For large DI's, the ion channels in the cell have time to recover to their rest states, and the following APD is close to the maximum APD. As the DI is decreased, some of the ion channels do not recover fully and the following APD is smaller. There is a minimum DI for which the ion channels have not recovered enough to produce another action potential. This results in a minimum APD larger than zero in the restitution of APD.
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. If the period chosen intersects the restitution curve at a point where the slope is less than one, a stable point (DI,APD) is obtained. However, if it intersects at a point with slope greater than one, oscillations of APD are produced that can result in conduction block.
Further reading on the APD map can be found in
Nolasco JB, Dahlen RW. (1968) J Appl Physiol 25, 191-196.