Characterizing the Transient Electrocardiographic Signature of Ischemic Stress Using Laplacian Eigenmaps for Dimensionality Reduction

Abstract

Objective:

Despite a long history of ECG-based monitoring of acute ischemia quantified by several widely used clinical markers, the diagnostic performance of these metrics is not yet satisfactory, motivating a data-driven approach to leverage underutilized information in the electrograms. This study introduces a novel metric for acute ischemia, created using a machine learning technique known as Laplacian eigenmaps (LE), and compares the diagnostic and temporal performance of the LE metric against traditional metrics.

Methods:

The LE technique uses dimensionality reduction of simultaneously recorded time signals to map them into an abstract space in a manner that highlights the underlying signal behavior. To evaluate the performance of an electrogram-based LE metric compared to current standard approaches, we induced episodes of transient, acute ischemia in large animals and captured the electrocardiographic response using up to 600 electrodes within the intramural and epicardial domains.

Results:

The LE metric generally detected ischemia earlier than all other approaches and with greater accuracy. Unlike other metrics derived from specific features of parts of the signals, the LE approach uses the entire signal and provides a data-driven strategy to identify features that reflect ischemia.

Conclusion:

The superior performance of the LE metric suggests there are underutilized features of electrograms that can be leveraged to detect the presence of acute myocardial ischemia earlier and more robustly than current methods.

Significance:

The earlier detection capabilities of the LE metric on the epicardial surface provide compelling motivation to apply the same approach to ECGs recorded from the body surface.

Graphical Abstract

1. Introduction

Electrocardiographic detection of acute myocardial ischemia is a common clinical approach but current techniques are plagued with poor sensitivity and specificity. [23] Myocardial ischemia occurs when the coronary perfusion in the heart is inadequate to provide for its metabolic demands, which elicits an electrochemical cascade that results in changes to the electrical and mechanical behavior of the heart. When left untreated, ischemia can lead to stunning and even death of the myocardial tissue, which can be pro-arrhythmic and thus a major factor in sudden cardiac death. ECG-based detection of ischemia is possible because of electrical changes in tissue that receives inadequate perfusion. The ECG has advantages over other methods including low cost, ease of use, safe and painless application, and the potential for continuous monitoring. However, despite these advantages and a long history of use [14], performance of ECG-based diagnosis of ischemia remains unsatisfactory.[23, 1]

The traditional ECG markers of acute ischemia include upward or downward shifts in the ST segment, which are thought to be driven by spatial differences in the plateau phase of transmembrane potentials between healthy and ischemic regions. Such potential differences give rise to what are known as ‘injury currents’, which drive diagnostic ST-segment shifts. [15] In addition to injury current effects, the process of electrical depolarization and repolarization of the myocardium results in morphological changes in the measured ECG that are complex, challenging to detect, and often non-unique identifiers of ischemia. In this context, the currently available metrics of ischemia attempt to simplify these however, simply measuring such markers often results in poor sensitivity and specificity. [23, 1, 17]

We propose that much of the uncertainty associated with Detection of ischemia based on traditional ECG markers stems from the tremendous variability of electrophysiological response to ischemia, including fluctuations over the duration of an ischemic episode, from one episode to another within the same individual, and across individuals. [3, 24] This high degree of variability is due to the interaction of many complex inter-related factors that mediate the cardiac perfusion and the electrophysiological response to ischemia. An example of this variability is exemplified in Fig. 1B with several intramural electrodes showing varying responses during the same induction of ischemia. In such situations, selecting one or a small set of fixed markers and then using them for diagnosis can lead to unreliable results. Indeed one factor in the tremendous recent growth of the use of machine learning for many classification tasks, including in health care, is the need to overcome such variability by designing algorithms that automatically find statistical regularity in the data. [5, 20]

Figure 1:

A color encoding that shows the change in morphology over time across a series of intramural needles. A) A schematic showing how ischemic stress is increased throughout the duration of the ischemic episode. A colormap is used on the electrograms depending on the time within the episode at which they were recorded B) Overlaid beats captured by the same intramural electrode during an episode of myocardial ischemia using the color scheme in A. Each plot is an individual electrode (6 electrodes throughout the envelope labeled N.E.#1–6).

In this study, we developed and tested such an approach in the setting of acute ischemia. One drawback with the use of machine learning approaches is the need for large volumes of annotated training data, typically with ground truth labels available. Typically, in the case of detection of ischemia from ECG measurements, access to well annotated signals during controlled episodes of ischemia is limited. This study utilizes a relatively large dataset of electrocardiographic measurements previously recorded in our laboratory from epicardial electrode arrays deployed on canine hearts. [3, 24] In the absence of unequivocal evidence (based on tissue perfusion) for ground truth labeling, we implemented a labeling scheme based on simultaneously recorded signals from intramural needle electrodes, which we assume provide rapid and sensitive response to the ischemic stress.

