Characterizing the transient electrocardiographic signature of ischemic stress using Laplacian Eigenmaps for dimensionality reduction.

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.

Effects of Interpolation on the Inverse Problem of Electrocardiography.

Electrocardiographic Imaging (ECGI) aims to reconstruct electrograms from the body surface potential measurements. Bad leads are usually excluded from the inverse problem solution. Alternatively, interpolation can be applied. This study explores how sensitive ECGI is to different bad-lead configurations and interpolation methods. Experimental data from a Langendorff-perfused pig heart suspended in a human-shaped torso-tank was used. Epicardial electrograms were acquired during 30 s (31 beats) of RV pacing using a 108-electrode array, simultaneously with torso potentials from 128 electrodes embedded in the tank surface. Six different bad lead cases were designed based on clinical experience. Inverse problem was solved by applying Tikhonov regularization i) using the complete data, ii) bad-leads-removed data, and iii) interpolated data, with 5 different methods. Our results showed that ECGI accuracy of an interpolation method highly depends on the location of the bad leads. If they are in the high-potential-gradient regions of the torso, a highly accurate interpolation method is needed to achieve an ECGI accuracy close to using complete data. If the BSP reconstruction of the interpolation method is poor in these regions, the reconstructed electrograms also have lower accuracy, suggesting that bad leads should be removed instead of interpolated. The inverse-forward method was found to be the best among all interpolation methods applied in this study in terms of both missing BSP lead reconstruction and ECGI accuracy, even for the bad leads located over the chest.

Image-based modeling of acute myocardial ischemia using experimentally derived ischemic zone source representations.

BACKGROUND: Computational models of myocardial ischemia often use oversimplified ischemic source representations to simulate epicardial potentials. The purpose of this study was to explore the influence of biophysically justified, subject-specific ischemic zone representations on epicardial potentials. METHODS: We developed and implemented an image-based simulation pipeline, using intramural recordings from a canine experimental model to define subject-specific ischemic regions within the heart. Static epicardial potential distributions, reflective of ST segment deviations, were simulated and validated against measured epicardial recordings. RESULTS: Simulated epicardial potential distributions showed strong statistical correlation and visual agreement with measured epicardial potentials. Additionally, we identified and described in what way border zone parameters influence epicardial potential distributions during the ST segment. CONCLUSION: From image-based simulations of myocardial ischemia, we generated subject-specific ischemic sources that accurately replicated epicardial potential distributions. Such models are essential in understanding the underlying mechanisms of the bioelectric fields that arise during ischemia and are the basis for more sophisticated simulations of body surface ECGs.

Reduction of Effects of Noise on the Inverse Problem of Electrocardiography with Bayesian Estimation.

To overcome the ill-posed nature of the inverse problem of electrocardiography (ECG) and stabilize the solutions, regularization is used. Despite several studies on noise, effect of prefiltering of ECG signals on the regularized inverse solutions has not been explored. We used Bayesian estimation for solving the inverse ECG problem with and without applying various prefiltering methods, and evaluated our results using experimental data that came from a Langendorff-perfused pig heart suspended in a human-shaped torso-tank. Epicardial electrograms were recorded during RV pacing using a 108-electrode array, simultaneously with ECGs from 128 electrodes embedded in the tank surface. Leave-one-beat-out protocol was used to obtain the prior probability density function (pdf) of electro-grams and noise statistics. Noise pdf was assumed to be zero mean-Gaussian, with covariance assumptions: a) independent and identically distributed (noi-iid), b) correlated (noi-corr). Reconstructed electrograms and activation times were compared to those directly recorded by the sock for 3 beats selected from the recording. Noi-corr is superior to noi-iid when the training set is a good match to data, but for applications requiring activation time derivation, careful selection of preprocessing methods, in particular to adequately remove high-frequency noise, and an appropriate noise model is needed.

Subject-specific, multiscale simulation of electrophysiology: a software pipeline for image-based models and application examples.

