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.

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.

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.

The effect of stimulus-frequency ratio on distortion product otoacoustic emission components.

A detailed measurement of distortion product otoacoustic emission (DPOAE) fine structure was used to extract estimates of the two major components believed to contribute to the overall DPOAE level in the ear canal. A fixed-ratio paradigm was used to record DPOAE fine structure from three normal-hearing ears over a range of 400 Hz for 12 different stimulus-frequency ratios between 1.053 and 1.36 and stimulus levels between 45 and 75 dB SPL. Inverse Fourier transforms of the amplitude and phase data were filtered to extract the early component from the generator region of maximum stimulus overlap and the later component reflected from the characteristic frequency region of the DPOAE. After filtering, the data were returned to the frequency domain to evaluate the impact of the stimulus-frequency ratio and stimulus level on the relative levels of the components. Although there were significant differences between data from different ears some consistent patterns could be detected. The component from the overlap region of the stimulus tones exhibits a bandpass shape, with the maximum occurring at a ratio of 1.2. The mean data from the DPOAE characteristic frequency region also exhibits a bandpass shape but is less sharply tuned and exhibits greater variety across ears and stimulus levels. The component from the DPOAE characteristic frequency region is dominant at ratios narrower than approximately 1.1 (the transition varies between ears). The relative levels of the two components are highly variable at ratios greater than 1.3 and highly dependent on the stimulus level. The reflection component is larger at all ratios at the lowest stimulus level tested (45/45 dB SPL). We discuss the factors shaping DPOAE-component behavior and some cursory implications for the choice of stimulus parameters to be used in clinical protocols.

Do forward- and backward-traveling waves occur within the cochlea? Countering the critique of Nobili et al.

The question of whether or not forward- and backward-traveling waves occur within the cochlea constitutes a long-standing controversy in cochlear mechanics recently brought to the fore by the problem of understanding otoacoustic emissions. Nobili and colleagues articulate the opposition to the traveling-wave viewpoint by arguing that wave-equation formulations of cochlear mechanics fundamentally misrepresent the hydrodynamics of the cochlea [e.g., Nobili et al. (2003) J. Assoc. Res. Otolaryngol. 4:478-494]. To correct the perceived deficiencies of the wave-equation formulation, Nobili et al. advocate an apparently altogether different approach to cochlear modeling--the so-called "hydrodynamic" or "Green's function" approach--in which cochlear responses are represented not as forward- and backward-traveling waves but as weighted sums of the motions of individual basilar membrane oscillators, each interacting with the others via forces communicated instantaneously through the cochlear fluids. In this article, we examine Nobili and colleagues' arguments and conclusions while attempting to clarify the broader issues at stake. We demonstrate that the one-dimensional wave-equation formulation of cochlear hydrodynamics does not misrepresent long-range fluid coupling in the cochlea, as claimed. Indeed, we show that the long-range component of Nobili et al.'s three-dimensional force propagator is identical to the hydrodynamic Green's function representing a one-dimensional tapered transmission line. Furthermore, simulations that Nobili et al. use to discredit wave-equation formulations of cochlear mechanics (i.e., cochlear responses to excitation at a point along the basilar membrane) are readily reproduced and interpreted using a simple superposition of forward- and backward-traveling waves. Nobili and coworkers' critique of wave-equation formulations of cochlear mechanics thus appears to be without compelling foundation. Although the traveling-wave and hydrodynamic formulations impose strikingly disparate conceptual and computational frameworks, the two approaches ultimately describe the same underlying physics.

Multiple internal reflections in the cochlea and their effect on DPOAE fine structure.

In recent years, evidence has accumulated in support of a two-source model of distortion product otoacoustic emissions (DPOAEs). According to such models DPOAEs recorded in the ear canal are associated with two separate sources of cochlear origin. It is the interference between the contributions from the two sources that gives rise to the DPOAE fine structure (a pseudoperiodic change in DPOAE level or group delay with frequency). Multiple internal reflections between the base of the cochlea (oval window) and the DP tonotopic place can add additional significant components for certain stimulus conditions and thus modify the DPOAE fine structure. DPOAEs, at frequency increments between 4 and 8 Hz, were recorded at fixed f2/f1 ratios of 1.053, 1.065, 1.08, 1.11, 1.14, 1.18, 1.22, 1.26, 1.30, 1.32, 1.34, and 1.36 from four subjects. The resulting patterns of DPOAE amplitude and group delay (the negative of the slope of phase) revealed several previously unreported patterns in addition to the commonly reported log sine variation with frequency. These observed "exotic" patterns are predicted in computational simulations when multiple internal reflections are included. An inverse FFT algorithm was used to convert DPOAE data from the frequency to the "time" domain. Comparison of data in the time and frequency domains confirmed the occurrence of these "exotic" patterns in conjunction with the presence of multiple internal reflections. Multiple internal reflections were observed more commonly for high primary ratios (f2/f1 > or = 1.3). These results indicate that a full interpretation of the DPOAE level and phase (group delay) must include not only the two generation sources, but also multiple internal reflections.