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. 2022 Jan:2:809532.
doi: 10.3389/fnetp.2022.809532. Epub 2022 Jan 26.

Stochastic termination of spiral wave dynamics in cardiac tissue

Affiliations

Stochastic termination of spiral wave dynamics in cardiac tissue

Wouter-Jan Rappel et al. Front Netw Physiol. 2022 Jan.

Abstract

Rotating spiral waves are self-organized features in spatially extended excitable media and may play an important role in cardiac arrhythmias including atrial fibrillation (AF). In homogeneous media, spiral wave dynamics are perpetuated through spiral wave breakup, leading to the continuous birth and death of spiral waves, but have a finite probability of termination. In non-homogeneous media, however, heterogeneities can act as anchoring sources that result in sustained spiral wave activity. It is thus unclear how and if AF may terminate following the removal of putative spiral wave sources in patients. Here, we address this question using computer simulations in which a stable spiral wave is trapped by an heterogeneity and is surrounded by spiral wave breakup. We show that, following ablation of spatial heterogeneity to render that region of the medium unexcitable, termination of spiral wave dynamics is stochastic and Poisson-distributed. Furthermore, we show that the dynamics can be accurately described by a master equation using birth and death rates. To validate these predictions in vivo, we mapped spiral wave activity in patients with AF and targeted the locations of spiral wave sources using radiofrequency ablation. Targeted ablation was indeed able to terminate AF, but only after a variable delay of up to several minutes. Furthermore, and consistent with numerical simulations, termination was not accompanied by gradual temporal or spatial organization. Our results suggest that spiral wave sources and tissue heterogeneities play a critical role in the maintenance of AF and that the removal of sources results in spiral wave dynamics with a finite termination time, which could have important clinical implications.

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Conflict of interest statement

SN: Co-author of IP owned by Stanford University and University of California Regents. Honoraria from Abbott, Inc. Consulting fees from the American College of Cardiology Foundation, Beyond Limits.ai and TDK, Inc. royalty income from UpToDate. DK: Consulting fees from Insilicomed and research grants from AHA and NIH. Institutional fellowship support from Medtronic, St. Jude Medical, Biosense Webster, Boston Scientific and Biotronik. AD: Speaking honoraria from Medtronic. TB: Consulting fees/honoraria from Medtronic and Biotronik. VS: Consulting fees/honoraria from Biosense Webster and research grants from Biosense Webster, Medtronic, Boston Scientific, St. Jude Medical and Biotronik. JM: Consulting fees/honoraria from Topera, Stereotaxis, Biosense Webster, Biotronik and Medtronic. W-JR: Co-author of IP owned by the University of California Regents.

The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Figures

FIGURE 1
FIGURE 1
Computational Simulations of Delayed AF Termination and Numerical Analyses. (A) Snapshot of a simulation in a 7.5 × 7.5 cm domain showing the activation pattern during spiral wave break up, with white (black) corresponding to activation (recovered) tissue and with spiral wave tips indicated by red symbols. A central portion of the computational domain, indicated by the white circle with radius of 0.75 cm, exhibits reduced excitability resulting in a stable spiral wave source. Scale bar: 1 cm. (B) Snapshot of the activation following ablation of the heterogeneous circular region in A, indicated in green, showing the removal of the spiral wave from the central region. All non-conducting boundaries are shown as orange lines. (C) Number of spiral tips as a function of time during a typical simulation with a domain size of 100 cm2. This number fluctuates and can reach zero (red square), resulting in the termination of SDC. (D–F), Distribution of termination times, computed using 400 independent simulations, for a domain size of 39 cm2 (D), 56.25 cm2 (E), and 100 cm2 (F). The dashed line is an exponential fit to the distribution.
FIGURE 2
FIGURE 2
Transition rates computed using numerical simulations. (A–D), The birth and death rates for the removal of a single (n→n−1 (A)) and a pair of spiral wave tips (n→n−2 (B)), along with the birth rates for the creation of a single (n→n+1 (C)) and a pair of spiral wave tips (n→n+2 (D)) computed in domains of various sizes. Error bars represent standard deviation. (E), The birth and death rates for a single tip, W±1, normalized by the perimeter of the domain, as a function of the density of tips, q = n/A net . (F), The birth and death rates for a pair of tips, W±2, normalized by the area of the domain, as a function of the density of tips. (G), The quasi-stationary distribution for different domain sizes computed using the simulations (lines) and computed using the transition matrix (symbols).
FIGURE 3
FIGURE 3
Electrical Organization of Atrial Fibrillation. (A,B): Snapshots of the WFF flow field (arrows) along with a color map of the vorticity during AF in a 45 years old male patient (A) and a 59 year old male patient (B). The value of the vorticity can range from -1, for counterclockwise rotating spiral waves, to +1, for clockwise rotating spiral waves.
FIGURE 4
FIGURE 4
Electrograms during termination. Electrograms from body surface (ECG) and inside the heart (intracardiac) showing termination of AF, indicated by the dashed red line, to sinus rhythm following ablation of spiral wave sources in a 45 year old male patient.
FIGURE 5
FIGURE 5
Dynamics of AF termination. (A–D), Mean cycle length CLμ (A), corresponding full width at half-maximum height (FWHM) (B), the average synchronization index <γ> (C), and the mean number of tips (D) in patients with AF, measured 3 min (T-3), 1min (T-1), and immediately preceding AF termination (T), averaged over all patients. For all quantities there is no significant increase or decrease in successive intervals. (E), Number of tips as a function of time for a 64 year old male patient in which AF converts to sinus rhythm.

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