Control of APD alternans on a ring

In this applet, an action potential that oscillates is produced because the ring is small and the restitution curve for the corresponding period has slope greater than one. It is possible to bring the APD to the unstable fixed point (which is approximately equal to (APD_max+APD_min)/2) by using a feedback control algorithm that relates the previous period with the existing one. The period at T-1 is recorded and used as a control by applying a current in a number of electrodes. The more electrodes used, the sooner control is achieved.

To use the applet, press the Start button to initiate the action potential. After two rotations, the control is automatically started. The blue dashed line represents the membrane potential of the previous period, while the black line represents the membrane potential of the current period. A simulation can be used using the stop button and resumed using the Continue button. A new simulation can be initiated by using the Restart button. The Faster and Slower buttons can be used to control the speed of the simulation.

Things to try:

  • Change the number of control points (indicated by red lines) by using the drop-down list.
  • Change the gain control parameter gamma by using the drop-down list. For a fixed number of electrodes, how does gamma affect the efficacy of the control algorithm?

    For more information see
    Rappel WJ, Fenton FH, Karma A. (1999) Phys Rev Lett 83, 456-459.