Donate Help Contact The AHA Sign In Home
American Heart Association
Circulation
Search: search_blue_button Advanced Search
« Previous Article | Table of Contents | Next Article »
Circulation. 1997;96:2813-2822

This Article
Right arrow Abstract Freely available
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow Request Permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Swerdlow, C. D.
Right arrow Articles by Kroll, M. W.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Swerdlow, C. D.
Right arrow Articles by Kroll, M. W.

(Circulation. 1997;96:2813-2822.)
© 1997 American Heart Association, Inc.

Articles

Application of Models of Defibrillation to Human Defibrillation Data

Implications for Optimizing Implantable Defibrillator Capacitance

Charles D. Swerdlow, MD; James E. Brewer, MS; Robert M. Kass, MD; ; Mark W. Kroll, PhD

From the Division of Cardiology, Department of Medicine (C.D.S.) and Department of Cardiovascular Surgery (R.M.K.), Cedars-Sinai Medical Center, and University of California Los Angeles School of Medicine. J.E. Brewer is now at SurVivalink Corp, Minneapolis, Minn; Dr Kroll is now at Pacesetter Corp, Sylmar, Calif.

Correspondence to Charles D. Swerdlow, MD, Cedars-Sinai Medical Towers, 8635 W Third St, Suite 1190 W, Los Angeles, CA 90048. E-mail swerdlow{at}ucla.edu


*    Abstract
up arrowTop
 *Abstract
down arrowIntroduction
 down arrowMethods
 down arrowResults
 down arrowDiscussion
 down arrowAppendix 1
 down arrowReferences
 
Background Theoretical models predict that optimal capacitance for implantable cardioverter-defibrillators (ICDs) is proportional to the time-dependent parameter of the strength-duration relationship. The hyperbolic model gives this relationship for average current in terms of the chronaxie (tc). The exponential model gives the relationship for leading-edge current in terms of the membrane time constant ({tau}m). We hypothesized that these models predict results of clinical studies of ICD capacitance if human time constants are used.

Methods and Results We studied 12 patients with epicardial ICDs and 15 patients with transvenous ICDs. Defibrillation threshold (DFT) was determined for 120-µF monophasic capacitive-discharge pulses at pulse widths of 1.5, 3.0, 7.5, and 15 ms. To compare the predictions of the average-current versus leading-edge-current methods, we derived a new exponential average-current model. We then calculated individual patient time parameters for each model. Model predictions were validated by retrospective comparison with clinical crossover studies of small-capacitor and standard-capacitor waveforms. All three models provided a good fit to the data (r2=.88 to .97, P<.001). Time constants were lower for transvenous pathways (53±7 {Omega}) than epicardial pathways (36±6 {Omega}) (tc, P<.001; average-current {tau}m, P=.002; leading-edge-current {tau}m, P<.06). For epicardial pathways, optimal capacitance was greater for either average-current model than for the leading-edge-current model (P<.001). For transvenous pathways, optimal capacitance differed for all three models (P<.001). All models provided a good correlation with the effect of capacitance on DFT in previous clinical studies: r2=.75 to .84, P<.003. For 90-µF, 120-µF, and 150-µF capacitors, predicted stored-energy DFTs were 3% to 8%, 8% to 16%, and 14% to 26% above that for the optimal capacitance.

Conclusions Model predictions based on measured human cardiac-muscle time parameter have a good correlation with clinical studies of ICD capacitance. Most of the predicted reduction in DFT can be achieved with {approx}90-µF capacitors.


Key Words: defibrillation • waves • heart-assist device


*    Introduction
up arrowTop
 up arrowAbstract
 *Introduction
down arrowMethods
 down arrowResults
 down arrowDiscussion
 down arrowAppendix 1
 down arrowReferences
 
Optimized capacitive-discharge waveforms are an important goal in the design of ICDs. Quantitative models have been proposed to facilitate optimizing these waveforms over a broad range of capacitances and pathway resistances.1 2 3 4 5 6 Although the models differ, each predicts that the DFT is minimized when the time constant of the shock waveform is close to the value of a parameter that characterizes the time-dependent response of cardiac tissue to the applied shock. These parameters may be determined from the strength-duration curve,7 which is a plot of shock strength at the DFT versus shock duration. Based on parameters determined from animal data, these models predict that optimal ICD capacitance for a 50-{Omega} pathway is 30 to 43 µF1 2 3 6 and that reduction in capacitance will result in substantial improvement in DFT.6 Small capacitors have performed better than conventional capacitors8 9 10 11 12 in animals, but they have shown modest13 or no14 15 16 17 18 19 benefit for the majority of clinical defibrillation pathways. The objective of this study was to test the hypothesis that these models predict results of clinical studies of ICD capacitance if human cardiac-muscle time parameters are used. A secondary objective was compare optimal capacitance predicted by average-current and leading-edge-current methods directly by use of the same data and parallel models.


*    Methods
up arrowTop
 up arrowAbstract
 up arrowIntroduction
 *Methods
down arrowResults
 down arrowDiscussion
 down arrowAppendix 1
 down arrowReferences
 
Models of Defibrillation
Capacitive-discharge waveforms are characterized by a {tau}s, which represents the exponential-decay time constant of the defibrillation pulse. {tau}s is the product of pathway resistance and ICD capacitance. Theoretical models1 2 4 define the optimal defibrillation waveform as that which minimizes stored-energy DFT, because stored energy is a critical determinant of ICD pulse generator size. Each model predicts the optimum value of {tau}s in terms of a time parameter that characterizes the response of cardiac tissue to the shock. Strength-duration equations are shown in the "Appendix."

