AI-Powered Noninvasive Electrocardiographic Imaging Using the Priori-to-Attention Network (P2AN) for Wearable Health Monitoring

The rapid development of smart wearable devices has significantly advanced noninvasive, continuous health monitoring, enabling real-time collection of vital biosignals. Electrocardiographic imaging (ECGI), a noninvasive technique that reconstructs transmembrane potential (TMP) from body surface potential, has emerged as a promising method for reflecting cardiac electrical activity. However, the ECG inverse problem's inherent instability has hindered its practical application. To address this, we introduce a novel Priori-to-Attention Network (P2AN) that enhances the stability of ECGI solutions. By leveraging the one-dimensional nature of electrical signals and the body's electrical propagation properties, P2AN uses small-scale convolutions for attention computation, integrating a priori physiological knowledge via cross-attention mechanisms. This approach eliminates the need for clinical TMP measurements and improves solution accuracy through normalization constraints. We evaluate the method's effectiveness in diagnosing myocardial ischemia and ventricular hypertrophy, demonstrating significant improvements in TMP reconstruction and lesion localization. Moreover, P2AN exhibits high robustness in noisy environments, making it highly suitable for integration with wearable electrocardiographic clothing. By improving spatiotemporal accuracy and noise resilience, P2AN offers a promising solution for noninvasive, real-time cardiovascular monitoring using AI-powered wearable devices.

A fast algorithm for spatiotemporal signals recovery using arbitrary dictionaries with application to electrocardiographic imaging

This paper presents a method to solve a linear regression problem subject to group lasso and ridge penalisation when the model has a Kronecker structure. This model was developed to solve the inverse problem of electrocardiography using sparse signal representation over a redundant dictionary or frame. The optimisation algorithm was performed using the block coordinate descent and proximal gradient descent methods. The explicit computation of the underlying Kronecker structure in the regression was avoided, reducing space and temporal complexity. We developed an algorithm that supports the use of arbitrary dictionaries to obtain solutions and allows a flexible group distribution.

ECG Imaging to Detect the Site of Ventricular Ischemia Using Torso Electrodes: A Computational Study

Electrocardiography provides some information useful for ischemic diagnosis. However, more recently there has been substantial growth in the area of ECG imaging, which by solving the inverse problem of electrocardiography aims to produce high-resolution mapping of the electrical and magnetic dynamics of the heart. Most inverse studies use the full resolution of the body surface potential (BSP) to reconstruct the epicardial potentials, however using a limited number of torso electrodes to interpolate the BSP is more clinically relevant and has an important effect on the reconstruction which must be quantified. A circular ischemic lesion on the right ventricle lateral wall 27 mm in radius is reconstructed using three Tikhonov methods along with 6 different electrode configurations ranging from 32 leads to 1,024 leads. The 2nd order Tikhonov solution performed the most accurately (~80% lesion identified) followed by the 1st (~50% lesion identified) and then the 0 order Tikhonov solution performed the worst with a maximum of ~30% lesion identified regardless of how many leads were used. With an increasing number of leads the solution produces less error, and the error becomes more localised around the lesion for all three regularisation methods. In noisy conditions, the relative performance gap of the 1st and 2nd order Tikhonov solutions was reduced, and determining an accurate regularisation parameter became relatively more difficult. Lesions located on the left ventricle walls were also able to be identified but comparatively to the right ventricle lateral wall performed marginally worse with lesions located on the interventricular septum being able to be indicated by the reconstructions but not successfully identified against the error. The quality of reconstruction was found to decrease as the lesion radius decreased, with a lesion radius of <20 mm becoming difficult to correctly identify against the error even when using >512 torso electrodes.

Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data

The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization.

The roles of mid-myocardial and epicardial cells in T-wave alternans development: a simulation study

Background

The occurrence of T-wave alternans in electrocardiographic signals was recently linked to susceptibility to ventricular arrhythmias and sudden cardiac death. Thus, by detecting and comprehending the origins of T-wave alternans, it might be possible to prevent such events.