Many simulation studies in biomedicine are based on a similar sequence of processing steps, starting from images and running through geometric model generation, assignment of tissue properties, numerical simulation and visualization of the results--a process known as image-based geometric modelling and simulation. We present an overview of software systems for implementing such a sequence both within highly integrated problem-solving environments and in the form of loosely integrated pipelines. Loose integration in this case indicates that individual programs function largely independently but communicate through files of a common format and support simple scripting, so as to automate multiple executions wherever possible. We then describe three specific applications of such pipelines to translational biomedical research in electrophysiology.

Accuracy and run-time comparison for different potential approaches and iterative solvers in finite element method based EEG source analysis.

Accuracy and run-time play an important role in medical diagnostics and research as well as in the field of neuroscience. In Electroencephalography (EEG) source reconstruction, a current distribution in the human brain is reconstructed noninvasively from measured potentials at the head surface (the EEG inverse problem). Numerical modeling techniques are used to simulate head surface potentials for dipolar current sources in the human cortex, the so-called EEG forward problem.In this paper, the efficiency of algebraic multigrid (AMG), incomplete Cholesky (IC) and Jacobi preconditioners for the conjugate gradient (CG) method are compared for iteratively solving the finite element (FE) method based EEG forward problem. The interplay of the three solvers with a full subtraction approach and two direct potential approaches, the Venant and the partial integration method for the treatment of the dipole singularity is examined. The examination is performed in a four-compartment sphere model with anisotropic skull layer, where quasi-analytical solutions allow for an exact quantification of computational speed versus numerical error. Specifically-tuned constrained Delaunay tetrahedralization (CDT) FE meshes lead to high accuracies for both the full subtraction and the direct potential approaches. Best accuracies are achieved by the full subtraction approach if the homogeneity condition is fulfilled. It is shown that the AMG-CG achieves an order of magnitude higher computational speed than the CG with the standard preconditioners with an increasing gain factor when decreasing mesh size. Our results should broaden the application of accurate and fast high-resolution FE volume conductor modeling in source analysis routine.

Electrographic Response of the Heart to Myocardial Ischemia.

Electrocardiographic (ECG) ST segment shifts are often used as markers for detecting myocardial ischemia. Literature suggests that the progression of ischemia, occurs from the endocardium and spreads towards the epicardium, eventually becoming transmural. Our study with animal models has found the progression of ischemia, characterized by ST elevations to be more complex and heterogeneous in its distribution. We used in situ canine preparations, wherein the animals were subjected to demand ischemia by reducing coronary flow and raising the heart rate through atrial pacing. At reduced flow, increasing the heart rate caused pockets of ST elevations to appear variously distributed in the sub-epicardial, midmyocardial and endocardial regions. Further reduction in coronary flow with simultaneous raising of the heart rate, increased the extent and magnitude of ST elevated regions, that in certain cases became transmural.

Influence of tissue conductivity anisotropy on EEG/MEG field and return current computation in a realistic head model: a simulation and visualization study using high-resolution finite element modeling.

To achieve a deeper understanding of the brain, scientists, and clinicians use electroencephalography (EEG) and magnetoencephalography (MEG) inverse methods to reconstruct sources in the cortical sheet of the human brain. The influence of structural and electrical anisotropy in both the skull and the white matter on the EEG and MEG source reconstruction is not well understood. In this paper, we report on a study of the sensitivity to tissue anisotropy of the EEG/MEG forward problem for deep and superficial neocortical sources with differing orientation components in an anatomically accurate model of the human head. The goal of the study was to gain insight into the effect of anisotropy of skull and white matter conductivity through the visualization of field distributions, isopotential surfaces, and return current flow and through statistical error measures. One implicit premise of the study is that factors that affect the accuracy of the forward solution will have at least as strong an influence over solutions to the associated inverse problem. Major findings of the study include (1) anisotropic white matter conductivity causes return currents to flow in directions parallel to the white matter fiber tracts; (2) skull anisotropy has a smearing effect on the forward potential computation; and (3) the deeper a source lies and the more it is surrounded by anisotropic tissue, the larger the influence of this anisotropy on the resulting electric and magnetic fields. Therefore, for the EEG, the presence of tissue anisotropy both for the skull and white matter compartment substantially compromises the forward potential computation and as a consequence, the inverse source reconstruction. In contrast, for the MEG, only the anisotropy of the white matter compartment has a significant effect. Finally, return currents with high amplitudes were found in the highly conducting cerebrospinal fluid compartment, underscoring the need for accurate modeling of this space.

