Problem Of Electrocardiography Research Articles

A Method for Normal Direction Judge Applied in Electrocardiographic Problem

Boundary Element Method (BEM) is widely used in electrocardiographic (ECG) problem. Formulations of these problems based on mathematical and numerical approximations of the known source in heart and the volume conductor that can transfer voltages on the surface of the body. To analyze the electric potentials on body surface or epicardial surface, a set of discrete equations derived from a boundary integral equations need to be solved. Solving these equations means to get the potential distribution eventually. In the process of solving, transfer matrix of discrete equations has received considerable attention, how to get an appropriate transfer matrix is an important issue. This paper found that the direction of normal vector could affect the results when calculating the transfer matrix and presents a method analogous to Mesh Current Method to deal with this direction problem. Several simulations have been carried out to verify the accurate results with the correct direction of normal vector using new method within a torso model given simultaneous epicardial and body surface potential recordings.

Real‐Time ECG Simulation for Hybrid Mock Circulatory Loops

Classically, mock circulatory loops only simulate mechanical properties of the circulation. To connect the hydraulic world with electrophysiology, we present a real-time electrical activity model of the heart and show how to integrate this model into a real-time mock loop simulation. The model incorporates a predefined conduction pathway and a simplified volume conductor to solve the bidomain equations and the forward problem of electrocardiography, resulting in a physiological simulation of the electrocardiogram (ECG) at arbitrary electrode positions. A complete physiological simulation of the heart's excitation would be too CPU intensive. Thus, in our model, complexity was reduced to allow real-time simulation of ECG-triggered medical systems in vitro; this decreases time and cost in the development process. Conversely, the presented model can still be adapted to various pathologies by locally changing the properties of the heart's conduction pathway. To simulate the ECG, the heart is divided into suitable areas, which are innervated by the hierarchically structured conduction system. To distinguish different cardiac regions, a segmentation of the heart was performed. In these regions, Prim's algorithm was applied to identify the directed minimal spanning trees for conduction orientation. Each node of the tree was assigned to a cardiac action potential generated by its hybrid automaton to represent the heart's conduction system by the spatial distribution of action potentials. To generate the ECG output, the bidomain equations were implemented and a simple model of the volume conductor of the body was used to solve the forward problem of electrocardiography. As a result, the model simulates potentials at arbitrary electrode positions in real-time. To verify the developed real-time ECG model, measurements were made within a hybrid mock circulatory loop, including a simple ECG-triggered ventricular assist device control. The model's potential value is to simulate physiological and pathological behavior for hardware-in-the-loop testing of medical devices in an ECG-triggered scenario.

Determination of the excitation origin in the ventricles from the ECG using support vector regression

Abstract A common treatment of focal ventricular tachycardia is the catheter ablation of triggering sites. They have to be found manually by the physician during an intervention in a catheter lab. Thus, a method for determining the position of the focus automatically is desired. The inverse problem of electrocardiography addresses this problem by reconstructing the source of the ectopic beats using the surface ECG. This problem is ill-posed and therefore needs specific methods for solving it. We propose a machine learning approach for localisation of the ectopic foci in the heart to assist cardiologists with their therapy planning.We simulated 600 120-lead ECGs with different known excitation origins in the heart using a cellular automaton followed by a forward calculation. Features from the ECGs were used as input for a support vector regression (SVR). We assumed a functional relation between features from the ECG and the excitation origin. To benchmark SVR, we also used the well-known Tikhonov 0th order regularisation to reconstruct the transmembrane potentials in the heart and detect the location of the ectopic foci. Parameters for SVR and regularisation were chosen using a grid search minimising the error between estimated and true excitation origin. Compared to the Tikhonov regularisation method, SVR achieved a smaller deviation between estimated and real excitation origin evaluated with 6-fold cross validation. Future work could investigate on the behaviour on data from simulations with other torso and electrophysiological models, the influence of other methods for feature extraction and finally the evaluation with clinical data.

