Introduction

The truncated exponential waveform from an implantable cardioverter defibrillator can be described by three quantities: the leading edge voltage, the waveform duration, and the waveform time constant (tau s). The goal of this work was to develop and test a mathematical model of defibrillation that predicts the optimal durations for monophasic and the first phase of biphasic waveforms for different tau s values. In 1932, Blair used a parallel resistor-capacitor network as a model of the cell membrane to develop an equation that describes stimulation using square waves. We extended Blair's model of stimulation, using a resistor-capacitor network time constant (tau m), equal to 2.8 msec, to explicitly account for the waveform shape of a truncated exponential waveform. This extended model predicted that for monophasic waveforms with tau s of 1.5 msec, leading edge voltage will be constant for waveforms 2 msec and longer; for tau s of 3 msec, leading edge voltage will be constant for waveforms 3 msec and longer; for tau s of 6 msec, leading edge voltage will be constant for waveforms 4 msec and longer. We hypothesized that the best phase 1 of a biphasic waveform is the best monophasic waveform. Therefore, the optimal first phase of a biphasic waveform for a given tau s is the same as the optimal monophasic waveform.

Methods and results

We tested these hypotheses in two animal experiments. Part I: Defibrillation thresholds were determined for monophasic waveforms in eight dogs. For tau s of 1.5 msec, waveforms were truncated at 1, 1.5, 2, 2.5, 3, 4, 5, and 6 msec. For tau s of 3 msec, waveforms were truncated at 1,2,3,4,5,6, and 8 msec. For tau s of 6 msec, waveforms were truncated at 2,3,4,5,6,8, and 10 msec. For waveforms with tau s of 1.5, leading edge voltage was not significantly different for the waveform durations of 1.5 msec and longer. For waveforms with tau s of 3 msec, leading edge voltage was not significantly different for waveform durations of 2 msec and longer. For waveforms with tau s of 6 msec, there was no significant difference in leading edge voltage for the waveforms tested. Part II: Defibrillation thresholds were determined in another eight dogs for the same three tau s values. For each value of tau s, six biphasic waveforms were tested: 1/1, 2/2, 3/3, 4/4, 5/5, and 6/6 msec. For waveforms with tau s of 1.5 msec, leading edge voltage was a minimum for the 2/2 msec waveform. For waveforms with tau s of 3 msec, leading edge voltage was a minimum for the 3/3 msec waveform. For waveforms with tau s of 6 msec, leading edge voltage was a minimum and not significantly different for the 3/3, 4/4, 5/5, and 6/6 msec waveforms.

Conclusions

The model predicts the optimal monophasic duration and the first phase of a biphasic waveform to within 1 msec as tau s varies from 1.5 to 6 msec: for tau s equal to 1.5 msec, the optimal monophasic waveform duration and the optimal first phase of a biphasic waveform is 2 msec, for tau s equal to 3.0 msec, the optimal duration is 3 msec, and for tau s equal to 6 msec, the optimal duration is 4 msec. For both monophasic and biphasic waveforms, optimal waveform duration shortens as the waveform time constant shortens.