Treatment of nerve impulse data for comparison with theory.

Abstract

A procedure is given for the comparison of nerve impulse data with model predictions. This method utilizes information in the nerve impulse train that is ignored by the post-stimulus-onset histogram and thereby gives an improved signal-to-noise ratio. Comparison of observed responses in the Limulus retina with predictions derived from a detailed model gives good agreement.The theory of the dynamical response of nerve networks has now advanced to the point such that detailed comparison can be made, in some cases, between nerve-impulse data collected in the laboratory and the theoretical prediction of how a neural network should respond to a specified input. This note presents some mathematical tools that facilitate an accurate comparison between theory and experiment.An example of the situation that is treated below is shown in Fig. 1. Fig. 1A shows neural response data as they are commonly presented, in terms of a "post-stimulus-onset histogram." The histogram was constructed from responses, to 128 replicate stimuli, of a neuron in the retinal network of the Limulus lateral eye. Fig. lB shows the theoretical prediction that corresponds to Fig. IA (1-3). The theoretical variable shown, which corresponds to the post-stimulus-onset histogram, is the "population firing rate" (4). We note that the noise level in the post-stimulus-onset histogram prevents a detailed comparison between theory and experiment.Fig . 1C treats the same nerve-impulse raw data in a different way, and it shows far less contamination by noise. It represents the estimated "mean individual rate" of the neuron. The superior signal-to-noise quality of this laboratory variable is achieved by a data treatment that utilizes information which the post-stimulus-onset histogram ignores-namely, that the impulse train of the Limulus visual neuron is not much affected by chance fluctuations in impulse arrival times. (Such a neuron will be referred to below as "sure-firing.") Fig (Fig. ID) is feasible; the noise problem in Fig. 1A has been surmounted. We observe, however, that the theoretical variable in Fig. ID, the mean individual rate, is different from the population firing rate of Fig. 1B. It is in fact a step removed from the primary theoretical analysis of the neural network dynamics, which proceeds in terms of the population firing rate. The derivation of the individual rate from the population rate will be presented below.To summarize, after the firing times of the sure-firing neuron's response have been recorded in the laboratory, the time course of that neuron's activity may be expressed by its "mean individual firing rate." On the other hand, the quantitative modeling of the response of a real neural network is phrased more naturally in terms of a different measure of activity, the "population firing rate." In order that theory may be used to predict the results of experiment, the convenient theoretical measure of activity must be transformed to the low-noise laboratory measure. That transformation, and the consequent quantitative compa...

Temporal aspects of neural coding in the retina and lateral geniculate

“…Such timecourses cannot be derived by binning or smoothing the spike train. However, a natural choice [189] for f (t) is a piecewise-constant function whose value on the interval between any two spikes is proportional to the reciprocal of the interspike interval.…”

Effect of boundaries on the response of a neural network

“…20 substituted. (For a special case where explicit forms occur, see Sirovich, 1979.) As a result Eq 19 is evaluated by discrete methods for which the Fast Fourier Transform (FFT) algorithm can be used.…”

“…transduction from r to or is required. A brief analytical discussion of this procedure is given in the Appendix; a full treatment may be found in Knight et al (1979).…”