basilar membrane in the human ear. The method was mainly carried out in four steps. Firstly, the noise samples in different seats of a car under different working conditions were collected through the vehicle interior noise test. Secondly, the subjective evaluation values (SEVs) of the noise samples were obtained by the adaptive grouped paired comparison method. In the third step, the statistical mean values of the basilar membrane displacement responses (SMVBMDR) were calculated in a lumped-parameter model of the human ear, and thereby a SMVBMDR-based feature matrix was established. Finally, taking the traditional psychoacoustic metrics and the extracted feature matrix as input, two BP neural network models for sound quality evaluation for the vehicle interior noise were established, respectively. To verify effectiveness of the new metric SMVBMDR, the correlations between this metric and the SEVs, as well as between the traditional psychoacoustic metrics and the SEVs were respectively analyzed. The results show that the SMVBDMDR has a higher correlation with the SEVs. Besides, the sound quality prediction of the model based on the SMVBMDR is more accurate than that of the model based on the traditional psychoacoustic metrics. The above results indicate that the new metric SMVBMDR can be used as an effective physiological acoustic metric for objective sound quality evaluation for the vehicle interior noise.

Peripheral compression is believed to play a major role in the masker phase effect (MPE). While compression is almost instantaneous, activation of the efferent system reduces compression in a temporally evolving manner. To study the role of efferent-controlled compression in the MPE, in experiment 1, simultaneous masking of a 30-ms 4-kHz tone by 40-ms Schroeder-phase harmonic complexes was measured with on- and off-frequency precursors as a function of masker phase curvature for two masker levels (60 and 90 dB sound pressure level). The MPE was quantified by the threshold range [min/max difference (MMD)] across the phase curvatures. For the 60-dB condition, the presence of on-frequency precursor decreased the MMD from 10 to 5 dB. Experiment 2 studied the role of the precursor on the auditory filter's bandwidth. The on-frequency precursor was found to increase the bandwidth, an effect incorporated in the subsequent modeling. A model of the auditory periphery including cochlear filtering and basilar membrane compression generally underestimated the MMDs. A model based on two-step compression, including compression of inner hair cells, accounted for the MMDs across precursor and level conditions. Overall, the observed precursor effects and the model predictions suggest an important role of compression in the simultaneous MPE.

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.

Distortion-product otoacoustic emissions (DPOAEs) emerge when presenting two primary tones with different frequencies f1 and f2 to the cochlea and are commonly used in diagnosis and research to evaluate the functional state of the cochlea. Optimal primary-tone stimulus levels accounting for the different level dependencies of the traveling-wave amplitudes of the two primary tones near the f2-tonotopic place on the basilar membrane are often used to maximize DPOAE amplitudes. However, parameters defining the optimal levels can be affected by wave interference between the nonlinear-distortion and coherent-reflection components of the DPOAE. Here, the components were separated in the time domain using a pulsed stimulus paradigm and optimal levels determined. Based on the amplitude dependence of the nonlinear-distortion components on primary-tone stimulus levels, level parameters yielding maximum DPOAE amplitudes were derived for six normal-hearing adults and compared to data recorded with continuous two-tone stimulation. The level parameters resulting from analysis of the nonlinear-distortion components show dependence on stimulus frequency and small standard deviations. DPOAE input/output functions derived for optimal levels exhibit larger slopes, wider dynamic range and less variability across subjects than those derived for conventional stimulus and analysis conditions, potentially increasing their reliability and sensitivity for assessing cochlea function.

Previous psychoacoustical and physiological studies indicate that the medial olivocochlear reflex (MOCR), a bilateral, sound-evoked reflex, may lead to improved sound intensity discrimination in background noise. The MOCR can decrease the range of basilar-membrane compression and can counteract effects of neural adaptation from background noise. However, the contribution of these processes to intensity discrimination is not well understood. This study examined the effect of ipsilateral, contralateral, and bilateral noise on the “mid-level hump.” The mid-level hump refers to intensity discrimination Weber fractions (WFs) measured for short-duration, high-frequency tones which are poorer at mid levels than at lower or higher levels. The mid-level hump WFs may reflect a limitation due to basilar-membrane compression, and thus may be decreased by the MOCR. The noise was either short (50 ms) or long (150 ms), with the long noise intended to elicit the sluggish MOCR. For a tone in quiet, mid-level hump WFs improved with ipsilateral noise for most listeners, but not with contralateral noise. For a tone in ipsilateral noise, WFs improved with contralateral noise for most listeners, but only when both noises were long. These results are consistent with MOCR-induced WF improvements, possibly via decreases in effects of compression and neural adaptation.

