Problem Of Electrocardiography Research Articles

Evaluation of five methods for the interpolation of bad leads in the solution of the inverse electrocardiography problem.

This study aims to assess the sensitivity of epicardial potential-based electrocardiographic imaging (ECGI) to the removal or interpolation of bad leads.
Approach. We utilized experimental data from two distinct centers. Langendorff-perfused pig (n=2) and dog (n=2) hearts were suspended in a human torso-shaped tank and paced from the ventricles. Six different bad lead configurations were designed based on clinical experience. Five interpolation methods were applied to estimate the missing data. Zero-order Tikhonov regularization was used to solve the inverse problem for complete data, data with removed bad leads, and interpolated data. We assessed the quality of interpolated ECG signals and ECGI reconstructions using several metrics, comparing the performance of interpolation methods and the impact of bad lead removal versus interpolation on ECGI.
Main results. The performance of ECG interpolation strongly correlated with ECGI reconstruction. The hybrid method exhibited the best performance among interpolation techniques, followed closely by the inverse-forward and Kriging methods. Bad leads located over high amplitude/high gradient areas on the torso significantly impacted ECGI reconstructions, even with minor interpolation errors. The choice between removing or interpolating bad leads depends on the location of missing leads and confidence in interpolation performance. If uncertainty exists, removing bad leads is the safer option, particularly when they are positioned in high amplitude/high gradient regions. In instances where interpolation is necessary, the inverse-forward and Kriging methods, which do not require training, are recommended.
Significance. This study represents the first comprehensive evaluation of the advantages and drawbacks of interpolating versus removing bad leads in the context of ECGI, providing valuable insights into ECGI performance.

Forward problem of electrocardiography based on cardiac source vector orientations

To localize the unusual cardiac activities non-invasively, one has to build a prior forward model that relates the heart, torso, and detectors. This model has to be constructed to mathematically relate the geometrical and functional activities of the heart. Several methods are available to model the prior sources in the forward problem, which results in the lead field matrix generation. In the conventional technique, the lead field assumed the fixed prior sources, and the source vector orientations were presumed to be parallel to the detector plane with the unit strength in all directions. However, the anomalies cannot always be expected to occur in the same location and orientation, leading to misinterpretation and misdiagnosis. To overcome this, the work proposes a new forward model constructed using the VCG signals of the same subject. Furthermore, three transformation methods were used to extract VCG in constructing the time-varying lead fields to steer to the orientation of the source rather than just reconstructing its activities in the inverse problem. In addition, the unit VCG loop of the acute ischemia patient was extracted to observe the changes compared to the normal subject. The abnormality condition was achieved by delaying the depolarization time by 15ms. The results involving the unit vectors of VCG demonstrated the anisotropic nature of cardiac source orientations, providing information about the heart’s electrical activity.

Basis and applicability of noninvasive inverse electrocardiography: a comparison between cardiac source models.

The body surface electrocardiogram (ECG) is a direct result of electrical activity generated by the myocardium. Using the body surface ECGs to reconstruct cardiac electrical activity is called the inverse problem of electrocardiography. The method to solve the inverse problem depends on the chosen cardiac source model to describe cardiac electrical activity. In this paper, we describe the theoretical basis of two inverse methods based on the most commonly used cardiac source models: the epicardial potential model and the equivalent dipole layer model. We discuss similarities and differences in applicability, strengths and weaknesses and sketch a road towards improved inverse solutions by targeted use, sequential application or a combination of the two methods.

A reduced complexity ECG imaging model for regularized inversion optimization

The resolution of the inverse problem of electrocardiography represents a major interest in the diagnosis and catheter-based therapy of cardiac arrhythmia. In this context, the ability to simulate several cardiac electrical behaviors was crucial for evaluating and comparing the performance of inversion methods. For this application, existing models are either too complex or do not produce realistic cardiac patterns. In this work, a low-resolution heart-torso model generating realistic whole heart cardiac mappings and electrocardiograms in healthy and pathological cases is designed. This model was built upon a simplified heart-torso geometry and implements the monodomain formalism by using the finite element method. In addition, a model reduction step through a sensitivity analysis was proposed where parameters were identified using an evolutionary optimization approach. Finally, the study illustrates the usefulness of the proposed model by comparing the performance of different variants of Tikhonov-based inversion methods for the determination of the regularization parameter in healthy, ischemic and ventricular tachycardia scenarios. First, results of the sensitivity analysis show that among 58 parameters only 25 are influent. Note also that the level of influence of the parameters depends on the heart region. Besides, the synthesized electrocardiograms globally present the same characteristic shape compared to the reference once with a correlation value that reaches 88%. Regarding inverse problem, results highlight that only Robust Generalized Cross Validation and Discrepancy Principle provide best performance, with a quasi-perfect success rate for both, and a respective relative error, between the generated electrocardiograms to the reference one, of 0.75 and 0.62.

