(A) Computer simulation of a spiral wave using the Fenton-Karma model (parameter set #1 from Ref. 24 ). Activation is plotted in all figures using a gray scale with white corresponding to depolarized tissue and black corresponding to repolarized tissue. The wavelength λspiral of the rotor indicates the spatial scale between successive arms of the spiral. The red curve is an Archimedean spiral with its wavelength adjusted such that it fits the activation front of the simulated spiral. (B) Isochrones of a rigidly rotating Archimedean spiral with a period τ and separated by τ/4 (white lines) and a square grid of electrodes with spatial discretization Δx (black dots). The wavelength of the spiral is λspiral = 4Δx and the corresponding spatially continuous isochronal regions at time t = T are shown using the indicated colorscheme and time interval ΔI = τ/4. For larger spatial resolution, the isochronal regions are no longer spatially continuous. (C) Computer simulation of a focal source with a wavelength λfocal and period τ using the same gray scale and parameter set as in (A). (D) Isochronal map of the focal beat of (C), along with isochrones separated by τ/4 (white lines), computed from a square grid with resolution Δx.
Computer simulation of a single-armed rotor spanning the entire field of view. (A) Snapshot of the activation (t = 45 ms) of a clock-wise rotating rotor simulated on a 200 × 200 grid, corresponding to a 5 × 5 cm domain. The activation is plotted using a gray scale while the meandering spiral tip of the rotor is shown in red. The green symbols are isochrones, 20 ms apart, superimposed onto the snapshots. Scalebar = 1 cm. (B) Isochrones computed on a 20 × 20 grid that was obtained by spatially coarsening the original 200 × 200 grid. Isochrones are again 20 ms apart and the scalebar represents the spatial resolution (Δx = 2.5 mm). (C) Same as (B) but now using an 8 × 8 grid and a spatial resolution of Δx = 6.25 mm. (D) Same as (B) and (C), using a 4 × 4 grid and a spatial resolution of Δx = 12.5 mm. This illustrative reentry pattern was generated using the FK model of Ref. 42 .
Snapshots of isochronal maps computed using the data of Fig. 2(D) . For visualization purposes, the 4 × 4 grid was bi-linearly interpolated. The activation of the grid points are binned in ΔI = 22 ms isochrone intervals (corresponding to approximately a quarter of the spiral period) and are color coded according to the colorbar. For example, red corresponds to all grid points that are activated in the first isochrone interval immediately preceding the snapshot at time T (i.e., in the interval (T- ΔI,T)). The white line in (F) indicates the direction of rotation of the rotor.
A simulated stable counterclockwise rotating rotor and its break-down. (A) A 15 × 15 cm computational domain, with spatial resolution Δx = 0.5 mm, contains a stable rotor with a meandering spiral tip path shown in red. The rotor was simulated using the 3-variable FK model (parameter set #3 from Ref. 24 ) and the break-down of the spiral was generated by assigning a different value of one of the parameters in the outer region of the computational domain (τr = 0.4 vs. τr = 0.27). Scalebar = 2 cm. (B) Isochronal map using a spatial resolution of Δx = 6 mm, as indicated by the scalebar, using the data from A. (C) Snapshot of an isochronal map on a 12 × 12 grid. The scale bar represents the spatial resolution (Δx = 12.5 mm). (D) Snapshot of an isochronal map on a 15 × 15 grid from an animated sequence. All isochronal maps used an isochronal interval of ΔI = 20 ms (enhanced online). [URL: http://dx.doi.org/10.1063/1.4807098.1]doi: 10.1063/1.4807098.1.
Focal pattern in a simulation. (A) A snapshot of the tissue activation of a focal source located at the center of the 15 × 15 cm domain (model parameters are as in Fig. 4 ). Scalebar = 1 cm. (B) Isochronal map using four ΔI = 25 ms isochronal intervals and a spatial resolution of Δx = 7.5 mm (indicated by the scale bar). Four separate and spatially continuous isochronal regions can be clearly identified. (C) Isochronal map using four ΔI = 25 ms isochronal intervals and a spatial resolution of Δx = 15 mm (indicated by the scale bar). The centrifugal activation pattern can no longer be identified at this resolution. Black corresponds to grid points that were not activated in any of the four preceding isochronal intervals.
(A) Schematic depiction of the data acquisition in patients. The atria are presented in an anterior (frontal) view (see torso) with the left atrium shown in red and the right atrium in gray. Some of the contact electrodes, inserted into the atria to record tissue activation, are shown. (B) The orientation of the electrodes are shown in the RA, which is opened between its poles with tricuspid annulus opened laterally and medially (the LA is opened along its equator, with mitral annulus opened superiorly and inferiorly 21 ). ((C)-(H)) Isochronal maps of the RA of a patient with persistent AF. The non-interpolated data on a 8 × 8 electrode grid with spatial resolution between 0.4 and 1 cm are shown in (C) while in (D)–(H), and in Figs. 7 and 8 , the electrode grid was bi-linearly interpolated for visualization purposes. The maps reveal a rotor with period τ = 220 ms in the low RA, as indicated by the white line if (F) resulting in ΔI = τ/4 = 55 ms. The solid square represents the minimal field of view and location that is required to capture the rotor. The dashed square shows an identically sized field of view at a different location that is not able to determine the existence of a rotor. The white bar in (C) represents the interelectrode spacing.
Isochronal maps of the LA of a patient with paroxysmal AF (ΔI = 50 ms). A rotor is visible in the low LA, visualized by the white line in (F), with more complex dynamics in the upper portion of the LA. The white bar in (A) represents the interelectrode spacing.
Isochronal maps of the LA of a patient with paroxysmal AF (ΔI = 50 ms). The maps show three successive focal sources from an origin, in the posterior LA mid-way between the pulmonary vein pairs and >2 cm from each pulmonary vein ostium, at the indicated times. Black corresponds to grid points that were not activated in any of the five preceding isochronal intervals. The white bar in (A) represents the interelectrode spacing.
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