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Circulation. 1996;94:2278-2284

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(Circulation. 1996;94:2278-2284.)
© 1996 American Heart Association, Inc.

Articles

Charge-Burping Theory Correctly Predicts Optimal Ratios of Phase Duration for Biphasic Defibrillation Waveforms

Charles D. Swerdlow, MD; Wei Fan, MD; James E. Brewer, MS

the Division of Cardiology, Cedars-Sinai Medical Center, Los Angeles, Calif.


*    Abstract
up arrowTop
 *Abstract
down arrowIntroduction
 down arrowMethods
 down arrowResults
 down arrowDiscussion
 down arrowReferences
 
Background For biphasic waveforms, it is accepted that the ratio of the duration of phase 2 to the duration of phase 1 (phase-duration ratio) should be <=1. The charge-burping theory postulates that the beneficial effects of phase 2 are maximal when it completely removes the charge delivered by phase 1. It predicts that the phase-duration ratio should be <1 when the time constant of the defibrillation system ({tau}s) exceeds the time constant of the cell membrane ({tau}m) but >1 when {tau}s<{tau}m. This study tested the hypothesis that the optimal phase-duration ratio depends on {tau}s (the product of the defibrillator capacitance and pathway resistance).

Methods and Results In a canine model of transvenous defibrillation (n=8), we determined stored-energy defibrillation thresholds (DFTs) for biphasic waveforms from conventional capacitors (140 µF, {tau}s=7.1±0.8 ms) and very small capacitors (40 µF, {tau}s=2.0±0.2 ms). Each capacitance was tested with phase-duration ratios of 0.5, 1, 2, and 3. The duration of phase 1 approximated the optimal monophasic waveform, 6.3±0.7 ms for 140-µF waveforms and 2.8±0.2 ms for 40-µF waveforms. For 140-µF waveforms, the DFT was lower for phase-duration ratios <=1 than for phase-duration ratios >1 (P=.0003). The reverse was true for 40-µF capacitors (P=.0008). There was a significant interaction between the effects of capacitance and phase-duration ratio on DFT (P=.0002). The lowest DFT for 40-µF waveforms was less than the lowest DFT for 140-µF waveforms (4.9±2.5 versus 6.4±2.4 J, P<.05).

Conclusions The optimal phase-duration ratio is <=1 for conventional capacitors and >1 for small capacitors. This supports the predictions of the charge-burping theory.


Key Words: defibrillation • charge burping • waves


*    Introduction
up arrowTop
 up arrowAbstract
 *Introduction
down arrowMethods
 down arrowResults
 down arrowDiscussion
 down arrowReferences
 
Biphasic truncated exponential waveforms have replaced monophasic waveforms in implantable cardioverter-defibrillators (ICDs) because they can reduce the defibrillation threshold (DFT).1 2 3 4 5 However, the mechanism(s) by which biphasic waveforms lower the DFT are incompletely understood,6 7 and no comprehensive model of biphasic defibrillation has gained widespread acceptance. Recently, a quantitative "charge-burping" model has been proposed.8 The model assumes that the first phase of the biphasic waveform is the optimal monophasic waveform and that the optimal second phase prevents refibrillation by removing or "burping" the charge deposited on myocardial cells by phase 1. This model predicts that the optimal ratio of the duration of phase 2 to the duration of phase 1 (phase-duration ratio) depends on the relationship between the time constant of the defibrillation system ({tau}s) and the time constant of myocardial cell membranes ({tau}m): The optimal phase-duration ratio should be <1 when {tau}s >={tau}m, but it should be >1 when {tau}s<{tau}m. Because {tau}s is the product of the capacitance of the ICD output circuit and the resistance of the defibrillation pathway, this model predicts that the optimal phase-duration ratio depends directly on the ICD capacitance.

Empirical studies have reported that the improved efficacy of biphasic waveforms over monophasic waveforms requires that the phase-duration ratio be <=1.1 9 10 11 These studies were performed with 150- to 175-µF capacitors, similar to those in approved ICDs. Their results are consistent with the predictions of the charge-burping theory, because the corresponding values of {tau}s (>=6 ms) exceed the highest estimates for {tau}m.8 12 13 However, recent theoretical,8 13 14 animal,15 and human studies16 17 have reported advantages for small-capacitor biphasic waveforms. The optimal phase-duration ratio for small-capacitor waveforms with {tau}s<{tau}m is unknown.

