A computational algorithm for computing nonlinear auditory frequency selectivity.

Computational algorithms that mimic the response of the basilar membrane must be capable of reproducing a range of complex features that are characteristic of the animal observations. These include complex input output functions that are nonlinear near the site's best frequency, but linear elsewhere. This nonlinearity is critical when using the output of the algorithm as the input to models of inner hair cell function and subsequent auditory-nerve models of low- and high-spontaneous rate fibers. We present an algorithm that uses two processing units operating in parallel: one linear and the other compressively nonlinear. The output from the algorithm is the sum of the outputs of the linear and nonlinear processing units. Input to the algorithm is stapes motion and output represents basilar membrane motion. The algorithm is evaluated against published chinchilla and guinea pig observations of basilar membrane and Reissner's membrane motion made using laser velocimetry. The algorithm simulates both quantitatively and qualitatively, differences in input/output functions among three different sites along the cochlear partition. It also simulates quantitatively and qualitatively a range of phenomena including isovelocity functions, phase response, two-tone suppression, impulse response, and distortion products. The algorithm is potentially suitable for development as a bank of filters, for use in more comprehensive models of the peripheral auditory system.     

Comment on "Mutual suppression in the 6 kHz region of sensitive chinchilla cochleae" [J. Acoust. Soc. Am. 121, 2805-2818 (2007)

Rhode [J. Acoust. Soc. Am. 121, 2805-2818 (2007)] acknowledges that two-tone neural rate responses for low-side suppression differ from those measured in basilar membrane mechanics, making one question whether this aspect of suppression has a mechanical correlate. It is suggested here that signal coding between mechanical and neural processing stages may be responsible for the fact that the total rate response (but not the basilar membrane response) for low-frequency suppressors is smaller than that for the probe-alone condition. For example, the velocity dependence of inner hair cell (IHC) transduction, membrane/synaptic filtering and the sensitivity difference between ac and dc components of the IHC receptor potential all serve to reduce excitability for low-side suppressors at the single-unit level. Hence, basilar membrane mechanics may well be the source of low-side suppression measured in the auditory nerve.     

A hardware cochlear nonlinear preprocessing model with active feedback

A hardware model of the nonlinear preprocessing established in the inner ear consisting of 90 sections corresponding to a frequency range from 900 to 8000 Hz is described. The model is based on assumptions described by Zwicker [Biol. Cybern. 35, 243-250 (1979)]: The outer hair cells act as saturating nonlinear mechanical amplifiers which feed back to the vibration of the basilar membrane while only the inner hair cells transfer information towards higher centers. The model shows many effects which correlate very closely to physiological and psychoacoustical counterparts. Quantitative data on the level-dependence of frequency responses and phase responses as well as an example of suppression are outlined.     

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.     

Frequency-dependent self-induced bias of the basilar membrane and its potential for controlling sensitivity and tuning in the mammalian cochlea

A displacement-sensitive capacitive probe technique was used in the first turn of guinea pig cochleas to examine whether the motion of the basilar membrane includes a displacement component analogous to the dc receptor potentials of the hair cells. Such a "dc" component apparently exists. At a given location on the basilar membrane, its direction toward scala vestibuli (SV) or scala tympani (ST) varies systematically with frequency of the acoustic stimulus. Furthermore, it appears to consist of two parts: a small asymmetric offset response to each gated tone burst plus a progressive shift of the basilar membrane from its previous position. The mean position shift is cumulative, increasing with successive tone bursts. The amplitude of the immediate offset response, when plotted as a function of frequency, appears to exhibit a trimodal pattern. This displacement offset is toward SV at the characteristic frequency (CF) of the location of the probe, while at frequencies either above or below the CF the offset is relatively larger, and toward ST. The mechanical motion of the basilar membrane therefore appears to contain the basis for lateral suppression. The cumulative mean position shift, however, appears to peak toward ST at the apical end of the traveling wave envelope and appears to be associated with a resonance, not of the basilar membrane motion directly, but coupled to it. The summating potential, measured concurrently at the round window, shows a more broadly tuned peak just above the CF of the position of the probe. This seems to correspond to the peak at the CF of the mechanical bias. As the preparation deteriorates, the best frequency of the vibratory displacement response decreases to about a half-octave below the original CF. There is a corresponding decrease in the frequency of the peaks of the trimodal pattern of the asymmetric responses to tone bursts. The trimodal pattern also broadens. In previous experiments the basilar membrane has been forced to move in response to a low-frequency biasing tone. The sensitivity to high-frequency stimuli varies in phase with the biasing tone. The amplitudes of slow movement in these earlier experiments and in the present experiments are of the same order of magnitude. This suggests strongly that the cumulative shift toward ST to a high-frequency acoustic stimulus constitutes a substantial controlling bias on the sensitivity of the cochlea in that same high-frequency region. Its effect will be to reduce the slope of neural rate-level functions on the high-frequency side of CF.     

