Sensitivity of a data-assimilation system for reconstructing three-dimensional cardiac electrical dynamics

Abstract

<jats:p>Modelling of cardiac electrical behaviour has led to important mechanistic insights, but important challenges, including uncertainty in model formulations and parameter values, make it difficult to obtain quantitatively accurate results. An alternative approach is combining models with observations from experiments to produce a data-informed reconstruction of system states over time. Here, we extend our earlier data-assimilation studies using an ensemble Kalman filter to reconstruct a three-dimensional time series of states with complex spatio-temporal dynamics using only surface observations of voltage. We consider the effects of several algorithmic and model parameters on the accuracy of reconstructions of known scroll-wave truth states using synthetic observations. In particular, we study the algorithm’s sensitivity to parameters governing different parts of the process and its robustness to several model-error conditions. We find that the algorithm can achieve an acceptable level of error in many cases, with the weakest performance occurring for model-error cases and more extreme parameter regimes with more complex dynamics. Analysis of the poorest-performing cases indicates an initial decrease in error followed by an increase when the ensemble spread is reduced. Our results suggest avenues for further improvement through increasing ensemble spread by incorporating additive inflation or using a parameter or multi-model ensemble.</jats:p> <jats:p>This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.</jats:p>

Reconstructing cardiac electrical excitations from optical mapping recordings

“…The choice of this measure is motivated by its convergence properties with respect to ensemble size and its simple interpretation rather than its particular relevance to cardiac state reconstruction. Alternative error measures have been used in other works, e.g., threshold-based error, 21 which makes reference to an unknown truth state, a prescribed threshold value, and knowledge of the dynamical properties of the model. Constructing a fair (in the sense of CRPS) measure of unknown state feature error requires the construction of a statistical model of the dynamics of the state itself, against which we might compare the expectations of the reconstructed state.…”

Long-Time Prediction of Arrhythmic Cardiac Action Potentials Using Recurrent Neural Networks and Reservoir Computing

“…We also note that there is a close connection between ML-based methods and data assimilation. In the cardiac case, Kalman filter-based methods including data assimilation have been used thus far for reconstruction (Muñoz and Otani, 2010 , 2013 ; Hoffman et al, 2016 ; Hoffman and Cherry, 2020 ; Marcotte et al, 2021 ), but they also can be used for forecasting, as is more typical in data assimilation's original weather forecasting context (Hunt et al, 2007 ). It may be beneficial to pursue approaches that seek to merge data assimilation and machine learning for this task (Albers et al, 2018 ; Brajard et al, 2020 ; Gottwald and Reich, 2021 ).…”

EP-PINNs: Cardiac Electrophysiology Characterisation Using Physics-Informed Neural Networks

“…Modern inverse problem solvers such as ensemble Kalman filters (12) sequential Monte Carlo (13) and parameter estimation based on Markov chain Monte Carlo ( 14) are often combined with reduced order models (15) or multi-fidelity approaches (16) to decrease the computational complexity of parameter estimation. These very complex methods typically make strong assumptions about the statistical distribution of model parameters and require dedicated problem-specific parameterisation.…”