The goal of this study was to test the novel prediction of the charge-burping theory that the optimal phase-duration ratio should be >1 when {tau}s<{tau}m. To test this hypothesis, we determined DFTs for very-small-capacitor 40-µF waveforms in a canine model of transvenous defibrillation. Conventional 140-µF-capacitor waveforms were used as a control.


*    Methods
up arrowTop
 up arrowAbstract
 up arrowIntroduction
 *Methods
down arrowResults
 down arrowDiscussion
 down arrowReferences
 
Surgical Preparations and Monitoring
Eight mongrel dogs (weight, 23±3 kg) were anesthetized with a 25- to 35-mg/kg bolus of pentobarbital,18 19 and anesthesia was maintained by a constant infusion at a rate of {approx}0.05 mg·kg-1·min-1. Each dog was intubated and ventilated with room air by a respirator (Harvard Apparatus). Surface ECG lead II and femoral arterial pressure were monitored continuously. Femoral arterial samples were analyzed every 30 to 60 minutes for pH, PO2, PCO2, base excess, and bicarbonate concentrations. The ventilator was adjusted to correct metabolic abnormalities. Temperature was monitored with a rectal probe, and a heating lamp and blanket were used to maintain a temperature of 36°C to 37°C. A bipolar pacing electrode was inserted through the right femoral vein into the right ventricle for pacing.

Electrode Configuration
The electrode configuration for defibrillation was selected to approximate the shock vectors and pathway resistances used with pectorally implanted transvenous ICDs. Under fluoroscopic guidance, a transvenous electrode with two defibrillating coils (model 4007, Angeion) was inserted through the right jugular vein so that the tip of the 5-cm-long distal electrode lay at the right ventricular apex and the 6-cm-long proximal electrode was in the high superior vena cava. The titanium electrode shell of an ICD (active can, model 2000, Angeion) was positioned subcutaneously on the left thorax over the point of maximal cardiac impulse. The distal electrode of the defibrillating electrodes served as the cathode for the first phase of the biphasic defibrillation waveforms. The can was linked to the proximal defibrillating coil to serve as the anode.

Defibrillation Waveforms
Fibrillation and defibrillation pulses were delivered by use of a research defibrillation system (ARD-9000, Angeion) composed of an IBM-compatible personal computer and a high-voltage linear amplifier. Experimental defibrillation waveforms were programmed into computer software (MatLab 3.5, MathWorks Inc), delivered by the linear amplifier, and measured with voltage and current meters calibrated for defibrillation shock pulses. These measured shock signals were digitized at a sampling rate of 10 kHz and stored in the computer. The waveform generator used the sampled shock pulse data and the method of continuous load adjustment to model capacitive discharge.20

The eight biphasic waveforms selected for this investigation are shown in Fig 1Down. They were distinguished by two variables: capacitance and phase-duration ratio. Capacitance was selected to be either 40 or 140 µF. Phase-duration ratios were selected to be 0.5, 1, 2, and 3. All waveform parameters were fixed to simulate a single-capacitor discharge: The capacitances for phases 1 and 2 were equal and the leading-edge voltage of phase 2 equaled the trailing-edge voltage of phase 1. There was a 0.2-ms time delay between phases.



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  		Figure 1. Defibrillation waveforms and membrane response curves. Top, Conventional-capacitor 140-µF waveforms corresponding to a defibrillation-system time constant ({tau}s) of 7 ms, assuming a pathway resistance of 50 {Omega}. Bottom, Very-small-capacitor 40-µF waveforms ({tau}s=2 ms). Abscissa shows time in ms. Ordinate along left axis shows applied shock voltage corresponding to solid line in each panel. Arrows indicate truncation of phase 2 ({phi}2) at phase-duration ratios ({phi}2/{phi}1) of 2 and 3. The leading-edge voltages and phase durations are typical of waveforms in this study. Compared with the conventional 140-µF waveforms, the 40-µF waveforms have a higher leading-edge voltage, steeper voltage decay, and shorter phase durations. Ordinate along right axis shows membrane-response voltage relative to zero at onset of phase 1. This corresponds to dotted lines in each panel, which represent predicted cell-membrane responses to applied shock voltages for cell-membrane time constants ({tau}m) of 3.0 and 4.2 ms. Cell response curves were computed as described by Kroll.8 See text for details.

