Spatiotemporal approximation of cardiac activation and recovery isochrones.

BACKGROUND: The sequence of myocardial activation and recovery can be studied in detail by invasive catheter recordings of cardiac electrograms (EGMs), or noninvasive inverse reconstructions thereof with electrocardiographic imaging (ECGI). Local activation and recovery times are obtained from a unipolar EGM by the moment of maximum downslope of the QRS complex or maximum upslope of the T wave, respectively. However, both invasive and noninvasive recordings of intracardiac EGMs may suffer from noise and fractionation, making reliable detection of these deflections nontrivial. METHODS: Here, we introduce a novel method that benefits from the spatial coupling of these processes, and incorporate not only the temporal EGM deflection, but also the spatial gradients. We validated this approach in computer simulations, in animal data with ECGI and invasive electrode recordings, and illustrated its use in a clinical case. RESULTS: In the simulated data, the spatiotemporal approach was able to incorporate spatial information to better select the correct deflection in artificially fractionated EGMs and outperformed the traditional temporal-only method. In experimental data, the accuracy of time estimation from ECGI compared to invasive recordings significantly increased from R = 0.73 (activation) and R = 0.58 (recovery) with the temporal-only method to R = 0.79 (activation) and R = 0.72 (recovery) with the novel approach. Localization of the pacing origin of paced beats improved significantly from 36 mm mean error with the temporal-only approach to 23 mm with the spatiotemporal approach. CONCLUSION: The spatiotemporal method to compute activation and recovery times from EGMs outperformed the traditional temporal-only approach in which spatial information was not taken into account.

Temporal Performance of Laplacian Eigenmaps and 3D Conduction Velocity in Detecting Ischemic Stress.

BACKGROUND: Myocardial ischemia has a complex and time-varying electrocardiographic signature that is used to diagnose and stratify severity. Despite the ubiquitous clinical use of the ECG to detect ischemia, the sensitivity and specificity of ECG based detection of myocardial ischemia are still inadequate. PURPOSE: The purpose of this study was to compare, using animal models, the performance of several traditional ECG-based metrics for detecting acute ischemia against two novel metrics, the Laplacian Eigenmap (LE) parameters and a three-dimensional estimate of Conduction Velocity (CV). METHODS: LE is a machine learning technique that reduces the dimensions of simultaneously recorded time signals using a non-linear embedding followed by an singular value decomposition to represent each multichannel recording as a single trajectory on a manifold. Perturbations in the trajectories suggest the presence of myocardial ischemia. CV was computed using a tetrahedral mesh created from the electrode locations of transmural plunge needles. To validate the results, we used electrograms collected over 95 episodes of acutely induced myocardial ischemia in 15 canine and 2 porcine subjects. The LE and CV metrics were compared against traditional metrics derived from the ST segment, the T wave, the QRS of the same electrograms. The response time and robustness of each metric was quantified using parameters we defined as time to threshold (TTT) and contrast ratio (CR). RESULTS: The temporal performance of the metrics evaluated throughout the ischemic episodes showed a consistent relationship; the LE metrics changed earlier than those from the T wave, which were followed by those from the ST segment, and finally from the QRS. The CV results showed median drops in conduction velocity throughout the perfusion bed of more than 23% in canines and over 12% during half of the induced ischemia episodes in swine. The other half of the episodes in swine produced a 76% drop. CONCLUSIONS: Our results suggest that the LE metric is more sensitive to acute ischemia than traditional single parameters used in previous studies, likely because it incorporates the entire QRST across multiple electrodes in a way that captures their most salient features in a low-dimensional space. The estimates of conduction velocity suggest substantial, in some cases dramatic slowing of the spread of activation, a finding that is not surprising but has not been documented in such three-dimensional detail before. The experiments and these new metrics provide a means to both explore details of the acute ischemic response not available from humans and suggest a path to translate this knowledge into improvements in clinical scoring of ischemia.

Novel Metric Using Laplacian Eigenmaps to Evaluate Ischemic Stress on the Torso Surface.