Vetesnik and Gummer [J. Acoust. Soc. Am. 131, 3914–3934 (2012)] obtained a stationary solution for distortion products (DPs) in a two-dimensionalcochlear model in which the impedance of the basilar membrane varied smoothly along its length. Their solution was used to study the dependence of the nonlinear-distortion source of distortion-product otoacoustic emission (DPOAE) on stimulus level [Vencovský et al., J. Acoust. Soc. Am. 145, 2909–2931 (2019); Vencovský et al., J. Acoust. Soc. Am. 146, EL92–EL98 (2019)]. Here, the solution is extended to “impedance irregularities” in the mechanics of the cochlea causing the generation of the coherent-reflection source of DPOAEs near the DP characteristic place. The coherent-reflection source of DPOAEs can be relatively pronounced in normal-hearing humans and the interference between the nonlinear-distortion and coherent-reflection components complicates the use of DPOAEs in routine clinical screening of the auditory periphery. The solution for the model with mechanical perturbation can be used to study the relationship between nonlinear-distortion and coherent-reflection components of DPOAEs.

Sound propagating through the scalae of the cochlea causes pressure changes which set the basilar membrane in motion. These pressure changes are studied in the present work with a simple model consisting of a tube with a varying diameter and a rigid wall. Analytical expressions are derived for the pressure changes in relation to the geometry of the tube, fluid friction, the acceleration of the liquid in the tube (perilymph) and stiffness of the membrane of the round window. Using a realistic parameter set, the pressure changes turn out to be dominated by the acceleration of the perilymph. The pressure changes are in phase with the acoustic stimulation and their amplitude depends on the geometry of the tube; tapering towards the middle (the helicotreme) turns out to be advantageous; the amplitudes of the differential pressure and the pressure change over the basilar membrane are maximized along the cochlear duct.

Nowadays, the steady-state responses of human ear to pure tone stimuli have been widely studied. However, the temporal responses to transient stimuli have not been investigated systematically to date. In this study, a comprehensive finite element (FE) model of the human ear is used to investigate the transient characteristics of the human ear in response to impulsive stimuli. There are two types of idealized impulses applied in the FE analysis: the square wave impulse (a single positive pressure waveform) and the A-duration wave impulse (both of positive and negative pressure waveforms). The time-domain responses such as the displacements of the tympanic membrane (TM), the stapes footplate (SF), the basilar membrane (BM), the TM stress distribution, and the cochlea input pressure are derived. The results demonstrate that the TM motion has the characteristic of spatial differences, and the umbo displacement is smaller than other locations. The cochlea input pressure response is synchronized with the SF acceleration response while the SF displacement response appears with some time delay. The BM displacement envelope is relatively higher in the middle cochlea and every portion of BM vibrates at its best frequency approximately. The present results provide a good understanding of the transient response of the human ear.

In the mammalian cochlea, the geometrical and mechanical properties of the organ of Corti complex (OCC, consisting of the tectorial membrane, the organ of Corti, and the basilar membrane) have fundamental consequences for understanding the physics of hearing. Despite efforts to correlate the mechanical properties of the OCC with cochlear function, experimental data of OCC stiffness are limited due to difficulties in measurement. Modern measurements of the OCC stiffness use microprobes exclusively, but suffer ambiguity when defining the physiologically relevant stiffness due to the high nonlinearity in the force-displacement relationship. The nonlinearity stems from two sources. First, microprobes apply local force instead of fluid pressure across the OCC. Second, to obtain the functionally relevant stiffness, the OCC is deformed well beyond in vivo levels (>10 μm). The objective of this study was to develop an alternative technique to overcome challenges intrinsic to the microprobe method. Using a custom-designed microfluidic chamber system, hydrostatic pressures were applied to the excised gerbil cochlea. Deformations of the OCC due to hydrostatic pressures were analyzed through optical-axis image correlation. The pressure-displacement relationship was linear within nanoscale displacement ranges (

