Unified mechanism of local drivers in a percolation model of atrial fibrillation

Fig. 1. The emergence of AF in the inhomogeneous model with simultaneous endo- (z = 0) and epicardial (z = 24) imaging. Smoothing has been applied for clarity. Red, excited nodes; blue, resting (excitable) nodes; other, refractory (unexcitable) nodes. (a) Planar wavefronts propagating during sinus rhythm. The dotted box indicates a gap in the wavefront formed by conduction block. (b) Endo view: The arrow indicates an excitation reentering the gap in the wavefront. Epi view: Reentry is not observed. (c) Emergence of fibrillatory activity. (d) Maintenance of fibrillatory activity. Epi view: Activity emerges on the surface as a point source (breakthrough activity) located at the star. See video A in Supplemental Material [37].

Fig. 2. A cross section of the model during AF showing a closeup of the x-z plane (fixed y coordinate). The cross section has been chosen to align with a reentrant circuit. Arrows indicate the movement of wavefronts. The top (bottom) surface of each panel corresponds to the epicardium (endocardium). A reentrant circuit can be seen near the endocardium with activity (a) moving around an isolated fiber, (b, c) reentering the isolated fiber, and (d) emitting fibrillatory waves from the left end of the isolated fiber. Fibrillatory activity spreads from the endocardium to the epicardium through the complex fiber structure of the model. This results in a wide variety of possible breakthrough patterns on the epicardial surface. When viewed from the endocardium, reentrant activity will be clearly visible since the isolated fiber lies along the endocardial surface. When viewed from the epicardial surface, the wavefronts propagating from the reentrant circuit may emerge as a single breakthrough point, or as multiple breakthrough points simultaneously. See video D in Supplemental Material [37]. Scale: 100 × 25 nodes.

Fig. 3. The average time spent in AF for the (a) homogeneous and (b) inhomogeneous models. Both models show a transition from sinus rhythm at large coupling (0% AF time) through paroxysmal AF (0% < AF time < 100%) to persistent AF (100% AF time). The gray parameter regions indicate coupling parameters below the percolation threshold, and are thus irrelevant to clinical AF. (a) Homogeneous coupling parameters, ν∥ and ν⊥. Blue, sinus rhythm; red, persistent AF. The white transition region corresponds to paroxysmal AF. Guidelines of positive (negative) gradient indicate constant Δθ (ν¯). Risk curve as a function of the inhomogenous coupling parameter, ν¯, (red graph). There is no AF for ν¯ ≳ 0.4. Decreasing ν¯ associated with decoupling nodes, there is a transition from sinus rhythm through paroxysmal AF to persistent AF. Inset: Histograms showing the distribution of reentrant circuits driving AF for paroxysmal AF (top) and persistent AF (bottom) as a function of depth z from the endocardium. Drivers cluster in the subendocardial region (z = 0) for paroxysmal AF but are uniformly distributed across the bulk for persistent AF.

Fig. 4. (a) An activation map adapted with permission from Ref. [14] showing reentry activity from subendo imaging and a focal source on the subepi side with four marked reference points. (b) The equivalent for our model. Smoothing has been applied to images for clarity. Red, excited nodes; blue, resting nodes; other, refractory nodes.

Fig. 5. (a) The global success rate of full depth focal ablation if the first reentrant circuit location is destroyed [single focal ablation (SFA), circles], and if the first ten locations are destroyed [multiple focal ablations (MFA), crosses] as a function of the coupling parameter, ν¯. The dashed line indicates the coupling value below which all simulated tissues harbour reentrant circuits. (b) The local success rate of a single focal ablation destroying reentrant circuits at the ablation site as a function of the ablation depth, z, for tissues with high coupling, ν¯ = 0.33 (plus), and low coupling, ν¯ = 0.27 (up triangle). The dashed (dot-dashed) lines correspond to the cumulative sum of the reentrant circuit depth probabilities for ν¯ = 0.33 (ν¯ = 0.27).

Fig. 6. Simulated ablation in a tissue with multiple drivers demonstrating how the ability to terminate fibrillatory activity is closely related to driver depth. AF emerges (a) in the bottom left corner from a reentrant circuit near the epicardium, and (b) at the top of the tissue from a separate reentrant circuit near the endocardium. (c) Two shallow ablations (solid red in bottom left and top center) are applied to the endocardial surface at the locations of the reentrant circuits penetrating part of the way into the tissue. (d) The circuit near the epicardium has not been destroyed by the ablation since the ablation has not penetrated far enough into the tissue. The circuit near the endocardium has been destroyed successfully. However, since an active circuit remains in the tissue, AF has not been terminated. (e) and (f) show the same ablation process as demonstrated in (c) and (d); however, the ablation is now transmural, penetrating the full distance through the tissue. This is indicated by the solid red regions on the subepi view in (e) and (f). The ablations have successfully destroyed both reentrant circuits. Hence, fibrillatory waves dissipate as shown in (f) and sinus rhythm…