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

Fast time-domain solution of the cochlear transmission line model in real-time applications

A fast numerical time-domain solution for a one-dimensional cochlear transmission-line model was proposed for real-time applications. In this approach, the three-dimensional solver developed by Murakami [J. Acoust. Soc. Am. 150(4), 2589-2599 (2021)] was modified to develop a solution for the one-dimensional model. This development allows the solution to accurately and quickly calculate cochlear responses. The present solution can solve the model in real-time under coarse grid conditions. However, under fine-grid conditions, the computation time is significantly longer than the duration of the signal. Nevertheless, calculations can be performed under the fine grid condition, which previously required much computation time. This fact is essential to applications.

Something in Our Ears Is Oscillating, but What? A Modeller's View of Efforts to Model Spontaneous Emissions

When David Kemp discovered "spontaneous ear noise" in 1978, it opened up a whole new perspective on how the cochlea works. The continuous tonal sound emerging from most healthy human ears, now called spontaneous otoacoustic emissions or SOAEs, was an unmistakable sign that our hearing organ must be considered an active detector, not just a passive microphone, just as Thomas Gold had speculated some 30 years earlier. Clearly, something is oscillating as a byproduct of that sensitive inbuilt detector, but what exactly is it? Here, we give a chronological account of efforts to model SOAEs as some form of oscillator, and at intervals, we illustrate key concepts with numerical simulations. We find that after many decades there is still no consensus, and the debate extends to whether the oscillator is local, confined to discrete local sources on the basilar membrane, or global, in which an assembly of micro-mechanical elements and basilar membrane sections, coupled by inner ear fluid, interact over a wide region. It is also undecided whether the cochlear oscillator is best described in terms of the well-known Van der Pol oscillator or the less familiar Duffing or Hopf oscillators. We find that irregularities play a key role in generating the emissions. This paper is not a systematic review of SOAEs and their properties but more a historical survey of the way in which various oscillator configurations have been applied to modelling human ears. The conclusion is that the difference between the local and global approaches is not clear-cut, and they are probably not mutually exclusive concepts. Nevertheless, when one sees how closely human SOAEs can be matched to certain arrangements of oscillators, Gold would no doubt say we are on the right track.

From the outer ear to the nerve: A complete computer model of the peripheral auditory system

Computer models of the individual components of the peripheral auditory system - the outer, middle, and inner ears and the auditory nerve - have been developed in the past, with varying level of detail, breadth, and faithfulness of the underlying parameters. Building on previous work, we advance the modeling of the ear by presenting a complete, physiologically justified, bottom-up computer model based on up-to-date experimental data that integrates all of these parts together seamlessly. The detailed bottom-up design of the present model allows for the investigation of partial hearing mechanisms and their defects, including genetic, molecular, and microscopic factors. Also, thanks to the completeness of the model, one can study microscopic effects in the context of their implications on hearing as a whole, enabling the correlation with neural recordings and non-invasive psychoacoustic methods. Such a model is instrumental for advancing quantitative understanding of the mechanism of hearing, for investigating various forms of hearing impairment, as well as for devising next generation hearing aids and cochlear implants.

A comparative study of eight human auditory models of monaural processing

A number of auditory models have been developed using diverging approaches, either physiological or perceptual, but they share comparable stages of signal processing, as they are inspired by the same constitutive parts of the auditory system. We compare eight monaural models that are openly accessible in the Auditory Modelling Toolbox. We discuss the considerations required to make the model outputs comparable to each other, as well as the results for the following model processing stages or their equivalents: Outer and middle ear, cochlear filter bank, inner hair cell, auditory nerve synapse, cochlear nucleus, and inferior colliculus. The discussion includes a list of recommendations for future applications of auditory models.

Link between stimulus otoacoustic emissions fine structure peaks and standing wave resonances in a cochlear model

In response to an external stimulus, the cochlea emits sounds, called stimulus frequency otoacoustic emissions (SFOAEs), at the stimulus frequency. In this article, a three-dimensional computational model of the gerbil cochlea is used to simulate SFOAEs and clarify their generation mechanisms and characteristics. This model includes electromechanical feedback from outer hair cells (OHCs) and cochlear roughness due to spatially random inhomogeneities in the OHC properties. As in the experiments, SFOAE simulations are characterized by a quasiperiodic fine structure and a fast varying phase. Increasing the sound pressure level broadens the peaks and decreases the phase-gradient delay of SFOAEs. A state-space formulation of the model provides a theoretical framework to analyze the link between the fine structure and global modes of the cochlea, which arise as a result of standing wave resonances. The SFOAE fine structure peaks correspond to weakly damped resonant modes because they are observed at the frequencies of nearly unstable modes of the model. Variations of the model parameters that affect the reflection mechanism show that the magnitude and sharpness of the tuning of these peaks are correlated with the modal damping ratio of the nearly unstable modes. The analysis of the model predictions demonstrates that SFOAEs originate from the peak of the traveling wave.

