Influence of direct current on dc receptor potentials from cochlear inner hair cells in the guinea pig

Inner hair cell responses to sound were monitored while direct current was applied across the membranous labyrinth in the first turn of the guinea pig cochlea. The current injection electrodes were positioned in the scala vestibuli and on the round window membrane. Positive and negative current (less than 100 microA) caused changes in the sound-evoked dc receptor potentials which were dependent on the sound frequency and intensity. The frequencies most affected by this extracellular current were those comprising the "tip" portion of the inner hair cell frequency tuning characteristic (FTC). The influence of current increased with increasing frequency. Positive current increased the amount of dc receptor potential for the affected frequencies while negative current decreased the potential. Current-induced changes (on a percentage basis) were greater for low intensity sounds and the negative current direction. These frequency specific changes are evidenced as a loss in sensitivity for the tip area of the FTC and a downward shift of the inner hair cell characteristic frequency. Larger current levels (greater than 160 microA) cause more complex changes including unrecoverable loss of cell performance. In separate experiments positive and negative currents (less than 1.1 microA) were injected into the inner hair cell from the recording electrode during simultaneous measurement of the sound-evoked dc receptor potential. This condition caused a shift in IHC sensitivity that was independent of sound frequency and intensity. Positive current decreased the sensitivity of the level of the cell while negative current increased the responses. The effect of current level on sound-evoked dc receptor potential was nonlinear, as comparatively greater increases in cell response were observed for negative than decreases for positive current. The intracellular current injection results are accounted for by the mechano-resistive model of hair cell transduction, where nonlinear responses with current level may reflect outward rectification. Response changes induced by extracellular current are evidence of current effects on both inner and outer hair cells. The frequency and intensity dependences are hypothesized to represent voltage mediated control of inner hair cell response by the outer hair cells.     

Realistic mechanical tuning in a micromechanical cochlear model

Two assumptions were made in the formulation of a recent cochlear model [P.J. Kolston, J. Acoust. Soc. Am. 83, 1481-1487 (1988)]: (1) The basilar membrane has two radial modes of vibration, corresponding to division into its arcuate and pectinate zones; and (2) the impedance of the outer hair cells (OHCs) greatly modifies the mechanics of the arcuate zone. Both of these assumptions are strongly supported by cochlear anatomy. This paper presents a revised version of the outer hair cell, arcuate-pectinate (OHCAP) model, which is an improvement over the original model in two important ways: First, a model for the OHCs is included so that the OHC impedance is no longer prescribed functionally; and, second, the presence of the OHCs enhances the basilar membrane motion, so that the model is now consistent with observed response changes resulting from trauma. The OHCAP model utilizes the unusual spatial arrangement of the OHCs, the Deiters cells, their phalangeal processes, and the pillars of Corti. The OHCs do not add energy to the cochlear partition and hence the OHCAP model is passive. In spite of the absence of active processes, the model exhibits mechanical tuning very similar to those measured by Sellick et al. [Hear. Res. 10, 93-100 (1983)] in the guinea pig cochlea and by Robles et al. [J. Acoust. Soc. Am. 80, 1364-1374 (1986)] in the chinchilla cochlea. Therefore, it appears that mechanical response tuning and response changes resulting from trauma should not be used as justifications for the hypothesis of active processes in the real cochlea.     

