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

Sundnes, Joakim; Wall, Samuel; Osnes, Harald; Thorvaldsen, Tom; McCulloch, Andrew D.

doi:10.1080/10255842.2012.704368

Cited by 39 publications

(45 citation statements)

References 35 publications

(80 reference statements)

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“…In particular, we have not included in the analysis the effect of stretch‐activated ionic channels, which typically adds the dependence of ionic current density on deformation. Stretch‐activated currents do improve the mechano‐electric feedback normally observed in the cardiac tissue …”

Section: Discussionmentioning

confidence: 99%

Uncertainty quantification of 2 models of cardiac electromechanics

Hurtado

Castro

Madrid

2017

Numer Methods Biomed Eng

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Computational models of the heart have reached a maturity level that render them useful for in silico studies of arrhythmia and other cardiac diseases. However, the translation to the clinic of cardiac simulations critically depends on demonstrating the accuracy, robustness, and reliability of the underlying computational models under the presence of uncertainties. In this work, we study for the first time the effect of parameter uncertainty on 2 state-of-the-art coupled models of excitation-contraction of cardiac tissue. To this end, we perform forward uncertainty propagation and sensitivity analyses to understand how variability in key maximal conductances affect selected quantities of interest, such as the action potential duration (APD ), maximum intracellular calcium concentration, cardiac stretch, and stress. Our results suggest a strong linear relationship between selected maximal conductances and quantities of interest for a variability in parameters up to 25%, which justifies the construction of linear response surfaces that are used to compute the empirical probability density functions of all the quantities of interest under study. For both electromechanical models analyzed, uncertainty in the material parameters associated to the passive mechanical response of cardiac tissue does not affect the duration of action potentials, neither the amplitude of intracellular calcium concentrations. Our results confirm the poor mechanoelectric feedback that classical models of cardiac electromechanics have, even under the presence of parameter uncertainty.

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Section: Discussionmentioning

confidence: 99%

Uncertainty quantification of 2 models of cardiac electromechanics

Hurtado

Castro

Madrid

2017

Numer Methods Biomed Eng

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“…We use the Conjugate Gradient (CG) method preconditioned by the Block Jacobi (BJ) or the Multilevel Hybrid Schwarz preconditioner with L levels (MHS(L)), studied in [50,51]. See also [53,56] for a general introduction to these methods. Inexact ILU(0) local solvers are used for the local problems on the subdomains.…”

Section: Discretization and Numerical Methodsmentioning

confidence: 99%

“…In the last years, several works have been devoted to the development of models for the mechanical cardiac contraction and to the numerical simulations of the electro-mechanical coupling models, see e.g. [21,24,12,23,36,37,49,34,55]. A few studies have focused on the development of efficient solvers for the quasi-static mechanical model, see [36,59] for a parallel GMRES solver and [25,24,23] for parallel direct solvers.…”

Section: Introductionmentioning

confidence: 99%

Parallel multilevel solvers for the cardiac electro-mechanical coupling

Franzone

Pavarino

Scacchi

2015

Applied Numerical Mathematics

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We develop a parallel solver for the cardiac electro-mechanical coupling. The electric model consists of two non-linear parabolic partial differential equations (PDEs), the socalled Bidomain model, which describes the spread of the electric impulse in the heart muscle. The two PDEs are coupled with a non-linear elastic model, where the myocardium is considered as a nearly-incompressible transversely isotropic hyperelastic material. The discretization of the whole electro-mechanical model is performed by Q1 finite elements in space and a semi-implicit finite difference scheme in time. This approximation strategy yields at each time step the solution of a large scale ill-conditioned linear system deriving from the discretization of the Bidomain model and a non-linear system deriving from the discretization of the finite elasticity model. The parallel solver developed consists of solving the linear system with the Conjugate Gradient method, preconditioned by a Multilevel Schwarz preconditioner, and the non-linear system with a Newton-KrylovAlgebraic Multigrid solver. Three-dimensional parallel numerical tests on a Linux cluster show that the parallel solver proposed is scalable and robust with respect to the domain deformations induced by the cardiac contraction.

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“…The material is modeled as almost incompressible, and the parameter C compr is used to control the volume changes. Eq (1) was discretized with a standard Galerkin finite element method, and the resulting nonlinear equations were solved with Newton’s method, see [28] for details.…”

Section: Methodsmentioning

confidence: 99%

Increased Cell Membrane Capacitance is the Dominant Mechanism of Stretch-Dependent Conduction Slowing in the Rabbit Heart: A Computational Study

et al. 2015

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Volume loading of the cardiac ventricles is known to slow electrical conduction in the rabbit heart, but the mechanisms remain unclear. Previous experimental and modeling studies have investigated some of these mechanisms, including stretch-activated membrane currents, reduced gap junctional conductance, and altered cell membrane capacitance. In order to quantify the relative contributions of these mechanisms, we combined a monomain model of rabbit ventricular electrophysiology with a hyperelastic model of passive ventricular mechanics. First, a simplified geometric model with prescribed homogeneous deformation was used to fit model parameters and characterize individual MEF mechanisms, and showed good qualitative agreement with experimentally measured strain-CV relations. A 3D model of the rabbit left and right ventricles was then compared with experimental measurements from optical electrical mapping studies in the isolated rabbit heart. The model was inflated to an end-diastolic pressure of 30 mmHg, resulting in epicardial strains comparable to those measured in the anterior left ventricular free wall. While the effects of stretch activated channels did alter epicardial conduction velocity, an increase in cellular capacitance was required to explain previously reported experimental results. The new results suggest that for large strains, various mechanisms can combine and produce a biphasic relationship between strain and conduction velocity. However, at the moderate strains generated by high end-diastolic pressure, a stretch-induced increase in myocyte membrane capacitance is the dominant driver of conduction slowing during ventricular volume loading.

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

Cited by 39 publications

References 35 publications

Uncertainty quantification of 2 models of cardiac electromechanics

Uncertainty quantification of 2 models of cardiac electromechanics

Parallel multilevel solvers for the cardiac electro-mechanical coupling

Increased Cell Membrane Capacitance is the Dominant Mechanism of Stretch-Dependent Conduction Slowing in the Rabbit Heart: A Computational Study

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