To this large set of electrocardiographic measurements we applied a data-driven approach to detect ischemia. One such family of methods is based on decomposition, which has proven successful in detecting ischemic changes in electrocardiographic signals by representing them in a space that can reveal otherwise hidden features. Laplacian Eigenmaps (LE) is one such algorithm from machine learning [6] that has proven sensitive to changes in electrocardiographic and electroencephalographic signals. [9, 12] In the specific context of ischemia, Erem et al. reported that the LE approach can reveal changes in the input signals brought about by ischemic stress and premature ventricular contractions in the ECG.[9] The LE transformation also reduces dimensionality, which simplifies exploration of high-dimensional data and makes the derivation of compact parameters such as those described in this study an attractive possibility. A further advantage of the LE approach is that the resulting search for usable features includes the entire signal, i.e., it is not biased towards ST segments or other signal features.

For this study, we hypothesized that LE-based metrics could detect myocardial ischemia earlier within an ischemic episode and with greater accuracy than traditional metrics. To both train the LE metric and test this hypothesis, we used the data from experiments that included repeated episodes of graded ischemia in large-animal models. In order to evaluate the utility of all possible ECG leads and to capture the entire spatial extent of the electrocardiographic response, we used a combination of 200–400 intramyocardial electrodes and a 247-lead epicardial array that covered uniformly the epicardium of the ventricles. The resulting extensive mapping of the heart by three-dimensional recording using the needle electrodes, supplied ground truth evidence of the occurrence and extent of ischemia. We applied the LE analysis to the epicardial measurements and compared the resulting metrics against standard electrocardiographic markers for the same epicardial electrograms. This study was unique both in terms of the search for novel means of detecting ischemia electrocardiographically and in the rich experimental data available.

2. Methods

2.1. Experimental Methods

The signals for this study came from 16 in situ canine experiments with induced ischemia. All experiments were performed under deep anesthesia using procedures approved by the Institutional Animal Care and Use Committee of the University of Utah and conforming to the Guide for the Care and Use of Laboratory Animals. Details on the experimental preparation such as the induction and grading of ischemia has been described previously [2, 4, 24]. Briefly, following measurements under control conditions, the blood flow was reduced and the heart rate increased in a stepwise fashion to replicate the effects of graded exercise, inducing ischemia via a supply-demand mismatch in the tissue perfused by the left anterior descending coronary artery (LAD). Flow rate through the LAD was modulated via a hydraulic occluder placed around the artery while the heart rate was controlled by electrically stimulating the right atrium. Each ischemic episode lasted 3–8 minutes (avg. 7.3 ± 1.5 min.) with a 30-minute recovery period between episodes to allow the heart to return to baseline conditions. The degree and extent of ischemia varied across the experiments, but always increased until the peak of the episode, when the occluder was released. Fig. 1 A contains a schematic, color coded representation of a single episode of graded ischemia. We captured cardiac electrograms throughout such ischemic episodes and extracted from them all the metrics for the study.

We measured intramyocardial electrograms using Utah plunge-needle arrays [2, 24] consisting of multiple 10-pole electrodes evenly distributed along the length of each needle (1.5 or 1.7 mm spacing, depending on the needle type). Between 20 and 40 needles were placed 5–15 mm apart within the expected perfusion bed of the LAD artery. Epicardial electrograms were captured using the Utah high-density epicardial sock array[2,24], consistingof247-electrodesspread evenly over the ventricular epicardium. All recordings were unipolar, referenced to the Wilson’s central terminal.

To capture the dynamics of each ischemic episode, recordings of all electrograms were sampled continuously at 1 kHz in continuous ‘runs’ of 3 s duration every 15 s during the 3–10 min (majority of episodes were 8 minutes in duration) of ischemia and every 10 min during the recovery period. Two such runs were acquired before the first episode of ischemia induction and used as a baseline measurement, or ‘control’ for processing subsequent runs. In all, we gathered signals from 16 separate experiments, 15 of which produced 98 separate episodes of acute myocardial ischemic stress. From the remaining experiment, we recorded a 30-minute period of control, without any ischemic load. We used this recording to create 101 true negative episodes by treating each 15-second epoch of the 30 minute recording as a single episode, extracting 30–40 representative beats, and processed them in a similar manner as all other episodes.

Each run was processed with our open-source, custom software PFEIFER [22] to adjust the gain of each channel, baseline correct the signal, and identify and isolate a representative beat from the run. Each representative beat was manually identified from the root-mean-squared time signal generated from all measured electrograms (needle and sock electrodes). Within each such representative beat, we manually identified temporal fiducials, including the start and end of the QRS complex and T wave as well as the time of the peak of the T wave. The product of these processing steps was, for each episode of ischemia, a sequence of 20–40 representative beats, each consisting of 450–650 simultaneously acquired electrograms and a set of temporal fiducials. Fig. 1 B shows a sample of such processed beats from 6 electrodes along a needle with each electrogram color-coded according to the time during the episode.