Predicting synapse counts in living humans by combining computational models with auditory physiology

Aging, noise exposure, and ototoxic medications lead to cochlear synapse loss in animal models. As cochlear function is highly conserved across mammalian species, synaptopathy likely occurs in humans as well. Synaptopathy is predicted to result in perceptual deficits including tinnitus, hyperacusis, and difficulty understanding speech-in-noise. The lack of a method for diagnosing synaptopathy in living humans hinders studies designed to determine if noise-induced synaptopathy occurs in humans, identify the perceptual consequences of synaptopathy, or test potential drug treatments. Several physiological measures are sensitive to synaptopathy in animal models including auditory brainstem response (ABR) wave I amplitude. However, it is unclear how to translate these measures to synaptopathy diagnosis in humans. This work demonstrates how a human computational model of the auditory periphery, which can predict ABR waveforms and distortion product otoacoustic emissions (DPOAEs), can be used to predict synaptic loss in individual human participants based on their measured DPOAE levels and ABR wave I amplitudes. Lower predicted synapse numbers were associated with advancing age, higher noise exposure history, increased likelihood of tinnitus, and poorer speech-in-noise perception. These findings demonstrate the utility of this modeling approach in predicting synapse counts from physiological data in individual human subjects.

Noise-robust text-dependent speaker identification using cochlear models

One challenging issue in speaker identification (SID) is to achieve noise-robust performance. Humans can accurately identify speakers, even in noisy environments. We can leverage our knowledge of the function and anatomy of the human auditory pathway to design SID systems that achieve better noise-robust performance than conventional approaches. We propose a text-dependent SID system based on a real-time cochlear model called cascade of asymmetric resonators with fast-acting compression (CARFAC). We investigate the SID performance of CARFAC on signals corrupted by noise of various types and levels. We compare its performance with conventional auditory feature generators including mel-frequency cepstrum coefficients, frequency domain linear predictions, as well as another biologically inspired model called the auditory nerve model. We show that CARFAC outperforms other approaches when signals are corrupted by noise. Our results are consistent across datasets, types and levels of noise, different speaking speeds, and back-end classifiers. We show that the noise-robust SID performance of CARFAC is largely due to its nonlinear processing of auditory input signals. Presumably, the human auditory system achieves noise-robust performance via inherent nonlinearities as well.

Individualized Cochlear Models Based on Distortion Product Otoacoustic Emissions

Auditory models have been adopted for years to simulate characteristics of the human auditory processing for normal and hearing-impaired listeners. However, individual differences due to varying degrees of frequency-dependent hearing damage hinders the simulation of auditory processing on an individualized basis. Here, with a view on precise auditory profiling, recorded distortion product otoacoustic emission (DPOAE) metrics are used to determine individual parameters of cochlear non-linearity to yield individualized human cochlear models, which can be used as pre-processors for hearing-aid and machine-hearing applications. We test whether individualized cochlear models based on DPOAE measurements can simulate the measured DPOAEs and audiograms of normal-hearing and hearing-impaired listeners. Results showed that cochlear models individualized based on DPOAE-grams measured at low stimulus levels or DPOAE thresholds, yield the smallest simulation errors.

Fast time-domain solution of a nonlinear three-dimensional cochlear model using the fast Fourier transform

A fast numerical time-domain solution of a nonlinear three-dimensional (3D) cochlear model is proposed. In dynamical systems, a time-domain solution can determine nonlinear responses, and the human faculty of hearing depends on nonlinear behaviors of the microscopically structured organs of the cochlea. Thus, time-domain 3D modeling can help explain hearing. The matrix product, an n² operation, is a central part of the time-domain solution procedure in cochlear models. To solve the cochlear model faster, the fast Fourier transform (FFT), an n log n operation, is used to replace the matrix product. Numerical simulation results verified the similarity of the matrix product and the FFT under coarse grid settings. Furthermore, applying the FFT reduced the computation time by a factor of up to 100 owing to the computational complexity of the proposed approach being reduced from n² to n log n. Additionally, the proposed method successfully computed 3D models under moderate and fine grid settings that were unsolvable using the matrix product. The 3D cochlear model exhibited nonlinear responses for pure tones and clicks under various gain distributions in a time-domain simulation. Thus, the FFT-based method provides fast numerical solutions and supports the development of 3D models for cochlear mechanics.

Denoising click-evoked otoacoustic emission signals by optimal shrinkage

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

A convolutional neural-network model of human cochlear mechanics and filter tuning for real-time applications

Auditory models are commonly used as feature extractors for automatic speech-recognition systems or as front-ends for robotics, machine-hearing and hearing-aid applications. Although auditory models can capture the biophysical and nonlinear properties of human hearing in great detail, these biophysical models are computationally expensive and cannot be used in real-time applications. We present a hybrid approach where convolutional neural networks are combined with computational neuroscience to yield a real-time end-to-end model for human cochlear mechanics, including level-dependent filter tuning (CoNNear). The CoNNear model was trained on acoustic speech material and its performance and applicability were evaluated using (unseen) sound stimuli commonly employed in cochlear mechanics research. The CoNNear model accurately simulates human cochlear frequency selectivity and its dependence on sound intensity, an essential quality for robust speech intelligibility at negative speech-to-background-noise ratios. The CoNNear architecture is based on parallel and differentiable computations and has the power to achieve real-time human performance. These unique CoNNear features will enable the next generation of human-like machine-hearing applications.

