Effect of fibre orientation and bulk value on the electromechanical modelling of the human ventricles
Sunday 16th February 2020
Azzolin, L.; Dede', L.; Gerbi, A.; Quarteroni, A.
Computational modelling has been proven to be a useful tool to simulate heart functioning and have been increasingly used in patient-specific treatments. Cardiac modelling is intricately multi-scale and multi-physics and this makes the problem really complex both to formulate and to solve. In this work, we propose an electromechanical model that, in bi-ventricle geometries, combines the monodomain equation, the Bueno-Orovio minimal ionic model, and 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. 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. In this paper, we study the influence of different fibre directions and incompressibility constraint values (bulk modulus) recently proposed and validated in [Barbarotta et al., IJNMBE, 2018] on the pressure-volume relation simulating a full heart beat. The coupled electromechanical problem is addressed by means of a fully segregated scheme. The numerical discretization is based on the Finite Element Method for the spatial discretization and on Backward Differentiation Formulas for the time discretization. The arising non-linear algebraic system coming from application of the implicit scheme is solved through the Newton method. Numerical simulations are carried out in a patient-specific bi-ventricle geometry to highlight the most relevant results of both electrophysiology and mechanics and to compare them with physiological data and measurements. We show that various fibre configurations and bulk values modify relevant clinical quantities such as stroke value, ejection fraction and ventricle contractility. It is therefore important to reconstruct subject specific fibre orientation to obtain physiological behaviors.