Measuring Defibrillator Surface Potentials: The Validation of a Predictive Defibrillation Computer Model

Abstract

Implantable cardioverter defibrillators (ICDs) are commonly used to reduce the risk in patients with life-threatening arrhythmias, however, clinicians have little systematic guidance to place the device, especially in cases of unusual anatomy. We have previously developed a computational model that evaluates the efficacy of a delivered shock as a clinical and research aid to guide ICD placement on a patient specific basis. We report here on progress to validate this model with measured ICD surface potential maps from patients undergoing ICD implantation and testing for defibrillation threshold (DFT). We obtained body surface potential maps of the defibrillation pulses by adapting a limited lead selection and potential estimation algorithm to deal with the limited space for recording electrodes. Comparison of the simulated and measured potential maps of the defibrillation shock yielded similar patterns, a typical correlation greater than 0.9, and a relative error less than 15%. Comparison of defibrillation thresholds also showed accurate prediction of the simulations. The high agreement of the potential maps and DFTs suggests that the predictive simulation generates realistic potential values and can accurately predict DFTs in patients. These validation results pave the way for use of this model in optimization studies prior to device implantation.

1. Introduction

Implantable cardioverter defibrillators (ICDs) are used to prevent fatal arrhythmias,^1,2,3,4 with approximately 100,000 implantations each year.⁵ Typically, these devices are designed for use in adults and implantation follows standardized techniques; however, neither the device nor the placement has been optimized for children or persons with abnormal cardiac anatomies or other congenital defects.⁶ As a result, there is a rise in alternate configurations, such as eliminating the lead placed in the subclavian vein or placing the ICD generator in the abdomen instead of the left upper chest. Each configuration seeks to maximize the efficiency of the device and ensure safety for the patient.⁷ A further motivation for exploring alternative ICD placement strategies are studies that associate negative consequences to either unnecessary or over-strength shocks. One study has shown that the discharge of the ICD can alter the Ca⁺⁺ dynamics of cardiac tissue, which may inhibit normal cell contraction, especially if the shock uses more energy than necessary.⁸ Such risks have motivated new implantation strategies for ICDs, including subcutaneous implantation^{9,10,11,12,13,14,15} and wearable external defibrillation devices.^16,17,18,19 With each new approach comes the need for optimization and testing, which can impede development, especially when each step requires animal and/or human experiments.

Mathematical modeling and computer simulation can efficiently accelerate the process of optimizing and testing of ICDs; to this end, we have developed a computational simulation pipeline that generates a patient-specific defibrillation model. With this pipeline, we can predict the potential field throughout the torso during defibrillation and estimate the defibrillation threshold (DFT), i.e., the lowest level of energy needed for defibrillation, for any given device design, implantation, and patient.^20,21,22,23 In previous studies, this simulation pipeline has shown accuracy in predicting the threshold energy required for successful defibrillation.²² However, our previous validation studies have been limited in their level of detail and complexity. We were able to compare holistic values such as the DFT, but could not evaluate how well the model predicted the actual distribution of potential over the heart and thorax. A more comprehensive verification requires comparison of our simulation to empirical data, ideally from clinical tests. To acquire such data in clinical studies, we have developed a method of measuring the body surface potential maps (BSPMs) generated by ICDs in humans.

The standard testing process that follows each ICD implantation provided the natural setting in which to acquire BSPMs during defibrillation shocks. Following implantation, the ICD is tested by inducing fibrillation in the patient and allowing the device to sense the arrhythmia and deliver a defibrillation shock to restore sinus rhythm. These test shocks provide a rare opportunity to record the ICD potential maps in patients. Although BSPM is a well established technique,^{24,25,26,27,28} using it during defibrillation and in the catheterization laboratory environment requires additional consideration to allow space on the torso surface for the sterile implantation region, the external defibrillation pads, and other instruments for the safety of the patient. Consequently, there is a highly limited and variable area of the torso surface that is available for the placement of validation BSPM lead systems. Fortunately, there are algorithms that use the spatial redundancy of potential recordings to estimate full torso surface potentials from a small number of electrodes.^29,30,31

In this study, we applied what is known as a limited lead selection and body surface estimation algorithm developed by Lux et al.^31,32,33 to deal with the restricted access to the torso surface. We adapted this algorithm for use with ICD potentials by training it with 3,870 sets of simulated defibrillation potentials that included different human torso geometries and also a wide range of realistic ICD placement locations. We also validated the resulting estimation technique on a small set of patient geometries.

