Distortion products and backward-traveling waves in nonlinear active models of the cochlea

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.

Section: Introductionmentioning

confidence: 95%

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

Vetešník

Gummer

2012

“…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.…”

Section: A Bm Ripples and Standing Wavesmentioning

confidence: 99%

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

Shera

Cooper

2013

Self Cite

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.

“…They found that forward propagation waves could be generated by the DP if the activity was sufficiently broad and the reflectivity of the stapes was realistic. Although the model of Sisto et al 22 is incomplete as it does not admit fast waves in the same way as a more complete two-duct model does (either an elegant post-processing step, as in Yoon et al 3 or our more straightforward approach would be needed to include this effect), it nicely points out that when activity is present, an internal force can generate forward traveling waves. Our model predicts such a situation when the best place of the stimulus frequency is apical to the force (see Fig.…”

Section: E Implications On the Dpoaementioning

confidence: 99%

“…The forcing at the DP frequency arising from the nonlinear interaction of the primaries is likely more complicated (with variable phases and amplitudes). Sisto et al 22 were able to control the width of the region of the DP force generation in a nonlinear cochlear model by varying the model parameters. They found that forward propagation waves could be generated by the DP if the activity was sufficiently broad and the reflectivity of the stapes was realistic.…”

Section: E Implications On the Dpoaementioning

confidence: 99%

“…The classical model found backward traveling waves dominate the emission. Sisto et al 22 used a onedimensional (1D) model of the cochlear fluid coupled to a nonlinear model of the BM to study distortion product emissions. They found a negative phase slope under some choices of stapes reflectivity and of the parameters of their active model.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Direction of wave propagation in the cochlea for internally excited basilar membrane

Grosh

2012

Otoacoustic emissions are an indicator of a normally functioning cochlea and as such are a useful tool for non-invasive diagnosis as well as for understanding cochlear function. While these emitted waves are hypothesized to arise from active processes and exit through the cochlear fluids, neither the precise mechanism by which these emissions are generated nor the transmission pathway is completely known. With regard to the acoustic pathway, two competing hypotheses exist to explain the dominant mode of emission. One hypothesis, the backward-traveling wave hypothesis, posits that the emitted wave propagates as a coupled fluid-structure wave while the alternate hypothesis implicates a fast, compressional wave in the fluid as the main mechanism of energy transfer. In this paper, we study the acoustic pathway for transmission of energy from the inside of the cochlea to the outside through a physiologically-based theoretical model. Using a well-defined, compact source of internal excitation, we predict that the emission is dominated by a backward traveling fluid-structure wave. However, in an active model of the cochlea, a forward traveling wave basal to the location of the force is possible in a limited region around the best place. Finally, the model does predict the dominance of compressional waves under a different excitation, such as an apical excitation.