Towards Personalized Auditory Models: Predicting Individual Sensorineural Hearing-Loss Profiles From Recorded Human Auditory Physiology

Over the past decades, different types of auditory models have been developed to study the functioning of normal and impaired auditory processing. Several models can simulate frequency-dependent sensorineural hearing loss (SNHL) and can in this way be used to develop personalized audio-signal processing for hearing aids. However, to determine individualized SNHL profiles, we rely on indirect and noninvasive markers of cochlear and auditory-nerve (AN) damage. Our progressive knowledge of the functional aspects of different SNHL subtypes stresses the importance of incorporating them into the simulated SNHL profile, but has at the same time complicated the task of accomplishing this on the basis of noninvasive markers. In particular, different auditory-evoked potential (AEP) types can show a different sensitivity to outer-hair-cell (OHC), inner-hair-cell (IHC), or AN damage, but it is not clear which AEP-derived metric is best suited to develop personalized auditory models. This study investigates how simulated and recorded AEPs can be used to derive individual AN- or OHC-damage patterns and personalize auditory processing models. First, we individualized the cochlear model parameters using common methods of frequency-specific OHC-damage quantification, after which we simulated AEPs for different degrees of AN damage. Using a classification technique, we determined the recorded AEP metric that best predicted the simulated individualized cochlear synaptopathy profiles. We cross-validated our method using the data set at hand, but also applied the trained classifier to recorded AEPs from a new cohort to illustrate the generalizability of the method.

Enhancing the sensitivity of the envelope-following response for cochlear synaptopathy screening in humans: The role of stimulus envelope

Auditory de-afferentation, a permanent reduction in the number of inner-hair-cells and auditory-nerve synapses due to cochlear damage or synaptopathy, can reliably be quantified using temporal bone histology and immunostaining. However, there is an urgent need for non-invasive markers of synaptopathy to study its perceptual consequences in live humans and to develop effective therapeutic interventions. While animal studies have identified candidate auditory-evoked-potential (AEP) markers for synaptopathy, their interpretation in humans has suffered from translational issues related to neural generator differences, unknown hearing-damage histopathologies or lack of measurement sensitivity. To render AEP-based markers of synaptopathy more sensitive and differential to the synaptopathy aspect of sensorineural hearing loss, we followed a combined computational and experimental approach. Starting from the known characteristics of auditory-nerve physiology, we optimized the stimulus envelope to stimulate the available auditory-nerve population optimally and synchronously to generate strong envelope-following-responses (EFRs). We further used model simulations to explore which stimuli evoked a response that was sensitive to synaptopathy, while being maximally insensitive to possible co-existing outer-hair-cell pathologies. We compared the model-predicted trends to AEPs recorded in younger and older listeners (N=44, 24f) who had normal or impaired audiograms with suspected age-related synaptopathy in the older cohort. We conclude that optimal stimulation paradigms for EFR-based quantification of synaptopathy should have sharply rising envelope shapes, a minimal plateau duration of 1.7-2.1 ms for a 120-Hz modulation rate, and inter-peak intervals which contain near-zero amplitudes. From our recordings, the optimal EFR-evoking stimulus had a rectangular envelope shape with a 25% duty cycle and a 95% modulation depth. Older listeners with normal or impaired audiometric thresholds showed significantly reduced EFRs, which were consistent with how (age-induced) synaptopathy affected these responses in the model.

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

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

Nonlinear Distortions and Parametric Amplification Generate Otoacoustic Emissions and Increased Hearing Sensitivity

The ear is able to detect low-level acoustic signals by a highly specialized system including a parametric amplifier in the cochlea. This is verified by a numerical mechanical model of the cochlea, which reduces the three-dimensional (3D) system to a one-dimensional (1D) approach. A formerly developed mechanical model permits the consideration of the fluid and the orthotropic basilar membrane in a 1D fluid-structure coupled system. This model shows the characteristic frequency to place transformation of the traveling wave in the cochlea. The additional inclusion of time and space dependent stiffness of outer hair cells and the signal level dependent stiffness of the string enables parametric amplification of the input signal. Due to the nonlinear outer hair cell stiffness change, nonlinear distortions follow as a byproduct of the parametric amplification at low levels constituting the compressive nonlinearity. More distortions are generated by the saturating displacements of the string at high input levels, which can be distinguished from the low-level distortions by the order of additional harmonics. Amplification factors of 15.5 d B and 24.0 d B are calculated, and a change of the traveling-wave mapping is postulated with parametric amplification representing the healthy state of the cochlea.

