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

Abstract

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.

Time-domain demonstration of distributed distortion-product otoacoustic emission components

“…The present study supplies new experimental evidence that supports Vetesnik and Gummer's (2012) conclusion. At narrow f 2 /f 1 ratios, where much of the data supporting IDWP were obtained, the present findings revealed complexities in the DPOAE time waveforms.…”

“…To obtain a more detailed insight into this problem, Vetesnik and Gummer (2012) compared the data of Ren and colleagues (Ren, 2004;He et al, 2008He et al, , 2010 to simulations of their experiments in a nonlinear cochlear model of DPOAE generation. From this analysis, they concluded that the appearance of the IDWP for DPOAEs might have been due to the DPOAE being at least partially generated basal to the measurement site.…”

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

“…The result is a measurable interference pattern near CF. As discussed elsewhere (Sisto et al, 2011;de Boer et al, 2011;Vetesnik and Gummer, 2012), analogous reasoning explains why studies that have used distortion products to look for reversetraveling waves on the BM have had difficulty finding them (e.g., Ren, 2004;He et al, 2008;de Boer et al, 2008)-the reverse wave, although present, is swamped out by the forward wave that subsequently arises from reflection at the stapes and is then boosted by the cochlear amplifier.…”

Auditory Distortions: Origins and Functions

“…Another recent theoretical approach (254) examines several conventional models of sound propagation in the cochlea, which consistently predict that slow reversetraveling transverse waves can produce negative phase slopes if two conditions are met: a broad enough distribution of DP sites of generation and a reasonably large stapes reflectivity. Even more recently, application of a two-dimensional nonlinear hydrodynamic cochlea model (283) to the analysis of Ren's experiments suggested that the DP generation sites were well basal to the measurement sites, thus reconciling the negative phase slopes with the possibility of slow-wave backward propagation. The distribution of generation sites basal to the f 2 CF location was estimated to 0.5 mm for f 2 ϭ 12 kHz, which emphasizes, once again, two important caveats.…”