Discordant Alternans as a Mechanism for Initiation of Ventricular Fibrillation In Vitro.

Background Ventricular tachyarrhythmias are often preceded by short sequences of premature ventricular complexes. In a previous study, a restitution-based computational model predicted which sequences of stimulated premature complexes were most likely to induce ventricular fibrillation in canines in vivo. However, the underlying mechanism, based on discordant-alternans dynamics, could not be verified in that study. The current study seeks to elucidate the mechanism by determining whether the spatiotemporal evolution of action potentials and initiation of ventricular fibrillation in in vitro experiments are consistent with model predictions. Methods and Results Optical mapping voltage signals from canine right-ventricular tissue (n=9) were obtained simultaneously from the entire epicardium and endocardium during and after premature stimulus sequences. Model predictions of action potential propagation along a 1-dimensional cable were developed using action potential duration versus diastolic interval data. The model predicted sign-change patterns in action potential duration and diastolic interval spatial gradients with posterior probabilities of 91.1%, and 82.1%, respectively. The model predicted conduction block with 64% sensitivity and 100% specificity. A generalized estimating equation logistic-regression approach showed that model-prediction effects were significant for both conduction block ( P<1×10-15, coefficient 44.36) and sustained ventricular fibrillation ( P=0.0046, coefficient, 1.63) events. Conclusions The observed sign-change patterns favored discordant alternans, and the model successfully identified sequences of premature stimuli that induced conduction block. This suggests that the relatively simple discordant-alternans-based process that led to block in the model may often be responsible for ventricular fibrillation onset when preceded by premature beats. These observations may aid in developing improved methods for anticipating block and ventricular fibrillation.

Clinical Perspective

What Is New?

This study describes a new in vitro examination of a mechanism for inducing sustained ventricular fibrillation via short sequences of premature ventricular complexes.

As part of this examination, the predictions of a restitution‐based computational model were compared with optical mapping data collected from canine preparations.

The main novel contribution of the study is a direct and detailed experimental verification of the idea, previously proposed using a relatively simple computer model, that certain sequences of cycle lengths reliably forecast discordant alternans patterns, conduction block, and the development of ventricular fibrillation.

What Are the Clinical Implications?

This study demonstrates that our computational model is helpful for predicting (1) spatial patterns of discordant alternans, (2) which premature stimulus sequences are more likely to induce conduction block, and (3) which premature stimulus sequences are unlikely to induce ventricular fibrillation.

This line of research may eventually lead to improved conduction block and ventricular fibrillation forecasting algorithms, along with computational models that identify arrhythmogenic patterns of premature complexes, which could lead to safer antitachycardia pacing strategies for implantable devices.

Introduction

Sudden cardiac death is a leading cause of mortality in the industrialized world, responsible for an estimated incidence of 180 000 to 450 000 deaths annually in the United States.1 A substantial proportion of sudden cardiac arrests, approximately half in a recent study,2 are associated with ventricular tachycardia (VT) or ventricular fibrillation (VF). It has been observed clinically that sustained VT and VF are often preceded by several irregularly timed premature complexes,3, 4 and studies conducted to explore this phenomenon have shown that specific coupling interval patterns of premature complexes, such as short‐long‐short5 and short‐short‐short,6 tend to lead to reentry and VT. Various researchers have examined the mechanism by which premature complexes or pacing history can interact with electrical restitution properties, including the dependence of action potential duration (APD) and conduction velocity (CV) on the preceding diastolic interval (DI) to produce dynamical heterogeneity of refractoriness, wave break, reentry, and VF7, 8, 9, 10, 11 (see elsewhere12, 13 for reviews).

A series of computational studies has been performed to gain insight into the effects of patterns of variable prematurity of ventricular complexes on inducibility of arrhythmias14, 15, 16, 17, 18, 19, 20; some of these studies14, 15, 16, 17, 18 have employed coupled maps models,21, 22, 23, 24, 25, 26 which are restitution‐based computational models that are well suited for rapid simulation of different wave propagation scenarios. Coupled maps models have been used to examine the effects of premature, irregularly timed stimuli on spatial heterogeneity of refractoriness, conduction block formation, and the vulnerable window for block.14, 15, 16, 17, 18 Gelzer et al27, 28 showed that sequences of premature stimuli that were more likely to cause conduction block in a one‐dimensional (1D) coupled maps model also predictably induced VF in canine hearts in vivo. It was surprising that this relatively simple 1D restitution model could make such accurate predictions about a process as complicated as the emergence of VF in intact hearts. The remarkable nature of these results led to the present study. We were interested in further investigating the nature of the predictive power of this model—whether the mechanism that led to block in the model could be seen in in vitro experiments, and whether this type of block would lead to VT and VF in these experiments.

Specifically, this study is centered on a hypothesized mechanism for sustained VF induction, in which certain patterns of premature complexes produce discordant alternans (ie, APD alternations that are spatially out of phase with one another), leading to conduction block, reentry, and VF. The results of Gelzer et al27, 28 were consistent with this hypothesized mechanism, but limitations of the in vivo experimental setup made it impossible to determine whether intermediate stages in the mechanism, such as discordant alternans, conduction block, and reentry, were evident, or whether the coupled maps model accurately predicted discordant‐alternans patterns or block. In order to further elucidate the mechanism for conduction block and VF, and to examine the accuracy of the coupled maps model, we conducted the present study, in which we tested the in vivo pacing protocols of Gelzer et al27, 28 in canine ventricles in vitro, and recorded the electrical responses using optical mapping methods.

Main Hypotheses

The main stages of the hypothesized mechanism leading to VF, examined here and in Gelzer et al,27, 28 are depicted in the top row of boxes in Figure 1. We note that the in vitro mechanism leading to VF illustrated in Figure 1 is highly simplified, since it omits intermediate stages, such as formation and breakup of spiral waves, along with alternate VF mechanisms, such as triggered activity, which were considered to be outside the scope of the present work. The computational model chosen for this study was a 1D coupled maps model.18, 27, 28 When provided with APD and CV restitution data, the model predicts whether a given combination of variable prematurity of stimuli will induce discordant alternans and/or conduction block. As shown in the bottom row of boxes in Figure 1, the model was only capable of explicitly representing the first 3 stages of the in vitro VF mechanism. For this study, we examined certain portions of the mechanism depicted in Figure 1.

Figure 1

Main stages of the hypothesized mechanism by which premature complexes induce VF. In the top row, premature complexes induce spatially discordant alternans, leading to conduction block, reentrant waves, and VF in vitro. The 1D coupled maps model is capable of simulating the first 3 stages in silico, as shown in the bottom row. Dashed lines indicate pairs of stages that were compared in each of the hypotheses of the study. For instance, the VF‐Prediction Hypothesis asserts that there was a relationship between model‐predicted block and observed VF (specifically that sequences of premature stimuli that tend to produce block in the model would predictably induce VF in vitro). 1D indicates 1‐dimensional; VF, ventricular fibrillation.

Our hypotheses were as follows:

Hypothesis 1 (Alternans‐Pattern‐Prediction Hypothesis): The computational model will correctly predict in vitro patterns in spatial gradients of APD and DI, including discordant alternans, resulting from the premature complexes.

Hypothesis 2 (Block‐Prediction Hypothesis): Sequences of premature stimuli that tend to produce conduction block in the coupled maps model will predictably induce conduction block in vitro.

Hypothesis 3 (VF‐Prediction Hypothesis): Sequences of premature stimuli that tend to produce conduction block in the coupled maps model will predictably induce VF in vitro.

Hypothesis 4 (Reentry‐Precedes‐VF Hypothesis): Instances of sustained VF will be preceded by reentrant waves in vitro.

To aid with recall, the hypotheses are hereafter referred to by their shortened names (eg, Alternans‐Pattern‐Prediction), rather than their numbers. To evaluate the VF‐Prediction Hypothesis, we reproduced the in vivo experiments of Gelzer et al27, 28 in a new environment (in vitro). Evaluation of the remaining hypotheses, which required acquisition of detailed spatiotemporal AP data, provided new, additional data beyond the work of Gelzer et al.27, 28

Methods

The data, analytic methods, and study materials will be made available, upon reasonable request, to other researchers for purposes of reproducing the results or replicating the procedure.

Experimental Preparations

Adult beagle dogs (n=9) of either sex were injected with heparin (300 U/kg), and after 10 minutes were euthanized using Fatal‐Plus (390 mg/mL pentobarbital sodium, Vortech Pharmaceuticals, 86 mg/kg IV), and their hearts were excised rapidly. The right ventricles (RVs) were cannulated through the circumflex coronary artery with polyethylene tubing, excised, and perfused with normal Tyrode's solution at a rate of 20 mL/min, temperature 37.0±1°C, and perfusion pressure 50 to 80 mm Hg. The preparations, which ranged in size from 4 to 8 cm in length, 4 to 5 cm in width, and 0.5 to 1 cm in depth, were stained with the voltage‐sensitive dye di‐4‐ANEPPS (0.5 μmol/L bolus over 15 minutes), then perfused with blebbistatin (8–40 μmol/L bolus in 500–600 mL Tyrode's solution) until the motion artifact was suppressed. The volume of Tyrode's solution was increased to yield 1 to 5 μmol/L working concentration of blebbistatin in 4L of solution.

Fluorescence emissions were collected simultaneously from the epicardial and endocardial surfaces using two Photometrics Cascade 128+ electron‐multiplied charge coupled devices, and the resulting signals (128×128 pixel grid, 500 fps) were recorded using custom‐written data collection software. A Fischer Bloom DTU 215A programmable stimulator was used to deliver sequences of rectangular electrical pulses (8–10 mA, 2–10 ms duration) through a bipolar electrode positioned on the endocardial surface of the tissue. APDs, DIs, and conduction block events were obtained from the endocardial data. This choice was made for consistency with Gelzer et al,27, 28 where monophasic action potentials were collected from the right and left endocardium. In the present study, both endocardial and epicardial data were used to examine the transition from stimulated beats to VF, and to confirm that the preparations were well perfused throughout the experiment.