Monophasic Models
Hyperbolic average-current model. The empirical hyperbolic strength-duration relationship20 21 may be applied to capacitive-discharge defibrillation pulses by expressing shock strength as average current during the pulse.22 23 This hyperbolic average-current model gives the DFT in terms of tc and the average-current rheobase, which is the DFT at an infinite pulse width. The waveform optimization strategy is summarized in the "Appendix." The optimal value of {tau}s is 0.796 tc1 2 and the optimum pulse duration is 1.045 tc.2

Leading-edge-current exponential model. A strength-duration relationship also can be derived from Blair's resistor-capacitor model of the cardiac cell membrane.24 25 This exponential formulation of the strength-duration relationship was extrapolated to describe stimulation by capacitive-discharge pulses26 and subsequently applied to defibrillation.3 5 This model assumes that defibrillation depends only on the peak cell response to a shock pulse rather than the average applied current during the pulse.4 5 6 26 The corresponding strength-duration relation gives leading-edge-current DFT for a capacitive-discharge pulse in terms of two time constants, {tau}s and Blair's24 25 "cell membrane" {tau}m. The third model parameter is the leading-edge-current rheobase at an infinite value of {tau}s. The optimum value of {tau}s and the optimum pulse duration are both equal to {tau}m.4 5 6 Fig 1Down shows the effect of varying the relationship between {tau}s and {tau}m on the predicted membrane-response and the corresponding strength-duration curves.



View larger version (29K):
[in this window]
[in a new window]
  		Figure 1. Exponential leading-edge-current model. Monophasic pulse duration is displayed on horizontal axis in units of {tau}m. Bottom, Predicted membrane response to applied shock; top, corresponding strength-duration relation. Vertical axis represents membrane voltage in bottom panel and normalized leading-edge current at DFT in top panel. Effect of changes in ratio of {tau}s to {tau}m on membrane-response and strength-duration curves is shown for {tau}s/{tau}m=0.1, 0.2, 0.5, 1, 2, 5, and 10. For each value of {tau}s, optimal duration is that which results in maximum voltage on cell membrane at end of pulse. Strength-duration curves decrease to rheobase at this optimal duration and remain constant for longer pulses. Rheobase decreases with increasing {tau}s. Stored energy is minimized when ratio of {tau}s to {tau}m is 1. Corresponding optimal pulse duration is then equal to {tau}m and is denoted by vertical dotted line. For longer-than-optimal pulses, negative slope of membrane response curve is steepest for low values of {tau}s and decreases as {tau}s increases. Exponential average-current strength-duration curve is shown for comparison. It corresponds to limit of leading-edge-current model as {tau}s->{infty}.

Exponential average-current model. The average-current model is based on the hyperbolic strength-duration relation, and the leading-edge-current model results in an exponential one. To permit direct comparison of predictions based on average current with those based on leading-edge current, we derived a new exponential average-current model. It gives the average-current DFT in terms of the average-current {tau}m and the average-current rheobase. The optimal value of {tau}s is {tau}m, and the optimum pulse duration is 1.337 {tau}m. Because average-current {tau}m and leading-edge-current {tau}m may differ, the predicted optimal values of {tau}s are not in general equal for the two exponential models. Fig 1Up shows that the exponential average-current model is the limit of the leading-edge-current model as {tau}s->{infty}.

Biphasic Models
The optimal first phase of the biphasic waveform is assumed to be the optimal monophasic waveform.3 4 Thus, predicted optimal {tau}s is equal for monophasic and biphasic models. The optimal second phase is assumed to prevent refibrillation by removing or "burping" the charge deposited on myocardial cells by phase 1.3 4 12 The initial conditions for phase 2 (cell-membrane voltage and ICD-capacitor voltage) are set equal to the corresponding values at the end of the optimal phase 1 as predicted by each monophasic model. The leading-edge-current model is then used to determine the optimal duration of phase 2. If phase 1 is optimized by an average-current method, the biphasic model becomes a hybrid model, using different methods for each phase.3

Experimental Methods
Patients
Patients undergoing ICD implantation participated in this study after giving written informed consent according to a protocol approved by the Human Subjects Committee. Because of the required number of fibrillation-defibrillation episodes, patients were excluded if their New York Heart Association class for heart failure was 3 or 4 after optimal therapy, their left ventricular ejection fraction was <.25, or a there was a proximal stenosis >=70% in a major coronary artery supplying viable myocardium. Patients were excluded if they had ever received amiodarone, and other antiarrhythmic drugs were discontinued for 5 half-lives. However, therapy with digoxin (4 patients), ß-blockers (7 patients), and calcium channel blockers (1 patient) was continued. Patients were studied at new implants of ICDs with a single transvenous electrode configuration (24 patients) or pulse generator change in patients with a single epicardial electrode configuration (12 patients). Six patients with transvenous ICDs were excluded from this study because the biphasic DFT was too high (see below), and the study was aborted in 1 patient with a transvenous ICD because of hypotension. Thus, complete data were available for 27 patients. They included 18 men and 9 women with a mean age of 59±15 years. The mean left ventricular ejection fraction was 0.39±0.11. Eighteen patients had coronary artery disease, 8 patients had myocardial or congenital disease, and 1 patient had idiopathic long-QT syndrome. The clinical arrhythmia was sustained monomorphic ventricular tachycardia in 16 patients and ventricular fibrillation in 11 patients.

Surgical Technique and Electrode Configurations
Patients were studied intraoperatively as described previously.18 The epicardial defibrillation pathway included a large patch electrode (Medtronic model 6921L) positioned posteriorly over the left ventricle and a large (5 patients) or medium (Medtronic model 6921M) (7 patients) patch electrode positioned anteriorly over the right ventricle. The left ventricular electrode was the cathode, and the right ventricular electrode was the anode. In patients with transvenous electrodes, a tripolar electrode with a 5-cm defibrillation coil (Medtronic model 6966 or 6936) was positioned in the right ventricular apex. The titanium shell of an ICD pulse generator (Active Can Emulator, 83 cm3) was positioned in a retropectoral pocket. The right ventricular coil served as the cathode, and the titanium shell served as the anode.

Defibrillation Waveforms
Models of defibrillation permit estimation of optimal biphasic waveforms from monophasic strength-duration data.3 4 We used monophasic waveforms to minimize the number of variables that might influence calculation of the defibrillation time parameters. Study waveforms were fixed-duration, truncated exponential pulses delivered by an external defibrillator with a nominal 120-µF output capacitance (model 2394, Medtronic Inc). Clinically indicated testing was performed using biphasic pulses with 65% tilt in each phase. Polarity was reversed for phase 2 of biphasic pulses.

Clinical Testing
First, the DFT was determined with biphasic pulses by a step-down or step-up method. The first programmed leading-edge voltage was 400 V, and the step size was 100 V. Patients were excluded from the study if the biphasic DFT exceeded 500 V to avoid the possibility that the monophasic DFT at a pulse width of 1.5 ms would exceed the maximum output of the external defibrillator. This excluded 6 patients with transvenous electrodes.