The influence of distributed source regions in the formation of the nonlinear distortion component of cubic distortion-product otoacoustic emissions

Distortion product otoacoustic emissions (DPOAEs) are evoked by two stimulus tones with frequency f₁ and f₂ of ratio f₂/f₁  in the range between approximately 1.05 and 1.4. This study theoretically and experimentally analyzes the cubic 2f₁-f₂ DPOAE for different stimulus levels of one of the tones while the other is constant. Simulations for f₂/f₁ 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.

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.

An analytic physically motivated model of the mammalian cochlea

In this paper, an analytic model of the mammalian cochlea is developed. A mixed physical-phenomenological approach by utilizing existing work on the physics of classical box-representations of the cochlea and behavior of recent data-derived wavenumber estimates is used. Spatial variation is incorporated through a single independent variable that combines space and frequency. This paper arrives at closed-form expressions for the organ of Corti velocity, its impedance, the pressure difference across the organ of Corti, and its wavenumber. Model tests using real and imaginary parts of chinchilla data from multiple locations and for multiple variables are performed. The model also predicts impedances that are qualitatively consistent with current literature. For implementation, the model can leverage existing efforts for both filter bank or filter cascade models that target improved algorithmic or analog circuit efficiencies. The simplicity of the cochlear model, its small number of model constants, its ability to capture the variation of tuning, its closed-form expressions for physically-interrelated variables, and the form of these expressions that allows for easily determining one variable from another make the model appropriate for analytic and digital auditory filter implementations as discussed here, as well as for extracting macromechanical insights regarding how the cochlea works.

Modeling Pitch Perception With an Active Auditory Model Extended by Octopus Cells

Pitch is an essential category for musical sensations. Models of pitch perception are vividly discussed up to date. Most of them rely on definitions of mathematical methods in the spectral or temporal domain. Our proposed pitch perception model is composed of an active auditory model extended by octopus cells. The active auditory model is the same as used in the Stimulation based on Auditory Modeling (SAM), a successful cochlear implant sound processing strategy extended here by modeling the functional behavior of the octopus cells in the ventral cochlear nucleus and by modeling their connections to the auditory nerve fibers (ANFs). The neurophysiological parameterization of the extended model is fully described in the time domain. The model is based on latency-phase en- and decoding as octopus cells are latency-phase rectifiers in their local receptive fields. Pitch is ubiquitously represented by cascaded firing sweeps of octopus cells. Based on the firing patterns of octopus cells, inter-spike interval histograms can be aggregated, in which the place of the global maximum is assumed to encode the pitch.

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

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

Analyzing transient-evoked otoacoustic emissions by concentration of frequency and time

The linear part of transient evoked otoacoustic emission (TEOAE) is thought to be generated via coherent reflection near the characteristic place of constituent wave components. Because of the tonotopic organization of the cochlea, high frequency emissions return earlier than low frequencies; however, due to the random nature of coherent reflection, the instantaneous frequency (IF) and amplitude envelope of TEOAEs both fluctuate. Multiple reflection components and synchronized spontaneous emissions can further make it difficult to extract the IF by linear transforms. This paper proposes to model TEOAEs as a sum of intrinsic mode-type functions and analyze it by a nonlinear-type time-frequency (T-F) analysis technique called concentration of frequency and time (ConceFT). When tested with synthetic otoacoustic emission signals with possibly multiple oscillatory components, the present method is able to produce clearly visualized traces of individual components on the T-F plane. Further, when the signal is noisy, the proposed method is compared with existing linear and bilinear methods in its accuracy for estimating the fluctuating IF. Results suggest that ConceFT outperforms the best of these methods in terms of optimal transport distance, reducing the error by 10% to 21% when the signal to noise ratio is 10 dB or below.

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

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

A framework for testing and comparing binaural models

Auditory research has a rich history of combining experimental evidence with computational simulations of auditory processing in order to deepen our theoretical understanding of how sound is processed in the ears and in the brain. Despite significant progress in the amount of detail and breadth covered by auditory models, for many components of the auditory pathway there are still different model approaches that are often not equivalent but rather in conflict with each other. Similarly, some experimental studies yield conflicting results which has led to controversies. This can be best resolved by a systematic comparison of multiple experimental data sets and model approaches. Binaural processing is a prominent example of how the development of quantitative theories can advance our understanding of the phenomena, but there remain several unresolved questions for which competing model approaches exist. This article discusses a number of current unresolved or disputed issues in binaural modelling, as well as some of the significant challenges in comparing binaural models with each other and with the experimental data. We introduce an auditory model framework, which we believe can become a useful infrastructure for resolving some of the current controversies. It operates models over the same paradigms that are used experimentally. The core of the proposed framework is an interface that connects three components irrespective of their underlying programming language: The experiment software, an auditory pathway model, and task-dependent decision stages called artificial observers that provide the same output format as the test subject.

