Off-site control of repolarization alternans in cardiac fibers

Repolarization alternans, a beat-to-beat alternation in action potential duration, has been putatively linked to the onset of cardiac reentry. Anti-alternans control strategies can eliminate alternans in individual cells by exploiting the rate dependence of action potential duration. The same approach, when applied to a common measuring/stimulating site at one end of a cardiac fiber, has been shown to have limited spatial efficacy. As a first step toward spatially distributed electrode control systems, we investigated “off-site” control in canine Purkinje fibers, in which the recording and control sites are different. We found experimentally that alternans can be eliminated at, or very near, the recording site, and that varying the location of the recording site along the fiber causes the node (the location with no alternans) to move along the fiber in close proximity to the recording site. Theoretical predictions based on an amplitude equation [B. Echebarria and A. Karma, Chaos 12, 923 (2002)] show that those findings follow directly from the wave nature of alternans: the most unstable mode of alternans along the fiber is a wave solution of a one-dimensional Helmholtz equation with a node position that only deviates slightly from the recording site by an amount dependent on electrotonic coupling. Computer simulations using a Purkinje fiber model confirm these theoretical and experimental results. Although off-site alternans control does not suppress alternans along the entire fiber, our results indicate that placing the node away from the stimulus site reduces alternans amplitude along the fiber, and may therefore have implications for antiarrhythmic strategies based on alternans termination.

Figure 1

(Color online) Representative example of off-site control in 2 cm Purkinje fiber stimulated from the left end. Left: APD of beat $n$ (blue/dark gray) and beat $n+1$ (red/light gray). Right: transmembrane potential during both beats. Traces are displayed in order from top (recording site 1) to bottom (recording site 6). (a) No control and (b)–(g) control at microelectrodes 1–6 indicated by arrows. This node placement occurred robustly in seven experiments in seven different fibers.

Figure 2

Off-site control in coupled maps model with $T^{\star }=180\text{ms}$. Black and gray curves are obtained from two successive beats at steady state. (a) No control, (b)–(g) control at locations $x_r=0.0$, 0.4 0.8, 1.2, 1.6, and 2.0 cm (indicated by arrows). Insets show close-ups of APD node positions relative to $x_r$ ($x$ axes from $x_r-0.1\text{cm}$ to $x_r+0.1\text{cm}$ in each inset).

Figure 3

Off-site control of spatially discordant alternans in coupled maps model with $T^{\star }=140\text{ms}$. (a) No control and (b)–(g) control at locations $x_r=0.0$, 0.4 0.8, 1.2, 1.6, and 2.0 cm (indicated by arrows).

Figure 4

(Color online) Effects of off-site control on average alternans amplitude $\left(⟨\Delta \text{APD}⟩\right)$. Numbers in inset indicate values of $x_r$. Prior to control, there is spatially concordant alternans for pacing-rates $T^{\star }=150–190\text{ms}$ and spatially discordant alternans at $T^{\star }=140\text{ms}$.

Figure 5

Alternans amplitude $\left(\Delta \text{APD}\right)$ profiles with off-site control applied at locations $x_r=0.0$, 0.4 0.8, 1.2, 1.6, and 2.0 cm (indicated by arrows). Theoretical profiles (solid lines) are computed from Eq. (6) with $A_1=28.2$, 39.2, 65.1, 65.4, 39.5, and 27.1 ms for panels (a)–(f). Also shown are results from coupled maps simulations (dashed lines) with $T^{\star }=180\text{cm}$ (as in Fig. 2) and experimental data (asterisks; same preparation as in Fig. 1).

Figure 6

(Color online) Dependence of node position $\left(x_0\right)$ for off-site control on the feedback gain, $\gamma /2$. (a) Analytical results [Eq. (7)]. (b) Simulation results. Both sets of data are obtained for $\gamma /2=0.8$ (blue), 0.5 (black), 0.3 (red), and 0.1 (magenta).