The two capacitance values of 40 and 140 µF were selected to result in values of {tau}s above and below the value of {tau}m. Assuming a pathway resistance of 50 {Omega}, the 140-µF value results in {tau}s of 7 ms and the 40-µF value results in {tau}s of 2 ms. Direct measurement of membrane responses indicates that {tau}m depends on both field strength and shock polarity.12 Thus, a single value may be an oversimplification. Nevertheless, estimates for {tau}m have averaged {approx}3 ms.8 12 13 Thus, although the value of {tau}m is unknown, it is likely that {tau}s<{tau}m for the 40-µF waveform and {tau}s>{tau}m for the 140-µF waveform. Fig 2Down, modified from Kroll,8 shows the optimal phase-duration ratios predicted by the charge-burping theory as a function of {tau}s.



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  		Figure 2. Predicted optimal phase durations and phase-duration ratio for biphasic defibrillation waveforms, modified from Kroll.8 Defibrillation-system time constant ({tau}s) is plotted on abscissa (lower border). Capacitance corresponding to a pathway resistance of 50 {Omega} is shown along upper border. Ordinate shows optimal durations for each phase in solid lines (left axis) and optimal phase-duration ratio as a dotted line (right axis). Total waveform duration is the sum of the two solid lines plus the 0.2 ms separating the two phases. This figure is based on a chronaxie of 3 ms and a cell {tau}m of 3 ms. However, chronaxie and {tau}m are not necessarily equal. Value of {tau}m is indicated by arrow on abscissa (lower border). Optimal durations of phase 1 ({phi}1) and phase 2 ({phi}2) are shown by solid lines and their ratio by heavy dotted line. Optimal duration of phase 1 increases linearly with a slope of 0.8; optimal duration of phase 2 decreases rapidly toward an asymptote. Curves cross when their durations are equal at {tau}s={tau}m. This corresponds to an optimal phase-duration ratio of 1, as indicated by light dotted line. For {tau}s>{tau}m, predicted optimal phase-duration ratio is <1; for {tau}s<{tau}m, predicted optimal phase-duration ratio is >1. Conventional-capacitor 140-µF waveform has a time constant of {tau}s=7 ms, and very-small-capacitor 40-µF waveform has a time constant of {tau}s=2 ms. Optimal durations for 140-µF waveform are predicted to be 5.8 ms for phase 1 and 2.7 ms for phase 2 (phase-duration ratio=0.46). Optimal durations for 40-µF waveform are predicted to be 2.9 ms for phase 1 and 5.8 ms for phase 2 (phase-duration ratio=2.0).

For 140-µF waveforms, the duration of phase 1 was determined by a tilt of 60% to correspond with present clinical practice.21 For 40-µF waveforms, no clinical or experimental data were available to determine the duration of phase 1. We selected the optimal value predicted on the basis of a model of monophasic defibrillation that assumes a hyperbolic strength-duration relation for phase 1.14 22 This duration is 0.58({tau}s+dc), where dc is the heart's chronaxie. Estimates for the defibrillation chronaxie have varied from 2 to 4 ms.22 The pacing chronaxie depends on various factors, including electrode configuration,23 and the defibrillation may show similar dependence. We determined a value of 2.9 ms in a pilot experiment using the same electrode configuration as in the present study. For simplicity, we optimized the 40-µF waveform for a chronaxie of 3 ms.

The waveform generator set the duration of phase 2 by applying the programmed phase-duration ratio to the measured duration of phase 1.

