When extra stimuli are used to probe the excitability of the heart in the interval between heart beats, there is a window of time, during which life threatening arrhythmias can be reproducible induced. This window is called the vulnerable period or the vulnerable window. The VP is readily demonstrated with any model of an excitable medium, and shown here are measures of the VP when the velocity of the initial wave is varied. Here are simulations based on the guarded receptor model of drug binding to sodium channels and the Beeler Reuter cardiac model. (Some will be critical of usint the BR model. My defence is that it is simple, and thus computationally fast; the VP is generic and therefore can be demonstrated with any model of an excitable medium; and there are no "complete" models of the cardiac electrophysiology. "More realistic" models are often mixtures of less realistic models, combined with empirical adjustments used to improve the quality of the fit. This, in my opinion, does not qualify as a "more realistic" model).

Note, however, a small puzzle with these results: there appear to be two VPs associated with a single value of the velocity of the conditioning wave. Early models of the VP were based on the time required for a critical point to cross the suprathreshold region of the s2 stimulation field - so VP = L/v where L is the length of the field and v is the velocity of the conditioning (s1) wave. Here we see that when the conduction velocity is slowed by simply reducing the maximum sodium conductance, gNa, the VP is shorter (blue line) than when the conduction velocity is slowed by use-dependent drug (red line). This is only possible, from the biophysical perspective, if the electrode length, L, were increased by an amount dependent on the dynamics of the drug-channel interactions.

Here is a model of the vulnerabible period. The key feature is to note that there is a bifurcation in the cellular excitability that separates refractory states from excitable states (labeled Transition point). Media to the left of this is excitable and supports wave formation and propagation. Media to the right of this point is inexcitable, and forming waves collapse. The VP based on this model is determined by the length of time the transition point requires to cross the electrode field: VP = L/v . However, numerical studies and clinical studies indicate that long time constant drugs may alter the VP, perhaps at the same velocity.

Here I demonstrate the critical nature of the bifurcation point. Plotted are action potentials (at 5 ms intervals after s2 stimulation) and Na channel availability gNa*h*j*(1-b) (approximating the excitability of a cell>. In addition, a drug that binds to the inactivated state of the No channel is included. Shown are the Na availability curves for different unbinding rates (the slowest, .0001/ms and the fasted, 0.1/ms) which demonstrate how the spatial gradient of excitability can be altered at the block-uni transition and the uni-bidirectional propagation interface. Note that the critical point is to the left of the s2 stimulus site (show is also the potential distribution due to the injected stimulus current). That all the availability curves intersect in the same region is evidemce that availability is a major determinant of the VP. Note that the right of the s2 stimulus site has fewer Na channels available for activation and results in unidirectional propagation.

Note in the figure below that the VP for control and drug is quite different when the conditioning velocity is the same - thus the above model needs to incorporate a feature that links blockade dynamics with the VP.

VP Boundaries and Na Channel Availability

Shown here are comparable profiles of recovery of Na channel availability under drug-free conditions. Using the Beeler Reuter model (all cardiac and neuronal models display this behavior), I plotted gna*h*j and normalized gna = 5 to 1. Note the steep gradient of excitability recovery which is determined by the inactivated to non-inactivated rate for the Na channel - typically at -80 mV about 1- 10 ms. Note the short distance between the repolarization tail of the conditioning action potential and the VP boundary. This is a measure of the refractory interval and is relatively small compared with the drug figure below.

The critical point is to the left of the stimulation site so that a collapsing antegrade wave is assured. As the stimulus field collapses, following termination of the stimulus pulse, it also propagates in a decremental manner slowly in the retrograde direction and as it approaches the critical point, propagation becomes incremental. The action potential traces at the bottom are at successive 5 ms intervals and clear show the dynamics of front formation and collapse.

Shown here is the other boundary of the VP. Note that the transition point is virtually superimposed over the electrode site so that the initial moments of propagation encounter marginally excitable media in both antegrade and retrograde directions leading to bidirectional propagation.

With a use-dependent Na channel blocker (class 1 antiarrhythmic) a significant number of channels are blocked during the conditioning action potential. Following repolarization, the drug slowly unbinds from the channel - but this slow process extends the spatial excitability gradient as seen below. Note that the refractory period is dramatically increased, a result of reduced excitability secondary to channel blockade.

Here the s2 stimulus is activated at the boundary that separates unidirectional conduction from bidirectional conduction. The lower traces (action potential) are shown for each unbinding rate as indicated on the right. For l = .0005 / ms, there are a series of traces, for each 5 ms following s2 stimulation. The dynamics of wave front formation and collapse are readily appreciated. Note the initial decremental propagation of the antegrade wave, as the initial front propagates into marginally excitable media. Note that the decremental conduction is reversed at approximatly the same place as the critical transition point at the time of s2 stimulation.

Displayed below is a plot of the VP for drugs with different unbinding rates. The measurement was made after a single conditioning pulse, in order to have comparable measurement by eliminating variations in the s1 velocity (i.e. no use-dependent drug accumulation). Shown is the conduction velocity and unbinding rate for drugs with time constants ranging from 10 ms to 2 sec. The linear relationship between VP and time constant is consistent with the above figures which portray the recovery of channel availability, in this case recovery is dominated by the drug unbinding process. Because recovery dynamics is dominated by the drug unbinding time constant, I hypothesize that the dynamics of wave-front formation is altered in proportion to the time constant of unbinding. The model for the VP is extended to now include 2 components: