FIG. 12.

Action potential duration (APD)–spatially discordant alternans (SDA) and Ca-SDA nodal ring dynamics in two-dimensional (2D) tissue of the amplitude equation (AE) model. (a) Schematic plots to illustrate the effects of Ca-SDA nodal ring (red) and curvature on APD-SDA nodal ring (dashed blues). The blue arrows indicate the force of the Ca-SDA nodal ring, and the green arrows indicate the force of the curvature on the APD-SDA ring. (b) The critical ring radius $\left(r_c\right)$ vs $\sigma$ determined via computer simulations of the AE model [Eqs. (20) and (21)]. $\alpha =0.5,\rho =0.5$, and $\gamma =0.1$. (c) Ring radius $r$ vs beat no. for different initial ring radius for $\sigma =0.1$. Left: The initial APD-SDA nodal ring (blue) radius $r>r_c$. Right: The initial APD-SDA nodal ring (green) radius $r<r_c$. (d) Ring radius $r$ vs beat no. for different initial ring radius for $\sigma =0.3$. Left: The initial APD-SDA nodal ring (blue) radius $r>r_c$. Right: The initial APD-SDA nodal ring (green) radius $r<r_c$. Simulations are done in a 2D tissue of 800 × 800 cells.