2.2. Laplacian Eigenmaps Applied to Ischemia

Laplacian eigenmaps (LE) is a nonlinear, dimensionality reduction method that can map multiple simultaneously recorded time signals onto a putative manifold. [6] In our [9], simultaneously recorded signals were decomposed and represented in a manifold space, or LE space, as a ring like, three-dimensional curve. Fig. 2A contains a representation of all the epicardial electrograms from a single beat mapped into the LE space. The set of white spheres represents the points in time that make up a single trajectory in the three-dimensional LE space. Each sphere, therefore, corresponds to a single time instant during the associated beat, visualized within the LE space. The selection of components of the LE space is arbitrary, however, previous results [9] suggest that three dimensions are sufficient for this application. We used the three most significant (other than the zero order corresponding to the mean value), labeled EV1–EV3 in Fig. 2 and implied throughout.

Figure 2:

Creating the mapping into LE space and populating it with subsequent beats. A) A set of simultaneously recorded time signals from the original signal space, from which we create a mapping using the LE approach to a low dimensional (in this case three) representation. The axes of this LE space are labeled arbitrarily EV1–3 and the loop of white spheres is the parametric representation of the same data, each sphere signifying an instant in time. This loop of white spheres is referred to as the control trajectory. B) Signals recorded during an episode (in this case ischemia) mapped into the same space. The red trajectory shows a single ischemic beat mapped into the LE space using the same mapping that was calculated from the control beat.

The trajectories of beats in LE space change with with ischemic stress, an example of which is contained in Fig. 2 B. The figure shows both three sample signals and the trajectory of a pre-ischemic control beat in white spheres (and black electrograms) and the subsequent trajectory (in red) from electrograms (in red) acquired late in the ischemia episode. Both trajectories were mapped into the same LE space, which in this case was defined from signals recorded before any episode of ischemia, a process we repeated through this study. The changes in trajectory were qualitatively consistent across ischemic episodes, an observation that encouraged us to develop metrics that we hypothesized would be sensitive to myocardial ischemia earlier and more robustly than traditional metrics.

To summarize the steps involved, we implemented the following algorithm, based on an extension to our previous approach[9]:

1. Identify a representative beat from the first control run of each episode, before ischemia is induced. Identify the major temporal fiducial times for this representative beat, i.e., QRS_on, T wave_off, etc., (see Sec. 2.1 for details). Then length normalize and interpolate the beat to have 1000 time samples from QRS_on to T wave_off. Let P = [p_{1, …,} p₁₀₀₀] be a matrix that contains the measured potentials (either from needles or the epicardial sock but not both), where each p_i is an N-dimensional vector whose elements are the electric potentials at the i^th time step from each of the N measurement electrodes within the heart. N was 247 for epicardial potentials and 200–400 depending on the number of needle electrodes for intramyocardial potentials.

2. Compute a matrix, R, of pairwise distances between all time points in the data set, P; R has elements $R_{i,j}$ $=p_i-p_j{}_2$. Then choose a tuning parameter, σ that serves to scale the subsequent exponent (here set equal to the largest element in R). Choosing the largest element in R was heuristic [9]; this choice served to prevent local differences being overemphasized and to make the approach closer to manifold embedding while making the choice of parameter automatic.

3. Compute a matrix, W, with elements $W_{i,j}={\exp }^{\left(-R_{i,j}^2/{\sigma }^2\right)}$. The elements of W thus emphasize local topology represented in R by deemphasizing larger values (corresponding to longer distances). Use W to compute a diagonal degree matrix $D=diag\left(\sum _i{W}_{i,:}\right)$ (where W_i: denotes the i^th row of W), whose entries are an estimate of the local sampling densities on the putative manifold, as inferred from the points in the data set.

4. Solve for the singular value decomposition of D⁻¹ W = USV.The columns of V correspond to the coordinate directions in the Laplacian eigenmaps space into which points are being mapped. Therefore, row k of V contains the LE coordinates of the point p_k. [9]

5. Truncate the representation in LE space to a desired number of coordinates. Here we discard the coordinate associated with the largest eigenvalue, which represents the mean of the dataset. We then retain the next three dimensions, which we have observed[9] are enough to capture relevant dynamics of electrocardiographic signals.

For each ischemic episode, we applied this algorithm to a control beat to create the LE mapping transformation for the entire experiment and then used this mapping to project each subsequent beat into this same space. Creating a new projection, or trajectory in LE space, for each beat allowed us to compare changes in trajectories across beats referenced to an experiment-specific, pre-ischemic control. To visualize the results, we applied the color scheme introduced in Fig. 1 to encode progression during the episode. Fig. 3 shows an example of both the sequence of electrograms and the morphology of the resulting LE trajectories from one ischemic episode.

