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The mammalian cochlea relies on the active forcing of sensory outer hair cells (OHCs) to amplify traveling wave responses along the basilar membrane. These forces are the result of electromotility, wherein current through the OHCs leads to conformational changes in the cells that provide stresses on surrounding structures. OHC transducer current can be detected via the voltage in the scala tympani (the cochlear microphonic, CM), and the CM can be used as an indicator of healthy cochlear operation. The CM represents a summation of OHC currents (the inner hair cell contribution is known to be small) and to use CM to probe the properties of OHC transduction requires a model that simulates that summation. We developed a finite element model for that purpose. The pattern of current generators (the model input) was initially based on basilar membrane displacement, with the current size based on in vitro data. The model was able to reproduce the amplitude of experimental CM results reasonably well when the input tuning was enhanced slightly (peak increased by ∼6 dB), which can be regarded as additional hair bundle tuning, and with a current/input value of 200–260 pA/nm, which is ∼4 times greater than the largest in vitro measures.

The human cochlea transforms sound waves into electrical signals in the acoustic nerve fibers with high acuity. This transformation occurs via vibrating anisotropic membranes (basilar and tectorial membranes) and frequency-specific hair cell receptors. Frequency-positions can be mapped within the cochlea to create a tonotopic chart which fits an almost-exponential function with lowest frequencies positioned apically and highest frequencies positioned at the cochlear base (Bekesy 1960, Greenwood 1961). To date, models of frequency positions have been based on a two-dimensional analysis with inaccurate representations of the cochlear hook region. In the present study, the first three-dimensional frequency analysis of the cochlea using dendritic mapping to obtain accurate tonotopic maps of the human basilar membrane/organ of Corti and the spiral ganglion was performed. A novel imaging technique, synchrotron radiation phase-contrast imaging, was used and a spiral ganglion frequency function was estimated by nonlinear least squares fitting a Greenwood-like function (F = A (10ax − K)) to the data. The three-dimensional tonotopic data presented herein has large implications for validating electrode position and creating customized frequency maps for cochlear implant recipients.

After Békésy the stapes base moves around two axes: for weaker sounds - rotates around its transverse axis; in case of a strong sound - it moves around its longitudinal axis. Békésy’s place theory cannot alone explain the frequency-distinguishing ability of the ear. However, the existence of active amplification further sharpens the frequency-analysing ability of the cochlea. In addition, the different frequency sensitivity of afferent nerve fibres of inner hair cells synergizes with the mechanisms above. Peaked resonance curves are consequences of different threshold sensitivities of nerves connecting to individual hair cells. The frequency, which belongs to the lowest stimulus threshold, is called the characteristic frequency of a nerve. This place assignment of nerve frequencies are formed by the following mechanism in the cochlea. The place of amplitude maxima of progressive waves excited in the basilar membrane shows slight frequency dependence. The mechanism of active amplification forming in outer hair cells amplifies and sharpens the resonances of the basilar membrane. In 1961, nobleman Georg von Békésy received the Nobel Prize in Medicine: “for his discoveries of the physical mechanisms of stimulation within the cochlea”.

A passive three-dimensional model of the human cochlea is described and analysed in the present article. One of its features is the implementation of a thermo-viscous boundary layer as a physically approved mechanism of mechanical damping. The model is solved numerically with the finite element method in ANSYS® and the simulation results are analysed with the help of MATLAB®. In this way curves of the basilar membrane's amplitude, phase and velocity for frequencies between 1000Hz and 8000Hz are calculated. A traveling wave develops on the basilar membrane and is damped after reaching its frequency-dependent maximum due to the boundary layer damping. A plot of the frequency-to-space transformation can be obtained which fits to the experimental data found in the literature. Furthermore, the study shows an energy analysis of the simulation verifying the boundary layer damping as a relevant physical effect for 3D-models of the cochlea.

The classic view of cochlear partition (CP) motion, generalized to be for all mammals, was derived from basal-turn measurements in laboratory animals. Recently, we reported motion of the human CP in the cochlear base that differs substantially from the classic view. We described a human soft tissue "bridge" (non-existent in the classic view) between the osseous spiral lamina (OSL) and basilar membrane (BM), and showed how OSL and bridge move in response to sound. Here, we detail relevant human anatomy to better understand the relationship between form and function. The bridge and BM have similar widths that increase linearly from base to apex, whereas the OSL width decreases from base to apex, leading to an approximately constant total CP width throughout the cochlea. The bony three-dimensional OSL microstructure, reconstructed from unconventionally thin, 2-μm histological sections, revealed thin, radially wide OSL plates with pores that vary in size, extent, and distribution with cochlear location. Polarized light microscopy revealed collagen fibers in the BM that spread out medially through the bridge to connect to the OSL. The long width and porosity of the OSL may explain its considerable bending flexibility. The similarity of BM and bridge widths along the cochlea, both containing continuous collagen fibers, may make them a functional unit and allow maximum CP motion near the bridge-BM boundary, as recently described. These anatomical findings may help us better understand the motion of the structures surrounding the organ of Corti and how they shape the input to the cochlear sensory mechanism.

