The transfer matrix for epicardial potential in a piece-wise homogeneous thorax model: the boundary element formulation

A Framework for the generation of digital twins of cardiac electrophysiology from clinical 12-leads ECGs

Cardiac digital twins (Cardiac Digital Twin (CDT)s) of human electrophysiology (Electrophysiology (EP)) are digital replicas of patient hearts derived from clinical data that match like-for-like all available clinical observations. Due to their inherent predictive potential, CDTs show high promise as a complementary modality aiding in clinical decision making and also in the cost-effective, safe and ethical testing of novel EP device therapies. However, current workflows for both the anatomical and functional twinning phases within CDT generation, referring to the inference of model anatomy and parameters from clinical data, are not sufficiently efficient, robust and accurate for advanced clinical and industrial applications. Our study addresses three primary limitations impeding the routine generation of high-fidelity CDTs by introducing; a comprehensive parameter vector encapsulating all factors relating to the ventricular EP; an abstract reference frame within the model allowing the unattended manipulation of model parameter fields; a novel fast-forward electrocardiogram (Electrocardiogram (ECG)) model for efficient and bio-physically-detailed simulation required for parameter inference. A novel workflow for the generation of CDTs is then introduced as an initial proof of concept. Anatomical twinning was performed within a reasonable time compatible with clinical workflows (<4h) for 12 subjects from clinically-attained magnetic resonance images. After assessment of the underlying fast forward ECG model against a gold standard bidomain ECG model, functional twinning of optimal parameters according to a clinically-attained 12 lead ECG was then performed using a forward Saltelli sampling approach for a single subject. The achieved results in terms of efficiency and fidelity demonstrate that our workflow is well-suited and viable for generating biophysically-detailed CDTs at scale.

Machine learning enables noninvasive prediction of atrial fibrillation driver location and acute pulmonary vein ablation success using the 12-lead ECG

BACKGROUND

Atrial fibrillation (AF) is the most common supraventricular arrhythmia, characterized by disorganized atrial electrical activity, maintained by localized arrhythmogenic atrial drivers. Pulmonary vein isolation (PVI) allows to exclude PV-related drivers. However, PVI is less effective in patients with additional extra-PV arrhythmogenic drivers.

OBJECTIVES

To discriminate whether AF drivers are located near the PVs vs extra-PV regions using the noninvasive 12-lead electrocardiogram (ECG) in a computational and clinical framework, and to computationally predict the acute success of PVI in these cohorts of data.

METHODS

AF drivers were induced in 2 computerized atrial models and combined with 8 torso models, resulting in 1128 12-lead ECGs (80 ECGs with AF drivers located in the PVs and 1048 in extra-PV areas). A total of 103 features were extracted from the signals. Binary decision tree classifier was trained on the simulated data and evaluated using hold-out cross-validation. The PVs were subsequently isolated in the models to assess PVI success. Finally, the classifier was tested on a clinical dataset (46 patients: 23 PV-dependent AF and 23 with additional extra-PV sources).

RESULTS

The classifier yielded 82.6% specificity and 73.9% sensitivity for detecting PV drivers on the clinical data. Consistency analysis on the 46 patients resulted in 93.5% results match. Applying PVI on the simulated AF cases terminated AF in 100% of the cases in the PV class.

CONCLUSION

Machine learning-based classification of 12-lead-ECG allows discrimination between patients with PV drivers vs those with extra-PV drivers of AF. The novel algorithm may aid to identify patients with high acute success rates to PVI.

Non-Invasive Characterization of Atrial Flutter Mechanisms Using Recurrence Quantification Analysis on the ECG: A Computational Study

OBJECTIVE

Atrial flutter (AFl) is a common arrhythmia that can be categorized according to different self-sustained electrophysiological mechanisms. The non-invasive discrimination of such mechanisms would greatly benefit ablative methods for AFl therapy as the driving mechanisms would be described prior to the invasive procedure, helping to guide ablation. In the present work, we sought to implement recurrence quantification analysis (RQA) on 12-lead ECG signals from a computational framework to discriminate different electrophysiological mechanisms sustaining AFl.

