Wiener kernel analysis of inner ear function in the American bullfrog.

The response of 17 primary auditory nerve fibers in the American bullfrog (Rana catesbeiana) to acoustic noise stimulation of the tympanic membrane was recorded. For each fiber, the first- and second-order Wiener kernels, k1 (tau 1) and k2 (tau 1, tau 2), were computed by cross correlation of the stimulus and the response. The kernels revealed amplitude and phase characteristics of auditory filters of both phase-locking and non-phase-locking fibers. Wiener kernels of high- and midfrequency fibers (best frequency, BF > 500 Hz), implied a simple sandwich model, consisting of a cascade of a linear bandpass filter, a static nonlinearity, a linear low-pass filter, and a spike generator. The bandpass filter was at least of order 7, and had a linear phase response, for both the high- and the midfrequency fibers. Averaged across fibers, filter order 2, and cutoff frequency 451 Hz for the second filter in the model was observed. The responses of low-frequency fibers (BF < 500 Hz) could not be fit with the sandwich model, because the Fourier transform K2 (f1,f2) of the second-order Wiener kernel showed significant components at off-diagonal frequencies f1 not equal to +/- f2. The presence of these off-diagonal components shows that, in addition to the phase and gain characteristics of auditory filters, the Wiener kernel analysis reveals nonlinear two-tone interactions.