Origin and characteristics of high Shannon entropy at the pivot of locally stable rotors: insights from computational simulation

Network determinants of cardiovascular calcification and repositioned drug treatments

Ectopic cardiovascular calcification is a highly prevalent pathology for which there are no effective novel or repurposed pharmacotherapeutics to prevent disease progression. We created a human calcification endophenotype module (ie, the "calcificasome") by mapping vascular calcification genes (proteins) to the human vascular smooth muscle-specific protein-protein interactome (218 nodes and 632 edges, P < 10^-5 ). Network proximity analysis was used to demonstrate that the calcificasome overlapped significantly with endophenotype modules governing inflammation, thrombosis, and fibrosis in the human interactome (P < 0.001). A network-based drug repurposing analysis further revealed that everolimus, temsirolimus, and pomalidomide are predicted to target the calcificasome. The efficacy of these agents in limiting calcification was confirmed experimentally by treating human coronary artery smooth muscle cells in an in vitro calcification assay. Each of the drugs affected expression or activity of their predicted target in the network, and decreased calcification significantly (P < 0.009). An integrated network analytical approach identified novel mediators of ectopic cardiovascular calcification and biologically plausible candidate drugs that could be repurposed to target calcification. This methodological framework for drug repurposing has broad applicability to other diseases.

Entropy Mapping Approach for Functional Reentry Detection in Atrial Fibrillation: An In-Silico Study

Catheter ablation of critical electrical propagation sites is a promising tool for reducing the recurrence of atrial fibrillation (AF). The spatial identification of the arrhythmogenic mechanisms sustaining AF requires the evaluation of electrograms (EGMs) recorded over the atrial surface. This work aims to characterize functional reentries using measures of entropy to track and detect a reentry core. To this end, different AF episodes are simulated using a 2D model of atrial tissue. Modified Courtemanche human action potential and Fenton–Karma models are implemented. Action potential propagation is modeled by a fractional diffusion equation, and virtual unipolar EGM are calculated. Episodes with stable and meandering rotors, figure-of-eight reentry, and disorganized propagation with multiple reentries are generated. Shannon entropy (ShEn), approximate entropy (ApEn), and sample entropy (SampEn) are computed from the virtual EGM, and entropy maps are built. Phase singularity maps are implemented as references. The results show that ApEn and SampEn maps are able to detect and track the reentry core of rotors and figure-of-eight reentry, while the ShEn results are not satisfactory. Moreover, ApEn and SampEn consistently highlight a reentry core by high entropy values for all of the studied cases, while the ability of ShEn to characterize the reentry core depends on the propagation dynamics. Such features make the ApEn and SampEn maps attractive tools for the study of AF reentries that persist for a period of time that is similar to the length of the observation window, and reentries could be interpreted as AF-sustaining mechanisms. Further research is needed to determine and fully understand the relation of these entropy measures with fibrillation mechanisms other than reentries.

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

BACKGROUND

The potential utility of entropy (En) for atrial fibrillation (AF) mapping has been demonstrated in previous studies by multiple groups, where an association between high bipolar electrogram (EGM) entropy and the pivot of rotors has been shown. Though En is potentially attractive new approach to ablation, no studies have examined its temporal stability and specificity, which are critical to the application of entropy to clinical ablation. In the current study, we sought to objectively measure the temporal stability and specificity of bipolar EGM entropy in medium to long term recordings using three studies: i) a human basket catheter AF study, ii) a tachypaced sheep AF study and iii) a computer simulation study.

OBJECTIVE

To characterize the temporal dynamics and specificity of Approximate, Sample and Shannon entropy (ApEn/SampEn/ShEn) in human (H), sheep (S), and computer simulated AF.

METHODS

64-electrode basket bi-atria sustained AF recordings (H:15 min; S:40 min) were separated into 5 s segments. ShEn/ApEn/SampEn were computed, and co-registered with NavX 3D maps. Temporal stability was determined in terms of: (i) global pattern stability of En and (ii) the relative stability the top 10% of En regions. To provide mechanistic insights into underlying mechanisms, stability characteristics were compared to models depicting various propagation patterns. To verify these results, cross-validation was performed across multiple En algorithms, across species, and compared with dominant frequency (DF) temporal characteristics. The specificity of En was also determined by looking at the association of En to rotors and areas of wave cross propagation.

RESULTS

Episodes of AF were analysed (H:26 epochs, 6040 s; S:15 epochs, 14,160 s). The global pattern of En was temporally unstable (CV- H:13.42% ± 4.58%; S:14.13% ± 8.13%; Friedman- H: p > 0.001; S: p > 0.001). However, within this dynamic flux, the top 10% of ApEn/SampEn/ShEn regions were relatively temporally stable (Kappa >0.6) whilst the top 10% of DF regions were unstable (Kappa <0.06). In simulated AF scenarios, the experimental data were optimally reproduced in the context of an AF pattern with stable rotating waves surrounded by wavelet breakup (Kappa: 0.610; p < 0.0001).

CONCLUSION

En shows global temporal instability, however within this dynamic flux, the top 10% regions exhibited relative temporal stability. This suggests that high En regions may be an appealing ablation target. Despite this, high En was associated with not just the pivot of rotors but also with areas of cross propagation, which suggests the need for future work before clinical application is possible.

