Hopf Bifurcation and Chaos

Biphasic APD Restitution Curve
and Chaos

(Click inside the applet to start)

The restitution function is a mesoscopic characteristic of cardiac tissue. It characterizes the duration of an action potential (APD, which is the time the cell is in an excited state) as a function of the preceding diastolic interval (DI, which is the time the cell is in an unexcited state).

Compared to the previous restitution function applet, the difference here is that instead of a monotonically decreasing APD restitution curve, a biphasic APD restitution curve is used. This kind of restitution curve has been known to occur in some cases when measuring the APD restitution. Chaos can be produced when periodic pacing is applied at short cycle lengths.

In this applet, the APD and DI are obtained when electrical stimulation is applied at a constant period. The period T is defined as APD + DI and corresponds to the black diagonal line shown after clicking in the graph. The trajectory of APD and DI is then displayed as the cell is paced at that period.

Further reading on biphasic APD restitutions and chaos can be found in
Qu Z, Weiss JN, Garfinkel A. (1997) Phys Rev Lett 78, 1387-1390.