A two-layer outer hair cell model with orthotropic piezoelectric properties: correlation of cell resonant frequencies with tuning in the cochlea

The frequency response of outer hair cells (OHCs) of different lengths is studied using a mathematical model of a two-layer cylindrical shell with orthotropic properties. Material properties in the model are determined from experimental measurements reported in the literature, and the variation of material properties with the cell length is studied. The cortical lattice's Poisson ratios are found to remain fairly constant with cell length, while its stiffness changes significantly with cell length. The natural frequencies corresponding to several modes of deformation of an OHC with intracellular and extracellular fluids are calculated from this model. Our results suggest that the best frequency in the cochlea at the position where the OHC is located corresponds to different modes of deformation of the OHC, depending on the OHC length. For short OHCs, the best frequency is close to the natural frequency of the axisymmetric mode; for long OHCs, it is close to the natural frequencies of the beam-like bending and pinched modes. Such a difference in resonant modes for short and long OHCs at the best frequency suggests that different modes of OHC elongation motility may be present in amplifying the basilar membrane motion in the high and low frequency regions of the cochlea.     

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.     

The endocochlear potential alters cochlear micromechanics

Acoustic stimulation gates mechanically sensitive ion channels in cochlear sensory hair cells. Even in the absence of sound, a fraction of these channels remains open, forming a conductance between hair cells and the adjacent fluid space, scala media. Restoring the lost endogenous polarization of scala media in an in vitro preparation of the whole cochlea depolarizes the hair cell soma. Using both digital laser interferometry and time-resolved confocal imaging, we show that this causes a structural refinement within the organ of Corti that is dependent on the somatic electromotility of the outer hair cells (OHCs). Specifically, the inner part of the reticular lamina up to the second row of OHCs is pulled toward the basilar membrane, whereas the outer part (third row of OHCs and the Hensen's cells) unexpectedly moves in the opposite direction. A similar differentiated response pattern is observed for sound-evoked vibrations: restoration of the endogenous polarization decreases vibrations of the inner part of the reticular lamina and results in up to a 10-fold increase of vibrations of the outer part. We conclude that the endogenous polarization of scala media affects the function of the hearing organ by altering its geometry, mechanical and electrical properties.     

Detection without deflection? A hypothesis for direct sensing of sound pressure by hair cells

It is widely thought that organisms detect sound by sensing the deflection of hair-like projections, the stereocilia, at the apex of hair cells. In the case of mammals, the standard interpretation is that hair cells in the cochlea respond to deflection of stereocilia induced by motion generated by a hydrodynamic travelling wave. But in the light of persistent anomalies, an alternative hypothesis seems to have some merit: that sensing cells (in particular the outer hair cells) may, at least at low intensities, be reacting to a different stimulus — the rapid pressure wave that sweeps through the cochlear fluids at the speed of sound in water. This would explain why fast responses are sometimes seen before the peak of the travelling wave. Yet how could cells directly sense fluid pressure? Here, a model is constructed of the outer hair cell as a pressure vessel able to sense pressure variations across its cuticular pore, and this ‘fontanelle’ model, based on the sensing action of the basal body at this compliant spot, could explain the observed anomalies. Moreover, the fontanelle model can be applied to a wide range of other organisms, suggesting that direct pressure detection is a general mode of sensing complementary to stereociliar displacement.     

Detection of Cochlear Amplification and Its Activation

The operation of the mammalian cochlea relies on a mechanical traveling wave that is actively boosted by electromechanical forces in sensory outer hair cells (OHCs). This active cochlear amplifier produces the impressive sensitivity and frequency resolution of mammalian hearing. The cochlear amplifier has inspired scientists since its discovery in the 1970s, and is still not well understood. To explore cochlear electromechanics at the sensory cell/tissue interface, sound-evoked intracochlear pressure and extracellular voltage were measured using a recently developed dual-sensor with a microelectrode attached to a micro-pressure sensor. The resulting coincident in vivo observations of OHC electrical activity, pressure at the basilar membrane and basilar membrane displacement gave direct evidence for power amplification in the cochlea. Moreover, the results showed a phase shift of voltage relative to mechanical responses at frequencies slightly below the peak, near the onset of amplification. Based on the voltage-force relationship of isolated OHCs, the shift would give rise to effective OHC pumping forces within the traveling wave peak. Thus, the shift activates the cochlear amplifier, serving to localize and thus sharpen the frequency region of amplification. These results are the most concrete evidence for cochlear power amplification to date and support OHC somatic forces as its source.     

