Critical phase transitions during ablation of atrial fibrillation

A Novel Tool for the Identification and Characterization of Repetitive Patterns in High-Density Contact Mapping of Atrial Fibrillation

Introduction

Electrical contact mapping provides a detailed view of conduction patterns in the atria during atrial fibrillation (AF). Identification of repetitive wave front propagation mechanisms potentially initiating or sustaining AF might provide more insights into temporal and spatial distribution of candidate AF mechanism and identify targets for catheter ablation. We developed a novel tool based on recurrence plots to automatically identify and characterize repetitive conduction patterns in high-density contact mapping of AF.

Materials and Methods

Recurrence plots were constructed by first transforming atrial electrograms recorded by a multi-electrode array to activation-phase signals and then quantifying the degree of similarity between snapshots of the activation-phase in the electrode array. An AF cycle length dependent distance threshold was applied to discriminate between repetitive and non-repetitive snapshots. Intervals containing repetitive conduction patterns were detected in a recurrence plot as regions with a high recurrence rate. Intervals that contained similar repetitive patterns were then grouped into clusters. To demonstrate the ability to detect and quantify the incidence, duration and size of repetitive patterns, the tool was applied to left and right atrial recordings in a goat model of different duration of persistent AF [3 weeks AF (3 wkAF, n = 8) and 22 weeks AF (22 wkAF, n = 8)], using a 249-electrode mapping array (2.4 mm inter-electrode distance).

Results

Recurrence plots identified frequent recurrences of activation patterns in all recordings and indicated a strong correlation between recurrence plot threshold and AF cycle length. Prolonged AF duration was associated with shorter repetitive pattern duration [mean maximum duration 3 wkAF: 74 cycles, 95% confidence interval (54-94) vs. 22 wkAF: 41 cycles (21-62), p = 0.03], and smaller recurrent regions within repetitive patterns [3 wkAF 1.7 cm² (1.0-2.3) vs. 22 wkAF 0.5 cm² (0.0-1.2), p = 0.02]. Both breakthrough patterns and re-entry were identified as repetitive conduction patterns.

Conclusion

Recurrence plots provide a novel way to delineate high-density contact mapping of AF. Dominant repetitive conduction patterns were identified in a goat model of sustained AF. Application of the developed methodology using the new generation of multi-electrode catheters could identify additional targets for catheter ablation of AF.

Is human atrial fibrillation stochastic or deterministic?-Insights from missing ordinal patterns and causal entropy-complexity plane analysis

The mechanism of atrial fibrillation (AF) maintenance in humans is yet to be determined. It remains controversial whether cardiac fibrillatory dynamics are the result of a deterministic or a stochastic process. Traditional methods to differentiate deterministic from stochastic processes have several limitations and are not reliably applied to short and noisy data obtained during clinical studies. The appearance of missing ordinal patterns (MOPs) using the Bandt-Pompe (BP) symbolization is indicative of deterministic dynamics and is robust to brief time series and experimental noise. Our aim was to evaluate whether human AF dynamics is the result of a stochastic or a deterministic process. We used 38 intracardiac atrial electrograms during AF from the coronary sinus of 10 patients undergoing catheter ablation of AF. We extracted the intervals between consecutive atrial depolarizations (AA interval) and converted the AA interval time series to their BP symbolic representation (embedding dimension 5, time delay 1). We generated 40 iterative amplitude-adjusted, Fourier-transform (IAAFT) surrogate data for each of the AA time series. IAAFT surrogates have the same frequency spectrum, autocorrelation, and probability distribution with the original time series. Using the BP symbolization, we compared the number of MOPs and the rate of MOP decay in the first 1000 timepoints of the original time series with that of the surrogate data. We calculated permutation entropy and permutation statistical complexity and represented each time series on the causal entropy-complexity plane. We demonstrated that (a) the number of MOPs in human AF is significantly higher compared to the surrogate data (2.7 ± 1.18 vs. 0.39 ± 0.28, p < 0.001); (b) the median rate of MOP decay in human AF was significantly lower compared with the surrogate data (6.58 × 10^-3 vs. 7.79 × 10^-3, p < 0.001); and (c) 81.6% of the individual recordings had a rate of decay lower than the 95% confidence intervals of their corresponding surrogates. On the causal entropy-complexity plane, human AF lay on the deterministic part of the plane that was located above the trajectory of fractional Brownian motion with different Hurst exponents on the plane. This analysis demonstrates that human AF dynamics does not arise from a rescaled linear stochastic process or a fractional noise, but either a deterministic or a nonlinear stochastic process. Our results justify the development and application of mathematical analysis and modeling tools to enable predictive control of human AF.