Non-linear coupling of atrial activation processes during atrial fibrillation in humans

The activation patterns underlying the electrical activity of the heart during atrial fibrillation (AF) are not entirely random. The aim of this study was to assess the local organization of the activation processes during AF by estimating the non-linear coupling between activation sequences (ASs) in two atrial sites. To quantitatively estimate the degree of non-linear coupling we extracted two indices based on a multivariate embedding procedure and on the estimation of the correlation dimension (CD) and correlation entropy (CE), termed independence of complexity and of independence of predictability, respectively. We analysed AS in two atrial sites in 30 informed subjects during chronic AF of type I, II and III (Wells' classification), ten 6-s-long episodes of each type. Surrogates were used to reject the hypothesis that the time series were generated by linear stochastic dynamics. We estimated CID and CE according to the coarse-grained approach, which leads to a fixed high value for the embedding dimension in all the analysed ASs, and a typical value for the distance between the two ASs in the phase space. Various degrees of organization, ranging from completely synchronized to fully de-coupled signals, were observed: significant degrees of non-linear coupling were found in segments belonging in types I and II AF, whereas type III electrograms always turned out to be weakly coupled. This finding links the morphology of single electrograms to the synchronization between pairs of closely spaced electrograms. Our bivariate approach suggests that the measurement of organization during AF should be based on the estimation of the non-linear coupling between two sites. This approach appears to be more reliable and sensitive than non-linear analysis of single electrograms or linear analysis of their coupling.