The impact of regularisation methods for ECGI reconstructions during regular rhythms in an animal torso-tank model

Electrocardiographic imaging (ECGI) is a promising non-invasive technique that reconstructs epicardial potentials by combining high-density body-surface recordings with patient-specific 3D geometries. To systematically compare the performance of the main ECGI regularisation methods, an experimental setup was developed using isolated Langendorff-perfused rabbit hearts. Panoramic optical mapping, epicardial electrograms, and torso-tank signals were acquired simultaneously during atrial sinus rhythm and ventricular tachycardia. A tailored pre-processing pipeline was applied prior to inverse reconstruction using multiple methods, including Tikhonov (orders 0-2), truncated singular value decomposition (TSVD), damped singular value decomposition (DSVD), generalised minimal residual (GMRES), and Bayesian approaches. Results showed that no single method was universally optimal, with performance strongly dependent on cardiac region, rhythm, and evaluation metric. Tikhonov regularisations achieved the highest waveform similarity, reaching mean cross-correlation (CC) values up to 0.84 in the right atrium during sinus and 0.83 during ventricular tachycardia, though performance varied across orders and regions. In contrast, TSVD- and DSVD-based approaches yielded lower correlations (typically 0.62-0.78). Second-order Tikhonov achieved the lowest localisation error during ventricular tachycardia (6.77 ± 3.65 mm), while GMRES offered a competitive balance between spatial precision (7.04 ± 2.36 mm) and temporal accuracy. Bayes showed the highest CC variability across electrodes. Despite these differences, all methods consistently preserved dominant activation frequencies found in the measured signals (≈1.7 Hz in sinus rhythm and ≈4.8 Hz in tachycardia).