Mechanical passive and active models of the human basilar membrane

Simple three-dimensional passive and active models of the human basilar membrane were built, solved using the Finite Element Method and tested. In the active model an active mechanism connected with electromotility of outer hair cells was included. In the active model the active mechanism was incorporated in the form of additional, local pressure load. In the passive model the active mechanism was neglected. Hydrodynamic coupling between the cochlear partition and cochlear fluid was excluded in both models. Geometrical and physical parameters of the model were chosen to be adequate to those of humans in the best possible way. However, some of these parameters had to be estimated. The models were tested by calculation of typical curves known from cochlear measurements performed mostly on animals. For the passive model a linear input-output function and very small values of the basilar membrane velocities were obtained. This behaviour is to be expected for the passive model and for the basilar membrane in the poor physiological condition. For the active model the compressed input-output functions, tuning curves, isointensity curves and reasonable BM velocities were obtained. Possible inadequacies, which could explain the differences between numerical results and measurements were described.     

Finding the impedance of the organ of Corti

Measurements of the nonlinear response of the basilar membrane to a pure tone are shown to have a simple form for moderate membrane velocities: V(x,f;Vu)/Vu approximately [V(x,f)/Vu]v(x,f), f less than or equal to fc(x), where the response V is the velocity of the membrane at measurement position x, Vu is the umbo velocity, f is the frequency of the stimulus, and fc(x) is the local characteristic frequency. The frequency dependence of the functions v(x,f) and V(x,f) is determined from the data, and v(x,f) and ln V(x,f) are shown to be analytic functions in the lower half of the complex frequency plane, with Re [v(x,f)] a monotonically increasing function of f at fixed x. The linear limit of basilar membrane motion is characterized by a transfer function T(x,f) = (V/V1)v/(1-v), estimated by extrapolating V(x,f;Vu)/Vu to a small membrane velocity V1.T(x,f) and ln T(x,f) are shown to be analytic functions in the lower half of the complex frequency plane. The inverse of the amplitude of the transfer function, which has both a deep dip at f approximately fc(x) and a broad shoulder at lower frequencies, bears a striking resemblance to the neural threshold tuning curve. The functional form of T(x,f) is used to deduce the equation governing the motion of a section of the organ of Corti. Each section acts like a negatively damped harmonic oscillator stabilized at time t by a feedback force proportional to the velocity at the previous time t-tau. The time delay tau is proportional to the oscillator period [tau approximately 1.75/fc(x)]. Like a laser, the organ of Corti pumps energy into harmonic traveling waves. Unlike the laser, the direction of energy flow abruptly reverses as the traveling wave approaches the point of maximum membrane velocity [fc(x) approximately f]. All accumulated wave energy is then pumped back into a small section of the organ of Corti where transduction presumably occurs. Outer hair cells are conjectured to be active elements contributing to the negative damping and feedback of the cochlear amplifier.     

Effects of electrical polarization on inner hair cell receptor potentials

Ac and dc receptor potential components in response to tone-burst stimuli were measured from inner hair cells in the third cochlear turn of the guinea pig. Comparisons were sought between conditions when constant polarizing current was injected into the cell through the recording electrode and when there was no extrinsic current. Hyperpolarization of the cell increased all responses, while depolarization decreased them. The input-output functions were vertically translated by current injection. The extent of translation was a function of current level. In addition, the amount of current-induced change was frequency dependent. Largest changes were seen at low frequencies and the current-induced change tended toward a constant high-frequency asymptote between 1-2 kHz. Changes in the dc response component were considerably in excess of those for the fundamental ac response. The frequency-dependent effects are quantified with the aid of a hair cell circuit model [P. Dallos, Hear. Res. 14, 281-291 (1984)]. It is assumed that the quantity altered by polarizing current (actually by the transmembrane voltage) is the resistance of the cell's basolateral membrane.     

