Testing coherent reflection in chinchilla: Auditory-nerve responses predict stimulus-frequency emissions

Coherent-reflection theory explains the generation of stimulus-frequency and transient-evoked otoacoustic emissions by showing how they emerge from the coherent "backscattering" of forward-traveling waves by mechanical irregularities in the cochlear partition. Recent published measurements of stimulus-frequency otoacoustic emissions (SFOAEs) and estimates of near-threshold basilar-membrane (BM) responses derived from Wiener-kernel analysis of auditory-nerve responses allow for comprehensive tests of the theory in chinchilla. Model predictions are based on (1) an approximate analytic expression for the SFOAE signal in terms of the BM traveling wave and its complex wave number, (2) an inversion procedure that derives the wave number from BM traveling waves, and (3) estimates of BM traveling waves obtained from the Wiener-kernel data and local scaling assumptions. At frequencies above 4 kHz, predicted median SFOAE phase-gradient delays and the general shapes of SFOAE magnitude-versus-frequency curves are in excellent agreement with the measurements. At frequencies below 4 kHz, both the magnitude and the phase of chinchilla SFOAEs show strong evidence of interference between short- and long-latency components. Approximate unmixing of these components, and association of the long-latency component with the predicted SFOAE, yields close agreement throughout the cochlea. Possible candidates for the short-latency SFOAE component, including wave-fixed distortion, are considered. Both empirical and predicted delay ratios (long-latency SFOAE delay/BM delay) are significantly less than 2 but greater than 1. Although these delay ratios contradict models in which SFOAE generators couple primarily into cochlear compression waves, they are consistent with the notion that forward and reverse energy propagation in the cochlea occurs predominantly by means of traveling pressure-difference waves. The compelling overall agreement between measured and predicted delays suggests that the coherent-reflection model captures the dominant mechanisms responsible for the generation of reflection-source otoacoustic emissions.     

Basilar membrane mechanics at the base of the chinchilla cochlea. I. Input-output functions, tuning curves, and response phases

Basilar membrane (BM) velocity was measured at a site 3.5 mm from the basal end of the chinchilla cochlea using the M?ssbauer technique. The threshold of the compound action potential recorded at the round window in response to tone bursts was used as an indicator of the physiological state of the cochlea. The BM input-output functions display a compressive nonlinearity for frequencies around the characteristic frequency (CF, 8 to 8.75 kHz), but are linear for frequencies below 7 and above 10.5 kHz. In preparations with little surgical damage, isovelocity tuning curves at 0.1 mm/s are sharply tuned, have Q10's of about 6, minima as low as 13 dB SPL, tip-to-tail ratios (at 1 kHz) of 56 to 76 dB, and high-frequency slopes of about 300 dB/oct. These mechanical responses are as sharply tuned as frequency-threshold curves of chinchilla auditory nerve fibers with corresponding CF. There is a progressive loss of sensitivity of the mechanical response with time for the frequencies around CF, but not for frequencies on the tail of the tuning curve. In some experiments the nonlinearity was maintained for several hours, in spite of a considerable loss of sensitivity of the BM response. High-frequency plateaus were observed in both isovelocity tuning curves and phase-frequency curves.     

New Evidence of Active Tuning in Cochlea

The wonderful performance of hearing systems is mainly attributed to the tuning tiltering of basilar membrane （BM）. Although theory of the cochlear mechanism has been greatly developed since the 1970s and the amplification or sensitivity of the cochlea has been concluded due to the out hair cells, the mechanics underlying the sharp-tuning or frequency selectivity of cochlea remains a puzzle. We use the cochlear translation function derived from the data of an experiment of the BM in vivo to calculate basilar responses to tone bursts, and find that there are resonant peaks with the characteristic frequency at the corresponding place in the initial and terminal part of the responses. However, when the translation function is shallower, there will be no resonant peaks in the responses. The result indicates that the sharp tuning is due to existence of the active resonant tuning mechanism.     

