Optimized cardiac simulation as a tool to understand patient specific mechanical function

Abstract

The muscular tissue of the heart is able to contract in the absence of external load. This behaviour is stimulated by a spontaneous electrical depolarization of cardiac cells in the sinoatrial node, which spreads electrical activation through the whole heart, that triggers the synchronized mechanical contraction of the heart muscle. This phenomenon, referred to as active contraction is commonly modelled mathematically using two approaches: the active stress and the active strain approach. The active stress approach has a more physiological basis, whereas the active strain approach, is more mathematically robust and is less computationally expensive. In this thesis, we aim to investigate if both approaches (though fundamentally different in their formulations), can produce identical simulation of ventricular stress in a patient-specific bi-ventricular model. We used a computational modelling and data assimilation framework called pulse-adjoint to create the personalized models. The finite element method was used to find a numerical solution to the force-balance equation, that models heart mechanics. A gradient-based optimization method, was used to assimilate clinical data (i.e. volume and regional circumferential strain) into the computational models. To validate the models, we predicted the longitudinal and radial strains not used in the optimization. Two personalized models were created for each subject used in this study; one based on the active stress approach and the other based on the active strain approach to enable comparison between both formulations. By applying the framework using data obtained from three patients with pulmonary arterial hypertension, we were able to extract ventricular stress in the fibre, circumferential, longitudinal and radial directions. Our results show that differences exist in the stress prediction using both approaches. However, total \textit{Cauchy} stress (in the fibre, circumferential and longitudinal directions) was simulated more closely between the two approaches, compared to the total stress in the radial direction or the deviatoric component of total stress in all four directions. We also showed that in a simple case, (simplified in terms of model geometry and myocardial fibre orientation), both approaches can produce very similar stress predictions.