Effects of a priori parameter selection in minimum relative entropy method on inverse electrocardiography problem

The goal in inverse electrocardiography (ECG) is to reconstruct cardiac electrical sources from body surface measurements and a mathematical model of torso–heart geometry that relates the sources to the measurements. This problem is ill-posed due to attenuation and smoothing that occur inside the thorax, and small errors in the measurements yield large reconstruction errors. To overcome this, ill-posedness, traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition and statistical approaches such as Bayesian Maximum A Posteriori estimation and Kalman filter have been applied. Statistical methods have yielded accurate inverse solutions; however, they require knowledge of a good a priori probability density function, or state transition definition. Minimum relative entropy (MRE) is an approach for inferring probability density function from a set of constraints and prior information, and may be an alternative to those statistical methods since it operates with more simple prior information definitions. However, success of the MRE method also depends on good choice of prior parameters in the form of upper and lower bound values, expected uncertainty in the model and the prior mean. In this paper, we explore the effects of each of these parameters on the solution of inverse ECG problem and discuss the limitations of the method. Our results show that the prior expected value is the most influential of the three MRE parameters.

The use of a simple model in the inverse characterization of cardiac ischemic regions

Abstract In this paper, we analyze the use of simple models for solving the inverse problem in electrocardiography (IPE), which aims at recovering the heart condition from a set of remote voltages measurements. Specifically, we consider here the problem of estimating the shape, size and location of cardiac ischemic regions. The forward problem to generate the data (voltage measurements) is formulated by using the Luo–Rudy model, which provides a detailed description of the electrical behavior of cardiac cells. As for the inversion process, we use the two-current phenomenological model. The inversion procedure also incorporates a semi-automatic stage to characterize the conduction properties of the cardiac tissue. The ischemic regions are modeled by using standard level set techniques. Numerical results show that the algorithm is capable of estimating the position, size and shape of cardiac ischemic regions from noisy voltage measurements, for both 2D and 3D geometries. Our inverse procedure is benchmarked against zero-order Tikhonov regularization. This work is a proof of principle demonstrating the possibility of using simple models in the IPE towards realistic situations.

Development of Cardiography: From the Ebers Papyrus to 3D-Mapping

Objective: The article is devoted to the development of cardiography as a means of diagnosing cardiovascular diseases. Cardiovascular diseases confidently lead the world in deadly diseases; therefore, relevance of studies related to the diagnosis of conditions and diseases of the cardiovascular system seems obvious. This article presents a system study of the history of cardiology, considers projects presented by different groups of scientists and physicians, aimed at identifying possible signs of sudden death from cardiovascular diseases. Methods: The author analyzed the history of cardiology as a science, and focused on a number of breakthroughs in cardiology from the times of ancient Egypt to the present day. This gave the possibility to identify modern trends in its development today and to predict its future prospects. Particular attention is paid to 3D - mapping based on multi-channel examination of patients and detailed computer modelling based on micropotentials taken from the patient's body. Results: The study showed that the methods based on solving the inverse problem in electrocardiography, provide non-invasive methods of getting the information, which diagnostic value is similar to the results provided by an invasive electrophysiological study of theheart. Conclusion: The paper proves the need for active introduction of new electrophysiological examination methods into clinical practice.

Lanczos bidiagonalization-based inverse solution methods applied to electrical imaging of the heart by using reduced lead-sets: A simulation study

In inverse problem of electrocardiography (ECG), electrical activity of the heart is estimated from body surface potential measurements. This electrical activity provides useful information about t...