Results

Here, we simulated T-wave alternans in a computer-generated human heart model by modulating the action potential duration and amplitude during the first part of the repolarization phase. We hypothesized that changes in the intracardiac alternans patterns of action potential properties would differentially influence T-wave alternans measurements at the body surface. Specifically, changes were simulated globally in the whole left and right ventricles to simulate concordant T-wave alternans, and locally in selected regions to simulate discordant and regional discordant, hereinafter referred to as “regional”, T-wave alternans. Body surface potential maps and 12-lead electrocardiographic signals were then computed. In depth discrimination, the influence of epicardial layers on T-wave alternans development was significantly higher than that of mid-myocardial cells. Meanwhile, spatial discrimination revealed that discordant and regional action potential property changes had a higher influence on T-wave alternans amplitude than concordant changes. Notably, varying T-wave alternans sources yielded distinct body surface potential map patterns for T-wave alternans amplitude, which can be used for location of regions within hearts exhibiting impaired repolarization. The highest ability for T-wave alternans detection was achieved in lead V1. Ultimately, we proposed new parameters Vector Magnitude Alternans and Vector Angle Alternans, with higher ability for T-wave alternans detection when using multi-lead electrocardiographic signals processing than for single leads. Finally, QT alternans was found to be associated with the process of T-wave alternans generation.

Conclusions

The distributions of the body surface T-wave alternans amplitude have been shown to have unique patterns depending on the type of alternans (concordant, discordant or regional) and the location of the disturbance in the heart. The influence of epicardial cells on T-wave alternans development is significantly higher than that of mid-myocardial cells, among which the sub-endocardial layer exerted the highest influence. QT interval alternans is identified as a phenomenon that correlate with T-wave alternans.

Scalable and Accurate ECG Simulation for Reaction-Diffusion Models of the Human Heart

Realistic electrocardiogram (ECG) simulation with numerical models is important for research linking cellular and molecular physiology to clinically observable signals, and crucial for patient tailoring of numerical heart models. However, ECG simulation with a realistic torso model is computationally much harder than simulation of cardiac activity itself, so that many studies with sophisticated heart models have resorted to crude approximations of the ECG. This paper shows how the classical concept of electrocardiographic lead fields can be used for an ECG simulation method that matches the realism of modern heart models. The accuracy and resource requirements were compared to those of a full-torso solution for the potential and scaling was tested up to 14,336 cores with a heart model consisting of 11 million nodes. Reference ECGs were computed on a 3.3 billion-node heart-torso mesh at 0.2 mm resolution. The results show that the lead-field method is more efficient than a full-torso solution when the number of simulated samples is larger than the number of computed ECG leads. While the initial computation of the lead fields remains a hard and poorly scalable problem, the ECG computation itself scales almost perfectly and, even for several hundreds of ECG leads, takes much less time than the underlying simulation of cardiac activity.

Geometrical constraint of sources in noninvasive localization of premature ventricular contractions

The inverse problem of electrocardiography for localization of a premature ventricular contraction (PVC) origin was solved and compared for three types of the equivalent cardiac electrical generator: transmembrane voltages, epicardial potentials, and dipoles. Instead of regularization methods usually used for the ill-posed inverse problems an assumption of a single point source representative of the heart generator was applied to the solution as a geometrical constraint. Body surface potential maps were simulated from eight modeled origins of the PVC in the heart model. Then the maps were corrupted by additional Gaussian noise with the signal-to-noise ratio (SNR) from 20 to 10dB and used as the input of the inverse solution. The inverse solution was computed from the first 30ms of the ventricular depolarization. It was assumed that during this period only a small part of the heart volume is activated thus it can be represented by a single point electrical source. Generally, the localization error was more dependent on the PVC origin position than on the type of the used heart generator. The most stable localization error between the inversely found results and the true PVC origin was not larger than 20mm for PVC origins located in the left ventricular wall and on the right ventricular anterior side. For such cases, the localization was robust to the noise up to SNR of 10dB for all studied types of the cardiac generator. For SNR 10dB the results became unstable mainly for the PVC origins in the septum and posterior right ventricle for the dipolar heart generator and for epicardial potentials defined on the pericardium when the range of the localization error increased up to 50mm. When the results for different electrical heart generators were considered altogether, the mean radius of the cloud of results did not exceed 20mm and the localization error of the cloud center was smaller than that obtained for a particular type of the cardiac generator. Combination of results from different models of a single point cardiac electrical generator can provide better information for the preliminary noninvasive localization of PVC than the use of one type of the generator.

