Nonlinear cochlear mechanics without direct vibration-amplification feedback

The tonotopic cochlea puzzle: A resonant transmission line with a "non-resonant" response peak

The peaked cochlear tonotopic response does not show the typical phenomenology of a resonant system. Simulations of a 2 D viscous model show that the position of the peak is determined by the competition between a sharp pressure boost due to the increase in the real part of the wavenumber as the forward wave enters the short-wave region, and a sudden increase in the viscous losses, partly counteracted by the input power provided by the outer hair cells. This viewpoint also explains the peculiar experimental behavior of the cochlear admittance (broadly tuned and almost level-independent) in the peak region.

Fluid Focusing Contributes to the BM Vibration Amplification by Boosting the Pressure

Two hydrodynamic effects are introduced in the standard transmission-line formalism, the focusing of the pressure and fluid velocity fields near the basilar membrane and the viscous damping at the fluid-basilar membrane interface, which significantly affect the cochlear response in the short-wave region. In this region, in which the wavelength is shorter than the cochlear duct height, only a layer of fluid of order of the wavelength is effectively involved in the traveling wave. This has been interpreted [8] as a reduced fluid contribution to the system inertia in the peak region, which is a viewpoint common to the 3-D FEM solutions. In this paper we propose an alternative approach, from a slightly different physical viewpoint. Invoking the fluid flux conservation along the traveling wave propagation direction, we can derive a rigorous propagation equation for the pressure integrated along the vertical axis. Consequently, the relation between the average pressure and the local pressure [4] at the fluid-BM interface can be written. The local pressure is amplified by a factor dependent on the local wavenumber with respect to the average pressure, a phenomenon we refer to as "fluid focusing", which plays a relevant role in the BM total amplification gain. This interpretation of the hydrodynamic boost to the pressure provides a physical justification to the strategy [10] of fitting the BM admittance with a polynomial containing both a conjugated pole and a zero. In the short-wave region, the sharp gradients of the velocity field yield a second important effect, a damping force on the BM motion, proportional to the local wavenumber, which stabilizes active models and shifts the peak of the response towards the base, with respect to the resonant place. This way, the peaked BM response is not that of a proper resonance, corresponding to a sharp maximum of the admittance, but rather a focusing-driven growth toward the resonant place, which is "aborted" before reaching it by the sharply increasing viscous losses. The large values of the wavenumber that ensure strong focusing are ultimately fueled, against viscosity, by the nonlinear OHC mechanism, hence the otherwise puzzling observation of a wide nonlinear gain dynamics with almost level-independent admittance.

The Shape of Noise to Come: Signal vs. Noise Amplification in the Active Cochlea

According to the dominant view, the mammalian cochlea spatially amplifies signals by actively pumping energy into the traveling wave. That is, signals are amplified as they propagate through a region where the medium's resistance is effectively negative. While signal amplification has been extensively studied in active cochlear models, the same cannot be said for amplification of internal noise. According to transmission-line theory, signals are amplified more than internal noise in regions where the net resistance is negative. Here we generalize this finding by showing that a distributed system composed of cascaded "noisy" amplifiers boosts signals more rapidly than the internal noise; the larger the amplifier gain, the larger the signal-to-noise ratio (SNR) of the amplified signal. We further show that this mechanism operates in existing active cochlear models: the cochlear amplifier increases the SNR of cochlear responses, and thus enhances cochlear sensitivity. When considering also that the cochlear amplifier narrows the bandwidth of the "cochlear filters", activation of the cochlear amplifiers dramatically increases the SNR (by about one order of magnitude in our simulations) from the tail to the peak of the traveling wave. We further demonstrate that the tapered ear-horn-like cochlear geometry significantly improves the SNR of basilar-membrane responses.

