Europace Advance Access originally published online on June 5, 2007
Europace 2007 9(9):711-716; doi:10.1093/europace/eum109
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IMPLANTABLE CARDIOVERTER-DEFIBRILLATORS
Parameters characterizing implantable defibrillator output: a proposal
1 Justus-Liebig-University, University Hospital, Friedrichstr. 18, 35392 Giessen, Germany
Manuscript submitted 28 February 2007. Accepted after revision 27 April 2007.
Corresponding author. Tel: +49 641 99 41390; fax: +49 641 99 41399. E-mail address: werner{at}irni.ch or irnich{at}technik.med.uni-giessen.de
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Abstract |
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 Top Abstract IntroductionConsiderations on defibrillationResultsDiscussionConclusionAppendix AAppendix BAcknowledgementReferences |
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Aims Recently, a discussion was carried out in Heart Rhythm on the specifications that could characterize implantable defibrillators. It is the intention of this paper to participate in this discussion on defibrillation characteristics and to give recommendations on how this problem could be solved.
Theoretical considerations and results There are different defibrillation theories, all finding that the defibrillation's efficacy depends on the time constant RC which is output capacitance C times load resistance R. Efficacy decreases with increasing RC. This means that (i) the knowledge of C is of paramount importance, (ii) the energy is ‘devalued’ with increasing RC and that those parameter settings such as tilt or pulse duration should be adjusted to the time constant, and (iii) the energy values given without further specification are not meaningful. As there is always a voltage drop across an internal resistance within the ICD, the measured voltage across the output differs from the capacitor voltage and is reduced which determines the efficiency of the device. From the data given by Thammanomai et al., one can determine the parameters maximum voltage, capacitance, internal resistance, and tilt. These parameters are adequate and necessary to describe an ICD device and to derive the effective energy for device comparison.
Discussion The ‘high output devices’ with their high nominal energy are reduced in their effective energies to a degree that they are comparable to the best ‘standard output devices’. They do not offer that superiority which is promised by the nominal energy. Moreover, if the tilt is fixed and larger than optimal, the energy requirements are still higher or the effective energy will further drop. The term ‘delivered energy’ is not used by us because the delivered energy increases with increasing tilt. However, today's tilts are too large as judged by theories, which means that high delivered energies can be worse than lower ones. The delivered energy is, therefore, not a meaningful parameter in judging ICDs.
Conclusion ICD devices should be characterized by: (i) voltage, (ii) capacitance, (iii) tilt or pulse duration (if not programmable), and (iv) internal resistance. All other parameters can be derived from them by simple calculations. Introduction of a ‘devaluation factor’ characterizes the decreasing efficacy with increasing time constant and renders the output characteristics transparent and comparable.
Key Words: Implantable defibrillator, Output specifications, Defibrillation theory, Technical efficiency, Physiological efficacy, Devaluation factor, Optimal truncation
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Introduction |
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TopAbstractIntroductionConsiderations on defibrillationResultsDiscussionConclusionAppendix AAppendix BAcknowledgementReferences |
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There was recently a paper by Thammanomai et al.1
and an editorial commentary by Swerdlow2 in Heart Rhythm discussing ‘ICD specifications that realistically characterize key aspects of product performance’. Whereas Thammanomai et al. remark on a lack of standardization in reporting output characteristics (mainly stored and delivered energy), Swerdlow2 states correctly that ‘voltage influence defibrillation directly. In contrast, energy does not’. His example of a 9 V battery that produces 30 J within 15 s into a 40 
load heart resistance is an excellent example of how misleading the parameter ‘energy’ can be and proving the correctness of the quotation that one has to differentiate between ‘bad joules and good joules in defibrillation’.3
It is the intention of this paper to participate in the discussion on defibrillation characteristics and to try to answer the question ‘what really matters?’ posed by Swerdlow.2 The data given will hopefully help ‘to choose the most suitable device to meet individual patients need’.1 Our recommendations are based on theoretical considerations on defibrillation which we developed and published during the last 19 years.3–5 To make them retraceable, Appendix A was added with the essential figures of our theory. Equally, the physical formulation and derivation of parameters of a capacitor discharge pulses are presented in Appendix B to have the following text not burdened by too many formulae which, however, are important to describe different ICD devices and to make them comparable.
Terminology used. Efficiency: engineering measure that means ratio of useful power output to the power input of a device, usually characterized by 
. Efficacy: physiological measure of how defibrillation pulse energy deviates from optimum (Appendix A) characterized by 
. Effectiveness: the product of: · = 
, combining both engineering and physiological aspects.
