Optimal SmallCapacitor Biphasic Waveform for External Defibrillation
Influence of Phase1 Tilt and Phase2 Voltage
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Abstract
Background—Biphasic waveforms have been reported to be more efficacious than monophasic waveforms for external defibrillation. This study examined the optimal phase1 tilts and phase2 leadingedge voltages with small capacitors (60 and 20 μF) for external defibrillation. We also assessed the ability of the “chargeburping” model to predict the optimal waveforms.
Methods and Results—Two groups of studies were performed. In group 1, 9 biphasic waveforms from a combination of 3 phase1 tilt values (30%, 50%, and 70%) and 3 phase2 leadingedge voltage values (0.5, 1.0, and 1.5 times the phase1 leadingedge voltage, V_{1}) were tested. Phase2 pulse width was held constant at 3 ms in all waveforms. Two separate 60μF capacitors were used in each phase. The energy value that would produce a 50% likelihood of successful defibrillation (E_{50}) decreased with increasing phase1 tilt and increased with increasing phase2 leadingedge voltage except for the 30% phase1 tilt waveforms. In group 2, 9 waveforms were identical to the waveforms in group 1, except for a 20μF capacitor for phase 2. E_{50} decreased with increasing phase1 tilt. Phase2 leadingedge voltage of 1.0 to 1.5 V_{1} appeared to minimize E_{50} for phase1 tilt of 50% and 70% but worsened E_{50} for phase1 tilt of 30%. There was a significant correlation between E_{50} and residual membrane voltage at the end of phase 2, as calculated by the chargeburping model in both groups (group 1, R^{2}=0.47, P<0.001; group 2, R^{2}=0.42, P<0.001).
Conclusions—The waveforms with 70% phase1 tilt were more efficacious than those with 30% and 50%. The relationship of phase2 leadingedge voltage to defibrillation efficacy depended on phase2 capacitance. The chargeburping model predicted the optimal external biphasic waveform.
Several internal defibrillation studies^{1} ^{2} have established the superiority of biphasic shock waveforms over comparable monophasic waveforms. Exponential biphasic waveforms can also provide improved external defibrillation efficacy.^{3} ^{4} ^{5}
Recently, a quantitative “chargeburping” model has been proposed to explain the improved efficacy of biphasic over monophasic shocks.^{6} A recent study^{7} supported this model by demonstrating that minimum residual membrane voltage as calculated by the chargeburping model predicted the optimal internal biphasic waveform.
Defibrillation efficacy may also be improved by optimizing capacitance values. On the basis of models of internal defibrillation,^{8} ^{9} optimal capacitance depends on shock impedance and the chronaxy of the strengthduration curve. Assuming a time constant of 2 to 4 ms and a mean impedance of 40 Ω, as reported in a previous swine external defibrillation study,^{4} the optimum capacitance is calculated by these theoretical models to be in the 50 to 100μF range.^{8} ^{9} Hence, a 60μF capacitor would be within this optimal range to provide maximal external defibrillation efficacy. Recent defibrillation studies^{10} ^{11} ^{12} ^{13} have shown that the biphasic waveform with changing capacitance at phase reversal may reduce the defibrillation threshold (DFT). However, the optimal combination of phase1 tilt and phase2 leadingedge voltage to maximize defibrillation efficacy has not been determined in such a changing capacitor external waveform.
The purpose of this study was (1) to assess the contribution of phase1 tilt and phase2 leadingedge voltage in optimizing the smallcapacitor (60/60μF) biphasic waveform for external defibrillation, (2) to determine the optimal timing and voltage of phase reversal to maximize external defibrillation efficacy in biphasic waveform with changing capacitor at phase reversal (60/20μF), and (3) to assess the ability of the chargeburping model to predict the optimal external defibrillation waveforms.
