Page 106 - Cardiac Electrophysiology | A Modeling and Imaging Approach

P. 106
of temporal oscillations in action potential duration, calcium transient, cycle length, conduction

velocity and diastolic interval. Examples are provided in Figure 3.23, which displays action
potential duration and peak magnitude of the calcium transient. As ring size was decreased from
panel A to B to C, oscillation patterns became more complex. Note that during alternans (panel
A) the amplitude of calcium oscillations was much larger than that of action potential duration.

Figure 3.24 shows an example of temporal oscillations in action potential duration (A), diastolic
interval (B) and cycle length (C). Note that the amplitude of cycle length oscillation is much
smaller than that of the other two parameters, and the cycle length oscillations are 90° out of
phase. Similar patterns were observed experimentally (Figure 3.24, right panel; from reference 236 )

and in theoretical studies performed in other ring models.

3.7 Propagation in Higher Spatial Dimensions

In previous sections, one-dimensional models were used to study the properties and ionic
mechanisms of action potential propagation in cardiac tissue. Similar to simplified experimental
preparations (e.g. isolated cells, synthetic strands, papillary muscle, rings of tissue), these
theoretical models are tractable and lend themselves to a thorough analysis, not only at the level

of the action potential but even at the level of membrane ionic currents, intracellular processes
(e.g., the calcium transient) and intercellular interactions through gap junctions. This is particularly
important in studying conduction because membrane ionic currents and their kinetic properties
cannot be measured experimentally during action potential propagation, but can be computed in

accurate and realistic action potential models. The principles and concepts determined in
simplified models (e.g. properties of source-sink relationships) can then be applied in analyzing
behaviors in the more complex cardiac tissue and the whole heart.

Conduction in a one-dimensional fiber or a ring model of reentry involves a planar wave
front. Moreover, the ring model of anatomical reentry assumes a central inexcitable obstacle.
Conduction in two-and three-dimensional cardiac tissue differs from one-dimensional
conduction in various properties that are not present in one-dimension. These include structural

factors (e.g., gap junction distribution, anisotropy) and the fundamental properties of wavefront
curvature and excitable core of functional reentry.

The velocity of a curved wave front depends not only on membrane excitability and tissue

structure, but also on the curvature itself. The velocity of a convex wave front is slower than the
velocity of a planar wave front in the same tissue with all other properties being identical. This is
because of a source-sink mismatch at the convex wave front, where excitatory current from the
front diverges into a larger area of unexcited cells. Conversely, for a concave wavefront the

excitatory current generated by the front converges in front of the propagating wave, supplying
a larger depolarizing charge per depolarizing cell to cause faster depolarization and faster
conduction than that of a planar wave. An experimental demonstration of curvature effects on