Doctoral thesis

Enhancing multi-scale cardiac simulations by coupling electrophysiology and mechanics : a flexible high performance approach to cardiac electromechanics


139 p

Thèse de doctorat: Università della Svizzera italiana, 2019

English This work focuses on the development of computational methods for the simulation of the propagation of the electrical potential in the heart and of the resulting mechanical contraction. The interaction of these two physical phenomena is described by an electromechanical model which consists of the monodomain system, which describes the propagation of the action potential in the cardiac tissue, and the equations of incompressible elasticity, which describe its mechanical response. In fully-coupled electromechanical simulations, two main computational challenges are usually identified in literature: the time integration of the monodomain system and the efficient solution of the equations of incompressible elasticity. These two are the actual bottlenecks in the realization of accurate and efficient fully-coupled electromechanical simulations. The first computational challenge arises from the discretization in time of the equations that describe the electrical activation of cardiac tissue. The monodomain system should be discretized employing both fine spatial grids and small time-steps, to capture the spatial steep gradients typical of the action potential and the behavior of the stiff gating variables, respectively. To obtain an accurate and computationally-cheap numerical solution, we propose a novel method based on coupling high-order backward differentiation formulae with high-order exponential time stepping schemes for the time integration of the monodomain system. We propose a novel quasi-Newton approach for the implicit discretization of the monodomain equation. We also compare this latter approach against a complex step differentiation-based approach. As a result, we show by means of numerical tests the accuracy of the developed strategies and how the use of high-order time integration schemes affects the simulation of post- processed quantities of clinical relevance such as the conduction velocity. The second computational challenge is due to the structure the discretization of the equations of incompressible elasticity. Due to the incompressibility constraint, the arising linear system has a saddle point structure for which standard solution methods such as multigrid or domain de- composition do not provide optimal convergence if not properly adapted. In order to overcome this problematic, we propose a segregated multigrid preconditioned solution method. The segregated approach allows to recast the saddle-point problem into two elliptic problems for which multigrid methods are shown to provide optimal convergence. The electromechanical model is employed to evaluate the effects of geometrical changes due to the contraction of the heart on simulated electrocardiograms. Finally, the effect of different electrical activations on the resulting pressure-volume loops is investigated by coupling the electromechanical model with a lumped model of the circulatory system.
  • English
Computer science
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