Methods
Surgical Procedures
A detailed description of these procedures was published previously.^{14} ^{15} ^{16} ^{17} Briefly, swine were premedicated with ketamine and morphine and anesthetized with intravenous sodium pentobarbital, with repeated doses of 1 to 2 mg/kg given as necessary to maintain anesthesia. Pancuronium bromide was given every 30 minutes to eliminate muscular contraction. The swine were ventilated with room air supplemented with oxygen as needed to maintain normal arterial blood gases. A transvenous defibrillation electrode (model 4007L, Angeion Corp) was inserted into the right ventricle (RV). An adhesive pad electrode was applied to the left high anterior shaved thorax. This skin patch in combination with the transvenous electrode was used to induce fibrillation and to deliver rescue shocks after failed test shocks.
Defibrillation Equipment and Protocol
The transthoracic defibrillation electrode system consisted of adhesive pad electrodes, each with a surface area of 75 cm^{2}, applied to the right high anterior shaved thorax and to the left lower anterolateral shaved thorax. Pad electrodes were connected to an external defibrillator custommade by SurVivaLink Corp. This custom external defibrillator delivered a monophasic or biphasic, highvoltage, timetruncated, capacitative discharge pulse. The defibrillator was equipped with 2 capacitor banks. Each capacitor bank was used for a phase of a monophasic or biphasic shock, with independent phase capacitance values in the range of 10 to 300 μF, in 10μF steps. Each capacitor bank was charged to a maximum of 4000 V and was programmed to deliver a pulse with predetermined initial voltage, capacitance, pulse width or tilt, and polarity. Together, the 2 capacitor banks delivered a biphasic shock. The defibrillator acquired data from current and voltage meters, and it sampled each meter at 10 kHz. All reported experimental parameters were measured and calculated from these waveform data acquired during the delivery of the shocks.
Ventricular fibrillation was induced with 60Hz alternating current (15 V) applied for 4 seconds through the RV electrode. The test biphasic waveform was delivered at 10 seconds after initiation of alternating current. The right high anterior pad was used as the cathode for phase 1. If ventricular fibrillation was not terminated by the test biphasic waveform, a monophasic rescue shock (450 to 900 V) was delivered via the RV electrode. A recovery period of at least 3 minutes was allowed between episodes of fibrillation. Fibrillation was not reinitiated until heart rate and blood pressure had returned to the preshock values.
E_{50} and V_{50}
Defibrillation efficacies of different waveforms were compared through the determination of E_{50} and V_{50} for each waveform, where E_{50} and V_{50} were defined as the estimated energy and voltage values that would produce a 50% likelihood of successful defibrillation. The protocol to determine E_{50} and V_{50} used a Bayesian approach.^{18} Ten defibrillation shocks were delivered with each waveform. The first shock had a 1650V phase1 leadingedge voltage. Subsequent shocks had the voltage decremented or incremented, depending on the success or failure of the preceding shock, respectively. The voltage changes in the sequence of defibrillation test shocks were 350, 200, 150, 150, 100, 100, 50, 50, and 0 V. This approach has been demonstrated to obtain an estimate of V_{50} with an error of <10%.^{18} The E_{50} for stored and delivered energy were calculated at V_{50}.
Defibrillation Waveforms
Nine biphasic waveforms were tested in each group. The description of each waveform in groups 1 and 2 is detailed in Figures 1⇓ and 2⇓, respectively. The 9 waveforms in each group were tested in random order in each experiment.
Residual Membrane Voltage
Calculation of residual membrane voltage for the purpose of testing the chargeburping hypothesis was performed according to the method described by Kroll^{6} and detailed in the Appendix.
Statistical Analysis
Group data were expressed as mean±SD. Repeatedmeasures 1way ANOVA was used to compare defibrillation parameters among the 9 waveforms in each group. Pairwise comparisons were performed by the method of contrasts.^{19} ANCOVA was used between the E_{50} for delivered energy and the normalized absolute residual membrane voltage at the end of phase 2 in each group. The null hypothesis was rejected for P<0.05.
Results
Group 1
Complete DFT data sets were obtained from 10 swine (33±3 kg). The waveform characteristics and the DFT parameters are detailed in Table 1⇓.
