Modelling and Estimation of Spatiotemporal Cardiac Electrical Dynamics

The heart is a complex biological system in which electrical activation signals initiate at the pacemaker cells, propagate through the heart tissue to both trigger and synchronise the mechanical contractions. Abnormalities in the cardiac electrical signals lead to dangerous cardiac arrhythmias. Therefore, understanding the functionalities of the cardiac electrical activity is essential for the development of novel techniques to facilitate advanced diagnosis and treatment for arrhythmia. By combining experimental or clinical electrophysiology data with mathematical models, system theoretic approaches can be used to provide quantitative insights into the normal and pathological mechanisms of the cardiac electrical activity. This thesis proposes model-based estimation methods to reconstruct and quantify the underlying spatiotemporal cardiac electrical dynamics from the cardiac electrogram measurements. Firstly, a statistical model-based estimation framework is proposed to reconstruct the tissue dynamics from the cardiac electrogram measurements. The reconstruction of the tissue dynamics is based on an integrated model of cardiac electrical activity, which incorporates the cardiac action potential dynamics at the cell-level, tissue-level and extracellular-level. The dynamics of the cardiac tissue is described using the monodomain tissue model, which is coupled with the continuous version of modified Mitchell-Schaeffer model. The resulting model equations are of infinite-dimensional form, which is converted into a finite-dimensional state-space representation via a model reduction method. In order to estimate the hidden state variables of the tissue dynamics from the cardiac electrogram measurements, a combined detection-estimation framework using a single filter unscented-transform based smoothing algorithm is proposed. The detection step in the proposed method enables the inclusion of localised stimulus events into the model-based estimation framework. The performance of the proposed algorithms are demonstrated using the modelled cardiac activation patterns of normal and reentrant conditions, in both one-dimensional and two-dimensional tissue field. The findings from this proposed study illustrate that the hidden state variables of the tissue model can be estimated from the electrogram measurements, simultaneously by detecting the stimulus events. Therefore, this method shows that the complex spatiotemporal cardiac activity can be reconstructed from the coarse electrograms using the state estimation methods. Secondly, a complex network modelling approach is proposed to quantify the spatiotemporal organisation of electrical activation during human ventricular fibrillation. The proposed network modelling approach includes three different methods based on correlation analysis, graph theoretical measures and hierarchical clustering. Using the proposed approach, the level of spatiotemporal organisation is quantified during three episodes of VF in ten patients, recorded using multi-electrode epicardial recordings with 30 s coronary perfusion, 150 s global myocardial ischaemia and 30 s reflow. The findings show a steady decline in spatiotemporal organisation from the onset of VF with coronary perfusion. Following this, a transient increases in spatiotemporal organisation is observed during global myocardial ischaemia. However, the decline in spatiotemporal organisation continued during reflow. The results are consistent across all patients, and are consistent with the numbers of phase singularities. The findings show that the complex spatiotemporal patterns can be studied using complex network analysis.