Overdrive pacing of spiral waves in a model of human ventricular tissue

Figures

• 

  Figure 1. Example of successful LVC with a period shorter than that of the spiral wave. X-axis, mm, is horizontal; Y-axis, mm, is vertical; colour shows potential, mV (colour legend is at the right). SL07, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{stim}}=228\,\mathrm{ms}$$\end{document}Tstim=228ms, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{sw}}=237.6\,\mathrm{ms}$$\end{document}Tsw=237.6ms, relative pacing period is 0.96. See animation in Supplementary video 1.

• 

  Figure 2. Example of unsuccessful LVC with the ‘Conduction block’ dynamic instability. X-axis, mm, is horizontal; Y-axis, mm, is vertical; colour shows potential, mV (colour legend is at the right). The tip of the spiral wave is shown as a black dot. SL14, norm, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{stim}}=232\,\mathrm{ms}$$\end{document}Tstim=232ms. We see the acceleration of a plain wave at the bottom left part of the tissue (b), then the tissue is not ready for the next stimulus (c), long action potential hinders the stimulation (d). See animation in Supplementary video 2.

• 

  Figure 3. Measured wave periods in 1D cable depending on the stimulation period. Models with parameters sets SL07 (a) and SL14 (b). APD-90 in SL07 model (c) and SL14 model (d). Dotted lines indicate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{1D}}$$\end{document}T1D.

• 

  Figure 4. Limits of the effective absolute stimulation periods (red solid lines) in models with normal and decreased conductivities for Na ionic current. No limits are shown in cases of unsuccessful LVC. Slopes 0.7 (a), 1.4 (b). Spiral wave periods (black dashed lines) and their limits in cases of meandering (vertical black segments); minimal assimilable pacing periods (blue dotted-and-dashed lines).

• 

  Figure 5. The width of the interval of effective stimulation periods for models with normal and decreased conductivities for CaL+Kr (verapamil effect), CaL and Na ionic currents. SL07 case.

• 

  Figure 6. Dynamic instability of the core type. The spiral wave is stable without the stimulation (on the left). When the wave train starts to touch its core zone, the spiral wave breaks up (in the middle). The instability leads to a global break-up (on the right). X-axis, mm, is horizontal; Y-axis, mm, is vertical; colour shows potential, mV (colour legend is at the right). SL11; Na75; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{stim}}=239\,\mathrm{ms}$$\end{document}Tstim=239ms. See animation in Supplementary video 3.

• 

  Figure 7. Example of transient core-type dynamic instability (jumps-type). Tip coordinates, mm, are plotted against time, s. The red line shows the x coordinate and the blue line shows the y coordinate. The spiral wave breaks up near its core as a result of the stimulation. The core then moves to another position and the wavefront annihilation zone shifts back toward the electrode. SL11; Na75; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{stim}}=247\,\mathrm{ms}$$\end{document}Tstim=247ms. See animation in Supplementary video 4.

• 

  Figure 8. Longitudinal velocity component of the induced drift. Slope 0.7.

• 

  Figure 9. Drift velocity component Vx for Na25 and four different slopes.