Gradient-based optimization of all-pass filter networks for non-invasive electroanatomical mapping - Engelhardt, Erik; Hoffmann, Johannes; Boueke, Moritz; Elsner, Lukas; Leye, Marius; Frey, Norbert; Schmidt, Gerhard (IEEE access, 2025)
Existing approaches to non-invasive electroanatomical mapping face a fundamental challenge: accurately representing the continuous propagation velocities crucial for cardiac arrhythmia localization. Current methods either sacrifice precision by using discrete delays or require computationally intensive biophysical models that limit clinical applicability. We investigated interconnected all-pass filter networks as a novel middle ground that enables continuous, differentiable representation of cardiac propagation velocities while maintaining computational tractability. Through systematic analysis of these networks’ fundamental properties and scaling behavior, we demonstrate successful gradient-based optimization of propagation velocities in networks of up to 50 filters and 2D arrangements of 5\times 5 voxels using magnetocardiographic measurements, while identifying critical scaling challenges in more complex geometries. Our experiments establish that reliable convergence requires at least 32-48 magnetic sensors operating below a noise threshold of approximately \mathrm 7 pT/\sqrt Hz . Runtime analysis shows linear computational scaling with system size, with GPU implementations achieving up to \mathrm 50 \times acceleration over CPU versions, processing a realistic cardiac model with about 30000 voxels in under 5 s per epoch. These findings establish the theoretical feasibility of all-pass filter networks for cardiac propagation velocity modeling while identifying practical implementation requirements for clinical applications. This approach could reduce patient risks by eliminating invasive catheterization procedures and enable longitudinal studies and research applications not feasible with current invasive methods.