Energy Flux in the Cochlea: Evidence Against Power Amplification of the Traveling Wave

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.

Assessment of cochlear synaptopathy by electrocochleography to low frequencies in a preclinical model and human subjects

Cochlear synaptopathy is the loss of synapses between the inner hair cells and the auditory nerve despite survival of sensory hair cells. The findings of extensive cochlear synaptopathy in animals after moderate noise exposures challenged the long-held view that hair cells are the cochlear elements most sensitive to insults that lead to hearing loss. However, cochlear synaptopathy has been difficult to identify in humans. We applied novel algorithms to determine hair cell and neural contributions to electrocochleographic (ECochG) recordings from the round window of animal and human subjects. Gerbils with normal hearing provided training and test sets for a deep learning algorithm to detect the presence of neural responses to low frequency sounds, and an analytic model was used to quantify the proportion of neural and hair cell contributions to the ECochG response. The capacity to detect cochlear synaptopathy was validated in normal hearing and noise-exposed animals by using neurotoxins to reduce or eliminate the neural contributions. When the analytical methods were applied to human surgical subjects with access to the round window, the neural contribution resembled the partial cochlear synaptopathy present after neurotoxin application in animals. This result demonstrates the presence of viable hair cells not connected to auditory nerve fibers in human subjects with substantial hearing loss and indicates that efforts to regenerate nerve fibers may find a ready cochlear substrate for innervation and resumption of function.

Interplay between traveling wave propagation and amplification at the apex of the mouse cochlea

Sounds entering the mammalian ear produce waves that travel from the base to the apex of the cochlea. An electromechanical active process amplifies traveling wave motions and enables sound processing over a broad range of frequencies and intensities. The cochlear amplifier requires combining the global traveling wave with the local cellular processes that change along the length of the cochlea given the gradual changes in hair cell and supporting cell anatomy and physiology. Thus, we measured basilar membrane (BM) traveling waves in vivo along the apical turn of the mouse cochlea using volumetric optical coherence tomography and vibrometry. We found that there was a gradual reduction in key features of the active process toward the apex. For example, the gain decreased from 23 to 19 dB and tuning sharpness decreased from 2.5 to 1.4. Furthermore, we measured the frequency and intensity dependence of traveling wave properties. The phase velocity was larger than the group velocity, and both quantities gradually decrease from the base to the apex denoting a strong dispersion characteristic near the helicotrema. Moreover, we found that the spatial wavelength along the BM was highly level dependent in vivo, such that increasing the sound intensity from 30 to 90 dB sound pressure level increased the wavelength from 504 to 874 μm, a factor of 1.73. We hypothesize that this wavelength variation with sound intensity gives rise to an increase of the fluid-loaded mass on the BM and tunes its local resonance frequency. Together, these data demonstrate a strong interplay between the traveling wave propagation and amplification along the length of the cochlea.

Rectifying and sluggish: Outer hair cells as regulators rather than amplifiers

In the cochlea, mechano-electrical transduction is preceded by dynamic range compression. Outer hair cells (OHCs) and their voltage dependent length changes, known as electromotility, play a central role in this compression process, but the exact mechanisms are poorly understood. Here we review old and new experimental findings and show that (1) just audible high-frequency tones evoke an ∼1-microvolt AC receptor potential in basal OHCs; (2) any mechanical amplification of soft high-frequency tones by OHC motility would have an adverse effect on their audibility; (3) having a higher basolateral K+ conductance, while increasing the OHC corner frequency, does not boost the magnitude of the high-frequency AC receptor potential; (4) OHC receptor currents display a substantial rectified (DC) component; (5) mechanical DC responses (baseline shifts) to acoustic stimuli, while insignificant on the basilar membrane, can be comparable in magnitude to AC responses when recorded in the organ of Corti, both in the apex and the base. In the basal turn, the DC component may even exceed the AC component, lending support to Dallos' suggestion that both apical and basal OHCs display a significant degree of rectification. We further show that (6) low-intensity cochlear traveling waves, by virtue of their abrupt transition from fast to slow propagation, are well suited to transport high-frequency energy with minimal losses (∼2-dB loss for 16-kHz tones in the gerbil); (7) a 90-dB, 16-kHz tone, if transmitted without loss to its tonotopic place, would evoke a destructive displacement amplitude of 564 nm. We interpret these findings in a framework in which local dissipation is regulated by OHC motility.