Pacing Protocols

The pacing protocols used in this study were based on those of the “Group B” experiments in Gelzer et al.27 In our first protocol, a sequence of 10 S1 stimuli (cycle length, 500 ms) was applied to the endocardial surface, followed by up to 4 premature stimuli (S2–S5). This protocol was designed to (1) identify the effective refractory periods (ERPs) and (2) test whether different combinations of premature stimuli would induce sustained VF (≥30 seconds). To begin to identify the S2 ERP, a single premature stimulus (S2) was delivered with an S1S2 interval of 250 ms directly after the sequence of 10 S1 stimuli. The premature stimulus was then delivered at progressively earlier times relative to the 10th S1 stimulus until S2 failed to capture. The S2 ERP was then defined as the minimum S1S2 interval at which S2 captured (S1S2,min). To identify the S3 ERP, the previous process was repeated after adding an S3 stimulus, and the size of the S2S3 interval was reduced until S3 failed to capture. S4 and S5 ERPs were identified similarly. If alterations were made to the timings of the premature stimuli, for example, if the timing of S3 was adjusted to change the S2S3 interval from S2S3,min to S2S3,min+50 ms, the values of all subsequent ERPs (S4 and S5) were affected and needed to be reidentified.

In the first protocol, interstimulus intervals ending with premature stimuli were categorized as short, intermediate, or long (S, I, or L), as follows. The difference between cycle length (SnSn+1) and ERP (SnSn+1,min) of the interval between Sn and Sn+1 was defined as ΔSnSn+1=SnSn+1–SnSn+1,min, for n=1, 2, 3, 4. Each cycle length (CL) that ended with a premature stimulus was classified as short (S), intermediate (I), or long (L), depending on the size of the ΔSnSn+1 value, that is, the amount by which the CL exceeded the ERP. The categories were defined as “S”: 0≤ΔSnSn+1≤5 ms, “I”: 5<ΔSnSn+1≤40 ms, and “L”: ΔSnSn+1>40 ms. Hence, an S2–S5 sequence with ΔS1S2=5 ms, ΔS2S3=50 ms, ΔS3S4=0 ms, ΔS4S5=2 ms, belongs to the category SLSS. “X” is a placeholder that refers to an interval of any length, thus XL includes all S2–S3 sequences in categories SL, IL, and LL. Different combinations of premature stimulus sequences were applied to the tissue, and it was noted whether any of them induced sustained VF. For each preparation, we attempted to test examples from as many distinct sequence categories as possible, starting with SX and SLSX, and progressing through other sequence categories as time permitted. This sequence search was interwoven with the ERP identification protocol, both due to the need to reidentify ERPs when changes were made to the preceding intervals, and because searching for ERP values automatically led to applying different premature stimulus combinations to the tissue. The complete list of sequences that were tested, along with VF outcomes, is described in Data S1 and shown in Table S1.

The second protocol was a dynamic pace‐down protocol used to generate APD‐DI restitution data.29 Sequences of 50 stimuli were delivered to the tissue at a constant cycle length, starting with S1S1=600 ms. After each round of 50 stimuli, the cycle length was decreased by 50 ms intervals until S1S1=300 ms, by 25 ms intervals until S1S1=200 ms, and then by 10 ms intervals until an arrhythmia was induced or 2:1 block occurred.

All experimental procedures were approved by the Institutional Animal Care and Use Committee of the Center for Animal Resources and Education at Cornell University.

Overview of Data Sets and Data Requirements

Three of our hypotheses, specifically the Alternans‐Pattern‐Prediction, Block‐Prediction, and VF‐Prediction Hypotheses, made claims about the predictive capabilities of the coupled maps model. Hence, to test these hypotheses, we needed to obtain all required inputs to the model, which included ΔSnSn+1 values, APD versus DI curves (called APD restitution curves), and CV versus DI restitution curves.

To test the Alternans‐Pattern‐Prediction and Block‐Prediction Hypotheses, we restricted our analysis to premature stimulus trials in the SLSS sequence category and nearby categories, that is, SLIX and SLSX. These patterns were of interest because SLSS sequences were shown to be arrhythmogenic in previous studies.27, 28 Due to the large number of steps currently required to process each premature stimulus trial, we randomly selected 18 trials (2 per dog for all 9 dogs) from the SLIX/SLSX group, as opposed to processing all trials, which numbered in the hundreds per dog. Selected trials were confined to recordings where all 5 stimuli (S1–S5) captured, to avoid certain trials where a stimulus failed to induce an AP or was preempted by a spontaneous complex. We are using the term stimulated complex to refer to an action potential induced by an Sn stimulus, where n = 1, 2, 3, 4, or 5, while spontaneous complex refers to a nonstimulated action potential. To test the Alternans‐Pattern‐Prediction Hypothesis, one additional trial, specifically the second of the 2 trials from the Dog 5 data set, was excluded from the 18 randomly selected trials, due to several missing APD measurements for the premature beats. The missing measurements were caused by incomplete repolarization of the premature APs; that is, the repolarizations for this trial did not all drop below APD50, which was the threshold chosen for the premature stimulus trials.

To test the VF‐Prediction Hypothesis, the main data source, in addition to the restitution curves, was the list of tested premature stimulus sequences and corresponding sustained VF outcomes, which is shown in Table S1. To evaluate the Reentry‐Precedes‐VF Hypothesis, we used videos of AP propagation across both the endocardial and epicardial surfaces, obtained from 15 recordings where sustained VF followed a sequence of premature stimuli.

Data Analysis

Normalization and averaging

As an initial step, the optical data files were read into a custom‐written Java processor.30 Membrane potential data were indexed by pixel coordinates (x, y) in the selected imaging plane (endocardial or epicardial) and by time (t). The data were normalized on a scale from 0 to 10 000, then time‐averaged using a uniformly weighted 7‐step average centered on time t, and spatially averaged using a Gaussian‐weighted average over a 13×13‐pixel grid centered on pixel (x, y), with a variance of 2 pixels squared. The normalized and averaged membrane potential value at location (x, y) and time t was denoted as V(x, y, t). All subsequent processing steps were carried out in MATLAB (Mathworks, Natick, MA).

APD computation and determination of APD restitution functions

The recordings contained endocardial and epicardial views of the right ventricles, along with parts of the surrounding heat bath. To exclude the heat bath from the recordings, pixels for which the temporal standard deviation of V(x, y, t) fell below a specified threshold were excluded from the data sets. The threshold was adjusted manually for each recording and was typically in the range of 1000 to 3000 in normalized membrane potential units. In cases where this method did not identify the tissue boundary clearly, the dish region was masked out manually. The remaining steps were applied to the endocardial data. Depolarization times were computed as the times at which local maxima of dVf/dt occurred, where Vf refers to V(x, y, t) time‐series data that were passed through a zero‐phase‐shift second‐order low‐pass Butterworth filter (cutoff frequency=0.15×Nyquist frequency). Filtering was used only at this stage to reduce noise in the dV/dt signals, which facilitated identification of the local maxima. The resting potential between successive APs was computed as the minimum V(x, y, t) value between successive depolarization times, except when an AP did not achieve full repolarization, in which case the resting potential following that AP was set equal to the most recent local minimum of V(x, y, t) that was preceded by full repolarization. The amplitude of each AP was computed as the difference between its maximum value over time and the preceding resting potential value. Repolarization times were marked at 50% (for premature stimulus data) or 75% (for dynamic pace‐down data) of full repolarization and used to compute APD50 and APD75 values, in milliseconds. For the dynamic pace‐down data, APD was modeled as a function of the preceding DI. For each preparation, an APD restitution curve was obtained by performing a nonlinear least squares fit of the function APD=a+b e−DI/c to APD and DI values derived from the pixel at the centroid of the endocardial region.

ERP computation

ΔSnSn+1 values (ie, ERPs subtracted from CLs) for S1–S5 were required for sorting premature stimulus trials into sequence categories for comparison with VF outcomes. For the 18 randomly selected trials, these values were used as inputs to the coupled maps model. Cycle lengths were imported from laboratory notes or determined from AP emergence times in optical mapping recordings. ERPs, which were measured using the protocol described previously, typically had an uncertainty of −0/+2 ms; for example, if capture was observed at 168 ms but not at 166 ms, then the ERP was known to be >166 ms but ≤168 ms. However, for certain trials, ERP measurements were either unavailable because of the ERP identification protocol being interrupted by an arrhythmia, or had higher uncertainty (≥10 ms) due to infrequent situations, such as ERP values drifting over time, that led us to be less certain of the threshold for capture. We computed averages of low‐uncertainty ERP values (organized by sequence category) by drawing from premature stimulus data for all 9 dogs, then used these average values to replace unavailable or highly uncertain ERP measurements.

Determination of APD and DI spatial gradients

For each of the 18 randomly selected trials, we computed ΔAPD/Δx (a measure of the spatial gradient of APD) for each AP. To start with, for each of the 9 dogs, we selected x prox=(x1prox, x2prox), a point proximal to the stimulating electrode, and x dist=(x1dist, x2dist), a point distal to the electrode. Both points were chosen on the endocardial surface based on visual inspections of wave front isochrone plots for S1–S5. x prox was chosen near the tip of the stimulating electrode, and x dist was chosen to lie on the proximal side of the region of wave front slowing (≤10 cm/s), over all trials selected for that dog, that was closest to the center of the tip of the stimulating electrode. The electrode tip was visible in each recording, and its location was estimated visually. The motivation for this selection method was to identify a span of tissue, bracketed by the proximal and distal points, that was uninterrupted by conduction block. The proximal and distal points were held fixed across trials within each dog but varied from one dog to the next.

To reduce the influence of noise and outliers on our measurements, we chose to first compute median APD values over proximal and distal regions, which we defined as squares, each with side length 0.5 cm. One vertex of the proximal square was anchored to x prox, a vertex of the distal square was anchored to x dist, and the squares were then aligned to avoid overlap with the electrode and with regions of wave front slowing. The spatial gradient of APD was then defined aswhere APDdist,med and APDprox,med are, respectively, the median APD values over the distal and proximal squares, and Δx=|x dist–x prox| is the Euclidean distance between x dist and x prox. ΔDI/Δx was computed similarly. ΔAPD/Δx and ΔDI/Δx values were computed from APD50 and DI50 data. While APD75 and DI75 would have been preferred to maintain consistency with the dynamic pace‐down measurements, the lack of full repolarization on many premature complexes made these quantities difficult to obtain. In future work, extrapolation methods31 could be explored as an alternative approach for estimating APD75.

Calculation of beat‐to‐beat changes in APD and DI spatial gradients

We defined Δ(ΔAPD/Δx)S3,S2,i (for i=1, 2, …, N) to be the value of ΔAPD/Δx measured for stimulus 3 minus the value of ΔAPD/Δx for stimulus 2 during the i‐th observation out of a total of N, with Δ(ΔAPD/Δx)S4,S3,i, and Δ(ΔAPD/Δx)S5,S4,i similarly defined. When Δ(ΔDI/Δx) was of interest, Δ(ΔDI/Δx)S3,S2,i, Δ(ΔDI/Δx)S4,S3,i, and Δ(ΔDI/Δx)S5,S4,i were defined analogously.

