Tracing Distortion Product (DP) Waves in a Cochlear Model

Basilar-membrane interference patterns from multiple internal reflection of cochlear traveling waves

At low stimulus levels, basilar-membrane (BM) mechanical transfer functions in sensitive cochleae manifest a quasiperiodic rippling pattern in both amplitude and phase. Analysis of the responses of active cochlear models suggests that the rippling is a mechanical interference pattern created by multiple internal reflection within the cochlea. In models, the interference arises when reverse-traveling waves responsible for stimulus-frequency otoacoustic emissions (SFOAEs) reflect off the stapes on their way to the ear canal, launching a secondary forward-traveling wave that combines with the primary wave produced by the stimulus. Frequency-dependent phase differences between the two waves then create the rippling pattern measurable on the BM. Measurements of BM ripples and SFOAEs in individual chinchilla ears demonstrate that the ripples are strongly correlated with the acoustic interference pattern measured in ear-canal pressure, consistent with a common origin involving the generation of SFOAEs. In BM responses to clicks, the ripples appear as temporal fine structure in the response envelope (multiple lobes, waxing and waning). Analysis of the ripple spacing and response phase gradients provides a test for the role of fast- and slow-wave modes of reverse energy propagation within the cochlea. The data indicate that SFOAE delays are consistent with reverse slow-wave propagation but much too long to be explained by fast waves.

A resonance approach to cochlear mechanics

BACKGROUND

How does the cochlea analyse sound into its component frequencies? In the 1850s Helmholtz thought it occurred by resonance, whereas a century later Békésy's work indicated a travelling wave. The latter answer seemed to settle the question, but with the discovery in 1978 that the cochlea emits sound, the mechanics of the cochlea was back on the drawing board. Recent studies have raised questions about whether the travelling wave, as currently understood, is adequate to explain observations.

APPROACH

Applying basic resonance principles, this paper revisits the question. A graded bank of harmonic oscillators with cochlear-like frequencies and quality factors is simultaneously excited, and it is found that resonance gives rise to similar frequency responses, group delays, and travelling wave velocities as observed by experiment. The overall effect of the group delay gradient is to produce a decelerating wave of peak displacement moving from base to apex at characteristic travelling wave speeds. The extensive literature on chains of coupled oscillators is considered, and the occurrence of travelling waves, pseudowaves, phase plateaus, and forced resonance in such systems is noted.

CONCLUSION AND SIGNIFICANCE

This alternative approach to cochlear mechanics shows that a travelling wave can simply arise as an apparently moving amplitude peak which passes along a bank of resonators without carrying energy. This highlights the possible role of the fast pressure wave and indicates how phase delays and group delays of a set of driven harmonic oscillators can generate an apparent travelling wave. It is possible to view the cochlea as a chain of globally forced coupled oscillators, and this model incorporates fundamental aspects of both the resonance and travelling wave theories.

Investigating the wave-fixed and place-fixed origins of the 2f(1)-f(2) distortion product otoacoustic emission within a micromechanical cochlear model

The 2f(1)-f(2) distortion product otoacoustic emission (DPOAE) arises within the cochlea due to the nonlinear interaction of two stimulus tones (f(1) and f(2)). It is thought to comprise contributions from a wave-fixed source and a place-fixed source. The generation and transmission of the 2f(1)-f(2) DPOAE is investigated here using quasilinear solutions to an elemental model of the human cochlea with nonlinear micromechanics. The micromechanical parameters and nonlinearity are formulated to match the measured response of the cochlea to single- and two-tone stimulation. The controlled introduction of roughness into the active micromechanics of the model allows the wave- and place-fixed contributions to the DPOAE to be studied separately. It is also possible to manipulate the types of nonlinear suppression that occur within the quasilinear model to investigate the influence of stimulus parameters on DPOAE generation. The model predicts and explains a variety of 2f(1)-f(2) DPOAE phenomena: The dependence of emission amplitude on stimulus parameters, the weakness of experiments designed to quantify cochlear amplifier gain, and the predominant mechanism which gives rise to DPOAE fine structure. In addition, the model is used to investigate the properties of the wave-fixed source and how these properties are influenced by the stimulus parameters.

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.