Direct Estimation of Equivalent Bioelectric Sources Based on Huygens' Principle.

An estimation of the electric sources in the heart was conducted using a novel method, based on Huygens' Principle, aiming at a direct estimation of equivalent bioelectric sources over the heart's surface in real time. The main scope of this work was to establish a new, fast approach to the solution of the inverse electrocardiography problem. The study was based on recorded electrocardiograms (ECGs). Based on Huygens' Principle, measurements obtained from the surfaceof a patient's thorax were interpolated over the surface of the employed volume conductor model and considered as secondary Huygens' sources. These sources, being non-zero only over the surface under study, were employed to determine the weighting factors of the eigenfunctions' expansion, describing the generated voltage distribution over the whole conductor volume. With the availability of the potential distribution stemming from measurements, the electromagnetics reciprocity theorem is applied once again to yield the equivalent sources over the pericardium. The methodology is self-validated, since the surface potentials calculated from these equivalent sources are in very good agreement with ECG measurements. The ultimate aim of this effort is to create a tool providing the equivalent epicardial voltage or current sources in real time, i.e., during the ECG measurements with multiple electrodes.

A two-step inverse solution for a single dipole cardiac source.

Introduction: The inverse problem of electrocardiography noninvasively localizes the origin of undesired cardiac activity, such as a premature ventricular contraction (PVC), from potential recordings from multiple torso electrodes. However, the optimal number and placement of electrodes for an accurate solution of the inverse problem remain undetermined. This study presents a two-step inverse solution for a single dipole cardiac source, which investigates the significance of the torso electrodes on a patient-specific level. Furthermore, the impact of the significant electrodes on the accuracy of the inverse solution is studied. Methods: Body surface potential recordings from 128 electrodes of 13 patients with PVCs and their corresponding homogeneous and inhomogeneous torso models were used. The inverse problem using a single dipole was solved in two steps: First, using information from all electrodes, and second, using a subset of electrodes sorted in descending order according to their significance estimated by a greedy algorithm. The significance of electrodes was computed for three criteria derived from the singular values of the transfer matrix that correspond to the inversely estimated origin of the PVC computed in the first step. The localization error (LE) was computed as the Euclidean distance between the ground truth and the inversely estimated origin of the PVC. The LE obtained using the 32 and 64 most significant electrodes was compared to the LE obtained when all 128 electrodes were used for the inverse solution. Results: The average LE calculated for both torso models and using all 128 electrodes was 28.8 ± 11.9mm. For the three tested criteria, the average LEs were 32.6 ± 19.9mm, 29.6 ± 14.7mm, and 28.8 ± 14.5mm when 32 electrodes were used. When 64 electrodes were used, the average LEs were 30.1 ± 16.8mm, 29.4 ± 12.0mm, and 29.5 ± 12.6mm. Conclusion: The study found inter-patient variability in the significance of torso electrodes and demonstrated that an accurate localization by the inverse solution with a single dipole could be achieved using a carefully selected reduced number of electrodes.

Influence of the Tikhonov Regularization Parameter on the Accuracy of the Inverse Problem in Electrocardiography.

