# A Population-Based Method for the Estimation of Defibrillation Energy Requirements in Humans

## Assessment of Time-Dependent Effects With a Transvenous Defibrillation System

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## Abstract

*Background* A weighted logistic regression analysis was developed to allow pooling of patient data for the study of the stability of defibrillation energy requirements with a new nonthoracotomy lead defibrillation system.

*Methods and Results *One hundred twenty patients were prospectively studied with a single-model nonthoracotomy implantable cardioverter defibrillator (ICD) system at the time of implant and at 3 months. The pooled data of all shocks delivered to all patients were fitted to a logistic function to construct a defibrillation voltage/energy dose-response relationship. The crude logit curve was weighted in quartiles according to the average shock energy delivered per patient. Shocks at implant (n=802; 6.6±2.5 shocks/patient) and follow-up (n=292; 2.4±1.2 shocks/patient) were analyzed. The modeled voltage/energy required for 50% successful defibrillation (95% CI) in the pooled data was 367 V (273, 461) and 9.8 J (6.7, 12.9) at implant and 338 V (264, 412) and 10.5 J (8, 13.0) at follow-up. The conventional measure of lowest successful voltage/energy (95% CI) was 430 V (411, 449) and 12.1 J (11, 13.2) at implant and 415 V (391, 439) and 11.3 J (10, 12.6) at follow-up. There were no statistically significant differences between implant and follow-up energy requirements with either method.

*Conclusions *The nonthoracotomy lead system used in this study demonstrated stability of defibrillation energy requirements at implant and 3-month follow-up. A new technique for the estimation of the defibrillation energy dose-response relationship was derived by using a weighted logistic regression analysis.

Quantification of defibrillation efficacy is commonly required in the assessment of implantable defibrillators. It is now appreciated that there is no single defibrillation threshold but rather a probabilistic function that describes the defibrillation energy dose-response relationship. This relationship can be modeled by using a logistical regression^{1} or other mathematical functions.^{2} By assessing the curve-fitted variables, the probability of successful defibrillation at a given voltage or energy can be estimated. In individual patients this would require the delivery of a large number of shocks that ideally would be randomized with respect to the energy dose given. However, this is impractical in the clinical context.

The compromise in general practice is to assess the minimum energy that successfully terminates induced VF.^{2} Test shocks of increasing or decreasing voltage and energy are delivered until at least one failed shock is preceded or followed by a success. This method gives a value commonly referred to as the defibrillation threshold, which corresponds in animal studies to the energy that would be successful in 50% to 60% of delivered defibrillating shocks.^{1} ^{2} ^{3} Conventional “single-point” defibrillation threshold measures exclude potentially useful data available from an analysis of all shocks delivered and cannot quantify data when all delivered shocks are successful. Furthermore, conventional defibrillation threshold measurement requires strict adherence to a uniform defibrillation protocol among participating centers. As a result, it is possible that a single-point measure of a defibrillation “threshold” may provide significant error in the assessment of the effects of new therapies or technological advances for ICD recipients. An alternative approach, used in this study, examines the defibrillation dose-response relationship by means of pooling the data from a population of patients. Such a method uses all data obtained from all shocks delivered to all patients and was used to assess the stability of a new transvenous defibrillation system in the same group of patients over a 3-month period.

Newer nonthoracotomy lead systems are now commonly available in which the shock pathway is between a combination of intrathoracic or extrathoracic electrodes including endovascular, subcutaneous sites, or the ICD pulse generator itself. Frequently, these systems use leads placed but not anchored in endovascular positions in the high right atrial–superior vena cava position or more proximally at the innominate vein–superior vena cava junction.^{4} The stability of defibrillation energy requirements for these systems in humans has had limited study. Some studies have found no change over time,^{5} ^{6} ^{7} whereas others have found a rise in energy requirements over a 6- to 12-week period.^{8} ^{9}

We hypothesized that the transvenous-lead system under study would demonstrate stability of defibrillation energy requirements over time. We further evaluated a new technique for summating all shocks delivered to allow a comparison of the energy and voltage requirements in the same population of patients over time and to compare these measures with the conventional LSE estimate of defibrillation threshold.