Coherent reflection in a two-dimensional cochlea: Short-wave versus long-wave scattering in the generation of reflection-source otoacoustic emissions

The theory of coherent reflection filtering explains the empirical form of the cochlear reflectance by showing how it emerges from the coherent "backscattering" of forward-traveling waves by impedance perturbations in the mechanics of the cochlear partition. Since the theory was developed using the one-dimensional (1-D) transmission-line model of the cochlea, an obvious logical shortcoming is the failure of the long-wavelength approximation near the peak of the traveling wave, where coherent backscattering is purported to occur. Indeed, existing theory suggests that wave reflection may be strongly suppressed in the short-wave regime. To understand how short-wave behavior near the peak modifies the predictions of the long-wave theory, this paper solves the scattering problem in the 2-D cochlear model. The 2-D problem is reduced to a 1-D wave equation and the solution expressed as an infinite series in which successive terms arise via multiple scattering within the cochlea. The cochlear reflectance is computed in response-matched models constructed by solving the inverse problem to control for variations in mechanical tuning among models of different heights and dimensionality. Reflection from the peak region is significantly enhanced by the short-wave hydrodynamics, but other conclusions of the 1-D analysis--such as the predicted relation between emission group delay and the wavelength of the traveling wave--carry over with only minor modifications. The results illustrate the important role of passive hydromechanical effects in shaping otoacoustic emissions and cochlear tuning.     

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.     

Stimulus-frequency-emission group delay: a test of coherent reflection filtering and a window on cochlear tuning

This paper tests and applies a key prediction of the theory of coherent reflection filtering for the generation of reflection-source otoacoustic emissions. The theory predicts that reflection-source-emission group delay is determined by the group delay of the basilar-membrane (BM) transfer function at its peak. This prediction is tested over a seven-octave frequency range in cats and guinea pigs using measurements of stimulus-frequency-emission (SFOAE) group delay. A comparison with group delays calculated from published measurements of BM mechanical transfer functions supports the theory at the basal end of the cochlea. A comparison across the whole frequency range based on variations in the sharpness of neural tuning with characteristic frequency (CF) suggests that the predicted relation holds in the basal-most 60% of the cochlea. At the apical end of the cochlea, however, the measurements disagree with neural and mechanical group delays. This disagreement suggests that there are important differences in cochlear mechanics and/or mechanisms of emission generation between the base and apex of the cochlea. Measurements in humans over a four-octave range indicate that human SFOAE group delays are roughly a factor of 3 longer than their counterparts in cat and guinea pig but manifest similar trends across CF. The measurements thus reveal global deviations from scaling whose form appears quantitatively similar in all three species. Interpreted using the theory of coherent reflection filtering, the group delay measurements indicate that the wavelength at the peak of the traveling wave decreases with increasing CF at a rate of roughly 25% per octave in the base of the cochlea. The measurements and analysis reported here illustrate the rich potential inherent in OAE measurements for obtaining valuable information about basic cochlear properties such as tuning.     

Medial olivocochlear efferent inhibition of basilar-membrane responses to clicks: evidence for two modes of cochlear mechanical excitation

Conceptualizations of mammalian cochlear mechanics are based on basilar-membrane (BM) traveling waves that scale with frequency along the length of the cochlea, are amplified by outer hair cells (OHCs), and excite inner hair cells and auditory-nerve (AN) fibers in a simple way. However, recent experimental work has shown medial-olivocochlear (MOC) inhibition of AN responses to clicks that do not fit with this picture. To test whether this AN-initial-peak (ANIP) inhibition might result from hitherto unrecognized aspects of the traveling-wave or MOC-evoked inhibition, MOC effects on BM responses to clicks in the basal turns of guinea pig and chinchilla cochleae were measured. MOC stimulation inhibited BM click responses in a time and level dependent manner. Inhibition was not seen during the first half-cycle of the responses, but built up gradually, and ultimately increased the responses' decay rates. MOC stimulation also produced small phase leads in the response wave forms, but had little effect on the instantaneous frequency or the waxing and waning of the responses. These data, plus recent AN data, support the hypothesis that the MOC-evoked inhibitions of the traveling wave and of the ANIP response are separate phenomena, and indicate that the OHCs can affect at least two separate modes of excitation in the mammalian cochlea.     

