An adaptive stochastic model for the neural coding process

Neural encoders translate information on the time-varying intensity of stimuli into sequences of membrane depolarization spikes. Their output can be considered the realization of a stochastic point process, the overall encoder behaviour being characterized through ensemble-averaged responses to identical stimuli and environmental conditions. A new mathematical model for the coding process is presented and analyzed. The model is an integrate and fire-at-threshold scheme, the stochastic features of its response resulting from random fluctuations in the firing threshold. As a consequence of feedback self-inhibition and threshold control, which is assumed to account for adaptive neutral responses, the model output is a self-exciting point process. An approximate description of the averaged encoder response is obtained by considering an ensemble of identical coding units as a whole, instead of concentrating on output sample-path evolution. This approach overcomes the difficulty inherent in analysing the global behaviour of self-exciting point processes. A conceptual decoding scheme implementing a coding unit in a feedback configuration is also introduced and discussed.