Binary optimization for source localization in the inverse problem of ECG

Systematic review of computational techniques, dataset utilization, and feature extraction in electrocardiographic imaging

This study aimed to analyze computational techniques in ECG imaging (ECGI) reconstruction, focusing on dataset identification, problem-solving, and feature extraction. We employed a PRISMA approach to review studies from Scopus and Web of Science, applying Cochrane principles to assess risk of bias. The selection was limited to English peer-reviewed papers published from 2010 to 2023, excluding studies that lacked computational technique descriptions. From 99 reviewed papers, trends show a preference for traditional methods like the boundary element and Tikhonov methods, alongside a rising use of advanced technologies including hybrid techniques and deep learning. These advancements have enhanced cardiac diagnosis and treatment precision. Our findings underscore the need for robust data utilization and innovative computational integration in ECGI, highlighting promising areas for future research and advances. This shift toward tailored cardiac care suggests significant progress in diagnostic and treatment methods.

Constructional Features of a Multielectrode Electrocardiology Screening System

The challenges of constructing a noninvasive screening system for electrocardiodiagnostics, focused on visualization of electric potential maps on the surface of the epicardium, is addressed. A functional diagram of a module for recording multiple-lead electrocardiosignals is proposed, the essential component of which is a vest (in several standard sizes) worn by the subject and carrying pre-installed electrodes. Results obtained from experimental verification of the operation of the recording module are presented. The issues of computer processing of electrocardiosignals were addressed and led to the ability to obtain 2D maps of the electric potential on a spherical quasi-epicardium, these 2D maps changing synchronously with changes in the position of the time marker on electrocardiograms familiar to cardiologists.

Inference of ventricular activation properties from non-invasive electrocardiography

The realisation of precision cardiology requires novel techniques for the non-invasive characterisation of individual patients’ cardiac function to inform therapeutic and diagnostic decision-making. Both electrocardiography and imaging are used for the clinical diagnosis of cardiac disease. The integration of multi-modal datasets through advanced computational methods could enable the development of the cardiac ‘digital twin’, a comprehensive virtual tool that mechanistically reveals a patient's heart condition from clinical data and simulates treatment outcomes. The adoption of cardiac digital twins requires the non-invasive efficient personalisation of the electrophysiological properties in cardiac models. This study develops new computational techniques to estimate key ventricular activation properties for individual subjects by exploiting the synergy between non-invasive electrocardiography, cardiac magnetic resonance (CMR) imaging and modelling and simulation. More precisely, we present an efficient sequential Monte Carlo approximate Bayesian computation-based inference method, integrated with Eikonal simulations and torso-biventricular models constructed based on clinical CMR imaging. The method also includes a novel strategy to treat combined continuous (conduction speeds) and discrete (earliest activation sites) parameter spaces and an efficient dynamic time warping-based ECG comparison algorithm. We demonstrate results from our inference method on a cohort of twenty virtual subjects with cardiac ventricular myocardial-mass volumes ranging from 74 cm³ to 171 cm³ and considering low versus high resolution for the endocardial discretisation (which determines possible locations of the earliest activation sites). Results show that our method can successfully infer the ventricular activation properties in sinus rhythm from non-invasive epicardial activation time maps and ECG recordings, achieving higher accuracy for the endocardial speed and sheet (transmural) speed than for the fibre or sheet-normal directed speeds.

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Estimation of the ventricular speeds and earliest activation sites from ECG and CMR.

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Evaluation with twenty virtual subjects shows the effect of anatomical variability.

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Bayesian-inspired simultaneous estimation of continuous and discrete parameters.

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Efficient dynamic time warping-based comparison of electrocardiograms (ECG).

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Changing fibre and sheet-normal speed does not affect healthy activation sequence.

ECG Localization Method Based on Volume Conductor Model and Kalman Filtering

The 12-lead electrocardiogram was invented more than 100 years ago and is still used as an essential tool in the early detection of heart disease. By estimating the time-varying source of the electrical activity from the potential changes, several types of heart disease can be noninvasively identified. However, most previous studies are based on signal processing, and thus an approach that includes physics modeling would be helpful for source localization problems. This study proposes a localization method for cardiac sources by combining an electrical analysis with a volume conductor model of the human body as a forward problem and a sparse reconstruction method as an inverse problem. Our formulation estimates not only the current source location but also the current direction. For a 12-lead electrocardiogram system, a sensitivity analysis of the localization to cardiac volume, tilted angle, and model inhomogeneity was evaluated. Finally, the estimated source location is corrected by Kalman filter, considering the estimated electrocardiogram source as time-sequence data. For a high signal-to-noise ratio (greater than 20 dB), the dominant error sources were the model inhomogeneity, which is mainly attributable to the high conductivity of the blood in the heart. The average localization error of the electric dipole sources in the heart was 12.6 mm, which is comparable to that in previous studies, where a less detailed anatomical structure was considered. A time-series source localization with Kalman filtering indicated that source mislocalization could be compensated, suggesting the effectiveness of the source estimation using the current direction and location simultaneously. For the electrocardiogram R-wave, the mean distance error was reduced to less than 7.3 mm using the proposed method. Considering the physical properties of the human body with Kalman filtering enables highly accurate estimation of the cardiac electric signal source location and direction. This proposal is also applicable to electrode configuration, such as ECG sensing systems.

