Page 89 - YORAM RUDY BOOK FINAL

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Figure 3.10 is a summary comparison between slow conduction due to reduced membrane

excitability (dashed curves) or reduced intercellular coupling (solid curves). Panel A highlights
the fact that reduced coupling can support very slow conduction, while reduced excitability
cannot. This fundamental difference is due to the very different properties of SF (panel B),
which decreases monotonically as excitability is reduced, but increases to a maximum prior to

conduction block as coupling is reduced.

Tissue Inhomogeneities

The fundamental concepts of source and sink and the principles of their role in conduction
are applicable at all scales of the cardiac tissue. Examples of tissue inhomogeneities on a scale of
many cells include regional differences in gap junction coupling, branching of fibers, and tissue
expansion. Such inhomogeneities have an important implication to cardiac arrhythmias, because

they introduce asymmetries in tissue properties that can cause unidirectional block and reentry.
In the simulations of Figure 3.11, inhomogeneity of gap junction coupling is introduced by
increasing gap junction conductance starting from the junction between cells 79 and 80 in a
fiber of 160 cells. In the left panels A-C, the fiber is stimulated at cell 0 and propagation is from

low-to-high conductance segments of the fiber (arrow). The velocity of propagation in the poorly
coupled segment is 10 cm/sec; it accelerates to 55 cm/sec in the well coupled fiber. The action
potential experiences a long conduction delay of 12 ms at the transition from cell 78 to cell 79,
which is much longer than intercellular delays in the homogenous segments of the fiber (1 msec

in the poorly coupled segment). This long delay results from source-sink mismatch at the
transition; cell 79 receives small current from cell 78 because of the poor coupling between them,
but loses large current to cell 80 because the increased coupling in this direction constitutes a
large electrical load. SF in the poorly coupled fiber (SF=2.73) is higher than that of the well coupled

fiber (SF=1.60) (Figure 3.11B), as expected based on Figure 3.8. It decreases sharply approaching
the transition region and reaches a value of 0.98 (locally below 1) at cell 79. In the adjacent cells SF
is 2.56 (cell 78) and 1.20 (cell 80), identifying the transition zone as the critical Achilles’ heel of
propagation. Note the high foot potential of long duration in cells just beyond the transition.

The bar graph in Figure 3.11B shows Q and Q at several locations along the fiber. In the
Na
Ca
homogeneous segments, away from the transition zone, Q :Q = 10 (poorly coupled segment)
Na
Ca
and Q :Q = 105 (well coupled segment), indicating dominance of I in sustaining conduction.
Ca
Na
Na
In cells near the transition zone, Q > Q (Q : Q = 0.35 in cell 78) and I Ca,L becomes a crucial
Na
Ca
Na
Ca
contributor of depolarizing charge. The mechanism of transition from I dominance to I Ca,L
Na
dependence in regions of long propagation delays was discussed in relation to Figure 3.9.
Peak values of I and I Ca,L during propagation along the fiber are shown in Figure 3.11C.
Na
Just beyond the transition region, I (a negative, inward current) is greatly reduced. The reduction
Na
is due to inactivation of sodium channels during the long elevated foot potentials (panel A)