DFT Testing
Four monophasic pulse durations were tested in random order in each patient: 1.5, 3, 7.5, and 15 ms. The DFT50 was estimated by a previously described delayed three-step up-down algorithm27 28 with 50-V steps. The method for selecting the strength of the first defibrillation test shock is described below. If this shock succeeded, the strength of the second defibrillation test shock was decreased by 50 V. If it failed, the strength of the second shock was increased by 50 V. This process was repeated until there was a reversal of response from success to failure or from failure to success. Then the strength of the next defibrillation test shock was changed by 50 V in the opposite direction. The shock strength before the first reversal of response was the first data point, and the strengths of the subsequent two shocks were the second and third data points. The fourth data point was predicted from the outcome of the third defibrillation shock but not tested. The average of these four data points was taken as the DFT50.

In a delayed up-down algorithm, the number of fibrillation-defibrillation episodes is minimized if the strength of the first test shock is near the DFT50. To estimate the strength of this first test shock, we determined the upper limit of vulnerability29 for the first of the four test waveforms. This approximates the DFT90.29 The method for determining the upper limit of vulnerability was modified to set the strength of the first monophasic upper-limit test shock at 200 V greater than the biphasic DFT and the step size to 100 V. We then set the strength of the first defibrillation test shock to 100 V below the upper limit of vulnerability. In the first 5 patients, the initial test shock for the second waveform tested was equal to the DFT50 for the first waveform. For the third and fourth waveforms, the initial test shock was equal to the average of the DFT50s for the preceding waveforms. Beginning with the sixth patient, the initial test voltage for shocks with duration of 1.5 ms was set 20% higher than that of the other three pulse durations. Defibrillation test shocks were given after 10 seconds of induced ventricular fibrillation. Overall, patients had 14.2±1.4 monophasic defibrillation shocks in this study. They also had three or four biphasic defibrillation shocks for clinical reasons.

Data Acquisition
This method has been described previously.18 Voltage and current waveforms were digitized at 100 kHz with the Mac-Adios Board (GW Instruments) and recorded on a Macintosh computer. A custom-modified oscilloscope emulation program (SuperScope II, GW Instruments) was used to record voltage and current waveforms and to detect the leading- and trailing-edge voltages and currents.

Data Analysis
Mean resistance was determined by averaging the point-by-point quotient of the voltage waveform divided by the current waveform. Pulse duration was calculated as the difference in timing of the leading-edge and trailing-edge voltages. Previously described methods were used to calculate stored energy16 and average current2 18 for shock pulses with a measured capacitance of 122.2±1.6 µF.18 Fig 2Down shows equivalent average-current waveforms for the truncated exponential waveforms tested. We constructed strength-duration curves for each patient by the method of least squares using Matlab 4.2 for the Macintosh (The MathWorks Inc). Average-current strength-duration data were fit to the hyperbolic average-current model of Equation 6Down in the "Appendix" to determine tc and to the exponential average-current model of Equation 9Down to determine average-current {tau}m. To characterize these two strength-duration relations quantitatively, we compared their rheobases and chronaxies. For a constant-current pulse, the relationship between exponential chronaxie and cell-membrane time constant is given by tc={tau}m ln 2=0.693{tau}m.30 Note that this relationship does not apply to the hyperbolic chronaxie and that the chronaxie is not an intrinsic parameter of the exponential model. Unless specified as the exponential chronaxie, we use the term chronaxie in its common usage, given by the hyperbolic model. Leading-edge-current data were fit to a composite curve to determine leading-edge-current {tau}m. The left side of this curve corresponding to t<topt was Equation 4aDown. The right side had a constant current for t>topt. Because of the possibility that time-dependent processes might falsely elevate the leading-edge-current DFT for long pulses,12 31 32 these curves were fit with (four points) and without (three points) the 15-ms data point. The three-point fits are used unless specifically indicated. Calculated time constants were then applied to the corresponding models to estimate optimal waveform parameters for each patient.



View larger version (24K):
[in this window]
[in a new window]
  		Figure 2. Truncated exponential current waveforms (solid lines) and corresponding average-current waveforms (dashed lines) for four pulse widths tested. Four pairs of waveforms result from discharge of 400-V shock into a 59.3-{Omega} transvenous pathway (transvenous patient 5). Leading-edge current is 6.74 A. Average currents for 1.5-, 3.0-, 7.5-, and 15-ms pulses are 6.19, 5.34, 4.17, and 2.84 A, respectively.

Retrospective Validation of Models
Model predictions were validated by retrospective comparison with results from clinical crossover studies of small-capacitor and standard-capacitor waveforms. We first performed a literature search for clinical crossover studies that compared DFTs for a standard 120- to 125-µF capacitor and a smaller capacitor. Studies were excluded if they did not include information required for model predictions, such as pathway resistance. When clinical data were available for both monophasic and biphasic waveforms, we used monophasic data. When only biphasic waveforms were used, we compared their predicted performance on the basis of the first phase. Waveforms with equal tilt were compared for each capacitance. The ratio of stored-energy DFTs of the experimental waveform to the stored-energy DFT of the standard waveform±SEM was determined for each study. To determine the corresponding predicted ratio, we first calculated the ratio of the lowest DFT for an arbitrary capacitance to the lowest DFT for the optimal capacitance for each model. This permitted a prediction of the expected ratio of stored-energy DFTs for the two capacitance values in each clinical study.

Statistical Analysis
We assessed the effect of pulse duration on DFT50 using one-factor repeated-measures ANOVA with pulse duration as the factor. Post hoc analysis was performed by Scheffé's test. The relationship between electrode configuration (epicardial or transvenous) and each time constant was assessed by the unpaired t test. The relationship between pathway resistance and each time constant was assessed by linear regression. In this analysis, resistance was the average value for all four pulse widths. We used SuperANOVA 1.11 for the Macintosh (Abacus Concepts) for ANOVA calculations. Goodness of fit was compared for different models by the paired t test. The relationship between observed DFT ratios in previous clinical studies and predicted ratios was assessed by linear regression. Data are presented as mean±SD. When multiple comparisons were performed, we required a value of P<.05 divided by the number of comparisons. Basic statistics were calculated with the paired two-tailed t test.