Some listeners with hearing loss show poor speech recognition scores in spite of using amplification that optimizes audibility. Beyond audibility, studies have suggested that suprathreshold abilities such as spectral and temporal processing may explain differences in amplified speech recognition scores. A variety of different methods has been used to measure spectral processing. However, the relationship between spectral processing and speech recognition is still inconclusive. This study evaluated the relationship between spectral processing and speech recognition in listeners with normal hearing and with hearing loss. Narrowband spectral resolution was assessed using auditory filter bandwidths estimated from simultaneous notched-noise masking. Broadband spectral processing was measured using the spectral ripple discrimination (SRD) task and the spectral ripple depth detection (SMD) task. Three different measures were used to assess unamplified and amplified speech recognition in quiet and noise. Stepwise multiple linear regression revealed that SMD at 2.0 cycles per octave (cpo) significantly predicted speech scores for amplified and unamplified speech in quiet and noise. Commonality analyses revealed that SMD at 2.0 cpo combined with SRD and equivalent rectangular bandwidth measures to explain most of the variance captured by the regression model. Results suggest that SMD and SRD may be promising clinical tools for diagnostic evaluation and predicting amplification outcomes.

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 cochlea is a spiral-shaped, liquid-filled organ in the inner ear that converts sound with high frequency selectivity over a wide pressure range to neurological signals that are eventually interpreted by the brain. The cochlear partition, consisting of the organ of Corti supported below by the basilar membrane and attached above to the tectorial membrane, plays a major role in the frequency analysis. In early fluid-structure interaction models of the cochlea, the mechanics of the cochlear partition were approximated by a series of single-degree-of-freedom systems representing the distributed stiffness and mass of the basilar membrane. Recent experiments suggest that the mechanical properties of the tectorial membrane may also be important for the cochlea frequency response and that separate waves may propagate along the basilar and tectorial membranes. Therefore, a two-dimensional two-compartment finite difference model of the cochlea was developed to investigate the independent coupling of the basilar and tectorial membranes to the surrounding liquid. Responses are presented for models using two- or three-degree-of-freedom stiffness, damping, and mass parameters derived from a physiologically based finite element model of the cochlear partition. Effects of changes in membrane and organ of Corti stiffnesses on the individual membrane responses are investigated.

As well as generating the far field pressure, which allows wave propagation in the cochlea, the vibration of an individual element of the basilar membrane (BM) will also generate a near field pressure, which increases its mass and gives rise to local longitudinal coupling. This paper compares the efficiency and accuracy of a number of different methods of calculating the near field pressure distribution, and explores the connections between them. In particular it is shown that a common approximation to the wavenumber description of the near field pressure is equivalent, in the spatial domain, to an exponential decay away from the point of excitation. Two important properties of the near field pressure are its maximum amplitude, which is finite if the vibrating element has a finite length, and the value of its spatial integral, which determines the added mass on the BM due to the fluid loading. These properties are calculated as a function of the BM width relative to the width of the fluid chamber. By parameterizing the near field pressure variation in this way, it can be readily incorporated into coupled models of the cochlea, without the considerable computational expense of calculating the full three dimensional pressure field.

The basilar membrane and organ of Corti in the cochlea are essential for sound detection and frequency discrimination in normal hearing. There are currently no methods used for real-time high resolution clinical imaging or vibrometry of these structures. The ability to perform such imaging could aid in the diagnosis of some pathologies and advance understanding of the causes. It is demonstrated that high frequency ultrasound can be used to measure basilar membrane vibrations through the round window of chinchilla cochleas in vivo. The basic vibration characteristics of the basilar membrane agree with previous studies that used other methods, although as expected, the sensitivity of ultrasound was not as high as optical methods. At the best frequency for the recording location, the average vibration velocity amplitude was about 4 mm/s/Pa with stimulus intensity of 50 dB sound pressure level. The displacement noise floor was about 0.4 nm with 256 trial averages (5.12 ms per trial). Although vibration signals were observed, which likely originated from the organ of Corti, the spatial resolution was not adequate to resolve any of the sub-structures. Improvements to the ultrasound probe design may improve resolution and allow the responses of these different structures to be better discriminated.