DFT Testing
Ventricular fibrillation was induced by delivery of a 1-second, 10-V alternating square wave through the defibrillation electrodes. Defibrillation test shocks were delivered after an additional 9 seconds of fibrillation. If the test shock failed, a rescue shock was delivered with a 20- to 40-J monophasic square wave. At least 3 minutes elapsed between fibrillation episodes to allow blood pressure and heart rate to return to normal. The eight biphasic waveforms were tested in each of the eight dogs in random order. For each waveform, all test shocks were given sequentially.

DFT testing was performed by the Bayesian, up-down method of Malkin et al.24 25 26 The shock strength at the 50% effective defibrillation dose was defined as the DFT. This method differs from a conventional up-down method27 in three ways. The conventional method selects the strength of a defibrillation test shock on the basis of the outcome of the immediately preceding test shock, whereas the Bayesian method selects the shock strength on the basis of the outcome of all previous test shocks. In the conventional method, shock strength is determined by increasing or decreasing the preceding shock strength by a fixed step. In the Bayesian method, shock strength is determined by increasing or decreasing the previous shock strength by a predetermined sequence of steps. In this study, we used sequential steps of 80, 60, and 50 V.24 25 In the conventional method, the number of reversals of response is fixed and the number of fibrillation-defibrillation episodes is variable. In the Bayesian method, the number of fibrillation-defibrillation episodes is fixed. The four-episode series selected for these experiments permitted determination of the DFT with a root-mean-square (RMS) error of {approx}11%.25 26 Each series of four episodes results in an ordered sequence of successes and/or failures. If a prior-probability function24 25 26 is known or assumed, each possible sequence corresponds to an estimate for the DFT with a known RMS error. The numerical method for calculating this estimate takes into account the number of both successes and failures and the order in which they occurred.24 25 26 These results can be summarized in a look-up table that was used for this study.24 The assumed prior-probability function for 140-µF waveforms was trapezoidal in shape, increasing from 150 to 200 V, constant from 200 to 700 V, and decreasing from 700 to 750 V.24 25 The prior-probability function for 40-µF waveforms was shifted by 200 V so that it was flat between 400 and 900 V. The initial leading-edge voltage was set to 300 V for 140-µF waveforms and 500 V for 40-µF waveforms. The RMS error may be greater if all shocks are successful or unsuccessful. Whenever this occurred, the initial voltage was decreased or increased by 100 V and the four-shock sequence was repeated.

Data Analysis
Resistance was determined by a point-by-point division of the measured-voltage waveform by the measured-current waveform. Computed values included the mean and leading-edge voltage, current, and resistance values for each phase, stored energy,28 and phase durations. The total waveform duration was the sum of the durations for each phase plus the 0.2-ms delay between phases.

Statistical Analysis
Data are presented as mean±SD. In each animal, the best 40-µF waveform (lowest DFT) was compared with the best 140-µF waveform by the paired t test. The effect of phase-duration ratio and capacitance on stored-energy DFT was assessed by two-factor, repeated measures ANOVA with phase-duration ratio and capacitance as factors. The significance of the interaction term was used to assess the presence or absence of a different effect of phase-duration ratio on DFT for the two capacitance values. We also analyzed the effect of phase-duration ratio on stored-energy DFT separately for each of the two capacitance values using one-factor, repeated measures ANOVA with phase-duration ratio as the factor. To further test the hypothesis that the optimal phase-duration ratio depends on capacitance, we compared the DFT for the two phase-duration ratios <=1 (ratios of 0.5 and 1) with the DFTs for the two phase-duration ratios >1 (ratios of 2 and 3) for each value of capacitance. This prospectively selected comparison was performed by the method of contrasts applied to the one-factor analyses with equal weight for each phase-duration ratio. All calculations were performed with SuperANOVA 1.11 for the Macintosh (Abacus Concepts). A value of P<.05 was considered statistically significant, except for one-factor ANOVA measurements, for which a value of P<.025 was required because two measurements were performed.


*    Results
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 up arrowIntroduction
 up arrowMethods
 *Results
down arrowDiscussion
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Defibrillation Thresholds
Table 1Down shows mean DFT data for all waveforms tested. For the group as a whole, pathway resistance was {approx}50 {Omega}, resulting in a {tau}s of {approx}2 ms for 40-µF waveforms and {approx}7 ms for 140-µF waveforms. The narrow range of pathway resistances resulted in minimal differences in phase durations among the animals in this study. Table 2Down shows individual stored-energy DFTs for all eight waveforms in all eight dogs.


