Electromechanical modelling of the human heart in bi-ventricle geometries
Wednesday 30th May 2018
Dedè, L.; Gerbi, A.
Mathematical and numerical modelling of the heart are receiving a growing attention in recent years due to the significant amount of natural deaths caused by cardiac diseases and the considerable cost for the social and healthcare systems. In this thesis, we consider a mathematical and numerical model for cardiac electromechanics, with focus on both the ventricles. We model the propagation of the electrical signal through the monodomain equation and we use the Bueno–Orovio minimal ionic model to capture the main features of the electrophysiology in the myocardial tissue. Since the distribution of the electric signal is dependent on the fibres orientation of the ventricles, we use a Laplace-Dirichlet Rule-Based algorithm to determine the myocardial fibres and sheets configuration in the whole bi-ventricle. Assuming the same mechanical behaviour for both the left and right ventricles, we consider the Holzapfel-Ogden strain energy function for the passive myocardial tissue modelling together with the active strain approach combined with a model for the transmurally heterogeneous thickening of the myocardium. In this thesis, we propose tackling the electromechanical modelling of the bi-ventricle geometry by carefully addressing the systolic phases, which is comprised of two isovolumic stages and ejection; as these phases are not aligned for the ventricles, modelling them is particularly challenging. The coupled electromechanical problem is addressed by means of a monolithic scheme. The numerical discretization consists in Finite Element Method for the spatial discretization and Backward Differentiation Formulas for the time discretization. The non-linear system coming from application of the implicit scheme is solved through the Newton method. A broad range of numerical simulation is carried out in patient-specific bi-ventricle geometries to highlight the most relevant results of both electrophysiology and mechanics and to compare them with physiological data and measurements. We investigate different scenarios, in particular, we highlight the role of the fibres and their impact on the cardiac cycle.