Targeting the Substrate in Ablation of Persistent Atrial Fibrillation: Recent Lessons and Future Directions

While isolation of the pulmonary veins is firmly established as effective treatment for the majority of paroxysmal atrial fibrillation (AF) patients, there is recognition that patients with persistent AF have substrate for perpetuation of arrhythmia existing outside of the pulmonary veins. Various computational approaches have been used to identify targets for effective ablation of persistent AF. This paper aims to discuss the clinical aspects of computational approaches that aim to identify critical sites for treatment. Various analyses of electrogram characteristics have been performed with this aim. Leading techniques for electrogram analysis are Complex Fractionated Atrial Electrograms (CFAE) and Dominant Frequency (DF). These techniques have been the subject of clinical trials of which the results are discussed. Evaluation of the activation patterns of atria in AF has been another avenue of research. Focal Impulse and Rotor Modulation (FIRM) mapping and forms of Body Surface Mapping aim to characterize multiple atrial wavelets, macro-reentry and focal sources which have been proposed as basic mechanisms perpetuating AF. Both invasive and non-invasive activation mapping techniques are reviewed. The presence of atrial fibrosis causes non-uniform anisotropic impulse propagation. Therefore, identification of fibrosis by imaging techniques is an avenue of potential research. The leading contender for imaging-based techniques is Cardiac Magnetic Resonance (CMR). As this technology advances, improvements in resolution and scar identification have positioned CMR as the mode of choice for analysis of atrial structure. AF has been demonstrated to be associated with obesity, inactivity and diseases of modern life. An opportunity exists for detailed computational analysis of the impact of risk factor modification on atrial substrate. This ranges from microstructural investigation through to examination at a population level via registries and public health interventions. Computational analysis of atrial substrate has moved from basic science toward clinical application. Future directions and potential limitations of such analyses are examined in this review.

Information Theory and Atrial Fibrillation (AF): A Review

Atrial Fibrillation (AF) is the most common cardiac rhythm disorder seen in hospitals and in general practice, accounting for up to a third of arrhythmia related hospitalizations. Unfortunately, AF treatment is in practice complicated by the lack of understanding of the fundamental mechanisms underlying the arrhythmia, which makes detection of effective ablation targets particularly difficult. Various approaches to AF mapping have been explored in the hopes of better pinpointing these effective targets, such as Dominant Frequency (DF) analysis, complex fractionated electrograms (CFAE) and unipolar reconstruction (FIRM), but many of these methods have produced conflicting results or require further investigation. Exploration of AF using information theoretic-based approaches may have the potential to provide new insights into the complex system dynamics of AF, whilst also providing the benefit of being less reliant on empirically derived definitions in comparison to alternate mapping approaches. This work provides an overview of information theory and reviews its applications in AF analysis, with particular focus on AF mapping. The works discussed in this review demonstrate how understanding AF from a signal property perspective can provide new insights into the arrhythmic phenomena, which may have valuable clinical implications for AF mapping and ablation in the future.

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

BACKGROUND

Conflicting evidence exists on the efficacy of focal impulse and rotor modulation on atrial fibrillation ablation. A potential explanation is inaccurate rotor localization from multiple rotors coexistence and a relatively large (9-11mm) inter-electrode distance (IED) of the multi-electrode basket catheter.

METHODS AND RESULTS

We studied a numerical model of cardiac action potential to reproduce one through seven rotors in a two-dimensional lattice. We estimated rotor location using phase singularity, Shannon entropy and dominant frequency. We then spatially downsampled the time series to create IEDs of 2-30mm. The error of rotor localization was measured with reference to the dynamics of phase singularity at the original spatial resolution (IED=1mm). IED has a significant impact on the error using all the methods. When only one rotor is present, the error increases exponentially as a function of IED. At the clinical IED of 10mm, the error is 3.8mm (phase singularity), 3.7mm (dominant frequency), and 11.8mm (Shannon entropy). When there are more than one rotors, the error of rotor localization increases 10-fold. The error based on the phase singularity method at the clinical IED of 10mm ranges from 30.0mm (two rotors) to 96.1mm (five rotors).

CONCLUSIONS

The magnitude of error of rotor localization using a clinically available basket catheter, in the presence of multiple rotors might be high enough to impact the accuracy of targeting during AF ablation. Improvement of catheter design and development of high-density mapping catheters may improve clinical outcomes of FIRM-guided AF ablation.

Electrophysiological Rotor Ablation in In-Silico Modeling of Atrial Fibrillation: Comparisons with Dominant Frequency, Shannon Entropy, and Phase Singularity

BACKGROUND

Although rotors have been considered among the drivers of atrial fibrillation (AF), the rotor definition is inconsistent. We evaluated the nature of rotors in 2D and 3D in- silico models of persistent AF (PeAF) by analyzing phase singularity (PS), dominant frequency (DF), Shannon entropy (ShEn), and complex fractionated atrial electrogram cycle length (CFAE-CL) and their ablation.

METHODS

Mother rotor was spatiotemporally defined as stationary reentries with a meandering tip remaining within half the wavelength and lasting longer than 5 s. We generated 2D- and 3D-maps of the PS, DF, ShEn, and CFAE-CL during AF. The spatial correlations and ablation outcomes targeting each parameter were analyzed.

RESULTS

1. In the 2D PeAF model, we observed a mother rotor that matched relatively well with DF (>9 Hz, 71.0%, p<0.001), ShEn (upper 2.5%, 33.2%, p<0.001), and CFAE-CL (lower 2.5%, 23.7%, p<0.001). 2. The 3D-PeAF model also showed mother rotors that had spatial correlations with DF (>5.5 Hz, 39.7%, p<0.001), ShEn (upper 8.5%, 15.1%, p <0.001), and CFAE (lower 8.5%, 8.0%, p = 0.002). 3. In both the 2D and 3D models, virtual ablation targeting the upper 5% of the DF terminated AF within 20 s, but not the ablations based on long-lasting PS, high ShEn area, or lower CFAE-CL area.

CONCLUSION

Mother rotors were observed in both 2D and 3D human AF models. Rotor locations were well represented by DF, and their virtual ablation altered wave dynamics and terminated AF.