Nonlinear analysis of the pharmacological conversion of sustained atrial fibrillation in conscious goats by the class Ic drug cibenzoline

Towards a repository of synthetic electrograms for atrial activation detection in atrial fibrillation

BACKGROUND

Recently, the analysis of the spatio-temporal behavior of atrial fibrillation activation patterns has been widely investigated with the aim to better understand the arrhythmia implications on the heart electrical activity. Most of the proposed techniques are based on atrial activation timing detections. Unfortunately atrial activation timings are not easily recognizable on the electrograms (EGMs) and an approach to support the validation of such techniques is highly desirable. The aim of this study is to provide an effective workflow for the generation of synthetic unipolar atrial electrograms (SEGMs) in atrial fibrillation (AF) condition and with different levels of noise.

METHOD

Real EGMs signals were obtained from a dataset of 6 subjects that underwent ablation. Each SEGM was obtained by modeling the three principal components of an EGM starting from real signals: atrial far-field (A_far), atrial near-field (A_near) and the ventricular far-field (V_far). A_far was generated using an autoregressive model applied on segments from real EGMs not characterized by ventricular or atrial activations; A_near and V_far were extracted directly from the real signals. A Gamma distribution and an atrio-ventricular node model were used to locate both A_near and V_far on A_far, respectively. Three electrophysiologists with different levels of expertise evaluated the realism of the SEGMs on a set of 100 randomly selected signals including 50 EGMs and 50 SEGMs. Analysis was repeated by the three experts on a subset of 21 signals.

RESULTS

The time required to generate the synthetic EGMs was less than 1 min once annotated EGMs are available. The cardiologists succeeded in distinguishing real from synthetic EGMs in 45%, 43% and 35% of the signals, respectively. By repeating the evaluation, 28%, 0% and 48% of signals were classified differently, including 67%, 52% and 36% of correct classifications.

CONCLUSION

The proposed approach proved to be effective in producing SEGMs which are difficult to distinguish from real EGMs. This study provides a tool for realistic SEGM generation from real EGMs in AF condition with different levels of noise and at different AF rates. The tool may be easily adopted to obtain SEGMs in different arrhythmic conditions. SEGMs generated in this study are shared with the scientific community as a first step towards a repository of synthetic and real atrial signals supporting the benchmarking of new approaches to investigate AF.

Nonlinear analysis of right atrial electrograms predicts termination of persistent atrial fibrillation within the left atrium by catheter ablation

The termination of long-standing persistent atrial fibrillation (LS-pAF) can be achieved by stepwise catheter ablation (step-CA) within the left atrium (LA). Our study aims to applying complexity measures derived from nonlinear time series analysis in order to characterize LS-pAF in terms of organization and to identify patients in whom AF can be terminated from those in whom AF cannot be terminated by step-CA within the LA. A total of 33 consecutive patients (age 61  ±  7 years, sustained AF duration 19  ±  11 months) with LS-pAF underwent step-CA. The organization of right bipolar electrograms before and during the ablation procedure was assessed using the coarse-grained correlation dimension. LS-pAF was terminated into sinus rhythm or atrial tachycardia in 22 patients during step-CA within the LA (left terminated patients-LT). In 11 patients the ablation procedure failed to terminate AF within LA (not left terminated patients-NLT). The statistical analysis of the estimated coarse-grained correlation dimension revealed that a higher right atrial (RA) organization before step-CA was associated to AF termination within the LA. During the ablation procedure, the level of RA organization displayed distinctive evolution between LT and NLT patients with a significant organization increase before AF termination for the LT patients.

Electropathological substrate of long-standing persistent atrial fibrillation in patients with structural heart disease: longitudinal dissociation

BACKGROUND

The electropathological substrate of persistent atrial fibrillation (AF) in humans is largely unknown. The aim of this study was to compare the spatiotemporal characteristics of the fibrillatory process in patients with normal sinus rhythm and long-standing persistent AF.