Noise within: Signal-to-noise enhancement via coherent wave amplification in the mammalian cochlea

The extraordinary sensitivity of the mammalian inner ear has captivated scientists for decades, largely due to the crucial role played by the outer hair cells (OHCs) and their unique electromotile properties. Typically arranged in three rows along the sensory epithelium, the OHCs work in concert via mechanisms collectively referred to as the "cochlear amplifier" to boost the cochlear response to faint sounds. While simplistic views attribute this enhancement solely to the OHC-based increase in cochlear gain, the inevitable presence of internal noise requires a more rigorous analysis. Achieving a genuine boost in sensitivity through amplification requires that signals be amplified more than internal noise, and this requirement presents the cochlea with an intriguing challenge. Here we analyze the effects of spatially distributed cochlear-like amplification on both signals and internal noise. By combining a straightforward mathematical analysis with a simplified model of cochlear mechanics designed to capture the essential physics, we generalize previous results about the impact of spatially coherent amplification on signal degradation in active gain media. We identify and describe the strategy employed by the cochlea to amplify signals more than internal noise and thereby enhance the sensitivity of hearing. For narrow-band signals, this effective, wave-based strategy consists of spatially amplifying the signal within a localized cochlear region, followed by rapid attenuation. Location-dependent wave amplification and attenuation meet the necessary conditions for amplifying near-characteristic frequency (CF) signals more than internal noise components of the same frequency. Our analysis reveals that the sharp wave cutoff past the CF location greatly reduces noise contamination. The distinctive asymmetric shape of the "cochlear filters" thus underlies a crucial but previously unrecognized mechanism of cochlear noise reduction.

The Noise Within: Signal-to-Noise Enhancement via Coherent Wave Amplification in the Mammalian Cochlea

The extraordinary sensitivity of the mammalian inner ear has captivated scientists for decades, largely due to the crucial role played by the outer hair cells (OHCs) and their unique electromotile properties. Typically arranged in three rows along the sensory epithelium, the OHCs work in concert via mechanisms collectively referred to as the "cochlear amplifier" to boost the cochlear response to faint sounds. While simplistic views attribute this enhancement solely to the OHC-based increase in cochlear gain, the inevitable presence of internal noise requires a more rigorous analysis. Achieving a genuine boost in sensitivity through amplification requires that signals be amplified more than internal noise, and this requirement presents the cochlea with an intriguing challenge. Here, we analyze the effects of spatially distributed cochlear-like amplification on both signals and internal noise. By combining a straightforward but powerful mathematical analysis with a simplified model of cochlear mechanics designed to capture the essential physics, we generalize previous results about the impact of spatially coherent amplification on signal degradation in active gain media. We identify and describe the strategy employed by the cochlea to amplify signals more than internal noise and thereby enhance the sensitivity of hearing. For narrowband signals, this elegant, wave-based strategy consists of spatially amplifying the signal within a localized cochlear region, followed by rapid attenuation. Location-dependent wave amplification and attenuation meet the necessary conditions for amplifying near-characteristic frequency (CF) signals more than internal noise components of the same frequency. Our analysis reveals that the sharp wave cut-off past the CF location greatly reduces noise contamination. The distinctive asymmetric shape of the "cochlear filters" thus underlies a crucial but previously unrecognized mechanism of cochlear noise reduction.

Intracochlear overdrive: Characterizing nonlinear wave amplification in the mouse apex

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

Otoacoustic emissions reveal the micromechanical role of organ-of-Corti cytoarchitecture in cochlear amplification

The intricate, crystalline cytoarchitecture of the mammalian organ of Corti presumably plays an important role in cochlear amplification. As currently understood, the oblique, Y-shaped arrangement of the outer hair cells (OHCs) and phalangeal processes of the Deiters cells serves to create differential "push-pull" forces that drive the motion of the basilar membrane via the spatial feedforward and/or feedbackward of OHC forces. In concert with the cochlear traveling wave, the longitudinal separation between OHC sensing and forcing creates phase shifts that yield a form of negative damping, amplifying waves as they propagate. Unlike active forces that arise and act locally, push-pull forces are inherently directional-whereas forward-traveling waves are boosted, reverse-traveling waves are squelched. Despite their attractions, models based on push-pull amplification must contend with otoacoustic emissions (OAEs), whose existence implies that amplified energy escapes from the inner ear via mechanisms involving reverse traveling waves. We analyze hybrid local/push-pull models to determine the constraints that reflection-source OAEs place on the directionality of cochlear wave propagation. By implementing a special force-mixing control knob, we vary the mix of local and push-pull forces while leaving the forward-traveling wave unchanged. Consistency with stimulus-frequency OAEs requires that the active forces underlying cochlear wave amplification be primarily local in character, contradicting the prevailing view. By requiring that the oblique cytoarchitecture produce predominantly local forces, we reinterpret the functional role of the Y-shaped geometry, proposing that it serves not as a push-pull amplifier, but as a mechanical funnel that spatially integrates local OHC forces.

