Introduction: Non-invasive electroanatomical mapping reconstructs electrophysiological activity within the heart's 3D volume using modalities such as magnetocardiography and magnetic resonance imaging (MRI). Current state-space methods discretize the volume into voxels and model propagation paths with direct voxel connections. Parameter optimization by gradient descent adapts the model to patient-specific data. However, this does not allow accurate modeling of propagation velocities. This study presents the novel use of all-pass filters to overcome this problem.
Methods: We implemented first-order all-pass filters that connect adjacent voxels. This allows for a continuously variable group delay between one and two cycles. Delays beyond this were obtained by introducing unit delays in sequence with the filters. The parameters for these filters were optimized using gradient descent by minimizing measurement residuals. When the all-pass filter parameters were pushed beyond the limits of one to two clock cycles, we changed the unit delay at the input of the filters and adjust the parameter accordingly. This ensured system stability and integrity of the action potential shape.
Results: The proposed methodology has been validated using a simulation with a voxel resolution of 2.5 mm. The spatial information was based on a cardiac MRI scan of a healthy subject. Propagation paths were consistent for the target and initial models, while the propagation velocities were varied by 10 percent. The optimization was based on one second signals from 48 magnetic sensors with a sampling frequency of 2 kHz. After 100 epochs, the mean measurement residuals were reduced by a factor of 98. Similarly, the mean local activation time errors decreased significantly.
Conclusion: We showed that all-pass filters allow per-voxel modeling of continuous, differentiable propagation velocities that can be refined by gradient descent on non-invasive measurement data. This advancement holds promise for the localization of arrhythmogenic substrates, thereby improving clinical diagnostic capabilities.