Modeling signal propagation in the human cochlea

The level-dependent component of the latency of human auditory brainstem responses (ABR) to tonebursts decreases by about 38% for every 20-dB increase in stimulus level over a wide range of both frequency and level [Neely, Norton, Gorga, and Jesteadt (1998). J. Acoust. Soc. Am. 31, 87-97]. This level-dependence has now been simulated in an active, nonlinear, transmission-line model of cochlear mechanics combined with an adaptation stage. The micromechanics in this model are similar to previous models except that a dual role is proposed for the tectorial membrane (TM): (1) passive sharpening the tuning of sensory-cell inputs (relative to basilar-membrane vibrations) and (2) providing an optimal phase shift (relative to basilar-membrane vibrations) of outer-hair-cell feedback forces, so that amplification is restricted to a limited range of frequencies. The adaptation stage, which represents synaptic adaptation of neural signals, contributes to the latency level-dependence more at low frequencies than at high frequencies. Compression in this model spans the range of audible sound levels with a compression ratio of about 2:1. With further development, the proposed model of cochlear micromechanics could be useful both (1) as a front-end to functional models of the auditory system and (2) as a foundation for understanding the physiological basis of cochlear amplification.

Psychophysical and modeling approaches towards determining the cochlear phase response based on interaural time differences

The cochlear phase response is often estimated by measuring masking of a tonal target by harmonic complexes with various phase curvatures. Maskers yielding most modulated internal envelope representations after passing the cochlear filter are thought to produce minimum masking, with fast-acting cochlear compression as the main contributor to that effect. Thus, in hearing-impaired (HI) listeners, reduced cochlear compression hampers estimation of the phase response using the masking method. This study proposes an alternative approach, based on the effect of the envelope modulation strength on the sensitivity to interaural time differences (ITDs). To evaluate the general approach, ITD thresholds were measured in seven normal-hearing listeners using 300-ms Schroeder-phase harmonic complexes with nine different phase curvatures. ITD thresholds tended to be lowest for phase curvatures roughly similar to those previously shown to produce minimum masking. However, an unexpected ITD threshold peak was consistently observed for a particular negative phase curvature. An auditory-nerve based ITD model predicted the general pattern of ITD thresholds except for the threshold peak, as well as published envelope ITD data. Model predictions simulating outer hair cell loss support the feasibility of the ITD-based approach to estimate the phase response in HI listeners.

Auditory brainstem response latency in forward masking, a marker of sensory deficits in listeners with normal hearing thresholds

In rodent models, acoustic exposure too modest to elevate hearing thresholds can nonetheless cause auditory nerve fiber deafferentation, interfering with the coding of supra-threshold sound. Low-spontaneous rate nerve fibers, important for encoding acoustic information at supra-threshold levels and in noise, are more susceptible to degeneration than high-spontaneous rate fibers. The change in auditory brainstem response (ABR) wave-V latency with noise level has been shown to be associated with auditory nerve deafferentation. Here, we measured ABR in a forward masking paradigm and evaluated wave-V latency changes with increasing masker-to-probe intervals. In the same listeners, behavioral forward masking detection thresholds were measured. We hypothesized that 1) auditory nerve fiber deafferentation increases forward masking thresholds and increases wave-V latency and 2) a preferential loss of low-spontaneous rate fibers results in a faster recovery of wave-V latency as the slow contribution of these fibers is reduced. Results showed that in young audiometrically normal listeners, a larger change in wave-V latency with increasing masker-to-probe interval was related to a greater effect of a preceding masker behaviorally. Further, the amount of wave-V latency change with masker-to-probe interval was positively correlated with the rate of change in forward masking detection thresholds. Although we cannot rule out central contributions, these findings are consistent with the hypothesis that auditory nerve fiber deafferentation occurs in humans and may predict how well individuals can hear in noisy environments.

Relation Between Cochlear Mechanics and Performance of Temporal Fine Structure-Based Tasks

This study examined whether the mechanical characteristics of the cochlea could influence individual variation in the ability to use temporal fine structure (TFS) information. Cochlear mechanical functioning was evaluated by swept-tone evoked otoacoustic emissions (OAEs), which are thought to comprise linear reflection by micromechanical impedance perturbations, such as spatial variations in the number or geometry of outer hair cells, on the basilar membrane (BM). Low-rate (2 Hz) frequency modulation detection limens (FMDLs) were measured for carrier frequency of 1000 Hz and interaural phase difference (IPD) thresholds as indices of TFS sensitivity and high-rate (16 Hz) FMDLs and amplitude modulation detection limens (AMDLs) as indices of sensitivity to non-TFS cues. Significant correlations were found among low-rate FMDLs, low-rate AMDLs, and IPD thresholds (R = 0.47-0.59). A principal component analysis was used to show a common factor that could account for 81.1, 74.1, and 62.9 % of the variance in low-rate FMDLs, low-rate AMDLs, and IPD thresholds, respectively. An OAE feature, specifically a characteristic dip around 2-2.5 kHz in OAE spectra, showed a significant correlation with the common factor (R = 0.54). High-rate FMDLs and AMDLs were correlated with each other (R = 0.56) but not with the other measures. The results can be interpreted as indicating that (1) the low-rate AMDLs, as well as the IPD thresholds and low-rate FMDLs, depend on the use of TFS information coded in neural phase locking and (2) the use of TFS information is influenced by a particular aspect of cochlear mechanics, such as mechanical irregularity along the BM.