*    Results
up arrowTop
 up arrowAbstract
 up arrowIntroduction
 up arrowMethods
 *Results
down arrowDiscussion
 down arrowAppendix 1
 down arrowReferences
 
Table 1Down shows group mean values for the DFT50 at each of the four pulse widths. DFT50 is higher at all pulse widths for transvenous pathways than epicardial pathways (P<.01). Table 2Down shows group mean time constants for each model. Fig 3Down shows best-fit strength-duration curves for each model.


View this table:
[in this window]
[in a new window]
  		Table 1. Defibrillation-Threshold Data


View this table:
[in this window]
[in a new window]
  		Table 2. Model Time Constants and Predicted Optimal Biphasic1 Waveforms



View larger version (25K):
[in this window]
[in a new window]
  		Figure 3. Strength-duration relationships for epicardial pathways (top) and transvenous pathways (bottom). Mean DFT50±SD is shown for average current ({circ}) and leading-edge current ({blacksquare}). For all three curves, cardiac time constants are shorter (P<.06) and rheobase is higher (P<.001) for transvenous pathways than for epicardial pathways. Average-current hyperbolic and exponential curves are similar. They diverge at very long and very short pulse durations beyond range of graph. Vertical lines denote chronaxie (tc) for hyperbolic model, membrane time constants ({tau}m) for two exponential models, and exponential chronaxie (*). See text for discussion.

Average-Current Models
Average-current DFT50 decreased monotonically as pulse width increased. Fig 3Up shows that both average-current models provide a good fit to the data for transvenous and epicardial pathways. For the group as a whole, r2=.97±.02 for the hyperbolic model and r2=.94±.04 for the exponential model. The curves diverge at very long and very short pulse widths. The exponential curves lie above the corresponding hyperbolic curves for very short pulses. As pulse width increases into the clinical range, the negative slope of the exponential curve is steeper, and it falls below the hyperbolic curve. It then makes a sharper bend, crossing the hyperbolic curve to reach a higher rheobase (epicardial: 3.2±0.4 versus 2.4±0.3 A, P<.001; transvenous: 4.8±0.9 versus 3.8±0.7 A, P<.001). This difference in curve shapes is reflected in the lower exponential chronaxie for both epicardial and transvenous pathways (epicardial: 2.7±0.3 versus 4.7±0.8 ms, P<.001; transvenous: 2.2±0.4 versus 3.5±0.5 ms; P<.001).

Leading-Edge-Current Model
The leading-edge-current DFT50 is highest for 1.5-ms pulses for both transvenous and epicardial pathways. The transvenous curve reaches a minimum at 7.5 ms and is unchanged at 15 ms. The epicardial curve has a minimum at 3.0 ms. The epicardial DFT50 is {approx}15% higher at 15 ms than at 3 ms or 7.5 ms. These differences are significant by the paired t test (P<.01) but not by Scheffé's test (3.0 versus 15 ms: P=.24; 7.5 versus 15 ms: P=.30). The fit to the data (r2=.88±.14 for three points, r2=.79±.24 for four points) is not as close as that for the hyperbolic average-current model (P<.005) or exponential average-current model (P<.03). When all four data points were used for curve fitting, the value of {tau}m was lower for epicardial pathways (2.4±0.8 ms, P=.003) but unchanged for transvenous pathways (2.3±0.4 ms, P=.86). Table 2Up shows that {tau}m is lower for the leading-edge-current model than the average-current model for both epicardial pathways (P<.001) and transvenous pathways (P<.001).

Correlation of Electrode Configuration, Pathway Resistance, and DFT With Model Parameters
Table 2Up shows that time parameters for all models were greater for epicardial pathways than for transvenous pathways: tc (P<.001), average-current {tau}m (P<.001), and leading-edge-current {tau}m (P=.06). For the group as a whole, there was a significant inverse correlation between resistance and the average-current time parameters (tc: r2=.48, P<.001; average-current {tau}m: r2=.56, P<.001) but not leading-edge-current {tau}m: r2=.04, P=.34. This correlation between resistance and the average-current time parameters was significant for transvenous pathways (tc=6.531-0.058xR: r2=.57, P=.001; average-current {tau}m=6.457-0.061xR: r2=.72, P<.001) but not for epicardial pathways (tc: r2=.001, P=.94; average-current {tau}m: r2=.01, P=.73).

There was no correlation between current, voltage, or stored-energy DFT and time parameter for any model. For example, r2 for leading-edge-current DFT varied from.004 to.12 for transvenous pathways (P=.21 to.83) and from.02 to.03 for epicardial pathways (P=.64 to.69).

Predicted Optimal Waveforms
Table 2Up shows predicted optimal ICD waveforms. For epicardial pathways, the two average-current models predict similar optimal {tau}s, whereas the leading-edge-current model predicts a lower value (P<.001). For transvenous pathways, optimal {tau}s was greatest for the exponential average-current model, intermediate for the hyperbolic average-current model, and lowest for the leading-edge-current model. All pairwise differences were significant at the level of P<.001. The leading-edge-current model predicts shorter optimal durations for phase 1 than the average-current models (P<.001) and for phase 2 than the hybrid biphasic models (P<.001).

Penalty for Suboptimal Capacitance
Fig 4Down shows the predicted effect on stored-energy DFT of varying capacitance (or {tau}s) for transvenous pathways, provided that the best waveform is used for each capacitance. The curves show each model's predicted "stored-energy penalty" for suboptimal capacitance. They have a steep descending limb for lower-than-optimal capacitance, a relatively flat valley with a nadir at the optimal capacitance, and a gradually sloping ascending limb for higher values. The range of penalties is 9% to 21%, 2% to 6%, 8% to 18%, and 20% to 45% for capacitance values that are 0.5, 1.5, 2, and 3 times optimal, respectively. The penalty for underestimating optimal capacitance by 50% approximates that for overestimating it by 100%. Expressed as multiples of optimal capacitance, the stored-energy penalty over this range is approximately twice as high for the exponential average-current model as either the hyperbolic average-current or leading-edge-current model. From a different perspective, the predicted reduction in DFT achieved by optimizing capacitance for current ICDs ranges from 14% to 21% for a 150-µF capacitor and 5% to 10% for a 100-µF capacitor. The predicted reduction is greatest for the leading-edge-current model, which has the lowest optimal capacitance.