The underlying pathophysiology of myocardial ischemia is incompletely understood, resulting in persistent difficulty of diagnosis. This limited understanding of underlying mechanisms encourages a data driven approach, which seeks to identify patterns in the ECG data that can be linked statistically to disease states. Laplacian Eigen-maps (LE) is a dimensionality reduction method popularized in machine learning that we have shown in large animal experiments to identify underlying ischemic stress both earlier in an ischemic episode, and more robustly, than typical clinical markers. We have now extended this approach to body surface potential mapping (BSPM) recordings acquired during acute, transient ischemia episodes from animal and human PTCA studies. Our previous studies, suggest that the LE approach is sensitive to the spatiotemporal electrocardiographic consequences of ischemia-induced stress within the heart and on the epicardial surface. In this study, we expand this technique to the body surface of animals and humans. Across 10 episodes of induced ischemia in animals and 200 human recordings during PTCA, the LE algorithm was able to detect ischemic events from BSPM as changes in the morphology of the resulting trajectories while maintaining the superior temporal performance the LE-metric has shown previously.

A Potential-Based Inverse Spectral Method to Noninvasively Localize Discordant Distributions of Alternans on the Heart From the ECG.

T-wave alternans (TWA), defined as the beat-to-beat alternation in amplitude of the T-waves, has been shown to be linked to ventricular fibrillation (VF). However, current TWA tests have high sensitivity but low specificity in determining who is at risk. To overcome this limitation, it might be helpful to determine the spatial distribution of any regions on the heart that alternate in opposite phase. Understanding these spatial distributions in relation to the regular activation of the heart could help explain the mechanism for the genesis of VF and thus disambiguate the low specificity of TWA. GOAL: Image the spatial distribution of TWA on the heart surface from ECG measurements. METHODS: We introduced the inverse spectral method (ISM), a tailored inverse (or ElectroCardioGraphic Imaging) solution designed specifically to noninvasively image cases of TWA on the heart. RESULTS: We evaluate the ISM on its capacity to reliably detect the spatial distributions of TWA compared against a standard TWA detection method applied directly to the electrograms on the heart surface. We report on results from both a series of synthetic simulations of TWA generated using the ECGSIM software and a set of continuous epicardial surface voltage recordings from a canine experiment. ISM detected TWA distributions that matched the phase of the true underlying out-of-phase regions over and of the heart surface, respectively. CONCLUSION: Our results suggest that ISM is capable of reliably detecting the different regions present in a TWA distribution across a wide variety of TWA locations on the heart in simulation and in the face of transients and nonidealities in the canine recordings.

Detecting Ischemic Stress to the Myocardium Using Laplacian Eigenmaps and Changes to Conduction Velocity.

The underlying pathophysiology of ischemia and its electrocardiographic consequences are poorly understood, resulting in unreliable diagnosis of this disease. This limited knowledge of underlying mechanisms suggests a data driven approach, which seeks to identify patterns in the ECG that can be linked statistically to underlying behavior and conditions of ischemic stress. The gold standard ECG metrics for evaluating ischemia monitor vertical deflections within the ST segment. However, ischemia influences all portions of the electrogram. Another metric that targets the QRS complex during ischemia is Conduction Velocity (CV). An even more inclusive, data driven approach is known as "Laplacian Eigenmaps" (LE), which can identify trajectories, or "manifolds", that respond to different spatiotemporal consequences of ischemic stress, and these changes to the trajectories on the manifold may serve as a clinically relevant biomarker. On this study, we compared the LE- and CV-based markers against two gold standards for detecting ischemic stress, both derived from the ST segment. We evaluated the response time and fidelity of each biomarker using a Time to Threshold (TTT) and Contrast Ratio (CR) measure, over 51 episodes recorded as cardiac electrograms from a canine model of controlled ischemia. The results show that metrics designed to monitor regions beyond the ST segment can perform at least as well, if not better, than traditional ST segment based metrics.

