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Computational modeling of chemo-electro-mechanical coupling: A novel implicit monolithic finite element approach
Date
2013-10-01
Author
Wong, J.
Göktepe, Serdar
Kuhl, E.
Metadata
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
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Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here, we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, whereas the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of 4days on a standard desktop computer. Copyright (c) 2013 John Wiley & Sons, Ltd.
Subject Keywords
Modelling and Simulation
,
Computational Theory and Mathematics
,
Software
,
Applied Mathematics
,
Molecular Biology
,
Biomedical Engineering
URI
https://hdl.handle.net/11511/37539
Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
DOI
https://doi.org/10.1002/cnm.2565
Collections
Department of Civil Engineering, Article