Input-Output Analysis of an IPFM Neural Model: Effects of Spike Regularity and Record Length

This paper analyzes a model neural modulating system in which the input is a continuous sinusoid and the output is a point process modulated (integral pulse frequency modulation or IPFM) by the output of a linear system. Analytical expressions for the spectrum of the output point process are used to evaluate transfer function estimation procedures. The detectability of the spectral peak at the modulation frequency depends on the record length and upon the bias and variance contributed by the underlying point process. Detectability is found to increase with regularity of the underlying point process when stimulus frequency is much lower than spike rate, decreases with regularity when the stimulus frequency is about equal to spike rate, and be nearly independent of regularity at high frequencies. These results suggest certain procedures for evaluating the transfer function: 1) at low stimulus frequencies direct estimate of the spectrum is appropriate, 2) at middle frequencies, close to the spike rate, an estimate of the period point density may improve the detectabiity of the spectral peak, and 3) at middle frequencies, broad-band noise added to the sinusoidal stimulus may improve the estimate by decreasing the regularity of the underlying point process. Evaluation of the transfer function using broad-band rather than sinusoidal stimulus may have the advantage of decreasing bias and variance due to regularity of the underlying process, but may introduce a bias of unknown spectral character due to the response of the linear system itself and contribute a nonuniform spectral density at high frequencies.