-Norm Regularization in Volumetric Imaging of Cardiac Current Sources

Advances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart. In comparison, our ability to observe and analyze cardiac electrical activities is much limited. The progress to computationally reconstruct cardiac current sources from noninvasive voltage data sensed on the body surface has been hindered by the ill-posedness and the lack of a unique solution of the reconstruction problem. Common L2- and L1-norm regularizations tend to produce a solution that is either too diffused or too scattered to reflect the complex spatial structure of current source distribution in the heart. In this work, we propose a general regularization with Lp-norm () constraint to bridge the gap and balance between an overly smeared and overly focal solution in cardiac source reconstruction. In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents. Through computer-simulated and real-data experiments, we further demonstrate the feasibility of the proposed method in imaging the complex structure of excitation wavefront, as well as current sources distributed along the postinfarction scar border. This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation

Non-Invasive Electrocardiographic Imaging of Ventricular Activities: Data-Driven and Model-Based Approaches

Die vorliegende Arbeit beleuchtet ausgewählte Aspekte der Vorwärtsmodellierung, so zum Beispiel die Simulation von Elektro- und Magnetokardiogrammen im Falle einer elektrisch stillen Ischämie sowie die Anpassung der elektrischen Potentiale unter Variation der Leitfähigkeiten. Besonderer Fokus liegt auf der Entwicklung neuer Regularisierungsalgorithmen sowie der Anwendung und Bewertung aktuell verwendeter Methoden in realistischen in silico bzw. klinischen Studien

Bayesian Optimization for the Inverse Problem in Electrocardiography

The inverse problem in electrocardiography is an ill-posed problem where the objective is to reconstruct the electrical activity of the epicardial surface of the heart, given the electrical activity on the thorax’ surface. In the forward problem, the electrical propagation from heart to thorax is modeled by the volume conductor equation with Dirichlet boundary conditions in the heart's surface, and null flux coming from the thorax. The inverse problem, however, does not have a unique solution. In order to find solutions for the inverse problem, techniques such as Tikhonov regularization are classically used, but they often deliver unrealistic solutions. As an alternative, we propose a novel approach, where a fixed solution of the volume conductor model with a source in a forward scheme is used to solve the inverse problem. The unknown values for parameters of the fixed solution can be found using optimization techniques. Due to the characteristics of the problem, where each single evaluation of the cost function is expensive, we use a specialized CMA-ES-based Bayesian optimization technique, that can deliver good results even with a reduced number of function evaluations. Experiments show that the proposed approach can deliver improved results for in-silico simulations

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality

The Application of Computer Techniques to ECG Interpretation

This book presents some of the latest available information on automated ECG analysis written by many of the leading researchers in the field. It contains a historical introduction, an outline of the latest international standards for signal processing and communications and then an exciting variety of studies on electrophysiological modelling, ECG Imaging, artificial intelligence applied to resting and ambulatory ECGs, body surface mapping, big data in ECG based prediction, enhanced reliability of patient monitoring, and atrial abnormalities on the ECG. It provides an extremely valuable contribution to the field

An Improved dipole-moment model based on near-field scanning for characterizing near-field coupling and far-field radiation from an IC

Radio Frequency Interference (RFI) problems are critical issues in wireless platform design. The accurate noise model of integrated circuits (ICs) is needed to help designers to diagnose and predict RFI problems. In this dissertation, an improved IC radiated emission model based on near-field measurements is proposed. The regularization technique and the truncated SVD method are employed together with the least square method to calculate the dipole moments from the near-field data. This dipole model has clear physical meaning: the electric and magnetic dipoles represent the voltage and the current in the circuit, respectively. One application of this dipole model is the prediction of heat sink radiation. In order to accurately predict the fields excited by a heat sink, an approach is proposed in this paper to include the exact excitation of the heat sink, which is described by some dipole moments constructed from the near-field scanning of the integrated circuit beneath the heat sink. Another contribution of the work is the proposal of effective dielectric properties of layered media for cavity model applications. With the effective properties. the cavity model can be generalized for either parallel plates or metal enclosures containing multiple dielectric layers. In the fourth paper a unified s-parameter (multimode s-parameter) representation for a multiport passive structure is proposed. Both mixed-mode and single-ended s-parameters arc included in the unified representation, which makes it more convenient to characterize structures --Abstract, page iv

