A canonical oscillator model of cochlear dynamics

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.

Modelling of Musical Perception using Spectral Knowledge Representation

We present a novel approach to representing perceptual and cognitive knowledge, spectral knowledge representation, that is focused on the oscillatory behaviour of the brain. The model is presented in the context of a larger hypothetical cognitive architecture. The model uses literal representations of waves to describe the dynamics of neural assemblies as they process perceived input. We show how the model can be applied to representations of sound, and usefully model music perception, specifically harmonic distance. We demonstrate that the model naturally captures both pitch and chord/key distance as empirically measured by Krumhansl and Kessler, thereby providing an underlying mechanism from which their toroidal model might arise. We evaluate our model with respect to those of Milne and others.

Testing a computational model for aural detection of aircraft in ambient noise

Computational models are used to predict the performance of human listeners for carefully specified signal and noise conditions. However, there may be substantial discrepancies between the conditions under which listeners are tested and those used for model predictions. Thus, models may predict better performance than exhibited by the listeners, or they may "fail" to capture the ability of the listener to respond to subtle stimulus conditions. This study tested a computational model devised to predict a listener's ability to detect an aircraft in various soundscapes. The model and listeners processed the same sound recordings under carefully specified testing conditions. Details of signal and masker calibration were carefully matched, and the model was tested using the same adaptive tracking paradigm. Perhaps most importantly, the behavioral results were not available to the modeler before the model predictions were presented. Recordings from three different aircraft were used as the target signals. Maskers were derived from recordings obtained at nine locations ranging from very quiet rural environments to suburban and urban settings. Overall, with a few exceptions, model predictions matched the performance of the listeners very well. Discussion focuses on those differences and possible reasons for their occurrence.

Modeling the tonotopic map using a two-dimensional array of neural oscillators

We present a model of a tonotopic map known as the Oscillatory Tonotopic Self-Organizing Map (OTSOM). It is a 2-dimensional, self-organizing array of Hopf oscillators, capable of performing a Fourier-like decomposition of the input signal. While the rows in the map encode the input phase, the columns encode frequency. Although Hopf oscillators exhibit resonance to a sinusoidal signal when there is a frequency match, there is no obvious way to also achieve phase tuning. We propose a simple method by which a pair of Hopf oscillators, unilaterally coupled through a coupling scheme termed as modified power coupling, can exhibit tuning to the phase offset of sinusoidal forcing input. The training of OTSOM is performed in 2 stages: while the frequency tuning is adapted in Stage 1, phase tuning is adapted in Stage 2. Earlier tonotopic map models have modeled frequency as an abstract parameter unconnected to any oscillation. By contrast, in OTSOM, frequency tuning emerges as a natural outcome of an underlying resonant process. The OTSOM model can possibly be regarded as an approximation of the tonotopic map found in the primary auditory cortices of mammals, particularly exemplified in the studies of echolocating bats.

Oscillatory Entrainment of the Frequency-following Response in Auditory Cortical and Subcortical Structures

There is much debate about the existence and function of neural oscillatory mechanisms in the auditory system. The frequency-following response (FFR) is an index of neural periodicity encoding that can provide a vehicle to study entrainment in frequency ranges relevant to speech and music processing. Criteria for entrainment include the presence of poststimulus oscillations and phase alignment between stimulus and endogenous activity. To test the hypothesis of entrainment, in experiment 1 we collected FFR data for a repeated syllable using magnetoencephalography (MEG) and electroencephalography in 20 male and female human adults. We observed significant oscillatory activity after stimulus offset in auditory cortex and subcortical auditory nuclei, consistent with entrainment. In these structures, the FFR fundamental frequency converged from a lower value over 100 ms to the stimulus frequency, consistent with phase alignment, and diverged to a lower value after offset, consistent with relaxation to a preferred frequency. In experiment 2, we tested how transitions between stimulus frequencies affected the MEG FFR to a train of tone pairs in 30 people. We found that the FFR was affected by the frequency of the preceding tone for up to 40 ms at subcortical levels, and even longer durations at cortical levels. Our results suggest that oscillatory entrainment may be an integral part of periodic sound representation throughout the auditory neuraxis. The functional role of this mechanism is unknown, but it could serve as a fine-scale temporal predictor for frequency information, enhancing stability and reducing susceptibility to degradation that could be useful in real-life noisy environments.SIGNIFICANCE STATEMENT Neural oscillations are proposed to be a ubiquitous aspect of neural function, but their contribution to auditory encoding is not clear, particularly at higher frequencies associated with pitch encoding. In a magnetoencephalography experiment, we found converging evidence that the frequency-following response has an oscillatory component according to established criteria: poststimulus resonance, progressive entrainment of the neural frequency to the stimulus frequency, and relaxation toward the original state on stimulus offset. In a second experiment, we found that the frequency and amplitude of the frequency-following response to tones are affected by preceding stimuli. These findings support the contribution of intrinsic oscillations to the encoding of sound, and raise new questions about their functional roles, possibly including stabilization and low-level predictive coding.

