Frequency responses of cat rapidly adapting mechanoreceptive fibers.

The frequency responses of 11 rapidly adapting (RA) fibers in cat were studied by representing the average firing rate as a function of sinusoidal stimulus amplitude and stimulus frequency. Specifically, rate-intensity functions at different stimulation frequencies were fitted by four-parameter (a0, a1, a2, a3), piece-wise linear functions using nonlinear regression (n = 59; R2 > 0.877). Rate-intensity functions at intermediate frequencies were found by linear interpolation. The result of this analysis is rate-amplitude-frequency functions plotted as two-dimensional surfaces. The surfaces consist of five regions separated and sufficiently defined by four space curves. At 14 different frequencies, the statistical distribution of each rate-intensity-function parameter could be approximated by a particular lognormal distribution (n = 56; R2 > 0.796). The Kolmogorov-Smirnov test fails to reject this hypothesis for each combination of frequency and parameter (56 tests; p > 0.39). Therefore, at a given frequency, the variation of the parameters can be represented by lognormal distributions with specific means and standard deviations. Responses of six RA fibers, which are different from the data-set used for modeling, were compared with the stochastic model at different frequencies. The parameters of those fibers were tested against the null hypotheses that they were sampled from the particular parameter distributions dictated by the model. The Kolmogorov-Smirnov test fails to reject all the hypotheses at the alpha = 0.05 level (44 tests). At the alpha = 0.10 level, only a few test parameters were found to be departing from the model (a0 and a1 at 5 Hz; a2 at 20 Hz; a2 and a3 at 50 Hz). The remaining test parameters could be accurately described by the model. Having confirmed the validity of the model, the logarithmic means and the logarithmic standard deviations of the lognormally distributed rate-intensity-function parameters were estimated in the frequency range of 4-200 Hz. The rate-amplitude-frequency surfaces sampled from the established stochastic model completely characterize the rate responses of RA fibers to sinusoidal stimuli and are superior to tuning curves which require selecting criterion responses. The current rate-response model is promising for future computational work, especially on population modeling.