Integral equations and boundary-element solution for static potential in a general piece-wise homogeneous volume conductor

Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from the standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.

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.

Noninvasive reconstruction of cardiac electrical activity: update on current methods, applications and challenges

Electrical activity at the level of the heart muscle can be noninvasively reconstructed from body-surface electrocardiograms (ECGs) and patient-specific torso-heart geometry. This modality, coined electrocardiographic imaging, could fill the gap between the noninvasive (low-resolution) 12-lead ECG and invasive (high-resolution) electrophysiology studies. Much progress has been made to establish electrocardiographic imaging, and clinical studies appear with increasing frequency. However, many assumptions and model choices are involved in its execution, and only limited validation has been performed. In this article, we will discuss the technical details, clinical applications and current limitations of commonly used methods in electrocardiographic imaging. It is important for clinicians to realise the influence of certain assumptions and model choices for correct and careful interpretation of the results. This, in combination with more extensive validation, will allow for exploitation of the full potential of noninvasive electrocardiographic imaging as a powerful clinical tool to expedite diagnosis, guide therapy and improve risk stratification.

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.

Computing volume potentials for noninvasive imaging of cardiac excitation

BACKGROUND

In noninvasive imaging of cardiac excitation, the use of body surface potentials (BSP) rather than body volume potentials (BVP) has been favored due to enhanced computational efficiency and reduced modeling effort. Nowadays, increased computational power and the availability of open source software enable the calculation of BVP for clinical purposes. In order to illustrate the possible advantages of this approach, the explanatory power of BVP is investigated using a rectangular tank filled with an electrolytic conductor and a patient specific three dimensional model.

METHODS

MRI images of the tank and of a patient were obtained in three orthogonal directions using a turbo spin echo MRI sequence. MRI images were segmented in three dimensional using custom written software. Gmsh software was used for mesh generation. BVP were computed using a transfer matrix and FEniCS software.

RESULTS

The solution for 240,000 nodes, corresponding to a resolution of 5 mm throughout the thorax volume, was computed in 3 minutes. The tank experiment revealed that an increased electrode surface renders the position of the 4 V equipotential plane insensitive to mesh cell size and reduces simulated deviations. In the patient-specific model, the impact of assigning a different conductivity to lung tissue on the distribution of volume potentials could be visualized.

CONCLUSION

Generation of high quality volume meshes and computation of BVP with a resolution of 5 mm is feasible using generally available software and hardware. Estimation of BVP may lead to an improved understanding of the genesis of BSP and sources of local inaccuracies.

Comparison of minimum-norm estimation and beamforming in electrocardiography with acute ischemia

In the electrocardiographic (ECG) inverse problem, the electrical activity of the heart is estimated from measured electrocardiogram. A model of thorax conductivities and a model of the cardiac generator is required for the ECG inverse problem. Limitations and errors in methods, models, and data will lead to errors in the estimates. However, in experimental applications, the use of limited or erroneous models is often inevitable due to necessary model simplifications and the difficulty of obtaining accurate 3D anatomical imaging data. In this work, we focus on two methods for solving the inverse problem of ECG in the case of acute ischemia: minimum-norm (MN) estimation and linearly constrained minimum-variance beamforming. We study how these methods perform with different sizes of ischemia and with erroneous conductivity models. The results indicate that the beamformer can localize small ischemia given an accurate model, but it cannot be used for estimating the size of ischemia. The MN estimator is tolerant to geometry errors and excels in estimating the size of ischemia, although the beamformer performs better with accurate model and small ischemia.

