Tracing Distortion Product (DP) Waves in a Cochlear Model

In many cases a cochlear model suffices to explain (by simulation) the properties of waves in the cochlea. This is not so in the case of a distortion product (DP) set up by presenting two primary tones to the cochlea. A three-dimensional model predicts, apart from a DP wave traveling in the apical direction, a DP wave that travels from the region of overlap of the two tone patterns towards the stapes-setting the stapes in motion so as to produce an otoacoustic emission at the DP frequency. Experimental research has shown, however, that the actual DP wave in the cochlea appears to travel in the opposite direction, from near the stapes to the overlap region. This feature has been termed "inverted direction of wave propagation" (IDWP). The forward wave could result from an unknown process such as a "hidden source" near the stapes. In the present study we have disproved this notion, by using a one-dimensional model of the cochlea. It is found that both reverse and forward waves are set up by the source of nonlinearity, in the same way as has been published in an earlier work. The present results reveal that IDWP in the data corresponds to the region where the DP wave, originally created as a reverse wave but reflected from the stapes, has received so much amplification that it starts to dominate over the reverse wave. Hence we conclude that IDWP in a one-dimensional model is a direct manifestation of cochlear amplification.

Inverse-solution method for a class of non-classical cochlear models

Measurements of distortion-product (DP) waves inside the cochlea have led to a conception of wave propagation that is at variance with the "classical" attitude. Of the several alternatives that have been proposed to remedy this situation, the feed-forward model could be a promising one. This paper describes a method to apply the inverse solution with the aim to attain a feed-forward model that accurately reproduces a measured response. It is demonstrated that the computation method is highly successful. Subsequently, it is shown that in a feed-forward model a DP wave generated by a two-tone stimulus is almost exclusively a forward-traveling wave which property agrees with the nature of the experimental findings. However, the amplitude of the computed DP wave is only substantial in the region where the stimulation patterns of the two primary tones overlap. In addition, the model developed cannot explain coherent reflection for single tones. It has been suggested that a forward transversal DP wave induced by a (retrograde) compression wave could be involved in DP wave generation. This topic is critically evaluated.

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.

Forward and reverse waves in nonclassical models of the cochlea

In "classical" models of the cochlea the mechanical properties of the cochlear partition (in which the basilar membrane plays a dominant role) depend only on the local longitudinal coordinate. Wave propagation in such models is the same for both propagation directions, towards the apex and towards the base. "Nonclassical" models contain mechanical properties that depend on variables at more than one location. In such models the properties of wave propagation may well be asymmetrical. This note presents an analysis of feed-forward and feed-backward models, with the emphasis on the properties of forward and reverse waves. In both of these classes of model, wave amplification for forward waves turns into wave attenuation for reverse waves. The slope of the phase pattern is nearly the same for the two types of waves, it is increased in feed-forward models and decreased in feed-backward models-with respect to a model without feedback.

Allen-Fahey and related experiments support the predominance of cochlear slow-wave otoacoustic emissions

Originally proposed as a method for measuring the power gain of the cochlear amplifier, Allen-Fahey experiments compare intracochlear distortion products and ear-canal otoacoustic emissions (OAEs) under tightly controlled conditions. In this paper Allen-Fahey experiments are shown to place significant constraints on the dominant mode of reverse energy propagation within the cochlea. Existing Allen-Fahey experiments are reviewed and shown to contradict the predictions of compression-wave OAE models recently proposed in the literature. In compression-wave models, distortion products propagate from their site of generation to the stapes via longitudinal compression waves in the cochlear fluids (fast waves); in transverse traveling-wave models, by contrast, distortion products propagate primarily via pressure-difference waves whose velocity and other characteristics depend on the mechanical properties of the cochlear partition (slow waves). Compression-wave models predict that the distortion-product OAEs (DPOAEs) measured in the Allen-Fahey paradigm increase at close primary-frequency ratios (or remain constant in the hypothetical absence of tuned suppression). The behavior observed experimentally is just the opposite-a pronounced decrease in DPOAE amplitude at close ratios. Since neither compression-wave nor simple conceptual "hybrid-wave" models can account for the experimental results--whereas slow-wave models can, via systematic changes in distortion-source directionality arising from wave-interference effects--Allen-Fahey and related experiments provide compelling evidence against the predominance of compression-wave OAEs in mammalian cochlear mechanics.

Wave propagation patterns in a "classical" three-dimensional model of the cochlea

The generation mechanisms of cochlear waves, in particular those that give rise to otoacoustic emissions (OAEs), are often complex. This makes it difficult to analyze wave propagation. In this paper two unusual excitation methods are applied to a three-dimensional stylized classical nonlinear model of the cochlea. The model used is constructed on the basis of data from an experimental animal selected to yield a smooth basilar-membrane impedance function. Waves going in two directions can be elicited by exciting the model locally instead of via the stapes. Production of DPOAEs was simulated by presenting the model with two relatively strong primary tones, with frequencies f1 and f2, estimating the driving pressure for the distortion product (DP) with frequency 2f1 - f2, and computing the resulting DP response pattern - as a function of distance along the basilar membrane. For wide as well as narrow frequency separations the resulting DP wave pattern in the model invariably showed that a reverse wave is dominant in nearly the entire region from the peak of the f2-tone to the stapes. The computed DP wave pattern was further analyzed as to its constituent components with the aim to isolate their properties.