Defibrillation Energy
Figure 3⇓ shows the E_{50} of delivered energy in each waveform. For 30% phase1 tilt waveforms, the E_{50} of the 30/0.5 phase1 leadingedge voltage (V_{1}) waveform was the lowest compared with the 30/1.0 V_{1} (P=0.0001) and the 30/1.5 V_{1} waveforms (P=0.0002). Similar to 30% phase1 tilt waveforms, the 50/0.5 V_{1} and the 70/0.5 V_{1} waveforms generated the lowest E_{50} within their corresponding 50% and 70% phase1 tilt waveforms (50/0.5 V_{1} versus 50/1.0 V_{1}, P=0.0151; versus 50/1.5 V_{1}, P=0.0001; 70/0.5 V_{1} versus 70/1.0 V_{1}, P=0.0438; versus 70/1.5 V_{1}, P=0.0028). Thus, the waveforms with phase2 leadingedge voltage equal to half of phase1 leadingedge voltage had the lowest E_{50} of delivered energy in all 3 tilts tested in these experiments.
When one compares the waveforms using the optimal phase2 leadingedge voltage (0.5 V_{1}) for each phase1 tilt, the E_{50} for the 30/0.5 V_{1} waveform was higher than the corresponding E_{50} of the 50/0.5 V_{1} (P=0.0482) and the 70/0.5 V_{1} waveforms (P=0.0168). There was no significant difference in E_{50} between the 50/0.5 V_{1} and the 70/0.5 V_{1} waveforms (P=0.6625). In a similar manner, the E_{50} in the 30/1.0 V_{1} waveform was higher than that of the 50/1.0 V_{1} (P=0.0001) and the 70/1.0 V_{1} waveforms (P=0.0001). There was again no significant difference between the E_{50} of the 50/1.0 V_{1} and the 70/1.0 V_{1} waveforms (P=0.3836). For waveforms with phase2 leadingedge voltage of 1.5 V_{1}, the E_{50} in the 30/1.5 V_{1} waveform was higher than the 70/1.5 V_{1} waveform (P=0.0019). Thus, the waveform with phase1 tilt of 50% or 70% had lower E_{50} of delivered energy than the waveform with the phase1 tilt of 30% when phase2 leadingedge voltage was constant.
Membrane Voltage
The residual membrane voltages at the end of phase 2, based on the chargeburping model for the test waveforms, are shown in Table 1⇑. The theoretical cell membrane response curves are illustrated as the thin lines in Figure 1⇑. As predicted by this model and illustrated in Figure 1⇑, the residual membrane voltage at the end of phase 2 for each fixed phase1 tilt increased with increasing phase2 leadingedge voltage. According to the chargeburping hypothesis, optimal DFT energies are obtained when phase 2 of the shock minimizes any residual cell membrane voltage. Figure 4⇓ shows the relationship between E_{50} of delivered energy and residual membrane voltage at the end of phase 2. There is a significant correlation between the residual membrane voltage at the end of phase 2 and the measured E_{50} of delivered energy.
Group 2
Complete DFT data sets were obtained from 10 swine (35±6 kg). The waveform characteristics and the DFT parameters are detailed in Table 2⇓.
Defibrillation Energy
Figure 5⇓ shows the E_{50} of delivered energy in each waveform. For 30% phase1 tilt waveforms, the E_{50} in the 30/0.5 V_{1} waveform was lower than in the 30/1.5 V_{1} waveform (P=0.0253). There was no difference in E_{50} between the 30/1.0 V_{1} and 30/1.5 V_{1} waveforms (P=0.0656). In contrast to the 30% phase1 tilt waveforms, the 50% and 70% phase 1 tilt waveforms had lower E_{50} at phase2 leadingedge voltages of 1.0 V_{1} (50/0.5 V_{1} versus 50/1.0 V_{1}, P=0.0391; 70/0.5 V_{1} versus 70/1.0 V_{1}, P=0.0414). However, the differences in E_{50} between the 50/0.5 V_{1} and 50/1.5 V_{1} waveforms (P=0.071) and between the 70/0.5 V_{1} and 70/1.5 V_{1} waveforms (P=0.087) did not reach statistical significance. Thus, the lowest E_{50} of delivered energy appeared to be associated with waveforms having longer phase1 durations (50% and 70%) and larger phase2 leadingedge voltages (1.0 V_{1}).