Multifrequency Hebbian plasticity in coupled neural oscillators

We study multifrequency Hebbian plasticity by analyzing phenomenological models of weakly connected neural networks. We start with an analysis of a model for single-frequency networks previously shown to learn and memorize phase differences between component oscillators. We then study a model for gradient frequency neural networks (GrFNNs) which extends the single-frequency model by introducing frequency detuning and nonlinear coupling terms for multifrequency interactions. Our analysis focuses on models of two coupled oscillators and examines the dynamics of steady-state behaviors in multiple parameter regimes available to the models. We find that the model for two distinct frequencies shares essential dynamical properties with the single-frequency model and that Hebbian learning results in stronger connections for simple frequency ratios than for complex ratios. We then compare the analysis of the two-frequency model with numerical simulations of the GrFNN model and show that Hebbian plasticity in the latter is locally dominated by a nonlinear resonance captured by the two-frequency model.

Hearing at threshold intensities: by slow mechanical traveling waves or by fast cochlear fluid pressure waves

The three modes of auditory stimulation (air, bone and soft tissue conduction) at threshold intensities are thought to share a common excitation mechanism: the stimuli induce passive displacements of the basilar membrane propagating from the base to the apex (slow mechanical traveling wave), which activate the outer hair cells, producing active displacements, which sum with the passive displacements. However, theoretical analyses and modeling of cochlear mechanics provide indications that the slow mechanical basilar membrane traveling wave may not be able to excite the cochlea at threshold intensities with the frequency discrimination observed. These analyses are complemented by several independent lines of research results supporting the notion that cochlear excitation at threshold may not involve a passive traveling wave, and the fast cochlear fluid pressures may directly activate the outer hair cells: opening of the sealed inner ear in patients undergoing cochlear implantation is not accompanied by threshold elevations to low frequency stimulation which would be expected to result from opening the cochlea, reducing cochlear impedance, altering hydrodynamics. The magnitude of the passive displacements at threshold is negligible. Isolated outer hair cells in fluid display tuned mechanical motility to fluid pressures which likely act on stretch sensitive ion channels in the walls of the cells. Vibrations delivered to soft tissue body sites elicit hearing. Thus, based on theoretical and experimental evidence, the common mechanism eliciting hearing during threshold stimulation by air, bone and soft tissue conduction may involve the fast-cochlear fluid pressures which directly activate the outer hair cells.

Mimicking the active cochlea with a fluid-coupled array of subwavelength Hopf resonators

We present a design for an acoustic metamaterial that mimics the behaviour of the active cochlea. This material is composed of a size-graded array of cylindrical subwavelength resonators, has similar dimensions to the cochlea and is able to per- form frequency separation of audible frequencies. Nonlinear amplification is introduced to the model in order to replicate the behaviour of the cochlear amplifier. This formulation takes the form of a fluid-coupled array of Hopf resonators. We seek solutions in the form of a modal decomposition, so as to retain the physically derived coupling between resonators.

A fully coupled subwavelength resonance approach to filtering auditory signals

The aim of this paper is to understand the behaviour of a large number of coupled subwavelength resonators. We use layer potential techniques in combination with numerical computations to study an acoustic pressure wave scattered by a graded array of subwavelength resonators. Using this approach, the spatial frequency separation properties of such an array can be understood. Our set-up is inspired by the graded structure of cochlear hair cells on the surface of the basilar membrane. We compute the resonant modes of the system and explore the model's ability to decompose incoming signals. We propose a mathematical explanation for phenomena identified with the cochlea's ‘travelling wave’ behaviour and tonotopic frequency map.