Physiology-based regularization of the electrocardiographic inverse problem

The inverse problem of electrocardiography aims at noninvasively reconstructing electrical activity of the heart from recorded body-surface electrocardiograms. A crucial step is regularization, which deals with ill-posedness of the problem by imposing constraints on the possible solutions. We developed a regularization method that includes electrophysiological input. Body-surface potentials are recorded and a computed tomography scan is performed to obtain the torso–heart geometry. Propagating waveforms originating from several positions at the heart are simulated and used to generate a set of basis vectors representing spatial distributions of potentials on the heart surface. The real heart-surface potentials are then reconstructed from the recorded body-surface potentials by finding a sparse representation in terms of this basis. This method, which we named ‘physiology-based regularization’ (PBR), was compared to traditional Tikhonov regularization and validated using in vivo recordings in dogs. PBR recovered details of heart-surface electrograms that were lost with traditional regularization, attained higher correlation coefficients and led to improved estimation of recovery times. The best results were obtained by including approximate knowledge about the beat origin in the PBR basis.

Regularization Techniques for ECG Imaging during Atrial Fibrillation: A Computational Study.

The inverse problem of electrocardiography is usually analyzed during stationary rhythms. However, the performance of the regularization methods under fibrillatory conditions has not been fully studied. In this work, we assessed different regularization techniques during atrial fibrillation (AF) for estimating four target parameters, namely, epicardial potentials, dominant frequency (DF), phase maps, and singularity point (SP) location. We use a realistic mathematical model of atria and torso anatomy with three different electrical activity patterns (i.e., sinus rhythm, simple AF, and complex AF). Body surface potentials (BSP) were simulated using Boundary Element Method and corrupted with white Gaussian noise of different powers. Noisy BSPs were used to obtain the epicardial potentials on the atrial surface, using 14 different regularization techniques. DF, phase maps, and SP location were computed from estimated epicardial potentials. Inverse solutions were evaluated using a set of performance metrics adapted to each clinical target. For the case of SP location, an assessment methodology based on the spatial mass function of the SP location, and four spatial error metrics was proposed. The role of the regularization parameter for Tikhonov-based methods, and the effect of noise level and imperfections in the knowledge of the transfer matrix were also addressed. Results showed that the Bayes maximum-a-posteriori method clearly outperforms the rest of the techniques but requires a priori information about the epicardial potentials. Among the purely non-invasive techniques, Tikhonov-based methods performed as well as more complex techniques in realistic fibrillatory conditions, with a slight gain between 0.02 and 0.2 in terms of the correlation coefficient. Also, the use of a constant regularization parameter may be advisable since the performance was similar to that obtained with a variable parameter (indeed there was no difference for the zero-order Tikhonov method in complex fibrillatory conditions). Regarding the different targets, DF and SP location estimation were more robust with respect to pattern complexity and noise, and most algorithms provided a reasonable estimation of these parameters, even when the epicardial potentials estimation was inaccurate. Finally, the proposed evaluation procedure and metrics represent a suitable framework for techniques benchmarking and provide useful insights for the clinical practice.

Effect of left atrial hypertrophy on P-wave morphology in a computational model

Abstract P-wave assessment is frequently used in clinical practice to recognize atrial abnormalities. However, the use of P-wave criteria to diagnose specific atrial abnormalities such as left atrial enlargement has shown to be of limited use since these abnormalities can be difficult to distinguish using P-wave criteria to date. Hence, a mechanistic understanding how specific atrial abnormalities affect the P-wave is desirable. In this study, we investigated the effect of left atrial hypertrophy on P-wave morphology using an in silico approach. In a cohort of four realistic patient models, we homogeneously increased left atrial wall thickness in up to seven degrees of left atrial hypertrophy. Excitation conduction was simulated using a monodomain finite element approach. Then, the resulting transmembrane voltage distribution was used to calculate the corresponding extracellular potential distribution on the torso by solving the forward problem of electrocardiography. In our simulation setup, left atrial wall thickening strongly correlated with an increased absolute value of the P-wave terminal force (PTF) in Wilson lead V1 due to an increased negative amplitude while P-wave duration was unaffected. Remarkably, an increased PTF-V1 has often been associated with left atrial enlargement which is defined as a rather increased left atrial volume than a solely thickened left atrium. Hence, the observed contribution of left atrial wall thickness changes to PTF-V1 might explain the poor empirical correlation of left atrial enlargement with PTF-V1.