The Remarkable Outer Hair Cell: Proceedings of a Symposium in Honour of W. E. Brownell

In 1985, Bill Brownell and colleagues published the remarkable observation that cochlear outer hair cells (OHCs) express voltage-driven mechanical motion: electromotility. They proposed OHC electromotility as the mechanism for the elusive "cochlear amplifier" required to explain the sensitivity of mammalian hearing. The finding and hypothesis stimulated an explosion of experiments that have transformed our understanding of cochlear mechanics and physiology, the evolution of hair cell structure and function, and audiology. Here, we bring together examples of current research that illustrate the continuing impact of the discovery of OHC electromotility.

The Long Outer-Hair-Cell RC Time Constant: A Feature, Not a Bug, of the Mammalian Cochlea

The cochlea of the mammalian inner ear includes an active, hydromechanical amplifier thought to arise via the piezoelectric action of the outer hair cells (OHCs). A classic problem of cochlear biophysics is that the RC (resistance-capacitance) time constant of the hair-cell membrane appears inconveniently long, producing an effective cut-off frequency much lower than that of most audible sounds. The long RC time constant implies that the OHC receptor potential-and hence its electromotile response-decreases by roughly two orders of magnitude over the frequency range of mammalian hearing, casting doubt on the hypothesized role of cycle-by-cycle OHC-based amplification in mammalian hearing. Here, we review published data and basic physics to show that the "RC problem" has been magnified by viewing it through the wrong lens. Our analysis finds no appreciable mismatch between the expected magnitude of high-frequency electromotility and the sound-evoked displacements of the organ of Corti. Rather than precluding significant OHC-based boosts to auditory sensitivity, the long RC time constant appears beneficial for hearing, reducing the effects of internal noise and distortion while increasing the fidelity of cochlear amplification.

Broad nonlinearity in reticular lamina vibrations requires compliant organ of Corti structures

In the mammalian cochlea, each longitudinal position of the basilar membrane (BM) has a nonlinear vibratory response in a limited frequency range around the location-dependent frequency of maximum response, known as the best frequency (BF). This nonlinear response arises from the electromechanical feedback from outer hair cells (OHCs). However, recent in vivo measurements have demonstrated that the mechanical response of other organ of Corti (OoC) structures, such as the reticular lamina (RL), and the electrical response of OHCs (measured in the local cochlear microphonic [LCM]) are nonlinear even at frequencies significantly below BF. In this work, a physiologically motivated model of the gerbil cochlea is used to demonstrate that the source of this discrepancy between the frequency range of the BM, RL, and LCM nonlinearities is greater compliance in the structures at the top of the OHCs. The predicted responses of the BM, RL, and LCM to pure tone and two-tone stimuli are shown to be in line with experimental evidence. Simulations then demonstrate that the sub-BF nonlinearity in the RL requires the structures at the top of the OHCs to be significantly more compliant than the BM. This same condition is also necessary for "optimal" gain near BF, i.e., high amplification that is in line with the experiment. This demonstrates that the conditions for OHCs to operate optimally at BF inevitably yield nonlinearity of the RL response over a broad frequency range.