Two-tone distortion in intracochlear pressure

Two-tone distortion was measured in the intracochlear pressure in the base of the gerbil cochlea, close to the sensory tissue, where the local motions and forces of the organ of Corti can be detected. The measurements probe both the underlying nonlinear process that generates two-tone distortion, and the filtering and spreading of the distortion products. Some of our findings are as follows: (1) The observations were consistent with previous observations of two-tone distortion in BM motion [J. Neurophysiol. 77, 2385-2399 (1997); J. Neurophysiol. 78, 261-270 (1997)]. (2) Frequency sweeps show distortion product tuning and phase-versus-frequency behavior that is similar, but not identical, to single tone tuning. (3) The decay of distortion products with distance from the basilar membrane confirms the feasibility that they could drive the stapes by a direct fluid route, as proposed by Ren [Nat. Neurosci. 7, 333-334 (2004)]. (4) The phases of the distortion products within a single family (the group of distortion products generated by a single primary pair) in some cases alternated between 0 degrees and 180 degrees when referenced to the phases of the primaries. This behavior is predicted by a simple compressive nonlinearity.     

On Riccati equations describing impedance relations for forward and backward excitation in the one-dimensional cochlea model

Recent experimental observations of otoacoustic emissions suggest the existence of spontaneous emitters of sound on the basilar membrane. These tend to send off waves not only in the normal direction of propagation. It is therefore significant to study the environmental conditions such an emitter finds inside the cochlea. The impedance relations seen by these emitters are described by the Riccati equation for an inhomogeneous transmission line. The results reported in this paper differ considerably for forward and backward excitation. This reflects the quite different behavior of the cochlea pertaining to waves traveling forward and backward. Because of reflections, backward waves cannot be treated with the Liouville-Green approximation.     

Basin boundaries in asymmetric vibrations of a circular plate

In order to investigate further nonlinear asymmetric vibrations of a clamped circular plate under a harmonic excitation, we reexamine a primary resonance, studied by Yeo and Lee [Corrected solvability conditions for non-linear asymmetric vibrations of a circular plate, Journal of Sound and Vibration 257 (2002) 653-665] in which at most three stable steady-state responses (one standing wave and two traveling waves) are observed to exist. Further examination, however, tells that there exist at most five stable steady-state responses: one standing wave and four traveling waves. Two of the traveling waves lose their stability by Hopf bifurcation and have a sequence of period-doubling bifurcations leading to chaos. When the system has five attractors: three equilibrium solutions (one standing wave and two traveling waves) and two chaotic attractors (two modulated traveling waves), the basin boundaries of the attractors on the principal plane are obtained. Also examined is how basin boundaries of the modulated motions (quasi-periodic and chaotic motions) evolve as a system parameter varies. The basin boundaries of the modulated motions turn out to have the fractal nature.     

A wave traveling over a Hopf instability shapes the cochlear tuning curve

The tuning curve of the cochlea measures how intense an input is required to elicit a given output level as a function of the frequency. It is a fundamental object of auditory theory, for it summarizes how to identify sounds on the basis of the cochlear output. A simple model is presented showing that only two elements are sufficient for establishing the cochlear tuning curve: a broadly tuned traveling wave, moving unidirectionally from high to low frequencies, and a set of mechanosensors poised at the threshold of an oscillatory (Hopf) instability. These two components generate the various frequency-response regimes needed for a cochlear tuning curve with a high slope.     