Figure 3:

Example of an ST40% and LE run-metric plot using the color encoding introduced in Fig. 1 A) This run-metric plot is the value of ST40% over the course of an episode of ischemia, in this case as measured by a single electrode. B) An overlay of the electrograms recorded by that same electrode during the same episode of ischemia. Yellow circles mark the temporal locations of ST40% in each time signal. C) This run-metric plot is the value of the LE metric over the course of the same ischemic episode. D) Two views of the LE manifold during the same episode of ischemia, colored using the scheme outlined in Panel A. The yellow spheres show the same normalized time instant used for the LE metric across beats mapped into the LE space. The choice of time instant is described in detail in section 2.4. The control trajectory for this episode, shown in magenta, is visible at the outer edge of this set of trajectories.

2.3. Electrogram-based metrics of ischemia

In order to apply detection algorithms to identify ischemia, it is necessary to derive statistical metrics from the recorded data which should characterize the dynamic changes in the electrograms over the course of each ischemic episode. The result should be a single time series that represents the behavior of each metric over an entire episode. We refer to this time series as a “run-metric”, which can be applied to parameters from a single lead or any collection of leads. In the case of the LE analysis, creating a run-metric requires reducing the entire set of mapped trajectories to a single scalar time series, a process we describe in the next section.

From the commonly used electrocardiographic metrics for ischemia, we selected five, two derived from the ST segment, two from the T wave, and one from the QRS complex. The two ST-segment based metrics were the ST40% and the ST60.[18, 2] The ST40% metric is defined as the electrocardiographic signal deflection from baseline at a time point situated 40% through the interval between the end of the QRS and the peak of the T wave; using a percentage of the ST interval compensates for timing changes in response to QT shortening as the heart rate increases. The ST60 metric is defined as the potential value at a fixed time point 60 ms after the end of the QRS. The two T wave-derived metrics were the T wave_peak and the T wave_int; T wave_peak measures the potential at the peak of the T wave, while the T wave_int metric measures the area under the T wave.[18,2] The QRS-derived metric was the QRS_int, measuring the area under the QRS complex.[21] Each metric was computed for each run over the duration of an ischemic episode and the value used to create the run-metric. An example of the ST40% run-metric, along with the beats from which it was extracted, are shown in Panel A of Fig. 3.

Ischemia due to constriction of a single coronary artery is localized and we expected the electrocardiographic response, especially on the epicardium, to also be localized. Any metric designed to sense such a localized response would therefore be diluted if applied globally, encouraging us to define regions of interest over which to apply the electrogram-based metrics.To illustrate these conditions, Panel A of Fig. 4 contains a volumetric representation of intramural ischemia from the peak of a sample episode, showing the very localized nature of the acute ischemia induced in the experiments. Panel B of Fig. 4 shows the epicardial distribution of ST40% from the same run, and Panel D shows the associated run-metric derived from all epicardial electrograms. The effect of ischemia, so clearly visible in the epicardial map is lost in the globally applied run-metric. Therefore, we applied a thresholding algorithm (described in more detail next paragraph) to identify a contiguous neighborhood of electrograms that sensed ischemic changes. The resulting epicardial distribution is captured in Panel C and, more importantly, the associated run-metric curve in Panel E shows a clear response to the ischemia.

Figure 4:

Visualization of needle and sock electrodes for one animal, as well as the selection of the subset of responding electrodes used for the ST40% analysis. The myocardium is visualized transparently while the blood pools and ventricular sock are opaque. A) The intramural needle electrodes placed throughout the LAD perfusion bed, color coded by ST40% metric amplitude along with the ground-truth estimate of the ischemic volume based on the measurements on those electrodes colored in orange. The orange volume is the tissue exceeding the CSTIR threshold at this time point in the ischemic episode. B) Visualization of the epicardial sock array on the myocardium. Color again shows ST40% amplitude. C) Visualization of the responding epicardial electrode neighborhood for the ST40% metric, defined as described in the text. D) A run-metric created by averaging all of the electrodes across the entire epicardium. E) A run-metric created by averaging only the responding electrodes visualized in part C. Registration and visualization follow a previously developed pipeline [8, 7, 24] using the SCIRun problem solving environment (http://www.sci.utah.edu/cibc-software/scirun.html).

Identifying the contiguous set of epicardial leads for each metric and ischemic episode required a set of steps. We first computed the global value for the metric by taking the average value across all epicardial electrograms. We then identified the largest contiguous neighborhood of leads that during the episode reached a metric value greater than this average plus two standard deviations for five consecutive time points. From this initial set of ‘responding leads’, we then recomputed the average metric values and then expanded to include adjacent neighborhoods wherever their mean value was within one standard deviation. Fig. 4B shows how this iterative process of identifying the responding leads reduced the entire set of epicardial electrograms in Panel B to the subset in Panel C. In cases for which no leads responded, we used the global average over all epicardial potentials to form the run-metric curve. The set of responding leads for each episode and metric then became the basis for all subsequent analysis of the electrocardiographic metrics.

