(a) Action potential duration (left) and conduction velocity restitution (right) for Steep and LowEx kinetics. These measurements were made in a simulated 2D sheet, using an S1 S2 protocol, with four S1 stimuli and S1-S1 intervals fixed at . (b) Snapshots showing unstable re-entry in an isotropic 2D tissue sheet with Steep kinetics. Brighter shades indicate active depolarized tissue (c) Time series of membrane voltage recorded from upper left corner of the sheet. (d, e) Corresponding snapshots of stable re-entry and time series for LowEx kinetics.
Geometry and filament orientation shortly after initiation. (a) Cube geometry, , showing three different initial alignments of the filament: P0 (left), P1 (middle-left), P2 (middle-right), and P3 (right). Circles indicate filament ends. (b) isotropic slab geometry. (c) anisotropic slab geometry, both shown to the same scale as the cube geometry. (d) Enlarged views of rabbit ventricle geometry showing snapshots of the initiation of re-entry in simulation with Steep kinetics, with shading indicating on the surface. Epicardial transmembrane voltage is color coded, with lighter shade showing depolarized tissue and darker shade resting tissue. First three panels show (i) , repolarization of the ventricles following pacing at the apex; (ii) , S2 stimulus delivered to LV free wall; (iii) , figure of eight re-entry in the LV free wall. The final panel shows the two filaments (arrowed) corresponding to the figure of eight re-entry at .
Example of filament identification and segmentation from simulation in anisotropic slab with Steep kinetics, after initiation. (a) Voltage field, with depolarized regions enclosed by an isosurface. (b) Filament voxels obtained from phase transformation and convolution kernel. (c) Filament voxels after smoothing. The voltage distribution on the lower surface is also shown as grayscale with brighter shades indicating depolarized regions, confirming that the filament intersections with the surface correspond to phase singularity points. (d) Segmentation of individual filaments, independent filaments are shown in different shades.
Filament number and orientation for the isotropic cube geometry with P0 initial condition. (a) Total number of filaments, number of transmural filaments, and number of ring filaments for Steep kinetics. (b) Snapshots of filaments showing initial breakup in the Steep simulation at after initiation, and snapshots showing later activity at 1000 and . See movie included as supplementary material (Ref. 32 ). (c) Total number of filaments, number of transmural filaments, and number of ring filaments for LowEx kinetics. (d) Snapshots of filaments showing initial breakup in the LowEx simulation at after initiation, and snapshots showing later activity at 1000 and . See movie included as supplementary material (Ref. 32 ).
Comparison of filament characteristics in cube geometry. First column shows the number of filaments for simulations with Steep (a) and LowEx (b) kinetics, showing influence of initial conditions. Second column shows mean filament volume for simulations with Steep (c) and LowEx (d) kinetics. Third column shows filament lifetimes for simulations with Steep (c) and LowEx (d) kinetics. Each horizontal line indicates the lifetime of a single filament; the start of the line indicates the time at which the filament originated from a birth or division, and the end of the line the time at which the filament ended with a death or amalgamation. See text for more details.
Number of filaments in simulations with Steep kinetics in (a) isotropic slab geometry, (b) anisotropic slab geometry, and (c) rabbit ventricle geometry, and LowEx kinetics in (d) isotropic slab geometry, (e) anisotropic slab geometry, and (f) rabbit ventricle geometry. Snapshots in each case show filaments at time indicated by gray line; after initiation for slab geometry and after initiation for rabbit ventricle. Movies showing the filaments in each of these simulations are provided as supplementary material (Ref. 32 ).
Filament lifetimes shown using the same scheme as in Fig. 5 . (a) Filament lifetimes in isotropic and anisotropic slab geometry, with Steep and LowEx kinetics. (b) Filament lifetimes in the rabbit geometry with Steep kinetics and LowEx kinetics.
Cumulative sum of filament births, deaths, divisions, and amalgamations in cube geometry with (a) Steep kinetics and (b) LowEx kinetics, anisotropic slab geometry with (c) Steep kinetics and (d) LowEx kinetics, and rabbit geometry with (e) Steep kinetics and (f) LowEx kinetics.
Parameter sets for Steep and LowEx tissue.
Filament properties calculated for the final of each simulation. Each entry shows deviation.
Filament lifetimes calculated throughout each simulation. For cube and slab geometries this is over , and for the rabbit ventricle is over .
Total number of filament transitions in each simulation shown in bold, and the total number occurring in the final of each simulation shown in brackets.
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