Karma Model

Karma model

For One Cell

This applet shows the voltage produced by a cell using the Karma model as a function of time after it is stimulated above its threshold.
This is a simplified model that concentrates only on the collective behavior of all ionic currents rather than the detailed description of each one, and its aim is to reproduce mesoscopic properties of cardiac tissue such as APD restitution and conduction velocity restitution.
The model is based on an analysis of the Noble model where the fast gate variables m and h are adiabatically eliminated.
The model equations are:

The Fast variable Vm represents the voltage in the cell and v represents the sodium slow inactivation and potassium slow actiavion wich are combined by the Heaviside step function.
For this applet we use the cubic form for the function h with delta = 0.23 and alpha =7.5. The value of gamma is chosen such that the system has an excitatory fixed point (for this case gamma =1.92). The parameters to vary in the model are then: Epsilon, which is a small parameter that relates the time scale of the upstroke with that of the maximum APD, xm describes the sensitivity of the wave front when propagating (as xm increases, dispersion decreases), and vstar controls the APD pulse dynamics.

As in the other cell models, the start button initiates the simulation and the reset button brings back the parameters to the initial values and the model parameters can be changed to observe different dynamics.
The AP generated with this model has a more realistic fast upstroke and slow recovery compared to that of the standard FHN model. Furthermore, it reproduces the oscillatory pulse dynamics observed in experiments with cardiac rings, which is one known mechanism for spiral breakup in two and three dimensions. See for example the breakup movie or reproduce and study it using the 2D applet version of the Karma model.

More Information about the Karma model can be found in: "Spiral Breakup in Model Equations of Action Potential Propagation in Cardiac Tissue", A. Karma, Phys. Rev. Lett. Vol 71, 1103-1106 (1993) and in: "Electrical Alternans and Spiral Wave Breakup in Cardiac Tissue", A. Karma, CHAOS vol. 4, 461-472 (1994).