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  		Table 1. Waveform Parameters and Defibrillation Thresholds


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  		Table 2. Individual Stored-Energy Defibrillation Thresholds for All 140-µF and 40-µF Waveforms Tested in All Eight Dogs

Interactive Effect of Capacitance and Phase-Duration Ratio on DFT
Two-factor ANOVA applied to the entire group demonstrated an overall significant difference in stored-energy DFTs between 40-µF waveforms and 140-µF waveforms (F=24.1, P=.002) but not among the four phase-duration ratios (F=2.1, P=.13). However, there was a significant interaction between the effect of capacitance and phase-duration ratio on DFT (F=10.5, P=.0002). One-factor ANOVA showed a significant effect of phase-duration ratio on DFT for both 40-µF waveforms (F=5.1, P=.008) and 140-µF waveforms (F=6.1, P=.004). For 40-µF waveforms, the DFT was lower for ratios >1 (P=.0008). For 140-µF waveforms, the DFT was lower for ratios <=1 (P=.0003).

For 40-µF waveforms, the DFT was lowest for a phase-duration ratio of 2 in three dogs and a ratio of 3 in two dogs; it was equal for ratios of 2 and 3 in three dogs. For 140-µF waveforms, the DFT was lowest for a ratio of 0.5 in four dogs and a ratio of 1 in one dog; it was equal for phase-duration ratios of 0.5 and 1 in three dogs.

Fig 3Down (left) illustrates the reverse effects of phase-duration ratio on stored-energy DFT for 40- and 140-µF waveforms. We did not perform pairwise comparisons of DFTs at each phase-duration ratio because of the statistical limitations of multiple comparisons. However, inspection of the data shows that the greatest effect of phase-duration ratio on DFT was between ratios of 1 and 2. There was substantially less effect between ratios of 0.5 and 1 and between ratios of 2 and 3. For 140-µF waveforms, DFTs for phase-duration ratios >1 exceeded DFTs for phase-duration ratios <=1 by a mean of 71% (5.0±4.2 J). For 40-µF waveforms, the mean effect in the reverse direction was 30% (1.7±1.0 J). The magnitude of the effect of phase-duration ratio on DFT was greater for 140- than for 40-µF waveforms (P=.06).



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  		Figure 3. Effect of phase-duration ratio and total waveform duration on defibrillation threshold (DFT). In each panel, stored-energy DFT is plotted on ordinate. Error bars indicate SEM. Left, Phase-duration ratio is plotted on abscissa. For 40-µF waveforms, DFT is lower for phase-duration ratios >1 (P=.0008). For 140-µF waveforms, DFT is lower for phase-duration ratios <=1 (P=.0003). Lowest DFTs for 40-µF waveforms are lower than lowest DFTs for 140-µF waveforms. Right, Mean total waveform duration is plotted on abscissa. Total waveform duration is similar for 140-µF waveforms and 40-µF waveforms with lowest DFTs. The 140-µF waveforms with longest total durations have highest DFTs.

Effect of Capacitance on Lowest DFT
Overall, the lowest DFT for 40-µF waveforms was lower than the lowest DFT for 140-µF waveforms (4.9±2.5 versus 6.4±2.4 J, P<.05). The lowest DFT for 40-µF waveforms never exceeded the lowest DFT for 140-µF waveforms by more than 0.5 J, regardless of the precise ratio associated with the lowest DFT.

Effect of Total Waveform Duration
Table 1Up and the right panel in Fig 3Up show DFT as a function of total waveform duration. The total durations of waveforms with the lowest DFTs for 40-µF capacitors (phase-duration ratios of 2 and 3) and 140-µF capacitors (phase-duration ratios of 0.5 and 1) overlap considerably. The 140-µF waveforms with the longest total duration have the highest DFTs.


