Nonlinear Analysis of Epicardial Atrial Electrograms of Electrically Induced Atrial Fibrillation in Man

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Abstract
We applied methods from the theory of nonlinear dynamics to characterize unipolar epicardial right atrial electrograms of electrically induced atrial fibrillation (AF) in man. Electrograms were selected from a high-density mapping study, which confirmed the existence of at least 3 different types of induced AF (types I, II, and III) in patients undergoing open chest surgery. We analyzed sets of 5 electrograms (4 sec, sampling frequency 1 kHz, resolution 8 bits) in 9 patients (AF type I, n = 3; type II, n = 3; type III, n = 3). The Grassberger-Procaccia method was applied to estimate the correlation dimension and correlation entropy from the electrograms. In 2 patients (AF type I) some electrograms (2 of 5 and 3 of 5, respectively) showed scaling at normalized distances ranging from 0.2 to 0.5 in phase space. Correlation dimension D ranged from 1.8 to 3.2 and correlation entropy K from 2.2 to 3.8 nats/sec. The patients were ranked according to increasing coarse-grained correlation dimension Dcg (range 3.7 to 7.9) and coarse-grained correlation entropy Kcg (range 5.6 to 18.6 nats/sec). The method of surrogate data was applied to detect nonlinearity in the electrograms. Using the correlation integral as test statistic, it could be excluded that electrograms of type I AF have been generated by linear stochastic dynamics. Episodes of sinus rhythm (D ranging from 1.0 to 5.1 and K from 2.0 to 8.6 nats/sec) and induced atrial flutter (D ranging from 2.7 to 4.2 and K from 2.2 to 4.2 nats/sec) in 2 different patients showed features of low-dimensional chaos. Nonlinear analysis discriminated between electrograms during electrically induced AF in humans. The results are consistent with a classification of AF into 3 types based on the spatiotemporal complexity of right atrial activation patterns.