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Considerations on defibrillation |
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TopAbstractIntroductionConsiderations on defibrillationResultsDiscussionConclusionAppendix AAppendix BAcknowledgementReferences |
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There are different defibrillation theories3
,6–8 all finding that the defibrillation's efficacy depends on the time constant RC of the output current pathway, which is output capacitance times load resistance (= lead resistance + tissue resistance). The curves for stored and delivered energy as a function of time constant RC are bowl-like (Figure 1) with a distinct minimum.3 Swerdlow calculated a time constant of 3.5 ms corresponding to a capacitance of 87.5 µF loaded with 40 , to be optimal.2 Other investigators3,6 found independently from each other that the optimal time constant RC is calculated to lie at 0.8 times chronaxie (about 2 ms) or RCoptimal = 1.6 ms. This would yield an optimal capacitance of 40 µF, if a load resistance of 40 is assumed. For other resistances, for instance, 35 or 50 , the optimal capacitance would change to 45.7 or 32 µF, respectively. These theoretical considerations are of clinical impact: all time constants larger than optimal need more energy to reach defibrillation threshold (Figure 1). This implies the following. - The knowledge of the output capacitance is of paramount importance.
- The product of load resistance times capacitance determines the efficacy of defibrillation.
- Parameter settings such as tilt or pulse duration should be adjusted to the time constant (Figures A.2 and A.3).
- Any energy value without further specification is not meaningful.
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Our theory on optimal truncation of defibrillation pulses which is briefly described in Appendix A predicts an increase in energy threshold with increasing time constant RC3 beyond the minimum of 1.6 ms or, in other words, the stored energy is less efficacious with increasing RC or the ‘joules’ are ‘devalued’. The stored energy at any time constant RC can be normalized to the most efficacious energy at RC = 1.6 ms yielding the normalized stored energy (NSE) as is depicted in Figure 1. The reciprocal value of NSE forms a ‘devaluation factor’
with which the efficacy of energies of ICDs with different capacitances can be judged (Figure 2). Table 1 lists the devaluation factor together with the tilt or the pulse duration for which it was calculated. Other tilts or pulse durations as given in Table 1 would yield still lower devaluation values, as a lower tilt or shorter pulse duration leaves unused but useful energy on the output capacitance. A higher tilt or pulse duration is unfavourable because it can cause refibrillation. The devaluation factor can also be approximated by Eq. (A.1), which was gained from Table 1 by a log–log correlation:
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As there is always a voltage drop across an internal resistance Rint in each ICD device, the measured voltage across the output differs from the voltage stored on the capacitor and is reduced by a factor r according to Eq. (A.5) in Appendix B. This factor r depends on the load resistance that is assumed. Thammanomai et al.1
used a load resistance of 40 as representative load. The same considerations can be carried out with any other load resistances; we also investigated 50 . The factor r2 yields the efficiency with respect to stored or delivered energy [Eq. (A.7) in Appendix B].
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Finally, the product of the efficiency
and the efficacy forms a ‘factor of overall effectiveness’ that comprises internal loss and physiological efficacy:
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Results |
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TopAbstractIntroductionConsiderations on defibrillationResultsDiscussionConclusionAppendix AAppendix BAcknowledgementReferences |
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From the data given by Thammanomai et al.,1
one can calculate with Eq. (A.3) the capacitances of the listed defibrillators from their stored energies and their maximum voltages (voltages with 75 were taken and corrected for internal loss). Thus, we can give with Table 2 a different version of the ICD characteristics than Thammanomai et al.1 gave with their Tables 1 and 2. The capacitance values in Table 2 are individual ones and may differ from manufacturer's information, as the capacitance tolerance may amount to up to 10%. We use the term ‘capacitance’ rather than ‘capacitor’ because most ICDs have for reasons of limiting voltage stress two output capacitors in series.
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The parameters maximum voltage, capacitance, internal resistance, and tilt (or corresponding pulse duration) are prerequisite to describe an ICD device adequately.
The maximum nominal stored energy can be calculated with Eq. (A.2), the efficiency with Eqs. (A.5), (A.6), and (A.7), and the efficacy may be taken from Table 1 or the corresponding approximation equation. The effective energy results from the nominal energy multiplied with the factor of effectiveness with Eqs. (A.13) and (A.14). All these derived parameters are now entered into Tables 3 and 4 that allow for comparison of the different devices for 40 or 50 load resistance, respectively. The manufacturer's tilt is also confronted with the optimal tilt (Appendix A) for the first phase of the defibrillation pulse according to our theory.