2.4. LE based metrics of ischemia

In order to carry out meaningful comparisons, it was necessary to reduce the full set of LE trajectories to a single run-metric time series. A simple approach that captures the progression of LE trajectories from control to ischemic conditions is to define two parameters: the maximum amount of deflection from one trajectory to the next and the time during the heart beat at which this maximum deflection occurs. To this end, we derived a (normalized) time point for which the trajectory-to-trajectory changes in LE space were both large and relatively early in the episode. The steps in generating these metrics were as follows:

1. For each normalized time instant in the beat, compute the Euclidean distances in LE space from the control trajectory to the equivalent time point in each subsequent trajectory to create a set of run-metrics.

2. From these 1000 run-metric curves, select the 20 with the largest overall amplitude, i.e., the largest movement in LE space during the ischemia episode.

3. From these 20 curves determine the one that shows the earliest response to ischemia, as indicated by the time instant at which it passes 1/3 of the overall amplitude of the run-metric. 1/3 of the amplitude was chosen heuristically in order to be a point that we observed is consistently above baseline variations in the metric’s evolution.

4. The resulting LE metric is used to characterize the ischemic episode.

An example of an LE metric derived in this manner is shown in Fig. 3C&D (arbitrary units represent the distance in LE space). The Euclidean distance from the control value to the sequence of yellow spheres in Fig. 3D is plotted as a run-metric in Fig. 3C, and can be compared to the ST40% run-metric in Panel A. [13] Unlike for the electrocardiographic metrics, there is no need to identify responding leads because LE intrinsically incorporates the entire set of epicardial recordings into the mapping and automatically determines a spatial weighting that highlights those signals and associated regions where there is change.

2.5. Evaluating the Metrics

This study is an extended and detailed exploration of preliminary findings reported previously in conference publications and a short journal submission. [12, 11, 13]

All of the metrics (A representing the value at any given point) described above can be captured as run-metrics, each expressed as

$$A_{i,j,l}^{(m)}(k)$$

where i indexes the experiment, j, the episode, l a set of leads from which the metric is derived, (m) the particular metric. and k each representative beat in that episode of that experiment.

As described in the introduction, we will use the intramural leads to determine, to within what we take as reasonable accuracy, ground truth, and then test the metrics estimated from the epicardial leads against that ground truth to determine their accuracy, sensitivity, and temporal responsiveness.

2.5.1. Classification of the Ischemic Episodes

Positive Detection Criterion:

To quantify the performance of the metrics we have identified required us to determine whether or not each episode was ischemic. For this step, we used the metrics derived from intramural leads by first computing their mean values $\overline{A_{r;i,j,l}}$ and standard deviation SD_A from control beats recorded before the ischemic episode. We then tested whether any set of five consecutive values of $A_{i,j,l}^{(m)}(k)$ during the entire remaining episode were all above $\overline{A_{r:i,je}}+2S{D}_A$ (we will drop the subscripts going forward). If this criterion was satisfied for any of the computed metrics, then the episode was labeled as a true positive (TP); if none of the metrics were above their respective criteria, the episode was labeled as a true negative (TN). The identification of TN and TP from intramural needles is illustrated on left side of Fig. 5. We found that only 9 of the 98 episodes recorded during the ischemia experiments were labeled as TN, so to balance the dataset for statistical testing, we added the 101 episodes from the experiment with no induced ischemia, all of which we confirmed to be true negatives.

Figure 5:

A diagram showing how epicardial and intramural signals (run-metric curves) are used in the analysis of the diagnostic and temporal performance of the LE and traditional electrogram-based metrics. Note there are three portions of the diagram requiring additional detail (See ‘Notes’). Intramural signals are used to determine TN and TP via the positive detection criteria in addition to the CSTIR analysis. Epicardial signals whose episodes meet the CSTIR criteria go through the positive detection criteria to be used in the temporal performance analysis.

The positive detection criterion was also used on epicardial signals as described in more detail in section 3.5.3.

CSTIR Criterion:

After determining which episodes were TP, we determined the region within the myocardium that experienced this ischemia. To do so, we developed a spatial criterion across neighboring intramural electrodes, the contiguous suprathreshold ischemic region (CSTIR). The CSTIR determination was based only on the ST40% metric (since it is the most widely used and validated metric in practice) and was defined as any intramural volume larger than 500 mm³ in which all leads met the positive detection criterion. For those episodes that met CSTIR criterion, we defined the reference time for onset of ischemia as the first episode during which all leads in the CSTIR volume passed the positive detection criterion—in other words, it was a rather conservative temporal detection marker intended to reflect uniform appearance of ischemic changes over a detectable volume. Fig. 5 shows how intramural signals are used in the CSTIR analysis and how only episodes meeting this criterion are used in the temporal analysis, which is ultimately performed on epicardial signals. Fig. 6 shows an example of a CSTIR volume in two views.