Dynamic Electrical Source Imaging (DESI) of Seizures and Interictal Epileptic Discharges Without Ensemble Averaging.

We propose an algorithm for electrical source imaging of epileptic discharges that takes a data-driven approach to regularizing the dynamics of solutions. The method is based on linear system identification on short time segments, combined with a classical inverse solution approach. Whereas ensemble averaging of segments or epochs discards inter-segment variations by averaging across them, our approach explicitly models them. Indeed, it may even be possible to avoid the need for the time-consuming process of marking epochs containing discharges altogether. We demonstrate that this approach can produce both stable and accurate inverse solutions in experiments using simulated data and real data from epilepsy patients. In an illustrative example, we show that we are able to image propagation using this approach. We show that when applied to imaging seizure data, our approach reproducibly localized frequent seizure activity to within the margins of surgeries that led to patients' seizure freedom. The same approach could be used in the planning of epilepsy surgeries, as a way to localize potentially epileptogenic tissue that should be resected.

Motion-Robust Diffusion-Weighted Brain MRI Reconstruction Through Slice-Level Registration-Based Motion Tracking.

This work proposes a novel approach for motion-robust diffusion-weighted (DW) brain MRI reconstruction through tracking temporal head motion using slice-to-volume registration. The slice-level motion is estimated through a filtering approach that allows tracking the head motion during the scan and correcting for out-of-plane inconsistency in the acquired images. Diffusion-sensitized image slices are registered to a base volume sequentially over time in the acquisition order where an outlier-robust Kalman filter, coupled with slice-to-volume registration, estimates head motion parameters. Diffusion gradient directions are corrected for the aligned DWI slices based on the computed rotation parameters and the diffusion tensors are directly estimated from the corrected data at each voxel using weighted linear least squares. The method was evaluated in DWI scans of adult volunteers who deliberately moved during scans as well as clinical DWI of 28 neonates and children with different types of motion. Experimental results showed marked improvements in DWI reconstruction using the proposed method compared to the state-of-the-art DWI analysis based on volume-to-volume registration. This approach can be readily used to retrieve information from motion-corrupted DW imaging data.

Evaluation of motion and its effect on brain magnetic resonance image quality in children.

BACKGROUND: Motion artifacts pose significant problems for the acquisition of MR images in pediatric populations. OBJECTIVE: To evaluate temporal motion metrics in MRI scanners and their effect on image quality in pediatric populations in neuroimaging studies. MATERIALS AND METHODS: We report results from a large pediatric brain imaging study that shows the effect of motion on MRI quality. We measured motion metrics in 82 pediatric patients, mean age 13.4 years, in a T1-weighted brain MRI scan. As a result of technical difficulties, 5 scans were not included in the subsequent analyses. A radiologist graded the images using a 4-point scale ranging from clinically non-diagnostic because of motion artifacts to no motion artifacts. We used these grades to correlate motion parameters such as maximum motion, mean displacement from a reference point, and motion-free time with image quality. RESULTS: Our results show that both motion-free time (as a ratio of total scan time) and average displacement from a position at a fixed time (when the center of k-space was acquired) were highly correlated with image quality, whereas maximum displacement was not as good a predictor. Among the 77 patients whose motion was measured successfully, 17 had average displacements of greater than 0.5 mm, and 11 of those (14.3%) resulted in non-diagnostic images. Similarly, 14 patients (18.2%) had less than 90% motion-free time, which also resulted in non-diagnostic images. CONCLUSION: We report results from a large pediatric study to show how children and young adults move in the MRI scanner and the effect that this motion has on image quality. The results will help the motion-correction community in better understanding motion patterns in pediatric populations and how these patterns affect MR image quality.

Extensions to a manifold learning framework for time-series analysis on dynamic manifolds in bioelectric signals.

