Proarrhythmic and antiarrhythmic actions of ion channel blockers on arrhythmias in the heart: model study

We explain why 1) some class I and IV antiarrhythmia drugs could exert proarrhythmic action, 2) some class III drugs are effective in controlling reentrant arrhythmias, and 3) cycle length (CL) oscillation is involved in the termination or initiation of reentry. To explain these phenomena, we employ the following three means: bifurcation analysis, simulation, and model construction. Antiarrhythmia drugs are modeled by varying maximal conductances of Na+, Ca2+, and time-dependent delayed rectifying and time-independent inward rectifying K+ channels in the Beeler-Reuter model, where the model cells are arranged in a ring. Bifurcation analysis predicts that there is a critical ring size (CRS) at which infinite ring behavior suddenly breaks down. Channel blockers can affect CRS in different manners: Na+ and Ca2+ blockers shorten CRS, whereas delayed rectifying K+ channel blockers and the inward K+ channel blockers lengthen CRS. This differential explains why some antiarrhythmia drugs are proarrhythmic (i.e., shorten CRS) whereas others are antiarrhythmic (i.e., lengthen CRS). Simulation is then used to investigate how the drugs affect reentrant rhythms in the neighborhood of the CRS. We find that, in this region, CL, conduction velocity, and action potential duration become oscillatory. As ring size shrinks, the pattern of the oscillation becomes more complex. When the ring shrinks to a certain size, reentry can no longer be sustained, and it terminates after a few oscillatory cycles. To explain the basic mechanism involved in CL oscillation, we then construct a minimal model that contains a low-threshold fast inward current and a high-threshold slow inward current. With this model, we show that the two inward currents, with vastly different activation and inactivation kinetics, cause CL oscillations. Our results thus give theoretical explanations for the experimental finding of Frame's group in canine atrial tricuspid ring in vitro that class IC drugs can bring about stable reentry from nonsustained transient reentry, whereas class III drugs transform stable reentry to complex oscillations in CL. Our results also support the result of Frame's group, in that, in "adjustable" tricuspid rings, CL oscillation becomes more complex and its period becomes shorter as an excitable gap is shortened.