With these novel techniques, we were able to gather BSPMs and DFT from patients receiving an ICD implantation and compare them to the results of patient-specific simulations. The results reported here establish the ability to accurately reconstruct ICD potential maps from both measurements and simulations, show a strong correlation between them, and demonstrate similar accuracy between simulated and actual DFTs.

2. Methods

In order to validate the defibrillation simulation pipeline, we measured body-surface potentials during ICD shocks and the DFTs of patients who underwent ICD implantation and compared these data to those predicted by the simulation. The validation, therefore, consisted of three stages: adapting a limited lead selection and body surface estimation algorithm for use with ICD potential maps, recording ICD potential maps and DFTs for each patient, and generating the patient-specific model for each patient to predict the potential field and DFT to compare them to the recorded values.

2.1. Body Surface Potential Estimation of ICD Shocks

We adapted a previously published limited lead selection and body-surface potential estimation algorithm³¹ for measuring body surface potentials during ICD implantation surgery. Figure 1 illustrates the application of the algorithm, which is composed of two processes. The first process is limited lead selection, which consists of finding the the optimal lead set for estimation by finding the most statistically unique locations one at a time until the desired number of leads (32 in our case) are found.³¹ We applied additional spatial constraints imposed by the implantation surgery, the sterile area, and the area covered by the external defibrillator pads (Figure 2), by removing from consideration the locations covered by these areas. From the resulting limited lead set, we modified the locations to fit regular strips of four leads for easier fabrication and application (Figure 2). The second process, body-surface potential estimation, determines the linear transform that predicts from the potentials measured with the lead set the potentials on the rest of the torso (Figure 1). This relationship is found from the covariance matrix of the training potential maps and is represented as a transformation matrix. This matrix is multiplied by the potential recordings from the 32 limited-lead locations to yield the full estimated potential map. While our modeling approach could generate potential maps at any time step, we used the relatively stable peak of the ICD pulse to allow for direct comparison with measurements. Implementing these two processes requires a database of potential maps to provide the statistical information needed to create a limited lead mapping system.

Figure 1:

Application of the limited lead selection and the body surface estimation algorithm from Lux et al.³¹ Original Data are body-surface potentials simulated from realistic ICD placements, and the Constraints are those imposed by the device implantation procedure. Lead selection follows iteratively to create reduced, constrained leadsets that we then used to create the estimation transform contained in the Transformation Matrix. Sparse Measurements are those signals acquired during each procedure.

Figure 2:

The optimal locations for measuring and from which to estimate full body surface maps during implantation surgery(red dots). The dark gray areas are generally covered by the external defibrillator pads, and the tan area indicates the sterile field where the device is implanted.

For both these first two processes, we used a database of simulated potential maps generated using our defibrillation simulation pipeline²² from a combination of 9 patient geometries, 43 tissue conductivity schemes, and 10 ICD placement geometries. Each of the resulting 3,870 simulated potential fields was sampled at the same 370 body-surface locations to meet the requirements of the algorithm. These three parameters, i.e., patient geometry, tissue conductivities, and ICD placement, were chosen to represent the range of such parameters expected in patients. Previous studies^{6,34,35,23,36,37} and our own preliminary simulation results showed that these parameters could be expected to affect the BSPM and DFTs consistent with bioelectric principles of conduction through an isotropic volume conductor. We tested the ability of the limited leads and estimation algorithm to reconstruct potentials on a separate database of simulated potential maps. This test dataset was generated with same 9 geometries, but a different set of 20 conductivity schemes and 10 different ICD placement geometries for a total of 1,800 potential maps representing the peak of the ICD pulse. The simulated potentials were sampled at the limited lead set locations, and the previously calculated transformation matrix was applied to generate the full estimated torso potentials. The quality of the estimation was evaluated with absolute error, correlation (ρ), relative error (RE), and normalized RMS error (Ē). We first evaluated the result of the estimation algorithm using an increasing number of leads from 5 to 100 to determine the number of leads required for acceptable estimation error. We also tested the sensitivity of the algorithm to changes in electrode location by evaluating the level of error from a variety of lead sets chosen to represent the placement variation likely to occur in the catheterization laboratory setting.

2.2. Recording Surface Potentials

We recorded the body surface potential maps from test shocks during standard ICD implantation surgery and testing. Table 1 lists each of the subjects used in the study with their weight, the device which was implanted, and geometric abnormalities. Surface recording electrodes (32 plus 2 electrodes for ground and reference) were applied to each subject as closely as possible to the locations described in Figure 2 after intubation but before surgery. The surface potentials during each biphasic test shock were recorded using a 32channel customized recording system (CVRTI, University of Utah) at 1 kHz or 4 kHz sampling rates. Ag/AgCl electrodes were used to mitigate the effects of electrode polarization on the measured potentials. To accommodate the large shock voltages (up to ∼ 750 V) in a system originally constructed for ECG acquisition, we added attenuation by a factor of 10⁴ using a voltage divider on each channel. Faulty leads were identified by the signal-to-noise ratio or pulse morphology and eliminated. The potentials for reconstruction were identified as the value at the first peak of the ICD pulse. The potential map was estimated using the transformation matrix described in Section 2.1, and compared to the simulated maps for each patient. Quantitative evaluation was by the same metrics as described in Section 2.1. The measured potentials from the 32-lead set were also compared to the simulated surface potentials and evaluated with the same metrics. The resulting error metrics are presented as mean ± standard deviation.

Table 1:

List of patients in the study with the ICD device manufacturer and geometric information. Acronyms are: atrioventricular septal defect (AVSD), left ventricle (LV), ventricular septal defect (VSD), pulmonary valve (PV).

age	weight	device	geometric abnormalities
6 years	25 kg	Medtronic Virtuoso II DR	Normal Anatomy
8 years	36 kg	Medtronic Virtuoso II DR	Normal Anatomy, Long QT
9 years	35 kg	St. Jude Promote	Prosthetic MV, repaired AVSD, LV dilation
15 years	46 kg	Medtronic Virtuoso II DR	Repaired AVSD, Scoliosis, Spinal Rods
16 years	65 kg	St. Jude Current DR	Normal Anatomy
17 years	70 kg	St. Jude Current DR	Aortic Atresia, Repaired VSD, Cardiac Reconstruction
17 years	60 kg	Medtronic Virtuoso II DR	Cardiac Reconstruction, Scoliosis
29 years	85 kg	St. Jude Unify	Tetralogy of Fallot, PV Homograft
32 years	60 kg	Medtronic Virtuoso II DR	Tetralogy of Fallot

2.3. Patient-Specific Simulation

We used the patient-specific simulation pipeline²² implemented in SCIRun^38,39 (http://www.scirun.org) to simulate the potential field within the torso and predict the DFT of each patient in the study. Nine patients identified as candidates for ICD implantation, with a range of ages from 6–32 years, were imaged using magnetic resonance prior to implantation using a 1.5 T MRI scanner with a double IR pulse sequence. From these scans, segmentations of 11 tissues^35,34 were generated using Seg3D⁴⁰ (http://www.seg3d.org) as shown in Figure 3, which provided torso geometries. Into this geometric model, we added the location of the implanted ICD from postoperative x-ray images. The torso and ICD geometries were then used as inputs in the simulation pipeline to predict the potential field through the body from the ICD for each shock level recorded for the patient. An example of how to run this simulation can be found on the SCIRun-Exchange (https://github.com/SCIInstitute/SCIRun-Exchange). The calculated potentials were sampled at the same 370 points for which we measured/estimated the shock potentials (Section 2.2) and were compared using the same metrics as for the other map errors. The DFT corresponding to the ICD geometry was also calculated for each patient using the critical mass hypothesis, which holds that 95% of the ventricular myocardium must have an electric field above 5 V/cm for successful defibrillation.⁴¹ The predicted DFTs were also compared with the clinically derived biphasic DFTs of each patient.