Identification of conduction block regions

For each of the 18 randomly selected trials, we marked the locations on the endocardial surface, if any, where conduction block occurred. To accomplish this, the CV magnitude at each (x, y) point was computed as the reciprocal of the magnitude of the gradient (in seconds per centimeter), computed using the “gradient” function in MATLAB, of the depolarization time at that point. Conduction block was defined as

Sufficiently slow speed, meaning a CV magnitude between 0.5 cm/s and 10 cm/s, where the lower bound was included to filter out weakly stained areas at the tissue border, and

Visual evidence that the orientation of the wave front isochrones changed direction between the proximal and distal sides of the proposed location of the line of block.

We included the second part of the definition to isolate areas of wave slowing that seemed more likely to be able to induce reentrant behavior. Condition (1) was verified using a MATLAB script that highlighted regions of slow speed on spatial maps of the endocardial surfaces. Condition (2) was verified by visual inspection of activation maps. Examples of conduction block regions are shown in the S5 AP activation maps in the Results section.

One‐Dimensional Coupled Maps Model

We used a 1D coupled maps model, shown in Equations [Link], (1), (2) below, that was previously used by Otani18 to predict the spatiotemporal evolution of APs resulting from premature stimuli applied at one end of the fiber. Eq. [Link] describes the n‐th APD as a function of distance x along a 1D fiber of length L, where the stimulus is applied at the left end (x=0), Eq. (1) describes how the n‐th basic cycle length (BCL) varies along the fiber due to the effects of CV restitution, and Eq. (2) relates DI, BCL, and APD at distance xj along the fiber. The APD and CV restitution functions, which are α(.) and v(.) respectively, are given in Table 1. For all simulations, each fiber was discretized into segments of uniform length dx=0.25 cm, where xj=j dx.

Table 1

Parameter Values for Coupled Maps Model Simulations

Parameter Name	Parameter Setting or Source
Fiber length	7 cm
Spatial step size, dx	0.25 cm
APD restitution parameters a, b, c APD=α(DI)=a+b e−DI/c in ms	Obtained from curve fit to pace‐down data (1 set of values per right ventricle)
DImin	Minimum DI, in milliseconds, measured during pace‐down (1 value per right ventricle)
Parameters from restitution function CV=v(DI)=72(1–e−(DI−DImin+34.82)/28.0)) in cm/s	Version used by Gelzer et al27, 28 modified to be consistent with typical measurements of DImin

APD indicates action potential duration; CV, conduction velocity; DI, diastolic interval.

For each right ventricle, coupled maps model simulations were conducted using APD restitution and DImin (the minimum DI value measured during the dynamic pace‐down protocol) parameters calibrated to dynamic pace‐down data obtained from that ventricle, along with CV restitution parameters (other than DImin) based on those of Gelzer et al.27, 28 Values and/or sources for the parameters are listed in Table 1.

Gelzer et al27, 28 computed APD restitution curves from their monophasic action potential data, but obtained the non‐DImin CV restitution parameters from a different study by Riccio et al,32 in which CV was measured in beagle myocardium. Gelzer et al had no means of measuring CV in their in vivo setup; hence, it was essential for them to obtain CV restitution curves from a different source. In our study, we aimed to make our prediction methods similar to those of Gelzer et al in order to make a fairer comparison with their results; therefore, we obtained APD restitution curves from our optical data but used CV restitution curve parameters based on those of Riccio et al.32 In accordance with Gelzer et al, we adjusted one CV restitution parameter, DImin, to match the value observed in each ventricle.

To test the Alternans‐Pattern and Block‐Prediction Hypotheses, for each of the randomly selected premature stimulus trials, a corresponding coupled maps simulation was performed in MATLAB with premature stimulus timings that matched the in vitro ΔSnSn+1 values. From these simulations, we recorded values of ΔAPD/Δx and ΔDI/Δx, along with the location of conduction block, if any. For the coupled maps model simulations, the spatial APD gradient was defined as:

Here, xprox was fixed at the left (stimulated) end of the fiber, and |xdist–xprox| was set to the smallest of the following quantities: the fiber length, the distance between the left end of the fiber and block (if any occurred), or the Δx value used in the corresponding in vitro trial. There was no need to take medians of APD values since the simulations were fully deterministic. ΔDI/Δx was computed in a similar fashion.

To test the VF‐Prediction Hypothesis, simulations of hundreds of thousands of combinations of premature stimuli were performed, covering 1 to 4 premature stimuli, and testing all possible combinations of CL − ERP (ie, ΔSnSn+1) values in the range of 0 to 70 ms, in increments of 1 ms, for each interstimulus interval. For each stimulus sequence tested in this manner, the block outcome (ie, whether block occurred) was recorded. Conduction block was treated as an indicator of the overall arrhythmogenic potential of a sequence: if ≥25% of the tested sequences in a category (eg, SS) yielded block in simulations, then that category was classified as being likely to produce VF in vitro.

Statistical Analysis

To test the Alternans‐Pattern‐Prediction Hypothesis, which asserts that the model will correctly predict in vitro spatial gradients of APD and DI, we focused on beat‐to‐beat changes in sign of these quantities. For the randomly selected trials, the possibility that Δ(ΔAPD/Δx) or Δ(ΔDI/Δx) alternate in sign, specifically that they follow a discordant‐alternans (−, +, −) pattern, was evaluated using a Bayesian statistical approach. Values of Δ(ΔAPD/Δx) or Δ(ΔDI/Δx) for the three pairs of adjacent complexes (S2–S3, S3–S4, and S4–S5) were formed into length‐3 vectors y i, i=1, 2,…, N. Here, i is the index of the observation, and d=3 is the number of elements in each vector y i; for example, when analyzing APD spatial gradients, the elements of y 5 are the 3 sequential values of Δ(ΔAPD/Δx) observed in the fifth trial in the set of randomly selected trials. We assumed that the y i's were independently generated by a Gaussian distribution with mean μ=(μ1, μ2, μ3) and precision matrix Λ. A classic noninformative prior known as the independence Jeffrey's prior33, 34 was chosen for (μ, Λ) with density function

By applying Bayes’ theorem, p(μ, Λ|x) ∝ p(x|μ, Λ) p(μ, Λ), where x represents the set of N observations y 1, y 2, …, y N, the posterior distribution of is known to be a normal‐Wishart distribution. More precisely, the posterior distribution may be expressed in the following categorical form where and . Integrating the posterior distribution over the entire domain of the precision matrix leads to the posterior marginal density function for μ:which is known to be a multivariate t‐distribution.

The posterior distribution p(μ|x), regarded as a function of μ, was then integrated over each of the 8 coordinate‐axis‐defined octants, yielding the posterior probability that μ (ie, the population vector means of Δ(ΔAPD/Δx) or Δ(ΔDI/Δx)) would have the set of signs associated with that octant. Each octant covers one of the 8 possible sequences of arithmetic signs, including (+, +, +), (−, −, −), (−, +, −), etc. The integration was carried out by applying Simpson's rule in all 3 directions using 101 grid points in each direction. The sum of these 8 probabilities was also checked to see if it was close to 1.0 to within acceptable error. The posterior probabilities for APD and DI gradient changes are given the Results section, with further detail provided in Tables S2 and S3. To help visualize the posterior distribution, the contour plots of the posterior marginal density functions for (μ1, μ2), (μ2, μ3) and (μ1, μ3) [denoted by p(μ1, μ2|x), p(μ2, μ3|x) and p(μ1, μ3|x), respectively] were also created and are shown in Figures S1 and S2. MATLAB was used for these computations.

To test the Block‐Prediction Hypothesis, we examined the coupled maps model's ability to predict conduction block instances that were observed in the optical data, by tallying simulated and observed block occurrences in a 2×2 table. While we considered using Fisher's exact test to test the hypothesis, we instead chose to apply a Wald test to a generalized estimating equation (GEE) logistic regression model, where the GEE model incorporates clustering by dog, to appropriately control for the dependence of observations on dogs. In the GEE model, the binary dependent variable was the occurrence of measured conduction block and the binary explanatory variable was the occurrence of simulated block. The comparisons between predicted and measured block were limited to block on the S5 wave front because, for the randomly selected trials, the model did not predict any instances of block on S1–S4 (this was a consequence of our choice to sample only from sequence categories near SLSS, for which the model is highly unlikely to predict block on S1–S4).

To test the VF‐Prediction Hypothesis, we indexed each in vitro test of a stimulus sequence category (such as SLSS) by (1) the dog; (2) model prediction, ie, whether ≥25% or <25% of the combinations of stimulus timings in that category produced block in simulations of the coupled maps model; and (3) outcome, ie, whether sustained VF was induced in vitro. Next, we analyzed the data using 2 different statistical methods to determine the significance of the association between the coupled maps predictions and the in vitro VF outcomes. In the first method, which was based on the statistical approach of Gelzer et al,27, 28 we used JMP (SAS Institute Inc., Cary, NC) to apply an effect likelihood ratio test to a logistic regression model of sustained VF responses, where the sustained VF outcome was the binary dependent variable, and the explanatory variables were the binary (≥25% or <25%) coupled maps model prediction and the dog index (1–9). This approach was included in this study to allow direct comparisons of our results with those of Gelzer et al.27, 28 In the second statistical method, a Wald test was applied to a GEE logistic regression model, with sustained VF outcome as the binary dependent variable, and coupled maps prediction as the binary explanatory variable, with clustering by dog. The GEE‐based method is considered to be more reliable than the first method because the GEE approach controls more appropriately for the dependence of observations on dogs. All GEE logistic regression models used in this study were constructed and analyzed in R (R Foundation for Statistical Computing), using logit.gee within the zelig package.35, 36, 37 For all statistical tests, a value of P<0.05 was considered statistically significant.