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

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

An outer hair cell-powered global hydromechanical mechanism for cochlear amplification

It is a common belief that the mammalian cochlea achieves its exquisite sensitivity, frequency selectivity, and dynamic range through an outer hair cell-based active process, or cochlear amplification. As a sound-induced traveling wave propagates from the cochlear base toward the apex, outer hair cells at a narrow region amplify the low level sound-induced vibration through a local feedback mechanism. This widely accepted theory has been tested by measuring sound-induced sub-nanometer vibrations within the organ of Corti in the sensitive living cochleae using heterodyne low-coherence interferometry and optical coherence tomography. The aim of this short review is to summarize experimental findings on the cochlear active process by the authors' group. Our data show that outer hair cells are able to generate substantial forces for driving the cochlear partition at all audible frequencies in vivo. The acoustically induced reticular lamina vibration is larger and more broadly tuned than the basilar membrane vibration. The reticular lamina and basilar membrane vibrate approximately in opposite directions at low frequencies and in the same direction at the best frequency. The group delay of the reticular lamina is larger than that of the basilar membrane. The magnitude and phase differences between the reticular lamina and basilar membrane vibration are physiologically vulnerable. These results contradict predictions based on the local feedback mechanism but suggest a global hydromechanical mechanism for cochlear amplification. This article is part of the Special Issue Outer hair cell Edited by Joseph Santos-Sacchi and Kumar Navaratnam.

An additional source of distortion-product otoacoustic emissions from perturbation of nonlinear force by reflection from inhomogeneities

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.

Whistling While it Works: Spontaneous Otoacoustic Emissions and the Cochlear Amplifier

Perhaps the most striking evidence for active processes operating within the inner ears of mammals and non-mammals alike is their ability to spontaneously produce sound. Predicted by Thomas Gold in 1948, some 30 years prior to their discovery, the narrow-band sounds now known as spontaneous otoacoustic emissions (SOAEs) remain incompletely understood, their origins controversial. Without a single equation in the main text, we review the essential concepts underlying the "local-" and "global-oscillator" frameworks for understanding SOAE generation. Comparing their key assumptions and predictions, we relate the two frameworks to unresolved questions about the biophysical mechanisms of cochlear amplification.

Cochlear outer hair cell electromotility enhances organ of Corti motion on a cycle-by-cycle basis at high frequencies in vivo

Mammalian hearing depends on an amplification process involving prestin, a voltage-sensitive motor protein that enables cochlear outer hair cells (OHCs) to change length and generate force. However, it has been questioned whether this prestin-based somatic electromotility can operate fast enough in vivo to amplify cochlear vibrations at the high frequencies that mammals hear. In this study, we measured sound-evoked vibrations from within the living mouse cochlea and found that the top and bottom of the OHCs move in opposite directions at frequencies exceeding 20 kHz, consistent with fast somatic length changes. These motions are physiologically vulnerable, depend on prestin, and dominate the cochlea's vibratory response to high-frequency sound. This dominance was observed despite mechanisms that clearly low-pass filter the in vivo electromotile response. Low-pass filtering therefore does not critically limit the OHC's ability to move the organ of Corti on a cycle-by-cycle basis. Our data argue that electromotility serves as the primary high-frequency amplifying mechanism within the mammalian cochlea.

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

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

Reflection-Source Emissions Evoked with Clicks and Frequency Sweeps: Comparisons Across Levels

According to coherent reflection theory, otoacoustic emissions (OAE) evoked with clicks (clicked-evoked, CE) or tones (stimulus frequency, SF) originate via the same mechanism. We test this hypothesis in gerbils by investigating the similarity of CE- and SFOAEs across a wide range of stimulus levels. The results show that OAE transfer functions measured in response to clicks and sweeps have nearly equivalent time-frequency characteristics, particularly at low stimulus levels. At high stimulus levels, the two OAE types are more dissimilar, reflecting the different dynamic properties of the evoking stimulus. At mid to high stimulus levels, time-frequency analysis reveals contributions from at least two OAE source components of varying latencies. Interference between these components explains the emergence of strong spectral microstructure. Time-frequency filtering based on mean basilar-membrane (BM) group delays (τ_BM) shows that late-latency OAE components (latency ~ 1.6τ_BM) dominate at low stimulus intensities and exhibit highly compressive growth with increasing stimulus intensity. In contrast, early-latency OAE components (~ 0.7τ_BM) are small at low stimulus levels but can come to dominate the overall response at higher intensities. Although the properties of long-latency OAEs are consistent with an origin via coherent reflection near the peak of the traveling wave, the generation place and/or mechanisms responsible for the early-latency OAE components warrant further investigation. Because their delay remains in constant proportion to τ_BM across sound intensity, long-latency OAEs, whether evoked with tones or clicks, can be used to predict characteristics of cochlear processing, such as the sharpness of frequency tuning, even at high stimulus levels.