The mechanical waveform of the basilar membrane. III. Intensity effects

Mechanical responses in the basal turn of the guinea-pig cochlea were measured with broad-band noise stimuli and expressed as input-output cross-correlation functions. The experiments were performed over the full range of stimulus intensities in order to try to understand the influence of cochlear nonlinearity on frequency selectivity, tuning, signal compression and the impulse response. The results are interpreted within the framework of a nonlinear, locally active, three-dimensional model of the cochlea. The data have been subjected to inverse analysis in order to recover the basilar-membrane (BM) impedance, a parameter function that, when inserted into the (linearized version of that) model, produces a model response that is similar to the measured response. This paper reports details about intensity effects for noise stimulation, in particular, the way the BM impedance varies with stimulus intensity. In terms of the underlying cochlear model, the decrease of the "activity component" in the BM impedance with increasing stimulus level is attributed to saturation of transduction in the outer hair cells. In the present paper this property is brought into a quantitative form. According to the theory [the EQ-NL theorem, de Boer, Audit. Neurosci. 3, 377-388 (1997)], the BM impedance is composed of two components, both intrinsically independent of stimulus level. One is the passive impedance Zpass and the other one is the "extra" impedance Zextra. The latter impedance is to be multiplied by a real factor gamma (0 < or = gamma < or = 1) that depends on stimulus level. This concept about the composition of the BM impedance is termed the "two-component theory of the BM impedance." In this work both impedances are entirely derived from experimental data. The dependence of the factor gamma on stimulus level can be derived by using a unified form of the outer-hair-cell transducer function. From an individual experiment, the two functions Zpass and Zextra are determined, and an approximation (Zpass + gamma Zextra) to the BM impedance constructed. Next, the model response (the "resynthesized" response) corresponding to this "artificial" impedance is computed. The same procedure is executed for several stimulus-level values. For all levels, the results show a close correspondence with the original experimental data; this includes correct prediction of the compression of response amplitudes, the reduction of frequency selectivity, the shift in peak frequency and, most importantly, the preservation of timing in the impulse response. All these findings illustrate the predictive power of the underlying model.     

The dynamic range of inner hair cell and organ of Corti responses

Inner hair cell (IHC) and organ of Corti (OC) responses are measured from the apical three turns of the guinea pig cochlea, allowing access to regions with best, or most sensitive, frequencies at approximately 250, 1000, and 4000 Hz. In addition to measuring both ac and dc receptor potentials, the average value of the half-wave rectified response (AVEHR) is computed to better reflect the signal that induces transmitter release. This measure facilitates comparisons with single-unit responses in the auditory nerve. Although IHC ac responses exhibit compressive growth, response magnitudes at high levels depend on stimulus frequency. For example, IHCs with moderate and high best frequencies (BF) exhibit more linear responses below the BF of the cell, where higher sound-pressure levels are required to approach saturation. Because a similar frequency dependence is observed in extracellular OC responses, this phenomenon may originate in cochlear mechanics. At the most apical recording location, however, the pattern documented at the base of the cochlea is not seen in IHCs with low BFs around 250 Hz. In fact, more linear behavior is measured above the BF of the cell. These frequency-dependent features require modification of cochlear models that do not provide for longitudinal variations and generally depend on a single stage of saturation located at the synapse. Finally, behavior of dc and AVEHR responses suggests that a single IHC is capable of coding intensity over a large dynamic range [Patuzzi and Sellick, J. Acoust. Soc. Am. 74, 1734-1741 (1983); Smith et al., in Hearing--Physiological Bases and Psychophysics (Springer, Berlin, 1983); Smith, in Auditory Function (Wiley, New York, 1988)] and that information compiled over wide areas along the cochlear partition is not essential for loudness perception, consistent with psychophysical results [Viemeister, Hearing Res. 34, 267-274 (1988)].     

High-synchrony cochlear compound action potentials evoked by rising frequency-swept tone bursts