View larger version (30K):
[in this window]
[in a new window]
  		Figure 4. Effect of suboptimal capacitance on predicted DFT. Vertical axis shows normalized stored-energy DFT. Lower horizontal axis shows {tau}s. Corresponding values of capacitance for typical 50-{Omega} transvenous pathway are shown on top horizontal axis. Asterisks denote optimal {tau}s for each model: hyperbolic average-current (*), exponential average-current (**), and leading-edge current (***). Each curve has gradual ascending slope for values of {tau}s between 1 and 3 times optimal, indicating that stored-energy penalty for greater-than-optimal ICD capacitance is small in this range. See text.

Comparison of Model Predictions With Results of Experimental Studies
We identified five clinical studies that met the criteria for retrospective analysis.13 14 15 18 19 Table 3Down shows observed and predicted DFT ratios. Most studies used biphasic waveforms. All three models provide reasonable agreement with observed results for transvenous pathways with experimental capacitance values of 60 to 90 µF. The leading-edge-current model overestimates the performance of 60-µF waveforms for epicardial pathways. The correlation coefficients are comparable for each model: hyperbolic average-current model r2=.80, P=.0011; exponential average-current model r2=.75, P=.0027; leading-edge-current model r2=.84, P=.0005. If the intercept is required to be zero, the correlation coefficients are higher: hyperbolic average-current model r2=.98; exponential average-current model r2=.99; leading-edge-current model r2=.98 (P<.001 for each model). The slope of the zero-intercept regression line (observed DFT ratio/predicted DFT ratio) was 1.04 for the hyperbolic average-current model, 1.04 for the exponential average-current model, and 1.09 for the leading-edge-current model. Thus, all three models underestimated the effect of capacitance on DFT, and the degree of underestimation was greatest for the leading-edge-current model.


View this table:
[in this window]
[in a new window]
  		Table 3. Ratio of Stored-Energy DFT for Experimental Capacitance to DFT for Standard Capacitance in Previous Clinical Studies


*    Discussion
up arrowTop
 up arrowAbstract
 up arrowIntroduction
 up arrowMethods
 up arrowResults
 *Discussion
down arrowAppendix 1
 down arrowReferences
 
The results of this study support the hypothesis that application of human time parameters to models of defibrillation provides a reasonable estimate of the results of clinical studies of ICD capacitance. These models predict that use of 90- to 100-µF capacitors in the present generation of ICDs realizes most of the reduction in DFT that can be achieved by optimizing capacitance.

New Findings Regarding Models of Defibrillation
There are three secondary findings.

1. The hyperbolic and exponential average-current models predict similar optimal waveforms. The exponential strength-duration curve has a higher rheobase and lower chronaxie.

2. Average-current models predict higher values of optimal {tau}s and capacitance than the leading-edge-current model. Average-current and leading-edge-current models are based on different fundamental assumptions. The leading-edge-current model explicitly assumes that the response to a defibrillating pulse depends only on the instantaneous peak value of membrane voltage. In contrast, the average-current models implicitly assume that the cell membrane responds to the average value of the applied field over the pulse. To compare these two methods by use of parallel exponential models, we used a new average-current model with an exponential formulation rather than a hyperbolic one.

3. Time parameters for lower-resistance epicardial pathways are greater than those for higher-resistance transvenous pathways. We found an inverse correlation between pathway resistance (or {tau}s) and both average-current time parameters (tc and {tau}m) for the group as a whole and for transvenous pathways. The minimal overlap in resistances for epicardial and transvenous pathways precluded an analysis to determine whether electrode configuration had an effect on time parameters independent of the effect of resistance. Further, because we studied acute transvenous electrodes and chronic epicardial electrodes, we do not know whether this difference contributed to the observed correlation between electrode configuration and defibrillation time parameters. This correlation was not present for leading-edge-current {tau}m.

Previous Estimates of Defibrillation Time Parameters
Estimates of tc for the hyperbolic average-current model have used average values from several studies in animals: 2.0 ms,1 2.0 ms,4 2.4 ms,3 and 2.7 ms.2 For transvenous defibrillation in dogs, Geddes and Bourland7 used data from Wessale et al33 to calculate a leading-edge-current {tau}m of 1.2, 1.5, and 1.8 ms for trapezoidal pulses with tilt of 50% to 80%. Cleland6 determined values for epicardial leading-edge-current {tau}m of 1.5 ms based on data from Tang et al34 and 1.3, 1.4, and 1.7 ms using three different sets of data from Walker et al.35 Walcott et al4 used the equation tc=0.693{tau}m30 to calculate a value of 2.8 ms for leading-edge-current {tau}m from reported values of hyperbolic average-current tc. However, this equation relates exponential average-current tc to exponential average-current {tau}m, not hyperbolic average-current tc to exponential leading-edge-current {tau}m, as they apply it. Use of time parameters derived by one method in a model based on another method may result in significant error. Our results confirm the prediction of Block et al36 that average-current defibrillation time parameters are higher in humans than in animals. There is only one previous estimate for tc in humans. In a preliminary report of the effect of waveform tilt on DFT, Shorofsky et al37 gave a value of 4.7 ms for pooled data from epicardial, transvenous, and hybrid electrode systems. This value is similar to tc for epicardial pathways in the present study.

Fit of Human Defibrillation Data to Models
Both hyperbolic and exponential average-current models provided a good fit over the range of pulse widths we tested. The better fit of our data to the average-current models than the leading-edge-current model may be due in part to fewer data points on the descending limb of the leading-edge-current curve or use of a composite curve-fitting method for this model. More data points near the anticipated value of {tau}m might have permitted a better fit. We cannot distinguish limitations of curve fitting from limitations of the model.