## Methods

### Data Acquisition

The study group was derived from a prospective multicenter study, using the same protocol in all centers. All patients received a model 4211 ICD (Telectronics Pacing Systems) with a two-lead transvenous-lead system. In all cases, the 100-cm, 6F ventricular lead (model 040-068) was passively implanted in the right ventricular apex. The 90-cm, 6F atrial lead (model 040-069) was passively implanted in the right atrial appendage with a defibrillating electrode positioned in the superior vena cava–right atrial junction area, 8 cm back from the tip of the lead. Intraoperative defibrillation testing was performed in all patients. The point estimate of defibrillation threshold used the LSV delivered (or its corresponding measure in joules), which was arrived at by using a modified up-down approach, starting at 550 V, with 100-volt downward steps and 50-V upward steps (Fig 1A⇓). Minimum implant criteria required three defibrillations (≤550 V) from induced VF. All intraoperative testing used a model 4510 implant support device (Telectronics Pacing Systems) with delivery of biphasic shocks at a 60:40 phase ratio (6-ms pulse duration) from a 150-microfarad capacitor. The implanted defibrillators delivered shocks of identical configuration. All shocks were initially started with a right ventricular anode–to–right atrial cathode configuration. If unsuccessful, polarity was reversed prior to changing to a subcutaneous lead.

A follow-up study was performed at 3 months in all patients. This study used the same shock pathway and configuration that were employed at the time of implant. At the follow-up study, the initial shock used was the LSV at the time of the implant. If successful, defibrillation was again attempted at this LSV minus 50 V. If unsuccessful, defibrillation was attempted at 100 V higher (Fig 1B⇑).

In all cases, failed shocks were followed by a rescue shock at the maximal output of the implant support device (750 V) or the implanted defibrillator (650 V). All VF inductions were induced with 50-Hz stimuli available through the implant support device at implant or via the device’s VF induction mode at follow-up. All testing was performed under general anesthesia with a balanced technique that included narcotics and inhalation anesthetics for implantation and propofol anesthesia at follow-up studies. Impedance to shock delivery was recorded as the impedance measured from a 500-V shock using the final implant configuration. This was compared with the impedance from a 500-V test shock at the follow-up study.

### Data Analysis

Clinical variables assessed included patient demographics and antiarrhythmic drug use. The shock parameters recorded were stored voltage, calculated delivered energy based on delivered voltage and measured impedance, and success or failure of the defibrillation shock. The analysis used success or failure of all delivered shocks (test or rescue) as the dependent variable; delivered voltage or energy and time (implant versus 3 months) were the covariates.

The data regarding shock voltage and energies delivered were fitted with a logistic function for the construction of a defibrillation voltage or energy dose-response relationship. By design, patients who received lower energy shocks were specially selected by virtue of their prior successful defibrillation at higher shock energies. As a result, the crude overall logit curve should be relatively shallow and skewed by the higher success rates for lower energy shocks. A new overall logit curve was derived by weighing a separate logit function for four equally sized, more homogenous patient groups that were divided in quartiles according to the average shock energy (in volts or joules) delivered per patient. The logit curve for each quartile gives a different estimate for the probability of shock defibrillation success for all energies given. In this manner, each curve describes how the entire population would behave if all patients acted according to a particular quartile. Each point on these four curves is then averaged to produce a weighted logit curve according to the equation where π_{i} is the predicted weighted success rate, α and β are constants, and ε*i* refers to an additive error term of discrepancies between the real data and the model. The goodness of fit for the weighted logit curve to the data was assessed with the average proportion of variation explained and the variance of the regression “success rate” on the energy level. (See “Appendix” for details of the statistical procedures used.)

From the weighted logit curve, the energies (or voltage) associated with a 50% or 80% probability of successful defibrillation (E_{50} or E_{80} in joules or V_{50} or V_{80} in volts) at implant and follow-up were obtained. These estimates were also compared with the conventional LSV at implant (LSV_{implant}) when available (ie, a failure preceded by a success pair available). The LSV at follow-up (LSV_{follow-up}) was limited to the two test defibrillation shocks used. A pair of test shocks could determine LSV_{follow-up} as either LSV_{implant}−50 V, LSV_{implant}, or LSV_{implant}+100 V, depending on the response to the abbreviated up-down protocol at follow-up. All descriptive data are presented as mean±SD. Comparison of continuous data was made by using the Student’s *t* test.

## Results

### Demographics

A total of 120 patients were available for analysis with the 3-month study, which was performed at 98±19 days after the implant. Patient data were available from 18 centers (5±8 patients per center; range, 1 to 26). Of the 120 patients studied, 4 required a change of polarity to achieve minimal implant criteria, and 26 required subcutaneous patch placement. Patient age was 62±13 years; left ventricular ejection fraction was 33±14%. Eighty-four (70%) patients had experienced a myocardial infarction, and 96 (80%) were male. ICD indications were 108 (90%) and 12 (10%) for VF/ventricular tachycardia and syncope, respectively.