The auditory compound action potential (CAP) represents synchronous VIIIth nerve activity. Clicks or impulses have been used in the past to produce this synchrony under the assumption that the wide spectral spread inherent in transient signals will activate a large portion of the cochlear partition. However, the observation that only auditory nerve units tuned above 3 kHz contribute to synchronous activity in the N1P1 complex of the CAP [Dolan et al., J. Acoust. Soc. Am. 73, 580-591 (1983)] suggests that temporal delays imposed by the traveling wave result in an asynchronous pattern of VIIIth nerve activation. In order to determine if units tuned below 3 kHz could be recruited into the CAP response, the present study uses tone bursts of exponentially rising frequency to hypothetically activate synchronous discharges of VIIIth nerve fibers along the length of the cochlear partition. The equations defining the frequency sweeps are calculated to be the inverse of the delay-line characteristics of the guinea pig cochlear partition. The resultant sweeps theoretically cause a constant phase displacement of a large portion of the cochlear partition at one time. Compound action potentials recorded in response to the rising frequency sweeps were compared to CAPs evoked by corresponding falling frequency sweeps and clicks. Analysis of the CAP waveforms showed narrower N1 widths and larger N1 and P1 amplitudes for rising sweeps when compared to falling sweeps. This is consistent with the hypothesis of increased synchrony. A further test of the hypothesis was made by using high-pass masking noise to evaluate the contributions of discrete cochlear locations to the CAP ("derived" CAP). Latency functions of the derived CAPs for clicks and falling frequency sweeps showed progressive increases in latency as the cutoff frequency of the high-pass filter was lowered. The latency of the derived CAP for these stimulus conditions reflects traveling wave delays [Aran and Cazals, "Electrocochleography: Animal studies," in Evoked Electrical Activity in The Auditory Nervous System (Academic, New York, 1978)]. In contrast, derived CAPs obtained from rising sweeps showed no change in latency for any cutoff frequencies, indicating a constant delay of response for fibers with different characteristic frequencies (CFs). These results support the theoretical premise underlying the derivation of the rising sweep: Spectral energy with the appropriate temporal organization, dictated by basilar membrane traveling wave properties, will increase CAP synchrony.     

A model for active elements in cochlear biomechanics

A linear, mathematical model of cochlear biomechanics is presented in this paper. In this model, active elements are essential for simulating the high sensitivity and sharp tuning characteristic of the mammalian cochlea. The active elements are intended to represent the motile action of outer hair cells; they are postulated to be mechanical force generators that are powered by electrochemical energy of the cochlear endolymph, controlled by the bending of outer hair cell stereocilia, and bidirectionally coupled to cochlear partition mechanics. The active elements are spatially distributed and function collectively as a cochlear amplifier. Excessive gain in the cochlear amplifier causes spontaneous oscillations and thereby generates spontaneous otoacoustic emissions.     

Induced resonant transparency of magnetic materials for gamma radiation: Propagation dynamics

The theory of spatiotemporal dynamics of gamma radiation in a resonant medium upon excitation of two-frequency gamma magnetic resonance in magnetic materials is considered. The radiation absorption at the fundamental frequency and the harmonic generation are investigated under conditions when the frequency of gamma radiation is shifted by the half-sum or half-difference of the frequencies of radio-frequency magnetic fields. It is shown that the propagation of gamma radiation through an absorber is characterized by a steady-state gamma intensity (resonant transparency). A consistent radio-frequency spectral analysis demonstrates that the intensities of harmonics drastically change at the transparency region boundaries due to nonlinear interference. The theory of quantum and dynamical beats of synchrotron radiation under conditions of induced resonant transparency is proposed.     

Intracochlear pressure and derived quantities from a three-dimensional model

Intracochlear pressure is calculated from a physiologically based, three-dimensional gerbil cochlea model. Olson [J. Acoust. Soc. Am. 103, 3445-3463 (1998); 110, 349-367 (2001)] measured gerbil intracochlear pressure and provided approximations for the following derived quantities: (1) basilar membrane velocity, (2) pressure across the organ of Corti, and (3) partition impedance. The objective of this work is to compare the calculations and measurements for the pressure at points and the derived quantities. The model includes the three-dimensional viscous fluid and the pectinate zone of the elastic orthotropic basilar membrane with dimensional and material property variation along its length. The arrangement of outer hair cell forces within the organ of Corti cytoarchitecture is incorporated by adding the feed-forward approximation to the passive model as done previously. The intracochlear pressure consists of both the compressive fast wave and the slow traveling wave. A Wentzel-Kramers-Brillowin asymptotic and numerical method combined with Fourier series expansions is used to provide an efficient procedure that requires about 1 s to compute the response for a given frequency. Results show reasonably good agreement for the direct pressure and the derived quantities. This confirms the importance of the three-dimensional motion of the fluid for an accurate cochlear model.     