This paper addresses the challenge of extracting meaningful information from measured bioelectric signals generated by complex, large scale physiological systems such as the brain or the heart. We focus on a combination of the well-known Laplacian eigenmaps machine learning approach with dynamical systems ideas to analyze emergent dynamic behaviors. The method reconstructs the abstract dynamical system phase-space geometry of the embedded measurements and tracks changes in physiological conditions or activities through changes in that geometry. It is geared to extract information from the joint behavior of time traces obtained from large sensor arrays, such as those used in multiple-electrode ECG and EEG, and explore the geometrical structure of the low dimensional embedding of moving time windows of those joint snapshots. Our main contribution is a method for mapping vectors from the phase space to the data domain. We present cases to evaluate the methods, including a synthetic example using the chaotic Lorenz system, several sets of cardiac measurements from both canine and human hearts, and measurements from a human brain.

Optimization of focality and direction in dense electrode array transcranial direct current stimulation (tDCS).

OBJECTIVE: Transcranial direct current stimulation (tDCS) aims to alter brain function non-invasively via electrodes placed on the scalp. Conventional tDCS uses two relatively large patch electrodes to deliver electrical current to the brain region of interest (ROI). Recent studies have shown that using dense arrays containing up to 512 smaller electrodes may increase the precision of targeting ROIs. However, this creates a need for methods to determine effective and safe stimulus patterns as the number of degrees of freedom is much higher with such arrays. Several approaches to this problem have appeared in the literature. In this paper, we describe a new method for calculating optimal electrode stimulus patterns for targeted and directional modulation in dense array tDCS which differs in some important aspects with methods reported to date. APPROACH: We optimize stimulus pattern of dense arrays with fixed electrode placement to maximize the current density in a particular direction in the ROI. We impose a flexible set of safety constraints on the current power in the brain, individual electrode currents, and total injected current, to protect subject safety. The proposed optimization problem is convex and thus efficiently solved using existing optimization software to find unique and globally optimal electrode stimulus patterns. MAIN RESULTS: Solutions for four anatomical ROIs based on a realistic head model are shown as exemplary results. To illustrate the differences between our approach and previously introduced methods, we compare our method with two of the other leading methods in the literature. We also report on extensive simulations that show the effect of the values chosen for each proposed safety constraint bound on the optimized stimulus patterns. SIGNIFICANCE: The proposed optimization approach employs volume based ROIs, easily adapts to different sets of safety constraints, and takes negligible time to compute. An in-depth comparison study gives insight into the relationship between different objective criteria and optimized stimulus patterns. In addition, the analysis of the interaction between optimized stimulus patterns and safety constraint bounds suggests that more precise current localization in the ROI, with improved safety criterion, may be achieved by careful selection of the constraint bounds.

Optimizing Stimulus Patterns for Dense Array tDCS With Fewer Sources Than Electrodes Using A branch and Bound Algorithm.

Dense array transcranial direct current stimulation (tDCS) has become of increasing interest as a noninvasive modality to modulate brain function. To target a particular brain region of interest (ROI), using a dense electrode array placed on the scalp, the current injection pattern can be appropriately optimized. Previous optimization methods have assumed availability of individually controlled current sources for each non-reference electrode. This may be costly and impractical in a clinical setting. However, using fewer current sources than electrodes results in a non-convex combinatorial optimization problem. In this paper, we present a novel use of the branch and bound (BB) algorithm to find sub-optimal stimulus patterns with fewer current sources than electrodes. We present simulation results for both focal and spatially extended cortical ROIs. Our results suggest that only a few (2-3) independently controlled current sources can achieve comparable results to a full set (125 sources) to a tolerance of 5%. BB is computationally 3-5 orders of magnitude less demanding than exhaustive search.

Novel Biomarker for Evaluating Ischemic Stress Using an Electrogram Derived Phase Space.