Cardiomagnetic source imaging

Magnetocardiographic (MCG) source imaging has received increasing interest in recent years. With a high enough localization accuracy of the current sources in the heart, valuable information can be provided, e.g., for the pre-ablative evaluation of arrhythmia patients. Furthermore, preliminary studies indicate that ischemic areas, i.e. areas which are suffering from lack of oxygen, and infarcted regions could be localized from multichannel MCG recordings. In this thesis, the accuracy of cardiomagnetic source imaging results, obtained by using different current source models, was investigated. In addition, the effect of the torso model on the localization accuracy was examined. In some studies, also body surface potential mapping (BSPM) data were used for comparison purposes. A high impact was given to clinical validation, i.e. how the calculation methods would work in patients. The equivalent current dipole (ECD) source model was found to produce accurate (within 3-11 mm) localizations of focal current sources in a thorax phantom and in 15 patients with a non-magnetic stimulation catheter in the heart. The accuracy was found to depend on the signal-to-noise ratio and on the goodness of fit of the localizations. The corresponding accuracy determined from simultaneous multichannel BSPM recordings in 10 patients was 25 mm. In order to localize wider source regions in the heart, distributed source models were also investigated in the thesis. Current density estimates (CDEs) were calculated in the catheter patients and in 13 patients with coronary artery disease (CAD). Promising results were obtained by using second-order Tikhonov regularization in the calculations. CDEs were found to localize both myocardial ischemia in single-vessel CAD patients, as well as more complex chronic ischemia in three-vessel CAD patients. In addition to the ECD and CDE source models, the uniform double layer (UDL) model was used in the source imaging studies. With the UDL model, the whole depolarization of the ventricles can be represented with a single inverse solution. In the validation of the activation time maps calculated from MCG and BSPM recordings, invasively measured epicardial electrograms were used to construct the reference epicardial activation times. The overall patterns of activation in the reference data were reproduced relatively well in the calculated activation time maps. The high quality of the inverse solutions obtained in this thesis prompts the use of cardiomagnetic source imaging in several clinical applications, such as in electrophysiological studies and in the estimation of myocardial viability.reviewe

Strategies for optimal design of biomagnetic sensor systems

Magnetic field imaging (MFI) is a technique to record contact free the magnetic field distribution and estimate the underlying source distribution in the heart. Currently, the cardiomagnetic fields are recorded with superconducting quantum interference devices (SQUIDs), which are restricted to the inside of a cryostat filled with liquid helium or nitrogen. New room temperature optical magnetometers allow less restrictive sensor positioning, which raises the question of how to optimally place the sensors for robust field reconstruction. The objective in this study is to develop a generic object-oriented framework for optimizing sensor arrangements (sensor positions and orientations) which supports the necessary constraints of a limited search volume (only outside the body) and the technical minimum distance of sensors (e.g. 1 cm). In order to test the framework, a new quasi-continuous particle swarm optimizer (PSO) component is developed as well as an exemplary goal function component using the condition number (CN) of the leadfield matrix. Generic constraint handling algorithms are designed and implemented, that decompose complex constraints into basic ones. The constraint components interface to an operational exemplary optimization strategy which is validated on the magnetocardiographic sensor arrangement problem. The simulation setup includes a three compartment boundary element model of a torso with a fitted multi-dipole heart model. The results show that the CN, representing the reconstruction robustness of the inverse problem, can be reduced with our optimization by one order of magnitude within a sensor plane (the cryostat bottom) in front of the torso compared to a regular sensor grid. Reduction of another order of magnitude is achieved by optimizing sensor positions on the entire torso surface. Results also indicate that the number of sensors may be reduced to 20-30 without loss of robustness in terms of CN. The original contributions are the generic reusable framework and exemplary components, the quasicontinuous PSO algorithm with constraint support and the composite constraint handling algorithms