Page 76 - Cardiac Electrophysiology | A Modeling and Imaging Approach

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Effects of Structural Discontinuities on Action Potential Shape

In the classic description of action potential propagation in a uniform continuous medium
(e.g., the nerve axon) the action potential shape is determined by the transmembrane currents. In

cardiac tissue, the structural discontinuities influence the morphology and shape of the
propagating action potential. The simulations in Figure 3.3 show the maximum upstroke
velocity, dV /dt , of a 1-dimensional multi-cellular strand, for a range of intercellular coupling
m max
(solid line). There is strong dependence of dV /dt on the degree of coupling; it displays a
m max
biphasic behavior – an increase to a maximum followed by a decrease – as gap junction coupling

is progressively reduced. The maximum value of dV /dt occurs when gap junction coupling is
m max
reduced by a factor of about 60 relative to its value in normal myocardium. The initial increase of
dV /dt results from greater confinement of depolarizing charge to individual cells of the fiber
m max
as coupling is reduced (decreased electrical load). The increase in available charge for local
depolarization accelerates the rate of depolarization to cause a steeper action potential upstroke.
The descending phase of dV /dt at very high levels of gap junction uncoupling is due to
m max
reduced availability of I source current. Because of the small axial current that can flow through
Na
the high resistance gap junctions, membrane depolarization to the excitation threshold is very

slow (long “foot” of the action potential). During this slow charging process, sodium channels
inactivate before reaching their activation threshold, reducing channel availability and
consequently I . Eventually, when gap junction coupling is sufficiently low, the confinement of
Na
charge to a depolarizing cell cannot compensate for the reduced I and conduction block occurs.
Na
The slight monotonic decrease of the I curve in Figure 3.3 (short-dashed line) during the
Na, max
phase of dV /dt increase establishes that membrane currents are not the primary cause of the
m max
dV /dt increase. Rather, the change of intercellular coupling affects souce-sink relationships in
m max
the fiber, which feeds back to alter the action of membrane currents. When coupling is extreme-

ly reduced, the I and dV /dt curves practically overlap, indicating that I determines
Na, max m max Na, max
dV /dt . Indeed, in an solated cell (a situation approximated by the highly uncoupled cells in the
m max
fiber) I is the sole determinant of dV /dt . The long-dashed line in Figure 3.3 shows
Na, max m max
dV /dt in a continuous fiber, for comparison. In this simulation, gap junctions were not present
m max
in the model and their resistance was contained in the lumped intracellular resistance of the
continuous fiber. Note that dV /dt is constant for all values of fiber conductance, consistent
m max
with the classical theory of action potential conduction in continuous media. In such media,
dV /dt is solely determined by membrane properties (membrane excitability). 179
m max

Similar considerations of source-sink relationships explain the cellular-scale spatial
variations of dV /dt and conduction velocity during action potential propagation. As the action
m max
potential approaches the cell end, before crossing the gap junction, conduction velocity and
dV /dt increase locally due to the relatively large resistance of the gap junction (reduced load).
m max
Inversely, just beyond the gap junction there is a slight slowing of conduction and decrease of
dV /dt , due to local increase of electrical load. These spatial variations relative to gap junction
m max