Beeler-Reuter Model for Ventricular Cells
One-dimensional Cable/Ring

This applet simulates the propagation of action potentials in a cable or ring geometry as selected using the Beeler-Reuter model. The length of the cable or ring can be varied between 0.5 cm and 20 cm. Initiation by a stimulus, propagation, and complex dynamics such as discordant alternans can be studied.

To use the applet, press the Start button. Initiate an action potential either by pressing the Apply S1 button or by clicking inside the plot. The strength, duration, length, and position of the stimulus can be set. The simulation can be paused with the Stop button and resumed using the simulation and the simulation will resume by using the Continue button. Click inside the plot to initiate more activations. The location of each activation corresponds to the location on the x-axis and the magnitude of the activation corresponds to the value on the y-axis. To make the simulation run faster or slower, use the Simulation Speed slider. To return the membrane potential of all cells to the rest value, click Reset. To adjust the size of the cable or ring, use the Cable Length slider. Use the drop-down list to select Cable or Ring geometry. The membrane voltage or other variables can be plotted by checking their boxes in the list.

Things to try:

  • Click the Start button and then the Apply S1 button to generate an action potential propagating to the right. As the wave front propagates, enlarge the cable to about 16 cm. When the wave front is close to the right boundary, click the Stop button and use the list box in the lower left corner to change the cable to a ring, then click the Continue button. This allows the wave to reenter, and after a few rotations around the ring it will be a steady wave with a fixed wavelength. Decrease the ring size slowly, and observe the formation of discordant alternans at a length of 10 cm and conduction block leading to wave termination at a length of 13 cm.
  • Repeat as above, but change the sodium and/or calcium conductances and find the lengths at which alternans appear.
  • Reset using the Reset button and study the threshold for excitation as a function of the stimulus parameters (strength, duration, and length) as well as the sodium and potassium conductances.
  • Induce multiple waves by clicking inside the window with the mouse. Each time the mouse is clicked, a voltage stimulus proportional to the height of the mouse position within the simulation window is added to the voltage at the location of the mouse along the cable. Try to induce a single reentrant wave along a ring.

    For more information about the Beeler-Reuter model, see the Beeler-Reuter applet for one cell.