# Complexity reduction in human atrial modeling using extended Kalman filter

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## Abstract

Human atrial tissue electrophysiology is modeled upon biophysical details obtained from cellular level measurements. Data collected for this purpose typically represent a unique state of the tissue. As reproducing dynamic cases such as subject-varied and/or disorder-varied electrophysiological properties is in question, such complex models are typically hard to use. Hence, there is a need for simpler yet biophysically accurate and mathematically tractable models to be used for case-specific reproductions and simulations. In this study, a scheme for parameter estimation of a phenomenological cardiac model to match a targeted behavior generated from a complex model is used. Specifically, an algorithm incorporating extended Kalman filter (EKF) into the scheme is proposed. Its performance is then compared to that of particle swarm optimization (PSO) and sequential quadratic programming (SQP), algorithms that have been widely used for parameter optimization. Both robustness and adaptability performance of the algorithms are tested through various designs. For this, reproducing action potential (AP) waveforms of varying remodeling states of atrial fibrillation (AF) at different stimulus protocols was targeted. Also, randomly generated initial parameter sets are included in the tests. In addition, AP duration (APD) restitution curve (RC) is used for a multiscale evaluation of fitting performance. Finally, wavefront propagation on 2D of a selected AF remodeling state using parameter solutions from each of the algorithms is simulated for a qualitative evaluation. In general, PSO yielded superior performances than EKF and SQP with respect to fitting AP waveforms. Considering both AP and APD RC, however, EKF yielded the best accuracies. Also, more accurate spiral wave reentry is obtained with EKF. Overall, EKF algorithm yielded the best performance in robustness and adaptability.

## Keywords

Parameter estimation Human atrial electrophysiology models Extended Kalman filter Action potential Cardiac electrical restitution Wavefront propagation## References

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