Individual Differences in Auditory Brainstem Response Wave Characteristics: Relations to Different Aspects of Peripheral Hearing Loss

Little is known about how outer hair cell loss interacts with noise-induced and age-related auditory nerve degradation (i.e., cochlear synaptopathy) to affect auditory brainstem response (ABR) wave characteristics. Given that listeners with impaired audiograms likely suffer from mixtures of these hearing deficits and that ABR amplitudes have successfully been used to isolate synaptopathy in listeners with normal audiograms, an improved understanding of how different hearing pathologies affect the ABR source generators will improve their sensitivity in hearing diagnostics. We employed a functional model for human ABRs in which different combinations of hearing deficits were simulated and show that high-frequency cochlear gain loss steepens the slope of the ABR Wave-V latency versus intensity and amplitude versus intensity curves. We propose that grouping listeners according to a ratio of these slope metrics (i.e., the ABR growth ratio) might offer a way to factor out the outer hair cell loss deficit and maximally relate individual differences for constant ratios to other peripheral hearing deficits such as cochlear synaptopathy. We compared the model predictions to recorded click-ABRs from 30 participants with normal or high-frequency sloping audiograms and confirm the predicted relationship between the ABR latency growth curve and audiogram slope. Experimental ABR amplitude growth showed large individual differences and was compared with the Wave-I amplitude, Wave-V/I ratio, or the interwaveI-W latency in the same listeners. The model simulations along with the ABR recordings suggest that a hearing loss profile depicting the ABR growth ratio versus the Wave-I amplitude or Wave-V/I ratio might be able to differentiate outer hair cell deficits from cochlear synaptopathy in listeners with mixed pathologies.

A comparative study of seven human cochlear filter models

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

Physiological motivated transmission-lines as front end for loudness models

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

The vibrating reed frequency meter: digital investigation of an early cochlear model

The vibrating reed frequency meter, originally employed by Békésy and later by Wilson as a cochlear model, uses a set of tuned reeds to represent the cochlea’s graded bank of resonant elements and an elastic band threaded between them to provide nearest-neighbour coupling. Here the system, constructed of 21 reeds progressively tuned from 45 to 55 Hz, is simulated numerically as an elastically coupled bank of passive harmonic oscillators driven simultaneously by an external sinusoidal force. To uncover more detail, simulations were extended to 201 oscillators covering the range 1–2 kHz. Calculations mirror the results reported by Wilson and show expected characteristics such as traveling waves, phase plateaus, and a response with a broad peak at a forcing frequency just above the natural frequency. The system also displays additional fine-grain features that resemble those which have only recently been recognised in the cochlea. Thus, detailed analysis brings to light a secondary peak beyond the main peak, a set of closely spaced low-amplitude ripples, rapid rotation of phase as the driving frequency is swept, frequency plateaus, clustering, and waxing and waning of impulse responses. Further investigation shows that each reed’s vibrations are strongly localised, with small energy flow along the chain. The distinctive set of equally spaced ripples is an inherent feature which is found to be largely independent of boundary conditions. Although the vibrating reed model is functionally different to the standard transmission line, its cochlea-like properties make it an intriguing local oscillator model whose relevance to cochlear mechanics needs further investigation.

Phase synchronization in the cochlea at transition from mechanical waves to electrical spikes

Measured auditory nervous spikes often show synchronization, phase-locking, or entrainment (P. Cariani, Neural Plast. 6(4), 142-172 (1999) and Kumaresana et al., J. Acoust. Soc. Am. 133(6), 4290-4310 (2013). Physiologically synchronization is found in the anteroventral cochlear nucleus (Joris et al., J. Neurophysiol. 71(3), 1022-1036 (1994)) or in the trapezoid body also between critical bandwidths (Louage et al., Auditory Signal Processing: Physiology, Psychoacoustics, and Models (Springer, New York, 2004), pp. 100-106). The effect is an enhancement of pitch detection, spatial localization, or speech intelligibility. To investigate the presence of synchronization already in the cochlea, in the present paper, a finite-difference time-domain model of the cochlea is implemented with conditions for spike excitation caused by mechanical basilar membrane displacement. This model shows synchronization already in the cochlea at the transition from mechanical waves to nerve spike excitation. Using a sound as model input consisting of ten harmonic overtones with random phase relations, the output spikes are strongly phase aligned after this transition. When using a two-sinusoidal complex as input, and altering the phase relations between the two sinusoidals, the output spikes show the higher sinusoidal shifting the phase of the lower one in its direction in a systematic way. Therefore, already during the transition from mechanical to electrical excitation within the cochlea, synchronization appears to be improving perception of pitch, speech, or localization.