This study proposes that the frequency tuning of the inner-hair-cell (IHC) stereocilia in the intact organ of Corti can be derived from the responses of the auditory fibers (AFs) using computational tools. The frequency-dependent relationship between the AF threshold and the amplitude of the stereocilia vibration is estimated using a model of the IHC-mediated mechanical to neural transduction. Depending on the response properties of the considered AF, the amplitude of stereocilia deflection required to drive the simulated AF above threshold is 1.4 to 9.2 dB smaller at low frequencies (= 4 kHz). The estimated frequency-dependent relationship between ciliary deflection and neural threshold is employed to derive constant-stereocilia-deflection contours from previously published AF recordings from the chinchilla cochlea. This analysis shows that the transduction process partially accounts for the observed differences between the tuning of the basilar membrane and that of the AFs. (C) 2017 Acoustical Society of America.

A box shape with constant area is often used to represent the complex geometry in the cochlea, although variation of the fluid chambers areas is known to be more complicated. This variation is account for here by an "effective area", given by the harmonic mean of upper and lower chamber area from previous measurements. The square root of this effective area varies linearly along the cochleae in the investigated mammalian species. This suggests the use of a linearly tapered box model, in which the fluid chamber width and height are equal, but decrease linearly along its length. The basilar membrane width is assumed to increase linearly along the model. An analytic form of the far-field fluid pressure difference due to basilar membrane motion is derived for this tapered model. The distributions of the passive basilar membrane response are calculated using both the tapered and uniform models and compared with human and mouse measurements. The discrepancy between the models is frequency-dependent and becomes small at low frequencies. The tapered model developed here shows a reasonable fit to experimental measurements, when the cochleae are cadaver or driven at high sound pressure level and provides a convenient way to incorporate cochlear geometrical variations.

Fluid motion resulting from the compressional excitation of the cochlear capsule due to bone conduction is examined in this paper. Vibrations of the skull deform the shape of the cochlear capsule and give rise to motion the fluid. A two-dimensional channel having a height to length ratio equal to e is used to model the cochlea. The cochlear pressure is expressed as an integral equation in the cochlear partition velocity. In the limit as e approaches zero the integral equation is solved and the cochlear pressure is expressed as an asymptotic expansion in e. Rapid spatial variation in the velocity of the cochlear partition requires one to treat high-order fluid modes within the cochlear fluid. Hence, evanescent pressure modes are included in the analysis. Asymmetry in the oval and the round window velocity is shown to give rise to a pressure gradient across the cochlear partition and basilar membrane displacement. The vibration amplitude of the cochlear partition is shown to depend on the value of the ratio of the oval and the round window impedance.

The mammalian cochlea is a complex system consisting of two fluid-filled ducts separated by a structure known as the organ of Corti. Fluid pressure in the cochlear ducts interact with the organ of Corti to stimulate the mechanoelectrical receptors responsible for hearing. Because, until recently, in vivo dynamic measurements were limited to the basilar membrane, most cochlear models consider only basilar membrane—fluid interactions. Recent measurements of tectorial membrane and reticular lamina motions using optical coherence tomography motivate us to develop cochlear models that takes into account separately coupling of the fluid with all these components of the organ of Corti. In this work, finite element models are used to simulate an apical slice of a mouse cochlea. Using experimentally measured motion of the stapes, reticular lamina, basilar membrane, and tectorial membrane [Lee et al., J. Neurosci. (2016)] as input, spatial variations of pressure in the cochlea are explored. This study investigates fluid dynamics in the cochlear ducts and explores the relationship between the motion of the organ of Corti and spatial pressure variations while providing a basis for future computational models to consider cochlear fluid dynamics in the entire cochlea.The mammalian cochlea is a complex system consisting of two fluid-filled ducts separated by a structure known as the organ of Corti. Fluid pressure in the cochlear ducts interact with the organ of Corti to stimulate the mechanoelectrical receptors responsible for hearing. Because, until recently, in vivo dynamic measurements were limited to the basilar membrane, most cochlear models consider only basilar membrane—fluid interactions. Recent measurements of tectorial membrane and reticular lamina motions using optical coherence tomography motivate us to develop cochlear models that takes into account separately coupling of the fluid with all these components of the organ of Corti. In this work, finite element models are used to simulate an apical slice of a mouse cochlea. Using experimentally measured motion of the stapes, reticular lamina, basilar membrane, and tectorial membrane [Lee et al., J. Neurosci. (2016)] as input, spatial variations of pressure in the cochlea are explored. This study investigates ...

