Stochastic Termination of Spiral Wave Dynamics in Cardiac Tissue

Figures

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  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.

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  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).

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  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.

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  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.

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  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.