An ideally parameterized unscented Kalman filter for the inverse problem of electrocardiography

Abstract ECG imaging as noninvasive method is aiming to reconstruct the distribution of the transmembrane voltage amplitudes (TMVs) from the body surface potential map (BSPM). Due to the ill-posedness, standard approaches like the Tikhonov regularization method cause blurring and artefacts in the solution. To suppress blurring and artefacts, this work investigated a model based approach, the unscented Kalman filter (UKF). The intention of this paper is to show the potential of an UKF approach by using an idealized parametrization.

Methods of noninvasive electrophysiological heart examination basing on solution of inverse problem of electrocardiography

The article represents the main noninvasive methods of heart electrical activity examination, theoretical bases of solution of electrocardiography inverse problem, application of different methods of heart examination in clinical practice, and generalized achievements in this sphere in global experience.

Forward Problem of Electrocardiography

The relationship between epicardial and body surface potentials defines the forward problem of electrocardiography. A robust formulation of the forward problem is instrumental to solving the inverse problem, in which epicardial potentials are computed from known body surface potentials. Here, the accuracy of different forward models has been evaluated experimentally. Body surface and epicardial potentials were recorded simultaneously in anesthetized closed-chest pigs (n=5) during sinus rhythm, and epicardial and endocardial ventricular pacing (65 records in total). Body surface potentials were simulated from epicardial recordings using experiment-specific volume conductor models constructed from magnetic resonance imaging. Results for homogeneous (isotropic electric properties) and inhomogeneous (incorporating lungs, anisotropic skeletal muscle, and subcutaneous fat) forward models were compared with measured body surface potentials. Correlation coefficients were 0.85±0.08 across all animals and activation sequences with no significant difference between homogeneous and inhomogeneous solutions (P=0.85). Despite this, there was considerable variance between simulated and measured body surface potential distributions. Differences between the body surface potential extrema predicted with homogeneous forward models were 55% to 78% greater than observed (P<0.05) and attenuation of potentials adjacent to extrema were 10% to 171% greater (P<0.03). The length and orientation of the vector between potential extrema were also significantly different. Inclusion of inhomogeneous electric properties in the forward model reduced, but did not eliminate these differences. These results demonstrate that homogeneous volume conductor models introduce substantial spatial inaccuracies in forward problem solutions. This probably affects the precision of inverse reconstructions of cardiac potentials, in which this assumption is made.

Numerical Solution of the Localized Inverse Problem of Electrocardiography

The localized inverse problem of electrocardiography is formulated and a solution method is proposed. The method allows determining the potential of the cardiac electric field on one of the heart sections.

Introduction to noninvasive cardiac mapping.

From the dawn of the twentieth century, the electrocardiogram (ECG) has revolutionized the way clinical cardiology has been practiced, and it has become the cornerstone of modern medicine today. Driven by clinical and research needs for a more precise understanding of cardiac electrophysiology beyond traditional ECG, inverse solution electrocardiography has been developed, tested, and validated. This article outlines the important progress from ECG development, through more extensive measurement of body surface potentials, and the fundamental leap to solving the inverse problem of electrocardiography, with a focus on mathematical methods and experimental validation.

Calculation of electric potentials generated by a dipole source in a circular conducting cylinder of a finite length

A realization of an analytic method for calculation (in the quasi-static approximation) of electric potentials excited by a dipole source in a circular conducting cylinder of a finite length is considered. Such an approach is oriented to determination of potentials on the surface of the chest with small computational expenses, which allows reconstruction of the source parameters from measured surface potentials in inverse problems of electrocardiography. Correction of expansions of the electric potential into double series of angular and radial variations is proposed on the basis of comparative analysis of different approaches. The obtained relationships are reduced to a form suitable for calculations. The proposed formulas are tested by comparing them with the results obtained with the use of numerical methods. The problem of selection of the number of terms in summation of double series is analyzed.

Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography

This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the definition of a model of the electromechanical contraction which is registered on ECG data but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish in this work the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in a unified consistent and efficient framework. Indeed, we aggregate a Luenberger observer for the mechanical state and a Reduced-Order Unscented Kalman Filter applied on the parameters to be identified and a POD projection of the electrical state. Then using synthetic data we show the benefits of our approach for the estimation of the electrical state of the ventricles along the heart beat compared with more classical strategies which only consider an electrophysiological model with ECG measurements. Our numerical results actually show that the mechanical measurements improve the identifiability of the electrical problem allowing to reconstruct the electrical state of the coupled system more precisely. Therefore, this work is intended to be a first proof of concept, with theoretical justifications and numerical investigations, of the advantage of using available multi-modal observations for the estimation and identification of an electromechanical model of the heart.

Investigations of sensitivity and resolution of ECG and MCG in a realistically shaped thorax model

Solving the inverse problem of electrocardiography (ECG) and magnetocardiography (MCG) is often referred to as cardiac source imaging. Spatial properties of ECG and MCG as imaging systems are, however, not well known. In this modelling study, we investigate the sensitivity and point-spread function (PSF) of ECG, MCG, and combined ECG+MCG as a function of source position and orientation, globally around the ventricles: signal topographies are modelled using a realistically-shaped volume conductor model, and the inverse problem is solved using a distributed source model and linear source estimation with minimal use of prior information. The results show that the sensitivity depends not only on the modality but also on the location and orientation of the source and that the sensitivity distribution is clearly reflected in the PSF. MCG can better characterize tangential anterior sources (with respect to the heart surface), while ECG excels with normally-oriented and posterior sources. Compared to either modality used alone, the sensitivity of combined ECG+MCG is less dependent on source orientation per source location, leading to better source estimates. Thus, for maximal sensitivity and optimal source estimation, the electric and magnetic measurements should be combined.

Impact of the Patient Torso Model on the Solution of the Inverse Problem of Electrocardiography

Cardiac diagnostics based on a solution of the inverse problem of electrocardiography offers new tools for visual assessment of cardiac ischemia. The accuracy of the inverse solution is influenced by fidelity of the patient torso model. As optimum, an individual torso model with real heart shape and position obtained from CT or MRI is desirable. However, imaging is not always available in clinical practice, hence we investigated, if a generic torso shape individually adjusted according to patient‘s chest dimensions, with a simplified heart model placed to a vertical position obtained from inverse localization of the early ventricular activation can result in an inverse solution close to the result obtained with an accurate torso model. Simulated inverse localization of 18 ischemic lesions for 9 subjects showed that the use of individually adjusted generic torso instead of real torso shape led to an acceptable increase of the lesion localization error from 0.7±0.7 cm to 1.1±0.7 cm when accurate heart model was used. However, if simplified heart model was used and placed in a vertical position according to the V2 lead level, the lesion localization error increased to 3.5±0.9 cm. Moving the simplified heart model to a position estimated by the inverse solution decreased the vertical heart positioning error from 1.6±2.3 cm to 0.2±1.2 cm but without adjusting the heart shape and rotation the lesion localization error did not improve and reached 3.7±1.0 cm.

Two-step genetic algorithm to solve the inverse problem in electrocardiography for cardiac sources

This study is concerned with the numerical analysis of the inverse problem in electrocardiography. We propose a new method (two-step algorithm) based on the application of genetic algorithm with the Tikhonov method to calculate the electrical sources on the heart. In the literature, the solution reconstructed by the classical Tikhonov method is based on the minimum energy norm using a closed geometry. This solution could be very different from the original source on the heart. Compared with the classical inverse problem method, the two-step algorithm improves the accuracy of the solution with respect to the original distribution. Finally, to validate our results, we create a distribution over the heart by using a model of electrical activity (Monodomain model), and then using our method, we make the reconstruction of the potential distribution.