Detection of Cochlear Amplification and Its Activation

The operation of the mammalian cochlea relies on a mechanical traveling wave that is actively boosted by electromechanical forces in sensory outer hair cells (OHCs). This active cochlear amplifier produces the impressive sensitivity and frequency resolution of mammalian hearing. The cochlear amplifier has inspired scientists since its discovery in the 1970s, and is still not well understood. To explore cochlear electromechanics at the sensory cell/tissue interface, sound-evoked intracochlear pressure and extracellular voltage were measured using a recently developed dual-sensor with a microelectrode attached to a micro-pressure sensor. The resulting coincident in vivo observations of OHC electrical activity, pressure at the basilar membrane and basilar membrane displacement gave direct evidence for power amplification in the cochlea. Moreover, the results showed a phase shift of voltage relative to mechanical responses at frequencies slightly below the peak, near the onset of amplification. Based on the voltage-force relationship of isolated OHCs, the shift would give rise to effective OHC pumping forces within the traveling wave peak. Thus, the shift activates the cochlear amplifier, serving to localize and thus sharpen the frequency region of amplification. These results are the most concrete evidence for cochlear power amplification to date and support OHC somatic forces as its source.     

Power Efficiency of Outer Hair Cell Somatic Electromotility

Cochlear outer hair cells (OHCs) are fast biological motors that serve to enhance the vibration of the organ of Corti and increase the sensitivity of the inner ear to sound. Exactly how OHCs produce useful mechanical power at auditory frequencies, given their intrinsic biophysical properties, has been a subject of considerable debate. To address this we formulated a mathematical model of the OHC based on first principles and analyzed the power conversion efficiency in the frequency domain. The model includes a mixture-composite constitutive model of the active lateral wall and spatially distributed electro-mechanical fields. The analysis predicts that: 1) the peak power efficiency is likely to be tuned to a specific frequency, dependent upon OHC length, and this tuning may contribute to the place principle and frequency selectivity in the cochlea; 2) the OHC power output can be detuned and attenuated by increasing the basal conductance of the cell, a parameter likely controlled by the brain via the efferent system; and 3) power output efficiency is limited by mechanical properties of the load, thus suggesting that impedance of the organ of Corti may be matched regionally to the OHC. The high power efficiency, tuning, and efferent control of outer hair cells are the direct result of biophysical properties of the cells, thus providing the physical basis for the remarkable sensitivity and selectivity of hearing.     

Optimal Electrical Properties of Outer Hair Cells Ensure Cochlear Amplification

The organ of Corti (OC) is the auditory epithelium of the mammalian cochlea comprising sensory hair cells and supporting cells riding on the basilar membrane. The outer hair cells (OHCs) are cellular actuators that amplify small sound-induced vibrations for transmission to the inner hair cells. We developed a finite element model of the OC that incorporates the complex OC geometry and force generation by OHCs originating from active hair bundle motion due to gating of the transducer channels and somatic contractility due to the membrane protein prestin. The model also incorporates realistic OHC electrical properties. It explains the complex vibration modes of the OC and reproduces recent measurements of the phase difference between the top and the bottom surface vibrations of the OC. Simulations of an individual OHC show that the OHC somatic motility lags the hair bundle displacement by ∼90 degrees. Prestin-driven contractions of the OHCs cause the top and bottom surfaces of the OC to move in opposite directions. Combined with the OC mechanics, this results in ∼90 degrees phase difference between the OC top and bottom surface vibration. An appropriate electrical time constant for the OHC membrane is necessary to achieve the phase relationship between OC vibrations and OHC actuations. When the OHC electrical frequency characteristics are too high or too low, the OHCs do not exert force with the correct phase to the OC mechanics so that they cannot amplify. We conclude that the components of OHC forward and reverse transduction are crucial for setting the phase relations needed for amplification.     

