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

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 can be used to fill in missing measurements, but to our knowledge, there have been few comparisons of different state estimation algorithms applied to the same cardiac action potential model. To help develop a framework for comparing performances of estimators, we applied two estimation algorithms, an unscented Kalman filter (UKF) and a gain-scheduled Kalman filter (GSKF), to a two-variable Karma model of a cardiac cell. We generated simulated data from the model and compared the abilities of the algorithms to infer the slow variable of the model from measurements of the fast variable and vice versa. The UKF performed well when the process noise variance was low relative to measurement noise, while the opposite was often true for the GSKF, and estimation errors tended to be smaller when the fast variable was chosen as the measurement.