Modelling passive cardiac conductivity during ischaemia.

The results of a geometric model of cardiac tissue, used to compute the bidomain conductivity tensors during three phases of ischaemia, are described. Ischaemic conditions were simulated by model parameters being changed to match the morphological and electrical changes of three phases of ischaemia reported in literature. The simulated changes included collapse of the interstitial space, cell swelling and the closure of gap junctions. The model contained 64 myocytes described by 2 million tetrahedral elements, to which an external electric field was applied, and then the finite element method was used to compute the associated current density. In the first case, a reduction in the amount of interstitial space led to a reduction in extracellular longitudinal conductivity by about 20%, which is in the range of reported literature values. Moderate cell swelling in the order of 10-20% did not affect extracellular conductivity considerably. To match the reported drop in total tissue conductance reported in experimental studies during the third phase of ischaemia, a ten fold increase in the gap junction resistance was simulated. This ten-fold increase correlates well with the reported changes in gap junction densities in the literature.

The influence of volume conduction effects on the EEG/MEG reconstruction of the sources of the Early Left Anterior Negativity.

To achieve a deeper understanding of language processing in the human brain, scientists and clinicians use Electroencephalography (EEG) and Magnetoencephalography (MEG) inverse methods to reconstruct sources of Event Related Potentials. There exists a persistent uncertainty regarding the influence of volume conduction effects such as the anisotropy of tissue conductivity of the skull and the white matter layers on the inverse results. In this paper, we will study the sensitivity to anisotropy of the source reconstruction of the Early Left Anterior Negativity (ELAN) component in language processing. For EEG, the presence of tissue anisotropy substantially compromises the restoration ability of an L1-norm current density approach. The centers of activity are strongly shifted along the Sylvian fissure in the anterior direction. In contrast, MEG in combination with the L1 norm approach is able to reconstruct the main features of the ELAN source distribution even in the presence of anisotropic conductivity.

Optimal electrocardiographic leads for detecting acute myocardial ischemia.

This study identifies the most sensitive electrocardiographic leads for monitoring ST-segment changes caused by acute coronary ischemia. The data set consisted of 120-lead electrocardiograms (ECGs) digitally recorded during balloon-inflation angioplasty in 3 groups of patients with single-vessel disease (left anterior descending [LAD], 32; right coronary artery [RCA], 36; left circumflex [LCx], 23). The ST deviation was measured in all recorded leads during baseline and ischemic states, and its difference between these 2 states (DeltaST) was calculated at 352 sites and plotted as DeltaST maps. The patients in each group were divided, by means of DeltaST criteria, into subgroups of "responders" and "nonresponders." Mean DeltaSTs for each group/subgroup were calculated and standardized by the corresponding standard deviation (SD); these values were plotted as mean DeltaST and t maps. Sites where extrema of DeltaST occurred most frequently were sought in bootstrap trials, performed in each group/subgroup. The results suggest that the optimal sites for the ischemia-sensitive leads are: V(3) (+) and just below V(8) (-) for LAD-related ischemia; the left iliac crest (+) and above V(3) at the third intercostal space (-) for RCA-related ischemia; and just below V(8) (+) and above V(2) at the third intercostal space (-) for LCx-related ischemia. Three "optimal" bipolar leads using these sites registered, in the responders from the LAD, RCA, and LCx groups, mean DeltaST (+/-SD) of 232 +/- 59, 245 +/- 96 and 158 +/- 91 microV, respectively; the corresponding t values were 15.14, 9.90, and 6.75. In the 12-lead ECG, only lead V(3) approached optimal DeltaST and t values for the LAD responders (187 +/- 61 microV; t = 11.75) and lead III for the RCA responders (191 +/- 76 microV; t = 9.73), but even these values were significantly suboptimal (P = 0.0011 and P = 0.0120, respectively). We found that the "optimal" bipolar leads can be derived, to an excellent approximation, from the 12 standard leads or from 3 EASI leads (with 3 electrodes at Frank's transverse level and 1 on the manubrium), by using precalculated regression coefficients. By means of bootstrap trials, we estimated the mean sensitivity (SE) and the mean positive predictive value (PPV) with which 3 "optimal" vessel-specific leads could identify ischemia related to the LAD, RCA, and LCx arteries, in the test set, as (SE/PPV) 94.7/92.8%, 78.7/80.9%, and 81.5/80.9%. A similar diagnostic performance can be achieved by vessel-specific leads derived from the 12-lead ECG (93.0/93.4%, 76.6/82.0%, and 82.7/77.1%) and, interestingly, from the EASI lead system (97.8/88.4%, 78.0/80.2%, and 76.8/83.2%). Thus, although the "optimal" bipolar leads for detecting ischemia related to each of the 3 coronary arteries were found to require sampling outside the 12-lead ECG, these leads can be derived from the full set of 12 standard leads or--for clinical monitoring applications--from the EASI lead system by using fewer electrodes at convenient locations.