Comparison of Model Predictions to Experimental Studies of ICD Capacitance
All three models predict that optimal capacitance is proportional to the model's time parameter and inversely proportional to pathway resistance. Experimental studies generally have found a greater beneficial effect of small capacitance on DFT in animals than in humans. In dogs and pigs, smaller 40- to 90-µF capacitors have performed better than conventional 120- to 140-µF capacitors.8 9 10 11 12 In humans, however, 60- to 90-µF capacitors have shown substantial benefit only for high-resistance transvenous pathways.14 18 They have shown modest13 or no14 15 16 17 18 19 benefit for the majority of current clinical transvenous pathways, and 60-µF capacitors have underperformed 120-µF capacitors for epicardial pathways.18

The shape of the predicted "stored-energy DFT penalty" curves provides a possible explanation for the differential effect of capacitance on DFT in animals and humans. For example, the predicted optimal capacitance in both animal and human transvenous pathways is substantially less than values in ICDs, 32 µF1 2 versus 57 µF for the hyperbolic average-current model and 30 µF6 7 versus 45 µF for the leading-edge-current model. However, the corresponding predicted DFT penalties for a 120-µF capacitor are 29% and 37% in animals but only 8% and 16% in humans. Cleland6 shows a similar DFT penalty curve based on animal data and the leading-edge-current model in Fig 7b of that article. Interpolation of this graph gives the penalty for a 120-µF capacitor as {approx}36%. Our results thus provide a conceptual basis for the observations that defibrillation-waveform studies in animals cannot be applied directly to humans. However, if animal time parameters are known, the human time parameters determined in this study may be applied to defibrillation models to estimate corresponding results in humans.

Retrospective comparison of model predictions with results of clinical crossover trials shows that all three models provide reasonable agreement with observed results for experimental capacitance values of 60 to 90 µF. All models underestimated the observed effect of capacitance on DFT. However, model predictions were for the best waveforms with each capacitance, whereas the tested waveforms were not in general optimal for each capacitance. For biphasic waveforms, the degree to which the second phase improved defibrillation efficacy might vary for different durations of each phase.3 12

Implications for Design of ICDs
The stored-energy penalty curves have important implications for design of ICDs because stored energy is a critical determinant of the pulse generator size38 and current capacitor technology limits maximum voltage to {approx}750 V. Suppose, for example, that the population DFT for an ICD with a 100-µF biphasic waveform is 10±4 J for a 50-{Omega} transvenous pathway.13 39 40 Because current technology limits the maximum voltage to {approx}750 V, the maximum output of 28.1 J exceeds the mean DFT+2 SD by 10 J. Using a near-optimal 60-µF waveform will decrease the mean DFT to 9.0 to 9.5±4 J. However, the maximum 16.9-J output of the 60-µF ICD is 0.1 to 0.6 J less than the mean DFT+2 SD. Newer bidirectional transvenous pathways that include both a superior vena cava and active-can electrode have resistances of 30 to 40 {Omega}.17 40 41 For a 35-{Omega} pathway, the predicted optimal capacitance is 65 to 105 µF, and the stored-energy penalty for a 100-µF waveform is 0% to 3%. These considerations suggest that for biphasic waveform defibrillation with current electrode configurations, the penalty incurred by use of {approx}100-µF capacitors in the present generation of ICDs is a small and appropriate price to ensure reliable defibrillation of the vast majority of patients. However, the penalty for 130- to 150-µF capacitors used in earlier ICDs is unnecessary.

Limitations
A major limitation is that current models of defibrillation are considered to be first-order approximations. However, the measured time parameters for human defibrillation can be applied to future models. A second major limitation related to curve fitting for the leading-edge-current model has been discussed. A third major limitation is the accuracy with which the DFT can be determined at four different pulse widths in humans. The number of fibrillation-defibrillation episodes in this study approaches a prudent maximum for clinical protocols. We wish to emphasize three other limitations: (1) {tau}m derived from the exponential strength-duration curves corresponds to a true cell-membrane time constant only in a simple resistor-capacitor model of the cell membrane.24 25 (2) The patient population may not be representative of ICD recipients in general. Because of the number of fibrillation-defibrillation episodes required, we excluded the sickest patients. We also excluded transvenous patients whose DFTs at a pulse duration of 1.5 ms had a high probability of exceeding the maximum output of the defibrillator. Despite this, determination of the transvenous DFT50 at 1.5 ms required shock strengths >800 V (38 J) in 6 patients (40%) and 900 V (49 J) in 2 patients (13%). (3) This study used a single value of capacitance. We do not know how variations in {tau}s caused by changes in capacitance might have affected our results.

Conclusions
When human time parameters are applied to models of defibrillation, they provide a good estimate of the results of clinical studies of ICD capacitance in the range 60 to 125 µF and predict the better performance of small-capacitor waveforms in animals than in humans. Use of 90- to100-µF capacitors realizes most of the predicted reduction in DFT that can be achieved by optimizing capacitance while maintaining a sufficient safety margin for current transvenous electrode configurations.


*    Selected Abbreviations and Acronyms
 
DFT = defibrillation threshold
DFT50 = shock strength with 50% probability of defibrillation
ICD = implantable cardioverter-defibrillator
tc = empirical time parameter chronaxie
{tau}m = time constant for leading-edge current
{tau}s = waveform or system time constant


*    Acknowledgments
 
This study was supported in part by an American Heart Association Greater Los Angeles Affiliate Grant-in-Aid (1085-GI1) and by a grant from the PM foundation to Dr Swerdlow.


*    Appendix 1
up arrowTop
 up arrowAbstract
 up arrowIntroduction
 up arrowMethods
 up arrowResults
 up arrowDiscussion
 *Appendix 1
down arrowReferences
 
Blair's Model
Blair24 25 developed a theoretical relation which describes the passive effects of a shock pulse applied to a cell. The relation is

(1)
where Vm(t) is the cell's membrane potential over time (t), and Vs(t) is the stimulus potential. For defibrillation, Vs(t) represents the field of the applied shock. Blair24 solved Equation 1Up for a stimulus with a constant amplitude. The resultant strength-duration relationship is

(2)
where I(t) is the applied current at the DFT (in this case a constant value) and Ir is the rheobase.

Exponential Leading-Edge-Current Model
This model is derived by solving Blair's relation of Equation 1Up for a capacitively discharged shock pulse described by

(3)
The optimal duration (topt) is the shortest duration that results in the maximum voltage on the cell membrane at the end of the pulse.4 5 6 For pulses shorter than this optimal duration, the strength-duration curve is given by4 5 26

(4A)

(4B)
where I(t) is the applied leading-edge current at the DFT and Inr is the leading-edge-current rheobase at an infinite value of {tau}s. For longer pulses, I(t) remains constant at the value given by Equation 5Down.