Tuned vibration modes in a miniature hearing organ: Insights from the bushcricket

Most hearing organs contain an array of sensory cells that act as miniature microphones, each tuned to its own frequency like piano strings. Acoustically communicating insects like bushcrickets have evolved miniscule hearing organs, typically smaller than 1 mm, in their forelegs. It is still unknown how the sensory structures inside the leg vibrate in response to sound. Using advanced imaging techniques, we meticulously mapped the nanovibrations in the bushcricket ear. We discovered a complex motion pattern in which structures separated by only 1/50 mm showed systematic tuning differences. Despite the insect ear’s tiny dimensions, its mode of operation strikingly resembled that of vertebrate ears. Apparently, evolution has provided similar solutions to the spectral processing of sounds.

Bushcrickets (katydids) rely on only 20 to 120 sensory units located in their forelegs to sense sound. Situated in tiny hearing organs less than 1 mm long (40× shorter than the human cochlea), they cover a wide frequency range from 1 kHz up to ultrasounds, in tonotopic order. The underlying mechanisms of this miniaturized frequency-place map are unknown. Sensory dendrites in the hearing organ (crista acustica [CA]) are hypothesized to stretch, thereby driving mechanostransduction and frequency tuning. However, this has not been experimentally confirmed. Using optical coherence tomography (OCT) vibrometry, we measured the relative motion of structures within and adjacent to the CA of the bushcricket Mecopoda elongata. We found different modes of nanovibration in the CA that have not been previously described. The two tympana and the adjacent septum of the foreleg that enclose the CA were recorded simultaneously, revealing an antiphasic lever motion strikingly reminiscent of vertebrate middle ears. Over the entire length of the CA, we were able to separate and compare vibrations of the top (cap cells) and base (dorsal wall) of the sensory tissue. The tuning of these two structures, only 15 to 60 μm (micrometer) apart, differed systematically in sharpness and best frequency, revealing a tuned periodic deformation of the CA. The relative motion of the two structures, a potential drive of transduction, demonstrated sharper tuning than either of them. The micromechanical complexity indicates that the bushcricket ear invokes multiple degrees of freedom to achieve frequency separation with a limited number of sensory cells.

State dependent effects on the frequency response of prestin's real and imaginary components of nonlinear capacitance

The outer hair cell (OHC) membrane harbors a voltage-dependent protein, prestin (SLC26a5), in high density, whose charge movement is evidenced as a nonlinear capacitance (NLC). NLC is bell-shaped, with its peak occurring at a voltage, V_h, where sensor charge is equally distributed across the plasma membrane. Thus, V_h provides information on the conformational state of prestin. V_h is sensitive to membrane tension, shifting to positive voltage as tension increases and is the basis for considering prestin piezoelectric (PZE). NLC can be deconstructed into real and imaginary components that report on charge movements in phase or 90 degrees out of phase with AC voltage. Here we show in membrane macro-patches of the OHC that there is a partial trade-off in the magnitude of real and imaginary components as interrogation frequency increases, as predicted by a recent PZE model (Rabbitt in Proc Natl Acad Sci USA 17:21880–21888, 2020). However, we find similar behavior in a simple 2-state voltage-dependent kinetic model of prestin that lacks piezoelectric coupling. At a particular frequency, F_is, the complex component magnitudes intersect. Using this metric, F_is, which depends on the frequency response of each complex component, we find that initial V_h influences F_is; thus, by categorizing patches into groups of different V_h, (above and below − 30 mV) we find that F_is is lower for the negative V_h group. We also find that the effect of membrane tension on complex NLC is dependent, but differentially so, on initial V_h. Whereas the negative group exhibits shifts to higher frequencies for increasing tension, the opposite occurs for the positive group. Despite complex component trade-offs, the low-pass roll-off in absolute magnitude of NLC, which varies little with our perturbations and is indicative of diminishing total charge movement, poses a challenge for a role of voltage-driven prestin in cochlear amplification at very high frequencies.

Interactions between Passive and Active Vibrations in the Organ of Corti In Vitro

