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Segregated Algorithms for the Numerical Simulation of Cardiac Electromechanics in the Left Human Ventricle

  • L. Dede’Email author
  • A. Gerbi
  • A. Quarteroni
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Part of the Lecture Notes in Mathematics book series (LNM, volume 2260)

Abstract

We propose and numerically assess three segregated (partitioned) algorithms for the numerical solution of the coupled electromechanics problem for the left human ventricle. We split the coupled problem into its core mathematical models and we proceed to their numerical approximation. Space and time discretizations of the core problems are carried out by means of the Finite Element Method and Backward Differentiation Formulas, respectively. In our mathematical model, electrophysiology is represented by the monodomain equation while the Holzapfel-Ogden strain energy function is used for the passive characterization of tissue mechanics. A transmurally variable active strain model is used for the active deformation of the fibers of the myocardium to couple the electrophysiology and the mechanics in the framework of the active strain model. In this work, we focus on the numerical strategy to deal with the solution of the coupled model, which is based on novel segregated algorithms that we propose. These also allow using different time discretization schemes for the core submodels, thus leading to the formulation of staggered algorithms, a feature that we systematically exploit to increase the efficiency of the overall computational procedure. By means of numerical tests we show that these staggered algorithms feature (at least) first order of accuracy. We take advantage of the efficiency of the segregated schemes to solve, in a High Performance Computing framework, the cardiac electromechanics problem for the human left ventricle, for both idealized and subject-specific configurations.

Notes

Acknowledgements

This research was partially supported by the Swiss Platform for Advanced Scientific Computing (PASC, project “Integrative HPC Framework for Coupled Cardiac Simulations”). We also gratefully acknowledge the Swiss National Supercomputing Center (CSCS) for providing the CPU resources for the numerical simulations under project IDs s635/s796.

We acknowledge Prof. J. Schwitter and Dr. P. Masci (CHUV, Lausanne) for providing the MRI images used in this work and for the enlightening discussions. We also thank Prof. P. Tozzi (CHUV, Lausanne) for the invaluable insights in the functioning of the human heart.

The authors acknowledge the ERC Advanced Grant iHEART, “An Integrated Heart Model for the simulation of the cardiac function”, 2017–2022, P.I. A. Quarteroni (ERC–2016–ADG, project ID: 740132).

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Authors and Affiliations

  1. 1.MOX–Modeling and Scientific Computing, Mathematics DepartmentPolitecnico di MilanoMilanoItaly
  2. 2.Institute of MathematicsÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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