Figure 3:

11 segmented tissues types included in the defibrillation simulation pipeline.

2.4. Collecting Patient Data

All patient data used in this study was collected with informed consent and under the direction of the local institutional review board of Primary Children’s Medical Center at the University of Utah.

3. Results

The results presented in this section demonstrate the ability of the simulation pipeline to recreate ICD potential and DFT values measured in the clinical setting. We show the results of four comparisons: known simulated potential maps to those estimated using the limited lead set and training data, bodysurface recordings at approximately 32 recording locations to simulated values at the same locations, potential maps estimated from the measured body-surface potentials to simulated surface potential maps, and predicted DFT to clinically measured DFT.

3.1. Reconstruction of Simulated Surface Potentials

When tested against simulated body-surface shock potentials, the limited lead selection and estimation algorithm showed a low error and a high correlation. The limited lead sites preferred by the algorithm tended to be locations as close to the ICD device and active coils as possible. When unconstrained, the majority of the selected leads were on the left, anterior chest. With constraints there was a high concentration of leads on the shoulders, along the mid-axillary lines, and near the xyphoid process. The error of the estimations as a function of number of leads demonstrated a general exponential reduction as shown in Figure 4. The minimum ρ for five or more leads was 0.993, the maximum RE was 1.8%, and the maximum Ē was 4.6%. Although the correlation changed very little with the number of leads used, the improved values for RE and Ē indicate substantial benefits are possible up to approximately 60 leads. The error did not significantly decrease when using more than 60 electrodes at which point the ρ = 0.999, RE = 0.47%, and Ē = 2.2%. The error using 32 electrodes was acceptably low with a ρ of 0.997, RE of 0.88%, and Ē of 3.1%.

Figure 4:

Mean estimation accuracy as the number of leads used in estimation algorithm was increased. Error is expressed by A) correlation (ρ), B) relative error (RE), and C) normalized RMS error (Ē).

The body surface estimation algorithm exhibited high accuracy when using a variety of lead sets when comparing estimated and simulated potential maps. The error was lowest using the unconstrained lead set, with a ρ of 0.99991±7×10⁻⁵, a Ē of 0.5±0.1%, RE of 0.02±0.02%, and a mean maximum error of 19±9 V. Using the chosen clinical lead set reduced the accuracy, yet the metrics should very high accuracy with a high ρ (0.999±2×10⁻³), low Ē (1.6±0.7%), and low RE (0.3±0.4%) between the estimated and simulated potential maps. The mean maximum error of the estimation was 68±39 V on shocks of 500 V. Comparing the Figure 5 shows the typical distribution of error, with highest values near the left upper chest, where the ICD was placed. The accuracy of estimated surface potentials was not sensitive to changes in the limited lead set, both in location and number of leads. The reconstruction of the lead set with the greatest error, based on the location and the number of the leads, did not change the mean Ē more than 0.9%, the mean RE more than 0.3%, and the mean ρ more than 2×10⁻³. These changes in the error metrics are within the standard deviation of the metrics from the limited lead set, with the exception of Ē, which was slightly higher than the standard deviation.

Figure 5:

Typical absolute error between actual and reconstructed potentials by location from a shock with 500 V magnitude.

3.2. Surface Potential Comparison

Comparison of the potentials measured at the lead locations against those from patient-specific simulation showed high correlation, with a varied RE and Ē, which ranged from 5.8 to 47.3 % and 8.1 to 23.1 % respectively. As shown in Table 2, the mean ρ, RE, and Ē were 0.97±0.02, 20±11%, and 15±4%, respectively. Comparing the potentials and the absolute error at the leads marked with black spheres in Figure 6 also shows that the simulated potentials were generally lower in amplitude than the measured potentials.

Table 2:

Metrics of comparison of the limited lead recordings and the simulated potentials at the corresponding location. Each row contains the results from a single test shock and there were variable numbers of test shocks from each subject.

Subject age	shock max	ρ	RE	Ē
6 yo	216 V	0.96	37.9 %	19.2 %
	279 V	0.956	42.8 %	20.5 %
8 yo	279 V	0.959	12.3 %	13.4 %
	395 V	0.962	10.6 %	12.4 %
	483 V	0.977	5.83 %	8.07 %
	624 V	0.962	11.6 %	13.1 %
9 yo	405 V	0.974	27.9 %	18.8 %
	573 V	0.972	25.8 %	18 %
15 yo	216 V	0.991	10.4 %	10.1 %
	279 V	0.991	13.2 %	11.5 %
	395 V	0.991	10.8 %	10.4 %
	483 V	0.991	13.9 %	11.7 %
16 yo	395 V	0.938	26.7 %	18 %
	583 V	0.93	19 %	14.2 %
17 yo	286 V	0.976	32.2 %	22.3 %
	405 V	0.976	26.3 %	20.2 %
	496 V	0.976	35.4 %	23.1 %
17 yo	483 V	0.978	16.3 %	13.6 %
	624 V	0.975	15.9 %	13.2 %
	738 V	0.976	13.5 %	12.4 %
29 yo	405 V	0.948	11 %	9.81 %
	496 V	0.944	11.2 %	10.1 %
	573 V	0.949	10.7 %	9.67 %
	701 V	0.936	12.8 %	10.9 %
32 yo	279 V	0.983	25.8 %	15.8 %
	395 V	0.983	25.9 %	16.2 %
	432 V	0.982	47.3 %	21.4 %
	624 V	0.983	19.7 %	14.4 %
	738 V	0.983	19.8 %	14.2 %
mean	458 V	0.969	20.4 %	14.7 %

Figure 6:

Surface potential comparison between the reconstruction obtained from surface recordings and the original, patient specific simulation. The results show a single shock for all 9 subject and include the limited leads (black circles) selected during the ICD implantation for each subject. The absolute error is included for each patient.

The body surface estimation algorithm was effective in generating potential maps of ICD discharges that are qualitatively and quantitatively similar to the maps from the patient-specific simulation. Figure 6 shows a comparison between the estimation from the ICD surface recordings and the patient-specific simulation. Qualitatively, the potential maps are similar, but there are regions of high error near the left, superior chest where the device was located. The quantitative comparison between the reconstruction and simulation also showed high accuracy, as listed in Table 3. The ρ for each shock was above 0.96, with a mean of 0.99±0.01 from 29 shocks. Similarly, the RE was low for all shocks with a mean of 13±9%. The normalized Ē demonstrated a similar level of accuracy of 6 ±2%.

Table 3:

Metrics relating the simulated potential maps to the maps generated from the surface recordings. Each row contains the results from a single test shock and there were variable numbers of test shocks from each subject.

Subject age	shock max	ρ	RE	Ē
6 yo	216 V	0.991	18.6 %	9.0 %
	279 V	0.982	26.9 %	10.8 %
8 yo	279 V	0.967	6.5 %	5.1 %
	395 V	0.97	6.0 %	4.8 %
	483 V	0.996	1.0 %	2.0 %
	624 V	0.967	7.0 %	5.0 %
9 yo	405 V	0.985	6.28 %	4.16 %
	573 V	0.976	6.19 %	3.94 %
15 yo	216 V	1.000	6.8 %	5 %
	279 V	0.999	10.9 %	6.3 %
	395 V	0.998	12.9 %	6.9 %
	483 V	0.998	16.8 %	7.9 %
16 yo	395 V	0.978	7.8 %	5.0 %
	583 V	0.964	7.3 %	4.5 %
17 yo	286 V	0.996	23.5 %	7.7 %
	405 V	0.996	22.9 %	7.7 %
	496 V	0.995	31.2 %	8.8 %
17 yo	483 V	0.997	15.2 %	7.7 %
	624 V	0.998	12.1 %	6.7 %
	738 V	0.994	13.5 %	7.2 %
29 yo	405 V	0.994	2.0 %	2.5 %
	496 V	0.99	2.2 %	2.7 %
	573 V	0.988	2.7 %	2.9 %
	701 V	0.978	4.6 %	3.5 %
32 yo	279 V	0.994	15.3 %	5.2 %
	395 V	0.992	18.4 %	5.7 %
	432 V	0.988	30.2 %	7.0 %
	624 V	0.99	19.3 %	6.0 %
	738 V	0.987	20.5 %	6.1 %
mean	458 V	0.990	12.9 %	5.6 %

Figure 7 shows the mean and standard deviation of the accuracy metrics for each patient as a condensed visualization of the information in Tables 2 & 3. This figure compares the accuracy of the simulation using both the full torso maps and the subsets for each patient form which we obtained measured signals. In general, the error is higher between the recorded potentials and the simulated potentials for the subset of the measured locations than in the full potential maps, however, the accuracy of the simulation varies among patients.

Figure 7:

Mean accuracy for each subject expressed by A) correlation (ρ), B) relative error (RE), and C) normalized RMS error (Ē). Error bars indicate standard deviation.

3.3. DFT Comparison

Table 4 shows the comparison between the clinically determined DFTs and the predicted DFTs. The predictions for the 6-, 9-, 16-, and 29-year-old patients were within the range of the clinically determined DFTs, indicating a high predictive accuracy for these patients. The 8-, 15-, 17-, and the 32-year-old patients demonstrated predicted DFT outside the clinically determined DFT range but typically by less than 2 J, which is less than or equal to the range tested for each patient. The highest difference in predicted and observed DFTs was recorded for the first 17-year-old patient. This difference was nearly double the observed range (~10 J).

Table 4:

Comparison of the DFTs found during clinical testing and predicted by simulation via the critical mass hypothesis. Biphasic pulses were used in clinical defibrillation testing and the peak electric field from both phases was used to satisfy the critical mass hypothesis for the prediction.

Subject age	Empirical DFT	Predicted DFT
6 years	0 – 3 J	2.7 J
8 years	10 – 15 J	8.31 J
9 years	10 – 15 J	14.5 J
15 years	3 – 5 J	5.2 J
16 years	14.6 – 20.7 J	20 J
17 years	5 – 10 J	19.9 J
17 years	20 – 25 J	26.8 J
29 years	15 – 20 J	18 J
32 years	10 – 12 J	12.9 J

4. Discussion

The results presented in this paper demonstrate three major findings: a) that the limited lead selection and estimation algorithm can be applied with high accuracy to capture the shock potential over the entire torso, b) that patient-specific simulation of defibrillation can generate surface potentials that are qualitatively and quantitatively similar to those obtained in measurements, and c) that simulations can predict DFT values comparable to those found clinically. These findings support the effectiveness of our simulation pipeline in predicting defibrillation in humans.

This study contains a new application of a well established approach, using limited lead selection and a body-surface potential reconstruction algorithm to estimate potential maps during ICD shocks. The lead selection algorithm suggested electrode placement locations that were as close as feasible to the electrical sources and sinks (the ICD and active leads), which is similar to findings using the same approach to identify limited leads to capture cardiac sources.³¹ We found that the number of leads for which the error statistics became stable was approximately 60, compared to 30 found in Lux et al.^31,42 However, the error using 30 leads to measure ICD shocks was still acceptably low (Figure 4), supporting our decision to use existing 32-lead acquisition systems. Another important finding was that the estimation was insensitive to changes in the specific limited lead set identified by the algorithm, which allowed us to add clinically dictated constraints on electrode placement, constraints that varied from case to case. A final finding was that using simulations of defibrillation to create the training data to identify viable limited leadsets was successful. Our results are supported by a previous application of the limited lead and estimation approach in the setting of activation mapping on the epicardium of the heart from leads located in the coronary veins.⁴³ All these results support the utility and robustness of this approach and encourage further applications.

This study also provides unique and compelling validation of the utility of simulation to predict defibrillation potentials in a patient specific manner. The comparison between simulated and measured values exhibited a high correlation, demonstrating that the simulation predicted generally accurate spatial distributions of defibrillation potentials. The level of normalized Ē and the correlation associated with the subset comparisons were similar to those from animal validation experiments in which an ICD was discharged in situ and potentials measured at several locations in the torso.⁴¹ Also, the full potential maps estimated from recorded potentials were qualitatively and quantitatively similar to simulated potential maps (Section 3.2, Figures 6 and 7). The errors in the comparison of the full maps were lower than those for the comparison of only the measured potentials, indicating that the estimation algorithm itself may contribute to reducing the error. A possible reason for this improvement is that the estimation algorithm captures features of the simulated defibrillation potentials, driving the estimation closer to the simulated distributions and improving the accuracy. Despite the possible bias, using estimated potential maps for evaluation allows for potential field comparison at locations on the torso that are likely impossible to directly record with contact electrodes, most notably near the ICD device, which is the location with the highest potentials amplitudes. However, Tables 2 & 3 show that high accuracy in comparisons with only the measured potentials generally correlates to high accuracy in the predicted full potential maps, indicating that the potential maps are driven by the recorded potentials.

A comparison of clinical and simulated DFTs further supports the accuracy of the simulation at the same time as it provides insight into the limitations of the model (Section 3.3). Generally, there was high agreement between the predicted and observed DFTs, which is similar to our previous findings.²² However, there was a notable exception with one of the 17-year-old patients. This patient experienced the highest error in DFT comparison (Table 4), the highest potential map RE (Figure 7), and a high Ē. A possible explanation for this exceptional result is that the cardiac anatomy of this patient was vastly different from normal due to major cardiac reconstruction of the atria, which could have significantly altered both the myocardium and scar tissue near the heart to affect the DFT. We chose this case to explore (albeit superficially) the impact of heart conductivity on the DFT and found that by reducing conductivity by a factor of 10, the DFT dropped to a value of 9.1 J, within the measured range, indicating that there may also be underlying tissue conductivity changes, such as scar formation or fibrosis, in addition to geometric changes that may need to be included in the model. A further potential source of error in predicting DFTs comes from Rantner et al.,⁴⁴ who questioned the ability of the critical mass hypothesis⁴⁵ to accurately predict defibrillation. Although they tested only one case, our single outlier case may provide further evidence that in some patients, the critical mass hypothesis may not be sufficient to predict the effect of defibrillation. This one case does not diminish the importance of the finding that the direct comparisons of DFTs predicted DFTs close to clinically observed values for all other patients (Table 4). With such high accuracy, we can show that in at least a substantial proportion of our cases, the critical mass hypothesis used in our model could accurately predict DFT.

We do not claim that these results support the critical mass hypothesis as an underlying explanation of the mechanisms of defibrillation, but rather aimed to apply it as an efficient estimation tool to calculate DFTs and measure the effectiveness of defibrillation. There are other mechanistic explanations that more completely explain many of the more intricate tissue behaviors during defibrillation, such as the virtual electrode hypothesis.⁴⁶ Calculating the DFT with these other underlying assumptions often require computationally costly methods such as bidomain simulation with active cell models to describe both the fibrillation and defibrillation wave-fronts and test multiple shock amplitudes for each ICD placement for success.^47,48,44 However, in the setting of guiding a clinical decision about ICD placement or settings it is necessary to be able to rapidly, ideally within seconds, evaluate many configurations, which, in turn, requires the efficiency of an approach like estimating DFTs based on the critical mass hypothesis. We welcome further progress in identifying new, efficient metrics of defibrillation and our computational pipeline is flexible enough to incorporate such improvements.

The occasional disparity of the error metrics in this study reveal the recurring challenge of comparing complex, three and four-dimensional results, of defining error metrics that capture the features that are most relevant to how the results will be used. For instance, there is an order of magnitude difference between the amplitudes of many of the measured potentials, differences not always reflected in the simulations and likely a product of controllable measurement error. Such amplitude fluctuations can combine with the mathematics of error metrics to result in distortions of the error metrics. In the calculation of RE, for example, simply swapping the nominally correct values between the measured and the simulated values can change the resulting error metrics by as much as a factor of two. Metrics that are less sensitive to these types of ambiguities, such as correlation and DFT, can provide less sensitive measures of the accuracy of simulations and comparisons, but come with their own bias and distortion.

