Abstract
In this paper, we propose a monolithic algorithm for the numerical solution of the electromechanics model of the left ventricle in the human heart. Our coupled model integrates the monodomain equation with the Bueno-Orovio minimal model for electrophysiology and the Holzapfel-Ogden constitutive law for the passive mechanics of the myocardium; a distinguishing feature of our electromechanics model is the use of the active strain formulation for muscle contraction, which we exploit -- for the first time in this context -- by means of a transmurally variable active strain formulation. We use the Finite Element method for space discretization and Backward Differentiation Formulas for time discretization, which we consider for both implicit and semi-implicit schemes. We compare and discuss the two schemes in terms of computational efficiency as the semi-implicit scheme poses significant restrictions on the timestep size due to stability considerations, while the implicit scheme yields instead a nonlinear problem, which we solve by means of the Newton method. Emphasis is laid on preconditioning strategy of the linear solver, which we perform by factorizing a block Gauss-Seidel preconditioner in combination with combination with parallel preconditioners for each of the single core models composing the integrated electromechanics model. We carry out several numerical simulations in the High Performance Computing framework for both idealized and patient-specific left ventricle geometries and meshes, which we obtain by segmenting medical MRI images. We produce personalized pressure-volume loops by means of the computational procedure, which we use to synthetically interpret and analyze the outputs of the electromechanics model.
Highlights
The heart plays the crucial role of pumping blood into the circulatory system by providing all sort of vital substances to the cells
In this paper, we propose a monolithic algorithm for the numerical solution of the electromechanics model of the left ventricle in the human heart
Semi-implicit schemes may impose strong limitations on the timestep size ∆t to ensure stability. This is what we observe from our numerical tests: the maximum timestep size that we used in order to ensure stability for the semi-implicit scheme is at least one order of magnitude smaller than the one that used for the implicit one, for which accuracy is the main factor driving the choice of ∆t
Summary
The heart plays the crucial role of pumping blood into the circulatory system by providing all sort of vital substances to the cells. A satisfactory model must be able to describe a wide range of different processes, such as the evolution of the transmembrane potential in the myocardium, the deformation caused by the muscles contraction, and the dynamics of the blood in the heart chambers and through the valves [31, 71, 76, 77, 96, 98, 99]. We use our monolithic electromechanics solver to perform numerical simulations in the High Performance Computing framework of the whole cardiac cycle, both for idealized and patient-specific LV geometries, and we analyze the numerical results in terms of clinically relevant indicators; we produce the so-called pressure-volume loops in order to assess the LV function and its properties.
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