Functional modeling of the human auditory brainstem response to broadband stimulation

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

The spiral staircase: tonotopic microstructure and cochlear tuning

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

Modeling auditory coding: from sound to spikes

Models are valuable tools to assess how deeply we understand complex systems: only if we are able to replicate the output of a system based on the function of its subcomponents can we assume that we have probably grasped its principles of operation. On the other hand, discrepancies between model results and measurements reveal gaps in our current knowledge, which can in turn be targeted by matched experiments. Models of the auditory periphery have improved greatly during the last decades, and account for many phenomena observed in experiments. While the cochlea is only partly accessible in experiments, models can extrapolate its behavior without gap from base to apex and with arbitrary input signals. With models we can for example evaluate speech coding with large speech databases, which is not possible experimentally, and models have been tuned to replicate features of the human hearing organ, for which practically no invasive electrophysiological measurements are available. Auditory models have become instrumental in evaluating models of neuronal sound processing in the auditory brainstem and even at higher levels, where they are used to provide realistic input, and finally, models can be used to illustrate how such a complicated system as the inner ear works by visualizing its responses. The big advantage there is that intermediate steps in various domains (mechanical, electrical, and chemical) are available, such that a consistent picture of the evolvement of its output can be drawn. However, it must be kept in mind that no model is able to replicate all physiological characteristics (yet) and therefore it is critical to choose the most appropriate model—or models—for every research question. To facilitate this task, this paper not only reviews three recent auditory models, it also introduces a framework that allows researchers to easily switch between models. It also provides uniform evaluation and visualization scripts, which allow for direct comparisons between models.

Relating the Variability of Tone-Burst Otoacoustic Emission and Auditory Brainstem Response Latencies to the Underlying Cochlear Mechanics

Forward and reverse cochlear latency and its relation to the frequency tuning of the auditory filters can be assessed using tone bursts (TBs). Otoacoustic emissions (TBOAEs) estimate the cochlear roundtrip time, while auditory brainstem responses (ABRs) to the same stimuli aim at measuring the auditory filter buildup time. Latency ratios are generally close to two and controversy exists about the relationship of this ratio to cochlear mechanics. We explored why the two methods provide different estimates of filter buildup time, and ratios with large inter-subject variability, using a time-domain model for OAEs and ABRs. We compared latencies for twenty models, in which all parameters but the cochlear irregularities responsible for reflection-source OAEs were identical, and found that TBOAE latencies were much more variable than ABR latencies. Multiple reflection-sources generated within the evoking stimulus bandwidth were found to shape the TBOAE envelope and complicate the interpretation of TBOAE latency and TBOAE/ABR ratios in terms of auditory filter tuning.

Effects of spontaneous otoacoustic emissions on pure-tone frequency difference limens

Pure-tone frequency difference limens (FDLs) have been shown to vary in the vicinity of spontaneous otoacoustic emissions (SOAEs). As lower FDLs have been observed near SOAEs when measured ipsi- and contralaterally to the emission ear, it has been proposed that prolonged ongoing stimulation of nerve cells tuned to the SOAE frequency could lead to a central oversensitivity to that frequency, hence a better frequency-discrimination ability. However, it is also known that tones close in frequency to an SOAE can "entrain" the emission to oscillate at their own frequency. This may instead explain the variations in FDL near SOAE frequencies as arising from peripheral interactions between SOAEs and external tones in the cochlea. To test these two hypotheses, SOAE entrainment patterns and FDLs were recorded in seven subjects with an ipsilateral SOAE and no neighboring contralateral SOAE. Ipsilateral FDLs were lowest in the SOAE entrainment region and worsened significantly when beating between the external tone and SOAE occurred. FDLs remained unaffected in the non-emission ear and did not alter with continuous ipsilateral or contralateral presentation of a pure tone aimed at emulating an SOAE. These findings suggest a mechanical rather than neural origin for the variations in FDL near SOAE frequencies.

Further tests of the local nonlinear interaction-based mechanism for simultaneous suppression of tone burst-evoked otoacoustic emissions

Tone burst-evoked otoacoustic emission (TBOAE) components measured in response to a 1 kHz tone burst (TB1) are suppressed by the simultaneous presence of an additional tone burst (TB2). This "simultaneous suppression of TBOAEs" has been explained in terms of a mechanism based on local nonlinear interactions between the basilar membrane (BM) travelling waves caused by TB1 and TB2. A test of this local nonlinear interaction (LNI)-based mechanism, as a function of the frequency separation (Δf, expressed in kHz) between TB1 and TB2, has previously been reported by Killan et al. (2012) using a simple mathematical model [Killan et al., Hear. Res. 285, 58-64 (2012)]. The two experiments described in this paper add additional data on the extent to which the LNI-based mechanism can account for simultaneous suppression, by testing two further hypotheses derived from the model predictions. Experiment I tested the hypothesis that TBOAE suppression is directly linked to TBOAE amplitude nonlinearity where ears that exhibit a higher degree of amplitude nonlinearity yield greater suppression than more linear ears, and this relationship varies systematically as a function of Δf. In order to test this hypothesis simultaneous suppression at a range of values of Δf at 60 dB peak-equivalent sound pressure level (p.e. SPL) and TBOAE amplitude nonlinearity from normal human ears was measured. In Experiment II the hypothesis that suppression will also increase progressively as a function of increasing tone burst level was tested by measuring suppression for a range of Δf and tone burst levels at 40, 50, 60 and 70 dB p.e. SPL. The majority of the findings from both experiments provide support for the LNI-based mechanism being primarily responsible for simultaneous suppression. However, some data were inconsistent with this view. Specifically, a breakdown in the relationship between suppression and TBOAE amplitude nonlinearity at Δf = 1 (i.e. when TB2 was reasonably well separated from, and had a higher frequency than TB1) and unexpected level-dependence, most notably at Δf = 1, but also where Δf = -0.5, was observed. Either the LNI model is too simple or an alternative explanation, involving response components generated at basal regions of the basilar membrane, is required to account for these findings.