Classification of Sign Patterns

To aid in the analysis of the Alternans‐Pattern‐Prediction Hypothesis, we sorted the randomly selected trials according to whether they showed good, intermediate, poor, or inverse agreement with the model‐predicted sequence of signs of beat‐to‐beat changes in spatial gradients of APDs and DIs. The model‐predicted sequence of signs was (−, +, −) for (Δ(ΔAPD/Δx)S3,S2, Δ(ΔAPD/Δx)S4,S3, Δ(ΔAPD/Δx)S5,S4) for the all of the randomly selected trials. The coupled maps model predicted the same sequence of signs for the Δ(ΔDI/Δx) quantities for the selected trials. Separate sets of agreement scores, one for Δ(ΔAPD/Δx) sequences, and another for Δ(ΔDI/Δx) sequences, were computed according to the following definitions. “Good” agreement was defined as 3 out of 3 measured signs (for example, for a sequence of Δ(ΔAPD/Δx) values) matching the model‐predicted signs; that is, both the measured and model‐predicted sign sequences were (−, +, −). “Intermediate” agreement was defined as 2 of 3 measured signs matching the predicted elements in the sign sequence; for example, an observed sequence of (−, +, +) would fit into the “intermediate” category because the first 2 elements match the model‐predicted signs. “Poor” agreement was defined as only one of the measured signs matching its model‐predicted counterpart; for example, (+, −, −) has poor agreement because only the last element matches with its predicted sign. The “inverse” category was defined as (+, −, +), in which each measured sign was the opposite of its model‐predicted counterpart. We checked the indexing of the APDs and DIs to ensure that any sequences in the “inverse” category were not the result of a mistake (eg, a 1‐step offset) in indexing of the APs.

Assessment of Reentry

To assess the Reentry‐Precedes‐VF Hypothesis, a qualitative visual review was performed of the 15 recordings (not limited to the randomly selected trials) where sustained VF followed a sequence of premature stimuli. This review consisted of watching the corresponding movies of AP progression and examining the events following the stimulated complexes. We made note of behavior that appeared to be consistent with reentry, such as wave front slowing of the final stimulated AP, followed by a shift in the direction of propagation, along with any behavior that did not appear to be reentrant, such as focal spontaneous complexes that emerged directly after the stimulated complexes. To illustrate our classification process further, examples of focal complexes and reentrant behavior are shown in the 2‐dimensional spatial membrane potential images in the Results section. Movies of AP propagation from premature stimulus trials are shown in Movies S1 through S18, of which, Movies S3 and [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link] correspond to the recordings of sustained VF that were observed to follow sequences of premature stimuli.

Results

Optical Mapping Data

Examples of activation maps showing S1 AP wave front arrival times are given in Figure 2. One activation map is shown for each of the 9 endocardial surfaces, where the maps were obtained from the randomly‐selected trials that were used to test the Alternans‐Pattern‐Prediction and Block‐Prediction Hypotheses. There were 2 to 3 S1 APs recorded during each of the randomly selected trials, and a representative S1 activation map is shown for each of the 9 right ventricles. These maps are provided to show the response to slow pacing for each of the ventricles, before the S2 to S5 stimuli were applied. Due to the length of the S1S1 interval (500 ms), the S1 AP propagation was expected to be relatively uniform, compared with the propagation of the S2 to S5 APs. The S1 AP propagation was relatively uniform for Dogs 1 to 8, but the wave front shapes were more complicated for Dog 9, as shown in Figure 2I, which includes an interior region of block that appears as a yellow spot surrounded by black border. Examination of the records for Dog 9 has not revealed any clear differences in anatomy, experimental conditions, or tissue health that would explain its more complex S1 AP propagation.

Figure 2

Activation maps of S1 APs for Dogs 1 through 9. Each 2‐dimensional map shows activation times (in milliseconds) measured on the endocardial surface for an S1 AP. Each map was obtained from one of the 18 randomly selected trials that were used to test the Alternans‐Pattern‐Prediction and Block‐Prediction Hypotheses. A, B, …, I correspond to Dogs 1, 2, …, 9, respectively. AP indicates action potential.

Agreement Scores for Discordant Alternans Sign Patterns

The percentages of randomly selected trials that fit into each of the 4 categories (good, intermediate, poor, and inverse) for discordant alternans sign patterns are shown in Table 2. The first row of Table 2 contains agreement scores for Δ(ΔAPD/Δx) patterns. The second row gives percentages corresponding to predictions for Δ(ΔDI/Δx). Table 2 shows that the majority of trials [64% for Δ(ΔAPD/Δx) and 82% for Δ(ΔDI/Δx)] had either good or intermediate agreement with the model‐predicted sign patterns.

Table 2

Model‐Agreement Scores for Beat‐to‐Beat Changes in APD and DI Spatial Gradients

Quantity	Good (3/3)	Intermediate (2/3)	Poor (1/3)	Inverse (0/3)
Δ(ΔAPD/Δx)	40%	24%	18%	18%
Δ(ΔDI/Δx)	35%	47%	18%	0%

APD indicates action potential duration; DI, diastolic interval.

The first row contains the percentages of premature stimulus trials that fell into each category of agreement (good, intermediate, poor, or inverse) with the sequence of signs predicted for Δ(ΔAPD/Δx) by the coupled‐maps model. For example, for a trial in the “good” category, the signs of all 3 elements in the measured (Δ(ΔAPD/Δx)S3,S2, Δ(ΔAPD/Δx)S4,S3, Δ(ΔAPD/Δx)S5,S4) list of values matched with the model‐predicted discordant alternans pattern of (−, +, −). Trials in the “intermediate,” “poor,” and “inverse” categories had, respectively, 2, 1, or 0 measured signs that matched with the model‐predicted signs. The second row gives percentages corresponding to predictions for Δ(ΔDI/Δx).

Detailed Comparisons of Predictions With Observations

In this section, we show detailed comparisons of selected trials with the stages of the theorized VF mechanism. Membrane potential time‐series data from 4 trials, labeled Trial NB, Trial 1, Trial VF, and Trial 2, where NB stands for “no block,” are shown in Figure 3A through 3D. Each of these trials corresponded to a test of a premature stimulus sequence in the SLSX category. Specifically, these trials are examples of outcomes from our S4S5 ERP identification protocol, where we had already identified ERPs for S1S2, S2S3, and S3S4, were holding S1S2, S2S3, and S3S4 constant in an SLS pattern, and were in the process of searching for the S4S5 ERP through successive reductions of S4S5. This resulted in a progression from SLSL to SLSI, with an intended destination of SLSS.

Figure 3

Time‐series optical data. In each subplot, membrane potential (dimensionless, normalized to a scale of 0 to 10 000) is plotted against time (milliseconds), for a pixel with coordinates near the center of the field of view on the endocardial surface. Stimulated APs are labeled S1, S2, etc. The remaining APs were not stimulated. Several of these nonstimulated APs (ie, spontaneous complexes) are labeled A1, A2, etc, for later reference. A, SLSL stimulus trial (Trial NB) recorded from pixel with coordinates (60, 60) in RV of Dog 4. The stimulus sequence was not predicted to cause block, and sustained VF did not occur in vitro. B, SLSI stimulus trial (Trial 1) recorded from pixel with coordinates (60, 60) in RV of Dog 4. The stimulus sequence was not predicted to cause block, and sustained VF did not occur in vitro. C, SLSI stimulus trial (Trial VF) recorded from pixel (60, 60) in RV of Dog 4. The stimulus sequence was not predicted to cause block, and sustained VF occurred in vitro. D, SLSI stimulus trial (Trial 2) recorded from pixel (70, 70) in RV of Dog 9. The stimulus sequence was predicted to cause block, and sustained VF did not occur in vitro. AP indicates action potential; RV, right ventricle; VF, ventricular fibrillation.

These 4 trials are of interest because they cover a range of levels of agreement and disagreement with model predictions, where one sequence of trials (Trials NB, 1, and VF) initially showed good agreement with model predictions, leading to the anticipated outcome of sustained VF, whereas the remaining trial (Trial 2) initially showed poor agreement with model predictions, and was part of a sequence of trials that did not lead to the anticipated outcome of sustained VF. In making these selections, we favored trials that were members of the randomly selected set of trials chosen for statistical analyses of discordant alternans and conduction block outcomes. The main settings and features of the four trials are summarized below, and the corresponding observations and model predictions for these trials are listed in Table 3.

Table 3

Summary of Experimental and Model‐Predicted Outcomes for Selected Trials

	Discordant Alternans Sign Pattern	S5 AP Conduction Block	Reentry	VF
Dog 4
Trial NB (SLSL)
Experimental outcome	Y	N	N	N
Model prediction	Y	N	N/A	N/A
Trial 1 (SLSI)
Experimental outcome	Y	Y	N	N
Model prediction	Y	N	N/A	N/A
Trial VF (SLSI)
Experimental outcome	Y	Y	Y	Y
Model prediction	Y	N	N/A	N/A
Dog 9
Trial 2 (SLSI)
Experimental outcome	N	Y	N	N
Model prediction	Y	Y	N/A	N/A

AP indicates action potential; NB, no block; VF, ventricular fibrillation.

“Y” indicates that the corresponding experimental outcome (eg, the discordant alternans (–, +, –) sign pattern) was observed in vitro, or that the model predicted that the outcome would occur. “N” indicates that the outcome was not observed in vitro, or was not predicted to occur by the model. Certain entries are labeled N/A (not applicable), since the model cannot directly represent reentry or VF.

Trial NB: This was a test of an SLSL sequence on the RV of Dog 4, with (S1S2, S2S3, S3S4, S4S5)=(160, 160, 102, 170) ms. This trial received “good” agreement scores for both APD and DI‐based discordant alternans sign patterns. The coupled maps model predicted that no S5 conduction block would occur, and conduction block was not observed in vitro. Hence, the trial was fully consistent with the model's predictions for both discordant alternans and block. As seen in Figure 3A, the S5 AP was followed by nine spontaneous complexes (ie, APs that occurred spontaneously rather than being induced directly by stimuli). Based on the corresponding movie of AP propagation (Movie S1), the complexes were judged to be focal in nature; the process used for distinguishing focal complexes from reentrant waves is illustrated in more detail later in this section. After the ninth spontaneous complex, no further activity was observed, and VF was not induced.

Trial 1: After Trial NB was recorded, the S4S5 interval was reduced in 2‐ms steps, eventually leading to Trial 1, which was a test of an SLSI sequence on the RV of Dog 4, with (S1S2, S2S3, S3S4, S4S5)=(160, 160, 102, 134) ms. This trial received “good” agreement scores for both APD and DI‐based discordant alternans sign patterns. The coupled maps model predicted that S5 conduction block would not occur, yet conduction block was observed in vitro. As seen in Figure 3B, the S5 AP was followed by eight spontaneous complexes, which were classified as focal, based on our review of Movie S2. After the spontaneous complexes, no further activity was observed, and VF was not induced.

Trial VF: After Trial 1 was recorded, the S4S5 interval was reduced in 2‐ms steps, leading to Trial VF, which was a test of an SLSI sequence on the RV of Dog 4, with (S1S2, S2S3, S3S4, S4S5)=(160, 160, 102, 120) ms. This trial received “good” agreement scores for both APD and DI‐based discordant alternans sign patterns. The coupled maps model predicted that S5 conduction block would not occur, yet conduction block was observed in vitro. As seen in Figure 3C, the S5 AP was followed by VF, and a review of the corresponding movie (Movie S3) showed evidence of reentry preceding VF. Unlike Trials NB, 1, and 2, Trial VF was not a member of the set of 18 randomly selected trials used for statistical analyses of alternans and block predictions, but data from Trial VF are shown here to provide an example of sustained VF induction.