High sensitivity and selectivity of hearing require an active cochlea. The cochlear sensory epithelium, the organ of Corti, vibrates because of external and internal excitations. The external stimulation is acoustic pressures mediated by the scala fluids, whereas the internal excitation is generated by a type of sensory receptor cells (the outer hair cells) in response to the acoustic vibrations. The outer hair cells are cellular actuators that are responsible for cochlear amplification. The organ of Corti is highly structured for transmitting vibrations originating from acoustic pressure and active outer hair cell force to the inner hair cells that synapse on afferent nerves. Understanding how the organ of Corti vibrates because of acoustic pressure and outer hair cell force is critical for explaining cochlear function. In this study, cochleae were freshly isolated from young gerbils. The organ of Corti in the excised cochlea was subjected to mechanical and electrical stimulation that are analogous to acoustic and cellular stimulation in the natural cochlea. Organ of Corti vibrations, including those of individual outer hair cells, were measured using optical coherence tomography. Respective vibration patterns due to mechanical and electrical stimulation were characterized. Interactions between the two vibration patterns were investigated by applying the two forms of stimulation simultaneously. Our results show that the interactions could be either constructive or destructive, which implies that the outer hair cells can either amplify or reduce vibrations in the organ of Corti. We discuss a potential consequence of the two interaction modes for cochlear frequency tuning.

Intracochlear Electrocochleography: Response Patterns During Cochlear Implantation and Hearing Preservation

OBJECTIVES

Electrocochleography (ECochG) obtained through a cochlear implant (CI) is increasingly being tested as an intraoperative monitor during implantation with the goal of reducing surgical trauma. Reducing trauma should aid in preserving residual hearing and improve speech perception overall. The purpose of this study was to characterize intracochlear ECochG responses throughout insertion in a range of array types and, when applicable, relate these measures to hearing preservation. The ECochG signal in cochlear implant subjects is complex, consisting of hair cell and neural generators with differing distributions depending on the etiology and history of hearing loss. Consequently, a focus was to observe and characterize response changes as an electrode advances.

DESIGN

In 36 human subjects, responses to 90 dB nHL tone bursts were recorded both at the round window (RW) and then through the apical contact of the CI as the array advanced into the cochlea. The specific setup used a sterile clip in the surgical field, attached to the ground of the implant with a software-controlled short to the apical contact. The end of the clip was then connected to standard audiometric recording equipment. The stimuli were 500 Hz tone bursts at 90 dB nHL. Audiometry for cases with intended hearing preservation (12/36 subjects) was correlated with intraoperative recordings.

RESULTS

Successful intracochlear recordings were obtained in 28 subjects. For the eight unsuccessful cases, the clip introduced excessive line noise, which saturated the amplifier. Among the successful subjects, the initial intracochlear response was a median 5.8 dB larger than the response at the RW. Throughout insertion, modiolar arrays showed median response drops after stylet removal while in lateral wall arrays the maximal median response magnitude was typically at the deepest insertion depth. Four main patterns of response magnitude were seen: increases > 5 dB (12/28), steady responses within 5 dB (4/28), drops > 5 dB (from the initial response) at shallow insertion depths (< 15 mm deep, 7/28), or drops > 5 dB occurring at deeper depths (5/28). Hearing preservation, defined as < 80 dB threshold at 250 Hz, was successful in 9/12 subjects. In these subjects, an intracochlear loss of response magnitude afforded a prediction model with poor sensitivity and specificity, which improved when phase, latency, and proportion of neural components was considered. The change in hearing thresholds across cases was significantly correlated with various measures of the absolute magnitudes of response, including RW response, starting response, maximal response, and final responses (p's < 0.05, minimum of 0.0001 for the maximal response, r's > 0.57, maximum of 0.80 for the maximal response).

CONCLUSIONS

Monitoring the cochlea with intracochlear ECochG during cochlear implantation is feasible, and patterns of response vary by device type. Changes in magnitude alone did not account for hearing preservation rates, but considerations of phase, latency, and neural contribution can help to interpret the changes seen and improve sensitivity and specificity. The correlation between the absolute magnitude obtained either before or during insertion of the ECochG and the hearing threshold changes suggest that cochlear health, which varies by subject, plays an important role.

The frequency limit of outer hair cell motility measured in vivo

Outer hair cells (OHCs) in the mammalian ear exhibit electromotility, electrically driven somatic length changes that are thought to mechanically amplify sound-evoked vibrations. For this amplification to work, OHCs must respond to sounds on a cycle-by-cycle basis even at frequencies that exceed the low-pass corner frequency of their cell membranes. Using in vivo optical vibrometry we tested this theory by measuring sound-evoked motility in the 13–25 kHz region of the gerbil cochlea. OHC vibrations were strongly rectified, and motility exhibited first-order low-pass characteristics with corner frequencies around 3 kHz– more than 2.5 octaves below the frequencies the OHCs are expected to amplify. These observations lead us to suggest that the OHCs operate more like the envelope detectors in a classical gain-control scheme than like high-frequency sound amplifiers. These findings call for a fundamental reconsideration of the role of the OHCs in cochlear function and the causes of cochlear hearing loss.

