Fast Waves at the Base of the Cochlea

Georg von Békésy observed that the onset times of responses to brief-duration stimuli vary as a function of distance from the stapes, with basal regions starting to move earlier than apical ones. He noticed that the speed of signal propagation along the cochlea is slow when compared with the speed of sound in water. Fast traveling waves have been recorded in the cochlea, but their existence is interpreted as the result of an experiment artifact. Accounts of the timing of vibration onsets at the base of the cochlea generally agree with Békésy’s results. Some authors, however, have argued that the measured delays are too short for consistency with Békésy’s theory. To investigate the speed of the traveling wave at the base of the cochlea, we analyzed basilar membrane (BM) responses to clicks recorded at several locations in the base of the chinchilla cochlea. The initial component of the BM response matches remarkably well the initial component of the stapes response, after a 4-μs delay of the latter. A similar conclusion is reached by analyzing onset times of time-domain gain functions, which correspond to BM click responses normalized by middle-ear input. Our results suggest that BM responses to clicks arise from a combination of fast and slow traveling waves.     

Tonotopically arranged traveling waves in the miniature hearing organ of bushcrickets

Place based frequency discrimination (tonotopy) is a fundamental property of the coiled mammalian cochlea. Sound vibrations mechanically conducted to the hearing organ manifest themselves into slow moving waves that travel along the length of the organ, also referred to as traveling waves. These traveling waves form the basis of the tonotopic frequency representation in the inner ear of mammals. However, so far, due to the secure housing of the inner ear, these waves only could be measured partially over small accessible regions of the inner ear in a living animal. Here, we demonstrate the existence of tonotopically ordered traveling waves covering most of the length of a miniature hearing organ in the leg of bushcrickets in vivo using laser Doppler vibrometery. The organ is only 1 mm long and its geometry allowed us to investigate almost the entire length with a wide range of stimuli (6 to 60 kHz). The tonotopic location of the traveling wave peak was exponentially related to stimulus frequency. The traveling wave propagated along the hearing organ from the distal (high frequency) to the proximal (low frequency) part of the leg, which is opposite to the propagation direction of incoming sound waves. In addition, we observed a non-linear compression of the velocity response to varying sound pressure levels. The waves are based on the delicate micromechanics of cellular structures different to those of mammals. Hence place based frequency discrimination by traveling waves is a physical phenomenon that presumably evolved in mammals and bushcrickets independently.     

Frequency-Dependent Properties of the Tectorial Membrane Facilitate Energy Transmission and Amplification in the Cochlea

The remarkable sensitivity, frequency selectivity, and dynamic range of the mammalian cochlea relies on longitudinal transmission of minuscule amounts of energy as passive, pressure-driven, basilar membrane (BM) traveling waves. These waves are actively amplified at frequency-specific locations by a mechanism that involves interaction between the BM and another extracellular matrix, the tectorial membrane (TM). From mechanical measurements of isolated segments of the TM, we made the important new (to our knowledge) discovery that the stiffness of the TM is reduced when it is mechanically stimulated at physiologically relevant magnitudes and at frequencies below their frequency place in the cochlea. The reduction in stiffness functionally uncouples the TM from the organ of Corti, thereby minimizing energy losses during passive traveling-wave propagation. Stiffening and decreased viscosity of the TM at high stimulus frequencies can potentially facilitate active amplification, especially in the high-frequency, basal turn, where energy loss due to internal friction within the TM is less than in the apex. This prediction is confirmed by neural recordings from several frequency regions of the cochlea.     

Experimental and Theoretical Explorations of Traveling Waves and Tuning in the Bushcricket Ear

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 (Z_mass). We used a theoretical wave analysis of wavelength data from a previous study to predict the crista acustica stiffness. The wave analysis also predicts Z_mass, and that result agreed reasonably well with the directly measured Z_mass, 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.     

