Conditional entropy approach for the evaluation of the coupling strength

A method that enables measurement of the degree of coupling between two sig nals is presented. The method is based on the definition of an uncoupling f unction calculating, by means of entropy rates, the minimum amount of indep endent information (i.e. the information carried by one signal which cannot be derived from the other). An estimator of the uncoupling function able t o deal with short segments of data (a few hundred samples) is proposed, thu s enabling the method to be used for usual experimental recordings. A synch ronisation index is derived from the estimate of the uncoupling function by means of a minimisation procedure. It quantifies the maximum amount of inf ormation exchanged between the two signals. Simulations in which non-linear coordination schemes are produced and changes in the coupling strength are artificially induced are used to check the ability of the proposed index t o measure the degree of synchronisation between signals. The synchronisatio n analysis is utilised to measure the coupling strength between the beat-to -beat variability of the sympathetic discharge and ventilation in decerebra te artificially ventilated cats and the degree of synchronisation between t he beat-to-beat variability of the heart period and ventricular repolarisat ion interval in normal subjects and myocardial infarction patients. The sym pathetic discharge and ventilation are strongly coupled and the coupling st rength is not affected by manoeuvres capable of increasing or depressing sy mpathetic activity. The synchronisation is lost after spinalisation. The sy nchronisation analysis confirms that the heart period and ventricular repol arisation interval are well coordinated. In normal subjects, the synchronis ation index is not modified by experimental conditions inducing changes in the sympathovagal balance. On the contrary, it strongly decreases after myo cardial infarction, thus detecting and measuring the uncoupling between the heart period and ventricular repolarisation interval.