Our ears give us our sense of hearing. Their job is to collect sounds and pass this information on to the brain. Hair cells, a special group of cells in the ear, are responsible for detecting sound vibrations and turning them into the electrical signals that our brains can understand.

The ear contains two populations of hair cells: inner hair cells that send signals to the brain, and outer hair cells that act as a protective ‘buffer’ by modulating sound vibrations entering the innermost part of the ear. When outer hair cells are damaged, the vibrations picked up by inner hair cells are much smaller than in a healthy ear. This has led to the idea that outer hair cells actively amplify sounds before passing them on. That is, outer hair cells simultaneously act like microphones (by receiving sound from the environment) and loudspeakers (by re-emitting magnified vibrations).

One problem with this amplifier theory is that it cannot explain how some animals are able to hear extremely high-pitched sounds. If the theory is true, outer hair cells should be able to re-emit ultrasonic vibrations. However, some observations suggest that they may not vibrate fast enough to do so.

To test the amplifier theory, Vavakou et al. measured how outer hair cells in the ear of Mongolian gerbils responded to different sounds. This revealed that the motion of these cells could keep up with moderately high sounds (around the upper end of a piano’s range), but were too sluggish to amplify ultrasound despite gerbils having good ultrasonic hearing. Further experiments showed that instead of acting like amplifiers, outer hair cells seem to monitor the loudness of sound and adjust the level accordingly before passing the vibrations on to the inner hair cells.

These results shed new light on how outer hair cells help our ears work. Since damage to these cells can cause hearing loss, understanding how they work could one day guide new methods of protecting or even restoring hearing in vulnerable patients.

Timing of the reticular lamina and basilar membrane vibration in living gerbil cochleae

Auditory sensory outer hair cells are thought to amplify sound-induced basilar membrane vibration through a feedback mechanism to enhance hearing sensitivity. For optimal amplification, the outer hair cell-generated force must act on the basilar membrane at an appropriate time at every cycle. However, the temporal relationship between the outer hair cell-driven reticular lamina vibration and the basilar membrane vibration remains unclear. By measuring sub-nanometer vibrations directly from outer hair cells using a custom-built heterodyne low-coherence interferometer, we demonstrate in living gerbil cochleae that the reticular lamina vibration occurs after, not before, the basilar membrane vibration. Both tone- and click-induced responses indicate that the reticular lamina and basilar membrane vibrate in opposite directions at the cochlear base and they oscillate in phase near the best-frequency location. Our results suggest that outer hair cells enhance hearing sensitivity through a global hydromechanical mechanism, rather than through a local mechanical feedback as commonly supposed.

What is the quietest sound the ear can detect? All sounds begin as vibrating air molecules, which enter the ear and cause the eardrum to vibrate. We can detect vibrations that move the eardrum by a distance of less than one picometer. That’s one thousandth of a nanometer, or about 100 times smaller than a hydrogen atom. But how does the ear achieve this level of sensitivity?

Vibrations of the eardrum cause three small bones within the middle ear to vibrate. The vibrations then spread to the cochlea, a fluid-filled spiral structure in the inner ear. Tiny hair cells lining the cochlea move as a result of the vibrations. There are two types of hair cells: inner and outer. Outer hair cells amplify the vibrations. It is this amplification that enables us to detect such small movements of the eardrum. Inner hair cells then convert the amplified vibrations into electrical signals, which travel via the auditory nerve to the brain.

The bases of outer hair cells are connected to a structure called the basilar membrane, while their tops are anchored to a structure called the reticular lamina. It was generally assumed that outer hair cells amplify vibrations of the basilar membrane via a local positive feedback mechanism that requires the hair cells to vibrate first. But by comparing the timing of reticular lamina and basilar membrane vibrations in gerbils, He et al. show that this is not the case. Outer hair cells vibrate after the basilar membrane, not before. This indicates that outer hair cells use a mechanism other than commonly assumed local feedback to amplify sounds.

The results presented by He et al. change our understanding of how the cochlea works, and may help bioengineers to design better hearing aids and cochlea implants. Millions of patients worldwide who suffer from hearing loss may ultimately stand to benefit.