Trial 2: This was a test of an SLSI sequence on the RV of Dog 9, with (S1S2, S2S3, S3S4, S4S5)=(184, 190, 148, 110) ms. This trial received “poor” agreement scores for both APD and DI‐based discordant alternans sign patterns. The coupled maps model predicted that S5 conduction block would occur, and conduction block was observed in vitro. As seen in Figure 3D and Movie S4, no further activity was observed after the S5 AP, and VF was not induced.

For Dog 4 (the source of Trials NB, 1, and VF), successive reductions of S4S5 eventually led to sustained VF. For Dog 9 (the source of Trial 2), sustained VF after SLSI was induced in an earlier trial with (S1S2, S2S3, S3S4, S4S5)=(184, 190, 144, 110) ms, and the corresponding VF induction is given in Movie S18. After testing different combinations of stimulus sequences, such as SL and SLS, on the RV of Dog 9, we returned to the SLSI category, during which Trial 2 was recorded, but we were unable to replicate the sustained VF induction that was observed earlier in the experiment, although reducing S4S5 in trials subsequent to Trial 2 sometimes yielded spontaneous complexes or non‐sustained VF (data not shown).

Comparison of Trial 1 and Trial 2

Trials 1 and 2 were chosen for a head‐to‐head comparison, since they both belonged to the SLSI category, but were very different in their degrees of agreement with model‐based predictions of discordant alternans. The corresponding model‐predicted and measured ΔAPD/Δx and ΔDI/Δx quantities, plotted against stimulus index (S1–S5), are shown in Figure 4. Trial 1 (Figure 4A and 4B), which was a member of the “good” agreement category for discordant alternans patterns, yielded relatively good agreement between the model‐predicted and measured sign patterns of APD and DI spatial gradients, while the second trial (Figure 4C and 4D), which was a member of the “poor” agreement category, showed comparatively poor agreement between predicted and observed patterns.

Figure 4

ΔAPD/Δx and ΔDI/Δx vs stimulus index for Trials 1 and 2. Black dashed lines with asterisks indicate model‐predicted values, and red solid lines with squares represent measured values. A and B, An example of good agreement between modeled and measured values, from an SLSI stimulus sequence applied to the RV of Dog 4. C and D, An example of poor agreement, from an SLSI stimulus sequence applied to the RV of Dog 9. APD indicates action potential duration; DI, diastolic interval; RV, right ventricle.

To explore in more detail the “good” and “poor” trial examples in Figure 4, the S2–S5 activation maps from Trials 1 and 2 are given in Figure 5. In each plot, the green square surrounds the proximal region, while the red square surrounds the distal region. The distal region selection was constrained by the need to find a proximal‐to‐distal span that was uninterrupted by conduction block, since the coupled maps model predicts wave behavior up to the point of block within a 1D fiber, but does not make any predictions in locations distal to the block site. Locations of conduction block (as defined in the Methods section) of the S5 AP wave front that occurred close to the electrode are indicated with pink arrows in Figure 5D and 5H.

Figure 5

Activation maps for S2–S5 APs for Trials 1 and 2. Endocardial activation times (in milliseconds) are shown for Trial 1 from Dog 4 and Trial 2 from Dog 9. The green squares surround the proximal regions, while the red squares surround the distal regions. A–D, Activation maps for S2–S5 APs for Trial 1, in which an SLSI premature stimulus sequence was applied to the RV of Dog 4. This trial was in the “good” category of agreement scores with coupled maps model predictions of discordant alternans patterns. E–H, Activation maps for S2–S5 APs for Trial 2, in which a SLSI premature stimulus sequence was applied to the RV of Dog 9. This trial was in the “poor” category of agreement scores with coupled maps model predictions of discordant alternans patterns. Regions of conduction block, on the S5 AP wave fronts, which are closest to the stimulating electrode are indicated with pink arrows in D and H. AP indicates action potential; RV, right ventricle.

Notable distinctions between the activation maps for Trials 1 and 2 include the greater number of instances of conduction block in Trial 2, along with the shorter distance between the proximal and distal locations in Trial 2. Possible reasons for the discrepancies in the degrees of agreement with model predictions are explored further in the Discussion section.

Comparisons of Trials NB, 1, and VF

Trials NB, 1, and VF were members of a sequence of trials that eventually led to sustained VF in the RV of Dog 4. As described previously, the stimulus timings up through S4 were the same for these trials, but each trial had a different S4S5 interval. The corresponding spatial gradients of APD, along with the S5 activation maps, are shown in Figure 6. For convenience in making comparisons, the APD and S5 activation time data from Trial 1, previously shown in Figures 4A and 5D, are reproduced in Figure 6B and 6E, respectively. All 3 trials met the criteria for the “good” category of agreement with predicted discordant alternans sign patterns, and from Figure 6A through 6C, it can be seen that the predicted and observed APD spatial gradients were similar for all 3 trials. Figure 6E and 6F show that conduction block occurred in vitro after S5 in Trials 1 and VF, and that in Trial VF, there were a number of additional regions of block that appeared in the region near the electrode. The model correctly predicted the absence of block of the S5 AP wave front in Trial NB but failed to predict the S5 AP block that was observed in Trials 1 and VF. The incorrect block prediction observed in Trials 1 and VF appeared to be part of a larger trend, where the model tended to underpredict conduction block, in general. This tendency is explored further in our statistical analysis of block and the related portion of the Discussion section.

Figure 6

Spatial gradients of APD and activation maps for S5 APs for Trials NB, 1, and VF. A–C, ΔAPD/Δx vs stimulus index for Trial NB (SLSL, left), Trial 1 (SLSI, middle) and Trial VF (SLSI, right), recorded from tests of premature stimulus sequences on RV of Dog 4. Black dashed lines with asterisks indicate model‐predicted values, and red solid lines with squares represent the measured values. D–F, 2‐dimensional spatial maps of activation times (in milliseconds) measured on the endocardial surface for the S5 AP, for Trial NB (left), Trial 1 (middle), and Trial VF (right). The green square surrounds the proximal region, while the red square surrounds the distal region. Regions of conduction block, on the S5 AP wave fronts, which are closest to the stimulating electrode, are indicated with pink arrows in E and F. AP indicates action potential; APD, action potential duration; NB, no block; RV, right ventricle; VF, ventricular fibrillation.

In Trial NB and Trial 1, the S5 AP was followed by spontaneous activity, seen in Figure 3A and 3B. The spontaneous activity seen in Trial 1 is contrasted with the reentrant behavior witnessed in Trial VF in Figures 7 and 8. A visual review of frames, shown in Figure 7, from the Trial 1 movie (Movie S2) indicated that the 8 spontaneous complexes in Trial 1 appeared to be focal in nature, in the sense that they appeared to originate from a localized region on the endocardium, rather than from the S5 AP reentering previously activated tissue. Examples of these localized regions are shown in Figure 7C and 7E, where complexes A1 and A2 were seen to emerge, and in Figure 7G through 7J, where the emergence locations of complexes A3 and A4 are shown. The 9 spontaneous complexes that were observed after the S5 AP in Trial NB were very similar to the A3 and A4 complexes in Figure 7G through 7J. The initial time, t=0 ms, for Figures 7 and 8, as well as for Movies S2 and S3, corresponds to t=800 ms in the time‐series plots (Figure 3B and 3C), since the movie start times were offset to begin shortly before the final S1 AP.

Figure 7

Spontaneous complexes following S5 AP during Trial 1. Endocardial view (left), with corresponding epicardial view (right) of 2‐dimensional spatial membrane potential data (dimensionless, normalized to a scale of 0 to 10 000), recorded from a test of an SLSI premature stimulus sequence on RV of Dog 4. Sustained VF was not induced. The spatial scales are the same in both the endocardial and epicardial images, and the epicardial view was registered to match the orientation of the endocardial view. Arrows indicate the directions of propagation of AP wave fronts and wave backs. A, Frame recorded at 730 ms shows the emergence of the S5 AP, along with the retreating wave back of the S4 AP. The stimulating electrode tip is located near the purple star. Pink parallel lines indicate the location of conduction block. B, Epicardial view at 730 ms. The S4 AP wave back was retreating, and the S5 AP had reached the epicardial surface. C and D, Views of the exiting S5 AP wave back at 808 ms. In C, a spontaneous complex, labeled A1, appeared at the location marked with a blue asterisk. A1 was classified as a “focal” spontaneous complex, since A1 appeared to emerge spontaneously from a localized region on the endocardium, rather than being caused by reentry. E and F, Views of the exiting A1 AP wave back at 920 ms. In E, another spontaneous focal complex, labeled A2, emerged from the location marked with a blue asterisk. G and H, Views from 1096 ms, showing a spontaneous focal complex, labeled A3, which appeared to emerge from the boundary of the RV (in the lower left corner of the image) and proceeded to propagate throughout the ventricle. I and J, Views from 1282 ms, showing a spontaneous focal complex, labeled A4, which appeared to emerge from the same location as A3. A4 subsequently propagated throughout the ventricle. After the events shown in this figure, 4 additional spontaneous complexes that behaved similarly to A3 and A4 were observed after A4, but no reentrant activity was observed. A movie of the optical mapping data from this trial is available in Movie S3. AP indicates action potential; RV, right ventricle; VF, ventricular fibrillation.

Figure 8

Reentry following S5 AP during Trial VF. Endocardial view (left), with corresponding epicardial view (right) of 2‐dimensional spatial membrane potential data (dimensionless, normalized to a scale of 0 to 10 000), recorded from a test of an SLSI premature stimulus sequence on RV of Dog 4. Sustained VF was induced. The spatial scales are the same in both the endocardial and epicardial images, and the epicardial view was registered to match the orientation of the endocardial view. Arrows indicate the directions of propagation of AP wave fronts and wave backs. A, Frame recorded at 804 ms shows the emergence of the S5 AP, along with the retreating wave back of the S4 AP. The stimulating electrode tip is located near the purple star. B, Epicardial view at 804 ms. The S4 AP wave back was retreating, while the S5 AP had not yet reached the epicardial surface. C and D, Views of S5 AP propagation at 880 ms. In C, a spontaneous complex, labeled A1, appeared at the location marked with a blue asterisk. E and F, Views of A1 AP propagation at 970 ms. In E, a spontaneous complex, labeled A2, emerged from the A1 AP, at the location marked with a blue asterisk, and propagated into the region near the electrode. G and H, Views from 1028 ms, showing the propagation of the A2 AP. In G, a portion of the A2 wave front encountered slow conduction near the region marked with a pink “x.” I and J, Views from 1070 ms, showing the propagation of the A2 AP. After activating the region of slow conduction, a portion of the A2 AP reentered the region near the electrode, as shown in I, where the reentrant wave front is labeled with an “R.” After the events shown in this figure, another cycle of reentry, similar to the process shown in G and I, was observed, followed by increasingly disorganized propagation and VF. A movie of the optical mapping data from this trial is available in Movie S3. AP indicates action potential; RV, right ventricle; VF, ventricular fibrillation.