Hypothesis on acoustic receptive fields

A hypothesis of acoustic receptive fields is studied, which is based on the fact that the cochlea of the internal ear is a wave guide with traveling waves and the resonance in the critical layer. When a harmonic sound influences the ear, the traveling wave reaches the critical layer for the corresponding frequency and generates there a train of decaying waves about 25 periods in duration, which form a steep slope of the envelope. The funnel-shaped convergence of all neurones innervating the acoustic receptors of the Corti organ along the slope of the envelope gives rise to acoustic receptive fields. The hypothesis is consistent with some other experimental data. Such an acoustic receptive field makes it possible to use the whole train of waves in the critical layer to measure the frequency of the acting sinusoidal sound with the greatest possible accuracy. Similarly, a high accuracy of recognition of short-time sound pulses is provided, which could not be explained earlier.     

A Resonance Approach to Cochlear Mechanics

Background

How does the cochlea analyse sound into its component frequencies? In the 1850s Helmholtz thought it occurred by resonance, whereas a century later Békésy''s work indicated a travelling wave. The latter answer seemed to settle the question, but with the discovery in 1978 that the cochlea emits sound, the mechanics of the cochlea was back on the drawing board. Recent studies have raised questions about whether the travelling wave, as currently understood, is adequate to explain observations.

Approach

Applying basic resonance principles, this paper revisits the question. A graded bank of harmonic oscillators with cochlear-like frequencies and quality factors is simultaneously excited, and it is found that resonance gives rise to similar frequency responses, group delays, and travelling wave velocities as observed by experiment. The overall effect of the group delay gradient is to produce a decelerating wave of peak displacement moving from base to apex at characteristic travelling wave speeds. The extensive literature on chains of coupled oscillators is considered, and the occurrence of travelling waves, pseudowaves, phase plateaus, and forced resonance in such systems is noted.

Conclusion and significance

This alternative approach to cochlear mechanics shows that a travelling wave can simply arise as an apparently moving amplitude peak which passes along a bank of resonators without carrying energy. This highlights the possible role of the fast pressure wave and indicates how phase delays and group delays of a set of driven harmonic oscillators can generate an apparent travelling wave. It is possible to view the cochlea as a chain of globally forced coupled oscillators, and this model incorporates fundamental aspects of both the resonance and travelling wave theories.     

Finite element modelling of human auditory periphery including a feed-forward amplification of the cochlea

A three-dimensional finite element model is developed for the simulation of the sound transmission through the human auditory periphery consisting of the external ear canal, middle ear and cochlea. The cochlea is modelled as a straight duct divided into two fluid-filled scalae by the basilar membrane (BM) having an orthotropic material property with dimensional variation along its length. In particular, an active feed-forward mechanism is added into the passive cochlear model to represent the activity of the outer hair cells (OHCs). An iterative procedure is proposed for calculating the nonlinear response resulting from the active cochlea in the frequency domain. Results on the middle-ear transfer function, BM steady-state frequency response and intracochlear pressure are derived. A good match of the model predictions with experimental data from the literatures demonstrates the validity of the ear model for simulating sound pressure gain of middle ear, frequency to place map, cochlear sensitivity and compressive output for large intensity input. The current model featuring an active cochlea is able to correlate directly the sound stimulus in the ear canal with the vibration of BM and provides a tool to explore the mechanisms by which sound pressure in the ear canal is converted to a stimulus for the OHCs.     

