State Estimation for Cardiac Action Potential Dynamics: A Comparison of Kalman Filter Designs

Laura Munoz and Christopher Beam
Rochester Institute of Technology


Motivation: Various technologies, such as electrocardiography, optical mapping, and patch clamping, have been developed to monitor cardiac electrophysiological behavior in live tissue. One limitation is that none of the available measurement methods is capable of monitoring simultaneously all quantities, such as intracellular ionic concentrations and ion-channel gating states, that may be important contributors to arrhythmia formation. Data assimilation strategies such as Kalman filtering have been developed to fill in missing measurements, but to our knowledge, there have been few direct comparisons of filtering algorithms applied to cellular action potential models.

Aims: This study aimed to apply two state estimation strategies to a nonlinear model of action potential (AP) dynamics and to compare their ability to reconstruct unmeasured dynamical variables.

Methods: We tested two state estimation algorithms on the Karma two-variable model, which is a nonlinear differential equation model of cardiac AP dynamics. State estimation algorithms allow for reconstruction of dynamical (or state) variables of a system, based on limited measurements, in cases where certain variables cannot be observed directly. We selected two algorithms, a gain-scheduled Kalman filter (GSKF), which is a modified version of a linear KF in which feedback gains are updated periodically, along with a nonlinear filter, the Unscented Kalman Filter (UKF). We used both filters to estimate the slow variable of the Karma model from noise-corrupted simulated measurements of the fast variable.

Results: In certain scenarios where model uncertainty was larger than measurement uncertainty, the 2-norm of the GSKF estimation error for the slow variable was smaller (0.20) than that of the UKF (5.2). The UKF estimation error was reduced when model uncertainty was smaller.

Conclusions: The GSKF showed advantages over the UKF under certain conditions of practical relevance.