The electrocardiogram (ECG) is the standard method in clinical practice to non-invasively analyze the electrical activity of the heart, from electrodes placed on the body's surface. The ECG can provide a cardiologist with relevant information to assess the condition of the heart and the possible presence of cardiac pathology. Nonetheless, the global view of the heart's electrical activity given by the ECG cannot provide fully detailed and localized information about abnormal electrical propagation patterns and corresponding substrates on the surface of the heart. Electrocardiographic imaging, also known as the inverse problem in electrocardiography, tries to overcome these limitations by non-invasively reconstructing the heart surface potentials, starting from the corresponding body surface potentials, and the geometry of the torso and the heart. This problem is ill-posed, and regularization techniques are needed to achieve a stable and accurate solution. The standard approach is to use zero-order Tikhonov regularization and the L-curve approach to choose the optimal value for the regularization parameter. However, different methods have been proposed for computing the optimal value of the regularization parameter. Moreover, regardless of the estimation method used, this may still lead to over-regularization or under-regularization. In order to gain a better understanding of the effects of the choice of regularization parameter value, in this study, we first focused on the regularization parameter itself, and investigated its influence on the accuracy of the reconstruction of heart surface potentials, by assessing the reconstruction accuracy with high-precision simultaneous heart and torso recordings from four dogs. For this, we analyzed a sufficiently large range of parameter values. Secondly, we evaluated the performance of five different methods for the estimation of the regularization parameter, also in view of the results of the first analysis. Thirdly, we investigated the effect of using a fixed value of the regularization parameter across all reconstructed beats. Accuracy was measured in terms of the quality of reconstruction of the heart surface potentials and estimation of the activation and recovery times, when compared with ground truth recordings from the experimental dog data. Results show that values of the regularization parameter in the range (0.01-0.03) provide the best accuracy, and that the three best-performing estimation methods (L-Curve, Zero-Crossing, and CRESO) give values in this range. Moreover, a fixed value of the regularization parameter could achieve very similar performance to the beat-specific parameter values calculated by the different estimation methods. These findings are relevant as they suggest that regularization parameter estimation methods may provide the accurate reconstruction of heart surface potentials only for specific ranges of regularization parameter values, and that using a fixed value of the regularization parameter may represent a valid alternative, especially when computational efficiency or consistency across time is required.

Sufficient Conditions for Observability in Electrocardiography Problem

The aim of this paper, is to study electrical cardiography problem. Thus, we construct the state space system of this model as mathematical model. Moreover, we present some definitions and results which is described some concepts of linear control system analysis related to this problem. More precisely, the sufficient conditions which characterize the observability notion of linear dynamical controlled system are presented and discussed. Finally, we prove that, the electrical cardiography model is completely observable system over finite time .

A Patchwork Method to Improve the Performance of Current Methods for Solving the Inverse Problem of Electrocardiography.

Noninvasive electrocardiographic imaging (ECGI) reconstructs cardiac electrical activity from body surface potential measurements. However, current methods have demonstrated inaccuracies in reconstructing sinus rhythm, and in particular breakthrough sites. This study aims to combine existing inverse algorithms, making the most of their advantages while minimizing their limitations. The "patchwork method" (PM) combines two classical numerical methods for ECGI: the method of fundamental solutions (MFS) and the finite-element method (FEM). We assume that the method with the smallest residual in the predicted torso potentials, computed using the boundary element method (BEM), provides the most accurate solution. The PM selects for each heart node and time step the method whose estimated reconstruction error is smallest. The performance of the PM was evaluated using simulated ectopic and normal ventricular beats. Cardiac potentials and activation maps obtained with the PM (CC = 0.63 ± 0.01 and 0.61 ± 0.05 respectively) were more accurate than MFS (CC = 0.61 ± 0.01 and 0.48 ± 0.05 respectively), FEM (CC = 0.58 ± 0.01 and 0.51 ± 0.02 respectively) or BEM (CC = 0.57 ± 0.02 and 0.49 ± 0.02 respectively). The PM also located all epicardial breakthrough sites, whereas the traditional numerical methods usually missed one. Furthermore, the PM showed its robustness and stability in the presence of Gaussian noise added to the torso potentials. The PM overcomes some of the limitations of classical numerical methods, improving the accuracy of mapping important features of activation during sinus rhythm and paced beats. This novel method for optimizing ECGI solutions opens a new avenue for improving not only ECGI but also other inverse problems.

A unique cardiac electrocardiographic 3D model. Toward interpretable AI diagnosis.

