Karma model on a 2D square


This applet implements the Karma model in two dimensions.

To use the applet, click on the Start button to initiate a plane wave from the left. To initiate a spiral wave, click on Reset h (reset half plane) when the plane wave is in the middle of the tissue. This will break the wave front to initiate the spiral wave. Some buttons are not functional yet, such as R IC (read initial conditions), W IC (write initial conditions), Tip off/on (finds and plots the tip trajectory of any spiral) and Periodic Boundary Conditions (for periodicity along one of the axes).

Things to try:

  • Record the signal at a given point in the tissue. Press the Trace button in the lower right and then click in the main plot to select the location from which to record. Use the check boxes to indicate whether ( Voltage, v-gate or both should be recorded. When you click on a new position in the tissue, the recording automatically switches to that location.
  • Stimulate the tissue directly. Click on the S1 button (its text will change to S1 on ) and set the size of the stimulus in the box below. Click anywhere in the tissue to introduce a stimulus at that location. Repeat as desired to form conduction blocks and multiple waves.
  • Use an extremely large stimulus to "defibrillate" the tissue.
  • Visualize either the Voltage field or v-gate field in 2D by using the radio buttons.
  • Change the color map using the drop-down list box.
  • Change the model's parameter values.
  • Change the tissue size (lowest box on the right). The size can vary between 50 and 200 units and the tissue is always a square (enter a number and retun).
  • Analyze oscillations in APD (alternans) that occur in this model. Oscillations of APD occur when the slope of the restitution curve is greater than one and the spiral wave period falls in this regime. To decrease the spiral period so that it is in this regime, either increase the parameter vstar or increase the parameter xm. For example, after initiating a spiral wave as described above, slowly increase vstar (using steps of 0.01) and observe the oscillatons and breakup as the value approaches 0.6. Alternatively, increase xm (using step values of 1) and observe the breakup and the complex spatiotemporal organization. Visualizing the voltage in the lower plot using Trace on is recommended.
  • (Experts only!) Change the integration dt and dx for the model as you change the parameters. Note that if you these values are too large you may crash the program.


    For more information see the single cell Karma model applet .