The mechanical waveform of the basilar membrane. IV. Tone and noise stimuli

Analysis of mechanical cochlear responses to wide bands of random noise clarifies many effects of cochlear nonlinearity. The previous paper [de Boer and Nuttall, J. Acoust. Soc. Am. 107, 1497-1507 (2000)] illustrates how closely results of computations in a nonlinear cochlear model agree with responses from physiological experiments. In the present paper results for tone stimuli are reported. It was found that the measured frequency response for pure tones differs little from the frequency response associated with a noise signal. For strong stimuli, well into the nonlinear region, tones have to be presented at a specific level with respect to the noise for this to be true. In this report the nonlinear cochlear model originally developed for noise analysis was modified to accommodate pure tones. For this purpose the efficiency with which outer hair cells modify the basilar-membrane response was made into a function of cochlear location based on local excitation. For each experiment, the modified model is able to account for the experimental findings, within 1 or 2 dB. Therefore, the model explains why the type of filtering that tones undergo in the cochlea is essentially the same as that for noise signals (provided the tones are presented at the appropriate level).     

A symmetry suppresses the cochlear catastrophe

When the independent spatial variable is defined appropriately, the empirical finding that the phase of the cochlear input impedance is small [Lynch et al., J. Acoust. Soc. Am. 72, 108-130 (1982)] is shown to imply that the wavelength of the pressure wave in the cochlea changes slowly with position near the stapes. As a result, waves traveling in either direction through the basal turn undergo little reflection, and the transfer of energy between the middle and inner ears remains efficient at low frequencies. The slow variation of the wavelength implies that the series impedance Z and shunt admittance Y of the cochlear transmission line are approximately proportional at low frequencies and thus requires that the width of the basilar membrane and the cross-sectional areas of the cochlear scalae taper in opposite directions. Maintenance of the symmetry between Z and Y is both necessary and sufficient to ensure that the spatial derivative of the wavelength, and hence the phase of the cochlear input impedance, remains small. Although introduced in another context, the model of Zweig ["Finding the impedance of the organ of Corti," J. Acoust. Soc. Am. 89, 1229-1254 (1991)] manifests the symmetry between Z and Y. In other transmission-line models of cochlear mechanics, however, that symmetry is absent, and the spatial derivative of the wavelength diverges at low frequencies--the "cochlear catastrophe." Those models therefore contradict the impedance measurements and predict little transfer of energy between the middle and inner ears.     

A two-dimensional cochlear fluid model based on conformal mapping

Using conformal mapping, fluid motion inside the cochlear duct is derived from fluid motion in an infinite half plane. The cochlear duct is represented by a two-dimensional half-open box. Motion of the cochlear fluid creates a force acting on the cochlear partition, modeled by damped oscillators. The resulting equation is one-dimensional, more realistic, and can be handled more easily than existing ones derived by the method of images, making it useful for fast computations of physically plausible cochlear responses. Solving the equation of motion numerically, its ability to reproduce the essential features of cochlear partition motion is demonstrated. Because fluid coupling can be changed independently of any other physical parameter in this model, it allows the significance of hydrodynamic coupling of the cochlear partition to itself to be quantitatively studied. For the model parameters chosen, as hydrodynamic coupling is increased, the simple resonant frequency response becomes increasingly asymmetric. The stronger the hydrodynamic coupling is, the slower the velocity of the resulting traveling wave at the low frequency side is. The model's simplicity and straightforward mathematics make it useful for evaluating more complicated models and for education in hydrodynamics and biophysics of hearing.     