When one compares the waveforms of differing tilts but the same 0.5 V_{1} phase2 leadingedge voltage, the E_{50} for the 30/0.5 V_{1} waveform was higher than the corresponding E_{50} of the 70/0.5 V_{1} waveform (P=0.0095) but not different from that of the 50/0.5 V_{1} waveform (P=0.1373). There was no significant difference in E_{50} between the 50/0.5 V_{1} and the 70/0.5 V_{1} waveforms (P=0.2496). For waveforms with phase2 leadingedge voltage of 1.0 V_{1}, the E_{50} in the 30/1.0 V_{1} waveform was higher than that of the 50/1.0 V_{1} (P=0.0001) and the 70/1.0 V_{1} waveforms (P=0.0001). There was again no significant difference between the E_{50} of the 50/1.0 V_{1} and the 70/1.0 V_{1} waveforms (P=0.2596). In a similar manner, for waveforms with phase2 leadingedge voltage of 1.5 V_{1}, the E_{50} in the 30/1.5 V_{1} waveform was higher than the 50/1.5 V_{1} waveform (P=0.0001) and the 70/1.5 V_{1} waveform (P=0.0001). Thus, the waveform with the phase1 tilt of 50% or 70% had lower E_{50} of delivered energy than the waveforms with the phase1 tilt of 30% for each phase2 leadingedge voltage.
Membrane Voltage
The absolute residual membrane voltage at the end of phase 2 based on the chargeburping model for the test waveforms are shown in Table 2⇑. The theoretical cell membrane response curves are illustrated as the thin lines in Figure 2⇑. Figure 6⇓ shows the relationship between E_{50} of delivered energy and absolute residual membrane voltage at the end of phase 2. Similar to group 1, there is a significant correlation between the absolute residual membrane voltage at the end of phase 2 and the measured E_{50} of delivered energy.
Discussion
This study investigated the effect of phase1 tilt and phase2 leadingedge voltage on external defibrillation efficacy with a 60μF capacitor for phase 1 and either a 60 or 20μF capacitor for phase 2. It appears that larger phase1 tilts, at least up to 70%, were more efficacious than the smaller tilts of 30% and 50%. The relationship of phase2 leadingedge voltage to defibrillation efficacy appeared more complex and depended on phase2 capacitance. When the same capacitance was used for both phases (60μF), a lower phase2 leadingedge voltage (0.5 V_{1}) appeared to be the most efficient. However, when a smaller phase2 capacitance of 20 μF was used, a higher phase2 leadingedge voltage appeared to be best. In addition, the results confirmed that the chargeburping model can predict the optimal biphasic waveform for external defibrillation.
Residual Membrane Voltage
Recently, a quantitative chargeburping model has been proposed.^{6} In this model, the optimal phase 1 of the biphasic waveform should be identical to the optimal monophasic waveform, while the optimal phase 2 discharges the residual charges left on the cell membranes by phase 1.^{6} A study by Swerdlow et al^{7} supported this model by demonstrating that the optimal ratio of phase1 pulse width to phase2 pulse width depended on the relationship between the time constant of the shocking system and the time constant of myocardial cell membranes. This result was predicted by the chargeburping model. In this study, we calculated the membrane response curves in each waveform using the same chargeburping model.^{6} There was a significant correlation between the absolute residual membrane voltage at the end of phase 2 and the E_{50} of delivered energy in both groups (Figure 4⇑ and 6⇑). This result suggests that minimizing the residual membrane voltage at the end of phase 2 as calculated by the chargeburping model correlates with the optimal phase 2 for generating the lowest delivered energy. The original chargeburping model postulated that biphasic waveforms may have little advantage over monophasic ones for external defibrillation.^{6} This hypothesis was based on the concept that internal defibrillation creates large voltage gradients in the heart, especially near the shocking electrodes, whereas external defibrillation would create relatively homogeneous voltage gradients within the heart. A few early experimental studies^{20} ^{21} supported this hypothesis. Recent external defibrillation studies,^{3} ^{4} ^{5} however, have found that biphasic waveforms do indeed improve defibrillation efficacy. Furthermore, our study suggests that the chargeburping model reasonably predicted the defibrillation efficacy of a particular phase1 waveform in combination with various phase2 pulses. Thus, it would appear that discharging the residual membrane voltage at the end of phase 1 may still be important even with external defibrillation.