*    Discussion
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 up arrowAbstract
 up arrowIntroduction
 up arrowMethods
 up arrowResults
 *Discussion
down arrowReferences
 
The principal finding of this prospective study is that optimal phase-duration ratio depends on the value of {tau}s. It is <=1 for 140-µF waveforms ({tau}s>{tau}m) but >1 for 40-µF waveforms ({tau}s<{tau}m). This finding was predicted by the charge-burping theory. A second finding is that the stored-energy DFT was 23% lower for the best 40-µF waveform in comparison with the best 140-µF waveform.

Optimal Phase-Duration Ratio: Prior Studies
Four previous empirical studies performed with 150- to 175-µF capacitors ({tau}s=6 to 8 ms) have reported that biphasic waveforms are most efficient when the phase-duration ratio is <1.1 9 10 11 The results of the present study regarding 140-µF waveforms ({tau}s=7 ms) are consistent with these reports. However, we found that the effect of phase-duration ratio on DFT differs markedly for very-small-capacitor 40-µF waveforms ({tau}s=2 ms).

Models of Defibrillation Waveforms
A capacitive-discharge, biphasic waveform is described by seven parameters: the leading-edge voltage of each phase, {tau}s of each phase, the duration of each phase, and the temporal separation between the two phases. Because varying all parameters in a single experiment is impractical, an accurate quantitative model would facilitate optimizing waveforms over a broad range of capacitances and defibrillation pathways. Recently, two quantitative models of single-capacitor, biphasic defibrillation have been proposed.8 13 Each assumes that the optimal first phase is the optimal monophasic pulse and that the optimal second phase prevents refibrillation by removing the charge deposited on myocardial cells by phase 1. These models differ in the method used to optimize phase 1. However, both predict that the optimal duration of phase 1 depends on the relationship between a biological cardiac time constant ({tau}m13 or chronaxie8 ) and {tau}s. Both also apply Blair's model of the myocardial cell29 30 to derive an expression for the time-varying voltage of the cell during phase 2. Kroll8 extrapolated this analysis to predict that the optimal phase-duration ratio depends on the relationship between {tau}s and {tau}m, as shown in Fig 2Up.

Comparison of Experimental Findings and Model Predictions
The dotted lines in Fig 1Up represent the predicted cell-membrane responses8 to the applied shock voltages. The cell-response curves depend on the value of {tau}s, which is known, and the value of {tau}m, which is unknown. Direct measurement of {tau}m for field strengths of <=6 V/cm in guinea pig papillary muscle has yielded values of 2.1 to 6.0 ms.12 Indirect measurement from defibrillation strength-duration curves in various animals has yielded values of 2.2 to 5.8 ms.9 13 31 32 33 Fig 1Up shows curves for representative values of 3.0 and 4.2 ms. The value of 3.0 ms was chosen because previous theoretical analyses have selected 2.8 ms13 or 3.0 ms.8 The value of 4.2 ms was calculated34 from strength-duration data obtained in a pilot study for the present experiment.

Fig 1Up illustrates the differences in cell responses to the voltage fields of the 140- and 40-µF waveforms predicted by the charge-burping theory. Phase 1 of the 140-µF waveform produces a weaker but longer-lasting field than phase 1 of the 40-µF waveform. The cell response to the applied 140-µF waveform is slower and continues longer. For phase 2, the leading-edge voltage is a greater fraction of the phase-1 leading-edge voltage for the 140-µF waveform, resulting in more rapid charge-burping for this waveform. In addition, the phase-2 negative applied voltage exceeds a minimal absolute value for a longer time for the 140-µF waveform, resulting in a persistent negative residual membrane voltage for high phase-duration ratios. The cell-response curves appear to be underdamped. In contrast, because the negative applied voltage decays rapidly for the 40-µF waveform, the cell response does not decrease below the relative zero value. The cell-response curves appear to be overdamped.

The charge-burping theory successfully explains our finding for 40-µF waveforms. Phase-duration ratios of 0.5 and 1 fail to return the cell-membrane voltage to the preshock level and thereby leave substantial residual charge on the membrane. In contrast, there is a broad range of phase-duration ratios between 2 and 3 that provide comparable and near-complete charge-burping for either value of {tau}m.

