Hopf bifurcation
Restitution Function
(Click inside the applet to start)
The restitution function is a mesoscopic characteristic of cardiac tissue.
It describes the duration of an action potential (APD, which is the
time the cardiac cell
is in an excited state)
as a function of the
diastolic interval (DI, which is the
time the cardiac cell is in an unexcited state).
At large DIs the ionic currents in the cell have time to go back into the rest state, and the corresponding APD is close to the maximum APD.
As the DI is decreased, some of the ionic currents are still activated and
the corresponding APD is smaller.
There is a minimum DI for which the ionic currents are so activated that
it is not possible to induce another action potential. This produces a
minimum APD different from zero in the restitution of APD.
For more detailed information on APD restitution curves please visit the
tutorial section.
In this Applet, one can see which will be the behavior of a pulse when a
constant period is applied.
The period T is defined as APD+DI and corresponds to the red line formed
when one clicks in the graph. The trajectory of APD and DI is then
displayed as one changes from the first period T to a second period.
If the period chosen intersects the restitution curve at a point with slope
less than one, then one obtains a stable point (DI,APD).
However, if it intersects at a point with slope greater than one,
oscillations of APD or conduction blocks are produced.
Further reading on the APD map can be found in: J. App. Physiol. Vol 25 191-196 1968 by J.B. Nolasco and R.W.
Dahlen.