Phase2 LeadingEdge Voltage
One recent internal defibrillation study^{22} compared defibrillation efficacy among 3 biphasic waveforms with equal phase1 tilt at 65% but shorter phase2 pulse width or smaller phase2 leadingedge voltage. Defibrillation energy requirements were significantly increased for the waveform with a smaller phase2 leadingedge voltage, whereas a short phase2 pulse width did not influence defibrillation efficacy. This result suggested that the amplitude of phase2 leadingedge voltage may be a more critical determinant than the phase2 pulse width for defibrillation success of biphasic waveforms in humans.^{22}
Although the 0.5 V_{1} phase2 leadingedge voltage always had the lowest DFT in the 60/60μF shocks (group 1), this relationship did not persist in the 60/20μF waveforms (group 2). For the optimal phase1 tilts in group 2, the best phase2 leadingedge voltages were higher in the 1.0 to 1.5 V_{1} range. Thus, when smaller phase2 capacitors are used, the optimal phase2 leadingedge voltage is higher than those waveforms when the same phase1 and phase2 capacitors are used.
Limitations
The characteristics of the defibrillation waveform in this study depended on shock impedance. The typical patient impedance for external shock is 60 to 80 Ω,^{3} ^{5} ^{23} but the shock impedance in our study was ≈40 Ω. Although the optimal phase1 tilt value is 70% with a phase1 pulse width of 3.0 ms in this study, this phase1 pulse width will be longer in a clinical setting because of the higher impedance. Thus, these results may need to be verified in humans because of this difference impedance.
Conclusions
The major findings of the present study are as follows: (1) the 60/60μF biphasic waveform with combination of phase1 70% tilt and phase2 leadingedge voltage of 0.5 times phase1 leadingedge voltage provided the maximal defibrillation efficacy, (2) the 60/20μF capacitor biphasic waveform with combination of phase1 50% and 70% tilt and phase2 leadingedge voltage of 1.0 and 1.5 times phase1 leadingedge voltage provided the optimal defibrillation efficacy, and (3) the residual membrane voltage as calculated by the chargeburping model predicted the optimal smallcapacitor external defibrillation biphasic waveform.
Appendix A1
Generalized Chargeburping Theory: φ_{2} Independent of φ_{1}
Chargeburping theory and its associated equations describe the time course of the membrane potential of a cell during a biphasic shock pulse. Chargeburping theory hypothesizes that an optimal pulse duration for phase 2 (φ_{2}) is the duration that leaves as little residual membrane potential remaining on a cell affected by phase 1 (φ_{1}) as possible. Ideally, affected cells are set back to “relative ground” with φ_{2}.
Generalized chargeburping theory for external defibrillation is based on the Kroll cardiac cell response model illustrated in Figure 7⇓. The Kroll design equations are extended to account for the transthoracic resistance and a chargeburping φ_{2} that is independent of φ_{1}. The generalized burping theory is based on incorporating an independent capacitor system for φ_{2}.
In the transthoracic extension of the Kroll model, the resistance variables are R_{S}=resistance of the defibrillator (including the electrodeelectrolyte interface), R_{TC}=resistance of the thoracic cage, R_{CW}=resistance of the chest wall, R_{LP}=resistance of the lungs in parallel, R_{LS}=resistance of the lungs in series, and R_{H}=resistance of the heart. R_{B} represents the combined parallel and series resistances of the patient’s body. Also, C_{1} represents the φ_{1} capacitor system, C_{2} represents the φ_{2} capacitor system, and the pair C_{m} and R_{m} represent the membrane series capacitance and resistance of a single cell. The node V_{S} represents the voltage between the electrodes, and V_{m} denotes the voltage across the cell membrane.