For 140-µF waveforms, the predictions of the charge-burping theory depend strongly on the unknown value of {tau}m. For {tau}m of 3.0 and 4.2 ms, the predicted optimal phase-duration ratios are 0.5 and 0.75, respectively. For {tau}m of 4.2 ms, a ratio of 0.5 provides substantial but incomplete charge burping, whereas a ratio of 1 provides slight overburping. Because the charge-burping theory predicts that the beneficial effect of phase 2 is related to the absolute value of the residual membrane voltage,8 DFTs are predicted to be similar for phase-duration ratios of 0.5 and 1 but lower for a ratio of 0.75. Thus, the charge-burping theory predicts that, for near-optimal waveforms, residual membrane voltages and DFTs are more sensitive to potential clinical variability in {tau}m for 140-µF waveforms than for 40-µF waveforms. In the present study, the essentially equal group-mean DFTs for phase-duration ratios of 0.5 and 1 are consistent with the predictions for {tau}m of 4.2 ms, but we do not know whether a phase-duration ratio of 0.75 would have resulted in a lower group-mean DFT.

Conventional-capacitor waveforms with high phase-duration ratios had the highest DFTs in the present study and have had higher DFTs than monophasic waveforms in previous studies.9 11 This indicates that residual membrane voltage is not the sole determinant of the performance of a biphasic waveform. Fig 1Up (top) shows that the absolute value of the negative residual voltage is greatest for a phase-duration ratio near 1.0 for {tau}m of 3.0 ms and 1.5 for {tau}m of 4.2 ms. The absolute value of the negative residual voltage decreases for higher ratios. Although a 6-ms value of {tau}m would result in a more negative residual voltage for a phase-duration ratio of 2 than for a ratio of 1, the positive residual voltage for a ratio of 0.5 would become substantial. Time-dependent factors that influence how the cell-membrane voltage affects the probability of refibrillation may be important for very long second phases: Gradients in the shock field may result in persistent gradients in the dynamic cell-membrane voltage. This may decrease synchronization of repolarization35 36 and increase vulnerability to refibrillation.7

Specific predictions of the charge-burping theory have been validated in two previous reports. Walcott et al13 prospectively evaluated the optimal durations of biphasic waveforms with equal phase durations and varying {tau}s. Kroll8 retrospectively correlated measured DFTs with predicted residual membrane voltage for 150- to 175-µF waveforms with phase-duration ratios <=1. The predictions of the charge-burping theory for waveforms with phase-duration ratios >1 have not been reported previously. Our data indicate that this model explains the response to these small-capacitor waveforms regardless of the phase-duration ratio.

Fig 1Up also shows that the predicted total waveform duration is similar for the best 140-µF waveforms and best 40-µF waveforms. Our results support this prediction, which is a consequence of the more general prediction shown in Fig 2Up. They extend previous observations that truncation is critical for conventional-capacitor waveforms37 but not for small-capacitor monophasic waveforms.32

Optimal Capacitance
Theoretical analysis using time constants derived from canine data indicates that optimal capacitance is in the range of 32 to 70 µF.8 13 14 Studies in experimental animals15 and humans16 17 have reported that 60- to 85-µF waveforms had lower DFTs than conventional 120- to 140-µF waveforms. In the only previous (canine) study of biphasic defibrillation using very small capacitors, Walcott et al13 reported DFTs for 37.5-µF capacitors ({tau}s=1.5 ms) and 150-µF capacitors ({tau}s=6.0 ms) for waveforms with equal phase durations. Calculations based on their reported voltage DFTs indicate that the best 37.5-µF waveform reduced the mean stored-energy DFT by 33% in comparison with the best 150-µF waveform (7.6 versus 11.4 J). However, the results might have differed if the phase durations had been optimized for each capacitance. In the present study, an optimized 40-µF waveform ({tau}s=2 ms) lowered the DFT by 23% compared with an optimized 140-µF waveform ({tau}s=7 ms).