Analytic treatment of the compound action potential: estimating the summed post-stimulus time histogram and unit response

The convolution of an equation representing a summed post-stimulus time histogram computed across auditory nerve fibers [P(t)] with an equation representing a single-unit wave form [U(t)], resulted in an analytic expression for the compound action potential (CAP). The solution was fit to CAPs recorded to low and high frequency stimuli at various signal levels. The correlation between the CAP and the analytic expression was generally greater than 0.90. At high levels the width of P(t) was broader for low frequency stimuli than for high frequency signals, but delays were comparable. This indicates that at high signal levels there is an overlap in the population of auditory nerve fibers contributing to the CAP for both low and high frequency stimuli but low frequencies include contributions from more apical regions. At low signal levels the width of P(t) decreased for most frequencies and delays increased. The frequency of oscillation of U(t) was largest for high frequency stimuli and decreased for low frequency stimuli. The decay of U(t) was largest at 8 kHz and smallest at 1 kHz. These results indicate that the hair cell or neural mechanisms involved in the generation of action potentials may differ along the cochlear partition.     

A cochlear model for acoustic emissions

Variability in cochlear emission properties among different species, particularly humans and small mammals, and within individuals in the same species, is modeled by a cochlear nonlinear transmission line. The difference between humans and animals is largely explained by a lower cochlear input impedance in human ears than in cats, gerbils, or chinchillas. Inconstancy in emission properties among individual human or animal subjects is related to structural variability among ears, which can be the result of a nonuniform connection between the outer hair cells cilia and the tectorial membrane. These structural differences are modeled by a nonuniform cochlear partition resistance along the cochlear length. The model predicts that an ear which has a uniform cochlear partition resistance and an adequate cochlear input impedance will emit acoustic distortion products (ADP), but not spontaneous acoustic emission (SAE), nor click-evoked emission (CE). Only a nonuniform cochlea emits SAE and CE in addition to enhanced ADPs. The model predictions agree quantitatively with cochlear emission data from humans and animals.     

Outer hair cell piezoelectricity: frequency response enhancement and resonance behavior

Stretching or compressing an outer hair cell alters its membrane potential and, conversely, changing the electrical potential alters its length. This bi-directional energy conversion takes place in the cell's lateral wall and resembles the direct and converse piezoelectric effects both qualitatively and quantitatively. A piezoelectric model of the lateral wall has been developed that is based on the electrical and material parameters of the lateral wall. An equivalent circuit for the outer hair cell that includes piezoelectricity shows a greater admittance at high frequencies than one containing only membrane resistance and capacitance. The model also predicts resonance at ultrasonic frequencies that is inversely proportional to cell length. These features suggest all mammals use outer hair cell piezoelectricity to support the high-frequency receptor potentials that drive electromotility. It is also possible that members of some mammalian orders use outer hair cell piezoelectric resonance in detecting species-specific vocalizations.     

Optical multistability in 1D photonic crystals with nonlinear Thue–Morse structure

A 1D photonic crystal structure contains 16 layers, 8 common dielectric layers and 8 layers with nonlinear medium, with an arrangement similar to the 5th generation, Thue–Morse multilayer is presented. The properties of photonics band gap, field distribution and optical multistability are investigated. On the band gap, 5 resonant modes is observed. On the behavior of output intensity versus input intensity around resonant frequencies, the multistability response observed. When the frequency of incident field is close to the resonant frequency, the threshold intensity of multistability is decreased.     

Location of structurally similar areas in chinchilla cochleas of different lengths

In chinchillas, the length of the organ of Corti was found to vary by as much as 26% of the mean (18.31 mm). In specimens of different lengths, areas in which the basilar membrane and organ of Corti have the same physical dimensions were found to be located at the same percentage distance along the cochlear partition. Average densities of the inner and outer hair cells were noted to decrease with increasing cochlear length. However, the rate of decrease in density was less than the rate of increase in length. These findings indicate that long cochleas have a greater amount of the organ of Corti (and hence more sensory cells) in a given frequency region.     

