Hopf bifurcation

Restitution Function


The restitution function is a mesoscopic characteristic of cardiac tissue that relates the action potential duration (APD) to the diastolic interval (DI) At large DIs the ion channels are able to recover fully, and the resultant APD is close to the maximum APD. As the DI is decreased during faster pacing, some of the ion channels have not recovered from inactivation and are not able to open, and so the resultant APD is smaller. There is a minimum DI greater than zero for which it is not possible to induce another action potential for a given stimulus strength.

In this applet, the behavior of an isolated cell subjected to periodic pacing is described using an iterative one-dimensional map. The period T is defined as APD+DI and corresponds to the black line shown after clicking in the graph. The resultant APD is then indicated by drawing a red vertical line starting from the initial DI and APD selected and ending at the restitution curve. The next DI is determined by drawing a red horizontal line from the last point on the restitution curve to the line representing the period, and the pattern is repeated to compute subsequent values for the APD and DI for the chosen period. If the line representing the period chosen intersects the restitution curve at a point where the slope is less than one, the series of DI,APD pairs produced converge to a single DI and APD. However, if the slope is greater than one at the intersection point, APD oscillations are produced, which for sufficiently short periods lead to conduction block.
To view the behavior over a range of periods, click to set an initial period and then while holding down the mouse button drag to show the behavior at different periods. In this case the line representing the initial period chosen remains black, but the current period line is shown in blue.