METHODS

20 different AFl mechanisms were generated in 8 atrial models and were propagated into 8 torso models via forward solution, resulting in 1,256 sets of 12-lead ECG signals. Principal component analysis was applied on the 12-lead ECGs, and six RQA-based features were extracted from the most significant principal component scores in two different approaches: individual component RQA and spatial reduced RQA.

RESULTS

In both approaches, RQA-based features were significantly sensitive to the dynamic structures underlying different AFl mechanisms. Hit rate as high as 67.7% was achieved when discriminating the 20 AFl mechanisms. RQA-based features estimated for a clinical sample suggested high agreement with the results found in the computational framework.

CONCLUSION

RQA has been shown an effective method to distinguish different AFl electrophysiological mechanisms in a non-invasive computational framework. A clinical 12-lead ECG used as proof of concept showed the value of both the simulations and the methods.

SIGNIFICANCE

The non-invasive discrimination of AFl mechanisms helps to delineate the ablation strategy, reducing time and resources required to conduct invasive cardiac mapping and ablation procedures.

Non-Invasive Identification of Atrial Fibrillation Driver Location Using the 12-lead ECG: Pulmonary Vein Rotors vs. other Locations

Atrial fibrillation (AF) is an irregular heart rhythm due to disorganized atrial electrical activity, often sustained by rotational drivers called rotors. In the present work, we sought to characterize and discriminate whether simulated single stable rotors are located in the pulmonary veins (PVs) or not, only by using non-invasive signals (i.e., the 12-lead ECG). Several features have been extracted from the signals, such as Hjort descriptors, recurrence quantification analysis (RQA), and principal component analysis. All the extracted features have shown significant discriminatory power, with particular emphasis to the RQA parameters. A decision tree classifier achieved 98.48% accuracy, 83.33% sensitivity, and 100% specificity on simulated data.Clinical Relevance-This study might guide ablation procedures, suggesting doctors to proceed directly in some patients with a pulmonary veins isolation, and avoiding the prior use of an invasive atrial mapping system.

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.

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.

Noninvasive identification of two lesions with local repolarization changes using two dipoles in inverse solution simulation study

BACKGROUND

The method for inverse localization and identification of two distinct simultaneous lesions with changed repolarization in the ventricular myocardium (two-vessel disease) is proposed and its robustness to errors in input data is tested in this simulation study.

METHOD

The inverse solution was obtained from the difference between STT integral body surface potential map computed with repolarization changes and the STT integral map from normal activation. In a numerical model of ventricles 48 cases of two simultaneous lesions and 48 cases of a single lesion were modeled. The effect of the lesions was taken to be represented by two dipoles. The input data were disturbed by three types of added noise. Twenty three characteristics of every obtained inverse solution were defined and four of them were used as the features in discriminant analysis task distinguishing the correct inverse solutions identifying two lesions.

RESULTS

The mean localization error for identified two lesions was 1.1±0.7cm. The sensitivity and specificity of quadratic discriminant analysis with cross-validation and feature selection was higher than 90%.

CONCLUSIONS

The combination of the inverse solution with two dipoles and discriminant analysis allows the identification of two simultaneous lesions without a priori information about the number of lesions.

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.

Characteristics of inverse-computed epicardial electrograms of Brugada syndrome patients

Brugada syndrome (BrS) causes sudden death in patients with structurally normal hearts. Manifestation of BrS in the ECG is dynamic and most patients do not show unequivocal signs of the syndrome during ECG screening. Electrograms (EGMs) of BrS patients show conduction delay and fractionation at the right ventricular outflow tract area (RVOT) and thus could be used for diagnosis, but their recording requires an invasive procedure. We have obtained 67-lead body surface potential mapping recordings (BSPM) of 6 BrS patients and 6 controls and computed their EGMs by solving the inverse problem of electrocardiography by using Tikhonov's regularization method. Inverse-computed EGMs presented similar activation times and durations in controls and BrS patients for apex and septum. However, RVOT EGMs showed a later activation in BrS patients than in controls (58 ± 7 vs. 39 ± 5 ms, p<0.01) and EGMs were longer (122 ± 22 vs. 85 ± 8 ms, p<0.01). Inverse-computed EGMs of BrS patients showed abnormalities consistent with those observed in electrophysiological studies and could be used for a non-invasive diagnosis and characterization of Brugada syndrome.