Origin and Characteristics of High Shannon Entropy at the Pivot of Locally Stable Rotors: Insights from Computational Simulation

Abstract

BackgroundRotors are postulated to maintain cardiac fibrillation. Despite the importance of bipolar electrograms in clinical electrophysiology, few data exist on the properties of bipolar electrograms at rotor sites. The pivot of a spiral wave is characterized by relative uncertainty of wavefront propagation direction compared to the periphery. The bipolar electrograms used in electrophysiology recording encode information on both direction and timing of approaching wavefronts.ObjectiveTo test the hypothesis that bipolar electrograms from the pivot of rotors have higher Shannon entropy (ShEn) than electrograms recorded at the periphery due to the spatial dynamics of spiral waves.Methods and ResultsWe studied spiral wave propagation in 2-dimensional sheets constructed using a simple cell automaton (FitzHugh-Nagumo), atrial (Courtemanche-Ramirez-Nattel) and ventricular (Luo-Rudy) myocyte cell models and in a geometric model spiral wave. In each system, bipolar electrogram recordings were simulated, and Shannon entropy maps constructed as a measure of electrogram information content. ShEn was consistently highest in the pivoting region associated with the phase singularity of the spiral wave. This property was consistently preserved across; (i) variation of model system (ii) alterations in bipolar electrode spacing, (iii) alternative bipolar electrode orientation (iv) bipolar electrogram filtering and (v) in the presence of rotor meander. Directional activation plots demonstrated that the origin of high ShEn at the pivot was the directional diversity of wavefront propagation observed in this location.ConclusionsThe pivot of the rotor is consistently associated with high Shannon entropy of bipolar electrograms despite differences in action potential model, bipolar electrode spacing, signal filtering and rotor meander. Maximum ShEn is co-located with the pivot for rotors observed in the bipolar electrogram recording mode, and may be an intrinsic property of spiral wave dynamic behaviour.

The contact electrogram and its architectural determinants in atrial fibrillation

“…With regards to the other organisational indices, another computational study found that Shannon entropy still detected pivot points, and is robust to changes in spatial resolution in detection of AF rotors (Ganesan, Kuklik, Gharaviri, et al, 2014). The results in this thesis concerned AF organisation rather than detection of AF mechanism, hence the contrasting data seen with F16 vs. F32 in figure 10.7.…”

Temporal stability and specificity of high bipolar electrogram entropy regions in sustained atrial fibrillation: Implications for mapping

“…AF mapping of rotors provides an interesting application of entropy, as several studies have demonstrated that the pivot of rotors experience spatial uncertainty in wavefront direction. This in turn generates bipolar EGM morphologies that are less predictable, which can be identified using entropy [19,24,31,32]. The concept of entropy is further discussed in Supplement S3.…”

“…ShEn, ApEn and SampEn were estimated in 5 s windows for each bipolar electrode. For ShEn, samples were binned depending on their amplitude using a voltage histogram, with bin sizes dependent on the standard deviation (SD) of the signal (bin size = 0.125 × SD), as used in previous literature [19]. For ApEn and SampEn, we set an epoch length of N = 5000 (the window length at which to segment the data), a vector length m = 2 (finds matches of the same m voltage values within the sequence N) and a tolerance r = 0.2 * SD (determines how often the following point m + 1 lies within tolerance r of matched vectors).…”

“…In addition, bipolar electrograms are the most commonly used recording modality in clinical electrophysiology, making these signals readily available for entropy analysis whilst also providing a direct and interpretable translation to what is seen clinically. Lastly, high bipolar electrogram Shannon entropy (ShEn) has been demonstrated by our group to be associated with the pivot of rotors [4,18,19], and subsequently entropy-based identification of the rotor pivot has been independently observed by multiple groups using a variety of entropy-based approaches, and in multiple model systems [20][21][22][23][24][25].…”

Impact of number of co-existing rotors and inter-electrode distance on accuracy of rotor localization

“…The standard methods to identify rotors include phase mapping [2], dominant frequency [23], and Shannon entropy [24,25]. In phase mapping, the electrograms in each region are mapped to a phase from −π to +π, and a rotor can be defined as a phase singularity [26] around which the phase progresses through a complete cycle from −π to +π [27].…”