Figure 6:

Volumetric and slice views of the intramural potentials and CSTIR regions during an episode of ischemia. Panel A): ST-segment potentials mapped to color, as shown in the legend, applied to the spheres that represent needle electrodes. The orange volumes indicate the CSTIR regions (the volume of tissue with potentials exceeding the CSTIR threshold). The myocardium is visualized transparently while the blood pools are opaque. Panel B): a cross section through the ventricles (shown with the dashed line mark ‘S’ in Panel A) with ST40% potentials coded in color. The red area outlines a slice through the CSTIR region (arrows in both Panels A and B).

To summarize the two criteria:

• Positive Detection: The value of the metric for any 5 consecutive beats during the episode exceeds the mean value (as measured prior to the induction of ischemia) plus two standard deviations.

• CSTIR: The ST40% value on all intramural electrodes in a volume greater than 500 mm³ meet the positive detection criterion

2.5.2. Run-metric Normalization and Quantifying Diagnostic Performance

We adopted a normalization scheme that preserved the dynamic range of the run-metric but allowed us to compare a number of metrics with a wide variability in range and to easily facilitate the receiver-operator characteristic (ROC) curve analysis. For each run-metric and each episode seperately, we computed along with $\overline{A_r}$, the maximum value of the metric for that episode, $\overline{A_m}$ over all representative beats in the episode, then normalize all values of A using:

$$\frac{A-\overline{A_r}}{\overline{A_m}}$$ (1)

This equation ensures that all run-metrics are bounded by 0 and 1, which facilitates the performance evaluations.

To create the ROC analysis curves, we followed standard methods in which the threshold for each normalized epicardial metric was varied from 1 to 0 and we computed the positive predictions and determined sensitivity and specificity. From the resulting ROC curves, we calculated the area under the curve (AUC) for each of the six metrics.

2.5.3. Quantifying Temporal Responsiveness

We also developed a metric to quantify the sensitivity of the run-metric for each episode, called contrast ratio (CR), as well as two metrics to quantify temporal responsiveness, time to detection (TTD) and delay in response (DR). TTD quantifies the temporal performance of the epicardial run-metric itself, while DR quantifies detection delay with respect to CSTIR time. It was most meaningful to focus the evaluation of the temporal performance on positive episiodes, i.e.,those in which the metric responded to ischemia. We also followed the paradigm of using intramural electrograms as ground truth and performing the CR, TTD, DR analyses using the epicardial electrograms on episodes meeting the positive detection criteria for that metric.

We defined, for each episode and each metric the contrast ratio:

$$CR=\frac{A_m}{\overline{A_r}}$$ (2)

To quantify run-metric temporal performance we defined a threshold at 1/3 of the dynamic range between the maximum and mean values of each metric for each episode and defined the time at which a given run-metric first crossed that threshold as its time to detection, TTD. For all episodes that met the CSTIR criterion, we then defined delay in response, DR, as the difference in seconds between TTD and the CSTIR time for that episode. Thus DR is a direct measure of the delay between intramural appearance of substantial robust ischemic response, as quantified by CSTIR, and its appearance on the epicardial subset of leads for a given metric, as quantified by TTD. The TTD, CR, and DR values for each electrogram-based metric were compared against those from the LE metric to determine if their distributions were statistically different, using a t-test and assuming a significance threshold of p <0.05. Evaluating the statistical significance indicates whether the differences in the TTD, CR, and DR measures were significant across the episodes we examined. The null hypothesis was that the temporal performance of the LE metric would be indistinguishable from one the traditional metrics.Our alternative hypothesis was that the temporal performance of the LE-based metric would be significantly better than traditional metrics for ischemia.

3. Results

3.1. Classification of the Ischemic Episodes

Of the 199 episodes studied, 89 were true positive (TP) episodes of ischemia leaving 110 episodes as true negatives (TN), 101 of which we collected in a separate experiment without any induced ischemic stress. Of the 89 true positives, 67 episodes met the more demanding CSTIR criteria and the average CSTIR time was 100 s, with a standard deviation of 59 s.

3.2. Quantifying Diagnostic Performance

Fig. 7A summarizes the diagnostic performance of the metrics from all ischemic episodes. A receiver-operator-characteristic (ROC) curve analysis compares the performance of metrics according to their ability to discriminate. Here we discriminate between the presence and absence of intramyocardial ischemia as detected by epicardial markers. Table 1 summarizes the same results in terms of the number of successful epicardial detections (as a percent of intramural positive detections) and the values for the areas under the ROC curves (AUC). The LE metric had the largest AUC (0.80) and the best rate of detection of ischemic episodes (61%), followed by a tight clustering of all the other metrics. The LE metric detected 10% more episodes successfully than the next highest performing metric.

Figure 7:

A summary of the diagnostic and temporal perofmance of the LE and traditional elcetrogram-based metrics. A) Receiver-operator characteristic (ROC) curves for all six ischemia metrics studied, as listed in the inset legend. B) The temporal response of 4 metrics over the same eight-minute episode of ischemia. The absolute values of run-metrics were normalized using the same scheme as employed for the ROC analysis.

Table 1.

