Computational Modeling for Cardiac Current Localization Using Sequence-Based Nelder–Mead Algorithm in Magnetocardiography

Background: Magnetocardiography (MCG) is a non-invasive technique that measures magnetic fields generated by cardiac electrical activity, offering superior spatial resolution compared to traditional electrocardiography (ECG) for localizing arrhythmic sources. Accurate dipole source localization remains a critical challenge in cardiac electrophysiology. Methods: This work developed a comprehensive computational framework integrating the Boundary Element Method (BEM) for forward electromagnetic modeling with the Nelder-Mead simplex algorithm for inverse source o ptimization. A realistic cardiac geometry was formed by extracting a standard dataset from ECGSIM software and strategically selected 16 nodes. An experimentally acquired 6 Hz pulse signal was used as the temporal pattern for current dipole sources; appropriate amplitude scaling was applied in the implementation to achieve physiologically realistic magnetic field strengths of 10– $100~~\mathrm {pT}$ consistent with clinical MCG measurements. Magnetic field distributions were computed at 25 sensor grid locations configured in a planar array. Forward field calculations are performed using the Biot-Savart law, while the inverse problem minimized the squared error between measured and simulated magnetic fields by iterative optimization of the dipole position. Results: Proposed model achieves sub-millimeter localization precision across multiple validation scenarios. Comprehensive testing in 16 locations yields a mean localization error of $0.715 \pm 0.192~\mathrm {mm}$ (range: 0.318–0.968 mm), which with algorithmic convergence was achieved in 15-46 iterations. Under noise-free conditions, optimization framework reliably converged to solutions meeting the clinically relevant 1 mm accuracy criterion. Noise analysis using signal-to-noise ratios from -10 to 20 dB shown clinically acceptable performance (