The underlying pathophysiology of ischemia is poorly understood, resulting in unreliable clinical diagnosis of this disease. This limited knowledge of underlying mechanisms suggested a data driven approach, which seeks to identify patterns in the ECG data that can be linked statistically to underlying behavior and conditions of ischemic tissue. Previous studies have suggested that an approach known as Laplacian eigenmaps (LE) can identify trajectories, or manifolds, that are sensitive to different spatiotemporal consequences of ischemic stress, and thus serve as potential clinically relevant biomarkers. We applied the LE approach to measured transmural potentials in several canine preparations, recorded during control and ischemic conditions, and discovered regions on an approximated QRS-derived manifold that were sensitive to ischemia. By identifying a vector pointing to ischemia-associated changes to the manifold and measuring the shift in trajectories along that vector during ischemia, which we denote as Mshift, it was possible to also pull that vector back into signal space and determine which electrodes were responsible for driving the observed changes in the manifold. We refer to the signal space change as the manifold differential (Mdiff). Both the Mdiff and Mshift metrics show a similar degree of sensitivity to ischemic changes as standard metrics applied during the ST segment in detecting ischemic regions. The new metrics also were able to distinguish between sub-types of ischemia. Thus our results indicate that it may be possible to use the Mshift and Mdiff metrics along with ST derived metrics to determine whether tissue within the myocardium is ischemic or not.

Identifying model inaccuracies and solution uncertainties in noninvasive activation-based imaging of cardiac excitation using convex relaxation.

Noninvasive imaging of cardiac electrical function has begun to move towards clinical adoption. Here, we consider one common formulation of the problem, in which the goal is to estimate the spatial distribution of electrical activation times during a cardiac cycle. We address the challenge of understanding the robustness and uncertainty of solutions to this formulation. This formulation poses a nonconvex, nonlinear least squares optimization problem. We show that it can be relaxed to be convex, at the cost of some degree of physiological realism of the solution set, and that this relaxation can be used as a framework to study model inaccuracy and solution uncertainty. We present two examples, one using data from a healthy human subject and the other synthesized with the ECGSIM software package. In the first case, we consider uncertainty in the initial guess and regularization parameter. In the second case, we mimic the presence of an ischemic zone in the heart in a way which violates a model assumption. We show that the convex relaxation allows understanding of spatial distribution of parameter sensitivity in the first case, and identification of model violation in the second.

Using transmural regularization and dynamic modeling for noninvasive cardiac potential imaging of endocardial pacing with imprecise thoracic geometry.

Cardiac electrical imaging from body surface potential measurements is increasingly being seen as a technology with the potential for use in the clinic, for example for pre-procedure planning or during-treatment guidance for ventricular arrhythmia ablation procedures. However several important impediments to widespread adoption of this technology remain to be effectively overcome. Here we address two of these impediments: the difficulty of reconstructing electric potentials on the inner (endocardial) as well as outer (epicardial) surfaces of the ventricles, and the need for full anatomical imaging of the subject's thorax to build an accurate subject-specific geometry. We introduce two new features in our reconstruction algorithm: a nonlinear low-order dynamic parameterization derived from the measured body surface signals, and a technique to jointly regularize both surfaces. With these methodological innovations in combination, it is possible to reconstruct endocardial activation from clinically acquired measurements with an imprecise thorax geometry. In particular we test the method using body surface potentials acquired from three subjects during clinical procedures where the subjects' hearts were paced on their endocardia using a catheter device. Our geometric models were constructed using a set of CT scans limited in axial extent to the immediate region near the heart. The catheter system provides a reference location to which we compare our results. We compare our estimates of pacing site localization, in terms of both accuracy and stability, to those reported in a recent clinical publication , where a full set of CT scans were available and only epicardial potentials were reconstructed.

New Additions to the Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment.