Study Limitations
The 140-µF waveform was optimized by use of experimental data rather than theoretical predictions. The predicted effect of a suboptimal duration of phase 1 on DFT may be calculated for Irnich's monophasic model14 by use of his Equation 5 and for Kroll's monophasic model22 by extrapolation of a previously reported analysis.17 Assuming a chronaxie of 3 ms, Irnich predicts an increase in DFT of 15% to 25%, whereas Kroll predicts an increase of {approx}1%. The strength-duration data of Chapman et al21 and limited human data38 39 show a minimal effect, as predicted by Kroll. Whatever the magnitude of this effect, the best duration of phase 2 for a suboptimal duration of phase 1 does not alter the general prediction of the charge-burping theory about the effect of {tau}s on optimal phase-duration ratio. The duration of phase 2 required to burp the residual membrane voltage at the end of a suboptimal phase 1 may be calculated as described by Kroll,8 except that the initial condition for phase 2 becomes the membrane voltage at the end of a suboptimal phase 1. For the experimental 140-µF waveform with a phase 1 duration of 6.3 ms, the best predicted phase-duration ratio is 0.44 for {tau}m of 3 ms and 0.59 for {tau}m of 4 ms. In contrast, for the experimental 40-µF waveform with a phase 1 duration of 2.8 ms, the best predicted phase-duration ratio is 1.94 for {tau}m of 3 ms; for {tau}m of 4 ms, the best predicted phase-duration ratio exceeds 10, but a phase-duration ratio of 3 would return the membrane to within 4% of its baseline voltage. Thus, at least one of the experimental waveforms in this study should have provided substantial charge burping for each capacitance, even if the duration of phase 1 was not optimal. However, our results regarding optimal phase-duration ratios might not apply if the duration of phase 1 is very short or very long.40 41

Although Kroll's formulation of the charge-burping theory does not require a specific relationship between chronaxie and {tau}m, theoretical analysis predicts that such a relationship should exist and that it should depend on the shape of the defibrillation waveform.34 This prediction has not been confirmed experimentally.

Clinical Significance
Our findings demonstrate the importance of optimizing the phase-duration ratio for the {tau}s of the specific defibrillation system used.17 In an ICD implant, a clinician must successfully combine an ICD pulse generator with a known capacitance and a defibrillation pathway with an unknown resistance. A pulse generator with a single capacitance is expected to perform well over a wide range of {tau}s.13 17 Although in the present study we varied {tau}s by altering capacitance, the same considerations regarding optimal phase-duration ratios should apply if {tau}s is varied by altering resistance.8 13 Programmable phase durations or automatic optimization of phase durations on the basis of the measured resistance may permit the pulse generator to deliver optimal phase durations for the resultant {tau}s.

Improved defibrillation by use of small capacitors is of potential clinical importance because it may permit development of smaller ICDs and thereby facilitate pectoral implantation and improve patient acceptance. In addition to reducing capacitor size, efficient very-small-capacitor waveforms may permit use of smaller batteries. However, we do not know how much reduction in capacitor size is possible while a sufficient defibrillation safety margin is maintained. Furthermore, high-voltage monophasic shocks have been reported to cause postshock conduction block42 and transient myocardial depression.43 Although biphasic shocks produce less conduction block44 and less dysfunction45 than monophasic shocks and shorter pulses produce less dysfunction than longer pulses,45 the safety of very-small-capacitor biphasic shocks is unknown.


*    Acknowledgments
 
This study was supported in part by American Heart Association Greater Los Angeles Affiliate Grant-in-Aid 1085-GI1 and by a grant from the PM Foundation to Dr Swerdlow. The authors wish to thank Avile McCullum for his technical assistance; Angeion Inc for supplying the waveform generator and electrodes; Robert Malkin, PhD, for his assistance with calculation of defibrillation thresholds; and Peng-Sheng Chen, MD, for his critical review of this manuscript.


*    Footnotes
 
Reprint requests to Charles D. Swerdlow, MD, Cedars-Sinai Medical Towers, 8635 W Third St, Suite 975 W, Los Angeles, CA 90048. E-mail swerdlow@ucla.edu.

Received February 21, 1996; revision received April 30, 1996; accepted May 1, 1996.


*    References
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 up arrowIntroduction
 up arrowMethods
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 *References
 

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