METHODS AND RESULTS

During cardiac surgery, epicardial mapping (244 electrodes) of the right atrium (RA), the left lateral wall (LA), and the posterior left atrium (PV) was performed in 24 patients with long-standing persistent AF. Twenty-five patients with normal sinus rhythm, in whom AF was induced by rapid pacing, served as a reference group. A mapping algorithm was developed that separated the complex fibrillation process into its individual elements (wave mapping). Parameters used to characterize the substrate of AF were (1) the total length of interwave conduction block, (2) the number of fibrillation waves, and (3) the ratio of block to collision of fibrillation waves (dissociation index). In 4403 maps of persistent AF, no evidence for the presence of stable foci or rotors was found. Instead, many narrow wavelets propagated simultaneously through the atrial wall. The lateral boundaries of these waves were formed by lines of interwave conduction block, predominantly oriented parallel to the atrial musculature. Lines of block were not fixed but continuously changed on a beat-to-beat basis. In patients with persistent AF, the total length of block in the RA was more than 6-fold higher than during acute AF (median, 21.1 versus 3.4 mm/cm(2); P<0.0001). The highest degree of interwave conduction block was found in the PV area (33.0 mm/cm(2)). The number of fibrillation waves during persistent AF was 4.5/cm(2) compared with 2.3 during acute AF, and the dissociation index was 7.3 versus 1.5 (P<0.0001). The interindividual variation of these parameters among patients was high.

CONCLUSIONS

Electric dissociation of neighboring atrial muscle bundles is a key element in the development of the substrate of human AF. The degree of the pathological changes can be measured on an individual basis by electrophysiological parameters in the spatial domain.

Assessment of cardiovascular regulation through irreversibility analysis of heart period variability: a 24 hours Holter study in healthy and chronic heart failure populations

We propose an approach based on time reversibility analysis to characterize the cardiovascular regulation and its nonlinearities as derived from 24 hours Holter recordings of heart period variability in a healthy population (n=12, age: median=43 years, range=34-55 years) and in a pathological group of age-matched chronic heart failure (CHF) patients (n=13, primarily in NYHA class II, age: median=37 years, range=33-56 years, ejection fraction: median=25%, range=13-30%). Two indices capable of detecting nonlinear irreversible dynamics according to different strategies of phase-space reconstruction (i.e. a fixed two-dimensional phase-space reconstruction and an optimal selection of the embedding dimension, respectively) are tested and compared with a more traditional nonlinear index based on local nonlinear prediction. Results showed that nonlinear dynamics owing to time irreversibility at short time scales are significantly present during daytime in healthy subjects, more frequently present in the CHF population and less frequently during night-time in both groups, thus suggesting their link with a dominant sympathetic regulation and/or with a vagal withdrawal. On the contrary, nonlinear dynamics owing to time irreversibility at longer, dominant time scales were insignificantly present in both groups. During daytime in the healthy population, irreversibility was mostly due to the presence of asymmetric patterns characterized by bradycardic runs shorter than tachycardic ones. Nonlinear dynamics produced by mechanisms different from those inducing temporal irreversibility were significantly detectable in both groups and more frequently during night-time. The present study proposes a method to distinguish different types of nonlinearities and assess their contribution over different temporal scales. Results confirm the usefulness of this method even when applied in uncontrolled experimental conditions such as those during 24 hours Holter recordings.

Non-invasive organization variation assessment in the onset and termination of paroxysmal atrial fibrillation

Atrial Fibrillation (AF) is the most common supraventricular tachyarrhythmia. Recently, it has been suggested that AF is partially organized on its onset and termination, thus being more suitable for antiarrhythmia and to avoid unnecessary therapy. Although several invasive and non-invasive AF organization estimators have been proposed, the organization time course in the first and last minutes of AF has not been quantified yet. The aim of this work is to study non-invasively the organization variation within the first and last minutes of paroxysmal AF. The organization was evaluated making use of sample entropy, which can robustly estimate electrical atrial activity organization from surface ECG recordings. This work proves an organization decrease in the first minutes of AF onset and an increase within the last minute before spontaneous AF termination. These results are in agreement with the conclusions reported by other authors who made use of invasive recordings.

Multiple testing strategy for the detection of temporal irreversibility in stationary time series

We propose a strategy for the detection of temporal irreversibility in stationary time series based on multiple bidimensional tests. The test is helpful to evaluate the displacement of irreversibility toward high dimensions. The test can be used independently of the theoretical functionals actually utilized to check irreversibility. The method was applied to simulated nonlinear signals generated by the delayed Henon map and a two-loop negative feedback model to show how the presence of a delay could produce the displacement of irreversibility toward higher dimensions. The method was applied also to series of a biological variable (i.e., heart period) that is known to be regulated by multiple feedback loops. Simulations and real data support the need of exploring progressively increasing embedding dimensions when assessing temporal irreversibility.