Inverted direction of wave propagation (IDWP) in the cochlea

The "classical" view on wave propagation is that propagating waves are possible in both directions along the length of the basilar membrane and that they have identical properties. Results of several recently executed experiments [T. Ren, Nat. Neurosci. 2, 333-334 (2004) and W. X. He, A. L. Nuttall, and T. Ren, Hear. Res., 228, 112-122 (2007)] appear to contradict this view. In the current work measurements were made of the velocity of the guinea-pig basilar membrane (BM). Distortion products (DPs) were produced by presenting two primary tones, with frequencies below the characteristic frequency f(0) of the BM location at which the BM measurements were made, with a constant frequency ratio. In each experiment the phase of the principal DP, with frequency 2f(1)-f(2), was recorded as a function of the DP frequency. The results indicate that the DP wave going from the two-tone interaction region toward the stapes is not everywhere traveling in the reverse direction, but also in the forward direction. The extent of the region in which the forward wave occurs appears larger than is accounted for by classical theory. This property has been termed "inverted direction of wave propagation." The results of this study confirm the wave propagation findings of other authors. The experimental data are compared to theoretical predictions for a classical three-dimensional model of the cochlea that is based on noise-response data of the same animal. Possible physical mechanisms underlying the findings are discussed.     

Using weak impulses to suppress traveling waves in excitable media

Here we propose mechanisms for suppressing non-steady-state motions--propagating pulses, spiral waves, spiral-wave chaos--in excitable media. Our approach is based on two points: (1) excitable media are multistable; and (2) traveling waves in excitable media can be separated into fast and slow motions, which can be considered independently. We show that weak impulses can be used to change the values of the slow variable at the front and back of a traveling wave, which leads to wave front and wave back velocities that are different from each other. This effect can destabilize the traveling wave, resulting in a transition to the rest state.     

Transmission of cochlear distortion products as slow waves: a comparison of experimental and model data

There is a long-lasting question of how distortion products (DPs) arising from nonlinear amplification processes in the cochlea are transmitted from their generation sites to the stapes. Two hypotheses have been proposed: (1) the slow-wave hypothesis whereby transmission is via the transverse pressure difference across the cochlear partition and (2) the fast-wave hypothesis proposing transmission via longitudinal compression waves. Ren with co-workers have addressed this topic experimentally by measuring the spatial vibration pattern of the basilar membrane (BM) in response to two tones of frequency f(1) and f(2). They interpreted the observed negative phase slopes of the stationary BM vibrations at the cubic distortion frequency f(DP) = 2f(1) - f(2) as evidence for the fast-wave hypothesis. Here, using a physically based model, it is shown that their phase data is actually in accordance with the slow-wave hypothesis. The analysis is based on a frequency-domain formulation of the two-dimensional motion equation of a nonlinear hydrodynamic cochlea model. Application of the analysis to their experimental data suggests that the measurement sites of negative phase slope were located at or apical to the DP generation sites. Therefore, current experimental and theoretical evidence supports the slow-wave hypothesis. Nevertheless, the analysis does not allow rejection of the fast-wave hypothesis.     

A hydromechanical biomimetic cochlea: experiments and models

The construction, measurement, and modeling of an artificial cochlea (ACochlea) are presented in this paper. An artificial basilar membrane (ABM) was made by depositing discrete Cu beams on a piezomembrane substrate. Rather than two fluid channels, as in the mammalian cochlea, a single fluid channel was implemented on one side of the ABM, facilitating the use of a laser to detect the ABM vibration on the other side. Measurements were performed on both the ABM and the ACochlea. The measurement results on the ABM show that the longitudinal coupling on the ABM is very strong. Reduced longitudinal coupling was achieved by cutting the membrane between adjacent beams using a laser. The measured results from the ACochlea with a laser-cut ABM demonstrate cochlear-like features, including traveling waves, sharp high-frequency rolloffs, and place-specific frequency selectivity. Companion computational models of the mechanical devices were formulated and implemented using a circuit simulator. Experimental data were compared with simulation results. The simulation results from the computational models of the ABM and the ACochlea are similar to their experimental counterparts.     

