Strongly and weakly coupled data assimilation for reconstruction of three-dimensional synthetic and experimental cardiac electrical excitation states with sparse observations

Data assimilation practitioners must make design decisions regarding the influence of uncertainties across space, time, and interdependent channels. Using the local ensemble transform Kalman filter, we investigate how different information sharing strategies, namely, strong and weak coupling, affect our ability to reconstruct electrical activity in the heart from sparse observations of state. These two coupling approaches differ in whether observations of one variable are allowed to influence others during the update step. We analyze the potential of a single observation to affect the ensemble weights and span through the spectral properties of the analysis operators. We apply weak and strong coupling in assimilations of observations generated from a numerical model of scroll-wave turbulence and find that restricting information flow from the observations across variable fields (weak coupling) in the low-model error case is effective at improving reconstruction accuracy and robustness. Weak coupling is relatively detrimental for high-model-error reconstructions, and strong coupling produces more reliable estimates of the state. We also consider a case where observations are derived from paced cardiac tissue where only surface voltage is recorded and find in that scenario that while both coupling methods achieve similar degrees of accuracy, strong coupling more closely approximates fine details in the observations, whereas weak coupling provides greater robustness. We conclude that coupling has marginal influence on reconstruction accuracy for cardiac electrical excitation except in extreme cases, i.e., where high-model error precludes accurate reconstruction.