Cardiac electrical imaging often requires the examination of different forward and inverse problem formulations based on mathematical and numerical approximations of the underlying source and the intervening volume conductor that can generate the associated voltages on the surface of the body. If the goal is to recover the source on the heart from body surface potentials, the solution strategy must include numerical techniques that can incorporate appropriate constraints and recover useful solutions, even though the problem is badly posed. Creating complete software solutions to such problems is a daunting undertaking. In order to make such tools more accessible to a broad array of researchers, the Center for Integrative Biomedical Computing (CIBC) has made an ECG forward/inverse toolkit available within the open source SCIRun system. Here we report on three new methods added to the inverse suite of the toolkit. These new algorithms, namely a Total Variation method, a non-decreasing TMP inverse and a spline-based inverse, consist of two inverse methods that take advantage of the temporal structure of the heart potentials and one that leverages the spatial characteristics of the transmembrane potentials. These three methods further expand the possibilities of researchers in cardiology to explore and compare solutions to their particular imaging problem.

Uncertainty Visualization in Forward and Inverse Cardiac Models.

Quantification and visualization of uncertainty in cardiac forward and inverse problems with complex geometries is subject to various challenges. Specific to visualization is the observation that occlusion and clutter obscure important regions of interest, making visual assessment difficult. In order to overcome these limitations in uncertainty visualization, we have developed and implemented a collection of novel approaches. To highlight the utility of these techniques, we evaluated the uncertainty associated with two examples of modeling myocardial activity. In one case we studied cardiac potentials during the repolarization phase as a function of variability in tissue conductivities of the ischemic heart (forward case). In a second case, we evaluated uncertainty in reconstructed activation times on the epicardium resulting from variation in the control parameter of Tikhonov regularization (inverse case). To overcome difficulties associated with uncertainty visualization, we implemented linked-view windows and interactive animation to the two respective cases. Through dimensionality reduction and superimposed mean and standard deviation measures over time, we were able to display key features in large ensembles of data and highlight regions of interest where larger uncertainties exist.

DIFFERENTIAL GEOMETRIC APPROXIMATION OF THE GRADIENT AND HESSIAN ON A TRIANGULATED MANIFOLD.

In a number of medical imaging modalities, including measurements or estimates of electrical activity on cortical or cardiac surfaces, it is often useful to estimate spatial derivatives of data on curved anatomical surfaces represented by triangulated meshes. Assuming the triangle vertices are points on a smooth manifold, we derive a method for estimating gradients and Hessians on locally 2D surfaces embedded in 3D directly in the global coordinate system. Accuracy of the method is validated through simulations on both smooth and corrugated surfaces.

A toolkit for forward/inverse problems in electrocardiography within the SCIRun problem solving environment.

Computational modeling in electrocardiography often requires the examination of cardiac forward and inverse problems in order to non-invasively analyze physiological events that are otherwise inaccessible or unethical to explore. The study of these models can be performed in the open-source SCIRun problem solving environment developed at the Center for Integrative Biomedical Computing (CIBC). A new toolkit within SCIRun provides researchers with essential frameworks for constructing and manipulating electrocardiographic forward and inverse models in a highly efficient and interactive way. The toolkit contains sample networks, tutorials and documentation which direct users through SCIRun-specific approaches in the assembly and execution of these specific problems.

Analysis of the criteria of activation-based inverse electrocardiography using convex optimization.

In inverse electrocardiography (ECG), the problem of finding activation times on the heart noninvasively from body surface potentials is typically formulated as a nonlinear least squares optimization problem. Current solutions rely on iterative algorithms which are sensitive to the presence of local minima. As a result, improved initialization approaches for this problem have been of considerable interest. However, in experiments conducted on a subject with Wolff-Parkinson-White syndrome, we have observed that there may be a mismatch between favorable solutions of the optimization problem and solutions with the desired physiological characteristics. In this work, we use a method based on a convex optimization framework to explore the solution space and analyze whether the optimization criteria target their intended objective.

Spatiotemporal estimation of activation times of fractionated ECGs on complex heart surfaces.

Identification of electrical activation or depolarization times on sparsely-sampled complex heart surfaces is of importance to clinicians and researchers in cardiac electrophysiology. We introduce a spatiotemporal approach for activation time estimation which combines prior results using spatial and temporal methods with our own progress on gradient estimation on triangulated surfaces. Results of the method applied to simulated and canine heart data suggest that improvements are possible using this novel combined approach.