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Methods from nonlinear dynamics were applied to test the hypothesis that the dynamics of sustained atrial fibrillation (AF) is modified by the class Ic drug cibenzoline during pharmacological conversion. The experiments were performed in conscious goats in which sustained AF was induced by continuous maintenance of AF via programmed electrical stimulation. Data were collected from electrophysiological experiments in five goats to terminate sustained AF by continuous infusion of cibenzoline. Sets of five unipolar epicardial electrograms of one minute duration were recorded from the left and right atrial free wall during sustained AF (control), and at three episodes during infusion of cibenzoline, when the mean AF interval had been prolonged to 25%, 50% and 85% with respect to control. Ventricular far-field potentials were removed from atrial electrograms by a coherent averaging procedure. Using the Grassberger-Procaccia method, the dynamics of the local atrial electrograms was investigated by estimating the (coarse-grained) correlation dimension and correlation entropy from the correlation integral. The results were related to a recently proposed classification (types I-III) of AF based on the degree of complexity of atrial activation patterns. The coarse-grained correlation dimension D(cg) and entropy K(cg) indicated that sustained AF corresponded to type II. During drug administration the coarse-grained parameters were not significantly different from control. Scaling regions in the correlation integral were observed after infusion of cibenzoline (3 out of 5 goats) suggesting that the drug introduced low-dimensional features (type I) in the dynamics of AF (correlation dimension D ranging from 2.8 to 4.4 and correlation entropy K from 1.6 to 6.2 nats/s). Sinus rhythm recorded shortly after cardioversion was very regular (D<2 and K<3 nats/s). The hypothesis that the electrograms during AF and sinus rhythm were generated by a static transformation of a linear Gaussian random process was rejected using a test for time reversibility. The nonlinear analysis revealed that cibenzoline does not significantly alter the dynamics of sustained AF during pharmacological conversion other than a slowing down of the atrial activation and a somewhat increasing global organization of the atrial activation pattern. The sudden change in the dynamical behavior at cardioversion suggests a mechanism that is reminiscent of a bifurcation. (c) 1997 American Institute of Physics.

In this study we applied both linear and nonlinear spatial correlation measures to characterize epicardial activation patterns of sustained atrial fibrillation in instrumented conscious goats. It was investigated if nonlinearity was involved in the spatial coupling of atrial regions and to what extent fibrillation was organized in the experimental model of sustained atrial fibrillation (AF) in instrumented goats.Data were collected in five goats during experiments to convert AF by continuous infusion of cibenzoline. Spatial organization during AF was quantified with the linear spatial cross correlation function and the nonlinear spatial cross redundancy which was calculated using the Grassberger-Procaccia correlation integral. Two different types of correlation were evaluated to distinguish simultaneous interaction from non-simultaneous interaction, for instance resulting from propagation of fibrillation waves. The nonlinear association length and the linear correlation length were estimated along the principal axes of iso-correlation contours in two-dimensional correlation maps of the nonlinear spatial redundancy and the linear spatial correlation function, respectively.To quantitatively assess the degree of nonlinearity, the association length was also estimated from the linearized spatial redundancy using multivariate surrogate data. The differences between the nonlinear and linearized association lengths indicated that a nonlinear component in the spatial organization of AF predominantly existed in the right atrium. The degree of organization characterized by association length along the short principal axis was higher in the right atrium (15 ± 7 mm) than in the left atrium (8 ± 4 mm). The spatial extension of coherent atrial patches was estimated from a surface of association equal to the area spanned by the principal axes of iso-correlation contours from the redundancy, including the effects from non-simultaneous interaction. Interpreting this area as the spatial domain of a fibrillation wavelet, the results suggest that the mapped region was activated on average by two wavelets in the left atrium and by one wavelet in the right atrium. Therefore, the activation pattern of sustained AF in goats was relatively organized, consistent with type II of AF. It is suggested that the surface of association is a measure of the number of independent wavelets present in the atria during sustained AF, and that larger association lengths result from fewer and larger reentrant circuits.

The nonlinear spatial redundancy and the linear spatial correlation function were used to investigate to what extent nonlinearity was involved in the coupling of atrial regions and how organization in activation patterns of sustained atrial fibrillation (AF) had been modified by administration of the class IC agent cibenzoline in the experimental model of sustained AF in instrumented conscious goats.Electrograms were measured in five goats during sustained AF and when the fibrillation interval had been prolonged to about 25%, 50% and 85% (CIB25, CIB50, CIB85) with respect to control. The nonlinear association length and linear correlation length were estimated along the principle axes of two-dimensional correlation maps estimated from the spatial redundancy and the spatial correlation function, respectively.The estimated short axis association length in the right atrium increased already shortly after the start of infusion (CIB25, +61%), and remained significantly different from control during the experiment, including the effects of non-simultaneous interaction. At CIB85 the association length had almost become twice as long with respect to control (increase from 16 to 29 mm, +89%), while in the left atrium changes were less pronounced (increase from 9 to 12 mm, +32%). The linearized association length which was estimated using multivariate surrogate data increased more gradually and was less sensitive to changes in spatial organization. The results of the spatial correlation analysis suggest that the druginduced nonlinearity in the spatio-temporal dynamics of sustained AF is related to activation patterns which are characterized by extended uniformly propagating fibrillation wavefronts (AF type I).We conclude that cibenzoline enhanced the spatial organization of sustained AF associated with a transition from type II to type I AF activation patterns. This may destabilize the perpetuation of AF since an increase in association length is equivalent to a reduction of atrial tissue mass available to support reentrant circuits. The results are consistent with the hypothesis that larger association lengths result from fewer and larger reentrant circuits. It is argued that effects of diminished curvature of fibrillation wavefronts are anti-arrhythmic under conditions of suppressed excitability imposed by cibenzoline. Termination of AF may be mediated by a mechanism resembling a bifurcation of the dynamics which sets in when the ends of fractionated wavefronts cannot sufficiently curve anymore to maintain a positive balance of newly generated wavelets needed to sustain AF.

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