Medial-olivocochlear-efferent inhibition of the first peak of auditory-nerve responses: evidence for a new motion within the cochlea

Despite the insights obtained from click responses, the effects of medial-olivocochlear (MOC) efferents on click responses from single-auditory-nerve (AN) fibers have not been reported. We recorded responses of cat single AN fibers to randomized click level series with and without electrical stimulation of MOC efferents. MOC stimulation inhibited (1) the whole response at low sound levels, (2) the decaying part of the response at all sound levels, and (3) the first peak of the response at moderate to high sound levels. The first two effects were expected from previous reports using tones and are consistent with a MOC-induced reduction of cochlear amplification. The inhibition of the AN first peak, which was strongest in the apex and middle of the cochlea, was unexpected because the first peak of the classic basilar-membrane (BM) traveling wave receives little or no amplification. In the cochlear base, the click data were ambiguous, but tone data showed particularly short group delays in the tail-frequency region that is strongly inhibited by MOC efferents. Overall, the data support the hypothesis that there is a motion that bends inner-hair-cell stereocilia and can be inhibited by MOC efferents, a motion that is present through most, or all, of the cochlea and for which there is no counterpart in the classic BM traveling wave.     

Cochlear micromechanics--a mechanism for transforming mechanical to neural tuning within the cochlea.

A linear mathematical model is proposed which will account for the differences observed between mechanically measured data of Rhode (1971) for basilar membrane motion, and the responses of neural tuning curves (Kiang et al., 1974). We show that theoretical tuning curves may be derived from mechanical responses by forming the difference between the pressure across the basilar membrane and its displacement. Some ramifications of this proposal are discussed. We then propose a hypothetical physical model which could perform such a function.     

Flow of endolymph in the inner spiral sulcus and the subtectorial space

Flows of endolymph within the inner spiral sulcus and the subtectorial space are studied analytically. These flows are driven by boundary displacements and scala media pressure, all prescribed in the form of traveling sine waves with uniform amplitude, wave speed, and wavelength. Prescribed boundary displacements have no axial components and are assumed "small." In the subtectorial space, waves are further assumed "long," and inner and outer hair cells' stereocilia are represented by permeable barriers. Boundary motions of the subtectorial space are assumed to be associated with basilar membrane motion. The localized boundary motions that would presumably accompany independent outer hair cell motions are not admitted. The pressure drop across the barrier representing the inner hair cells' stereocilia is evaluated for four specific input conditions. The results are used to assess its relative sensitivity to three types of boundary displacement and to examine the contribution of endolymph flow to the "second filter." The model predicts the introduction of appreciable tuning (102.3 dB/octave) into the auditory signal between the stages of relative normal displacement of the boundaries of the subtectorial space and the generation of a pressure drop across the inner hair cells' stereocilia. The outer barrier is removed from the model, and the pressure drop across the inner barrier is reevaluated for the same four cases to study its sensitivity to destruction of the outer hair cells' stereocilia. These results are examined in light of data by Robertson and Johnstone [D. Robertson and B. M. Johnstone, J. Acoust. Soc. Am. 66, 466-469 (1979)].     

The oscillatory instability of a spatially homogeneous state in large aspect ratio systems of fluid dynamics

We derive the generalized Ginzburg-Landau equation for the case of an oscillatory instability of a spatially homogeneous state in systems whose geometry is characterized by two entirely different length scales. This evolution equation is applied to describe the spatio-temporal behaviour of the onset of convection in binary fluid mixtures in large aspect ratio systems. We obtain time periodic traveling wave motions, quasiperiodic fluid motions with two and more frequencies modulating the intensities of the traveling waves as well as chaotic temporal behaviour.     

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.