Reentry was observed before VF in Trial VF. The initiation of reentry after S5 is shown in Figure 8. Figure 8C shows that the S5 wave back moved away from the electrode, while a spontaneous complex, labeled A1, appeared near the location marked with a blue asterisk. A spontaneous complex, labeled A2, emerged from the A1 AP and propagated into the region near the electrode (Figure 8E), and a portion of the A2 wave front encountered slow conduction near the region marked with a pink “x” (Figure 8G). After activating the region of slow conduction, a portion of the A2 AP reentered the region near the electrode (Figure 8I), where the reentrant wave front is labeled with an “R.” After the events shown in this figure, another cycle of reentry, similar to the process shown in Figure 8G and 8I, was observed, followed by increasingly disorganized propagation and VF. A movie of optical mapping recordings for Trial VF, showing the evolution of the S1–S5 APs followed by reentry and VF, is included in Movie S3. The observed sequence of events (discordant APD alternation, block, reentry, VF) in Trial VF was fully consistent with the in vitro mechanism in the top row of Figure 1.

Converting the SLSI stimulus sequence from the nonarrhythmogenic combination used in Trial 1 to the VF‐inducing combination in Trial VF was a simple matter of reducing the S4S5 interval, but other, more complex patterns of agreement and disagreement with the theorized VF mechanism were observed, for example in Trial 2, which showed block but no evidence of discordant alternans or reentry.

Hypothesis Testing

We conducted analyses to test each of our 4 hypotheses, to determine to what extent, if any, the predicted phenomena were present in the data. To test the Alternans‐Pattern‐Prediction Hypothesis, we measured spatial gradients of APD and DI in each of the randomly selected premature stimulus trials and compared the results with values simulated with the coupled maps model. The coupled maps model predictions shown in Figure 4 suggest that differences in ΔAPD/Δx and ΔDI/Δx for successive stimuli alternate in sign. That is, the coupled maps model predicted that the signs of both Δ(ΔAPD/Δx) and Δ(ΔDI/Δx) should follow a discordant‐alternans (−, +, −) pattern. To evaluate this tendency, we used the Δ(ΔAPD/Δx) and Δ(ΔDI/Δx) data to calculate posterior probability distributions of the means of these quantities under the assumed Gaussian distribution. These distributions were then used to determine the posterior probabilities for all possible sequences of signs of the means of Δ(ΔAPD/Δx) and Δ(ΔDI/Δx) for S3 relative to S2, S4 relative to S3, and S5 relative to S4, with the expectation that the predominantly likely sequences should alternate. We found that, for the Δ(ΔAPD/Δx) data, the (−, +, −) pattern of signs was most likely, with a posterior probability of 91.1%. All other sequences of signs had posterior probabilities of less than 6%. For the Δ(ΔDI/Δx) data, the most likely sequence was again (−, +, −), with a posterior probability of 82.1%. The next most likely sequence was (−, +, +) with a posterior probability of 17.3%. All other sequences had posterior probabilities of less than 0.4%. These results may be compared to 12.5% (=1/8), which is the prior probability for all 8 possible sequences if no data were available and no pattern of signs were present. A complete listing of probabilities for all possible sign patterns, along with contour plots of the probability density functions, are given in Tables S2 and S3 and Figures S1 and S2.

To test the Block‐Prediction Hypothesis, we tallied the occurrences of model‐predicted and experimentally observed conduction block that occurred on S5 wave fronts for each of the 18 randomly selected trials. The results are summarized in Table 4. The sensitivity and specificity were 64% and 100%, respectively. A Wald test applied to the GEE logistic regression model of conduction block, with clustering by dog, showed that the effect of the coupled maps model prediction of block was significant (P<1×10−15), with a regression coefficient estimate of 44.36 and standard error 0.76. The scale parameter estimate was 0.5, with a standard error of 0.15.

Table 4

Percentages of S5 APs, Organized by Experimental Observation of Conduction Block vs Model Prediction of Conduction Block

Experimental Outcome	Model Prediction
	Block Occurred, %	Block Did Not Occur, %
Block was observed	100 (9/9)	56 (5/9)
Block was not observed	0 (0/9)	44 (4/9)

APs indicates action potentials.

“Experimental Outcome” refers to whether block of the S5 AP wave front was observed in vitro, and “Model Prediction” refers to whether block occurred on the S5 AP wave front in corresponding simulations of the coupled maps model. Numbers in parentheses are the percentages rewritten as fractions of the total number of S5 APs in each of the 2 model prediction categories.

To test the VF‐Prediction Hypothesis, our data set was the complete list of categories of premature stimulus sequences tested in vitro, along with the outcome (whether sustained VF was induced), as shown in Table S1. The sequences most commonly associated with sustained VF were SLSI, which preceded 40% of the recorded inductions, followed by SI, which preceded 27% of the inductions. Our premature stimulus protocol included successive tests of SLSL, SLSI, and SLSS, which were achieved through progressive reductions of S4S5, but SLSS sequences were often unreachable due to instances of VF induced by SLSI (S4S5 could not be reduced further without inducing an arrhythmia). These results are consistent with the predictions of the coupled maps model, which tended to classify SLSI and SLSS sequences as likely to induce VF. Model predictions and experimental outcomes corresponding to the n=184 sets of (sequence, VF outcome) pairs shown in Table S1 are summarized in Table 5. Using the model prediction as a binary predictor of the ability to induce sustained VF yielded a sensitivity of 53% and a specificity of 82%. Applying the Gelzer et al27, 28 statistical method to the data showed that the effect of the model prediction was significant (P<0.0001) according to an effect likelihood ratio test. The P value for the effect of dog (P=0.0485) was close to our chosen threshold for significance (P=0.05), and the implications of this result are explored in the Discussion section. The regression coefficient for the model prediction effect was 1.26 with a standard error of 0.32 (P<0.0001). Next, a Wald test applied to the GEE logistic regression model of VF outcomes, with clustering by dog, showed that the effect of the coupled maps model prediction was significant (P=0.0046), with a regression coefficient estimate of 1.63 and standard error 0.57. The scale parameter estimate was 1.0, with a standard error of 0.98.

Table 5

Percentages of Stimulus Sequence Categories, Organized by Experimental Outcome vs Model Prediction

Experimental Outcome	Model Prediction
	≥25% of Combinations Yielded Block, %	<25% of Combinations Yielded Block, %
VF was inducible	21 (8/39)	5 (7/145)
VF could not be induced	79 (31/39)	95 (138/145)

VF indicates ventricular fibrillation.

“Experimental Outcome” refers to whether sustained VF was induced in vitro, and “Model Prediction” refers to whether ≥25% or <25% of the combinations in the stimulus sequence category yielded block in simulations of the coupled maps model. Numbers in parentheses are percentages rewritten as fractions of the total number of stimulus sequence categories tested in each of the 2 model prediction categories.

To test the Reentry‐Precedes‐VF Hypothesis, we performed a qualitative visual review of the 15 movies (Movies S3 and [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link], [Link]) where sustained VF was observed to follow sequences of premature stimuli. Fourteen (93%) of these instances of VF were judged as likely to have been induced by reentry, according to the approach described in the Methods section. For the remaining instance (Movie S5), VF appeared to have been preceded by spontaneous focal complexes, rather than reentrant waves. Figures 7 and 8 illustrate the types of visual assessments that were used to distinguish between focal complexes and reentrant waves.

Discussion

New Findings and Comparisons With Other Studies

The present study expands upon the mechanistic insights of earlier work,27, 28 which examined the relationship between premature complexes and VF. As described by Gelzer et al27 and outlined in Figure 1, it is hypothesized that specific sequences of premature stimulus intervals (including SLSS and similar sequences) can, through the influence of APD and CV restitution, cause enhanced spatial dispersion of repolarization, leading to spatially discordant APD alternans, conduction block, reentry, and VF. This sequence of events provides an explanation for the observation that certain patterns of premature complexes, including short‐long‐short,5 long‐short3 and short‐long,4 promote reentry, VT, and VF. In this study, we confirmed that the coupled maps model, when supplied with APD restitution data from canine right ventricles, predicted the presence of discordant alternans, in the form of beat‐to‐beat patterns of sign changes in spatial gradients of APD and DI, when compared with observations from optical mapping data. Next, we showed that the model predicted which sequences of premature stimuli were more likely to induce conduction block in vitro. The logistic regression analyses showed that the model‐based classification scheme (≥25% of stimulus combinations yielding block) was a statistically significant predictor of VF in vitro. Our visual assessment of optical recordings indicated that instances of sustained VF were typically preceded by reentry.

Discordant alternans

The results of the posterior probability analysis were consistent with our Alternans‐Pattern‐Prediction Hypothesis, which claims that the computational model will correctly predict in vitro patterns in spatial gradients of APD and DI resulting from the premature complexes. However, observed gradients did not always match model‐predicted patterns, as shown in Figure 4C and 4D and Table 2. This large variability in observed patterns may have been due to variations in the measured APD and DI gradients across individuals, uncertainties in these measurements, and factors (such as spatial heterogeneity of APD and DI) that influence the measured values but are not present in the coupled maps model.

The largest measured spatial gradient in APD shown in Figure 4A has a magnitude of approximately 8 ms/cm and corresponds to a trial where the S5 wave front encountered block in vitro. This magnitude lies within the range of block‐inducing APD gradients (5–50 ms/cm) found in the simulation study of Sampson and Henriquez,38 but well below the range of 100 to 1200 ms/cm reported by Restivo et al for live infarcted canine hearts.39 A number of factors may account for disagreement between our gradient values and those of certain other studies, including differences in experimental conditions, stimulus protocols, and measurement methods.

