On a unified point process approach for the characterization of bioelectric discrete phenomena

This paper discusses a unified method based on the theory of point processes to characterize various types of bioelectric discrete signals such as heart beat timing, myoelectric activity, discharge of primary sensory neurons or neurons in the central nervous systems. The doubly stochastic point processes, in which the discrete event occurring intensity is stochastic, forms the most general class to characterize the discrete phenomena. In this paper the self-exciting process has been shown to be useful to characterize wide range of discrete biosignals. The modeling of conditional intensity function is the essential part of the characterization. When the intensity has a parametric model, the maximum likelihood parameter estimation will be the useful way to characterize the phenomena. The effectiveness of the method is demonstrated by a specific modeling of the spontaneous neuronal burst discharges recorded from the brain thalamus during the neuro surgery. The first approximation model has four parameters obtained by the instantaneous nonlinearly transformed sinusoidal function. An extended model allows arbitrary periodic intensity with refractory period. Predicted interval histograms show good agreement with the observed ones indicating the validity of the proposed method.