A total of 93 (77%) patients at implant and 84 (70%) at the 3-month follow-up did not take antiarrhythmic medications. A total of 6 (5%) and 10 (8%) patients were on class Ia drugs, and 22 (18%) and 26 (22%) were on class III drugs at implant and 3-month follow-up, respectively. Sixteen patients (13%) had a change of drug usage between implant and follow-up. These changes were evenly spread in all possible directions (4 patients from class Ia to class III, 4 patients from class III to Ia, 4 patients from class Ia to no therapy, and 4 patients from class III therapy to no therapy).

### Defibrillation Voltage and Energy

A total of 1094 shocks were available for analysis. Of these, 864 (79%) were successful and 230 (21%) were not successful. At implant, 802 shocks were delivered (6.6±2.5 shocks per patient), and 292 shocks were delivered during follow-up studies (2.4±1.2 shocks per patient). The distribution of shock energies used, in volts or joules, at implant and follow-up, are shown in Fig 2⇓. The median voltage of all shocks was 500 V at implant and 450 V at the 3-month follow-up (Fig 2A⇓ and 2B⇓). The corresponding median energies for shock delivery were 16.4 and 13.4 J at implant and follow-up, respectively (Fig 2C⇓ and 2D⇓). The distribution of delivered shock energies were divided into four equal-sized groups for the calculation of the weighted logit curve.

The logistic regression curves, based on all patients, are illustrated in Figs 3⇓ and 4⇓. The effects of weighting the logit curve according to the distribution of shock energies used are illustrated in Fig 3B⇓ and 3C⇓. All data in Fig 3⇓ refer to the population of patients studied at the time of implant, with the delivered shock measured in volts. The accompanying mean defibrillation success data points for the population at these delivered voltages are superimposed on the logit curve. Note that the raw overall logit curve in Fig 3A⇓ is relatively shallow. As expected, this is consistent with the generally higher proportion of successful defibrillation results among the selected patients who received low energies because of their prior successful defibrillation at higher energies. Fig 3B⇓ illustrates the four different logit curves obtained when the predicted success rate over the entire energy range was calculated based only on the results from the relatively more homogenous subgroup that received a different quartile of net delivered voltages, ie, from 0% to 25% (group 1), 25% to 50% (group 2), 50% to 75% (group 3), and 75% to 100% (group 4) of all delivered voltages. These four curves were then averaged to produce the weighted logit curve for the overall population that is shown in Fig 3C⇓. Note that the weighting increased the shape and shifted the calculated curve downward into the domain of the independent variable. From this final weighted logit curve, the V_{50} and V_{80} were calculated as summarized in the Table⇓.

By the same techniques, a weighted logit curve was constructed for voltage requirements at the 3-month follow-up and for energy (in joules) at implant and the 3-month follow-up. These results are illustrated in Fig 4A⇑ (for volts) and 4B (for joules). There is no statistical difference between these two curves, ie, the covariate “time” did not statistically alter the logit model, unlike the parameters of voltage (*P*<.01) and joules (*P*<.01). The goodness of fit, as assessed by the average proportion of variation explained by the predicted logit function, was 31.8% for the weighted logit curve when energy was expressed in volts and 23.9% in joules at baseline and 35.7% (volts) and 37.7% (joules) at the 3-month follow-up.

Conventional point estimates of defibrillation threshold, ie, LSV (or corresponding energy) are summarized in the Table⇑. The mean±SD defibrillation threshold defined as LSV or joules was 430±81 V and 12.0±4.9 J at implant and 416±90 V and 11.3±4.8 J at the 3-month follow-up, respectively. At implant, successful defibrillation at all test shocks delivered occurred in 26 of 120 patients, precluding measurement of the LSV_{implant} in these patients. In 8 of these 26 patients, a minimal voltage of 250 V was reached. Similarly, an LSV_{follow-up} value could not be obtained in 46 of 120 patients at follow-up, largely because of physician preference to discontinue the protocol due to failure of a first test shock (n=5), after delivery of at least two shocks (n=14), or with only one test shock delivered at LSV_{implant} (n=13) or higher (n=14). There were no instances of a failure of test shock at LSV_{implant} followed by failure at LSV_{implant}+100 V.