Imaging electrically evoked micromechanical motion within the organ of corti of the excised gerbil cochlea

The outer hair cell (OHC) of the mammalian inner ear exhibits an unusual form of somatic motility that can follow membrane-potential changes at acoustic frequencies. The cellular forces that produce this motility are believed to amplify the motion of the cochlear partition, thereby playing a key role in increasing hearing sensitivity. To better understand the role of OHC somatic motility in cochlear micromechanics, we developed an excised cochlea preparation to visualize simultaneously the electrically-evoked motion of hundreds of cells within the organ of Corti (OC). The motion was captured using stroboscopic video microscopy and quantified using cross-correlation techniques. The OC motion at approximately 2-6 octaves below the characteristic frequency of the region was complex: OHC, Deiter's cell, and Hensen's cell motion were hundreds of times larger than the tectorial membrane, reticular lamina (RL), and pillar cell motion; the inner rows of OHCs moved antiphasic to the outer row; OHCs pivoted about the RL; and Hensen's cells followed the motion of the outer row of OHCs. Our results suggest that the effective stimulus to the inner hair cell hair bundles results not from a simple OC lever action, as assumed by classical models, but by a complex internal motion coupled to the RL.     

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.     

Evoked acoustic oto-emissions: effects of atropine

The Evoked Otoacoustic Emissions (EOE) are a sinusoidal wave complex coming from the contractile properties of the cochlea and particularly of the outer hair cells. This activity is influenced by the centrifugal pathways whose transmitter is acetylcholine. In order to study the effects of the functional block of the cochlea, ten young normal subjects were examined recording the EOE before and ten mins after the i.v. infusion of 1 mg of atropine. The statistical analysis of the results has shown a significant decrease only in EOE appearance threshold in absence of modifications of the saturation level. These data have led us to believe that atropine blocking of the centrifugal pathways causes a disfunction of the outer hair cells that accept less energy to be transduced into a neural stimulus and on the other hand more energy as EOEs.     

Preferential expression of transient potassium current (IA) by 'short' hair cells of the chick's cochlea

We have made a comparative study of the membrane properties of tall and short hair cells isolated from a selected region of the chick's cochlea. Tall hair cells are analogous to inner cochlear hair cells of mammals, and like those, are presynaptic to the majority of afferent neurons in the cochlea. Short hair cells, like mammalian outer hair cells, are the postsynaptic targets of efferent neurons that inhibit the cochlea. Voltage-clamp recordings have revealed that short hair cells have an inactivating potassium (K) current, IA, whereas tall hair cells have little or none. Short hair cells are also sensitive to the cholinergic agonist carbachol, whereas tall hair cells are not. This pattern is in accord with the selective distribution of efferent cholinergic synapses in the cochlea. Although IA is completely inactivated at the resting potential of the short hair cells, cholinergic agonists can hyperpolarize these cells by as much as 30 mV. This hyperpolarization removes inactivation and allows IA to modulate subsequent voltage-dependent processes in short hair cells. It is concluded that IA could increase the high frequency response of the hair cell by decreasing membrane resistance and thus the membrane time constant after inhibition. This will be of particular importance to cochlear function if short hair cells produce voltage-dependent movements, as do mammalian outer hair cells.     

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.     

Modified Protein Expression in the Tectorial Membrane of the Cochlea Reveals Roles for the Striated Sheet Matrix

The tectorial membrane (TM) of the mammalian cochlea is a complex extracellular matrix which, in response to acoustic stimulation, displaces the hair bundles of outer hair cells (OHCs), thereby initiating sensory transduction and amplification. Here, using TM segments from the basal, high-frequency region of the cochleae of genetically modified mice (including models of human hereditary deafness) with missing or modified TM proteins, we demonstrate that frequency-dependent stiffening is associated with the striated sheet matrix (SSM). Frequency-dependent stiffening largely disappeared in all three TM mutations studied where the SSM was absent either entirely or at least from the stiffest part of the TM overlying the OHCs. In all three TM mutations, dissipation of energy is decreased at low (<8 kHz) and increased at high (>8 kHz) stimulus frequencies. The SSM is composed of polypeptides carrying fixed charges, and electrostatic interaction between them may account for frequency-dependent stiffness changes in the material properties of the TM. Through comparison with previous in vivo measurements, it is proposed that implementation of frequency-dependent stiffening of the TM in the OHC attachment region facilitates interaction among tones, backward transmission of energy, and amplification in the cochlea.     