Regarding the effects of noise, Uzelac and Fenton observed that, for an optical mapping setup that is very similar to ours in terms of equipment, frame rates, and experimental procedures, the signal‐to‐noise ratio is rarely >10 for membrane potential fluorescence data.40 To help address uncertainties in the optical signals, in our Bayesian analysis of discordant alternans, we referred to a base case of 12.5% (=1/8), which is the prior probability for all 8 possible sequences of sign patterns, if no data were available and no pattern of signs were present. That is, we can consider a worst‐case scenario where our Δ(ΔAPD/Δx) (or Δ(ΔDI/Δx)) data are essentially all noise, in which case we could liken the process to a random sign generator that produces 1 of 2 values, “+” or “−,” for each of the S2S3, S3S4, and S4S5 intervals. If the random binary sign generator behaves as a sequence of unweighted, independent coin tosses, then the probability of any ordered triple of 3 coin tosses following the (−, +, −) pattern, or any other pattern, is 12.5% because there are 23=8 possible sequences of 3 signs. Because the posterior probabilities for the (−, +, −) discordant alternans pattern were much larger than 12.5%, this is an indication that a mechanism promoting the discordant pattern is likely present in the data. The signless case, where the beat‐to‐beat change in either spatial gradient is zero, could also have been considered, but zero values did not appear in our Δ(ΔAPD/Δx) or Δ(ΔDI/Δx) data.

Conduction block

The 0% false‐positive rate indicates that the model is accurate when it predicts that block will occur, which was consistent with our Block‐Prediction Hypothesis. However, examination of the data revealed that the model predicted fewer instances of block than were actually observed. A probable reason for the underprediction of in vitro block is the spatially homogeneous nature of the model parameters. Presumably, including heterogeneities in the model would increase the frequency of block occurrences in silico.

In Gelzer et al,27, 28 a fixed fiber length of 7 cm was used for all coupled maps simulations, and no attempt was made in those studies to calibrate the simulated fiber lengths to match closely with the sizes of the intact hearts. In this study, we used the same fiber length of 7 cm for all simulations, even though the RVs varied in size (4–8 cm in length, 4–5 cm in width). The fact that the coupled maps model was found to underpredict block in vitro suggests that reducing certain simulated fiber lengths, to match more closely with the smaller RVs, would not improve the accuracy of the block predictions. Reducing the length of the fiber makes block even less likely to occur in silico, since there is less room for a simulated AP wave front to catch up with a slow‐moving wave back. Including spatial heterogeneity in the model may be a more promising means of increasing the predicted block rate, compared with reducing the fiber length.

As described in the Methods section, we used a 2‐part definition of conduction block, where (1) CV magnitude between 0.5 cm/s and 10 cm/s and (2) visual evidence that the wave front was changing direction across the proposed line of block were both required to conclude that conduction block had occurred in vitro. During the study design phase, we included part 2 of the definition because we anticipated a need to distinguish between instances of “plane‐wave” slowing, where a wave front slows temporarily, but then proceeds along its initial heading, compared with instances where a wave front was slowing and changing its direction. In retrospect, the second part of the definition did not need to be included because all of the observed instances of in vitro block on the S5 AP wave fronts satisfied both parts 1 and 2 of the definition. Hence, if the definition of conduction block were reduced to just the first portion (0.5 cm/s

By providing a direct comparison with in vitro block instances, our findings constitute an extension of the work of Gelzer et al,27, 28 where limitations of the in vivo experimental setup prevented direct observation of block. Other studies24, 41 have made comparisons between numerical predictions and in vitro measurements of block but differed from our approach in one or more respects. For example, Fox et al24 examined discordant alternans and block, using a coupled maps model, an ionic model, and data from Purkinje fibers in vitro. Their study provided evidence for a mechanism similar to the one described in Figure 1, but their approach was centered on rapid pacing rather than premature, irregularly timed stimuli.

Reentry and sustained VF

We found that the coupled maps model's classification of whether a sequence was likely to cause block was a statistically significant predictor of sustained VF. These results corroborate those of Gelzer et al,27, 28 where the same type of prediction method was found to be a statistically significant predictor of VF in canines in vivo. SLSI was the sequence that most often preceded VF in vitro, accounting for 40% of recorded inductions. In our protocol, tests of SLSI progressed to SLSS through successive reductions of S4S5. This process was often interrupted by VF induction following an SLSI sequence, whereas SLSS was reached more frequently in vivo.27 Despite this difference, the results are consistent with predictions of the coupled maps model, which tended to classify both SLSI and SLSS as arrhythmogenic.

Our application of the statistical approach of Gelzer et al,27, 28 showed that the effect of dog in the logistic regression model was close to the threshold for statistical significance. This result is not consistent with those of the earlier studies,27, 28 where the effect of dog was found to be insignificant. From the perspective of a computational modeler, it is more convenient to have an insignificant effect of dog because a lack of significance suggests that the coupled maps parameters may not need to be fine‐tuned to each individual in order to generate accurate VF predictions. Hence, referring to the in vitro effect of dog as significant is the less favorable (or more conservative) interpretation of our result. Table S4 summarizes how the statistical results were affected by uncertainties in ERP measurements.

Table 5 indicates a false‐positive rate of 18% for VF predictions, which is higher than the 2% reported in Gelzer et al.27 The positive predictive values for the in vitro and in vivo27 studies were 21% and 75%, respectively, while corresponding negative predictive values were 95% and 92%. While the model accurately identified premature stimulus sequences that did not induce VF both in vivo and in vitro, the low in vitro positive predictive value was not consistent with the VF‐Prediction Hypothesis, in the sense that the model performed relatively poorly at identifying VF‐inducing sequences. A likely explanation is that the in vitro RV preparations, due to being smaller than intact hearts, may have been less intrinsically heterogeneous than the intact hearts studied by Gelzer et al27; thus, the risk of sustained VF was greater in vivo. In addition, the in vitro preparations may have had insufficient myocardial mass to provide a VF risk that was comparable with that of intact hearts. Determining the causes of the discrepancies between the in vitro and in vivo outcomes is a subject of ongoing work.

Our conclusion that 93% of the observed instances of sustained VF were preceded by reentry, which was largely consistent with our Reentry‐Precedes‐VF Hypothesis, was based on a qualitative visual review of the optical recordings. Examples of our review process are given in Figures 7 and 8. Movies of the sustained VF inductions have been included in the Supplement so that readers may make their own assessments.

Hypothesized mechanism for VF

A main focus of this study was to determine whether the observations agreed with the block and VF mechanisms described in Figure 1. Detailed comparisons between the hypothesized mechanism and events observed in selected trials are provided in Figures 4, 5, 6, 7 through 8 and in Table 3. To give an idea of the types of correspondences and discrepancies we witnessed, we refer to the trials first shown in Figure 4, which were chosen as examples of good (Trial 1) and poor (Trial 2) agreement between predicted and measured gradients. Examination of the optical data, as shown in Figure 5, revealed that the S5 wave front encountered conduction block in both trials, but sustained VF was not observed in either trial. The lack of VF in Trial 1 appeared to depend on the length of S4S5, as reducing S4S5 in a series of trials following Trial 1 produced block followed by reentry of the S5 AP and, subsequently, sustained VF (see Figures 6, 7 through 8 in the Results section and Movies S2 and S3). By contrast, reducing S4S5 in trials subsequent to Trial 2 sometimes yielded spontaneous complexes or nonsustained VF (data not shown), but sustained VF was not induced.

To determine possible causes for the poor agreement between observed Trial 2 gradients and model predictions of ΔAPD/Δx and ΔDI/Δx sign patterns, we note two ways in which Trial 2 differed from Trial 1, namely, that (1) Trial 2 showed more complex AP propagation patterns, including a larger number of regions of conduction block, including block on the S1 wave front (Figure 2), and (2) Trial 2 had a shorter distance between proximal and distal regions. The distances between proximal and distal regions, measured from the outer vertices of the proximal and distal squares, ranged from 1.1 to 1.6 cm over the 9 dogs. Comparing model agreement scores in Table 2 to these distances has not revealed any clear relationship between scores and distances. However, data from Dog 9 (the source of Trial 2) accounted for 3 out of a total of 5 trials that collectively appeared in either the APD‐ or DI‐based “poor” categories in Table 2. Hence, it is possible that there were differences specific to either Dog 9's right ventricle, which could also explain its more complex S1 AP propagation shown in Figure 2I, or the region chosen for APD and DI gradient measurements for that ventricle, that accounted the poor agreement with model‐predicted sign patterns.

The varying patterns of agreement and disagreement with model predictions were not unexpected. Our coupled maps model makes predictions about conduction block, but on its own does not predict when block will subsequently degenerate into reentry. Nevertheless, block of action potential waves is widely thought to render the resulting wave pattern more susceptible to reentry, which, under the right conditions, leads to the development of VT, wave break, and/or VF. Thus, it is not surprising that we see a tendency, but not an outright inevitability, for conditions theoretically predicted to result in block to also lead to these other, more serious wave patterns.

Study Limitations

While the 1D coupled maps model is computationally efficient, it can represent only part of one possible pathway to VF and does not make any predictions about higher‐dimensional reentrant phenomena. Modeling these phenomena or generating predictions for multiple distinct VF mechanisms would require us to use more complex computational models. Other links in the VF mechanism (eg, a possible relationship between block and reentry) could have been explored here, but to maintain tractability, the study was limited to the relationships covered by our hypotheses.

A limitation of our experimental setup is that it only allows measurements to be taken from the endocardial and epicardial surfaces, which is insufficient to capture all 3 spatial components of CV. In this study, measured CV magnitudes were used to distinguish between fast and slow propagation along the endocardial surfaces, and conduction block on a surface was defined on the basis of the measurable components of CV. However, block confined to the ventricle interior is not detectable using this setup. Determining the impact of the missing CV component on the accuracy of conduction block measurements and CV restitution parameters is a subject intended for future work.

Following the methodology of Gelzer et al,27, 28 we estimated one set of APD restitution parameters per dog, using pace‐down data from each dog, while CV parameters were fit to microelectrode data from a different study32 and were held fixed across dogs, except for the DImin parameter, which affected CV predictions and was obtained from the data from each dog. An alternative approach would be to recalibrate the remaining CV parameters using measurements from the optical data, to determine whether recalibrating the parameters would improve the accuracy of our predictions.

In addition to the CV parameters, other model parameters and settings (such as fiber length) could be adjusted to determine their effect on the quality of the predictions. However, to facilitate comparisons, one of our main goals in this study was to keep the model calibration procedures as consistent as possible with those of Gelzer et al,27, 28 rather than to determine which adjustments to the model would maximize the accuracy of its predictions. We feel that the latter goal is sufficiently complex to warrant a separate study.