The diagnostic performance of the metrics. The AUC (Area Under the Curve) values are also shown and were determined from the ROC analysis displayed in Fig. 7. The number of episodes meeting the positive detection criteria on the epicardial signals is shown to see how the diagnostic performance is related between intramural and epicardial manifestation of ischemia.

Metric	AUC	# of Detected Episodes
LE	0.80	54(61%)
ST40%	0.74	39(44%)
ST60	0.75	43(48%)
T wavepeak	0.68	38(43%)
T waveint	0.75	45(51%)
QRSint	0.75	35(39%)

3.3. Quantifying Temporal Performance

Fig. 7B shows a sample of the temporal performance of a subset of the metrics as an overlay of run-metrics derived from LE, the T wave, ST segment, and QRS for a single episode. Table 2 contains summary statistics that compare performance across all ischemic episodes. The LE metric had the smallest mean DR to the underlying ischemia (106 s), followed after at least 30 s by the T wave metrics, the ST metrics, and finally the QRS metric. Furthermore, the CR results show that the T wave_int and LE metrics were similarly robust to the variability in the metric values at baseline, followed by the two ST-based metrics and the T wave_peak metric. The QRS_int response was the least robust.

Table 2.

Temporal performance values of the six metrics used to detect ischemic stress. TTD (Time to Detection) measured the response time of the metric and the CR (Contrast Ratio) measured the robustness of that response. The value of DR (Delay in Response) was the TTD of each episode across each metric minus the CSTIR time for that episode expressed as mean ± standard deviation (max value). The significance of the distributions relative to the LE metric is shown next to the reported TTD, CR, and Delay in Response metrics.

Metric	TTD (s)	DR(s)	CR
LE	209 ± 92	106 ± 85 (304)	4.4 ± 2.8
ST40%	261 ± 99*	148 ± 108* (370)	3.5 ± 4.0
ST60	259 ± 104*	148 ± 110* (367)	3.6 ± 4.1
T wavepeak	252 ± 137	136 ± 134 (425)	3.4 ± 2.8
T waveint	258 ± 125*	147 ± 127* (364)	4.1 ± 4.2
QRSint	296 ± 107*	183 ± 116* (375)	2.9 ± 1.7*

^*Significance of p < 0.05 is indicated with.

3.4. Time Points Chosen by the LE metric Across All Episodes Detected.

Fig. 8 shows the frequency histogram of the time points within the heartbeat selected by the metric in the LE space across all 89 detected episodes of ischemia. The intervals most often selected by the LE metric were roughly 20% and 95%intotheQRST,correspondingapproximatelytotheends of the QRS and the T wave, respectively.

Figure 8:

Histogram showing the time instances chosen by the LE algorithm for all episodes in the study.

4. Discussion

The goal of this study was to evaluate the diagnostic performance of a novel electrocardiographic metric derived using Laplacian Eigenmaps (LE) to detect ischemic stress. The electrocardiographic signals used for the evaluation came from experimental studies in which acute, transient, graduated ischemia was induced in a canine model. The measurements came from 400–650 separate electrodes placed within the heart and on the epicardial surface; the intramyocardial signals provided the gold standard for the presence of ischemia and the epicardial signals were used for testing the metrics.

We compared the performance of the LE-based metric against five other, more traditional markers derived directly from signal features of the electrograms using receiver-operator characteristic (ROC) curve analysis, the response time of each metric, and their robustness to noise. The results showed that the LE metric had the best diagnostic performance and responded earliest with the highest degree of robustness to noise.

The anticipated application of this novel metric is primarily the clinical stress test, a test with chronically unsatisfactory diagnostic accuracy [23, 1] and so the experimental preparation was designed to mimic such tests. It was not feasible to have the animals perform actual exercise in a study in which hundreds of electrodes were located within an exposed heart. Partially restricted blood flow combined with rapid pacing of the heart elicits an ischemic response that is similar to that seen in vivo, as we have reported previously [2, 4, 24] and recently correlated with simultaneous body-surface ECG recordings [24].

A challenge with any data-driven or machine-learning approach is to identify robust and practical paradigms to learn the manifold projection that will be used to measure the presence of ischemia. Given the anticipated application of this metric in the setting of exercise stress testing, we performed training only on control recordings and then tested its performance on subsequent recordings during ischemic episodes. Including electrograms acquired during the ischemic stress period into the training might be expected to improve diagnostic performance, however, true utility of a new metric lies in its ability to work in real time, during the stress test. Post-processing might improve performance but the results would not be available during the test, which is typically terminated as soon as a patient reveals signs of ischemia. Another source of improvement in training might come from including only those electrograms (or eventually ECGs) that ultimately showed changes during ischemia, as we did with the traditional metrics of ischemia. However, such information is not present before a clinical stress test and so we included all electrograms in the training phase and yet still showed that the resulting LE-based metrics had clear performance benefits. The LE metrics outperformed the traditional metrics, which incorporated a great deal more a priori information based on widespread experience with ECG-based metrics. We have reported previous success applying LE approaches to ECG’s recorded from human subjects experiencing controlled ischemia during coronary angioplasty[10]. In that study it was possible to train the algorithm from pre-intervention body surface potential maps (from the same and other patients) and detect subsequent ischemia.