用共聚焦显微镜观察ACh及ATP对豚鼠耳蜗外毛细胞Ca^2＋的调控

用激光扫描共聚焦显微镜研究了一般公认的耳蜗传出神经递质乙酰胆碱（ＡＣｈ）和三磷酸腺苷（ＡＴＰ）对豚鼠耳蜗外毛细胞（ＯＨＣｓ）胞内游离Ｃａ＾２＋浓度（Ｃａ＾２＋）的作用,ＯＨＣｓ用Ｃａ＾２＋敏感荧光染料Ｆｌｕｏ－３着色,胞内Ｃａ＾２＋的分布以细胞底部稍强。ＡＣｈ在ＯＨＣ底部引起Ｃａ＾２＋的缓慢上长并维持在一个较高水平。ＡＴＰ在整个ＯＨＣ引起一个急剧的Ｃａ＾２＋升高,升高幅度在ＯＨＣ顶部最大。随着ＡＴ     

Electromotility of outer hair cells from the cochlea of the echolocating bat,Carollia perspicillata

Isolated outer hair cells (OHCs) and explants ot the organ of Corti were obtained from the cochlea of the echolocating bat, Carollia perspicillata, whose hearing range extends up to about 100 kHz. The OHCs were about 10–30 m long and produced resting potentials between-30 to -69 mV. During stimulation with a sinusoidal extracellular voltage field (voltage gradient of 2 mV/m) cyclic length changes were observed in isolated OHCs. The displacements were most prominent at the level of the cell nucleus and the cuticular plate. In the organ of Corti explants, the extracellular electric field induced a radial movement of the cuticular plate which was observed using video subtraction and photodiode techniques. Maximum displacements of about 0.3–0.8 m were elicited by stimulus frequencies below 100 Hz. The displacement amplitude decreased towards the noise level of about 10–30 nm for stimulus frequencies between 100–500 Hz, both in apical and basal explants. This compares well with data from the guinea pig, where OHC motility induced by extracellular electrical stimulation exhibits a low pass characteristic with a corner frequency below 1 kHz. The data indicate that fast OHC movements presumably are quite small at ultrasonic frequencies and it remains to be solved how they participate in amplifying and sharpening cochlear responses in vivo.Abbreviations BM basilar membrane - FFT fast Fourier Transfer - IHC inner hair cell - OHC outer hair cell     

Expression of alpha and beta parvalbumin is differentially regulated in the rat organ of corti during development

The expression of two calcium-binding proteins of the parvalbumin (PV) family, the alpha isoform (alphaPV) and the beta isoform known as oncomodulin (OM), was investigated in the rat cochlea during postnatal development and related to cholinergic efferent innervation. Using RT-PCR analysis, we found that OM expression begins between postnatal day 2 (P2) and P4, and peaks as early as P10, while alphaPV mRNA begins expression before birth and remains highly expressed into the adult period. Both in situ hybridization and immunoreactivity confirm that OM is uniquely expressed by the outer hair cells (OHCs) in the rat cochlea and occurs after efferent innervation along the cochlear spiral between P2 and P4. In contrast to OM expression, alphaPV immunoreactivity is expressed in both inner hair cells (IHCs) and OHCs at birth. Following olivocochlear efferent innervation, OHCs demonstrate weak OM immunoreactivity beginning at P5 and diminished alphaPV immunoreactivity after P10. In organ cultures isolated prior to the efferent innervation of OHCs, OM immunoreactivity failed to develop in OHCs, but alphaPV immunoreactivity remained present in both IHCs and OHCs. In contrast, organ cultures isolated after efferent innervation of OHCs show OHCs with low levels of OM immunoreactivity and high levels of alphaPV immunoreactivity. This study suggests that OM and alphaPV are differentially regulated in OHCs during cochlear development. Our findings further raise the possibility that the expression of PV proteins in OHCs may be influenced by efferent innervation.