Improved discretisation and linearisation of active tension in strongly coupled cardiac electro-mechanics simulations

Author
Sundnes, Joakim
Wall, Samuel Thomas
Osnes, Harald
Thorvaldsen, Tom
McCulloch, Andrew
Date Issued
2012
Keywords
TermsetEmneord::Differensialligninger
TermsetEmneord::Elektromekanikk
TermsetEmneord::Biomekanikk
Permalink
http://publications.ffi.no/handle/123456789/444
DOI
10.1080/10255842.2012.704368
Collection
Articles
Description
Sundnes, Joakim; Wall, Samuel Thomas; Osnes, Harald; Thorvaldsen, Tom; McCulloch, Andrew. Improved discretisation and linearisation of active tension in strongly coupled cardiac electro-mechanics simulations. Computer Methods in Biomechanics and Biomedical Engineering 2014 ;Volum 17.(6) s. 604-615
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Abstract
Mathematical models of cardiac electro-mechanics typically consist of three tightly coupled parts: systems of ordinary differential equations describing electro-chemical reactions and cross-bridge dynamics in the muscle cells, a system of partial differential equations modelling the propagation of the electrical activation through the tissue and a nonlinear elasticity problem describing the mechanical deformations of the heart muscle. The complexity of the mathematical model motivates numerical methods based on operator splitting, but simple explicit splitting schemes have been shown to give severe stability problems for realistic models of cardiac electro-mechanical coupling. The stability may be improved by adopting semi-implicit schemes, but these give rise to challenges in updating and linearising the active tension. In this paper we present an operator splitting framework for strongly coupled electro-mechanical simulations and discuss alternative strategies for updating and linearising the active stress component. Numerical experiments demonstrate considerable performance increases from an update method based on a generalised Rush–Larsen scheme and a consistent linearisation of active stress based on the first elasticity tensor.
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