ChargeBurping Theory Correctly Predicts Optimal Ratios of Phase Duration for Biphasic Defibrillation Waveforms
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Abstract
Background For biphasic waveforms, it is accepted that the ratio of the duration of phase 2 to the duration of phase 1 (phaseduration ratio) should be ≤1. The chargeburping 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 phaseduration ratio should be <1 when the time constant of the defibrillation system (τ_{s}) exceeds the time constant of the cell membrane (τ_{m}) but >1 when τ_{s}<τ_{m}. This study tested the hypothesis that the optimal phaseduration ratio depends on τ_{s} (the product of the defibrillator capacitance and pathway resistance).
Methods and Results In a canine model of transvenous defibrillation (n=8), we determined storedenergy defibrillation thresholds (DFTs) for biphasic waveforms from conventional capacitors (140 μF, τ_{s}=7.1±0.8 ms) and very small capacitors (40 μF, τ_{s}=2.0±0.2 ms). Each capacitance was tested with phaseduration ratios of 0.5, 1, 2, and 3. The duration of phase 1 approximated the optimal monophasic waveform, 6.3±0.7 ms for 140μF waveforms and 2.8±0.2 ms for 40μF waveforms. For 140μF waveforms, the DFT was lower for phaseduration ratios ≤1 than for phaseduration ratios >1 (P=.0003). The reverse was true for 40μF capacitors (P=.0008). There was a significant interaction between the effects of capacitance and phaseduration ratio on DFT (P=.0002). The lowest DFT for 40μF waveforms was less than the lowest DFT for 140μF waveforms (4.9±2.5 versus 6.4±2.4 J, P<.05).
Conclusions The optimal phaseduration ratio is ≤1 for conventional capacitors and >1 for small capacitors. This supports the predictions of the chargeburping theory.
Biphasic truncated exponential waveforms have replaced monophasic waveforms in implantable cardioverterdefibrillators (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 “chargeburping” 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 (phaseduration ratio) depends on the relationship between the time constant of the defibrillation system (τ_{s}) and the time constant of myocardial cell membranes (τ_{m}): The optimal phaseduration ratio should be <1 when τ_{s} ≥τ_{m}, but it should be >1 when τ_{s}<τ_{m}. Because τ_{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 phaseduration ratio depends directly on the ICD capacitance.
Empirical studies have reported that the improved efficacy of biphasic waveforms over monophasic waveforms requires that the phaseduration ratio be ≤1.^{1} ^{9} ^{10} ^{11} These studies were performed with 150 to 175μF capacitors, similar to those in approved ICDs. Their results are consistent with the predictions of the chargeburping theory, because the corresponding values of τ_{s} (≥6 ms) exceed the highest estimates for τ_{m}.^{8} ^{12} ^{13} However, recent theoretical,^{8} ^{13} ^{14} animal,^{15} and human studies^{16} ^{17} have reported advantages for smallcapacitor biphasic waveforms. The optimal phaseduration ratio for smallcapacitor waveforms with τ_{s}<τ_{m} is unknown.
The goal of this study was to test the novel prediction of the chargeburping theory that the optimal phaseduration ratio should be >1 when τ_{s}<τ_{m}. To test this hypothesis, we determined DFTs for verysmallcapacitor 40μF waveforms in a canine model of transvenous defibrillation. Conventional 140μFcapacitor waveforms were used as a control.
Methods
Surgical Preparations and Monitoring
Eight mongrel dogs (weight, 23±3 kg) were anesthetized with a 25 to 35mg/kg bolus of pentobarbital,^{18} ^{19} and anesthesia was maintained by a constant infusion at a rate of ≈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, Po_{2}, Pco_{2}, 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 5cmlong distal electrode lay at the right ventricular apex and the 6cmlong 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 (ARD9000, Angeion) composed of an IBMcompatible personal computer and a highvoltage 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 1⇓. They were distinguished by two variables: capacitance and phaseduration ratio. Capacitance was selected to be either 40 or 140 μF. Phaseduration ratios were selected to be 0.5, 1, 2, and 3. All waveform parameters were fixed to simulate a singlecapacitor discharge: The capacitances for phases 1 and 2 were equal and the leadingedge voltage of phase 2 equaled the trailingedge voltage of phase 1. There was a 0.2ms time delay between phases.