Transmission line cochlear models: improved accuracy and efficiency

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

The effect of stimulus bandwidth on the nonlinear-derived tone-burst-evoked otoacoustic emission

Intermodulation distortion has been hypothesized as a mechanism contributing to the generation of short-latency (SL) components in the transient-evoked otoacoustic emission (TEOAE). Presumably, nonlinear interactions between the frequency components within the evoking stimulus induce cochlear distortion products, which mix in the cochlea and ear canal with reflected energy from each stimulus-frequency's tonotopic place. The mixing of these different components is evidenced in the bandpass-filtered emission waveform as a series of different latency peaks. The current study tested the hypothesis that intermodulation distortion, induced within the spectral bandwidth of the evoking stimulus, is the primary mechanism through which the SL components are generated. The nonlinear-derived tone-burst-evoked OAE (TBOAEnl) was evoked using 2-kHz tone bursts with durations of 3, 6, 12, and 24 cycles. As tone burst duration doubled, the spectral bandwidth was halved. It was hypothesized that contributions to the TBOAEnl from SL components would decrease as tone burst duration increased and spectral bandwidth decreased, if the SL components were generated through intermodulation distortion. Despite differences in spectral bandwidth between the evoking stimuli, the latencies and magnitudes of the different latency components between the 3- and 6-cycle TBOAEnl were comparable. The 12- and 24-cycle TBOAEnl envelopes were characteristic of destructive phase interactions between different latency components overlapping in time. The different latency components in the 3- and 6-cycle TBOAEnl introduced a characteristic level dependency to TBOAEnl magnitude and latency when analyzed across a broad time window spanning the different components. A similar dependency described the 12- and 24-cycle TBOAEnl input/output and latency-intensity functions, suggesting that the SL components evident in the shorter-duration TBOAEnl equally contributed to the longer-duration TBOAEnl, despite reductions in spectral bandwidth. The similarity between the different TBOAEnl suggests that they share a common generation mechanism and casts doubt on intermodulation distortion as the generation mechanism of SL TEOAE components in humans.

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

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

Generation place of the long- and short-latency components of transient-evoked otoacoustic emissions in a nonlinear cochlear model

Time-domain numerical solutions of a nonlinear active cochlear model forced by click stimuli are analyzed with a time-frequency wavelet technique to identify the components of the otoacoustic response associated with different generation mechanisms/places. Previous experimental studies have shown evidence for the presence of at least two components in the transient otoacoustic response: A long-latency response, growing compressively with increasing stimulus level, and a shorter-latency response, characterized by faster growth. The possible mechanisms for the generation of the two components are discussed using the results of the numerical simulations. The model is a one-dimensional (1-D) transmission line model with nonlinear and nonlocal active terms representing the anti-damping action of the "cochlear amplifier." The dependence on the stimulus level of latency and level was measured for the different components of the response. The generation mechanisms/places of the different components were identified by varying the stimulus level and by turning off the cochlear roughness in well-defined cochlear regions. The results suggest that reflections from roughness coming from basal regions of the cochlea may give a relevant contribution to the early otoacoustic response, whereas nonlinear mechanisms seem to produce a much smaller additional contribution.

On the possibility of a place code for the low pitch of high-frequency complex tones

Harmonics are considered unresolved when they interact with neighboring harmonics and cannot be heard out separately. Several studies have suggested that the pitch derived from unresolved harmonics is coded via temporal fine-structure cues emerging from their peripheral interactions. Such conclusions rely on the assumption that the components of complex tones with harmonic ranks down to at least 9 were indeed unresolved. The present study tested this assumption via three different measures: (1) the effects of relative component phase on pitch matches, (2) the effects of dichotic presentation on pitch matches, and (3) listeners' ability to hear out the individual components. No effects of relative component phase or dichotic presentation on pitch matches were found in the tested conditions. Large individual differences were found in listeners' ability to hear out individual components. Overall, the results are consistent with the coding of individual harmonic frequencies, based on the tonotopic activity pattern or phase locking to individual harmonics, rather than with temporal coding of single-channel interactions. However, they are also consistent with more general temporal theories of pitch involving the across-channel summation of information from resolved and/or unresolved harmonics. Simulations of auditory-nerve responses to the stimuli suggest potential benefits to a spatiotemporal mechanism.