FRACTAL CHARACTER OF THE NEURAL SPIKE TRAIN IN THE VISUAL-SYSTEM OF THE CAT

We used a variety of statistical measures to identify the point proces s that describes the maintained discharge of retinal ganglion cells (R GC's) and neurons in the lateral geniculate nucleus (LGN) of the cat. These measures are based on both interevent intervals and event counts and include the interevent-interval histogram, rescaled range analysi s, the event-number histogram, the Fano factor, the Allan factor, and the periodogram. In addition, we applied these measures to surrogate v ersions of the data, generated by random shuffling of the order of int erevent intervals. The counting statistics reveal 1/f-type fluctuation s in the data (long-duration power-law correlation), which are not pre sent in the shuffled data. Estimates of the fractal exponents measured for RGC- and their target LGN-spike trains are similar in value, indi cating that the fractal behavior either is transmitted from one cell t o the other or has a common origin. The gamma-r renewal process model, often used in the analysis of visual-neuron interevent intervals, des cribes certain short-term features of the RGC and LGN data reasonably well but fails to account for the long-duration correlation. We presen t a new model for visual-system nerve-spike firings: a gamma-r renewal process whose mean is modulated by fractal binomial noise. This fract al, doubly stochastic point process characterizes the statistical beha vior of both RGC and LGN data sets remarkably well. (C) 1997 Optical S ociety of America.