A. Normal AP (left) and an AP with a phase 2 EAD (solid) or phase 3 (dashed) EAD (right). B. A schematic plot of L-type Ca channel conductance (G_Ca,L) vs membrane voltage (mV) showing the window I_Ca,L region (cross-hatched) where the steady state activation (SSA) and steady state inactivation (SSI) curves overlap and a fraction of Ca channels remain continuously open. Dashed lines show a potential therapeutic intervention that shifts the SSA and SSI curves to reduce the overlapping window current region. C. Schematic diagram illustrating the interaction between time-dependent I_Ca,L reactivation (blue dashed lines) and time-dependent deactivation of repolarizing currents (I_K) (dashed red lines) in the window voltage range during AP repolarization. For the normal AP (left), repolarization rate is too fast for I_Ca,L to grow larger than I_K. If repolarization rate is too slow, however, I_Ca,L can grow larger than I_K,, thereby reversing repolarization to cause an EAD.

Dynamical chaos in the logistic equation. A. Iteration of the logistic equation (Eq.1 in text) produces different behaviors (periodic, alternating, chaotic) depending on the value of α. B. Bifurcation diagram showing the steady state behavior as a function of α.

A. Rate-dependence of irregular EAD behavior in a patch-clamped rabbit ventricular myocyte. EADs occur on every AP at a pacing cycle length (PCL) of 6s, and are suppressed at PCL 2s, but occur irregularly in between, as illustrated by the variation in APD in the graph below). B. Analogous behavior in a rabbit ventricular AP model with no randomness, indicating that the irregularity is due to dynamical chaos.

Mechanism of EAD chaos. A. During irregular EAD behavior shown in Fig. 3, the APD restitution curve shows a very steep region, indicating a sensitive dependence of APD on DI, for both the real myocyte (left panel) and the rabbit AP model (middle and right panels). The circled points in the real myocyte data were reproduced in the AP model by adding a small amount of random noise (right panel). B. AP traces in a simplified 3-variable AP model illustrating the sensitive dependence of EAD formation on the DI of a premature S2 beat (left). The full APD restitution curve (middle), when iterated, produces the irregular APD variation (right), which exhibits sensitive dependence on initial conditions for a slight difference in the initial DI (blue vs red trace). From 22 with permission

Synchronization of chaotic EADs. A. In a simulated 1D array of myocytes exhibiting chaotically irregular EADs, slight differences in initial conditions lead to a completely asynchronous and irregular pattern of APD distribution on each beat if the myocytes are uncoupled (left). When myocytes are coupled by gap junctions, however, electronic current flow prevents marked APD differences between adjacent myocytes, creating smooth a APD gradient over the length of the cable, which differs on each beat. B. Same for 2D tissue (4.5×4.5 cm), showing the formation of EAD islands (red) separated by regions without EADs, which vary dramatically from beat-to-beat. From 22 with permission.

Mixed focal-reentrant PVT as a result of EAD-mediated PVCs arising from EAD islands in simulated 2D homogeneous tissue. The tissue was paced from the left edge at a slow rate. Four successive voltage snapshots show an EAD (upper left quadrant) that generates a PVC (red trace). The PVC then initiates reentry by reentering (white arrow) the receding waveback of the region without EADs (blue trace). The voltage trace below from a representative cell shows multiple EADs followed by a rapid tachycardia due to a mixture of triggered activity and reentry.

Mixed focal-reentrant PVT due to synchronization of chaotic EADs. A. Simulations in a anatomic rabbit ventricles model. First 3 panels show voltage snapshots of focal activations (red) emerging from 3 discrete sites, which have changed location at the later time (4^th–6^th panels). B. Similar shifting focal activations observed in an optically-mapped Langendorff rabbit heart exposed to H₂O₂ to induce EADs (blue-green-yellow red color scale indicates most repolarized to most derepolarized). Electrocardiographic traces below show PVT. From 22 with permission.