Vibration hotspots reveal longitudinal funneling of sound-evoked motion in the mammalian cochlea

The micromechanical mechanisms that underpin tuning and dynamic range compression in the mammalian inner ear are fundamental to hearing, but poorly understood. Here, we present new, high-resolution optical measurements that directly map sound-evoked vibrations on to anatomical structures in the intact, living gerbil cochlea. The largest vibrations occur in a tightly delineated hotspot centering near the interface between the Deiters' and outer hair cells. Hotspot vibrations are less sharply tuned, but more nonlinear, than basilar membrane vibrations, and behave non-monotonically (exhibiting hyper-compression) near their characteristic frequency. Amplitude and phase differences between hotspot and basilar membrane responses depend on both frequency and measurement angle, and indicate that hotspot vibrations involve longitudinal motion. We hypothesize that structural coupling between the Deiters' and outer hair cells funnels sound-evoked motion into the hotspot region, under the control of the outer hair cells, to optimize cochlear tuning and compression.

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.

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.

Hair Cell Transduction, Tuning, and Synaptic Transmission in the Mammalian Cochlea

Sound pressure fluctuations striking the ear are conveyed to the cochlea, where they vibrate the basilar membrane on which sit hair cells, the mechanoreceptors of the inner ear. Recordings of hair cell electrical responses have shown that they transduce sound via submicrometer deflections of their hair bundles, which are arrays of interconnected stereocilia containing the mechanoelectrical transducer (MET) channels. MET channels are activated by tension in extracellular tip links bridging adjacent stereocilia, and they can respond within microseconds to nanometer displacements of the bundle, facilitated by multiple processes of Ca2+-dependent adaptation. Studies of mouse mutants have produced much detail about the molecular organization of the stereocilia, the tip links and their attachment sites, and the MET channels localized to the lower end of each tip link. The mammalian cochlea contains two categories of hair cells. Inner hair cells relay acoustic information via multiple ribbon synapses that transmit rapidly without rundown. Outer hair cells are important for amplifying sound-evoked vibrations. The amplification mechanism primarily involves contractions of the outer hair cells, which are driven by changes in membrane potential and mediated by prestin, a motor protein in the outer hair cell lateral membrane. Different sound frequencies are separated along the cochlea, with each hair cell being tuned to a narrow frequency range; amplification sharpens the frequency resolution and augments sensitivity 100-fold around the cell's characteristic frequency. Genetic mutations and environmental factors such as acoustic overstimulation cause hearing loss through irreversible damage to the hair cells or degeneration of inner hair cell synapses. © 2017 American Physiological Society. Compr Physiol 7:1197-1227, 2017.

Reticular lamina and basilar membrane vibrations in living mouse cochleae

It is commonly believed that the exceptional sensitivity of mammalian hearing depends on outer hair cells which generate forces for amplifying sound-induced basilar membrane vibrations, yet how cellular forces amplify vibrations is poorly understood. In this study, by measuring subnanometer vibrations directly from the reticular lamina at the apical ends of outer hair cells and from the basilar membrane using a custom-built heterodyne low-coherence interferometer, we demonstrate in living mouse cochleae that the sound-induced reticular lamina vibration is substantially larger than the basilar membrane vibration not only at the best frequency but surprisingly also at low frequencies. The phase relation of reticular lamina to basilar membrane vibration changes with frequency by up to 180 degrees from ∼135 degrees at low frequencies to ∼-45 degrees at the best frequency. The magnitude and phase differences between reticular lamina and basilar membrane vibrations are absent in postmortem cochleae. These results indicate that outer hair cells do not amplify the basilar membrane vibration directly through a local feedback as commonly expected; instead, they actively vibrate the reticular lamina over a broad frequency range. The outer hair cell-driven reticular lamina vibration collaboratively interacts with the basilar membrane traveling wave primarily through the cochlear fluid, which boosts peak responses at the best-frequency location and consequently enhances hearing sensitivity and frequency selectivity.

Cochlear Outer-Hair-Cell Power Generation and Viscous Fluid Loss

Since the discovery of otoacoustic emissions and outer hair cell (OHC) motility, the fundamental question of whether the cochlea produces mechanical power remains controversial. In the present work, direct calculations are performed on power loss due to fluid viscosity and power generated by the OHCs. A three-dimensional box model of the mouse cochlea is used with a feed-forward/feed-backward approximation representing the organ of Corti cytoarchitecture. The model is fit to in vivo basilar membrane motion with one free parameter for the OHCs. The calculations predict that the total power output from the three rows of OHCs can be over three orders of magnitude greater than the acoustic input power at 10 dB sound pressure level (SPL). While previous work shows that the power gain, or the negative damping, diminishes with intensity, we show explicitly based on our model that OHC power output increases and saturates with SPL. The total OHC power output is about 2 pW at 80 dB SPL, with a maximum of about 10 fW per OHC.

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.