Model 2a on a 1D Ring

The slope of the APD restitution curve is greater than one for periods less than 300 ms, but electrotonic effects prevent alternans for periods below 130 ms although the restitution slope is greater than three.

The applet reproduces the results shown with the blue dashed lines (Model 2a, see Figure 3 caption in paper for more information).

The applet simulates the propagation of an action potential on a ring (the edge at the right is the same as the edge at the left).


The Start button generates one action potential which is blocked on the right so that it only propagates to the left.
The Stop button then can stop the simulation at any time. The simulation can be resumed by using the Continue button that replaces the Stop button when the simulation is stopped.
The simulation speed can be increased or decreased by clicking on the Faster or Slower buttons repeatedly until the desired speed is reached.
The Reset button brings the membrane potential of all the cells back to the rest state.
The Restart button reinitiates the original single pulse.


The period of the propagating action potential depends on the size of the ring, so that by changing the ring size the period is also changed. At the begining of the simulation the pulse (after a few rotations) will have a period of 309 ms (APD=215 ms, DI=94 ms) for the initial size of the ring (365 points).

Slowly decrease the ring size by clicking on the Smaller ring button (each click decreases the ring size by 5 points). Once a period below 305 ms (360 points) is reached, sustained alterans will develop with a small amplitude of 5 ms. The alternans magnitude increases as the period is decreased further (see panel A above). For example, at a period of 263 ms (290 points) large-magnitude discordant alternans can be observed. At a period of 137 ms (135 points), however, the magnitude of the alternans begins to decrease due to electrotonic effects although the slope of the APD restitution curve is about three (see panel B above). Alternans does not occur for smaller periods even though the restitution slope remains above one. The minimum period is 64 ms (APD=52 ms DI=12 ms, 40 points).

Note that changing the ring size while the wave front is at the edges may terminate the reentry. To avoid this problem, change the ring size only when the wave front is not near the left and right boundaries.