Cochlear amplification of basilar membrane traveling waves is thought to occur between a tone’s characteristic frequency (CF) place and within one octave basal of the CF. Evidence for this view comes only from the cochlear base. Stimulus-frequency otoacoustic emissions (SFOAEs) provide a noninvasive alternative to direct measurements of cochlear motion that can be measured across a wide range of CF regions. Coherent reflection theory indicates that SFOAEs arise mostly from the peak region of the traveling wave, but several studies using far-basal suppressor tones claimed that SFOAE components originate many octaves basal of CF. We measured SFOAEs while perfusing guinea pig cochleas from apex to base with salicylate or KCl solutions that reduced outer-hair-cell function and SFOAE amplification. Solution effects on inner hair cells reduced auditory nerve compound action potentials (CAPs) and provided reference times for when solutions reached the SFOAE-frequency CF region. As solution flowed from apex to base, SFOAE reductions generally occurred later than CAP reductions and showed that the effects of cochlear amplification usually peaked ∼1/2 octave basal of the CF region. For tones ≥2 kHz, cochlear amplification typically extended ∼1.5 octaves basal of CF, and the data are consistent with coherent reflection theory. SFOAE amplification did not extend to the basal end of the cochlea, even though reticular lamina motion is amplified in this region, which indicates that reticular lamina motion is not directly coupled to basilar membrane traveling waves. Previous reports of SFOAE-frequency residuals produced by suppressor frequencies far above the SFOAE frequency are most likely due to additional sources created by the suppressor. For some tones

Objective The intracochlear position of an electrode array may influence the outcome after cochlear implantation. The design of the electrode array can increase the risk of trauma causing penetration of the basilar membrane or shift of the electrode array into the scala vestibuli. The aim of the present study was to identify a scalar shift after implantation of two different electrode arrays developed by one manufacturer. Study design Retrospective analysis. Setting Tertiary referral center. Patients and intervention Cochlear implant recipients implanted between 2010 and 2014 and receiving either a mid-scala (n = 30) or a perimodiolar (n = 30) electrode array. Main outcome measure Occurrence of scalar shift in association with the electrode type. Results Scalar shift occurred in 26.7% (8 of 30) of the patients implanted with a perimodiolar electrode array and in 6.7% (2 of 30) of the patients implanted with the mid-scala electrode array. The mean insertion depth in the patients experiencing scalar shift after implantation of the mid-scala electrode was much deeper (21.59 ± 0.34 mm) when compared with the mean insertion depth of the patients with scalar shift after implantation with a perimodiolar electrode array (17.85 ± 2.19 mm). There tends to be a correlation between the cochlear length and the occurrence of a scalar shift. However, the number of patients with scalar shift in the mid-scala group is rather small. Conclusion Based on the presented data, more patients implanted with a perimodiolar electrode array have a scalar shift when compared with the midscalar electrode array.

A WKB solution to the cochlear wave equation is derived, which results from the interaction between the passive dynamics of the basilar membrane and the 1D fluid coupling in the scalae, including both fluid viscosity and compressibility. The effect of various nondimensional parameters on the form of this solution is discussed. A nondimensional damping parameter and a nondimensional phase-shift parameter are shown to have the greatest influence on the response under normal conditions in the cochlea, with the fluid viscosity and compressibility only playing a minor role. It is then shown that in the case of an acoustic rainbow sensor, comprised of a discrete series of Helmholtz resonators in a duct, the governing wave equation in the continuous limit has the same form as the cochlear wave equation. The nondimensional compressibility parameter in this case is governed by the ratio of the Helmholtz resonator volume to that of the connecting duct and this parameter can be much larger than in the cochlea, and so plays a more dominant role in determining the response.

We present a 3-D finite element (FE) model of the chinchilla's inner ear consisting of the entire cochlea structure and the vestibular system. The reaction of the basilar membrane to the head rotation and the reaction of ampulla to the stapes movement were investigated. These results demonstrate the existence of hearing-vestibular system interaction. They provide an explanation to the clinical finding on the coexistence between hearing loss and equilibration dysfunction. It is a preliminary, yet critical step toward the development of a comprehensive FE model of an entire ear for mechano-acoustic analysis.

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.

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. This article is part of the Special Issue Outer hair cell Edited by Joseph Santos-Sacchi and Kumar Navaratnam.

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.

A three-dimensional finite-element (FE) model of a human head including the auditory periphery was developed to obtain a better understanding of bone-conducted (BC) hearing. The model was validated by comparison of cochlear and head responses in both air-conducted (AC) and BC hearing with experimental data. Specifically, the FE model provided the cochlear responses such as basilar membrane velocity and intracochlear pressure corresponding to BC stimulations applied to the mastoid or the conventional bone-anchored-hearing-aid (BAHA) positions. This is a strength of the model because it is difficult to obtain the cochlear responses from experiments corresponding to the BC stimulation applied at a specific position on the head surface. In addition, there have been few studies based on an FE model that can calculate the head and cochlear responses simultaneously from a BC stimulation. Moreover, in this study, the intracochlear sound pressure at multi-positions along the BM length was calculated and used to clarify the effect of stimulating force direction on the cochlear and promontory velocities in BC hearing. Also, the relationship between BC and AC stimulation and the basilar membrane velocity in the FE model was used to calculate the stimulation level at hearing thresholds which has been investigated only by psychoacoustical methods.

The article is devoted to the specific consideration of the cochlear transduction for the low level sound intensities, which correspond to the regions near the perception threshold. The basic cochlea mechanics is extended by the new concept of the molecular filters, which allows discussing the transduction mechanism on the molecular level in the space‐time domain. The molecular filters are supposed to be built on the set of the stereocilia of every inner hair cell. It is hypothesized that the molecular filters are the sensors in the feedback loop, which includes also outer hair cells along with the tectorial membrane and uses the zero compensation method to evaluate the traveling wave shape on the basilar membrane. Besides the compensation, the feedback loop, being spatially distributed along the cochlea, takes control over the tectorial membrane strain field generated by the outer hair cells, and implements it as the mechanism for the automatic gain control in the sound transduction. The numerical simulations of the traveling waves for the real sound intensities alsoconfirm the low values of the basilar membrane deformations.