Reconciling the highly tuned and nonlinear basilar membrane (BM) response at the base with the nearly low-pass and weakly nonlinear response at the apex has presented a longstanding challenge to cochlear mechanics modelers. Recent experiments have shown that the BM centric view of cochlear mechanics is incomplete and have highlighted the importance of modeling and measuring the dynamics of the organ of Corti (OoC). Here, we describe a new computational model of the guinea pig cochlea that can correctly simulate the response at all frequencies. The model shows that the electromotile force from the outer hair cells modulate the differential motion between the reticular lamina and the BM. Model calculations at the apex show that the geometric taper of the scalae duct as well as the cytoarchitecture of the OoC breaks the scaling symmetry observed at the base. Further, the model predicts that the neural tuning at the base is primarily governed by the macroscopic dynamics of the cochlear partition, while the micro-scale fluid dynamics and the nano-scale channel dynamics dominate the neural tuning at the apex. Overall, the model provides a physiological explanation for the differences between high and low frequency hearing observed in psychophysical experiments. [Work supported by NIH-R01-04084.]

Current models of the initial stages of auditory processing in mammals usually agree that the input signals are split into a bank of bandpass filters. However, the available models differ substantially in their level of complexity and the number of parameters needed. In the current work, the varying levels of complexity in filterbank models of the basilar membrane have been evaluated in the context of modeling the cochlear processing of natural biosonar echoes in horseshoe bats. To this end, three different types of filterbank models have been implemented to represent the range of complexity spanned by models that are in use for the human inner ear: The simplest model, a gammatone filterbank, is a linear model with symmetric filter transfer functions. The gammachirp filterbank is also linear, but mimics the asymmetric transfer functions of the basilar membrane. Finally, the dual resonance nonlinear (DRNL) model adds a level-dependent behavior. Here, all three models have been adapted to the specifics of the basilar membrane of horseshoe bats which is characterized by an “auditory fovea” with exceptionally high filter qualities. The outputs of the different models have been encoded into a sequence of neural spike times before being evaluated with various information-theoretic methods.

In a recent paper [J. Acoust. Soc. Am. 133, 2224-2239 (2013)], Shera and Cooper report on the impulse response of the basilar membrane (BM) of a chinchilla, a waveform which shows repetitive bursts. They explain the bursts in terms of repeated coherent reflection at BM discontinuities and partial reflection at the stapes ("coherent reflection filtering"). Here the same waveform is examined in detail, highlighting features which indicate that the coherent reflection model, with calls for the same repetitive process to act on each successive burst, does not fully account for the shape of the measured impulse response. (C) 2015 Acoustical Society of America.

Distortion-product otoacoustic emissions (DPOAEs) were measured in rabbits as time waveforms by employing a phase-rotation technique to cancel all components in the final average, except the 2f1-f2 DPOAE. Subsequent filtering allowed the DPOAE waveform to be clearly visualized in the time domain. In most conditions, f2 was turned off for 6 ms, which produced a gap so that the DPOAE was no longer generated. These procedures allowed the DPOAE onset as well as the decay during the gap to be observed in the time domain. DPOAEs were collected with L1 = L2 = 65-dB sound pressure level primary-tone levels for f2/f1 ratios from 1.25 to 1.01 in 0.02 steps. Findings included the appearance of complex onsets and decays for the DPOAE time waveforms as the f2/f1 ratio was decreased and the DPOAE level was reduced. These complexities were unaffected by interference tones (ITs) near the DPOAE frequency place (fdp), but could be removed by ITs presented above f2, which also increased DPOAE levels. Similar outcomes were observed when DPOAEs were measured at a sharp notch in the DPOAE level as a function of the f2 primary tone frequency, i.e., DP-gram. Both findings were consistent with the hypothesis that the DPOAE-ratio function, and some notches in the DP-gram, are caused by interactions of distributed DPOAE components with unique phases.

Estimates of human basilar membrane gain and compression obtained using temporal masking curve (TMC) and additivity of forward masking (AFM) methods with long-duration maskers or long masker-signal silent intervals may be affected by olivocochlear efferent activation, which reduces basilar membrane gain. The present study introduces a fixed-duration masking curve (FDMC) method, which involves a comparison of off- and on-frequency forward masker levels at threshold as a function of masker and signal duration, with the total masker-signal duration fixed at 25 ms to minimize efferent effects. Gain and compression estimates from the FDMC technique were compared with those from TMC (104-ms maskers) and AFM (10- and 200-ms maskers) methods. Compression estimates over an input-masker range of 40-60 dB sound pressure level were similar for the four methods. Maximum compression occurred at a lower input level for the FDMC compared to the TMC method. Estimates of gain were similar for TMC and FDMC methods. The FDMC method may provide a more reliable estimate of BM gain and compression in the absence of efferent activation and could be a useful method for estimating effects of efferent activity when used with a precursor sound (to trigger efferent activation), presented prior to the combined masker-signal stimulus.

