Neural network aided extended Kalman filtering for inverse imaging of cardiac transmembrane potential

The aim of this study is to address the limitations in reconstructing the electrical activity of the heart from the body surface electrocardiogram, which is an ill-posed inverse problem. Current methods often assume values commonly used in the literature in the absence of a priori knowledge, leading to errors in the model. Furthermore, most methods ignore the dynamic activation process inherent in cardiomyocytes during the cardiac cycle. Approach: To overcome these limitations, we propose an extended Kalman filter (EKF)-based neural network approach to dynamically reconstruct cardiac transmembrane potential. Specifically, a recurrent neural network is used to establish the state estimation equation of the EKF, while a convolutional neural network is used as the measurement equation. The Jacobi matrix of the network undergoes a correction feedback process to obtain the Kalman gain. Main Results: After repeated iterations, the final estimated state vector, i.e., the reconstructed image of the transmembrane potential, is obtained. The results from both the final simulation and real experiments demonstrate the robustness and accurate quantification of the model. Significance: This study presents a new approach to cardiac transmembrane potential reconstruction that offers higher accuracy and robustness compared to traditional methods. The use of neural networks and EKFs allows dynamic modelling that takes into account the activation processes inherent in cardiomyocytes and does not require a priori knowledge of inputs such as forward transition matrices.