The role of heart rate in myocardial ischemia from restricted coronary perfusion.

Despite many years of study, certain aspects of myocardial ischemia remain incompletely understood. One observation that motivated this study is that acute, complete occlusion produces elevations but never depression of the ST-segment potentials in electrocardiographic leads over the ischemic zone. Limited flow, on the other hand, leads to ST-segment depression, both in in situ experiments and during clinical stress tests. The prevailing biophysical theory of ischemia suggests that complete occlusion should produce at least transient ST-segment depression, a finding we have neither observed in our own studies nor uncovered in the literature. Our goal with these experiments was to understand the difference between complete occlusion and reduced coronary flow, specifically the behavior at the transition between the two. We have performed experiments by using isolated dog hearts with a cannulated left anterior descending artery suspended in a human shaped electrolytic tank. To create a range of ischemic conditions, we changed coronary flow rates both suddenly and in controlled sequences and varied the heart rate of the isolated heart. The main finding was that in the isolated heart preparation, epicardial ST-segment depression over the ischemic zone arose only under conditions of combined restricted flow and elevated heart rate. Reduced coronary flow alone never produced ST-segment depression. These findings suggest that heart rate and probably metabolic work create the conditions necessary for subendocardial ischemia that reduced flow alone cannot provoke. They furthermore suggest that the degree of ST-segment depression for a given restriction in coronary flow may depend on heart rate, which supports the notion of rate correction for clinical stress electrocardiogram testing.

Estimates of repolarization dispersion from electrocardiographic measurements.

BACKGROUND: Repolarization dispersion (Rd) is frequently mentioned as a predictor of cardiac abnormalities. We present a new measure of Rd based on the root-mean-square (RMS) curve of an ECG lead set and compare its performance with that of the commonly used QT dispersion (QTd) measure with the use of recovery times measured from directly recorded canine electrograms. METHODS AND RESULTS: Using isolated, perfused canine hearts suspended in a torso-shaped electrolytic tank, we simultaneously recorded electrograms from 64 epicardial sites and ECGs from 192 "body surface" sites. RMS curves were derived from 4 lead sets: epicardial, body surface, precordial, and a 6-lead optimal set. Repolarization was altered by changing cycle length, temperature, and activation sequence. Rd, calculated directly from recovery times of the 64 epicardial potentials, was then compared with the width of the T wave of the RMS curve and with QTd for each of these 4 lead sets. The correlation between T-wave width and Rd for each lead set, respectively, was epicardium, 0.91; body surface, 0.84; precordial, 0.72; and optimal leads, 0.81. The correlation between QTd and Rd for each lead set was epicardium, 0.46; body surface, 0.47; precordial, 0.17; and optimal leads, 0.11. CONCLUSIONS: RMS curve analysis provides an accurate method of estimating Rd from the body surface. In contrast, QTd analysis provides a poor estimate of Rd.