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.

We have developed a high-frequency pulsed-wave Doppler ultrasound probe as a promising minimally-invasive technique for measuring intracochlear mechanics without damaging the cochlea. Using a custom high-frequency ultrasound system, we have measured dynamic motion of intracochlear structures by recording the pulsed-wave Doppler signal resulting from the vibration of the basilar and round window membranes. A 45 MHz needle-mounted Doppler probe was fabricated and placed against the round window membranes of eight different fresh human temporal bones. Pulsed-wave ultrasonic Doppler measurements were performed on the basilar membrane and round window membrane during the application of pure tones to the external ear canal. Doppler vibrational information for acoustic input frequencies ranging from 100–2000 Hz was collected and normalized to the sound pressure in the ear canal. The middle ear resonance, located at approximately 1000 Hz, could be characterized from the membrane velocities, which agreed well with literature values. The maximum normalized mean velocity of the round window and the basilar membrane were 180 μm/s/Pa and 27 μm/s/Pa at 800 Hz. The mean phase difference between the membrane displacements and the applied ear canal sound pressure showed a flat response almost up to 500 Hz where it began to accumulate. This is the first study that reports the application of high frequency pulsed wave Doppler ultrasound for measuring the vibration of basilar membrane through the round window. Since it is not required to open or damage the cochlea, this technique might be applicable for investigating cochlear dynamics, in vivo.

The operation of each hair cell within the cochlea generates a change in electrical potential at the frequency of the vibrating basilar membrane beneath the hair cell. This electrical potential influences the operation of the cochlea at nearby locations and can also be detected as the cochlear microphonic signal. The effect of such potentials has been proposed as a mechanism for the non-local operation of the cochlear amplifier, and the interaction of such potentials has been thought to be the cause of the broadness of cochlea microphonic tuning curves. The spatial extent of influence of these potentials is an important parameter for determining the significance of their effects. Calculations of this extent have typically been based on calculating the longitudinal resistance of each of the scalae from the scala cross sectional area, and the conductivity of the lymph. In this paper, the range of influence of the electrical potential is examined using an electrical finite element model. It is found that the range of influence of the hair cell potential is much shorter than the conventional calculation, but is consistent with recent measurements.

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.

Hand–arm vibration syndrome (HAVS) is collectively a vasospastic and neurodegenerative occupational disease. One of the major symptoms of HAVS is vibration white finger (VWF) caused by exaggerated vasoconstriction of the arteries and skin arterioles. While VWF is a very painful and costly occupational illness, its pathology has not been well understood. In this study a small artery is modeled as a fluid filled elastic tube whose diameter changes along the axial direction. Equations of motion are developed by considering interactions between the fluid, artery wall and soft-tissue bed. It is shown that the resulting wave equation is the same as that of the basilar membrane in the cochlea of mammals. Therefore, the artery system shows a spatial resonance as in the basilar membrane, which responds with the highest amplitude at the location determined by the vibration frequency. This implies that a long-term use of one type of tool will induce high-level stresses at a few identical locations of the artery that correspond to the major frequency components of the tool. Hardening and deterioration of the artery at these locations may be a possible cause of VWF.

Multiple internal reflection of cochlear traveling waves has been argued to provide a plausible explanation for the waxing and waning and other temporal structures often exhibited by the envelopes of basilar-membrane (BM) and auditory-nerve responses to acoustic clicks. However, a recent theoretical analysis of a BM click response measured in chinchilla concludes that the waveform cannot have arisen via any equal, repetitive process, such as iterated intracochlear reflection [Wit and Bell (2015), J. Acoust. Soc. Am. 138, 94-96]. Reanalysis of the waveform contradicts this conclusion. The measured BM click response is used to derive the frequency-domain transfer function characterizing every iteration of the loop. The selfsame transfer function that yields waxing and waning of the BM click response also captures the spectral features of ear-canal stimulus-frequency otoacoustic emissions measured in the same animal, consistent with the predictions of multiple internal reflection. Small shifts in transfer-function phase simulate results at different measurement locations and reproduce the heterogeneity of BM click response envelopes observed experimentally.