(5)
Note that Equation 4aUp reduces to Equation 2Up as {tau}s->{infty}. Intuitively, this can be appreciated by noting that a truncated-exponential waveform approaches a constant-current pulse as {tau}s->{infty}.

Average-Current Hyperbolic Model
The empirical strength-duration relation is

(4)
where Iavg is the average-current DFT of a pulse with duration (t), tc is the chronaxie, and Ir is the average-current rheobase. Note that {tau}s does not appear explicitly as a term in the average-current hyperbolic model. Instead, it is implicit in the expression for average current of a truncated exponential pulse in Equation 7Down

(6)
where C is the capacitance of the ICD and V is the leading-edge voltage.

Effective Current
Kroll developed the concept of effective current (Ie) to derive the optimal pulse width and {tau}s (or capacitance) for the hyperbolic average-current model. For a shock pulse, Ie is defined as "the rheobase requirement that it can satisfy."2

(7)
Kroll2 used this concept of Ie to optimize pulse width and capacitance or {tau}s in two steps. First, he found the pulse width that maximized Ie for a given {tau}s. Then, using this optimal pulse width, he determined the value of {tau}s that maximized Ie for a fixed stored energy (Es).

Exponential Average-Current Model
This model is based on the strength-duration relation in Equation 2Up if the constant current (I) is replaced by the average current over the pulse (Iavg).

(8)
Note that as in the hyperbolic average-current model, {tau}s is implicit in the expression for average current. The optimal value of pulse width and {tau}s are derived by use of the effective-current method in analogy to Kroll's approach for the hyperbolic average-current model. We insert the expression for average current of a truncated exponential pulse from Equation 7Up into Equation 9Down, substitute Ie for Ir, and solve for Ie:

(9)
We then calculate the optimal pulse width and {tau}s by Kroll's method for the hyperbolic average-current model. First, the pulse width that maximizes Ie for a given {tau}s is determined by differentiating Equation 9Up with respect to t and solving for its zero. This gives topt =1.337x{tau}m. Then this optimal pulse width is substituted into Equation 9Up. Remembering that V=(2Es/C), where Es is stored energy, we differentiate Ie with respect to {tau}s for a fixed stored energy (Es) and solve for its zero. We find that {tau}s={tau}m maximizes Ie with respect to {tau}s for a fixed value of Es.

Received April 3, 1997; revision received June 16, 1997; accepted June 19, 1997.


*    References
up arrowTop
 up arrowAbstract
 up arrowIntroduction
 up arrowMethods
 up arrowResults
 up arrowDiscussion
 up arrowAppendix 1
 *References
 