Low-passed outer hair cell response and apical-basal transition in a nonlinear transmission-line cochlear model

The low-pass characteristic of the outer hair cell (OHC) voltage response to mechanical stimulation could be considered a serious problem for cochlear models aiming at explaining high-frequency active amplification by introducing instantaneous nonlinear terms because active gain would dramatically decrease at high frequency. Evidence from experimental studies by Nam and Fettiplace [(2012). PloS One 7, e50572] suggests that the local cutoff frequency significantly increases approaching the cochlear base, somehow mitigating this problem. In this study, low-pass filtering of an internal force term, derived from a physiologically plausible OHC schematization by Lu, Zhak, Dallos, and Sarpeshkar [(2006). Hear. Res. 214, 45-67] is included in a simple one-dimensional (1-D) two-degrees-of-freedom transmission-line model by Sisto, Shera, Altoè, and Moleti [(2019). J. Acoust. Soc. Am. 146, 1685-1695] The frequency dependence of the low-pass filter phase-shift naturally yields a transition from sharp tuning and wide dynamical gain range in the basal cochlea to low tuning and poor dynamical range in the apical region. On the other hand, the frequency-dependent attenuation of low-pass filtering makes it more difficult to obtain the high gain (40-50 dB) of the basal basilar membrane response that is experimentally measured in mammals at low stimulus levels. Pressure focusing in the short-wave resonant region, which is not accounted for in this 1-D model, may help in acquiring the additional gain necessary to match the experimental data.

The cochlear ear horn: geometric origin of tonotopic variations in auditory signal processing

While separating sounds into frequency components and subsequently converting them into patterns of neural firing, the mammalian cochlea processes signal components in ways that depend strongly on frequency. Indeed, both the temporal structure of the response to transient stimuli and the sharpness of frequency tuning differ dramatically between the apical and basal (i.e., the low- and high-frequency) regions of the cochlea. Although the mechanisms that give rise to these pronounced differences remain incompletely understood, they are generally attributed to tonotopic variations in the constituent hair cells or cytoarchitecture of the organ of Corti. As counterpoint to this view, we present a general acoustic treatment of the horn-like geometry of the cochlea, accompanied by a simple 3-D model to elucidate the theoretical predictions. We show that the main apical/basal functional differences can be accounted for by the known spatial gradients of cochlear dimensions, without the need to invoke mechanical specializations of the sensory tissue. Furthermore, our analysis demonstrates that through its functional resemblance to an ear horn (aka ear trumpet), the geometry of the cochlear duct manifests tapering symmetry, a felicitous design principle that may have evolved not only to aid the analysis of natural sounds but to enhance the sensitivity of hearing.

The cochlear outer hair cell speed paradox

Cochlear outer hair cells (OHCs) are among the fastest known biological motors and are essential for high-frequency hearing in mammals. It is commonly hypothesized that OHCs amplify vibrations in the cochlea through cycle-by-cycle changes in length, but recent data suggest OHCs are low-pass filtered and unable to follow high-frequency signals. The fact that OHCs are required for high-frequency hearing but appear to be throttled by slow electromotility is the "OHC speed paradox." The present report resolves this paradox and reveals origins of ultrafast OHC function and power output in the context of the cochlear load. Results demonstrate that the speed of electromotility reflects how fast the cell can extend against the load, and does not reflect the intrinsic speed of the motor element itself or the nearly instantaneous speed at which the coulomb force is transmitted. OHC power output at auditory frequencies is revealed by emergence of an imaginary nonlinear capacitance reflecting the phase of electrical charge displacement required for the motor to overcome the viscous cochlear load.