The two capacitance values of 40 and 140 μF were selected to result in values of τ_{s} above and below the value of τ_{m}. Assuming a pathway resistance of 50 Ω, the 140μF value results in τ_{s} of 7 ms and the 40μF value results in τ_{s} of 2 ms. Direct measurement of membrane responses indicates that τ_{m} depends on both field strength and shock polarity.^{12} Thus, a single value may be an oversimplification. Nevertheless, estimates for τ_{m} have averaged ≈3 ms.^{8} ^{12} ^{13} Thus, although the value of τ_{m} is unknown, it is likely that τ_{s}<τ_{m} for the 40μF waveform and τ_{s}>τ_{m} for the 140μF waveform. Fig 2⇓, modified from Kroll,^{8} shows the optimal phaseduration ratios predicted by the chargeburping theory as a function of τ_{s}.
For 140μF waveforms, the duration of phase 1 was determined by a tilt of 60% to correspond with present clinical practice.^{21} For 40μF 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 strengthduration relation for phase 1.^{14} ^{22} This duration is 0.58(τ_{s}+d_{c}), where d_{c} 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 40μF waveform for a chronaxie of 3 ms.
The waveform generator set the duration of phase 2 by applying the programmed phaseduration ratio to the measured duration of phase 1.
DFT Testing
Ventricular fibrillation was induced by delivery of a 1second, 10V 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 40J 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, updown 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 updown method^{27} 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 fibrillationdefibrillation episodes is variable. In the Bayesian method, the number of fibrillationdefibrillation episodes is fixed. The fourepisode series selected for these experiments permitted determination of the DFT with a rootmeansquare (RMS) error of ≈11%.^{25} ^{26} Each series of four episodes results in an ordered sequence of successes and/or failures. If a priorprobability function^{24} ^{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 lookup table that was used for this study.^{24} The assumed priorprobability function for 140μF 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 priorprobability function for 40μF waveforms was shifted by 200 V so that it was flat between 400 and 900 V. The initial leadingedge voltage was set to 300 V for 140μF waveforms and 500 V for 40μF 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 fourshock sequence was repeated.
Data Analysis
Resistance was determined by a pointbypoint division of the measuredvoltage waveform by the measuredcurrent waveform. Computed values included the mean and leadingedge 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 0.2ms delay between phases.
Statistical Analysis
Data are presented as mean±SD. In each animal, the best 40μF waveform (lowest DFT) was compared with the best 140μF waveform by the paired t test. The effect of phaseduration ratio and capacitance on storedenergy DFT was assessed by twofactor, repeated measures ANOVA with phaseduration ratio and capacitance as factors. The significance of the interaction term was used to assess the presence or absence of a different effect of phaseduration ratio on DFT for the two capacitance values. We also analyzed the effect of phaseduration ratio on storedenergy DFT separately for each of the two capacitance values using onefactor, repeated measures ANOVA with phaseduration ratio as the factor. To further test the hypothesis that the optimal phaseduration ratio depends on capacitance, we compared the DFT for the two phaseduration ratios ≤1 (ratios of 0.5 and 1) with the DFTs for the two phaseduration 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 onefactor analyses with equal weight for each phaseduration 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 onefactor ANOVA measurements, for which a value of P<.025 was required because two measurements were performed.
Results
Defibrillation Thresholds
Table 1⇓ shows mean DFT data for all waveforms tested. For the group as a whole, pathway resistance was ≈50 Ω, resulting in a τ_{s} of ≈2 ms for 40μF waveforms and ≈7 ms for 140μF waveforms. The narrow range of pathway resistances resulted in minimal differences in phase durations among the animals in this study. Table 2⇓ shows individual storedenergy DFTs for all eight waveforms in all eight dogs.
Interactive Effect of Capacitance and PhaseDuration Ratio on DFT
Twofactor ANOVA applied to the entire group demonstrated an overall significant difference in storedenergy DFTs between 40μF waveforms and 140μF waveforms (F=24.1, P=.002) but not among the four phaseduration ratios (F=2.1, P=.13). However, there was a significant interaction between the effect of capacitance and phaseduration ratio on DFT (F=10.5, P=.0002). Onefactor ANOVA showed a significant effect of phaseduration ratio on DFT for both 40μF waveforms (F=5.1, P=.008) and 140μF waveforms (F=6.1, P=.004). For 40μF waveforms, the DFT was lower for ratios >1 (P=.0008). For 140μF waveforms, the DFT was lower for ratios ≤1 (P=.0003).
For 40μF waveforms, the DFT was lowest for a phaseduration 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 140μF 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 phaseduration ratios of 0.5 and 1 in three dogs.
Fig 3⇓ (left) illustrates the reverse effects of phaseduration ratio on storedenergy DFT for 40 and 140μF waveforms. We did not perform pairwise comparisons of DFTs at each phaseduration ratio because of the statistical limitations of multiple comparisons. However, inspection of the data shows that the greatest effect of phaseduration 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 140μF waveforms, DFTs for phaseduration ratios >1 exceeded DFTs for phaseduration ratios ≤1 by a mean of 71% (5.0±4.2 J). For 40μF waveforms, the mean effect in the reverse direction was 30% (1.7±1.0 J). The magnitude of the effect of phaseduration ratio on DFT was greater for 140 than for 40μF waveforms (P=.06).
Effect of Capacitance on Lowest DFT
Overall, the lowest DFT for 40μF waveforms was lower than the lowest DFT for 140μF waveforms (4.9±2.5 versus 6.4±2.4 J, P<.05). The lowest DFT for 40μF waveforms never exceeded the lowest DFT for 140μF waveforms by more than 0.5 J, regardless of the precise ratio associated with the lowest DFT.
Effect of Total Waveform Duration
Table 1⇑ and the right panel in Fig 3⇑ show DFT as a function of total waveform duration. The total durations of waveforms with the lowest DFTs for 40μF capacitors (phaseduration ratios of 2 and 3) and 140μF capacitors (phaseduration ratios of 0.5 and 1) overlap considerably. The 140μF waveforms with the longest total duration have the highest DFTs.
Discussion
The principal finding of this prospective study is that optimal phaseduration ratio depends on the value of τ_{s}. It is ≤1 for 140μF waveforms (τ_{s}>τ_{m}) but >1 for 40μF waveforms (τ_{s}<τ_{m}). This finding was predicted by the chargeburping theory. A second finding is that the storedenergy DFT was 23% lower for the best 40μF waveform in comparison with the best 140μF waveform.
Optimal PhaseDuration Ratio: Prior Studies
Four previous empirical studies performed with 150 to 175μF capacitors (τ_{s}=6 to 8 ms) have reported that biphasic waveforms are most efficient when the phaseduration ratio is <1.^{1} ^{9} ^{10} ^{11} The results of the present study regarding 140μF waveforms (τ_{s}=7 ms) are consistent with these reports. However, we found that the effect of phaseduration ratio on DFT differs markedly for verysmallcapacitor 40μF waveforms (τ_{s}=2 ms).
Models of Defibrillation Waveforms
A capacitivedischarge, biphasic waveform is described by seven parameters: the leadingedge voltage of each phase, τ_{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 singlecapacitor, 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 (τ_{m}^{13} or chronaxie^{8} ) and τ_{s}. Both also apply Blair's model of the myocardial cell^{29} ^{30} to derive an expression for the timevarying voltage of the cell during phase 2. Kroll^{8} extrapolated this analysis to predict that the optimal phaseduration ratio depends on the relationship between τ_{s} and τ_{m}, as shown in Fig 2⇑.
Comparison of Experimental Findings and Model Predictions
The dotted lines in Fig 1⇑ represent the predicted cellmembrane responses^{8} to the applied shock voltages. The cellresponse curves depend on the value of τ_{s}, which is known, and the value of τ_{m}, which is unknown. Direct measurement of τ_{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 strengthduration curves in various animals has yielded values of 2.2 to 5.8 ms.^{9} ^{13} ^{31} ^{32} ^{33} Fig 1⇑ 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 ms^{13} or 3.0 ms.^{8} The value of 4.2 ms was calculated^{34} from strengthduration data obtained in a pilot study for the present experiment.
Fig 1⇑ illustrates the differences in cell responses to the voltage fields of the 140 and 40μF waveforms predicted by the chargeburping theory. Phase 1 of the 140μF waveform produces a weaker but longerlasting field than phase 1 of the 40μF waveform. The cell response to the applied 140μF waveform is slower and continues longer. For phase 2, the leadingedge voltage is a greater fraction of the phase1 leadingedge voltage for the 140μF waveform, resulting in more rapid chargeburping for this waveform. In addition, the phase2 negative applied voltage exceeds a minimal absolute value for a longer time for the 140μF waveform, resulting in a persistent negative residual membrane voltage for high phaseduration ratios. The cellresponse curves appear to be underdamped. In contrast, because the negative applied voltage decays rapidly for the 40μF waveform, the cell response does not decrease below the relative zero value. The cellresponse curves appear to be overdamped.
The chargeburping theory successfully explains our finding for 40μF waveforms. Phaseduration ratios of 0.5 and 1 fail to return the cellmembrane voltage to the preshock level and thereby leave substantial residual charge on the membrane. In contrast, there is a broad range of phaseduration ratios between 2 and 3 that provide comparable and nearcomplete chargeburping for either value of τ_{m}.
For 140μF waveforms, the predictions of the chargeburping theory depend strongly on the unknown value of τ_{m}. For τ_{m} of 3.0 and 4.2 ms, the predicted optimal phaseduration ratios are 0.5 and 0.75, respectively. For τ_{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 chargeburping 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 phaseduration ratios of 0.5 and 1 but lower for a ratio of 0.75. Thus, the chargeburping theory predicts that, for nearoptimal waveforms, residual membrane voltages and DFTs are more sensitive to potential clinical variability in τ_{m} for 140μF waveforms than for 40μF waveforms. In the present study, the essentially equal groupmean DFTs for phaseduration ratios of 0.5 and 1 are consistent with the predictions for τ_{m} of 4.2 ms, but we do not know whether a phaseduration ratio of 0.75 would have resulted in a lower groupmean DFT.
Conventionalcapacitor waveforms with high phaseduration 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 1⇑ (top) shows that the absolute value of the negative residual voltage is greatest for a phaseduration ratio near 1.0 for τ_{m} of 3.0 ms and 1.5 for τ_{m} of 4.2 ms. The absolute value of the negative residual voltage decreases for higher ratios. Although a 6ms value of τ_{m} would result in a more negative residual voltage for a phaseduration ratio of 2 than for a ratio of 1, the positive residual voltage for a ratio of 0.5 would become substantial. Timedependent factors that influence how the cellmembrane 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 cellmembrane voltage. This may decrease synchronization of repolarization^{35} ^{36} and increase vulnerability to refibrillation.^{7}
Specific predictions of the chargeburping theory have been validated in two previous reports. Walcott et al^{13} prospectively evaluated the optimal durations of biphasic waveforms with equal phase durations and varying τ_{s}. Kroll^{8} retrospectively correlated measured DFTs with predicted residual membrane voltage for 150 to 175μF waveforms with phaseduration ratios ≤1. The predictions of the chargeburping theory for waveforms with phaseduration ratios >1 have not been reported previously. Our data indicate that this model explains the response to these smallcapacitor waveforms regardless of the phaseduration ratio.
Fig 1⇑ also shows that the predicted total waveform duration is similar for the best 140μF waveforms and best 40μF waveforms. Our results support this prediction, which is a consequence of the more general prediction shown in Fig 2⇑. They extend previous observations that truncation is critical for conventionalcapacitor waveforms^{37} but not for smallcapacitor 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 animals^{15} and humans^{16} ^{17} have reported that 60 to 85μF waveforms had lower DFTs than conventional 120 to 140μF waveforms. In the only previous (canine) study of biphasic defibrillation using very small capacitors, Walcott et al^{13} reported DFTs for 37.5μF capacitors (τ_{s}=1.5 ms) and 150μF capacitors (τ_{s}=6.0 ms) for waveforms with equal phase durations. Calculations based on their reported voltage DFTs indicate that the best 37.5μF waveform reduced the mean storedenergy DFT by 33% in comparison with the best 150μF 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 40μF waveform (τ_{s}=2 ms) lowered the DFT by 23% compared with an optimized 140μF waveform (τ_{s}=7 ms).
Study Limitations
The 140μF 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 model^{14} by use of his Equation 5 and for Kroll's monophasic model^{22} 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 ≈1%. The strengthduration data of Chapman et al^{21} and limited human data^{38} ^{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 chargeburping theory about the effect of τ_{s} on optimal phaseduration 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 140μF waveform with a phase 1 duration of 6.3 ms, the best predicted phaseduration ratio is 0.44 for τ_{m} of 3 ms and 0.59 for τ_{m} of 4 ms. In contrast, for the experimental 40μF waveform with a phase 1 duration of 2.8 ms, the best predicted phaseduration ratio is 1.94 for τ_{m} of 3 ms; for τ_{m} of 4 ms, the best predicted phaseduration ratio exceeds 10, but a phaseduration 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 phaseduration ratios might not apply if the duration of phase 1 is very short or very long.^{40} ^{41}
Although Kroll's formulation of the chargeburping theory does not require a specific relationship between chronaxie and τ_{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 phaseduration ratio for the τ_{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 τ_{s}.^{13} ^{17} Although in the present study we varied τ_{s} by altering capacitance, the same considerations regarding optimal phaseduration ratios should apply if τ_{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 τ_{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 verysmallcapacitor 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, highvoltage monophasic shocks have been reported to cause postshock conduction block^{42} and transient myocardial depression.^{43} Although biphasic shocks produce less conduction block^{44} and less dysfunction^{45} than monophasic shocks and shorter pulses produce less dysfunction than longer pulses,^{45} the safety of verysmallcapacitor biphasic shocks is unknown.
Acknowledgments
This study was supported in part by American Heart Association Greater Los Angeles Affiliate GrantinAid 1085GI1 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 PengSheng Chen, MD, for his critical review of this manuscript.
Footnotes

Reprint requests to Charles D. Swerdlow, MD, CedarsSinai Medical Towers, 8635 W Third St, Suite 975 W, Los Angeles, CA 90048. Email swerdlow@ucla.edu.
 Received February 21, 1996.
 Revision received April 30, 1996.
 Accepted May 1, 1996.
 Copyright © 1996 by American Heart Association
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 ChargeBurping Theory Correctly Predicts Optimal Ratios of Phase Duration for Biphasic Defibrillation WaveformsCharles D. Swerdlow, Wei Fan and James E. BrewerCirculation. 1996;94:22782284, published online before print November 1, 1996http://dx.doi.org/10.1161/01.CIR.94.9.2278
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 ChargeBurping Theory Correctly Predicts Optimal Ratios of Phase Duration for Biphasic Defibrillation WaveformsCharles D. Swerdlow, Wei Fan and James E. BrewerCirculation. 1996;94:22782284, published online before print November 1, 1996http://dx.doi.org/10.1161/01.CIR.94.9.2278
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