To use the applet, click the Start button to initiate the simulation and the Reset button to return the parameters to their initial values. Check the box for each variable to plot it in the window.
In 1977, Beeler and Reuter developed a model using four of eight different ionic conductances known at the time in cardiac muscle. They implemented an initial fast inward sodium current INa, similar to the one used by Hodgkin and Huxley, but they added an inactivator slow gate variable denoted by j, a time-activated outward current Ix1, a time-independent potassium outward current IK1, and a secondary slow inward current Is carried primarily by calcium ions. Calcium is responsible for the contraction of a cardiac cells and produces a much larger AP plateau in cardiac cells than in nerve cells. The total ionic current in the BR model is given by four currents and uses eight variables: membrane potential, six ionic gates ( m, h, j, x1, f, and j ) and the intracellular calcium concentration [Ca]i.
When the applet is started, it shows two action potentials generated by two consecutive stimuli. The difference in plateau duration, shape and restitution response can be compared to the Hodgkin-Huxley and FitzHugh-Nagumo models. The duration of an action potential in Human ventricular cardiac tissue is on the order of 200-300 ms. In the applet, varying the ionic currents can change the duration and action potential shape given by the model. For instance, the calcium current is largely responsible for the plateau phase of the action potential, so that decreasing the calcium conductance gs decreases the calcium current and thus the action potential duration. Decreasing gs from 0.09 to 0.04 mmho/cm2 shortens the action potential duration by about 50 percent, and the action potential shape becomes more triangular. A further decrease of gs to 0.01 yields an action potential similar to the HH model. On the other hand, increasing gs to 0.2 mmho/cm2 prolongs the action potential and changes its shape yet again by making the secondary rise in potential more prominent. As in the Hodgkin-Huxley model, the sodium conductance gNa is responsible for the rise of the action potential, and changes to this value also can affect the action potential shape and duration. Reducing gNa to 1.0 or to 0.9, for example, decreases the maximum depolarization, allowing less time for the calcium current to activate and producing a smaller action potential. Increasing gNa increases the excitability of the system and makes it easier to induce activations. By changing gNa to 20 mmho/cm2 , for instance, the second activation becomes substantially longer because the increased sodium conductance allows a higher depolarization and therefore more time for the calcium current to activate. Under these conditions, it is easier to induce subsequent activations.
In this model the restitution relation is very strong at small diastolic intervals; that is, the smaller the difference in time between the end of the first activation and the application of the second stimulus, the shorter the second activation. Observe, for example, the small activation that is obtained when S1 is 20 ms and S2 is 320 ms. The timing of S2 must be increased much farther to about 500 ms, lengthening the diastolic interval to roughly the duration of the first action potential, to produce a second activation whose duration is almost the same as the initial action potential duration. Applying a second stimulus before about 315 ms does not affect the membrane potential much since a new activation cannot be produced yet, and the system continues to return to the rest state. However, when gNa is larger, a second activation can be produced earlier (e.g., at 312 ms when gNa is increased to 20 mmho/cm2 ).
Beeler GW, Reuter H. (1977) J Physiol 268, 177-210.