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Discussion |
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TopAbstractIntroductionConsiderations on defibrillationResultsDiscussionConclusionAppendix AAppendix BAcknowledgementReferences |
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From Tables 3 and 4, one can derive what portion of the nominal energy is only physically efficient due to internal loss of energy, characterized by the factor
, and what portion is physiologically efficacious due to the increase in threshold with time constant, characterized by the devaluation factor . This devaluation factor in Table 1 is the key for comparing the effective energies of different ICD devices. By the way, the above example of a 9 V DC battery delivering 30 J into a 40 load, as mentioned by Swerdlow2 can be judged by theory: if RC goes to infinity (this means DC), is going to zero or defibrillation with 9 V is impossible.
The so-called ‘high output devices’ in Tables 3 and 4 (the first four models) with their high nominal energies are reduced in effective energies to a degree that they are comparable to the best ‘standard output devices’. In any case, they do not offer that superiority which is promised by the nominal energy. Moreover, if the tilt is fixed and larger than optimal, the energy requirements are still higher or the effective energy will further drop. The GDT standard output devices are so unfavourable because of their high capacitance that lowers the devaluation factor to 76 or 68%, respectively.
We do not use ‘delivered energy’ at all for the three reasons.
- Equations (A.11) and (A.12) indicate that the delivered energy is higher if the tilt is greater. However, today's tilts are too large as judged by theories. This means that high delivered energies can be worse than lower ones.
- It is questionable whether the delivered energy of only the first phase or both phases of a biphasic pulse counts in defibrillation.
- According to Eq. (A.12), the tilt T derives unambiguously the delivered energy from the stored energy; both are not independent from another.
The delivered energy is, therefore, no meaningful parameter in judging ICDs in our opinion.
Tables 3 and 4, now, contain the data which help ‘to choose the most suitable device to meet individual patients need’.1 The tilts of MDT Maximo and Marquis are close to the optimal tilt if 40 or 50 can be assumed. The programmable tilt (or the corresponding pulse duration) would best-fit patients need regardless of their RC values.5 The best system with lowest energy loss in Tables 3 and 4 is the SJM Epic as it has the highest devaluation factor due to its smallest output capacitance. Tables 3 and 4 demonstrate further how misleading nominal energy can be. The highest nominal energy is in the high output device ‘Atlas’ with 42 J, but its effective energy is with 32 J (40 )/31 J (50 ) only 14.3/14.8% higher than that of its ‘standard output’ brother ‘Epic’. If the tilt is larger than optimal (right column in Table 3), the effective energy is further reduced. Under this aspect, the ‘high output devices’ with 60 or 65% tilts are surely less effective than the best devices with standard output and optimized pulse duration or tilt.
If the load is assumed with 50 instead of 40 , the efficiency increases but the efficacy decreases. The overall effectiveness , therefore, does not change much; it decreases to 95.9% (mean value) for 50 when compared with 40 . Table 4 in comparison with Table 3 shows the influence of the time constant on the effective energy and on the optimal tilt. The higher the load resistance is, the more unfavourable is a fixed tilt setting.
It remains to be explained why we use ‘stored energy’ as the describing parameter, though it is physically the electric field via the voltage that influences defibrillation directly. The defibrillation community is so accustomed to ‘energy’ and its associated ‘joules’ that any other parameter is unlikely to gain wide acceptance. Though energy is acting indirectly on defibrillation, the devaluation factor takes into account that two energies with equal amount of joules are not equally efficacious if the time constants are different.
Our proposal of using a theoretically derived devaluation factor for ICD comparison provokes the question whether our theory has been verified by experimental investigations. The answer is clearly ‘yes’. There are four published defibrillation studies9–12 that confirm, in practice, that the stored energy is lowest if the tilt is close to our theoretical value. We could explain the results in the light of our theory and published them as letters to the editor.13–16
Despite all discussions on pulse duration or tilt adjustment as a function of time constant, manufacturers have not yet rid themselves from the philosophy that there is only one optimal tilt under all circumstances. Initially, this tilt was 80%, then it was reduced to 65% to have a higher leading edge voltage for the second phase in biphasic pulses. That the manufacturer SJM with its pulse duration programmability recommends a 65% tilt for every output resistance is a clear evidence thereof.
