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Figure 3.20. Ring-shaped fiber model,
consisting of up to 1500 cells. A primary
stimulus was applied at the top of the
ring (cell 1) and a premature stimulus
at cell 3 during the relative refractory
period of the primary AP. Solid arrows
inside the ring represent propagation
of the premature (reentrant) AP. It blocks
in the antegrade direction (=symbol)
and reenters in the retrograde direction.
Dashed arrows outside the ring
represent propagation of the primary
AP. Due to symmetry, it collides and
blocks at the bottom cell of the ring.
From Quan and Rudy [222], with
permission from Wolters Kluwer
Health, Inc.

decreases, cycle length and action potential duration decrease; for 600 cells action potential
duration is 245 msec, while for 100 cells it is only 60 msec. For both rings the action potential
duration is constant and reentry is stable. For medium size rings between these two extremes
(length~λ), action potential duration oscillates dynamically from beat to beat. The amplitude of
these beat-to-beat oscillations (alternans) is maximum at a ring size of 350 cells and decreases in

either direction (decrease or increase in ring size). This is seen clearly in Figure 3.21B, where
action potential duration from different size rings is shown as a function of the corresponding
cycle length. The upper curve (solid symbols) corresponds to the long action potential and the

bottom curve (open symbols) to the short action potential of consecutive beats. Inspection of the
underlying ionic currents (not shown) clarifies that alternating kinetics of I (incomplete deactiva-
Ks
tion after the long action potential and complete deactivation following the short action potential)
is the major mechanism of action potential duration alternans, with additional contribution from
I . Note that for ring size of 50 cells reentry is not sustained.
Ca,L

For sufficiently small rings, sodium channels which determine conduction velocity, do
not recover completely from inactivation between beats and their availability alternates. Conse-

quently, cycle length oscillations appear together with oscillations of action potential duration
(Figure 3.22A). 238 Note that the amplitude of cycle length oscillations is smaller than that of the
action potential duration at any point of the reentrant pathway, as observed experimentally. When
plotted spatially along the pathway (Figure 3.22B), cycle length and action potential duration are
not constant during one cycle. These spatial variations are functional in nature, as the ring is

intrinsically homogeneous. This behavior implies that concepts such as the wavelength of
excitation are location dependent; for the entire reentry pathway they can only be defined in an
average sense. More recent simulations, 239 over long time periods, revealed more complex patterns