Mathematical models of cardiac electrical activity are one of the most important tools for elucidating information about heart diagnostics. In this paper, we present an efficient mathematical formulation for this modeling simple enough to be easily parameterized and rich enough to provide realistic signals. It relies on a five dipole representation of the cardiac electric source, each one associated with the well-known waves of the electrocardiogram signal. Beyond the physical basis of the model, the parameters are physiologically interpretable as they characterize the wave shape, similar to what a physician would look for in signals, thus making them very useful in diagnosis. The model accurately reproduces the electrocardiogram signals of any diseased or healthy heart. This new discovery represents a significant advance in electrocardiography research. It is especially useful for diagnosis, patient follow-up or decision-making on new therapies; is also a promising tool for well-performing, transparent and interpretable AI approaches.

On uniqueness theorems for the inverse problem of electrocardiography in the Sobolev spaces

AbstractWe consider a mathematical model related to reconstruction of cardiac electrical activity from ECG measurements on the body surface. An application of recent developments in solving boundary value problems for elliptic and parabolic equations in Sobolev type spaces allows us to obtain uniqueness theorems for the model. The obtained results can be used as a sound basis for creating numerical methods for non‐invasive mapping of the heart.

Bariatric surgery reverses ventricular repolarisation heterogeneity in obesity: mechanistic insights into fat-related arrhythmic risk

Abstract Background Obesity is a growing global health problem that confers higher risks of atrial arrhythmias and sudden cardiac death. Despite this, the proarrhythmic substrate in obesity and its reversibility with weight loss has not been studied in-depth. Purpose To characterise the proarrhythmic substrate in obese patients, and its reversibility with bariatric surgery, using electrocardiographic imaging (ECGi). Methods ECGi was performed in 16 obese patients pre-bariatric surgery (PreSurg; mean age 43±12 years, 13 female) and 16 age- and sex-matched non-obese (lean) individuals (42±11 years). 12 of the 16 obese patients also underwent ECGi after bariatric surgery (PostSurg). Over 2000 atrial and ventricular epicardial electrograms were computed using high density body surface mapping (256-lead ECG) and heart-torso geometries from cardiac magnetic resonance imaging, by solving the inverse problem of electrocardiography. Local atrial and ventricular epicardial activation times (AT) were calculated as the steepest downslope of their respective activation complexes, and local ventricular repolarisation times (RT) as the steepest upslope of the T-wave. Atrial activation gradients (ATG) and ventricular repolarisation gradients (RTG) were calculated as the maximum difference within 10 mm radius divided by the corresponding distance. Results Body mass index was greater in PreSurg vs lean (46.7±5.5 vs 22.8±2.6 kg/m2, p<0.0001) and decreased with surgery (PostSurg 36.8±6.5 kg/m2, p<0.0001). Epicardial adipose tissue (EAT) was greater in PreSurg vs lean (83±56 vs 28±13 ml, p<0.0001) and decreased post-surgery (PostSurg 69±45 ml, p=0.0010). Total atrial AT was prolonged in PreSurg vs lean (62±15 vs 46±12 ms, p=0.0028), which persisted post-surgery (PostSurg 67±15 ms, p=0.86). Atrial ATG were also greater in PreSurg vs lean (26±11 vs 14±8 ms, p=0.0007) and did not change with weight loss (PostSurg 25±12, p=0.44). Ventricular RTG were greater in PreSurg vs lean (26±11 vs 15±7 ms/mm, p=0.0024) and decreased with weight loss (PostSurg 19±8, p=0.0009). Ventricular RTG were similar between PostSurg and lean (p=0.20). EAT from lean and PreSurg individuals correlated with atrial ATG (r=0.36, p=0.044) and ventricular RTG (r=0.54, p=0.0014). Ventricular AT were similar between lean (31±6 ms), PreSurg (34±5 ms) and PostSurg (35±9 ms); all p>0.05. Conclusion Steep ventricular repolarisation gradients and prolonged atrial activation contribute to the proarrhythmic substrate in obesity. Ventricular repolarisation gradients correlate with epicardial adiposity and both regress post-bariatric surgery. By contrast, atrial activation remains prolonged after weight loss. These results provide mechanistic insights into obesity-related arrhythmic risks and their reversibility with weight loss following bariatric surgery. Funding Acknowledgement Type of funding sources: Other. Main funding source(s): British Heart FoundationNational Institute for Health Research (NIHR) Imperial Biomedical Research Centre (BRC).