Bioelectromagnetic forward problem: isolated source approach revis(it)ed

Electro- and magnetoencephalography (EEG and MEG) are non-invasive modalities for studying the electrical activity of the brain by measuring voltages on the scalp and magnetic fields outside the head. In the forward problem of EEG and MEG, the relationship between the neural sources and resulting signals is characterized using electromagnetic field theory. This forward problem is commonly solved with the boundary-element method (BEM). The EEG forward problem is numerically challenging due to the low relative conductivity of the skull. In this work, we revise the isolated source approach (ISA) that enables the accurate, computationally efficient BEM solution of this problem. The ISA is formulated for generic basis and weight functions that enable the use of Galerkin weighting. The implementation of the ISA-formulated linear Galerkin BEM (LGISA) is first verified in spherical geometry. Then, the LGISA is compared with conventional Galerkin and symmetric BEM approaches in a realistic 3-shell EEG/MEG model. The results show that the LGISA is a state-of-the-art method for EEG/MEG forward modeling: the ISA formulation increases the accuracy and decreases the computational load. Contrary to some earlier studies, the results show that the ISA increases the accuracy also in the computation of magnetic fields.

Application of L1-norm regularization to epicardial potential reconstruction based on gradient projection

The epicardial potential (EP)-targeted inverse problem of electrocardiography (ECG) has been widely investigated as it is demonstrated that EPs reflect underlying myocardial activity. It is a well-known ill-posed problem as small noises in input data may yield a highly unstable solution. Traditionally, L2-norm regularization methods have been proposed to solve this ill-posed problem. But the L2-norm penalty function inherently leads to considerable smoothing of the solution, which reduces the accuracy of distinguishing abnormalities and locating diseased regions. Directly using the L1-norm penalty function, however, may greatly increase computational complexity due to its non-differentiability. We propose an L1-norm regularization method in order to reduce the computational complexity and make rapid convergence possible. Variable splitting is employed to make the L1-norm penalty function differentiable based on the observation that both positive and negative potentials exist on the epicardial surface. Then, the inverse problem of ECG is further formulated as a bound-constrained quadratic problem, which can be efficiently solved by gradient projection in an iterative manner. Extensive experiments conducted on both synthetic data and real data demonstrate that the proposed method can handle both measurement noise and geometry noise and obtain more accurate results than previous L2- and L1-norm regularization methods, especially when the noises are large.

Cardiac anisotropy in boundary-element models for the electrocardiogram

The boundary-element method (BEM) is widely used for electrocardiogram (ECG) simulation. Its major disadvantage is its perceived inability to deal with the anisotropic electric conductivity of the myocardial interstitium, which led researchers to represent only intracellular anisotropy or neglect anisotropy altogether. We computed ECGs with a BEM model based on dipole sources that accounted for a “compound” anisotropy ratio. The ECGs were compared with those computed by a finite-difference model, in which intracellular and interstitial anisotropy could be represented without compromise. For a given set of conductivities, we always found a compound anisotropy value that led to acceptable differences between BEM and finite-difference results. In contrast, a fully isotropic model produced unacceptably large differences. A model that accounted only for intracellular anisotropy showed intermediate performance. We conclude that using a compound anisotropy ratio allows BEM-based ECG models to more accurately represent both anisotropies.

Electrocardiographic inverse problem: spatial characterization of the left ventricle potential

In this work, we present a method for spatial characterization of the electrical activity of the left ventricle (LV). The presented method, electrocardiographic LV imaging, aims at characterization of main morphological features of the LV electrical activity via simple inverse reconstruction of the electrocardiogram on a standard LV segment model. The method is demonstrated with a case study dealing with the spatial characterization of an old myocardial infarction (MI). The results are encouraging: the centroid of the MI region is localized correctly, and the shape of the reconstructed infarcted region is similar to that in the golden standard solution, even though a patient-specific thorax model was not used.