Psychophysical tuning curves and auditory thresholds after hair cell damage in the chinchilla

Chinchillas were treated with kanamycin sulfate (150--200 mg/kg/day) to produce high-frequency hearing loss extending to about 4.0 kHz. Thresholds and psychophysical tuning curves (PTCs) were obtained before and after treatment, utilizing a shuttlebox avoidance procedure, and cochlear hair cells were evaluated under phase contrast microscopy. Hair cell loss resulting from kanamycin treatment varied from restricted lesions of the outer hair cells (OHCs) in the cochlear base, with no loss of inner hair cells (IHCs), to more extensive lesions involving both OHCs and IHCs. Threshold shift of at least 40 dB was always associated with OHC loss. PTCs obtained from frequency regions exhibiting 40--50 dB of threshold shift were normal in shape. With threshold shift in excess of 50 dB, PTCs were progressively distorted, with truncation of the tip segment and in some cases increased sensitivity of the tail segment. The results suggest that the threshold of optimally functional IHCs after kanamycin-induced OHC loss is about 40 dB higher than normal. Threshold shift in excess of 40 dB may represent IHC damage. IHCs are capable of transducing the fine-frequency information necessary for generating normally sharp PTCs in the absence of OHCs. However, with threshold shift in excess of approximately 50 dB, this frequency resolution is increasingly compromised.     

用紧束缚方法描述光子晶体缺陷耦合的共振频率移动

通常采用含两个耦合参数的紧束缚近似，就能很好地描述光子晶体缺陷因耦合而导致的共振频率分裂.然而，缺陷耦合造成的共振频率移动，即包含奇数个缺陷的耦合系统的中央共振频率位置与原来单缺陷时的共振频率位置存在差异，则只有采用含三个耦合参数的严格紧束缚方法才能正确描述.根据耦合参数与共振频率的关系，利用三缺陷耦合系统的模拟计算结果确定了三个耦合参数的具体值，从而在理论上能够预言由任意个缺陷构成的耦合系统的共振频率的移动和分裂.理论预言与基于有限时域差分法的数值计算完全相符.     

Modeling the growth rate of distortion product otoacoustic emissions by active nonlinear oscillators

In this work, growth-rate curves of the 2 f1-f2 distortion product otoacoustic emission (DPOAE) are analyzed in a population of 30 noise exposed subjects, including both normal-hearing and hearing impaired subjects. A particular embedded limit-cycle oscillator equation is used to model the cochlear resonant response at the cochlear places of the primary and secondary tone frequencies (f2 and 2 f1-f2). The parameters of the oscillator equation can be directly interpreted in terms of effectiveness of the cochlear feedback mechanisms associated with the active filter amplification. A two-sources paradigm is included in the model, in agreement with experimental evidence and with the assumptions of more detailed full cochlear models based on the transmission line formalism. According to this paradigm, DPOAEs are nonlinearly generated at the cochlear place that is resonant at frequency f2, and coherently reflected at the 2 f1-f2 place. The analysis shows that the model, which had been previously used to describe the relaxation dynamics of transient evoked otoacoustic emissions (TEOAEs), also correctly predicts the observed growth rate of the DPOAE response as a function of the primary tones amplitude. A significant difference is observed between normal and impaired ears. The comparison between the growth rate curves at different frequencies provides information about the dependence of cochlear tuning on frequency.     

Vibration responses of the organ of Corti and the tectorial membrane to electrical stimulation

Coupling of somatic electromechanical force from the outer hair cells (OHCs) into the organ of Corti is investigated by measuring transverse vibration patterns of the organ of Cori and tectorial membrane (TM) in response to intracochlear electrical stimulation. Measurement places at the organ of Corti extend from the inner sulcus cells to Hensen's cells and at the lower (and upper) surface of the TM from the inner sulcus to the OHC region. These locations are in the neighborhood of where electromechanical force is coupled into (1) the mechanoelectrical transducers of the stereocilia and (2) fluids of the organ of Corti. Experiments are conducted in the first, second, and third cochlear turns of an in vitro preparation of the adult guinea pig cochlea. Vibration measurements are made at functionally relevant stimulus frequencies (0.48-68 kHz) and response amplitudes (<15 nm). The experiments provide phase relations between the different structures, which, dependent on frequency range and longitudinal cochlear position, include in-phase transverse motions of the TM, counterphasic transverse motions between the inner hair cell and OHCs, as well as traveling-wave motion of Hensen's cells in the radial direction. Mechanics of sound processing in the cochlea are discussed based on these phase relationships.