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.

PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by means of partial differential equations (PDEs), to carry out the task at hand. The goal is to estimate the epicardial potential field from measurements of the electric potential at a discrete set of points on the body surface. The employment of deep learning techniques in this context is made difficult by the low amount of clinical data at disposal, as measuring cardiac potentials requires invasive procedures. Suitably exploiting the underlying physically based mathematical model allowed circumventing the data availability issue and led to the development of fast-training and low-complexity models. Physical awareness has been pursued by means of two elements: the projection of the epicardial potential onto a space-time reduced subspace, spanned by the numerical solutions of the governing PDEs, and the inclusion of a tensorial reduced basis solver of the forward problem in the network architecture. Numerical tests have been conducted only on synthetic data, obtained via a full order model approximation of the problem at hand, and two variants of the model have been addressed. Both proved to be accurate, up to an average $\ell^1$-norm relative error on epicardial activation maps of 3.5%, and both could be trained in $\approx$$15$ min. Nevertheless, some improvements, mostly concerning data generation, are necessary in order to bridge the gap with clinical applications.

Solving Inverse Electrocardiographic Mapping Using Machine Learning and Deep Learning Frameworks.

Electrocardiographic imaging (ECGi) reconstructs electrograms at the heart’s surface using the potentials recorded at the body’s surface. This is called the inverse problem of electrocardiography. This study aimed to improve on the current solution methods using machine learning and deep learning frameworks. Electrocardiograms were simultaneously recorded from pigs’ ventricles and their body surfaces. The Fully Connected Neural network (FCN), Long Short-term Memory (LSTM), Convolutional Neural Network (CNN) methods were used for constructing the model. A method is developed to align the data across different pigs. We evaluated the method using leave-one-out cross-validation. For the best result, the overall median of the correlation coefficient of the predicted ECG wave was 0.74. This study demonstrated that a neural network can be used to solve the inverse problem of ECGi with relatively small datasets, with an accuracy compatible with current standard methods.

Impulse Data Models for the Inverse Problem of Electrocardiography

To develop, train and test neural networks for predicting heart surface potentials (HSPs) from body surface potentials (BSPs). The method re-frames traditional inverse problems of electrocardiography into regression problems, constraining the solution space by decomposing signals with multidimensional Gaussian impulse basis functions. Impulse HSPs were generated with single Gaussian basis functions at discrete heart surface locations and projected to corresponding BSPs using a volume conductor torso model. Both BSP (inputs) and HSP (outputs) were mapped to regular 2D surface meshes and used to train a neural network. Predictive capabilities of the network were tested with unseen synthetic and experimental data. A dense full connected single hidden layer neural network was trained to map body surface impulses to heart surface Gaussian basis functions for reconstructing HSP. Synthetic pulses moving across the heart surface were predicted from the neural network with root mean squared error of 9.1±1.4%. Predicted signals were robust to noise up to 20 dB and errors due to displacement and rotation of the heart within the torso were bounded and predictable. A shift of the heart 40 mm toward the spine resulted in a 4% increase in signal feature localization error. The set of training impulse function data could be reduced, and prediction error remained bounded. Recorded HSPs from in-vitro pig hearts were reliably decomposed using space-time Gaussian basis functions. Activation times calculated from predicted HSPs for left-ventricular pacing had a mean absolute error of 10.4±11.4 ms. Other pacing scenarios were analyzed with similar success. Impulses from Gaussian basis functions are potentially an effective and robust way to train simple neural network data models for reconstructing HSPs from decomposed BSPs. The HSPs predicted by the neural network can be used to generate activation maps that non-invasively identify features of cardiac electrical dysfunction and can guide subsequent treatment options.

Spatio-temporal analysis the results of solving the inverse problem of electrocardiography

The results of the development and testing an algorithm for the physiological interpretation the results of solving the inverse problem of electrocardiography are presented. The solution to the inverse problem of electrocardiography is the distributions of equivalent current sources on the quasi-epicardium, restored from the electric potentials created by the heart on the surface of the chest. The developed algorithms are based on the space-time analysis of the distributions of equivalent current sources on the quasi-epicardium. The development and testing of the algorithm was carried out using a simulation model of the electrical activity of the heart based on cellular automata. The efficiency of the algorithm has been demonstrated when simulating the electrical activity of the heart in normal conditions, as well as in the presence of pathological changes in the myocardium in the form of areas with delayed conduction of excitation.

