ON THE PARAMETER-ESTIMATION FOR DIFFUSION-MODELS OF SINGLE NEURONS ACTIVITIES .1. APPLICATION TO SPONTANEOUS ACTIVITIES OF MESENCEPHALIC RETICULAR-FORMATION CELLS IN SLEEP AND WAKING STATES

For the Ornstein-Uhlenbeck neuronal model a quantitative method is pro posed for the estimation of the two parameters characterizing the unko wn input process, namely the neuron's mean input per unit time mu and the infinitesimal standard deviation per unit time sigma. This method is based on the experimentally observed first- and second-order moment s of interspike intervals. The dependence of the estimates <(mu)over c ap> and <(sigma)over cap> on the moments of the observed interspike in tervals and on the neuronal parameters is clarified, and a comparison is made between the estimates based on the classical Wiener model and those yielded by the Ornstein-Uhlenbeck model. Comprehensive tables ar e included in which the displayed values of <(mu)over cap> and <(sigma )over cap> have been calculated in terms of physiologically realistic pairs of first- and second-order moments. Our method is finally applie d to interspike interval data recorded from neurons in the mesencephal ic reticular formation of the cat during hypothetical sleep, slow-wave sleep stage, and wake stage.