Additionally, we have investigated defibrillation thresholds in 12 pigs. We found that an optimized pulse from an output capacitance of 148 µF needed 30.2% lower stored energy than a 65/65% tilt pulse to reach thresholds. This result is highly significant (P = 0.001). Even a pulse with half the optimal pulse duration had a 13.7% lower energy (P = 0.03) than a 65/65% tilt pulse. The time constants ranged between 5.6 and 8.1 ms, mean value 6.6 ms, which is practically the same time constant range as that of Tables 3 and 4 (4.1–8.4 ms). These results are not published yet.
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Conclusion |
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TopAbstractIntroductionConsiderations on defibrillationResultsDiscussionConclusionAppendix AAppendix BAcknowledgementReferences |
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In our opinion, implantable defibrillation devices should be characterized by: (i) maximum voltage, (ii) capacitance, (iii) tilt or pulse duration (if not programmable), and (iv) internal resistance. All other parameters can be derived from them by simple calculations. Introduction of the devaluation factor
characterizing the decreasing efficacy with increasing time constant renders the output characteristics transparent and comparable. The need for programmable tilts or pulse durations can be deduced from our results. |
Appendix A |
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TopAbstractIntroductionConsiderations on defibrillationResultsDiscussionConclusionAppendix AAppendix BAcknowledgementReferences |
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Theoretical considerations
Optimal truncation of exponential pulses
We have developed within nearly two decades a theory of stimulation, defibrillation, and shock wave optimization3
–5 that allows determination and calculation of nearly all parameters of shock delivery (see Table A in Irnich3). The term ‘theory’ seems us to be insofar adequate as it comprises ‘a system of assumptions, accepted principles, and rules of procedure devised to analyze, predict or otherwise explain the nature of a specified set of phenomena’.17 Starting point is a stimulation model that assumes activation of sodium channels by exogenic electric fields. This idea leads to a stimulation law that we called ‘fundamental law of electrostimulation’ in analogy to Weiss' ‘formule fondamentale’ as it combines the electric field model4 with the straight threshold line of Weiss18 and with the terminology of Lapicque.19 Optimization of defibrillation pulses is based on two assumptions.3 They are as follows. - Defibrillation obeys the ‘fundamental law of electrostimulation’, i.e. a hyperbolic strength–duration relationship exists similar to that of cardiac stimulation.3,20 This means that the integral over the electric field E of the defibrillation pulse depends on pulse duration PD in a linear manner3,4:
where Erheo is the rheobase field strength with PD going to infinity, tch the chronaxie time, at which E(t) is twice the rheobase.
(A.1)
- To avoid refibrillation, any capacitor-discharge voltage must not drop below rheobase (Figure A.1), beneath which no further contribution to defibrillation is achieved. Thus, we assume the trailing edge voltage to be equal to rheobase voltage. This assumption is used in analysing the characteristics of an exponentially decaying pulse resulting from the discharge of a capacitor into a pure resistance.3
To produce an adequate electric field, a voltage is needed that, for its part, must be adjusted to a ‘hyperbolic strength-duration-function’ with the parameters ‘chronaxie’ and ‘rheobase’. Together with the current flow, an energy is consumed that can be calculated according to the rules of electrical physics. All physical parameters are not independent from each other so that defibrillation can be described in several terms that are physically combined (see Table A of Irnich3), but all dependent on time constant RC of a capacitor discharge.
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Truncation when rheobase is reached is insofar ‘optimal’ as a tilt or pulse duration shorter than optimal means that there is useful energy left on the output capacitance which remains, however, unused. A tilt or pulse duration longer than optimal can be refibrillating. This means that there is a specific optimal pulse duration or tilt depending on the time constant of the capacitor discharge pulse (Figures A.2 and A.3). Knowing the pulse generator's output capacitance and measuring the load resistance (lead and tissue resistance) provide the time constant that can be used together with the chronaxie to obtain the optimal pulse duration or optimal tilt that should be programmed.
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Our optimization theory allows for determination of all relevant physical parameters of delivery of a shock (see Table A in Irnich3). Figure 1 shows the normalized stored energy (NSE), i.e. it is related to the minimum energy which is situated at RC = 1.6 ms.3
The energy needed to reach threshold level increases with increasing time constant RC. The same fact can also be expressed in that the energy is ‘devalued’ with increasing time constant RC. Thus, the reciprocal value of the NSE, as it is depicted in Figure 2, can be used as a ‘devaluation factor’ which is a measure of efficacy of the stored energy as a function of time constant RC. Conflict of interest: none declared.
