A self-exciting stochastic point process model for nerve-spike discharges: Application to gerbil auditory nerve

A stochastic point-process model for the occurrence times of spike discharges in the auditory nerve (Gaumond, J. Neurophys., 48, pp. 856-873, 1982) has been analyzed and applied to a study of the peripheral auditory system of the Mongolian gerbil. This model expresses the discharge intensity as the product of an excitation function S(t), which represents stimulus dependence, and a recovery function {dollar}R(tau){dollar}, which represents discharge-history dependence.; Methods for computing the mean discharge intensity of the model for given {dollar}S(t){dollar} and {dollar}R(tau){dollar} parameter functions were developed and used to investigate the effects of post-discharge recovery in model responses to constant, periodic, and transient excitation functions.; Joint maximum-likelihood estimators of {dollar}S(t){dollar} and {dollar}R(tau){dollar} were derived to permit the separation of stimulus-dependent and discharge-history-dependent effects in a neural discharge sequence. A new method was derived for combining discharge statistics obtained in response to multiple stimulus conditions in a single unit to estimate a single "ensemble" recovery function as well as a set of individual excitation functions. Practical methods for evaluating these estimators were developed and the performance of estimators analyzed.; Ensemble recovery functions have been estimated from the continuous-tone responses of 22 auditory-nerve units in gerbil. These estimates appear to fall into two groups distinguished by the duration of the absolute refractory interval, the slope of the initial rise after the absolute refractory interval, and the interval at which {dollar}R(tau){dollar} reaches its asymptotic value. The maximum driven rate, {dollar}Qsb{lcub}10dB{rcub}{dollar}, and rate adaptation parameters of the units appear to be distributed differently for these two groups. No significant difference between the characteristic level and spontaneous rate parameters is seen for units in the two groups.; The degree of consistency between neural discharge data and the form of the multiplicative-intensity model was examined and the effect of one source of inconsistency, {dollar}tau{dollar}-dependent delay, on estimates of {dollar}S(t){dollar} and {dollar}R(tau){dollar} was demonstrated. The model was extended to allow compensation for {dollar}tau{dollar}-dependent delay in neural discharge sequences.