The mammalian auditory system exhibits rich characteristics that has inspired research for decades. Some of these key characteristics include frequency selectivity of the basilar membrane (BM), nonlinear amplification of low-level stimuli, and compressive nonlinearity that enables the ear to sense over a large range of sound pressure levels (0–120 dB in humans). Cochlear outer hair cells (OHCs) play a vital role in the nonlinear amplification and compression of input signals and this behavior is referred to as the cochlear amplifier. Damage to OHCs due to aging, diseases, and environmental conditions often results in a sensorineural hearing loss. As a result, there is a need to develop better hearing prosthesis that transduce sound-induced vibrations to electrical signals by mimicking OHCs. In the present work, active artificial hair cells (AHCs) made of piezoelectric cantilever beams are developed to mimic the nonlinear behavior of the OHCs. In literature, AHC based prosthesis operate over a spectrum by developing an array of AHCs with different fundamental frequencies. The present work extends the frequency bandwidth of each AHC to sense over multiple resonant frequencies, unlike conventional single-channel AHCs. Therefore, a single active multi-frequency resonant AHC is presented to minimize the need for more artificial hair cells to cover the desired bandwidth of interest in an array format. Herein, the response of a 26 mm AHC to a base excitation is controlled by applying a phenomenological feedback control law that tunes the system close to a Hopf bifurcation near the first and second natural frequencies. The experimental results show a power relation of about one-third, between the output and input of the AHC. This is very similar to the compressive nonlinearity seen in the mammalian cochlea. The present effort is a continuation of the authors’ previous studies in bio-inspired nonlinear control of AHCs, which can lead to an implantable cochlear device, acoustic, or flow sensor in future.

Mammals detect sound through mechanosensitive cells of the cochlear organ of Corti that rest on the basilar membrane (BM). Motions of the BM and organ of Corti have been studied at the cochlear base in various laboratory animals, and the assumption has been that the cochleas of all mammals work similarly. In the classic view, the BM attaches to a stationary osseous spiral lamina (OSL), the tectorial membrane (TM) attaches to the limbus above the stationary OSL, and the BM is the major moving element, with a peak displacement near its center. Here, we measured the motion and studied the anatomy of the human cochlear partition (CP) at the cochlear base of fresh human cadaveric specimens. Unlike the classic view, we identified a soft-tissue structure between the BM and OSL in humans, which we name the CP “bridge.” We measured CP transverse motion in humans and found that the OSL moved like a plate hinged near the modiolus, with motion increasing from the modiolus to the bridge. The bridge moved almost as much as the BM, with the maximum CP motion near the bridge–BM connection. BM motion accounts for 100% of CP volume displacement in the classic view, but accounts for only 27 to 43% in the base of humans. In humans, the TM–limbus attachment is above the moving bridge, not above a fixed structure. These results challenge long-held assumptions about cochlear mechanics in humans. In addition, animal apical anatomy (in SI Appendix) doesn’t always fit the classic view.

The cochlear cavity is filled with viscous fluids, and it is partitioned by a viscoelastic structure called the organ of Corti complex. Acoustic energy propagates toward the apex of the cochlea through vibrations of the organ of Corti complex. The dimensions of the vibrating structures range from a few hundred (e.g., the basilar membrane) to a few micrometers (e.g., the stereocilia bundle). Vibrations of microstructures in viscous fluid are subjected to energy dissipation. Because the viscous dissipation is considered to be detrimental to the function of hearing-sound amplification and frequency tuning-the cochlea uses cellular actuators to overcome the dissipation. Compared to extensive investigations on the cellular actuators, the dissipating mechanisms have not been given appropriate attention, and there is little consensus on damping models. For example, many theoretical studies use an inviscid fluid approximation and lump the viscous effect to viscous damping components. Others neglect viscous dissipation in the organ of Corti but consider fluid viscosity. We have developed a computational model of the cochlea that incorporates viscous fluid dynamics, organ of Corti microstructural mechanics, and electrophysiology of the outer hair cells. The model is validated by comparing with existing measurements, such as the viscoelastic response of the tectorial membrane, and the cochlear input impedance. Using the model, we investigated how dissipation components in the cochlea affect its function. We found that the majority of acoustic energy dissipation of the cochlea occurs within the organ of Corti complex, not in the scalar fluids. Our model suggests that an appropriate dissipation can enhance the tuning quality by reducing the spread of energy provided by the outer hair cells' somatic motility.

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

Mammalian hearing sensitivity and frequency selectivity depend on a mechanical amplification process mediated by outer hair cells (OHCs). OHCs are situated within the organ of Corti atop the basilar membrane (BM), which supports sound-evoked traveling waves. It is well established that OHCs generate force to selectively amplify BM traveling waves where they peak, and that amplification accumulates from one location to the next over this narrow cochlear region. However, recent measurements demonstrate that traveling waves along the apical surface of the organ of Corti, the reticular lamina (RL), are amplified over a much broader region. Whether OHC forces accumulate along the length of the RL traveling wave to provide a form of “global” cochlear amplification is unclear. Here we examined the spatial accumulation of RL amplification. In mice of either sex, we used tones to suppress amplification from different cochlear regions and examined the effect on RL vibrations near and far from the traveling-wave peak. We found that although OHC forces amplify the entire RL traveling wave, amplification only accumulates near the peak, over the same region where BM motion is amplified. This contradicts the notion that RL motion is involved in a global amplification mechanism and reveals that the mechanical properties of the BM and organ of Corti tune how OHC forces accumulate spatially. Restricting the spatial buildup of amplification enhances frequency selectivity by sharpening the peaks of cochlear traveling waves and constrains the number of OHCs responsible for mechanical sensitivity at each location.SIGNIFICANCE STATEMENTOuter hair cells generate force to amplify traveling waves within the mammalian cochlea. This force generation is critical to the ability to detect and discriminate sounds. Nevertheless, how these forces couple to the motions of the surrounding structures and integrate along the cochlear length remains poorly understood. Here we demonstrate that outer hair cell-generated forces amplify traveling-wave motion on the organ of Corti throughout the wave's extent, but that these forces only accumulate longitudinally over a region near the wave's peak. The longitudinal coupling of outer hair cell-generated forces is therefore spatially tuned, likely by the mechanical properties of the basilar membrane and organ of Corti. Our findings provide new insight into the mechanical processes that underlie sensitive hearing.

The ability to detect airborne sound is essential for many animals. Examples from the inner ear of mammals and bushcrickets demonstrate that similar detection strategies evolved in taxonomically distant species. Both mammalian and bushcricket ears possess a narrow strip of sensory tissue that exhibits an anatomical gradient and traveling wave motion responses used for frequency discrimination. We measured pressure and motion in the bushcricket ear to investigate physical properties, stiffness, and mass, which govern the mechanical responses to sound. As in the mammalian cochlea, sound-induced fluid pressure and motion responses were tonotopically organized along the longitudinal axis of the crista acustica, the bushcricket’s hearing organ. The fluid pressure at the crista and crista motion were used to calculate the acoustic impedance of the organ-bounded fluid mass (Zmass). We used a theoretical wave analysis of wavelength data from a previous study to predict the crista acustica stiffness. The wave analysis also predicts Zmass, and that result agreed reasonably well with the directly measured Zmass, lending support to the theoretical wave analysis. The magnitude of the crista stiffness was similar to basilar membrane stiffness in mammals, and as in mammals, the stiffness decreased from the high-frequency to the low-frequency region. At a given location, the stiffness increased with increasing frequency, corresponding to increasing curvature of the traveling wave (decreasing wavelength), indicating that longitudinal coupling plays a substantial role in determining crista stiffness. This is in contrast to the mammalian ear, in which stiffness is independent of frequency and longitudinal coupling is relatively small.

Besides the normal hearing pathway known as air conduction (AC), sound can also transmit to the cochlea through the skull, known as bone conduction (BC). During BC stimulation, the cochlear walls demonstrate rigid body motion (RBM) and compressional motion (CPM), both inducing the basilar membrane traveling wave (TW). Despite numerous measuring and modeling efforts for the TW phenomenon, the mechanism remains unclear, especially in the case of BC. This paper proposes a 3D finite element cochlea model mimicking the TW under BC. The model uses a traditional “box model” form, but in a spiral shape, with two fluid chambers separated by the long and flexible BM. The cochlear fluid was enclosed by bony walls, the oval and round window membranes. Contingent boundary conditions and stimulations are introduced according to the physical basis of AC and BC. Particularly for BC, both RBM and CPM of the cochlea walls are simulated. Harmonic numerical solutions are obtained at multiple frequencies among the hearing range. The BM vibration amplitude ( $$U_{{{\text{BM}}}}$$ ) and its relation with volume displacement difference between the oval and round windows $$(\Delta {\text{Vol}})$$ , as well as the pressure difference at the base of the cochlea ( $$P_{{{\text{SV}}}} \left( 0 \right) - P_{{{\text{ST}}}} \left( 0 \right)$$ ), are analyzed. The simulated BM response at 12 mm from the base is peaked at about 3 k Hz, which is consistent with published experimental data. The TW properties under AC and BC are the same and have a common mechanism. (1) $$U_{{{\text{BM}}}}$$ is proportional to $${\Delta }Vol$$ at low frequencies. (2) $$U_{{{\text{BM}}}}$$ is also proportional to $$P_{{{\text{SV}}}} \left( 0 \right) - P_{{{\text{ST}}}} \left( 0 \right)$$ , within 5 dB error at high frequencies such as 16 k Hz. This study partly reveals the common quantitative relations between the TW and related factors under AC and BC hearing.

Although auditory harmonic distortion has been demonstrated psychophysically in humans and electrophysiologically in experimental animals, the cellular origin of the mechanical harmonic distortion remains unclear. To demonstrate the outer hair cell-generated harmonics within the organ of Corti, we measured sub-nanometer vibrations of the reticular lamina from the apical ends of the outer hair cells in living gerbil cochleae using a custom-built heterodyne low-coherence interferometer. The harmonics in the reticular lamina vibration are significantly larger and have broader spectra and shorter latencies than those in the basilar membrane vibration. The latency of the second harmonic is significantly greater than that of the fundamental at low stimulus frequencies. These data indicate that the mechanical harmonics are generated by the outer hair cells over a broad cochlear region and propagate from the generation sites to their own best-frequency locations., He and Ren measured sub-nanometer vibrations of the reticular lamina from the apical ends of the outer hair cells in living gerbil cochleae using a custom-built low-coherence interferometer. Their results indicate that mechanical harmonics are generated by the motile outer hair cells and can propagate to their best-frequency locations.

The cochlea, the auditory portion of the inner ear, is coiled upon itself around the modiolus like a snail shell and makes 2½ to 2¾ turns. The basal turn (the largest in diameter) is the medial wall of the middle ear, which is a domelike prominence called the promontory. The actual starting point of the basal turn which is located within the hook region near the round window could not be shown on the outer surface of the cochlea (Erixon et al. 2009). There are three compartments within the cochlea. Two of them, the scala vestibuli (associated with the vestibular window) and the scala tympani (associated with the cochlear window), contain perilymph. The third, the cochlear duct, contains endolymph. The organ of Corti, the neural end organ of hearing, rests on the basilar membrane, which connects the medial spiral lamina and lateral spiral ligament.

The inner ear, or cochlea, is a fluid-filled organ housing the mechanosensitive hair cells. Sound stimulation is relayed to the hair cells through waves that propagate on the elastic basilar membrane. Sensorineural hearing loss occurs from damage to the hair cells and cannot currently be cured. Although drugs have been proposed to prevent damage or restore functionality to hair cells, a difficulty with such treatments is ensuring adequate drug delivery to the cells. Because the cochlea is encased in the temporal bone, it can only be accessed from its basal end. However, the hair cells that are responsible for detecting speech-frequency sounds reside at the opposite, apical end. In this paper we show that steady streaming can be used to transport drugs along the cochlea. Steady streaming is a nonlinear process that accompanies many fluctuating fluid motions, including the sound-evoked waves in the inner ear. We combine an analytical approximation for the waves in the cochlea with computational fluid dynamic simulations to demonstrate that the combined steady streaming effects of several different frequencies can transport drugs from the base of the cochlea further towards the apex. Our results therefore show that multi-frequency sound stimulation can serve as a non-invasive method to transport drugs efficiently along the cochlea.

The inner hair cells in the mammalian cochlea transduce mechanical signals to electrical signals that provide input to the auditory nerve. The spatial-temporal displacement of the inner hair cell stereocilia (IHCsc) relative to basilar membrane (BM) displacement is central to characterizing the transduction process. This study specifically focuses on measuring displacement of the stereocilia hair bundles in the radial dimensions where they are most sensitive. To simplify the mechanical response of the cochlear partition, a mechanical probe was used to drive the BM. Optical imaging was used to measure radial displacement of the inner hair cell stereocilia local to the probe in ex vivo gerbil cochleae. The mechanical probe displaced the BM in the transverse direction using sinusoidal stimuli with frequencies ranging from 10 Hz to 42.5 kHz. IHCsc displacement measurements were made in the radial dimension as a function of their longitudinal location along the length of the BM. The results were used to quantify the frequency response, longitudinal space coupling, traveling wave velocity, and wavelength of the radial displacement of the stereocilia. The measurements were centered at two best frequency locations along the BM: Proximal to the round window (first turn), and in the second turn. At both locations, frequency tuning was seen that was consistent with published place maps. At both locations, traveling waves were observed simultaneously propagating basal and apical from the probe. The velocity of the traveling waves at the center frequency (CF) of the location was higher in the first turn than in the second. As the stimulus frequency increased and approached CF for a location, the traveling wavelength decreased. Differential motion of the BM and IHCsc was observed in the second turn as the stimulus frequency increased toward CF. The longitudinal coupling measured in this study was longer than observed in previous studies. In summary the results suggest that the shape of the wave patterns present on the BM are not sufficient to characterize the displacement of the IHCsc.

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.

The spatial extent of the cochlear region that actually contributes to the DPOAE signal measured in the ear canal may be evaluated experimentally using interference tones or computed numerically using nonlinear cochlear models. A nonlinear transmission-line cochlear model is used in this study to evaluate whether the recently reported nonlinear behavior of the reticular lamina (RL) over a wide basal region may be associated with generation of a significant distortion product otoacoustic emission (DPOAE) component. A two-degrees-of-freedom 1-D nonlinear model was used as discussed by Sisto et al. (2019), in which each local element consists of two coupled oscillators, roughly representing the basilar membrane (BM) and the RL. In this model, the RL shows a strongly nonlinear response over a wide region basal to the characteristic place, whereas the BM response is linear outside the narrow peak region. Such a model may be considered as that using the minimal number of degrees of freedom necessary to separately predict the motion of the BM and RL, while preserving important cochlear symmetries, such as the zero-crossing invariance of the impulse response. In the numerical simulations, the RL nonlinearity generates indeed a large intracochlear distortion product source, extended down to very basal cochlear regions. Nevertheless, due to the weak and indirect coupling between the RL motion and the differential fluid pressure in the basal part of the traveling wave path, no significant contribution from this mechanism is predicted by the model to the generation of the DPOAE signal that is eventually measured in the ear canal.

The mechanical motions that deflect outer-hair-cell (OHC) stereocilia and the resulting effects of OHC motility are reviewed, concentrating on high-frequency cochlear regions. It has been proposed that a tectorial-membrane (TM) resonance makes the phase of OHC stereocilia motion be appropriate to produce cochlear amplification, i.e. so that the OHC force that pushes the basilar membrane (BM) is in the same direction as BM velocity. Evidence for and against the TM-resonance hypothesis are considered, including new cochlear-motion measurements using optical coherence tomography, and it is concluded that there is no such TM resonance. The evidence points to there being an advance in the phase of reticular lamina (RL) radial motion at a frequency approximately ½ octave below the BM characteristic frequency, and that this is the main source of the phase difference between the TM and RL radial motions that produces cochlear amplification. It appears that the change in phase of RL radial motion comes about because of a transition between different organ-of-Corti (OoC) vibrational modes that changes RL motion relative to BM and TM motion. The origins and consequences of the large phase change of RL radial motion relative to BM motion are considered; differences in the reported patterns of these changes may be due to different viewing angles. Detailed motion data and new models are needed to better specify the vibrational patterns of the OoC modes and the role of the various OoC structures in producing the modes and the mode transition.

Stimulus-frequency otoacoustic emissions (SFOAEs) are generated by coherent reflection of forward traveling waves by perturbations along the basilar membrane. The strongest wavelets are backscattered near the place where the traveling wave reaches its maximal amplitude (tonotopic place). Therefore, the SFOAE group delay might be expected to be twice the group delay estimated in the cochlear filters. However, experimental data have yielded steady-state SFOAE components with near-zero latency. A cochlear model is used to show that short-latency SFOAE components can be generated due to nonlinear reflection of the compressor or suppressor tones used in SFOAE measurements. The simulations indicate that suppressors produce more pronounced short-latency components than compressors. The existence of nonlinear reflection components due to suppressors can also explain why SFOAEs can still be detected when suppressors are presented more than half an octave above the probe-tone frequency. Simulations of the SFOAE suppression tuning curves showed that phase changes in the SFOAE residual as the suppressor frequency increases are mostly determined by phase changes of the nonlinear reflection component.

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.

A protein in the cochlear basilar membrane promotes frequency-specific mechanical responses and auditory frequency resolution., The detection of different frequencies in sound is accomplished with remarkable precision by the basilar membrane (BM), an elastic, ribbon-like structure with graded stiffness along the cochlear spiral. Sound stimulates a wave of displacement along the BM with maximal magnitude at precise, frequency-specific locations to excite neural signals that carry frequency information to the brain. Perceptual frequency discrimination requires fine resolution of this frequency map, but little is known of the intrinsic molecular features that demarcate the place of response on the BM. To investigate the role of BM microarchitecture in frequency discrimination, we deleted extracellular matrix protein emilin 2, which disturbed the filamentous organization in the BM. Emilin2−/− mice displayed broadened mechanical and neural frequency tuning with multiple response peaks that are shifted to lower frequencies than normal. Thus, emilin 2 confers a stiffness gradient on the BM that is critical for accurate frequency resolution.

The mechanical and electrical responses of the mammalian cochlea to acoustic stimuli are nonlinear and highly tuned in frequency. This is due to the electromechanical properties of cochlear outer hair cells (OHCs). At each location along the cochlear spiral, the OHCs mediate an active process in which the sensory tissue motion is enhanced at frequencies close to the most sensitive frequency (called the characteristic frequency CF). Previous experimental results showing an approximate 0.3 cycle phase shift in the OHC-generated extracellular voltage relative the basilar membrane displacement that is initiated at a frequency approximately one-half octave lower than the CF are repeated in the present paper with similar findings. This shift is significant because it brings the phase of the OHC-derived electromotile force near to that of the basilar membrane velocity at frequencies above the shift, thereby enabling the transfer of electrical to mechanical power at the basilar membrane. In order to seek a candidate physical mechanism for this phenomenon, we used a comprehensive electromechanical mathematical model of the cochlear response to sound. The model predicts the phase shift in the extracellular voltage referenced to the basilar membrane at a frequency approximately one-half octave below CF, in accordance with the experimental data. In the model, this feature arises from a minimum in the radial impedance of the tectorial membrane and its limbal attachment. These experimental and theoretical results are consistent with the hypothesis that a tectorial membrane resonance introduces the correct phasing between mechanical and electrical responses for power generation, effectively turning on the cochlear amplifier.SIGNIFICANCEThe mechanical and electrical responses of the mammalian cochlea are nonlinear exhibiting up to a thousand-fold difference in gain depending on the frequency and level of sound stimulus. Cochlear outer hair cells (OHC) are broadband electro-mechanical energy converters that mediate this nonlinear active process. However, the mechanism by which the OHC electromotile force acquires the appropriate phase to power this nonlinearity remains unknown. By analyzing new and existing experimental data and using a mathematical model, we address this open issue. We present evidence which suggests that a relatively simple feature, the frequency dependence of the radial impedance of the tectorial membrane, provides requisite mechanics to turn on the frequency-specific nonlinear process essential for healthy hearing.

In mammals, audition is triggered by travelling waves that are evoked by acoustic stimuli in the cochlear partition, a structure containing sensory hair cells and a basilar membrane. When the cochlea is stimulated by a pure tone of low frequency, a static offset occurs in the vibration in the apical turn. In the high-frequency region at the cochlear base, multi-tone stimuli induce a quadratic distortion product in the vibrations that suggests the presence of an offset. However, vibrations below 100 Hz, including a static offset, have not been directly measured there. We therefore constructed an interferometer for detecting motion at low frequencies including 0 Hz. We applied the interferometer to record vibrations from the cochlear base of guinea pigs in response to pure tones. When the animals were exposed to sound at an intensity of 70 dB or higher, we recorded a static offset of the sinusoidally vibrating cochlear partition by more than 1 nm towards the scala vestibuli. The offset’s magnitude grew monotonically as the stimuli intensified. When stimulus frequency was varied, the response peaked around the best frequency, the frequency that maximised the vibration amplitude at threshold sound pressure. These characteristics are consistent with those found in the low-frequency region and are therefore likely common across the cochlea. The offset diminished markedly when the somatic motility of mechanosensitive outer hair cells, the force-generating machinery that amplifies the sinusoidal vibrations, was pharmacologically blocked. Therefore, the partition offset appears to be linked to the electromotile contraction of outer hair cells. Electronic supplementary material The online version of this article (10.1007/s00424-020-02373-6) contains supplementary material, which is available to authorized users.

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.

Piston prostheses of the middle ear do not ensure sufficient audibility of high and low sounds. To find out the reason, the amplitudes of the vibrations for the stapes footplate and the piston end were compared. It was seen that for a given force that oscillates with a low frequency, the amplitude of the piston end was higher than the amplitude of the stapes footplate. This means that the stiffness of the tissue sealing up the piston in the footplate hole is lower than the stiffness of the stapes plate suspension. It was shown that as a result, for the case of the higher frequencies, the amplitude of the piston vibrations drops several times. Next, it was compared a sound propagation in the healthy ear with that in the ear after the stapedotomy. To do it, a previously prepared model of sound propagation in the ear was used. The model is simplified, but it gives all parameters of the sound wave in the cochlear fluid. According to it, a motion of the stapes footplate forms a plane wave, while the piston motion initially gives a wave similar to the spherical one. A part of the spherical wave with the front directed towards the apex forms the primary wave running in the cochlea. However, the rest of this wave has the front directed towards the stapes footplate. This wave part, after a reflection from the stapes footplate, creates a secondary wave that follows the primary wave. A splitting of the wavefront around the edge of the piston end is a source of disruptions in the sound perception. The shift of the secondary wave reduces the power of the primary wave; it disturbs the waving of the basilar membrane and may cause extra noise. To justify it, a graph of the level of the cochlear amplification for the ear with the piston prosthesis was shown. The result compared with a simulation for the healthy ear gave the values 5 dB lower. To remove these drawbacks, it was proposed to place the piston end, not inside the cochlea, but in a guide in the form of a tube ended with a funnel fixed in the hole made in the stapes footplate. The piston was suspended in a guide tube on an O-ring formed of silicone gel. It was shown that when the piston is in the guide, the level of cochlear amplification was the same as that in the healthy ear. Some design details of the new piston guide are given. It enables us to make the new piston prosthesis easily and put it into practice.

Recent in vivo recordings from the mammalian cochlea indicate that although the motion of the basilar membrane appears actively amplified and nonlinear only at frequencies relatively close to the peak of the response, the internal motions of the organ of Corti display these same features over a much wider range of frequencies. These experimental findings are not easily explained by the textbook view of cochlear mechanics, in which cochlear amplification is controlled by the motion of the basilar membrane (BM) in a tight, closed-loop feedback configuration. This study shows that a simple phenomenological model of the cochlea inspired by the work of Zweig [J. Acoust. Soc. Am. 138, 1102 (2015)] can account for recent data in mouse and gerbil. In this model, the active forces are regulated indirectly, through the effect of BM motion on the pressure field across the cochlear partition, rather than via direct coupling between active-force generation and BM vibration. The absence of strong vibration-amplification feedback in the cochlea also provides a compelling explanation for the observed intensity invariance of fine time structure in the BM response to acoustic clicks.

The organ of Corti (OC) in the cochlea is a significant structure for feeling sound. The components of OC and the interaction of the part with the surroundings contribute to the fact that the passive tuning of the cochlear macrostructure is unclear. Based on the interaction between the basilar membrane (BM), tectorial membrane (TM), reticular lamina (RL), and various parts of OC, a mechanical model of the cochlea is established to study the motion patterns of each part under the action of a certain pressure. The variational principle is applied to the calculation of the analytical expression of the displacement of the BM. The results of the analytical solution differ little from the experimental value, and the variation trend is consistent, which presents the correctness of the model. The parameter sensitivity analysis is carried out for obtaining the interaction principle and the primary and secondary roles of each component in the process of the sense of sound. The results show that the absence of the TM and the decrease in the stiffness of the outer hair cells (OHCs) and OHC bundles will shift vibratory response patterns to lower frequencies, in which the lack of TM will result in the greatest reduction of CF. The absence of RL exerts a negative influence on the CF as well as the amplitude of BM and thereby loss of hearing. Therefore, both TM and RL are essential structures during the process of the sense of sound. At the same time, the resonance frequency at the base of the BM is concentrated on the high-frequency segment, while the apex of the BM is mainly in the low frequency. Different points of BM correspond to different CF, which demonstrates the frequency selectivity of the BM.

It has been demonstrated that isolated auditory sensory cells, outer hair cells, can generate distortion products at low frequencies. It remains unknown, however, whether or not motile outer hair cells are able to generate two-tone distortion at high frequencies in living cochleae under the mechanical loads caused by surounding tissues and fluids. By measuring sub-nanometer vibration directly from the apical ends of outer hair cells using a custom-built heterodyne low-coherence interferometer, here we show outer hair cell-generated two-tone distortion in reticular lamina motion in the living cochlea. Reticular-lamina distortion is significantly greater and occurs at a broader frequency range than that of the basilar membrane. Contrary to expectations, our results indicate that motile outer hair cells are capable of generating two-tone distortion in vivo not only at the locations tuned to primary tones but also at a broad region basal to these locations., Ren et al. used an in house heterodyne low-coherence interferometer to measure sub-nanometer vibrations, a proxy for distortion products, in living cochleae of gerbils. They were able to locate the generation source of the outer hair cell in the reticular lamina versus the basilar membrane in vivo.

For better understanding of bone-conducted (BC) hearing, a mechanical BC model is formulated using the Wentzel-Kramers-Brillouin (WKB) method. The BC hearing can be generally described by three main mechanisms: (1) cochlear fluid inertia, (2) in-phase motion of the outer bony shell, and (3) out-of-phase motion of the outer bony shell. Specifically, the second and third mechanisms can be identically explained by symmetric pressure compression-expansion and anti-symmetric compression-expansion, respectively. In this study, simulation results show that both the symmetric and anti-symmetric compression-expansion modes become significant at frequencies above 7 kHz while the fluid inertial mode is dominant at lower frequencies. The density difference between the scala fluid and soft cells of basilar membrane and the amplitude of the anti-symmetric compression-expansion input are identified as the difference between the air conduction and bone conduction. The natural frequency of the cochlear duct wall determines the magnitudes between the three mechanism and is approximated to be in the order of 10 MHz and above.

This study is focused on the perceived roughness of two simultaneous harmonic complex tones with ratios between their fundamental frequencies set to create intervals on just-tempered (JT) and equal-tempered (ET) scales. According to roughness theories, ET intervals should produce more roughness. However, previous studies have shown the opposite for intervals in which the lower fundamental frequency of the complex was equal to 261.6 Hz. The aim of this study is to verify and explain these results by using intervals composed of complexes whose spectral components were generated with either a sine starting phase or with a random starting phase. Results of the current study showed the same phenomenon as previous studies. To examine whether the explanation of the phenomenon lies in the function of the peripheral ear, three roughness models based upon this function were used: the Daniel and Weber (1997) model, the synchronization index (SI) model, and the model based on a hydrodynamic cochlear model. For most of the corresponding JT and ET intervals, only the Daniel and Weber (1997) model predicted less roughness in the ET intervals. In addition to this, the intervals were analyzed by a model simulating the auditory periphery. The results showed that a possible cause for the roughness differences may be in the frequencies of fluctuations of the signal in the peripheral ear. For JT intervals the fluctuations in the adjacent places on the simulated basilar membrane had either the same frequency or integer multiples of that frequency and were synchronized. Since a previous study showed that synchronized fluctuations in adjacent auditory filters lead to higher roughness than out of phase fluctuations (Terhardt, 1974), this may cause more roughness across JT and ET intervals.

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.

For the processing and detection of speech and music, the human cochlea has an exquisite sensitivity and selectivity of frequency and a dynamic range. How the cochlea performs these remarkable functions has fascinated auditory scientists for decades. Because it is not possible to measure sound-induced vibrations within the cochlea in a living human being, mathematical modeling has played an important role in cochlear mechanics. For this study, a three-dimensional human cochlear model with a fluid‒structure coupling was constructed. Time-domain analysis was performed to calculate the displacement, velocity, and stress of the basilar membrane (BM) and osseous spiral lamina (OSL) at different times in response to a pure tone stimulus. The model reproduced the traveling-wave motion of the BM. The model also showed that the cochlea's spiral shape can induce asymmetrical mechanical behavior of the BM and cause cochlear fluid to move in a radial direction; this may contribute to human sound perception. The cochlea's spiral shape not only enhances a low-frequency vibration of the BM but also changes the maximization of the positions of vibration. Therefore, the spiral's characteristics play a key role in the cochlea's frequency selectivity for low-frequency sounds. And this suggests that the OSL can react to sound as quickly as the BM. Furthermore, the basal region of the BM tends to have more stress than its other regions, and this may explain the clinical observation that human sensorineural hearing loss often occurs at high frequencies.

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

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

This paper used PATRAN software to establish a three-dimensional spiral cochlear model according to the actual human ears, combined with NASTRAN software to conduct a harmonic response analysis on it and studied the impact of curvature on the amplitude of basilar membrane when spiral basilar membrane was excited. The computational result of the model was consistent with the experimental result reported by previous researchers, which verified the correctness of the model established by this paper. Research found the change rule of ratio of outer radius amplitude to inner radius amplitude in the longitudinal direction of basilar membrane and the change trend of the horizontal amplitude with frequency along the basilar membrane. At high frequencies, it was found that curvature had a great influence on the horizontal amplitude of basilar membrane. In the meanwhile, the structural form of spiral basilar membrane and its change trend with frequency at the position of 12 mm reflected the basilar membrane’s amplification for sound intensity. Regarding the controversial issue in the academic at present, does travelling wave exist in basilar membrane? The theory of travelling wave in basilar membrane was supported by a lot of phase accumulation and delay as shown in phase diagram.

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

KEY POINTS A popular conception of mammalian cochlear physiology is that tuned mechanical vibration of the basilar membrane defines the frequency response of the innervating auditory nerve fibres However, the data supporting these concepts come from vibratory measurements at cochlear locations tuned to high frequencies (>7 kHz). Here, we measured the travelling wave in regions of the guinea pig cochlea that respond to low frequencies ( 7 kHz, not in regions sensitive to lower frequencies where human speech is encoded. Here, we overcame historical technical limitations and non-invasively measured sound-induced vibrations at four locations distributed over the apical two turns of the guinea pig cochlea. In turn 3, the responses demonstrated low-pass filter characteristics. In turn 2, the responses were low-pass-like, in that they occasionally did have a slight peak near the corner frequency. The corner frequencies of the responses were tonotopically tuned and ranged from 384 to 668 Hz. Non-linear gain, or amplification of the vibrations in response to low-intensity stimuli, was found both below and above the corner frequencies. Post mortem, cochlear gain disappeared. The non-linear gain was typically 10-30 dB and was broad-band rather than sharply tuned. However, the gain did reach nearly 50 dB in turn 2 for higher stimulus frequencies, nearly the amount of gain found in basal cochlear regions. Thus, our data prove that mechanical responses do not match neural responses and that cochlear amplification does not appreciably sharpen frequency tuning for cochlear regions that respond to frequencies

A three-dimensional inner stereocilium model is established by PATRAN. According to the relevant data, the corresponding pressure is applied to one side of the inner stereocilia. The top displacement of the inner stereocilia along the cross section of the basilar membrane (the x-displacement) is similar to the available data in the literature, which verifies the correctness of the model. Based on Castigliano’s theorem, the displacement of a single stereocilium is achieved under the inverted triangle force. The results are in good agreement with the data obtained from the finite element (FE) model, which confirms the validity of the formula. With the FE model, the effects of the movement of the hair cells and fluid in the cochlear duct on the x-displacements of the inner stereocilia are studied. The results show that the movement of the hair cells affects the x-displacements of the inner stereocilia, especially for the shortest stereocilium, and the fluid in the cochlear duct affects the x-displacements of the inner stereocilia, especially for the middle stereocilium. Moreover, compared with the effects of the hair cells on the stereocilia, the effect of the cochlear duct fluid is greater.