Estimates of repolarization and its dispersion from electrocardiographic measurements: direct epicardial assessment in the canine heart.

This study investigates a technique to estimate dispersion based on the root mean square (RMS) signal of multiple electrocardiographic leads. Activation and recovery times were measured from 64 sites on the epicardium of canine hearts using acute in situ or Langendorff perfused isolated heart preparations. Repolarization and its dispersion were altered by varying cycle length, myocardial temperature, or ventricular pacing site. Mean and dispersion of activation and recovery times, and activation-recovery interval (ARI) were calculated for each beat. The waveform was then calculated from all leads. Estimates of mean and dispersion of activation and recovery times and mean ARI were derived using only inflection points from the RMS waveform. QT intervals were also measured and QT dispersion was determined. Estimates determined from the RMS waveform provided accurate estimates of repolarization and were, in particular, a better measure of repolarization dispersion than QT dispersion.

Noninvasive ECG imaging of electrophysiologically abnormal substrates in infarcted hearts : A model study.

BACKGROUND: Myocardial infarction and subsequent remodeling create substrates with altered electrophysiological (EP) properties that are highly arrhythmogenic. Existing ECG methods cannot always detect the existence of such substrates nor provide any detailed information about their EP characteristics. A noninvasive method with such capabilities is greatly needed for identifying patients at risk of arrhythmias and for guidance and evaluation of therapy. Recently, we developed a noninvasive ECG imaging modality that can reconstruct epicardial EP information from body surface potentials. We extended its application to hearts with structural disease and examined its ability to detect and characterize abnormal EP substrates. METHODS AND RESULTS: Epicardial potentials were recorded with a 490-electrode sock from an open-chest dog. Recordings were obtained from a normal heart and from the same heart 2 hours after left anterior descending coronary artery occlusion and ethanol injection to create an infarct. Body surface potentials were generated from these epicardial potentials in a human torso model. Realistic geometry errors and measurement noise were added to the torso data, which were then used to noninvasively reconstruct epicardial potentials and electrograms (EGMs), with excellent accuracy. EP characteristics associated with the infarct substrate were reconstructed, including (1) a negative region over the infarct, (2) EGMs with large predominant negative deflections (eg, Q-wave EGMs), (3) Q-wave EGMs with superimposed RS deflections reflecting local activation of surviving myocardium within the infarct border zone, (4) reduced magnitudes of EGM negative derivatives, and (5) negative QRS integrals of EGMs over the infarct. CONCLUSIONS: ECG imaging can noninvasively detect and map abnormal EP substrates associated with infarction and structural heart disease.

Computing and visualizing electric potentials and current pathways in the thorax.

The long-term goal of electrocardiography is to relate electric potentials on the body surface with activities in the heart. Many previously reported studies have focused on direct links between heart and body surface potentials. The goals of this study were first to validate computational methods of determining volume potentials and currents with high-resolution experimental measurements and then to use interactive visualization of thoracic currents to understand features of the electrocardiographic fields from measured cardiac sources. We developed both simulation and experimental studies based on a realistic shaped torso phantom containing an isolated, perfused dog heart. Interventions included atrial pacing, single pacing and simultaneously pacing at multiple locations on the ventricles. Simulated torso volume potentials closely matched measured potentials in the torso-tank preparation (mean correlation coefficients of 0.95). Simulation further provided a means of estimating the current field in the torso from the computed torso volume potentials and the local geometric and conductive properties of the medium. Applying these techniques to the torso electric fields under a variety of pacing conditions, we have further demonstrated that thoracic current can provide many insights into the relationship between heart surface potential and body surface potentials. Specifically, we have shown that geometric factors including cardiac source configuration and location play an important role in determining to what extent electric activity in the heart is directly visible on the body surface electrocardiogram. The computation and visualization toolkit we developed in this study to explore current fields associated with cardiac events may provide new insights into electrocardiology.

Effects of heart position on the body-surface electrocardiogram.

