Spatial differentiation as an auditory ’’second filter’’: Assessment on a nonlinear model of the basilar membrane

Abstract

The mechanical tuning of the basilar membrane does not appear to be sharp enough to account for frequency selectivity of primary auditory‐nerve fibers. Various ’’second filters’’ have been proposed to provide the required sharpening. We have studied the properties of one such mechanism, in which the spatial derivative of membrane displacement is taken as the excitatory signal for primary fibers, on a nonlinear computational model of the basilar membrance. Because the wavelength in response to a tone decreases as the wave travels from base to characteristic place, both the slope and curvature of membrane response are enhanced in the neighborhood of the characteristic place. Thus spatial differentiation produces sharpening resembling the difference between mechanical and neural tuning. Phase (as a function of frequency) of the spatial derivative is similar to phase of the displacement, but frequency selectivity (amplitude as a function of frequency) for frequencies below the characteristic frequency is sharpened. In addition, spatial differentiation provides the distinction between mechanical nonlinearity (related in the model to membrane velocity) and neural excitatory signal required to account for suppression of response to a tone at the characteristic frequency f₁ by a second tone at a lower frequency f₂. Without this distinction, a tone at frequency f₂ intense enough to suppress the f₁ component of response at the f₁ place would itself introduce a large component of response at frequency f₂.