Space-time shape uncertainties in the forward and inverse problem of electrocardiography.

In electrocardiography, the “classic” inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being affected by noise and obtained with limited resolution due to clinical constraints, a possibly large uncertainty may be perpetuated in the inverse reconstruction. The purpose of this work is to study the effect of shape uncertainty on the forward and the inverse problem of electrocardiography. To this aim, the problem is first recast into a boundary integral formulation and then discretised with a collocation method to achieve high convergence rates and a fast time to solution. The shape uncertainty of the domain is represented by a random deformation field defined on a reference configuration. We propose a periodic‐in‐time covariance kernel for the random field and approximate the Karhunen–Loève expansion using low‐rank techniques for fast sampling. The space–time uncertainty in the expected potential and its variance is evaluated with an anisotropic sparse quadrature approach and validated by a quasi‐Monte Carlo method. We present several numerical experiments on a simplified but physiologically grounded two‐dimensional geometry to illustrate the validity of the approach. The tested parametric dimension ranged from 100 up to 600. For the forward problem, the sparse quadrature is very effective. In the inverse problem, the sparse quadrature and the quasi‐Monte Carlo method perform as expected, except for the total variation regularisation, where convergence is limited by lack of regularity. We finally investigate an H1/2 regularisation, which naturally stems from the boundary integral formulation, and compare it to more classical approaches.

Spatiotemporal regularization for inverse ECG modeling

Advanced sensing such as the wearable sensor network provides an unprecedented opportunity to capture a wealth of information pertinent to space-time electrical activity of the heart, and facilitate the inverse electrocardiographic (ECG) modeling with the readily available data of body surface potential mapping. However, it is often challenging to derive heart-surface potentials from body-surface measurements, which is called the “inverse ECG problem.” Traditional regression is not concerned about spatiotemporal dynamic variables in complex geometries, and tends to be limited in the ability to handle high-dimensional spatiotemporal data for solving the inverse ECG problem. This paper presents a comparison study of regularization methods in the performance to achieve robust solutions of the inverse ECG problem. We first introduce the forward and inverse ECG problems. Second, we propose two spatiotemporal regularization (STRE) models to increase the robustness of inverse ECG modeling. Finally, case studies are conducted on the two-sphere geometry, as well as a real-world torso-heart geometry to evaluate the performance of different regularization methods. Experimental results show that STRE models effectively tackle the ill-conditioned inverse ECG problem and yield 56.3% and 67.3% performance improvement compared to the traditional Tikhonov regularization in the two-sphere and the torso-heart geometries, respectively. The spatiotemporal regularization methodology is shown to have strong potential to achieve robust solutions for high-dimensional predictive modeling in the inverse ECG problem.

IRN-MLSQR: An improved iterative reweight norm approach to the inverse problem of electrocardiography incorporating factorization-free preconditioned LSQR

The inverse problem of electrocardiography (ECG) of computing epicardial potentials from body surface potentials, is an ill-posed problem and needs to be solved by regularization techniques. The L2-norm regularization can cause considerable smoothing of the solution, while the L1-norm scheme promotes a solution with sharp boundaries/gradients between piecewise smooth regions, so L1-norm is widely used in the ECG inverse problem. However, large amount of computation and long computation time are needed in the L1-norm scheme. In this paper, by combining iterative reweight norm (IRN) with a factorization-free preconditioned LSQR algorithm (MLSQR), a new IRN-MLSQR method was proposed to accelerate the convergence speed of the L1-norm scheme. We validated the IRN-MLSQR method using experimental data from isolated canine hearts and clinical procedures in the electrophysiology laboratory. The results showed that the IRN-MLSQR method can significantly reduce the number of iterations and operation time while ensuring the calculation accuracy. The number of iterations of the IRN-MLSQR method is about 60%–70% that of the conventional IRN method, and at the same time, the accuracy of the solution is almost the same as that of the conventional IRN method. The proposed IRN-MLSQR method may be used as a new approach to the inverse problem of ECG.