Active strain and activation models in cardiac electromechanics

SUMMARYWe propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the active strain assumption, in which it is assumed that there is a multiplicative decomposition of the deformation tensor into a passive and active part holds, the latter carrying the information of the electrical potential propagation and anisotropy of the cardiac tissue into the equations of either incompressible or compressible nonlinear elasticity, governing the mechanical response of the biological material. In addition, by changing from a Eulerian to a Lagrangian configuration, the bidomain or monodomain equations modeling the evolution of the electrical propagation exhibit a nonlinear diffusion term. Piecewise quadratic finite elements are employed to approximate the displacements field, whereas for pressure, electrical potentials and ionic variables are approximated by piecewise linear elements. Various numerical tests performed with a parallel finite element code illustrate that the proposed model can capture some important features of the electromechanical coupling and show that our numerical scheme is efficient and accurate.

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“…The ODE system modeling the kinetics of the membrane and of the activation γ l is given by

\partial_{t} v MathClass-rel= I_{ion} (v MathClass-punc, bold-italicw) MathClass-punc, \partial_{t} bold-italicw MathClass-rel= H (v MathClass-punc, bold-italicw) MathClass-punc, \partial_{t} γ_{l} MathClass-rel= G (bold-italicw MathClass-punc, γ_{l}) MathClass-punc.

…”

Section: Formulation Of the Electromechanical Problemmentioning

confidence: 99%

An active strain electromechanical model for cardiac tissue

Nobile

Quarteroni

Ruiz–Baier

2011

Numer Methods Biomed Eng

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“…The governing ODE for the activation corresponds to (14.9), as introduced in Rossi et al (2011) and Nobile et al (2012), with the specification G(γ f , w 3 ) = −0.02w 3 − 0.04γ f .…”

Section: Numerical Simulationmentioning

confidence: 99%

Activation Models for the Numerical Simulation of Cardiac Electromechanical Interactions

Ruiz–Baier

Ambrosi

Pezzuto

et al. 2013

Computer Models in Biomechanics

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This contribution addresses the mathematical modeling and numerical approximation of the excitation-contraction coupling mechanisms in the heart. The main physiological issues are preliminarily sketched along with an extended overview to the relevant literature. Then we focus on the existing models for the electromechanical interaction, paying special attention to the active strain formulation that provides the link between mechanical response and electrophysiology. We further provide some critical insight on the expected mathematical properties of the model, the ability to provide physiological results, the accuracy and computational cost of the numerical simulations. This chapter ends with a numerical experiment studying the electromechanical coupling on the anisotropic myocardial tissue

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“…In addition, one research line has been oriented to the coupling of electrocardiology with cardiac mechanics. Hyperelasticity problems based on non-trivial mixed and primal formulations with applications in cardiac biomechanics have been studied in Rossi et al [2011Rossi et al [ , 2012. LifeV-based simulations of fully coupled electromechanics (using modules for the abstract coupling of solvers) can be found in Nobile et al [2012], Ruiz-Baier et al [2013], , Andreianov et al [2015] for whole organ models, and in , , Ruiz-Baier [2015] for single-cell problems.…”

Section: Heart Dynamicsmentioning

confidence: 99%

The LifeV library: engineering mathematics beyond the proof of concept

Bertagna,

Deparis,

Formaggia

et al. 2017

Preprint

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LifeV is a library for the finite element (FE) solution of partial differential equations in one, two, and three dimensions. It is written in C++ and designed to run on diverse parallel architectures, including cloud and high performance computing facilities. In spite of its academic research nature, meaning a library for the development and testing of new methods, one distinguishing feature of LifeV is its use on real world problems and it is intended to provide a tool for many engineering applications. It has been actually used in computational hemodynamics, including cardiac mechanics and fluid-structure interaction problems, in porous media, ice sheets dynamics for both forward and inverse problems. In this paper we give a short overview of the features of LifeV and its coding paradigms on simple problems. The main focus is on the parallel environment which is mainly driven by domain decomposition methods and based on external libraries such as MPI, the Trilinos project, HDF5 and ParMetis.Dedicated to the memory of Fausto Saleri.

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Active strain and activation models in cardiac electromechanics

Cited by 6 publications

References 5 publications

An active strain electromechanical model for cardiac tissue

An active strain electromechanical model for cardiac tissue

Activation Models for the Numerical Simulation of Cardiac Electromechanical Interactions

The LifeV library: engineering mathematics beyond the proof of concept

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