The Table⇑ shows the E_{50}, E_{80,} V_{50}, and V_{80} and the 95% CIs derived from the weighted logit curve, in joules and volts, at baseline and 3 months, respectively. There was no significant change between any of these values. Also in the Table⇑ are the available conventional single-point measures of LSE, which are within the 95% CI for E_{50} at baseline and the 3-month follow-up. There was no effect of age, sex, ejection fraction, or drug use on defibrillation energy requirements.

The impedance for a 500-V shock was 48.2±7.8 Ω at implant and 58.5±9.6 Ω at the 3-month follow-up (*P*<.05).

## Discussion

The chief finding of this study is that there was no difference in the average voltage or energy requirements for successful defibrillation between implant and 3-month follow-up in a population of patients all implanted with the same transvenous-lead system. The absence of a significant difference over time was seen using either a conventional LSE measure or a weighted logistic regression model to estimate energy requirements. Previous human studies have suggested that defibrillation energy requirements are stable with some systems^{5} ^{6} ^{7} or slightly increased with others over a 6- or 12-week period.^{8} ^{9} To a degree, some of the differences between studies could reflect particularities of the ICD system (device plus leads) under study, subtle lead movements over time, more lenient (and therefore perhaps less stable) minimal implant criteria, or the technique used to assess defibrillation energy requirements.

It should also be noted that 18% of the patients in this series required additional implantation of a subcutaneous patch. This may be related to the relatively stringent criteria used for establishing minimal implant success (550 V or ≈13 J) or to the positioning of the shock cathode on the atrial lead. Nonetheless, since the data were compared in a pairwise fashion, the stability of the measures obtained, using whatever configuration was ultimately required, remains the same.

A further result of this study is the derivation of a weighted logistical regression model to assess the measurement of defibrillation energy requirements in a clinical population. Such a population-based method to assess energy needs may have certain advantages over commonly used methods. Most importantly, it allows the use of all shocks given to all patients in the assessment of therapy, even in situations in which relatively few shocks per patient are delivered or detailed defibrillation testing protocols have been incomplete or violated. This analysis pools all shocks delivered to a population independently of the type of defibrillation protocol used. By allowing the measurement of the predicted energy for 50% shock success rather than the use of an LSV, this method may also be more reliable for the study of effects of new therapies or interventions in ICD patients. Furthermore, it is possible that information based on the “shape” of the derived curve fitted to the data (ie, the calculated parameters for energies other than E_{50}) may have relevance to clinical or basic research. The logistic function used in this study has been found to be a valid model to fit defibrillation energy requirements in both porcine^{2} and canine^{1} data. It is a function common to many biological models and, because of its sigmoidal shape, can model data in the low range of energy deliveries, unlike an exponential or other mathematical function.^{2}

In contrast, all previous studies of defibrillation in humans have relied on the use of a single LSE, or “defibrillation threshold,” as the measure of defibrillation energy requirements. Because not enough shocks are delivered in individual patients to assess the energy–defibrillation success relationship, pooling data from all shocks in all patients allows useful estimates of this relation in the population under study. Importantly, published studies of defibrillation threshold, by design, exclude patients in whom defibrillation thresholds could not be obtained. The effects of a systematic bias in favor of those in whom a failure-success reversal is obtainable are unknown, but such a bias could lead to underestimation or overestimation of the utility of new therapies. The pooling of population data for modeling defibrillation efficacy has been attempted in animal models only.^{3} ^{10} ^{11} None of these attempts tried to weigh the effects of homogenous subgroups of the population as used in the present study, and none provided details of the statistical models used.

The use of a derived logit function for the pooled assessment of all shocks delivered in a patient population requires the assumption that interpatient variability is largely or entirely mediated through effects of shock magnitude on defibrillation success and not by any other factor. Similar to other studies, we found no influence of sex or left ventricular function on our results.^{12} ^{13} ^{14} Furthermore, all patients were analyzed twice, such that the entire data set represents paired-data information. Antiarrhythmic drugs could have had some confounding effects on the results; however, the relative magnitude of drug usage was low, and changes in drug use were evenly divided among all possible combinations.

The impedance measure differed at the time of implant and at the 3-month follow-up. The mechanism of this difference is not known and may be related to either time-dependent variabilities in the defibrillation lead-tissue interface, the defibrillation threshold, or an artifact related to differences in anesthetic agents or the surgical setting in this patient population. By whatever mechanism, the changes in impedance over time support the utility of assessing defibrillation energy requirements with respect to the actual voltage delivered by a device rather than a calculated energy parameter that is in turn dependent on the impedance to shock delivery.