Certain portions of the data analysis relied on qualitative visual assessments. To check the second part of the conduction block definition, we viewed the activation maps to determine whether wave fronts had changed direction across the proposed line of block. As discussed earlier, the second part of the definition, along with the corresponding visual review, could have been eliminated without having any impact on the results. In addition, determining whether reentry preceded VF involved reviewing movies of AP propagation to distinguish reentrant behavior from other causes. Ideally, this portion of the analysis could be automated, but this would require us to find and adapt an appropriate identification algorithm or to develop a new approach, either of which seems sufficiently challenging to be better suited for a separate study. In lieu of an automated method, we have provided examples of nonreentrant behavior (in the form of spontaneous focal complexes) and reentrant waves in Figures 7 and 8 to illustrate our classification approach.

Conclusions

In this study, we investigated a theoretical mechanism linking premature complexes to VF. To accomplish this, we collected optical mapping data from canine right ventricles, and compared in vitro observations with predictions from a 1D coupled maps model. The model was shown to be effective in predicting (1) patterns of discordant alternans, (2) which premature stimulus sequences were more likely to induce conduction block, and (3) which premature stimulus sequences were unlikely to induce VF. The confirmation of the model’s ability to predict alternans and block, along with the confirmation that reentry typically preceded VF, provided evidence for the theoretical mechanism beyond what was possible using the methods of Gelzer et al.27, 28 We continue to find that, while our 1D model clearly does not include all the dynamics present, it is nevertheless remarkable in its ability to predict and reasonably represent the dynamics of block leading up to VT and VF onset, despite its simplicity. Thus, our study suggests that the discordant‐alternans mechanism observed in the model is likely to be playing an important role in the development of instances of VT and VF that follow premature beats. This line of research may eventually lead to improved block and VF forecasting algorithms, along with programs that evaluate the arrhythmogenic potential of planned patterns of premature stimuli, which could lead to safer antitachycardia pacing strategies for implantable devices.

Sources of Funding

This study was supported by Award Number R01HL089271 from the National Heart, Lung, and Blood Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Heart, Lung, and Blood Institute or the National Institutes of Health. In addition, this material is based upon work supported by the National Science Foundation under Grant No. 1446675.

Disclosures

None.

Movie S1. Movie of optical data corresponding to Trial NB in Figure 3A, recorded from a test of an SLSL premature stimulus sequence on RV of Dog 4. Sustained VF was not induced. Stimulating electrode tip is located near pixel (50, 100). S1 to S5 APs become visible at the following times: 122, 296, 442, 572, and 714 ms. Nine spontaneous complexes were observed following S5, with the first spontaneous complex becoming visible at 886 ms.

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Movie S2. Movie of optical data corresponding to Trial 1 in Figure 3B, recorded from a test of an SLSI premature stimulus sequence on RV of Dog 4. Sustained VF was not induced. Stimulating electrode tip is located near pixel (50, 100). S1 to S5 APs become visible at the following times: 142, 318, 464, 598, and 708 ms. Eight spontaneous complexes were observed following S5, with the first spontaneous complex becoming visible at 804 ms in the left panel.

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Movie S3. Movie of optical data corresponding to Trial VF in Figure 3C, recorded from a test of an SLSI premature stimulus sequence on RV of Dog 4. Sustained VF was induced. Stimulating electrode tip is located near pixel (50, 100). S1 to S5 APs become visible at the following times: 244, 420, 566, 700, and 798 ms. Spontaneous complexes, followed by VF, were observed following S5, with the first spontaneous complex becoming visible at 880 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

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Movie S4. Movie of optical data corresponding to Trial 2 in Figure 3D, recorded from a test of an SLSI premature stimulus sequence on RV of Dog 9. Sustained VF was not induced. Stimulating electrode tip is located near pixel (40, 80). S1 to S5 APs become visible at the following times: 188, 394, 564, 730, and 862 ms.

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Movie S5. Movie of optical data recorded from a test of an S1 to S3 premature stimulus sequence on RV of Dog 1. Sustained VF was induced. Based on a review of this movie, it was concluded that S3 most likely did not capture, resulting in a premature stimulus sequence that was effectively a single “S” interval. Stimulating electrode tip is located near pixel (40, 90). The S1 and S2 APs become visible at 150 and 280 ms, respectively. Spontaneous complexes, followed by VF, were observed following S2, with the first spontaneous complex becoming visible at 408 ms in the left panel. This instance of VF did not appear to have been preceded by reentry (the initial stages of the arrhythmia appear to involve focal complexes).

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Movie S6. Movie of optical data recorded from a test of an SI premature stimulus sequence on RV of Dog 2. Sustained VF was induced. Stimulating electrode tip is located near pixel (70, 100). S1 to S3 APs become visible at the following times: 122, 310, and 416 ms. Spontaneous complexes, followed by VF, were observed following S3, with the first spontaneous complex becoming visible at 522 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

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Movie S7. Movie of optical data recorded from a test of an SLSI premature stimulus sequence on RV of Dog 2. Sustained VF was induced. Stimulating electrode tip is located near pixel (70, 100). S1 to S5 APs become visible at the following times: 158, 336, 518, 662, and 760 ms. Spontaneous complexes, followed by VF, were observed following S5, with the first spontaneous complex becoming visible at 856 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

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Movie S8. Movie of optical data recorded from a test of an SS premature stimulus sequence on RV of Dog 3. Sustained VF was induced. Stimulating electrode tip is located near pixel (40, 80). S1 to S3 APs become visible at the following times: 174, 328, and 414 ms. Spontaneous complexes, followed by VF, were observed following S3, with the first spontaneous complex becoming visible at 498 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

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Movie S9. Movie of optical data recorded from a test of an SLSI premature stimulus sequence on RV of Dog 3. Sustained VF was induced. Stimulating electrode tip is located near pixel (40, 80). S1 to S5 APs become visible at the following times: 170, 324, 466, 578, and 652 ms. Spontaneous complexes, followed by VF, were observed following S5, with the first spontaneous complex becoming visible at 726 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

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Movie S10. Movie of optical data recorded from a test of an SI premature stimulus sequence on RV of Dog 4. Sustained VF was induced. Stimulating electrode tip is located near pixel (45, 100). S1 to S3 APs become visible at the following times: 102, 278, and 384 ms. Spontaneous complexes, followed by VF, were observed following S3, with the first spontaneous complex becoming visible at 482 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

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Movie S11. Movie of optical data recorded from a test of an LSI premature stimulus sequence on RV of Dog 4. Sustained VF was induced. Stimulating electrode tip is located near pixel (45, 100). S1 to S4 APs become visible at the following times: 134, 352, 500, and 606 ms. Spontaneous complexes, followed by VF, were observed following S4, with the first spontaneous complex becoming visible at 680 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

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Movie S12. Movie of optical data recorded from a test of an LLIS premature stimulus sequence on RV of Dog 4. Sustained VF was induced. Stimulating electrode tip is located near pixel (45, 100). S1 to S5 APs become visible at the following times: 126, 344, 522, 658, and 776 ms. Spontaneous complexes, followed by VF, were observed following S5, with the first spontaneous complex becoming visible at 864 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

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Movie S13. Movie of optical data recorded from a test of an SS premature stimulus sequence on RV of Dog 6. Sustained VF was induced. Stimulating electrode tip is located near pixel (100, 80). S1 to S3 APs become visible at the following times: 102, 344, and 462 ms. Spontaneous complexes, followed by VF, were observed following S3, with the first spontaneous complex becoming visible at 558 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

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Movie S14. Movie of optical data recorded from a test of an SLSI premature stimulus sequence on RV of Dog 6. Sustained VF was induced. Stimulating electrode tip is located near pixel (100, 80). S1 to S5 APs become visible at the following times: 120, 288, 430, 556, and 650 ms. Spontaneous complexes, followed by VF, were observed following S5, with the first spontaneous complex becoming visible at 728 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

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Movie S15. Movie of optical data recorded from a test of an SI premature stimulus sequence on RV of Dog 8. Sustained VF was induced. Stimulating electrode tip is located near pixel (70, 105). S1 to S3 APs become visible at the following times: 126, 318, and 446 ms. Spontaneous complexes, followed by VF, were observed following S3, with the first spontaneous complex becoming visible at 574 ms in the right panel. This instance of VF appeared to have been preceded by reentry.

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Movie S16. Movie of optical data recorded from a test of an SLSI premature stimulus sequence on RV of Dog 8. Sustained VF was induced. Stimulating electrode tip is located near pixel (70, 105). S1 to S5 APs become visible at the following times: 128, 310, 480, 608, and 708 ms. Spontaneous complexes, followed by VF, were observed following S5, with the first spontaneous complex becoming visible at 814 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

Click here for additional data file.

Movie S17. Movie of optical data recorded from a test of an SI premature stimulus sequence on RV of Dog 9. Sustained VF was induced. Stimulating electrode tip is located near pixel (40, 80). S1 to S3 APs become visible at the following times: 130, 324, and 460 ms. Spontaneous complexes, followed by VF, were observed following S3, with the first spontaneous complex becoming visible at 584 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

Click here for additional data file.

Movie S18. Movie of optical data recorded from a test of an SLSI premature stimulus sequence on RV of Dog 9. Sustained VF was induced. Stimulating electrode tip is located near pixel (40, 80). S1 to S5 APs become visible at the following times: 142, 336, 516, 676, and 774 ms. Spontaneous complexes, followed by VF, were observed following S5, with the first spontaneous complex becoming visible at 904 ms in the left panel. This instance of VF appeared to have been preceded by reentry.

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Data S1. Stimulus Sequence Categories Tested In Vitro.

Table S1. Premature Stimulus Sequence Categories Tested In Vitro, With VF Outcomes

Table S2. Posterior Probabilities for Sequences of Signs of Mean Values of Δ(ΔAPD/Δx)

Table S3. Posterior Probabilities for Sequences of Signs of Mean Values of Δ(ΔDI/Δx)

Table S4. P Values for Effect Likelihood Ratio Tests Under Different ERP Estimation Schemes

Figure S1. Contour plots of the posterior marginal density functions based on Δ(ΔAPD/Δx) data. A, p(μ1, μ2 | x), B, p(μ2, μ3 | x) and C, p(μ1, μ3 | x). Vertical and horizontal lines indicate the coordinate axes.

Figure S2. Contour plots of the posterior marginal density functions based on Δ(ΔDI/Δx) data. A, p(μ1, μ2 | x), B, p(μ2, μ3 | x) and C, p(μ1, μ3 | x). Vertical and horizontal lines indicate the coordinate axes.

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