One premise of this study was that intramural detection of ischemia was robust enough to define the gold standard. We also assumed (and found) that ischemia would be visible earlier within the episodes from the intramural signals than those recorded on the epicardium. Indeed, of the 98 induced episodes of ischemia, 89 showed overt electrocardiographic signs within the intramural electrograms large enough to meet the ‘positive detection criteria’. Performance of metrics based only on epicardial electrograms was much lower overall (35–54 episodes of ischemia detected). We achieved the best performance from the LE metric with 54 (61%) correctly detected episodes compared to 45 (51%) for T wave_int. The temporal performance of intramyocardial metrics was also clearly superior to those based on epicardial potentials, even using the demanding CSTIR criterion. A sizable region with ST-segment changes was detected from intramyocardial electrograms between 1–2 minutes after commencing the stepped ischemia protocol, however, detection from the epicardium took another another 1–4 minutes. Here, again, the LE metric performed best with a mean delay in response of 106 s compared to 136 s for the T wave_peak.

The ranking of performance of the traditional metrics of ischemia matched the evidence from previous studies [14]. Metrics based on repolarization changes (i.e., ST segments and T waves) performed better and more quickly than those based on the QRS complex. During graded myocardial ischemia one would expect to see changes to repolarization due to extracellular potassium accumulation before changes in depolarization that require altered behavior of sodium and calcium channels [19, 16, 13].

The superior performance of the LE metrics suggests that signs of ischemic stress exist within a low-order space that can be evaluated and ultimately quantified using simple metrics to measure the deformation of the manifold in LE space. The LE approach has another advantage in that it maintains the temporal context of the input signals while representing those signals in a manifold space. As a result, the changes seen in those regions in manifold space can be related to time instances in the original signals.

Within the LE manifold space, we designed the LE metric to identify regions undergoing large deformations and then determined, within that subspace, which time instant experienced these deformations most rapidly. This strategy allowed us to minimize temporal response time while maintaining a robust response to the ischemic episode. The resulting advantages in both the diagnostic and temporal performance may be explained by the ability of the metric to focus on regions of the signal that are changing, on an episodic basis, while ignoring stable regions. It was therefore not surprising that the time intervals the metric selected fell approximately 20% and 95% into the QRST, i.e., at the start and end of repolarization, suggesting that there may be diagnostic information near the end of the QRS that could respond faster than more traditional electrocardiographic metrics based on ST segments or T waves. In order to establish what time intervals were chosen most often by the LE algorithm the signals were normalized to have 1000 time points. Using length normalized signals increased the computation time from 2–3 minutes (including training steps) to 8–15 minutes per episode.

This analysis of the signals and their metrics underscored the observation that the electrocardiographic signature of ischemia is transient and spatiotemporally complex and hence challenging to capture and interpret in clinical settings. Only by characterizing these patterns in the controlled setting of animal experiments can we hope to infer the underlying level of ischemic stress present and generate useful, practical metrics. The differences in the temporal evolution of the metrics we tested, e.g., LE changes preceding T wave changes, etc., suggest that novel metrics may exist that could improve the clinical performance of the ECG. Future research using the LE metric will be focused on evaluating the limits of the algorithm and how it might translate to the clinical environment. A primary consideration will be whether or not the heightened performance of the LE metric from epicardial electrograms will translate to the body surface ECGs. Our previous results applying LE approaches to body surface potential maps [10] provide encouraging support for this application.

5. Conclusion

This study presented and evaluated a novel metric for detecting ischemic stress, the LE metric, and introduced a framework for evaluating the temporal performance of any metric of a dynamic behavior like ischemia. To gauge overall predictive performance, we applied a receiver-operator curve analysis on each metric. We found that the LE metric was able to detect ischemia earlier, more robustly, and with a higher AUC than standard electrocardiographic metrics. In addition, we also found a consistent trend in the order in which metrics responded to ischemic episodes: the LE metric typically detected the episode first, followed by T wave based metrics, ST-based metrics, and lastly QRS-based metrics. Furthermore, we found evidence that ischemic stress is present, to a sizable extent, within the intramural space before it can be detected on the epicardium, even using the LE approach.

Highlights

• Therewas a consistent trend in the order in which metrics responded to ischemic episodes: the Laplacian eigenmap (LE) metric typically detected the episode first, followed by T wave based metrics, ST-based metrics, and lastly QRS-based metrics

• The LE metric was able to detect ischemia earlier, more robustly, and with a higher AUC than standard electrocardiographic metrics used to detect myocardial ischemia.

• We found evidence that ischemic stress is present, to a sizable extent, within the intramural space before it can be detected on the epicardium, even using the LE metric.