Volumetric Non-Invasive Cardiac Mapping for Accessible Global Arrhythmia Characterization

Technical Summary: Volumetric Non-Invasive Cardiac Mapping for Accessible Global Arrhythmia Characterization

Problem Statement
Cardiac arrhythmias pose significant health risks, yet current diagnostic and treatment strategies often rely on invasive procedures or limited non-invasive tools. Electrocardiographic Imaging (ECGI) has emerged as a non-invasive alternative, reconstructing cardiac electrical activity from body surface potentials. However, conventional ECGI is restricted to epicardial (surface) reconstructions. This limitation reduces reliability when arrhythmogenic substrates reside in deeper myocardial structures (e.g., intramural or endocardial layers), such as the septal region of the Right Ventricular Outflow Tract (RVOT), or in complex conduction disorders like Left Bundle Branch Block (LBBB) and Wolff-Parkinson-White (WPW) syndrome. Furthermore, traditional ECGI often requires CT or MRI for geometric modeling, creating barriers to accessibility in resource-constrained settings. The authors aim to overcome these limitations by developing a method capable of reconstructing three-dimensional (3D) cardiac activation throughout the entire myocardial volume without relying on dedicated imaging.

Methodology
The authors propose a volumetric ECGI approach that shifts the inverse problem formulation from estimating surface potentials to estimating volumetric cardiac sources.

• Mathematical Framework: Unlike conventional ECGI, which solves a Cauchy problem for Laplace's equation (assuming the heart is a passive conductor with no internal sources), the proposed method formulates the problem using Poisson's equation. This explicitly models cardiac sources ($f(x)$) within the myocardial volume. The transfer between body surface potentials and these volumetric sources is established using Green's functions under Neumann boundary conditions.
• Inverse Problem: The system solves a linear inverse source problem ($Bf = g$), where $B$ is the transfer matrix derived from Green's functions, $f$ represents the cardiac sources (a scalar field acting as a surrogate for the depolarization wavefront), and $g$ represents the measured body surface potentials.
• Regularization: To address the ill-posed nature of the inverse problem, zero-order Tikhonov regularization is applied, with the regularization parameter selected via the L-curve criterion.
• Geometry and Data Acquisition: The system utilizes an "imageless" pipeline. Torso geometry is reconstructed via photogrammetry from a 128-electrode vest, while cardiac geometry is estimated using a Statistical Shape Model (SSM). This eliminates the need for CT/MRI scans.
• Post-Processing: Local Activation Times (LATs) are computed from the estimated cardiac sources by identifying the time of maximum positive rate of deflection (temporal slope) of the source signal.
• Validation: The method was validated using:
  1. Simulated Data: 16 Premature Ventricular Contraction (PVC) scenarios generated using the bidomain model in openCARP, with origins in the ventricular base, septum, and free wall.
  2. Clinical Cases: Four patients with distinct pathologies (RVOT PVC, LBBB, Septal Ventricular Tachycardia, and WPW) and two open-source cases from the 2007 PhysioNet Challenge involving myocardial infarction.

Key Contributions

1. Volumetric Formulation: The paper introduces a novel formulation that reconstructs 3D activation patterns throughout the myocardial volume, rather than being restricted to the epicardial surface.
2. Green's Function Implementation: The authors implement a computationally efficient linear inverse source model using Green's functions to relate body surface potentials to volumetric sources, avoiding the need for complex vector field reconstructions or multi-step forward simulations.
3. Imageless Accessibility: By combining the volumetric algorithm with statistical shape modeling and photogrammetry, the method enables 3D mapping without the cost and time of dedicated cardiac imaging (CT/MRI).
4. Multi-Chamber Capability: The approach allows for the simultaneous reconstruction of activation in both atria and ventricles, addressing limitations in single-chamber models.

Results

• Simulation Performance: In the simulated PVC dataset, volumetric ECGI significantly outperformed surface-only (epicardial) ECGI.
  • Localization Error: Volumetric ECGI achieved a 59.3% reduction in geodesic error and a 54.6% reduction in Euclidean error compared to epicardial ECGI.
  • Regional Accuracy: The improvement was most pronounced in deep or complex regions. For septal PVCs, geodesic error decreased from 51.62 mm (epicardial) to 20.65 mm (volumetric). For ventricular base PVCs, geodesic error decreased from 46.65 mm to 14.02 mm.
• Clinical Validation:
  • RVOT PVC: The method successfully localized the ectopic focus in the complex RVOT region, matching invasive electroanatomical maps.
  • LBBB: The reconstructed activation maps correctly identified delayed and dyssynchronous conduction patterns consistent with the clinical diagnosis.
  • Ventricular Tachycardia (VT): The system resolved a reentrant circuit confined to a septal fibrotic substrate, consistent with fibrosis maps derived from ADAS 3D.
  • WPW: The method successfully characterized the accessory pathway by integrating atrial and ventricular activation, matching invasive findings.
  • Myocardial Infarction: In the open dataset, the method identified infarct locations and extents with reasonable accuracy, though some spatial displacement was noted in complex dual-infarct cases.

Significance and Claims
The paper claims that volumetric ECGI addresses a fundamental limitation of surface-restricted methods by enabling non-invasive, accessible, three-dimensional mapping of cardiac activation. The authors assert that this capability:

• Improves Localization Accuracy: Specifically in anatomically complex regions (septum, ventricular base) where traditional ECGI struggles due to the passive conductor assumption.
• Supports Clinical Planning: The enhanced resolution may support more accurate pre-procedural planning, help guide ablation targets (particularly for deep substrates), and refine the selection of candidates for Cardiac Resynchronization Therapy (CRT).
• Enhances Accessibility: By removing the dependency on CT/MRI, the technique offers a pathway for advanced arrhythmia characterization in resource-constrained environments.

The authors maintain a modest tone regarding clinical deployment, noting that while the method shows agreement with clinical diagnoses and invasive maps in the presented cases, further validation in larger cohorts with quantitative error metrics against invasive ground truth is required before it can be established as a routine clinical tool. They explicitly avoid claiming definitive intramural localization accuracy without such rigorous quantitative validation.