Comparison between distortion product otoacoustic emissions and nerve fiber responses from the basilar papilla of the frog

The basilar papilla (BP) is one of the three end organs in the frog inner ear that is sensitive to airborne sound. Its anatomy and physiology are unique among all classes of vertebrates. Essentially, the BP functions as a single auditory filter presumably arising from a mechanically-tuned mechanism. As such, both neural and distortion product otoacoustic emission (DPOAE) tuning may reflect a single mechanical filtering mechanism. Using the Duffing oscillator as a simple model for both neural and DPOAE tuning from the BP, two predictions can be made: [1] the characteristic frequency (CF) of neural tuning and the best frequency (BF) of DPOAE tuning will coincide and [2] the neural tuning curve and DPOAE-audiogram have a similar shape when the neural tuning curve is scaled by a factor of 4 along the y-axis. We recorded both neural tuning curves and DPOAE-audiograms from the BP of the leopard frog. These recordings show good agreement with the model predictions when the stimulus tones are related by relatively small stimulus frequency ratios. For larger stimulus frequency ratios, DPOAE recordings clearly deviate from model predictions. These differences are most likely caused by the oversimplified representation of the frog BP by the model.     

A Brownian energy depot model of the basilar membrane oscillation with a braking mechanism

High auditory sensitivity, sharp frequency selectivity, and spontaneous otoacoustic emissions are signatures of active amplification of the cochlea. The human ear can also detect very large amplitude sounds without being damaged, as long as the exposed time is not too long. The outer hair cells are believed to be the best candidate for the active force generator of the mammalian cochlea. In this paper, we propose a new model for the basilar membrane oscillation which describes both an active and a protective mechanism by employing an energy depot concept and a critical velocity of the basilar membrane. The compressive response of the basilar membrane at the characteristic frequency and the dynamic response to the stimulation are consistent with the experimental results. Although our model displays a Hopf bifurcation, our braking mechanism results in a hyper-compressive response to intense stimuli which is not generically observed near a Hopf bifurcation. Asymmetry seen in experimental recordings between the onset and the offset of the basilar membrane response to a sound burst is also observed in this model.     

Some observations on cochlear mechanics.

A set of experiments was conducted using the M?ssbauer effect to determine the vibratory characteristics of the basilar membrane, Reissner's membrane, the malleus, incus, and oval window in squirrel monkey. A few measurements were also made in guinea pig in the basal cochlear region. The nonlinear vibration properties of the basilar membrane are described in detail for the midfrequency region in the squirrel monkey. Only in this region have nonlinear effects been observed. A comparison of mechanical and neural data indicates good qualitative agreement.     

Frequency map of the spiral ganglion in the cat

A frequency map of the cat spiral ganglion has been determined on the basis of reconstructed cochleas in which individual spiral ganglion cells were labeled with horseradish peroxidase following determination of their characteristic frequency; the cochleas were the same as those used by Liberman and Oliver [J. Comp. Neurol. 223, 163-176 (1984)]. By matching this map to one previously described for the organ of Corti [M. C. Liberman, J. Acoust. Soc. Am. 72, 1441-1449 (1982)], an estimate of the afferent innervation density of the inner hair cells was derived. Counts of myelinated nerve fibers at the habenula perforata and inner hair cells were also performed and yielded similar results in all but the most basal 10%-15% of the cochlea. Between 0.1 and 20 kHz there is a gradual monotonic increase as a function of frequency in the number of spiral ganglion cells terminating on each inner hair cell, from about eight ganglion cells per inner hair cell to about 30 ganglion cells per inner hair cell. Above 20 kHz, it seems there is a decrease to about ten ganglion cells per inner hair cell. The greatest innervation density is at approximately the region of the basilar membrane with the greatest density of inner hair cells per millimeter.     

