Eliminating spiral waves pinned to an anatomical obstacle in cardiac myocytes by high-frequency stimuli

The unpinning of spiral waves by the application of high-frequency wave trains was studied in cultured cardiac myocytes. Successful unpinning was observed when the frequency of the paced waves exceeded a critical level. The unpinning process was analyzed by a numerical simulation with a model of cardiac tissue. The mechanism of unpinning by high-frequency stimuli is discussed in terms of local entrainment failure, through a reduction of the two-dimensional spatial characteristics into one dimension.

Figure 1

(Color online) Activation time maps of rotating spiral waves in experiments of cultured cardiac myocytes. (a) Schematic view defining the local activation time $T_a\left(t\right)$ and local activation interval $T^n$. By mapping $T_a\left(t\right)$ for every pixel, we obtained activation time maps of free (b) and pinned (c) spiral waves. The curved arrows indicate the direction of rotation of the spiral wave. The black circle in (c) indicates an anatomical obstacle, where no cells exist.

Figure 2

(Color online) Successful and unsuccessful unpinning in experiments of cultured cardiac myocytes as a response to a high-frequency stimulus. (a) Before starting periodic pacing. The position of the pacing electrode is shown by an asterisk. The arrow indicates the rotating direction of pinned spiral wave. (b) Snapshots of unsuccessful unpinning by pacing at $1.3\mathrm{Hz}$. (c) Snapshots of successful unpinning by pacing at $1.5\mathrm{Hz}$. (d) Close-up view of phase singularity after successful unpinning by pacing at $1.5\mathrm{Hz}$. Indexes such as “no. 27” indicate the wave number of the pacing wave, and other indexes such as “22.80” at the lower right of the panels indicate the time on the second time scale.

Figure 3

(Color online) Time evolution of local activation intervals. The propagating wave was indexed and the activation intervals plotted for $A$, $B$, and $C$ shown in Fig. 2d. Each point includes four pixels and the averaged values are shown with bars of minimum and maximum values.

Figure 4

(Color online) Numerical results for the unpinning process by a periodic stimulus at different frequencies. (a) Initial state before pacing. (b) Unsuccessful unpinning with periodic pacing at $130.0\mathrm{ms}$. (c) Successful unpinning with periodic pacing at $120.0\mathrm{ms}$. (d) Close-up snapshot. (e) Time evolution of local activation intervals.