Analysis of sequences of events with random displacements applied to biological systems

Abstract

A stationary and ergodic point process is considered, specified by the probability density function, expectation density function and serial correlation coefficients of the intervals between the events. The same quantities are computed after the events have been subjected to random displacements. The model is applied to data on heartbeat irregularities indicated by the duration of R-R intervals on the electrocardiogram. From an analysis of the expectation density function of R-R intervals reported in the literature for one healthy subject and three patients with atrial fibrillation, an estimate is given of the degree of irregularity in the pacemaker period relative to the range of variations in conduction time through the heart tissue.

By means of an example concerning a thalamic neuron, it is shown how the theory may be used to investigate the relation between presynaptic and postsynaptic unitary nervous activity. Further applications relate to waiting-time problems in operations research where events are scheduled to take place according to a timetable but each event is influenced by factors that may retard or speed up its occurence.