Solving the Inverse Problem of Electrocardiography on the Endocardium Using a Single Layer Source

Toward Enabling Cardiac Digital Twins of Myocardial Infarction Using Deep Computational Models for Inverse Inference

Cardiac digital twins (CDTs) have the potential to offer individualized evaluation of cardiac function in a non-invasive manner, making them a promising approach for personalized diagnosis and treatment planning of myocardial infarction (MI). The inference of accurate myocardial tissue properties is crucial in creating a reliable CDT of MI. In this work, we investigate the feasibility of inferring myocardial tissue properties from the electrocardiogram (ECG) within a CDT platform. The platform integrates multi-modal data, such as cardiac MRI and ECG, to enhance the accuracy and reliability of the inferred tissue properties. We perform a sensitivity analysis based on computer simulations, systematically exploring the effects of infarct location, size, degree of transmurality, and electrical activity alteration on the simulated QRS complex of ECG, to establish the limits of the approach. We subsequently present a novel deep computational model, comprising a dual-branch variational autoencoder and an inference model, to infer infarct location and distribution from the simulated QRS. The proposed model achieves mean Dice scores of 0.457 ±0.317 and 0.302 ±0.273 for the inference of left ventricle scars and border zone, respectively. The sensitivity analysis enhances our understanding of the complex relationship between infarct characteristics and electrophysiological features. The in silico experimental results show that the model can effectively capture the relationship for the inverse inference, with promising potential for clinical application in the future. The code is available at https://github.com/lileitech/MI_inverse_inference.

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.

Electrocardiographic imaging to guide ablation of ventricular arrhythmias and agreement between two different systems

BACKGROUND AND AIM

A recent study using an epicardial-only electrocardiographic imaging (ECGI), suggests that the agreement of ECGI activation mapping and that of the contact mapping for ventricular arrhythmias (VA) is poor. The aim of this study was to assess the diagnostic value of two endo-epicardial ECGI systems using different cardiac sources and the agreement between them.

METHODS

We performed 69 ECGI procedures in 52 patients referred for ablation of VA at our center. One system based on the extracellular potentials was used in 26 patients, the other based on the equivalent double layer model in 9, and both in 17 patients. The first uses up to 224 leads and the second just the 12‑lead ECG. The localization of the VA was done using a segmental model of the ventricles. A perfect match (PM) was defined as a predicted location within the same anatomic segment, whereas a near match (NM) as a predicted location within the same segment or a contiguous one.

RESULTS

44 patients underwent ablation, corresponding to 58 ECGI procedures (37 with the first and 21 with the second system). The percentage of PMs and NMs was not significantly different between the two systems, respectively 76% and 95%, p = 0.077, and 97% and 100%, p = 1.000. In 14 patients that underwent ablation and had the ECGI performed with both systems, raw agreement for PMs was 79%, p = 0.250 for disagreement.

CONCLUSIONS

ECGI systems were useful to identify the origin of the VAs, and the results were reproducible regardless the cardiac source.

Emerging ECG methods for acute coronary syndrome detection: Recommendations & future opportunities

Despite being the mainstay for the initial noninvasive assessment of patients with symptomatic coronary artery disease, the 12‑lead ECG remains a suboptimal diagnostic tool for myocardial ischemia detection with only acceptable sensitivity and specificity scores. Although myocardial ischemia affects the configuration of the QRS complex and the STT waveform, current guidelines primarily focus on ST segment amplitude, which constitutes a missed opportunity and may explain the suboptimal diagnostic performance of the ECG. This possible opportunity and the low cost and ease of use of the ECG provide compelling motivation to enhance the diagnostic accuracy of the ECG to ischemia detection. This paper describes numerous computational ECG methods and approaches that have been shown to dramatically increase ECG sensitivity to ischemia detection. Briefly, these emerging approaches can be conceptually grouped into one of the following four approaches: (1) leveraging novel ECG waveform features and signatures indicative of ischemic injury other than the classical ST-T amplitude measures; (2) applying body surface potentials mapping (BSPM)-based approaches to enhance the spatial coverage of the surface ECG to detecting ischemia; (3) developing an inverse ECG solution to reconstruct anatomical models of activation and recovery pathways to detect and localize injury currents; and (4) exploring artificial intelligence (AI)-based techniques to harvest ECG waveform signatures of ischemia. We present recent advances, shortcomings, and future opportunities for each of these emerging ECG methods. Future research should focus on the prospective clinical testing of these approaches to establish clinical utility and to expedite potential translation into clinical practice.

Stable Numerical Identification of Sources in Non-Homogeneous Media

In this work, we present a numerical algorithm to solve the inverse problem of volumetric sources from measurements on the boundary of a non-homogeneous conductive medium, which is made of conductive layers with constant conductivity in each layer. This inverse problem is ill-posed since there is more than one source that can generate the same measurement. Furthermore, the ill-posedness is due to the fact that small variations (or errors) in the measurement (input data) can produce substantial variations in the identified source location. We propose two steps to solve this inverse problem in some classes of sources: we first recover the harmonic part of the volumetric source, and, in a second step, we compute the non-harmonic part of the source. For the reconstruction of the harmonic part of the source, we follow a variational approach based on the reformulation of the inverse problem as a distributed control problem, for which the cost function incorporates a penalized term with the input data on the boundary. This cost function is minimized by a conjugate gradient algorithm in combination with a finite element discretization. We recover the non-harmonic component of the source using a priori information and an iterative algorithm for some particular classes of sources. To validate the numerical methodology, we develop synthetic examples both in circular (simple) and irregular (complex) regions. The numerical results show that the proposed methodology allows to recover the complete source and produce stable and accurate numerical solutions.

