Page 73 - Cardiac Electrophysiology | A Modeling and Imaging Approach

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SF = 1 is the critical value; the amount above 1 indicates the margin of safety (robustness) of con-

duction .
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3.2 Discontinuous Conduction

Cardiac tissue is composed of discrete cells (about 100 microns long and 20 microns in
diameter) that are inter-connected electrically through gap junctions. In normal myocardium,
the resistance of gap junctions at intercalated disc structures that span well less than a micron, is
similar to the resistance of the entire cardiomyocyte cytoplasm that spans 100 microns or more.
175
Clearly, at the cellular (microscopic) scale, resistive discontinuities are introduced by the tissue
architecture. The effects of these structural discontinuities on action potential propagation have
been studied in experimental preparations and theoretical models that allow detailed

analysis. 176,177

Figure 3.1 shows simulations of action potential propagation in a linear strand of cardiac
cells. The action potential upstroke is shown at two locations in each of two neighboring cells in
the fiber: the proximal and distal ends of an upstream cell (locations 1 and 2, respectively) and the

proximal and distal ends of its downstream neighbor (locations 3 and 4). For normal (tight) gap
junction coupling (Figure 3.1A, gap junction conductance g = 2.5µS) the macroscopic
j
conduction velocity is 54 cm/s, a typical value measured in normal myocardium. As stated

above, for these conditions the gap junction conductance between cells equals the myoplasmic
conductance of the entire cell. Consequently, the time spent by the action potential in crossing
the gap junction (~0.1ms, shaded in Figure 3.1A) equals its conduction time across the entire cell.
Because of the large difference in the dimensions of these structures, propagation at the
cellular scale is discontinuous even when cell-to-cell coupling is normal, with the action

potential experiencing conduction delays at the gap junctions. Similar behavior was observed
experimentally in a synthetic linear strand of neonatal rat ventricular myocytes. In these smaller
cells the average cellular conduction time was 38 µS, while gap junction crossing time was 80 µS .
178
Note (Figure 3.1A) that on a macroscopic scale of many cells, conduction appears uniform and the
gap junction delays are not detectable. As stated above, a uniform global conduction velocity
(54 cm/s in the simulation) can be assigned to the macroscopic conduction. In the simulation
of Figure 3.1B, gap junction coupling was reduced 10-folds (g = 0.25 µS ) while keeping the
j
intracellular myoplasmic resistivity unchanged. Under these conditions, charge leakage out of the

cell (loading) is reduced and intracellular cytoplasmic conduction time decreases dramatically,
while a long conduction delay (0.5 ms, shaded in Figure 3.1B) is introduced at each intercellular
gap junction. In fact, the entire cell depolarizes almost simultaneously as one unit; it generates

an action potential, but the conduction velocity of this action potential is determined by the
long delays in crossing from cell to cell across the gap junctions. In this respect, this highly
discontinuous conduction differs from conduction under normal gap junction coupling
(Figure 3.1A) because the macroscopic velocity over many cells is determined by the gap
junction delays with negligible contribution from conduction time across individual cells.