Rate-intensity functions in the emu auditory nerve

Rate-versus-intensity functions recorded from mammalian auditory-nerve fibers have been shown to form a continuum of shapes, ranging from saturating to straight and correlating well with spontaneous rate and sensitivity. These variations are believed to be a consequence of the interaction between the sensitivity of the hair-cell afferent synapse and the nonlinear, compressive growth of the cochlear amplifier that enhances mechanical vibrations on the basilar membrane. Little is known, however, about the cochlear amplifier in other vertebrate species. Rate-intensity functions were recorded from auditory-nerve fibers in chicks of the emu, a member of the Ratites, a primitive group of flightless birds that have poorly differentiated short and tall hair cells. Recorded data were found to be well fitted by analytical functions which have previously been shown to represent well the shapes of rate-intensity functions in guinea pigs. At the fibers' most sensitive frequencies, rate-intensity functions were almost exclusively of the sloping (80.9%) or straight (18.6%) type. Flat-saturating functions, the most common type in the mammal, represented only about 0.5% of the total in the emu. Below the best frequency of each fiber, the rate-intensity functions tended more towards the flat-saturating type, as is the case in mammals; a similar but weaker trend was seen above best frequency in most fibers, with only a small proportion (18%) showing the reverse trend. The emu rate-intensity functions were accepted as supporting previous evidence for the existence of a cochlear amplifier in birds, the conclusion was drawn further that the nonlinearity observed is probably due to saturation of the hair-cell transduction mechanism.     

Outer hair cell active force generation in the cochlear environment

Outer hair cells are critical to the amplification and frequency selectivity of the mammalian ear acting via a fine mechanism called the cochlear amplifier, which is especially effective in the high-frequency region of the cochlea. How this mechanism works under physiological conditions and how these cells overcome the viscous (mechanical) and electrical (membrane) filtering has yet to be fully understood. Outer hair cells are electromotile, and they are strategically located in the cochlea to generate an active force amplifying basilar membrane vibration. To investigate the mechanism of this cell's active force production under physiological conditions, a model that takes into account the mechanical, electrical, and mechanoelectrical properties of the cell wall (membrane) and cochlear environment is proposed. It is shown that, despite the mechanical and electrical filtering, the cell is capable of generating a frequency-tuned force with a maximal value of about 40 pN. It is also found that the force per unit basilar membrane displacement stays essentially the same (40 pNnm) for the entire linear range of the basilar membrane responses, including sound pressure levels close to hearing threshold. Our findings can provide a better understanding of the outer hair cell's role in the cochlear amplifier.     

Modeling auditory-nerve responses for high sound pressure levels in the normal and impaired auditory periphery

This paper presents a computational model to simulate normal and impaired auditory-nerve (AN) fiber responses in cats. The model responses match physiological data over a wider dynamic range than previous auditory models. This is achieved by providing two modes of basilar membrane excitation to the inner hair cell (IHC) rather than one. The two modes are generated by two parallel filters, component 1 (C1) and component 2 (C2), and the outputs are subsequently transduced by two separate functions. The responses are then added and passed through the IHC low-pass filter followed by the IHC-AN synapse model and discharge generator. The C1 filter is a narrow-band, chirp filter with the gain and bandwidth controlled by a nonlinear feed-forward control path. This filter is responsible for low and moderate level responses. A linear, static, and broadly tuned C2 filter followed by a nonlinear, inverted and nonrectifying C2 transduction function is critical for producing transition region and high-level effects. Consistent with Kiang's two-factor cancellation hypothesis, the interaction between the two paths produces effects such as the C1/C2 transition and peak splitting in the period histogram. The model responses are consistent with a wide range of physiological data from both normal and impaired ears for stimuli presented at levels spanning the dynamic range of hearing.     

Effects of background noise level on behavioral estimates of basilar-membrane compression

Hearing-impaired (HI) listeners often show poorer performance on psychoacoustic tasks than do normal-hearing (NH) listeners. Although some such deficits may reflect changes in suprathreshold sound processing, others may be due to stimulus audibility and the elevated absolute thresholds associated with hearing loss. Masking noise can be used to raise the thresholds of NH to equal the thresholds in quiet of HI listeners. However, such noise may have other effects, including changing peripheral response characteristics, such as the compressive input-output function of the basilar membrane in the normal cochlea. This study estimated compression behaviorally across a range of background noise levels in NH listeners at a 4 kHz signal frequency, using a growth of forward masking paradigm. For signals 5 dB or more above threshold in noise, no significant effect of broadband noise level was found on estimates of compression. This finding suggests that broadband noise does not significantly alter the compressive response of the basilar membrane to sounds that are presented well above their threshold in the noise. Similarities between the performance of HI listeners and NH listeners in threshold-equalizing noise are therefore unlikely to be due to a linearization of basilar-membrane responses to suprathreshold stimuli in the NH listeners.     