Mechanisms of Atrial Fibrillation Termination by Pure Sodium Channel Blockade in an Ionically-Realistic Mathematical Model

The mechanisms by which Na + -channel blocking antiarrhythmic drugs terminate atrial fibrillation (AF) remain unclear. Classical “leading-circle” theory suggests that Na + -channel blockade should, if anything, promote re-entry. We used an ionically-based mathematical model of vagotonic AF to evaluate the effects of applying pure Na + -current (I Na ) inhibition during sustained arrhythmia. Under control conditions, AF was maintained by 1 or 2 dominant spiral waves, with fibrillatory propagation at critical levels of action potential duration (APD) dispersion. I Na inhibition terminated AF increasingly with increasing block, terminating all AF at 65% block. During 1:1 conduction, I Na inhibition reduced APD (by 13% at 4 Hz and 60% block), conduction velocity (by 37%), and re-entry wavelength (by 24%). During AF, I Na inhibition increased the size of primary rotors and reduced re-entry rate (eg, dominant frequency decreased by 33% at 60% I Na inhibition) while decreasing generation of secondary wavelets by wavebreak. Three mechanisms contributed to I Na block–induced AF termination in the model: (1) enlargement of the center of rotation beyond the capacity of the computational substrate; (2) decreased anchoring to functional obstacles, increasing meander and extinction at boundaries; and (3) reduction in the number of secondary wavelets that could provide new primary rotors. Optical mapping in isolated sheep hearts confirmed that tetrodotoxin dose-dependently terminates AF while producing effects qualitatively like those of I Na inhibition in the mathematical model. We conclude that pure I Na inhibition terminates AF, producing activation changes consistent with previous clinical and experimental observations. These results provide insights into previously enigmatic mechanisms of class I antiarrhythmic drug-induced AF termination. The full text of this article is available online at http://circres.ahajournals.org

Spatial correlation analysis of the pharmacological conversion of sustained atrial fibrillation in conscious goats by cibenzoline

The nonlinear spatial redundancy and the linear spatial correlation function were used to investigate to what extent non-linearity 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 principal 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 drug-induced 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.

Spatial correlation analysis of atrial activation patterns during sustained atrial fibrillation in conscious goats

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.

Symbolic approach for measuring temporal "irreversibility"

We describe a symbolic approach for measuring temporal "irreversibility" in time-series measurements. Temporal irreversibility is important because it excludes Gaussian linear dynamics and static transformations of such dynamics from the set of possible generating processes. A symbolic method for measuring temporal irreversibility is attractive because it is computationally efficient, robust to noise, and simplifies statistical analysis of confidence limits. We propose a specific algorithm, called "false flipped symbols," for establishing the presence of temporal irreversibility without the need for generating surrogate data. Besides characterizing experimental data, our results are relevant to the question of selecting alternative models. We illustrate our points with numerical model output and experimental measurements.

Non-linear analysis of intracranial human EEG in temporal lobe epilepsy

OBJECTIVE

Intracranial EEG recordings from patients suffering from medically intractable temporal lobe epilepsy were analyzed with the aim of characterizing the dynamics of EEG epochs recorded before and during a seizure and comparing the classification of the EEG epochs on the basis of visual inspection to the results of the numerical analysis.

METHODS

The stationarity of the selected EEGs was assessed qualitatively. The coarse-grained correlation dimension and coarse-grained correlation entropy were used for the non-linear characterization of the EEG epochs.

RESULTS

High-pass filtering was necessary in order to make the majority of the epochs appear stationarity beyond a time scale of about 2 s. It was found that the dimension of the ictal EEGs decreased with respect to the epochs containing ongoing (interictal) activity. The entropy of the ictal recordings however increased. A scaling of the entropy was applied and it was found that the scaled entropy of the ictal EEG decreased, consistent with the increased regularity of the ictal EEG. The coarse-grained quantities discriminated well between EEG epochs recorded prior to and during seizures at locations displaying ictal activity and classification improved by including the linear autocorrelation time in the analysis.

CONCLUSIONS

It is concluded that ictal and non-ictal EEG can be well distinguished on the basis of non-linear analysis. The results are in good agreement with the visual analysis.