The present PSpice analysis of the cross-sectional profile of longitudinal propagation velocities of simulated APs through a small-diameter bundle of cardiac muscle fibers indicates that velocity is lower in the depths of the bundle than at the surface. This difference was apparent when there were 0, 1 or 10 gj-channels at the cell junctions. The cross-sectional profile was bell-shaped when there were 0 or 1 gj-channels and bullet-shaped when there were 100 channels. The ratio of the velocity at the bundle surface to that at the bundle core was over 2.0 when there were 0 or 1 gj-channels (Table 1 A, B). This ratio was greatly reduced when there were 10 channels (Table 1). With 100 channels, the ratio was reduced to 1.00 and the cross-sectional profile was flat (Table 1 C).
Increasing the value of the longitudinal resistance of the interspace between the parallel chains (Rol2) 10-fold to 2000 KΩ greatly accelerated propagation at the core, and so reduced the ratio, when there were 0 gj-channels (Table 1E). When there were 10 or 100 channels, the elevation of Rol2 had very little effect (Table 1 F, G).
Increasing both the bundle termination resistance (RBT) and Rol2 10-fold (each to 2000 KΩ) greatly accelerated (almost doubled) the velocity of propagation at both the bundle surface and the core, but the surface/core ratio remained high when there were 0 gj-channels (Table 1 H). When there were 100 channels, there was almost no effect (Table 1 I).
Lowering Rol2 by 10-fold (to 20 KΩ) had only a small effect at 0 gj-channels (Table 1 J) and at 10 or 100 channels (Table 1 L, M). When RBT was also lowered 10-fold (to 20 KΩ), the propagation velocity was greatly reduced at the surface at 0 gj-channels but was almost unaffected at the core, and the surface/core ratio was reduced to less than 1.00 (Table 1 K).
Lowering Rol2 4-fold (to 50 KΩ) had almost no effect (Table 1 N). Raising Rol2 4-fold (to 800 KΩ) had an intermediate effect (Table 1 O), i.e. it increased the propagation velocity in the core and thereby reduced the surface/core ratio.
Thus, when cell-to-cell transmission is by the electric field (EF) mechanism (0 or 1 gj-channel), the surface/core ratio is high (about 2.0). This means that propagation velocity at the core of the bundle is about half that at the surface. In contrast, when cell-to-cell transmission is by local-circuit currents through gj-channels, the surface/core ratio is about 1.0 and the cross-sectional profile is flat. Hence, propagation velocity is uniform at all depths of the bundle. Since non-uniform velocities could contribute to re-entrant types of arrhythmias, any decrease in the number of functional gj-channels under pathophysiological conditions (such as transient ischemia) might give rise to arrhythmias.
As expected, the velocity of propagation increases as more and more gj-channels are inserted (compare A, B, C and D of Table 1). The velocity increased from 36.6 cm/s (0 channels) to 36.8 cm/s (1 channel), 46.6 cm/s (10 channels) and 397 cm/s (100 channels). The last of these values is well above that measured physiologically. In adult canine atria, the longitudinal conduction velocity varies from about 85 to 105 cm/s (depending on cycle length), and in infant atria the range is about 35 to 50 cm/s; the transverse velocity varied from 11 to 18 cm/s for adults and 8 to 14 cm/s for infants .
Note that when Rol2 was increased 10-fold, the core velocity increased greatly (from 17.0 cm/s to 29.0 cm/s) when there were zero gj-channels (Table 1 E vs. 1 A). This effect caused the surface/core ratio to drop from 2.15 to 1.13. Hence, when cell-to-cell transmission of excitation is by the EF mechanism , raising Rol2 increases the velocity, consistent with our previous finding . Since the surface fibers are exposed to Roland Ror, not to Rol2, the velocity at the surface does not change. Consistent with this interpretation, when both RBT and Rol2, were raised 10-fold, the velocity at the surface greatly increased as well, bringing the surface/core ratio back close to 2.0 (Table 1H). Lowering Rol2 10-fold had almost no effect (Table 1 J, L). In contrast, lowering RBT 10-fold when there were zero gj-channels produced a large decrease in velocity at the surface, thus decreasing the surface/core ratio to 0.9 (Table 1 K).
We cannot explain the finding of a bell-shaped profile (for 0 or 1 gj-channel) (Fig 3 A, B; Fig 4 A, B). We expected a bullet-shaped profile under the standard parameters. However, when Rol2 was increased 10-fold, the profile changed from bell-shaped to bullet-shaped (with a dimple) (Fig. 5 A). The profile was bullet-shaped under standard parameters when there were 10 gj-channels (Fig. 4C), but the surface/core velocity ratio was low. This profile remained bullet-shaped even when Rol2 was raised 10-fold (Fig 5 B).
The present results using PSpice analysis are in very good agreement with those reported by Wang et al. , who used a computer model with programs written in C language. Their studies showed that, when there was no transverse coupling between the fibers (chains) in the cardiac muscle bundle, the velocity of propagation in the core fiber was much lower than that in the surface fiber. (In their model, the myocardial cells were very long, so many longitudinally-oriented gj-channels were, in effect, present.) When the distance between the parallel fibers was 100 Å or less, there was a large interstitial potential (equivalent to our EF mechanism), which increased in magnitude as the distance was reduced (equivalent to increasing Rol2 in the present study). When there was strong transverse coupling between the parallel chains, the propagation velocity in the core chain was the same as that in the surface chain, as found in the present study.
In summary, the present study demonstrates that longitudinal propagation velocity in a simulated small-diameter bundle of cardiac muscle is markedly lower in the depths and core of the bundle than at the surface. However, such slower propagation occurs only when there are no or few gj-channels (0, 1 or 10). When there were many gj-channels, the velocity profile was flat and the surface/core ratio of velocities was 1.0. Therefore, under pathophysiological conditions that can render some gj-channels non-functional, the observed phenomenon can lead to reentrant arrhythmias. The finding by Poelzing et al. [14, 15] that there is heterogeneous expression of connexin43 across the ventricular wall of canine heart, and that this may produce arrhythmias in heart failure, provides some evidence that alterations in the number of functioning gj-channels can have serious consequences.