Electrocardiographic imaging (ECGI): What is the minimal number of leads needed to obtain a good spatial resolution?

AIMS

Assess the minimal number of ECGI leads needed to obtain a good spatial resolution.

METHODS

We enrolled 20 patients that underwent ablation of premature ventricular or atrial contractions using Carto and ECGI with AMYCARD. We evaluated the agreement regarding the site of origin of the arrhythmia between the ECGI and Carto, the area and diameter of the earliest activation site obtained with the ECGI (EASa and EASd). Based on previous studies with pacemapping, we considered a good spatial resolution of the ECGI when the EASd measured on the isopotential map was less than 18 mm. In presence of agreement the ECGI was reprocessed: a) with half the number of electrode bands (8 leads per electrode band) and b) with 6 electrode bands.

RESULTS

The initial map was obtained with 23 (22-23) electrode bands per patient, corresponding to 143 (130-170) leads. Agreement rate was 85%, the median EASa and EASd were: 0.7 (0.5-1.3) cm² and 9 (8-13) mm. With half the number of electrode bands including 73 (60-79) leads, agreement rate was 80%, the EASa and EASd were: 2.1 (1.5-6.2) cm² and 16 (14 -28) mm. With only six electrode bands using 38 (30-42) leads, agreement rate was 55%, EASa and EASd were: 4.0 (3.3-5.0) cm² and 23 (21-25) mm. The number of leads was a predictor of agreement with a good spatial resolution, OR (95% CI) of 1.138 (1.050-1.234), p = .002. According to the ROC curve, the minimal number of leads was 74 (AUC 0.981; 95% CI: 0.949-1.00, p < .0001).

CONCLUSION

Reducing the number of leads was associated with a lower agreement rate and a significant reduction of spatial resolution. However, the number of leads needed to achieve a good spatial resolution was less than the maximal available.

An FPGA-based analysis of trade-offs in the presence of ill-conditioning and different precision levels in computations

Several areas, such as physical and health sciences, require the use of matrices as fundamental tools for solving various problems. Matrices are used in real-life contexts, such as control, automation, and optimization, wherein results are expected to improve with increase of computational precision. However, special attention should be paid to ill-conditioned matrices, which can produce unstable systems; an inadequate handling of precision might worsen results since the solution found for data with errors might be too far from the one for data without errors besides increasing other costs in hardware resources and critical paths. In this paper, we make a wake-up call, using 2 × 2 matrices to show how ill-conditioning and precision can affect system design (resources, cost, etc.). We first demonstrate some examples of real-life problems where ill-conditioning is present in matrices obtained from the discretization of the operational equations (ill-posed in the sense of Hadamard) that model these problems. If these matrices are not handled appropriately (i.e., if ill-conditioning is not considered), large errors can result in the computed solutions to the systems of equations in the presence of errors. Furthermore, we illustrate the generated effect in the calculation of the inverse of an ill-conditioned matrix when its elements are approximated by truncation. We present two case studies to illustrate the effects on calculation errors caused by increasing or reducing precision to s digits. To illustrate the costs, we implemented the adjoint matrix inversion algorithm on different field-programmable gate arrays (FPGAs), namely, Spartan-7, Artix-7, Kintex-7, and Virtex-7, using the full-unrolling hardware technique. The implemented architecture is useful for analyzing trade-offs when precision is increased; this also helps analyze performance, efficiency, and energy consumption. By means of a detailed description of the trade-offs among these metrics, concerning precision and ill-conditioning, we conclude that the need for resources seems to grow not linearly when precision is increased. We also conclude that, if error is to be reduced below a certain threshold, it is necessary to determine an optimal precision point. Otherwise, the system becomes more sensitive to measurement errors and a better alternative would be to choose precision carefully, and/or to apply regularization or preconditioning methods, which would also reduce the resources required.

Noninvasive localization of cardiac arrhythmias using electromechanical wave imaging

Cardiac arrhythmias are a major cause of morbidity and mortality worldwide. The 12-lead electrocardiogram (ECG) is the current noninvasive clinical tool used to diagnose and localize cardiac arrhythmias. However, it has limited accuracy and is subject to operator bias. Here, we present electromechanical wave imaging (EWI), a high-frame rate ultrasound technique that can noninvasively map with high accuracy the electromechanical activation of atrial and ventricular arrhythmias in adult patients. This study evaluates the accuracy of EWI for localization of various arrhythmias in all four chambers of the heart before catheter ablation. Fifty-five patients with an accessory pathway (AP) with Wolff-Parkinson-White (WPW) syndrome, premature ventricular complexes (PVCs), atrial tachycardia (AT), or atrial flutter (AFL) underwent transthoracic EWI and 12-lead ECG. Three-dimensional (3D) rendered EWI isochrones and 12-lead ECG predictions by six electrophysiologists were applied to a standardized segmented cardiac model and subsequently compared to the region of successful ablation on 3D electroanatomical maps generated by invasive catheter mapping. There was significant interobserver variability among 12-lead ECG reads by expert electrophysiologists. EWI correctly predicted 96% of arrhythmia locations as compared with 71% for 12-lead ECG analyses [unadjusted for arrhythmia type: odds ratio (OR), 11.8; 95% confidence interval (CI), 2.2 to 63.2; P = 0.004; adjusted for arrhythmia type: OR, 12.1; 95% CI, 2.3 to 63.2; P = 0.003]. This double-blinded clinical study demonstrates that EWI can localize atrial and ventricular arrhythmias including WPW, PVC, AT, and AFL. EWI when used with ECG may allow for improved treatment for patients with arrhythmias.