Previous studies have examined the influence of body position, respiration, and habitus on body surface potentials. However, the authors could only estimate the sources of the effects they documented. Among the proposed origin of changes in body surface potentials from those studies were the position of the heart, alterations in autonomic tone, differences in ventricular blood volume, and variations in torso resistivity. The goal of this study was to investigate specifically the role of geometric factors in altering body surface potentials and the electrocardiogram. For this, we used experiments with an isolated, perfused dog heart suspended in a realistically shaped electrolytic torso tank. The experimental preparation allowed us to measure epicardial and tank surface potentials simultaneously, and then reconstruct the geometry of both surfaces. Our results mimicked some of the features described by previous investigators. However, our results also showed differences that included considerably larger changes in the peak QRS and T-wave amplitudes with heart movement than those reported in human studies. We detected smaller values of root-mean-squared variability from heart movements than those reported in a human study comparing body surface potentials during change in inspiration and body position. There was better agreement with relative variability, which in these studies ranged from 0.11 to 0.42, agreeing well with an estimate from human studies of 0.40. Our results suggest that the isolated heart/torso tank preparation is a valuable tool for investigating the effects of geometric variation. Furthermore, the geometric position of the heart appears to be a large source of variation in body surface potentials. The size of these variations easily exceeded thresholds used to distinguish pathologic conditions and thus such variations could have important implications on the interpretation of the standard electrocardiogram.

Three-dimensional activation mapping in ventricular muscle: interpolation and approximation of activation times.

Interpolation plays an important role in analyzing or visualizing any scalar field because it provides a means to estimate field values between measured sites. A specific example is the measurement of the electrical activity of the heart, either on its surface or within the muscle, a technique known as cardiac mapping, which is widely used in research. While three-dimensional measurement of cardiac fields by means of multielectrode needles is relatively common, the interpolation methods used to analyze these measurements have rarely been studied systematically. The present study addressed this need by applying three trivariate techniques to cardiac mapping and evaluating their accuracy in estimating activation times at unmeasured locations. The techniques were tetrahedron-based linear interpolation, Hardy's interpolation, and least-square quadratic approximation. The test conditions included activation times from both high-resolution simulations and measurements from canine experiments. All three techniques performed satisfactorily at measurement spacing < or = 2 mm. At the larger interelectrode spacings typical in cardiac mapping (1 cm), Hardy's interpolation proved superior both in terms of statistical measures and qualitative reconstruction of field details. This paper provides extensive comparisons among the methods and descriptions of expected errors for each method at a variety of sampling intervals and conditions.

Estimation of epicardial activation maps from intravascular recordings.

Multielectrode catheters provide a percutaneous means of recording activation near the epicardium but only for a relatively small number of sites that are restricted to the major coronary vessels. We have applied a statistical signal processing technique to estimate the value of activation time over the entire epicardium (490 sites) from leadsets consisting of 4 to 40 sites aligned with major branches of the coronary veins. We tested this method using data from high-resolution epicardial mapping from six dog hearts and 153 activation sequences. A study including data from both normal and infarcted dog hearts yielded estimates of activation time, with mean correlation coefficients ranging from 0.97 to 0.84 and achieved localization of earliest site of activation to within 3 to 15 mm, depending on training parameters and leadset. These results suggest that with 10 to 15 catheter-mounted electrodes, it may be possible to reconstruct epicardial activation maps from percutaneous recordings.

Inverse electrocardiography by simultaneous imposition of multiple constraints.

We describe two new methods for the inverse problem of electrocardiography. Both employ regularization with multiple constraints, rather than the standard single-constraint regularization. In one method, multiple constraints on the spatial behavior of the solution are used simultaneously. In the other, spatial constraints are used simultaneously with constraints on the temporal behavior of the solution. The specific cases of two spatial constraints and one spatial and one temporal constraint are considered in detail. A new method, the L-Surface, is presented to guide the choice of the required pairs of regularization parameters. In the case when both spatial and temporal regularization are used simultaneously, there is an increased computational burden, and two methods are presented to compute solutions efficiently. The methods are verified by simulations using both dipole sources and measured canine epicardial data.