  1. Irnich W. Optimal truncation of defibrillation pulses. Pacing Clin Electrophysiol. 1995;18:673-688.
  2. Kroll M. A minimal model of the monophasic defibrillation pulse. Pacing Clin Electrophysiol. 1993;16:769-777.[Medline] [Order article via Infotrieve]
  3. Kroll M. A minimal model of the single capacitor biphasic defibrillation waveform. Pacing Clin Electrophysiol. 1994;17:1782-1792.[Medline] [Order article via Infotrieve]
  4. Walcott G, Walker R, Cates A, Krassowska W, Smith W, Ideker R. Choosing the optimum monophasic and biphasic waveforms for defibrillation. J Cardiovasc Electrophysiol. 1995;6:700-710.[Medline] [Order article via Infotrieve]
  5. Cleland B. A conceptual basis for pacing waveforms. Pacing Clin Electrophysiol. 1996;19:1177-1185.[Medline] [Order article via Infotrieve]
  6. Cleland B. A conceptual basis for defibrillation waveforms. Pacing Clin Electrophysiol. 1996;19:1186-1195.[Medline] [Order article via Infotrieve]
  7. Geddes L, Bourland J. Tissue simulation: theoretical considerations and practical applications. Pacing Clin Electrophysiol. 1988;11:131-137.
  8. DeGroot P, Norenberg M, Mehra R. Effect of capacitance on defibrillation threshold in dogs. Am Heart J. 1994;128:640. Abstract.
  9. Hahn S, Heil J, Lin Y, Derfus D, Lang D. Improved defibrillation with small capacitance and optimized biphasic waveform. Circulation. 1994;90(suppl I):I-175. Abstract.
  10. Leonelli F, Kuo C-S, Fujimura O, Kroll MW, Koch C. Defibrillation thresholds are lower with small output capacitor values. Pacing Clin Electrophysiol. 1993;16-II:888. Abstract.
  11. Rist K, Tchou P, Mowrey K, Kroll M, Brewer J. Smaller capacitors improve the biphasic waveform. J Cardiovasc Electrophysiol. 1994;5:771-776.[Medline] [Order article via Infotrieve]
  12. Swerdlow C, Fan W, Brewer J. Charge-burping theory correctly predicts optimal ratios of phase duration for biphasic defibrillation waveforms. Circulation. 1996;94:2278-2284.[Abstract/Free Full Text]
  13. Bardy G, Poole J, Kudenchuk P, Dolack G, Raitt M, Jones G, Mehra R, Troutman C, Anderson J, Johnson G. A prospective randomized comparison in humans of biphasic waveform 60-µF and 120-µF 65% capacitance pulses using a unipolar defibrillation system. Circulation. 1995;91:91-95.[Abstract/Free Full Text]
  14. Swerdlow C, Kass R, Hwang C, Raissi S, Chen P. Short biphasic pulses from 90 microfarad capacitors lower defibrillation threshold. Pacing Clin Electrophysiol. 1996;19:1053-1060.[Medline] [Order article via Infotrieve]
  15. Block M, Hammel D, Bocker D, Brunn J, Seifert T, Scheld H, Breithardt G. ICD device size can be reduced by smaller capacitors. J Am Coll Cardiol. 1995;25:86A. Abstract.
  16. Block M, Breithardt G. Optimizing defibrillation through improved waveforms. Pacing Clin Electrophysiol. 1995;18:536-538.
  17. Jung W, Moosdorf R, Korte T, Wolpert C, Spehl S, Bauer T, Manz M. Effect of capacitance on the defibrillation threshold in patients using a new unipolar defibrillation system. Circulation. 1994;90(suppl I):I-229. Abstract.
  18. Swerdlow C, Kass R, Hwang C, Chen P-S, Raissi S. Effect of capacitor size and pathway resistance on defibrillation threshold for implantable defibrillators. Circulation. 1994;90:1840-1846.[Abstract/Free Full Text]
  19. Poole J, Kudenchuk P, Dolack G, Raitt M, Jones G, Mehra R, Troutman C, Anderson J, Johnson G, Bardy G. A prospective randomized comparison in humans of 90 µF and 120 µF biphasic pulse defibrillation using a unipolar pectoral transvenous defibrillation system. J Cardiovasc Electrophysiol. 1995;6:1097-1100.[Medline] [Order article via Infotrieve]
  20. Weiss G. Sur la possibilité de rendre comparable entre eux les appareils survant a l'excitation electrique. Arch Ital Biol. 1901;35:413-446.
  21. Lapicque L. Definition expérimentalle de l'excitabilité. Proc Soc Biol. 1909;77:280-285.
  22. Bourland JD, Tacker WA, Geddes LA. Comparative efficacy of damped sine waves and square wave current for transchest ventricular defibrillation in animals. Med Instrum. 1978;12:42-45.[Medline] [Order article via Infotrieve]
  23. Bourland JD, Tacker WA, Geddes LA. Strength duration curves for trapezoidal waveforms of various tilts for transchest defibrillation in animals. Med Instrum. 1978;12:38-41.[Medline] [Order article via Infotrieve]
  24. Blair H. On the intensity-time relations for stimulation by electric currents, I. J Gen Physiol. 1932;15:709-729.[Abstract/Free Full Text]
  25. Blair H. On the intensity-time relations for stimulation by electric currents, II. J Gen Physiol. 1932;15:731-755.[Abstract/Free Full Text]
  26. Reilly J, Larkin W. Electrocutaneous stimulation with high voltage capacitive discharges. IEEE Trans Biomed Eng. 1983;30:631-641.[Medline] [Order article via Infotrieve]
  27. McDaniel W, Schuder J. An up-down algorithm for estimation of the cardiac ventricular defibrillation threshold. Med Instrum. 1988;22:286-292.
  28. Tacker W, Geddes L. Electrical Defibrillation. Boca Raton, Fla: CRC Press; 1980:41.
  29. Swerdlow C, Ahern T, Kass R, Davie S, Mandel W, Chen P-S. Upper limit of vulnerability is a good estimator of shock strength associated with 90% probability of successful defibrillation in humans with transvenous implantable cardioverter defibrillators. J Am Coll Cardiol. 1996;27:1112-1117.[Abstract]
  30. Plonsey R, Barr R. Bioelectricity: A Quantitative Approach. New York, NY: Plenum Press; 1988:143-144.
  31. Schuder J, Stoeckle H, JA W. Transthoracic ventricular defibrillation in the dog with truncated exponential stimuli. IEEE Trans Biomed Eng. 1971;18:410-415.[Medline] [Order article via Infotrieve]
  32. Chapman PD, Wetherbee JN, Vetter JW, Troup P, Souza J. Strength-duration curves of fixed pulse width variable tilt truncated exponential waveforms for nonthoracotomy internal defibrillation in dogs. Pacing Clin Electrophysiol. 1988;11:1045-1050.[Medline] [Order article via Infotrieve]
  33. Wessale J, Bourland J, Tacker W, Geddes L. Bipolar catheter defibrillation in dogs using trapezoidal waveforms of various tilts. J Electrocardiol. 1980;13:359-366.[Medline] [Order article via Infotrieve]
  34. Tang A, Yabe S, Wharton J, Dolker M, Smith W, Ideker R. Ventricular defibrillation using biphasic waveforms: the importance of phasic defibrillation. J Am Coll Cardiol. 1989;13:207-214.[Abstract]
  35. Walker R, Walcott G, Smith W, Ideker R. Strength duration curves for short time constant truncated exponential monophasic waveforms. Pacing Clin Electrophysiol. 1993;16:915. Abstract.
  36. Block M, Hammel D, Bocker D, Borggrefe M, Budde T, Isbruch F, Scheld H, Breithardt G. Biphasic defibrillation using a single capacitor with large capacitance: reduction of voltages and ICD device size. Pacing Clin Electrophysiol. 1996;19:207-214.[Medline] [Order article via Infotrieve]
  37. Shorofsky S, Foster A, Gold M. The effect of tilt on defibrillation efficacy. J Am Coll Cardiol. 1994;23:86A. Abstract.
  38. Nelson R. The pulse generator. In: Kroll M, Lehmann M, eds. Implantable Cardioverter-Defibrillator Therapy: The Engineering-Clinical Interface. Norwell, Mass: Kluwer Academic Publishers; 1996:241-256.
  39. Bardy G, Yee R, Jung W. Multicenter experience with a pectoral unipolar implantable defibrillator. J Am Coll Cardiol. 1996;28:400-410.[Abstract]
  40. Bardy G, Dolack G, Kudenchuk P, Poole J, Mehra R, Johnson G. Prospective, randomized comparison in humans of a unipolar defibrillation system with that using an additional superior vena cava electrode. Circulation. 1994;89:1090-1093.[Abstract/Free Full Text]
  41. Taylor P, Haugh C, Estes M, Prystowsky E. A randomized clinical trial comparing the Ventak PRx III HC with the Ventak PRx III implantable defibrillator. Pacing Clin Electrophysiol. 1996;19:653. Abstract.



This article has been cited by other articles:


Home page
 Am. J. Physiol. Heart Circ. Physiol.Home page
F. Qu, L. Li, V. P. Nikolski, V. Sharma, and I. R. Efimov
Mechanisms of superiority of ascending ramp waveforms: new insights into mechanisms of shock-induced vulnerability and defibrillation
Am J Physiol Heart Circ Physiol, August 1, 2005; 289(2): H569 - H577.
[Abstract] [Full Text] [PDF]

Home page
 EuropaceHome page
K. A. Mowrey, Y. Cheng, P. J. Tchou, and I. R. Efimov
Kinetics of defibrillation shock-induced response: design implications for the optimal defibrillation waveform
Europace, January 1, 2002; 4(1): 27 - 39.
[Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow