Low-passed outer hair cell response and apical-basal transition in a nonlinear transmission-line cochlear model

Optimal Scale-Invariant Wavelet Representation and Filtering of Human Otoacoustic Emissions

Otoacoustic emissions (OAEs) are generated in the cochlea and recorded in the ear canal either as a time domain waveform or as a collection of complex responses to tones in the frequency domain (Probst et al. J Account Soc Am 89:2027-2067, 1991). They are typically represented either in their original acquisition domain or in its Fourier-conjugated domain. Round-trip excursions to the conjugated domain are often used to perform filtering operations in the computationally simplest way, exploiting the convolution theorem. OAE signals consist of the superposition of backward waves generated in different cochlear regions by different generation mechanisms, over a wide frequency range. The cochlear scaling symmetry (cochlear physics is the same at all frequency scales), which approximately holds in the human cochlea, leaves its fingerprints in the mathematical properties of OAE signals. According to a generally accepted taxonomy (Sher and Guinan Jr, J Acoust Soc Am 105:782-798, 1999), OAEs are generated either by wave-fixed sources, moving with frequency according with the cochlear scaling (as in nonlinear distortion) or by place-fixed sources (as in coherent reflection by roughness). If scaling symmetry holds, the two generation mechanisms yield OAEs with different phase gradient delay: almost null for wave-fixed sources, and long (and scaling as 1/f) for place-fixed sources. Thus, the most effective representation of OAE signals is often that respecting the cochlear scale-invariance, such as the time-frequency domain representation provided by the wavelet transform. In the time-frequency domain, the elaborate spectra or waveforms yielded by the superposition of OAE components from different generation mechanisms assume a much clearer 2-D pattern, with each component localized in a specific and predictable region. The wavelet representation of OAE signals is optimal both for visualization purposes and for designing filters that effectively separate different OAE components, improving both the specificity and the sensitivity of OAE-based applications. Indeed, different OAE components have different physiological meanings, and filtering dramatically improves the signal-to-noise ratio.

Crucial 3-D viscous hydrodynamic contributions to the theoretical modeling of the cochlear response

This study uses a 3-D representation of the cochlear fluid to extend the results of a recent paper [Sisto, Belardinelli, and Moleti (2021b). J. Acoust. Soc. Am. 150, 4283-4296] in which two hydrodynamic effects, pressure focusing and viscous damping of the BM motion, both associated with the sharp increase in the wavenumber in the peak region, were analyzed for a 2-D fluid, coupled to a standard 1-D transmission-line WKB approach to cochlear modeling. The propagation equation is obtained from a 3-D fluid volume conservation equation, yielding the focusing effect, and the effect of viscosity is represented as a correction to the local 1-D admittance. In particular, pressure focusing amplifies the BM response without modifying the peak admittance, and viscous damping determines the position of the response peak counteracting focusing, as sharp gradients of the velocity field develop. The full 3-D WKB formalism is necessary to represent satisfactorily the behavior of the fluid velocity field near the BM-fluid interface, strictly related to viscous losses. As in finite element models, a thin layer of fluid is effectively attached to the BM due to viscosity, and the viscous force associated with the vertical gradient of the fluid vertical velocity acts on the BM through this layer.

Fluid focusing and viscosity allow high gain and stability of the cochlear response

This paper discusses the role of two-dimensional (2-D)/three-dimensional (3-D) cochlear fluid hydrodynamics in the generation of the large nonlinear dynamical range of the basilar membrane (BM) and pressure response, in the decoupling between cochlear gain and tuning, and in the dynamic stabilization of the high-gain BM response in the peak region. The large and closely correlated dependence on stimulus level of the BM velocity and fluid pressure gain [Dong, W., and Olson, E. S. (2013). Biophys. J. 105(4), 1067-1078] is consistent with a physiologically oriented schematization of the outer hair cell (OHC) mechanism if two hydrodynamic effects are accounted for: amplification of the differential pressure associated with a focusing phenomenon, and viscous damping at the BM-fluid interface. The predictions of the analytical 2-D Wentzel-Kramers-Brillouin (WKB) approach are compared to solutions of a 3-D finite element model, showing that these hydrodynamic phenomena yield stable high-gain response in the peak region and a smooth transition among models with different effectiveness of the active mechanism, mimicking the cochlear nonlinear response over a wide stimulus level range. This study explains how an effectively anti-damping nonlinear outer hair cells (OHC) force may yield large BM and pressure dynamical ranges along with an almost level-independent admittance.