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An ensemble-based data assimilation approach to the simulation and reconstruction of chaotic cardiac states

2023-05-02 , Badr, Shoale

Complexities in time-dependent real-world systems pose several difficulties when forecasting their future dynamics. Advancements in the field of meteorology, with the purpose of improving weather forecasting (which behaves chaotically), over the last few decades have led to the development of data assimilation, which is a technique that combines predictive numerical mathematical models with real measurements, or observations, to form more refined estimates of system states over time. As reconstruction of chaos in the tissue of the heart presents a similar forecasting problem, we apply data assimilation to the cardiac domain in this thesis. Within the assimilation algorithm, we use three widely-known mathematical cardiac models tuned to produce specific types of complex cardiac electrical dynamics, including stable spiral waves and spiral wave breakup, corresponding to tachy- cardia and fibrillation, respectively. We generate synthetic observations from each model by subsampling their solutions in space and time and restricting utilizing only one variable representing voltage, then adding Gaussian noise, and use the resulting datasets to test our implementation. By leveraging the public availability of data assimilation filtering algorithms (primarily Kalman filters) through the Parallel Data Assimilation Framework (PDAF) and adding extensions necessary for the cardiac setting, we present how two- dimensional chaotic electro-cardiac voltage behavior can be reconstructed with ensemble-based data assimilation in the presence of several experimental conditions including noise, sparse observations, and model error. This thesis presents the first application, to our knowledge, of ensemble Kalman filtering to the reconstruction of complex cardiac electrical dynamics in the 2-D domain. We found that the Error Subspace Transform Kalman Filter (ESTKF) we used is sensitive to model error and the frequency at which states are assimilated (assimilation interval). We also propose several possible improvements that can be made to our assimilation system so that it may improve state reconstruction accuracy. These preliminary findings suggest promising future experimental results, both using synthetic observations (with different model dynamics initialization) and with true experimental data.

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