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Appendix B |
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TopAbstractIntroductionConsiderations on defibrillationResultsDiscussionConclusionAppendix AAppendix BAcknowledgementReferences |
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Physical considerations
If voltage V and capacitance C are known, the stored energy Es can simply be calculated by Eq. (A.2):
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| (A.2) |
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| (A.3) |
The delivered energy needs the additional knowledge of the voltage to which the capacitance was discharged during pulse duration from the initial leading edge voltage Vlead to the trailing edge voltage Vtrail:
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| (A.4) |
As there is always a voltage drop across an internal resistance Rint associated with each ICD device, the measured voltage across the output Vmeas differs from the capacitor voltage Vcap and is reduced by a factor r according to Eq. (A.5)1:
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| (A.5) |
The ratio Rint/Rload depends on load resistance; with 40 assumed, it is on the order of about 4%, so that an approximation can be introduced to simplify Eq. (A.5):
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| (A.6) |
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| (A.7) |
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| (A.8) |
) and (8) can be substituted by the tilt:
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| (A.9) |
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| (A.10) |
Equation (A.8) can, then, be expressed by:
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| (A.11) |
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Eq. (A.11) can be written as:
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| (A.12) |
with the efficacy factor yields the effectiveness factor as the product:
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| (A.13) |
Thus, the effective stored energy can be derived from efficiency and efficacy as:
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| (A.14) |
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Acknowledgement |
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TopAbstractIntroductionConsiderations on defibrillationResultsDiscussionConclusionAppendix AAppendix BAcknowledgementReferences |
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We cordially thank Dr Mary-Kay Steen-Mueller for her valuable linguistic assistance.
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References |
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TopAbstractIntroductionConsiderations on defibrillationResultsDiscussionConclusionAppendix AAppendix BAcknowledgementReferences |
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[1] Thammanomai A, Sweeney MO, Eisenberg SR. A comparison of the output characteristics of several implantable cardioverter-defibrillators. Heart Rhythm (2006) 3:1053–9.[CrossRef][Web of Science][Medline]
[2] Swerdlow ChD. Editorial commentary: ICD waveforms: what really matters? Heart Rhythm (2006) 3:1060–2.[CrossRef][Web of Science][Medline]
[3] Irnich W. Optimal truncation of defibrillation pulses. Pacing Clin Electrophysiol (1995) 18:673–88.[CrossRef][Medline]
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[5] Irnich W. How to program pulse duration or tilt in implantable cardioverter defibrillators. Pacing Clin Electrophysiol (2003) 26:453–6.[CrossRef][Medline]
[6] Kroll MW. A minimal model of the monophasic defibrillation pulse. Pacing Clin Electrophysiol (1993) 16:769–77.[CrossRef][Medline]
[7] Cleland BG. A conceptual basis for defibrillation waveforms. Pacing Clin Electrophysiol (1996) 19:1186–95.[CrossRef][Medline]
[8] 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) 90:1840–6.
[9] Natale A, Sra J, Krum D, Dhala A, Deshpande S, Jazayeri M, et al. Relative efficacy of different tilts with biphasic defibrillation in humans. Pacing Clin Electrophysiol (1996) 19:197–206.[CrossRef][Medline]
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[11] Schauerte P, Schoendube FA, Grossmann M, Messmer BJ, Hanrath P, Stellbrink Ch. Optimized pulse durations minimize the effect of polarity reversal on defibrillation efficacy with biphasic shocks. Pacing Clin Electrophysiol (1999) 22:790–7.[CrossRef][Medline]
[12] Sweeney MO, Natale A, Volosin K, Swerdlow ChD, Baker JH, Degroot P. Prospective randomized comparison of 50%/50% versus 65%/65% tilt biphasic waveform on defibrillation in humans. Pacing Clin Electrophysiol (2001) 24:60–5.[CrossRef][Medline]
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[15] Irnich W. Polarity reversal and optimal truncation—letter to the editor. Pacing Clin Electrophysiol (1999) 22:1851.[CrossRef][Medline]
[16] Irnich W. Letter to the editor: is the optimal tilt really unknown? Pacing Clin Electrophysiol (2001) 24:1577–8.[CrossRef][Medline]
[17] Morris W, ed. The American Heritage Dictionary of the English Language (1976) Boston: Houghton Mifflin Company. 1335.
[18] Weiss G. Sur la possibilité de rendre comparable entre eux les appareils servant a l'excitation électrique. Arch Ital Biol (1901) 35:413–46.[Medline]
[19] Lapicque L. Définition experimental de l'exabilité. Soc Biol (1909) 77:280–3.
[20] Tacker WA, Geddes LA. Electrical Defibrillation (1980) Boca Raton FL: CRC Press. Chapter 1.
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