The Importance of the Hook Region of the Cochlea for Bone-Conduction Hearing

For the most part, the coiled shape of the cochlea has been shown to have only minor importance for air-conducted hearing. It is hypothesized, however, that this coiled shape may play a more significant role for the bone-conducted (BC) route of hearing, through inertial forces exerted by the middle ear and cochlear fluid, and that this can be tested by comparing the results of applying BC stimuli in a variety of different directions. A three-dimensional finite element model of a human middle ear coupled to the inner ear was formulated. BC excitations were simulated by applying rigid-body vibrations normal to the surface of the basilar membrane (BM) at 0.8 (d¹), 5.8 (d²), 15.6 (d³), and 33.1 (d⁴) mm from the base of the cochlea, such that relative motions of the fluid within the cochlea produced excitations of the BM. The vibrational direction normal to the BM surface at the base of the cochlea (d¹) produced the highest BM velocity response across all tested frequencies—higher than an excitation direction normal to the BM surface at the nonbasal locations (d²–d⁴), even when the stimulus frequency matched the best frequency for each location. The basal part of the human cochlea features a well-developed hook region, colocated with the cochlear vestibule, that features the largest difference in fluid volume between the scala vestibuli (SV) and scala tympani (ST) found in the cochlea. The proximity of the hook region to the oval and round windows, combined with it having the biggest fluid-volume difference between the SV and ST, is thought to result in a maximization of the pressure difference between the SV and ST for BC stimuli normal to the BM in this region, and consequently a maximization of the resulting BM velocity.     

The group delay and suppression pattern of the cochlear microphonic potential recorded at the round window

Background

It is commonly assumed that the cochlear microphonic potential (CM) recorded from the round window (RW) is generated at the cochlear base. Based on this assumption, the low-frequency RW CM has been measured for evaluating the integrity of mechanoelectrical transduction of outer hair cells at the cochlear base and for studying sound propagation inside the cochlea. However, the group delay and the origin of the low-frequency RW CM have not been demonstrated experimentally.

Methodology/Principal Findings

This study quantified the intra-cochlear group delay of the RW CM by measuring RW CM and vibrations at the stapes and basilar membrane in gerbils. At low sound levels, the RW CM showed a significant group delay and a nonlinear growth at frequencies below 2 kHz. However, at high sound levels or at frequencies above 2 kHz, the RW CM magnitude increased proportionally with sound pressure, and the CM phase in respect to the stapes showed no significant group delay. After the local application of tetrodotoxin the RW CM below 2 kHz became linear and showed a negligible group delay. In contrast to RW CM phase, the BM vibration measured at location ∼2.5 mm from the base showed high sensitivity, sharp tuning, and nonlinearity with a frequency-dependent group delay. At low or intermediate sound levels, low-frequency RW CMs were suppressed by an additional tone near the probe-tone frequency while, at high sound levels, they were partially suppressed only at high frequencies.

Conclusions/Significance

We conclude that the group delay of the RW CM provides no temporal information on the wave propagation inside the cochlea, and that significant group delay of low-frequency CMs results from the auditory nerve neurophonic potential. Suppression data demonstrate that the generation site of the low-frequency RW CM shifts from apex to base as the probe-tone level increases.     

The Importance of the Hook Region of the Cochlea for Bone-Conduction Hearing

For the most part, the coiled shape of the cochlea has been shown to have only minor importance for air-conducted hearing. It is hypothesized, however, that this coiled shape may play a more significant role for the bone-conducted (BC) route of hearing, through inertial forces exerted by the middle ear and cochlear fluid, and that this can be tested by comparing the results of applying BC stimuli in a variety of different directions. A three-dimensional finite element model of a human middle ear coupled to the inner ear was formulated. BC excitations were simulated by applying rigid-body vibrations normal to the surface of the basilar membrane (BM) at 0.8 (d¹), 5.8 (d²), 15.6 (d³), and 33.1 (d⁴) mm from the base of the cochlea, such that relative motions of the fluid within the cochlea produced excitations of the BM. The vibrational direction normal to the BM surface at the base of the cochlea (d¹) produced the highest BM velocity response across all tested frequencies—higher than an excitation direction normal to the BM surface at the nonbasal locations (d²–d⁴), even when the stimulus frequency matched the best frequency for each location. The basal part of the human cochlea features a well-developed hook region, colocated with the cochlear vestibule, that features the largest difference in fluid volume between the scala vestibuli (SV) and scala tympani (ST) found in the cochlea. The proximity of the hook region to the oval and round windows, combined with it having the biggest fluid-volume difference between the SV and ST, is thought to result in a maximization of the pressure difference between the SV and ST for BC stimuli normal to the BM in this region, and consequently a maximization of the resulting BM velocity.     

Microstructures in the Organ of Corti Help Outer Hair Cells Form Traveling Waves along the Cochlear Coil

According to the generally accepted theory of mammalian cochlear mechanics, the fluid in the cochlear scalae interacts with the elastic cochlear partition to generate transversely oscillating displacement waves that propagate along the cochlear coil. Using a computational model of cochlear segments, a different type of propagating wave is reported, an elastic propagating wave that is independent of the fluid-structure interaction. The characteristics of the propagating wave observed in the model, such as the wavelength, speed, and phase lag, are similar to those observed in the living cochlea. Three conditions are required for the existence of the elastic propagating wave in the cochlear partition without fluid-interaction: 1), the stiffness gradient of the cochlear partition; 2), the elastic longitudinal coupling; and 3), the Y-shaped structure in the organ of Corti formed by the outer hair cell, the Deiters cell, and the Deiters cell phalangeal process. The elastic propagating waves in the cochlear partition disappeared without the push-pull action provided by the outer hair cell and Deiters cell phalangeal process. The results suggest that the mechanical feedback of outer hair cells, facilitated by the organ of Corti microstructure, can control the tuning and amplification by modulating the cochlear traveling wave.     

Microstructures in the Organ of Corti Help Outer Hair Cells Form Traveling Waves along the Cochlear Coil

According to the generally accepted theory of mammalian cochlear mechanics, the fluid in the cochlear scalae interacts with the elastic cochlear partition to generate transversely oscillating displacement waves that propagate along the cochlear coil. Using a computational model of cochlear segments, a different type of propagating wave is reported, an elastic propagating wave that is independent of the fluid-structure interaction. The characteristics of the propagating wave observed in the model, such as the wavelength, speed, and phase lag, are similar to those observed in the living cochlea. Three conditions are required for the existence of the elastic propagating wave in the cochlear partition without fluid-interaction: 1), the stiffness gradient of the cochlear partition; 2), the elastic longitudinal coupling; and 3), the Y-shaped structure in the organ of Corti formed by the outer hair cell, the Deiters cell, and the Deiters cell phalangeal process. The elastic propagating waves in the cochlear partition disappeared without the push-pull action provided by the outer hair cell and Deiters cell phalangeal process. The results suggest that the mechanical feedback of outer hair cells, facilitated by the organ of Corti microstructure, can control the tuning and amplification by modulating the cochlear traveling wave.     

Waves on Reissner's membrane: a mechanism for the propagation of otoacoustic emissions from the cochlea

Sound is detected and converted into electrical signals within the ear. The cochlea not only acts as a passive detector of sound, however, but can also produce tones itself. These otoacoustic emissions are a striking manifestation of the cochlea's mechanical active process. A controversy remains of how these mechanical signals propagate back to the middle ear, from which they are emitted as sound. Here, we combine theoretical and experimental studies to show that mechanical signals can be transmitted by waves on Reissner's membrane, an elastic structure within the cochlea. We develop a theory for wave propagation on Reissner's membrane and its role in otoacoustic emissions. Employing a scanning laser interferometer, we measure traveling waves on Reissner's membrane in the gerbil, guinea pig, and chinchilla. The results are in accord with the theory and thus support a role for Reissner's membrane in otoacoustic emissions.     

Physical and physiological properties of the crayfish antennal flagellum.

(1) Mechanoreceptors in the crayfish antennae are divided into four functional categories: vibration (13%), bidirectional displacement (19%), unidirectional displacement (45%), and position (23%) receptors. The distribution of receptors along the length of the flagellum follows a logarithmic progression, decreasing from about 40% at the base to less than 5% at the tip. (2) Vibratory stimulation of the antennae was found to induce a traveling wave. Because of an impedance gradient along the length of the flagellum, the traveling wave moves most efficiently from base to tip. The wave was observed to travel at an average velocity of 6.0 m/sec. (3) Large deflections of the tip are not uniformly transferred to the base, but decrease logarithmically. This due to the existence of the impedance gradient. (4) Receptor output probability was found to be greatest when low frequency/high intensity stimulation was applied to the flagellar base. (5) Characteristics of large (2 cm) posterior-going deflections of the flagellar tip that are effective in producing response differences are displacement: (a) amplitude, (b) velocity, and (c) acceleration.     

