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.