Spontaneous basilar-membrane oscillation (SBMO) and coherent reflection

In a previous report (in JARO) we have described a relatively high-frequency (15 kHz) spontaneous oscillation of the basilar membrane (SBMO) in a guinea pig ear; this oscillation was accompanied by a spontaneous otoacoustic emission (SOAE) at the same frequency. During the spontaneous oscillation and after it had subsided, the mechanical frequency response of the basilar membrane was measured by way of a wide-band random-noise stimulus, and it showed a number of spectral peaks, one of which having the frequency of the original oscillation. This pattern of peaks cannot be explained by assuming a single place of reflection in the cochlea. In this paper the process of 'coherent reflection' is artificially evoked in a three-dimensional model of the cochlea by imposing random place-fixed irregularities to the basilar-membrane impedance. It is shown that in the model a series of peaks arises in the frequency spectrum of the basilar-membrane response which phenomenon resembles the one found in the experimental animal. It is also shown that these peaks are actually due to superposition of the primary wave and a wave resulting from 'coherent reflection' which is reflected at the stapes. When the intensity of the acoustic stimulus signal is increased, the relative sizes of these peaks in the simulation diminish in about the same way as in the experiment. It is concluded that coherent reflection most likely is the cause of the 'extra peaks', and that this concept can also explain the observed level dependence of these peaks. The findings of this study lead to a minor refinement regarding the actual requirements for coherent reflection to arise.

The Allen-Fahey experiment extended

An ingenious experiment has been performed by Allen and Fahey [J. Acoust. Soc. Am. 92, 178-188 (1992)], in which they attempted to estimate the gain of the cochlear amplifier by comparing responses to the 2 f1-f2 distortion product (DP) in the outer ear canal (otoacoustic emissions) and from an auditory-nerve fiber. Results were essentially negative: no evidence of cochlear amplification was found in that experiment. A variation of that experiment is reported here, where DP responses in the outer ear canal are compared with mechanical responses of the basilar membrane. This variation does not suffer from the major limitation in the original experiment in the choice of possible frequency ratios. Results confirm and extend those of Allen and Fahey entirely. Apparently, the gain of the cochlear amplifier cannot be measured in this way. It is argued that the retrograde wave going to the stapes is most likely reduced in magnitude by wave interference when the two primary frequencies approach each other. Such a reduction does not take place in the forward-going wave to the location tuned to the DP frequency. This explanation is illustrated on the basis of results of earlier experiments on the movements of the basilar membrane.

High-frequency electromotile responses in the cochlea

Mammalian outer hair cells (OHCs) convert electrical energy into mechanical energy. The significance of this electromotility rests in the ability of the OHCs to modulate the vibrations of the cochlear partition in vivo. While high-frequency electromotility of isolated OHCs has been demonstrated at frequencies up to 100 kHz, a similar measure of the effect of OHC electromotility on motion of the sensory epithelium has not been made in vivo. In this study, in vivo electrical stimulation of the guinea pig cochlea is found to induce a mechanical response of the basilar membrane for frequencies to at least 100 kHz, nearly twice the upper limit of hearing for the guinea pig. The perfusion of salicylate in the cochlea reversibly reduces the electromotile response, indicating that an OHC-mediated process is the key contributor.

Basilar-membrane responses to multicomponent (Schroeder-phase) signals: understanding intensity effects

Harmonic complexes comprised of the same spectral components in either positive-Schroeder (+Schr) or negative-Schroeder (-Schr) phase [see Schroeder, IEEE Trans. Inf. Theory 16, 85-89 (1970)] have identical long-term spectra and similar waveform envelopes. However, localized patterns of basilar-membrane (BM) excitation can be quite different in response to these two stimuli. Measurements in chinchillas showed more modulated (peakier) BM excitation for +Schr than -Schr complexes [Recio and Rhode, J. Acoust. Soc. Am. 108, 2281-2298 (2000)]. In the current study, laser velocimetry was used to examine BM responses at a location tuned to approximately 17 kHz in the basal turn of the guinea-pig cochlea, for +Schr and -Schr complexes with a 203-Hz fundamental frequency and including 101 equal-amplitude components from 2031 to 22,344 Hz. At 35-dB SPL, +Schr response waveforms showed greater amplitude modulation than -Schr responses. With increasing stimulation level, internal modulation decreased for both complexes. To understand the observed phenomena quantitatively, responses were predicted on the basis of a linearized model of the cochlea. Prediction was based on an "indirect impulse response" measured in the same animal. Response waveforms for Schroeder-phase signals were accurately predicted, provided that the level of the indirect impulse used in prediction closely matched the level of the Schroeder-phase stimulus. This result confirms that the underlying model, which originally was developed for noise stimuli, is valid for stimuli that produce completely different response waveforms. Moreover, it justifies explanation of cochlear filtering (i.e., differential treatment of different frequencies) in terms of a linear system.

In vivo micromechanical measurements of the organ of Corti in the basal cochlear turn

Cochlear mechanical measurements of organ of Corti motion are generally accomplished in the apical or basal turn as in vivo or in vitro studies. In the apex it is possible to observe and measure tectorial membrane vibration as well as vibrations of structures such as the reticular lamina or the basilar membrane (BM). However, compared to the basal turn, cochlear amplification and nonlinearity are not strong in the apex. Basal turn studies have typically been limited to point location measurements of the BM but improved technology for laser interferometry is now making possible the spatial mapping of BM motion. The 'complexity' of BM motion in the radial direction (particularly the phase variation) is important to new models of cochlear wave amplification. In future work it may be possible to learn about vibration of structures within the organ of Corti.