Evaluation of multivariate adaptive non-parametric reduced-order model for solving the inverse electrocardiography problem: a simulation study

In the inverse electrocardiography (ECG) problem, the goal is to reconstruct the heart's electrical activity from multichannel body surface potentials and a mathematical model of the torso. Over the years, researchers have employed various approaches to solve this ill-posed problem including regularization, optimization, and statistical estimation. It is still a topic of interest especially for researchers and clinicians whose goal is to adopt this technique in clinical applications. Among the wide range of mathematical tools available in the fields of operational research, inverse problems, optimization, and parameter estimation, spline-based techniques have been applied to inverse problems in several areas. If proper spline bases are chosen, the complexity of the problem can be significantly reduced while increasing estimation accuracy. However, there are few studies within the context of the inverse ECG problem that take advantage of this property of the spline-based approaches. In this paper, we evaluate the performance of Multivariate Adaptive Regression Splines (MARS)-based method for the solution of the inverse ECG problem using two different collections of simulated data. The results show that the MARS-based method improves the inverse ECG solutions and is "robust" to modeling errors, especially in terms of localizing the arrhythmia sources. Graphical Abstract Multivariate adaptive non-parametric model for inverse ECG problem.

Electrocardiographic Imaging Using a Spatio-Temporal Basis of Body Surface Potentials-Application to Atrial Ectopic Activity

Electrocardiographic imaging (ECGI) strongly relies on a priori assumptions and additional information to overcome ill-posedness. The major challenge of obtaining good reconstructions consists in finding ways to add information that effectively restricts the solution space without violating properties of the sought solution. In this work, we attempt to address this problem by constructing a spatio-temporal basis of body surface potentials (BSP) from simulations of many focal excitations. Measured BSPs are projected onto this basis and reconstructions are expressed as linear combinations of corresponding transmembrane voltage (TMV) basis vectors. The novel method was applied to simulations of 100 atrial ectopic foci with three different conduction velocities. Three signal-to-noise ratios (SNR) and bases of six different temporal lengths were considered. Reconstruction quality was evaluated using the spatial correlation coefficient of TMVs as well as estimated local activation times (LAT). The focus localization error was assessed by computing the geodesic distance between true and reconstructed foci. Compared with an optimally parameterized Tikhonov-Greensite method, the BSP basis reconstruction increased the mean TMV correlation by up to 22, 24, and 32% for an SNR of 40, 20, and 0 dB, respectively. Mean LAT correlation could be improved by up to 5, 7, and 19% for the three SNRs. For 0 dB, the average localization error could be halved from 15.8 to 7.9 mm. For the largest basis length, the localization error was always below 34 mm. In conclusion, the new method improved reconstructions of atrial ectopic activity especially for low SNRs. Localization of ectopic foci turned out to be more robust and more accurate. Preliminary experiments indicate that the basis generalizes to some extent from the training data and may even be applied for reconstruction of non-ectopic activity.

Comparison of Baseline Wander Removal Techniques considering the Preservation of ST Changes in the Ischemic ECG: A Simulation Study

The most important ECG marker for the diagnosis of ischemia or infarction is a change in the ST segment. Baseline wander is a typical artifact that corrupts the recorded ECG and can hinder the correct diagnosis of such diseases. For the purpose of finding the best suited filter for the removal of baseline wander, the ground truth about the ST change prior to the corrupting artifact and the subsequent filtering process is needed. In order to create the desired reference, we used a large simulation study that allowed us to represent the ischemic heart at a multiscale level from the cardiac myocyte to the surface ECG. We also created a realistic model of baseline wander to evaluate five filtering techniques commonly used in literature. In the simulation study, we included a total of 5.5 million signals coming from 765 electrophysiological setups. We found that the best performing method was the wavelet-based baseline cancellation. However, for medical applications, the Butterworth high-pass filter is the better choice because it is computationally cheap and almost as accurate. Even though all methods modify the ST segment up to some extent, they were all proved to be better than leaving baseline wander unfiltered.

ECG imaging of ventricular tachycardia: evaluation against simultaneous non-contact mapping and CMR-derived grey zone

ECG imaging is an emerging technology for the reconstruction of cardiac electric activity from non-invasively measured body surface potential maps. In this case report, we present the first evaluation of transmurally imaged activation times against endocardially reconstructed isochrones for a case of sustained monomorphic ventricular tachycardia (VT). Computer models of the thorax and whole heart were produced from MR images. A recently published approach was applied to facilitate electrode localization in the catheter laboratory, which allows for the acquisition of body surface potential maps while performing non-contact mapping for the reconstruction of local activation times. ECG imaging was then realized using Tikhonov regularization with spatio-temporal smoothing as proposed by Huiskamp and Greensite and further with the spline-based approach by Erem et al. Activation times were computed from transmurally reconstructed transmembrane voltages. The results showed good qualitative agreement between the non-invasively and invasively reconstructed activation times. Also, low amplitudes in the imaged transmembrane voltages were found to correlate with volumes of scar and grey zone in delayed gadolinium enhancement cardiac MR. The study underlines the ability of ECG imaging to produce activation times of ventricular electric activity-and to represent effects of scar tissue in the imaged transmembrane voltages.