The results of this study show that the simulation pipeline we have developed is generally accurate, but some areas can be improved specifically in the patient-specific model. Many assumptions and sources of error contribute to the discrepancies apparent in the computation of both potentials and DFTs, e.g., patient geometry and conductivity values. Previous studies suggest that the model is highly sensitive to changes in the myocardium and blood conductivity, i.e., that these factors can most affect the potential distribution on the torso surface.³⁴ However, animal studies also suggest only a modest change in error when such conductivities are modified, even when a voltage drop is applied to the interface of the defibrillator.⁴¹ Therefore, scalar changes in conductivity values may not provide a sufficient improvement in the simulation to significantly reduce error.

One additional source of error is the anisotropy of conductivity in the heart. In the current model, the myocardium was modeled as an electrically isotropic tissue. Previous studies of propagation of excitation have shown a marked increase in accuracy in the predicted electric field by including the anisotropy of the heart.^36,37 It is also evident from other studies that the myocardial fiber direction significantly affects the electric field around and through the myocardium.⁴⁹ Adding anisotropy to the myocardium based on fiber direction will likely change the electric field around the heart and may provide a significant change in the surface potentials, thereby increasing the accuracy of our model to predict the electric field in the torso.

The subjects used in this study were cases following corrective surgery for congenital cardiac defects, and therefore much younger than typical ICD recipients. They also differed from typical ICD recipients in that the causes of their arrhythmias were rooted in their congenital defects and the subsequent corrective surgery and not, for example, myocardial infarcts suffered in adulthood. While their diseases were pediatric, many of the subjects were at least teenagers and two were mature adults (29 and 32 years of age) so that factors of torso size and organ development were similar to patients in the aging population. Our results also showed that patient-specific applications of this modeling approach were accurate across a range of patient sizes and cardiac anatomical abnormalities. Clinical experience also suggests that these types of patients would likely benefit most from the patient-specific modeling of their ICD placement.^20,35 Placement of ICDs in adults with arrhythmias originating from other structural or nonstructural causes have become largely standardized and successful so that such patient-specific modeling is less justified. Finally, our approach modeling the patient geometry and function is highly adaptable and so could be easily modified for more typical adult cases.

Another use of the simulation pipeline would be to test the affects of variations in patient geometry, tissue conductivity,³⁴ and ICD position and type^35,23 on the expected DFT and the resulting BSPMs. The simulation framework we describe could be used to vary any number of patient geometry parameters, including: heart size, wall thickness, torso size, and any other change in the geometry of the patient and then to evaluate the changes in DFTs and BSPMs. By testing a wide range of geometric parameters in a rigorous and systematic fashion, some general trends could emerge that may provide guidance to physicians placing ICDs in patients with abnormal geometries. We have previously carried out similar studies using our model to derive general clinical guidelines for ICD placement²³

The accuracy demonstrated in this study provides important validation of our simulation approach and of the application of estimation of potentials to this new domain. High agreement in potential field recordings and DFT comparisons shows that such simulations can accurately predict the electric potentials on the surface of the body and likely throughout the torso. The main application of this model is to improve ICD use in a patient-specific case, for example, patients with abnormal cardiac anatomy. More generally, there is a pressing need for optimization of ICD placement for pediatric cases or subcutaneous ICD configurations.²³ The accuracy of our simulation compared to recorded potentials demonstrated in this study provides confidence in our simulation pipeline, which could further the usefulness of ICD for many patients. We also note that all elements of the software described in this study are part of an open-source software suite created for bioelectric field simulations. The software is available completely freely at http://www.sci.utah.edu/cibc-software.html.

Highlights:

• Limited lead selection and body surface estimation can by applied to potentials generated from implantable cardioverter defibrillators.

• Patient-specific modeling can predict body surface potentials that qualitatively and quantitatively agree with potentials recorded from patients during implantable cardioverter defibrillator implantation and testing.

• The defibrillation model can predict defibrillation thresholds comparable to clinically observed values.

• High agreement between measured and predicted potential maps and defibrillation thresholds supports the use of this patient-specific pipeline in guiding defibrillation placement strategies.