Model of cochlear microphonic explores the tuning and magnitude of hair cell transduction current

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.     

Tuning the cochlea: wave-mediated positive feedback between cells

Frequency analysis by the mammalian cochlea is traditionally thought to occur via a hydrodynamically coupled ‘travelling wave’ along the basilar membrane. A persistent difficulty with this picture is how sharp tuning can emerge. This paper proposes, and models, a supplementary or alternative mechanism: it supposes that the cochlea analyses sound by setting up standing waves between parallel rows of outer hair cells. In this scheme, multiple cells mutually interact through positive feedback of wave-borne energy. Analytical modelling and numerical evaluation presented here demonstrate that this can provide narrow-band frequency analysis. Graded cochlear tuning will then rely on the distance between rows becoming greater as distance from the base increases (as exhibited by the actual cochlea) and on the wave’s phase velocity becoming slower. In effect, tuning is now a case of varying the feedback delay between the rows, and a prime candidate for a wave exhibiting suitably graded phase velocity—a short-wavelength ‘squirting wave’—is identified and used in the modelling. In this way, resonance between rows could supply both amplification and high Q, characteristics underlying the ‘cochlear amplifier’—the device whose action has long been evident to auditory science but whose anatomical basis and mode of operation are still obscure.     

Physical and physiological properties of the crayfish antennal flagellum

• (1) Mechanoreceptors in the crayfish antennae are divided into four functional categories: vibration (13%), bidirectional displacement (19%), unidirectional displacement (45%), and position (23%) receptors. The distribution of receptors along the length of the flagellum follows a logarithmic progression, decreasing from about 40% at the base to less than 5% at the tip.
• (2) Vibratory stimulation of the antennae was found to induce a traveling wave. Because of an impedance gradient along the length of the flagellum, the traveling wave moves most efficiently from base to tip. The wave was observed to travel at an average velocity of 6.0 m/sec.
• (3) Large deflections of the tip are not uniformly transferred to the base, but decrease logarithmically. This is due to the existence of the impedance gradient.
• (4) Receptor output probability was found to be greatest when low frequency/high intensity stimulation was applied to the flagellar base.
• (5) Characteristics of large (2 cm) posterior-going deflections of the flagellar tip that are effective in producing response differences are displacement: (a) amplitude, (b) velocity, and (c) acceleration.

     

On the mysterious propulsion of Synechococcus

We propose a model for the self-propulsion of the marine bacterium Synechococcus utilizing a continuous looped helical track analogous to that found in Myxobacteria [1]. In our model cargo-carrying protein motors, driven by proton-motive force, move along a continuous looped helical track. The movement of the cargo creates surface distortions in the form of small amplitude traveling ridges along the S-layer above the helical track. The resulting fluid motion adjacent to the helical ribbon provides the propulsive thrust. A variation on the helical rotor model of [1] allows the motors to be anchored to the peptidoglycan layer, where they drive rotation of the track creating traveling helical waves along the S-layer. We derive expressions relating the swimming speed to the amplitude, wavelength, and velocity of the surface waves induced by the helical rotor, and show that they fall in reasonable ranges to explain the velocity and rotation rate of swimming Synechococcus.     

The Spatial Origins of Cochlear Amplification Assessed by Stimulus-Frequency Otoacoustic Emissions

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 <2 kHz, SFOAE amplification extended two octaves apical of CF, which highlights that different vibratory motions produce SFOAEs and CAPs, and that the amplification region depends on the cochlear mode of motion considered. The concept that there is a single “cochlear amplification region” needs to be revised.