Wave Emission from Heterogeneities Opens a Way to Controlling Chaos in the Heart

The effectiveness of chaos control in large systems increases with the number of control sites. We find that electric field induced wave emission from heterogeneities (WEH) in the heart gives a unique opportunity to have as many control sites as needed. The number of pacing sites grows with the amplitude of the electric field. We demonstrate that WEH has important advantages over methods used in clinics, and opens a new way to manipulate vortices in experiments, and potentially to radically improve the clinical methods of chaos control in the heart.

Figure 1

Modifying the number and positions of pacing sites by changing the electric field. Obstacles are shown as white circles and ellipses. (a–c) The electric field is horizontal and increases from (a) to (c). (a) A field $E=0.5\mathrm{V}/\mathrm{cm}$, 10 ms duration results in wave emission from 1 site. The short arrows indicate direction of the wave propagation. (b) With $E=0.55\mathrm{V}/\mathrm{cm}$, waves are emitted from 2 sites. (c) With $E=0.8\mathrm{V}/\mathrm{cm}$, waves are emitted from 4 sites. (d–e) The electric field changes direction from horizontal (d) to vertical (e), as indicated by the arrows. (d) $E_X=0.55\mathrm{V}/\mathrm{cm}$, $E_Y=0$. (e) $E_X=0$, $E_Y=0.55\mathrm{V}/\mathrm{cm}$. Note that wave emitting sites are different in (d) and (e). (f) Potential change $e_{\max }^{\prime }$ vs radius $R^{\prime }$ of a circular obstacle. Dimensionless coordinates: $e_{\max }^{\prime }=e_{\max }/E_0\lambda$, $R^{\prime }=R/\lambda$, $\lambda =0.08\mathrm{cm}$ is the electrotonic constant. Simulations done in the LR model.

Figure 2

Termination of rotating waves by WEH. (A) Electric field $E=1.1\mathrm{V}/\mathrm{cm}$. Rotating waves are removed. (A1) $t=0.795\mathrm{s}$: Several rotating waves are seen. (A2) $t=0.85\mathrm{s}$ and (A3)  $t=1.155\mathrm{s}$: Pacing waves initiated from 2 big and 6 small obstacles by electric field pulses 10 ms duration are seen. (A4) 1.98 s: All rotating waves are terminated. (B) Electric field $E=0.6\mathrm{V}/\mathrm{cm}$. Rotating waves are not removed. (B1) $t=0.750\mathrm{s}$: Two rotating waves are seen. (B2) $t=0.850\mathrm{s}$ and (B3) $t=1.155\mathrm{s}$: Seen that pacing waves are initiated only from two big obstacles but not from 6 small obstacles. (B4) $t=2.040\mathrm{s}$: Two rotating waves are still seen. The arrhythmia is not terminated. (A1), (B1) also show obstacles. (C) Power spectra of the pseudo ECG. Peak $S$ is induced by rotating waves, frequency $\sim 9\mathrm{Hz}$. Peak $E$ is induced by electric field pulses 10 ms duration with pacing frequency $f=10.2\mathrm{Hz}$. In all figures, period of pacing $T=98\mathrm{ms}$. Meandering spirals, rotation time $T_s\sim 110–115\mathrm{ms}.$.

Figure 3

WEH waves in cultured cardiac myocytes. (A) WEH waves. Initiation (a) and propagation (b). A pulse $1\mathrm{V}/\mathrm{cm}$, 9 ms duration was delivered before frame (a). (c) shows the structure of the cell layer (transmitted light), where the heterogeneities are seen in the lower right corner. (B) Termination of a rotating wave by $1.5\mathrm{V}/\mathrm{cm}$ pulses. $t=0$. A rotating wave is shown. A curved arrow indicates the rotation direction. A small white square indicates wave tip position. Waves are induced by the far field pulses, from an heterogeneity not seen in the field of view. They propagate from the left upper corner, in the direction shown by the rectilinear arrow at $t=0.57\mathrm{s}$, 1.07 s, 1.57 s. Every of them induces a shift of the wave tip (white square) to the right, and it disappears from the field of view at $t=1.57\mathrm{s}$. All figures show a field of view of $2\mathrm{mm}\times 2\mathrm{mm}$.