Coupling of somatic electromechanical force from the outer hair cells (OHCs) into the organ of Corti is investigated by measuring transverse vibration patterns of the organ of Cori and tectorial membrane (TM) in response to intracochlear electrical stimulation. Measurement places at the organ of Corti extend from the inner sulcus cells to Hensen’s cells and at the lower (and upper) surface of the TM from the inner sulcus to the OHC region. These locations are in the neighborhood of where electromechanical force is coupled into (1) the mechanoelectrical transducers of the stereocilia and (2) fluids of the organ of Corti. Experiments are conducted in the first, second, and third cochlear turns of an in vitro preparation of the adult guinea pig cochlea. Vibration measurements are made at functionally relevant stimulus frequencies (0.48–68 kHz) and response amplitudes (

A discrete model of cochlear mechanics is introduced that includes a full, three-dimensional, description of fluid coupling. This formulation allows the fluid coupling and basilar membrane dynamics to be analyzed separately and then coupled together with a simple piece of linear algebra. The fluid coupling is initially analyzed using a wavenumber formulation and is separated into one component due to one-dimensional fluid coupling and one comprising all the other contributions. Using the theory of acoustic waves in a duct, however, these two components of the pressure can also be associated with a far field, due to the plane wave, and a near field, due to the evanescent, higher order, modes. The near field components are then seen as one of a number of sources of additional longitudinal coupling in the cochlea. The effects of non-uniformity and asymmetry in the fluid chamber areas can also be taken into account, to predict both the pressure difference between the chambers and the mean pressure. This allows the calculation, for example, of the effect of a short cochlear implant on the coupled response of the cochlea.

The cochlea transforms incoming sound pressure into vibrations of the basilar membrane which give rise to neural impulses. Although it has been an object of research for several decades, complete understanding of its behavior is far from complete. Many experiments on real cochlea and many mathematical models have been developed in the past decades. In the biophysical cochlear model of Mammano and Nobili [1, 2], both mechanical and hydrodynamical aspects are treated at a level adequate to the complexity of realistic cochlear structures. In this paper, we analyze the time-frequency resolution of this biophysical cochlear model: analysis is first applied to the passive cochlear model and then extended to the active nonlinear model. Further, we propose the method for signal reconstruction from the cochlear time-frequency response. When applied to active cochlear model response, it could result with the signal which human ear actually hears (with some spectral enhancements and noise suppression).

International audience; Young deaf children using a cochlear implant develop speech abilities on the basis of speech temporal envelope signals distributed over a limited number of frequency bands. A Headturn Preference Procedure was used to measure looking times in 6-month-old, normal-hearing infants during presentation of repeating or alternating sequences composed of different tokens of /aba/and /apa/ processed to retain envelope information below 64 Hz while degrading temporal fine structure cues. Infants attended longer to the alternating sequences, indicating that they perceive the voicing contrast on the basis of envelope cues alone in the absence of fine spectral and temporal structure information

The phase versus frequency function of the distortion product otoacoustic emission (DPOAE) at 2f(1) - f(2) is approximately invariant at frequencies above 1.5 kHz in human subjects when recorded with a constant f(2)/f(1). However, a secular break from this invariance has been observed at lower frequencies where the phase-gradient becomes markedly steeper. Apical DPOAEs, such as 2f(1) - f(2), are known to contain contributions from multiple sources. This experiment asked whether the phase behavior of the ear canal DPOAE at low frequencies is driven by the phase of the component from the distortion product (DP) region at 2f(1) - f(2), which exhibits rapid phase accumulation. Placing a suppressor tone close in the frequency to 2f(1) - f(2) reduced the contribution of this component to the ear canal DPOAE in normal-hearing adult human ears. When the contribution of this component was reduced, the phase behavior of the ear canal DPOAE was not altered, suggesting that the breaking from DPOAE phase invariance at low frequencies is an outcome of apical-basal differences in cochlear mechanics. The deviation from DPOAE phase invariance appears to be a manifestation of the breaking from approximate scaling symmetry in the human cochlear apex.