Conditional entropy approach for the evaluation of the coupling strength.

A method that enables measurement of the degree of coupling between two signals is presented. The method is based on the definition of an uncoupling function calculating, by means of entropy rates, the minimum amount of independent information (i.e. the information carried by one signal which cannot be derived from the other). An estimator of the uncoupling function able to deal with short segments of data (a few hundred samples) is proposed, thus enabling the method to be used for usual experimental recordings. A synchronisation index is derived from the estimate of the uncoupling function by means of a minimisation procedure. It quantifies the maximum amount of information 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 to measure the degree of synchronisation between signals. The synchronisation analysis is utilised to measure the coupling strength between the beat-to-beat variability of the sympathetic discharge and ventilation in decerebrate artificially ventilated cats and the degree of synchronisation between the beat-to-beat variability of the heart period and ventricular repolarisation interval in normal subjects and myocardial infarction patients. The sympathetic discharge and ventilation are strongly coupled and the coupling strength is not affected by manoeuvres capable of increasing or depressing sympathetic activity. The synchronisation is lost after spinalisation. The synchronisation analysis confirms that the heart period and ventricular repolarisation interval are well coordinated. In normal subjects, the synchronisation index is not modified by experimental conditions inducing changes in the sympathovagal balance. On the contrary, it strongly decreases after myocardial infarction, thus detecting and measuring the uncoupling between the heart period and ventricular repolarisation interval.