### Limitations

There are some important limitations in this study. There may still be unidentified sources of variation within a heterogeneous patient population, despite attempts to mitigate the effects of interpatient heterogeneity by grouping patients into quartiles of delivered energies. The comparator used in this trial was that of the conventional LSE. Others have suggested that single-point measures of LSE are reproducible and accurate if performed in triplicate.^{2} This could not be addressed in the present study; however, triplicate measures of LSE have not been routinely performed in published human studies.

### Conclusion

Transvenous defibrillation thresholds are stable over time using the defibrillator system described. An analysis using a summation of all shocks delivered in the aggregate may be a useful alternative to the defibrillation “threshold” for estimating defibrillation energy requirements. Such a method allows a large number of data points to be fitted to a weighted logistic function, allowing for the construction of a defibrillation energy dose-response relationship to human data. This method allows estimates of the V_{50} and E_{50} of clinically relevant delivered energies.

## Selected Abbreviations and Acronyms

ICD | = | implantable cardioverter defibrillator |

LSE | = | lowest successful energy |

LSV | = | lowest successful voltage |

VF | = | ventricular fibrillation |

## Appendix A1

The dose-response curve was estimated by regressing defibrillation success rates on energy doses with the use of a weighted logistic model. The patients were grouped based on the quartiles of the independent variable x̅_{i}’s (shock intensity in volts or joules) distribution. The mean values x̅_{i} of the independent variable *x*_{ij} were calculated. Based on the quartiles of x̅_{i}’s distribution, the samples were divided into four groups as follows

1. the samples are ranked in terms of the x̅_{i}

2. if x̅_{i}≤*Q*_{25}, then *i* ∈ *G*_{1}

3. if *Q*_{25}<x̅_{i}≤*Med*, then *i* ∈ *G*_{2}

4. if *Med*<x̅_{i}≤*Q*_{75}, then *i* ∈ *G*_{3}

5. if x̅_{i}≤*Q*_{75}, then *i* ∈ *G*_{4}

6. where *G*_{i} *L*=1,2,3,4 are the four groups.

Within each group the success rate of the *x* variable was modeled with a logistic regression, where and *x* is the continuous independent variable. The predicted success rate within each group is used to predict the overall success rate for the whole population at each level of variable *x* as follows where _{l}(*x*) and *k*_{l} are the predicted success rate and the number of samples within each group, respectively. The logit transformation is used on the weighted predicted success rate. A linear regression that describes the logit of the weighted predicted success rate as a function of the independent variable *x* is derived as follows where The weighted logistic regression is where π_{i} is the predicted weighted success rate and ε_{i} refers to an additive error term of discrepancies between the real data and the model.

The weighted predicted *P*_{WG,i} describes the success rate for the whole group. The π_{i} designed by linearizing the logit transformation enables the development of an overall logistic curve for the whole data. The curve fitting between *g*_{i} and *x*_{i} indicated in all cases a coefficient of multiple determination, ie, *R*^{2} ≈ 1. The first step, partitioning of samples into homogenous groups, allowed a better description of the data. The second step, which involves the combination of heterogeneous groups, resulted in a better fit to the success rate for the whole population by significantly decreasing the variance of the regression “success rate” on the variable *x*.

The estimated value of the independent variable *x* for any level of success rate is obtained as follows and for *p*=0.5, *x*_{50}=−α/β

The goodness of fit of the model was assessed by using the average proportion of variation explained (AVPE) derived by Gordon et al^{15} and reviewed by Hosmer and Lemenshow^{16} where *, and q̅=1−p̅, and by the unbiased estimator of the variance of the regression “success rate” on the independent variable **x* measured by The estimated variance of an estimated level of variable *x* is where *s*_{0}^{2} is the unbiased estimator of the variance of the regression “success rate” (SR) on the independent variable *x*.

The 95% CIs for *x*_{p} are calculated with the *t* distribution with *n*-2 degrees of freedom as follows

## Acknowledgments

This study was supported by the Heart and Stroke Foundation of Ontario, Canada, and Telectronics Pacing Systems Inc, Denver, Colo. The authors acknowledge the secretarial support of Beverley Leroux in the preparation of this manuscript.

- Received October 7, 1996.
- Revision received December 17, 1996.
- Accepted January 9, 1997.

- Copyright © 1997 by American Heart Association

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- A Population-Based Method for the Estimation of Defibrillation Energy Requirements in HumansDavid Newman, Aiala Barr, Mary Greene, David Martin, Miney Ham, Sally Thorne and Paul DorianCirculation. 1997;96:267-273, originally published July 1, 1997https://doi.org/10.1161/01.CIR.96.1.267
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