The discharge of a capacitor system is modeled by V=V_{1}e^{−t/τ1} for an initial C_{1} capacitor system with a leadingedge voltage of V_{1}. Using the abstract circuit of Figure 7⇑, an equation for V_{m} may be determined to be where Ω_{S} and Ω_{B} are nonlinear resistance representations of the transthoracic resistive elements, τ_{m}=R_{m}C_{m} represents the time constant of the myocardial cell in the circuit model, and τ_{1}=(R_{S}+R_{B}) · C_{1} represents the time constant of φ_{1}. The ordinary differential equation (ODE) in Equation 1 models the effects of a transchest, monophasic, timetruncated, capacitordischarged shock pulse on the myocardium. Equation 1 is an initialvalue, firstorder, linear differential equation. Assuming that the initial value for V_{m1} is V_{m1} (0)=V_{G}=0 (“cell ground”) and applying the initial condition to this equation, the solution to the equation for φ_{1}, in terms of phase1 cell potential V_{m1}, is
For φ_{2}, an analysis identical to Equations 1, and 2 is derived. The differences are 2fold. First, a biphasic waveform reverses the flow of current through the myocardium during φ_{2}. Reversing the flow of current in the circuit model changes the sign on the current. The sign changes on the right hand side of Equation 1. Second, the φ_{2} part of the waveform is assumed to be independent of φ_{1}. Therefore, the φ_{2} ODE incorporates an independent leadingedge voltage, V_{2}, for the φ_{2} portion of the pulse. Let τ_{2} represent the φ_{2} time constant. With these considerations, the φ_{2} ODE becomes Equation 3 is again a initialvalue, firstorder, linear differential equation. At the end of φ_{1}, the (initial) value for V_{m2} is V_{m2} (0)=V_{m1} (d_{φ1})=V_{φ1} where d_{φ1} is the overall time of discharge for φ_{1} and V_{φ1} is the voltage left on the cell at the end of φ_{1}. Applying the initial condition to equation 3, the solution for phase2 cell potential V_{m2} is Equation 4 provides a means to calculate the residual membrane potential at the end of φ_{2} for those cells that were not depolarized by φ_{1}. Equation 4 is set equal to zero and is solved for t. The solution for t is the optimal chargeburping pulse duration for φ_{2}, denoted by d_{φ2}. Arranging the exponential functions to 1 side and taking the logarithm of both sides, we solve for d_{φ2} to get
Acknowledgments
This work was supported by a grant from the SurVivaLink Corporation.
Footnotes

A part of this manuscript was selected as a finalist for the Cournand and Comroe Young Investigator Prizes in Cardiopulmonary and Critical Care at the 70th Scientific Sessions of the American Heart Association, Orlando, Fla, November 10–13, 1997.
 Received July 7, 1998.
 Revision received July 28, 1998.
 Accepted July 30, 1998.
 Copyright © 1998 by American Heart Association
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Kerber RE, Jensen SR, Gascho JA, Grayzel J, Hoyt R, Kennedy J. Determinants of defibrillation: prospective analysis of 183 patients. Am J Cardiol. 1983;52:739–745.To investigate the effect of phase1 tilt and phase2 leadingedge voltage on external defibrillation efficacy with small capacitors, defibrillation efficacies were evaluated among several different biphasic waveforms with 60/60μF and 60/20μF capacitors (phase 1/phase 2). A larger phase1 tilt was evaluated as more efficacious than smaller tilts in both waveforms. A lower phase2 leadingedge voltage appeared to be the most efficient in the 60/60μF waveform, but a higher phase2 leadingedge voltage appeared to be best in the 60/20μF waveform. In addition, the results confirmed that the “chargeburping” model can predict the optimal biphasic waveform for external defibrillation.
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 Optimal SmallCapacitor Biphasic Waveform for External DefibrillationYoshio Yamanouchi, James E. Brewer, Kent A. Mowrey, Ann M. Donohoo, Bruce L. Wilkoff and Patrick J. TchouCirculation. 1998;98:24872493, published online before print December 1, 1998http://dx.doi.org/10.1161/01.CIR.98.22.2487
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 Optimal SmallCapacitor Biphasic Waveform for External DefibrillationYoshio Yamanouchi, James E. Brewer, Kent A. Mowrey, Ann M. Donohoo, Bruce L. Wilkoff and Patrick J. TchouCirculation. 1998;98:24872493, published online before print December 1, 1998http://dx.doi.org/10.1161/01.CIR.98.22.2487
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