Burak Erem

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.

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.

Manifold learning for analysis of low-order nonlinear dynamics in high-dimensional electrocardiographic signals

The dynamical structure of electrical recordings from the heart or torso surface is a valuable source of information about cardiac physiological behavior. In this paper, we use an existing data-driven technique for manifold identification to reveal electrophysiologically significant changes in the underlying dynamical structure of these signals. Our results suggest that this analysis tool characterizes and differentiates important parameters of cardiac bioelectric activity through their dynamic behavior, suggesting the potential to serve as an effective dynamic constraint in the context of inverse solutions.

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 electrophys-iology. 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.

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.

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.

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.

A convex relaxation framework for initialization of activation-based inverse electrocardiography

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. In this work, we establish a mathematical optimization framework for the inverse problem, formally show that it is non-convex, and construct a convex relaxation whose solution we use to initialize an iterative algorithm for the original problem. We use simulated experiments based on real canine heart data to test and evaluate this method.

Time invariant multi electrode averaging for biomedical signals

One of the biggest challenges in averaging ECG or EEG signals is to overcome temporal misalignments and distortions, due to uncertain timing or complex non-stationary dynamics. Standard methods average individual leads over a collection of epochs on a time-sample by time-sample basis, even when multi-electrode signals are available. Here we propose a method that averages multi electrode recordings simultaneously by using spatial patterns and without relying on time or frequency.

Interactive deformable registration visualization and analysis of 4D computed tomography

This paper presents a new interactive method for analyzing 4D Computed Tomography (4DCT) datasets for patient care and research. Deformable registration algorithms are commonly used to observe the trajectories of individual voxels from one respiratory phase to another. Our system provides users with the capability to visualize these trajectories while simultaneously rendering anatomical volumes, which can greatly improve the accuracy of deformable registration.