Inter-relationship between different psychoacoustic measures assumed to be related to the cochlear active mechanism

The active mechanism in the cochlea is thought to depend on the integrity of the outer hair cells (OHCs). Cochlear hearing loss is usually associated with damage to both inner hair cells (IHCs) and OHCs, with the latter resulting in a reduction in or complete loss of the function of the active mechanism. It is believed that the active mechanism contributes to the sharpness of tuning on the basilar membrane (BM) and is also responsible for compressive input-output functions on the BM. Hence, one would expect a close relationship between measures of sharpness of tuning and measures of compression. This idea was tested by comparing three different measures of the status of the active mechanism, at center frequencies of 2, 4, and 6 kHz, using subjects with normal hearing, with unilateral or highly asymmetric cochlear hearing loss, and with bilateral loss. The first measure, HLOHC, was an indirect measure of the amount of the hearing loss attributable to OHC damage; this was based on loudness matches between the two ears of subjects with unilateral hearing loss and was derived using a loudness model. The second measure was the equivalent rectangular bandwidth (ERB) of the auditory filter, which was estimated using the notched-noise method. The third measure was based on the slopes of growth-of-masking functions obtained in forward masking. The ratio of slopes for a masker centered well below the signal frequency and a masker centered at the signal frequency gives a measure of BM compression at the place corresponding to the signal frequency; a ratio close to 1 indicates little or no compression, while ratios less than 1 indicate that compression is occurring at the signal place. Generally, the results showed the expected pattern. The ERB tended to increase with increasing HLOHC. The ratio of the forward-masking slopes increased from about 0.3 to about 1 as HLOHC increased from 0 to 55 dB. The ratio of the slopes was highly correlated with the ERB (r = 0.92), indicating that the sharpness of the auditory filter decreases as the compression on the BM decreases.     

Using acoustic distortion products to measure the cochlear amplifier gain on the basilar membrane.

Most models of the cochlea developed during the last decade have explained frequency selectivity and sensitivity of the cochlea at threshold by the use of power amplification of the acoustic wave on the basilar membrane. This power amplification has been referred to as the cochlear amplifier (CA). In this paper, a method to measure the cochlear amplifier gain as a function of position along the basilar membrane is derived from a simple model. Next, experimental evidence is presented that strongly restricts the properties of these proposed cochlear amplifier models. Specifically, it is shown that small signals generated by mechanical nonlinearities in the basilar membrane motion are not amplified during basilar membrane propagation, contrary to what would be expected from the cochlear amplifier hypotheses. This paper describes a method of measuring the cochlear power gain as a function of frequency and position, from the stapes to within 2 mm of the place corresponding to the frequency being measured. Experimental results in the cat indicate that the total gain of the cochlear amplifier, over the range of positions measured, must be less than 10 dB. The simplest interpretation of the experimental results is that there is no cochlear amplifier. The results suggest that the cochlea must achieve its frequency selectivity by some other means.     

Structural and functional effects of acoustic exposure in goldfish: evidence for tonotopy in the teleost saccule

Background  

Mammalian and avian auditory hair cells display tonotopic mapping of frequency along the length of the cochlea and basilar papilla. It is not known whether the auditory hair cells of fishes possess a similar tonotopic organization in the saccule, which is thought to be the primary auditory receptor in teleosts. To investigate this question, we determined the location of hair cell damage in the saccules of goldfish (Carassius auratus) following exposure to specific frequencies. Subjects were divided into six groups of six fish each (five treatment groups plus control). The treatment groups were each exposed to one of five tones: 100, 400, 800, 2000, and 4000 Hz at 176 dB re 1 μPa root mean squared (RMS) for 48 hours. The saccules of each fish were dissected and labeled with phalloidin in order to visualize hair cell bundles. The hair cell bundles were counted at 19 specific locations in each saccule to determine the extent and location of hair cell damage. In addition to quantification of anatomical injury, hearing tests (using auditory evoked potentials) were performed on each fish immediately following sound exposure. Threshold shifts were calculated by subtracting control thresholds from post-sound exposure thresholds.