174 research outputs found
Multilevel Schwarz and multigrid preconditioners for the Bidomain system
No full textTwo parallel and scalable multilevel preconditioners for the Bidomain
system in computational electrocardiology are introduced and studied. The Bido-
main system, consisting of two degenerate parabolic reaction-diffusion equations
coupled with a stiff system of several ordinary differential equations, generates very
ill-conditioned discrete systems when discretized with semi-implicit methods in time
and finite elements in space. The multilevel preconditioners presented in this paper
attain the best performance to date, both in terms of convergence rate and solution
time and outperform the simpler one-level preconditioners previously introduced.
Parallel numerical results, using the PETSc library and run on Linux Clusters,
show the scalability of the proposed preconditioners and their efficiency on large-
scale simulations of a complete cardiac cycle
“Chained to Hope”: A Short Story by Noni Carter
No full textIntroduction to "Chained to Hope", an unpublished short story by young author Noni Carter, written specifically for this issue of RSA Journal dedicated to #BL
Dynamical effects of myocardial ischemia in anisotropic cardiac models in three dimensions
No full textThe interaction between the presence of moderate or severe
subendocardial ischemic regions and the anisotropic structure of the cardiac
muscle is investigated here by means of numerical simulations based on
anisotropic Bidomain and Monodomain models. The ischemic effects on cardiac
excitation, recovery and distribution of action potential duration are
discussed, showing the presence of ischemic epicardial markers. Extracellular
potential distributions during the ST and TQ intervals are computed separately
using non-stationary models. During the ST interval, the extracellular
potential patterns differ from those simulated with stationary models used in
the literature. These differences are explained by decomposing the cardiac
current sources into conormal, axial and orthogonal components and determining
which component is dominant during the ST and TQ intervals
Relationship between cardiac electrical and mechanical activation markers by coupling bidomain and deformation models
No full text
Cardiac excitation mechanisms, wavefront dynamics and strength - interval curves predicted by 3D orthotropic bidomain simulations
No full textThe assessment and understanding of cardiac excitation mechanisms is very important for the development and improvement of implantable cardiac devices, pacing protocols, and arrhythmia treatments. Previous bidomain simulation studies have investigated cathodal and anodal make/break mechanisms of cardiac excitation and strength–interval (S–I) curves in two-dimensional sheets or cylindrical domains, that by symmetry reduce to the two-dimensional case. In this work, cathodal and anodal S–I curves are studied by means of detailed bidomain simulations which include: (i) three-dimensional cardiac slabs; (ii) transmural fiber rotation; (iii) unequal orthotropic anisotropy of the conducting media; (iv) incorporation of funny and electroporation currents in the ventricular membrane model. The predicted shape of cathodal and anodal S–I curves exhibit the same features of the S–I curves observed experimentally and the break/make transition coincides with the final descending phase of the S–I curves. Away from the break/make transition, only the break or make excitation mechanism is observed independently of the stimulus strength, whereas within an interval at the break/make transition, new paradoxical excitation behaviors are observed that depend on the stimulus strength
Bioelectrical effects of mechanical feedbacks in a strongly coupled cardiac electro-mechanical model
No full textThe aim of this work is to investigate by means of numerical simulations the effects of myocardial deformation due to muscle contraction on the bioelectrical activity of the cardiac tissue. The three-dimensional electro-mechanical model considered consists of the following four components: the quasi-static orthotropic finite elasticity equations for the deformation of the cardiac tissue; the active tension model for the intracellular calcium dynamics and cross-bridge binding; the orthotropic Bidomain model for the electrical current flow through the tissue; the membrane model of the cardiac myocyte, including stretch-activated currents (ISAC). In order to properly take into account cardiac mechanical feedbacks, the electrical current flow is described in a strongly coupled framework by the Bidomain model on the deformed tissue. We then derive a novel formulation of the Bidomain model in the reference configuration, with complete mechanical feedbacks affecting not only the conductivity tensors but also a convective term depending on the velocity of the deformation. The numerical simulations are based on our finite element parallel solver, which employs both Multilevel Additive Schwarz preconditioners for the solution of linear systems arising from the discretization of the Bidomain equations and Newton-Krylov-Algebraic Multigrid methods for the solution of nonlinear systems arising from the discretization of the finite elasticity equations. The results have shown that: (i) the ISAC current prolongs action potential duration (APD) of about 10-15 ms; (ii) the inclusion into the model of both ISAC current and the convective term reduces the dispersion of repolarization of about 7% (from 139 to 129 ms) and increases the dispersion of APD about three times (from 13 to 45 ms). These effects indicate that mechanical feedbacks might influence arrhythmogenic mechanisms when combined with pathological substrates
A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures
No full textWe introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks
GDSW preconditioners for composite Discontinuous Galerkin discretizations of multicompartment reaction–diffusion problems
No full textThe aim of the present work is to design, analyze theoretically, and test numerically, a generalized Dryja–Smith–Widlund (GDSW) preconditioner for composite Discontinuous Galerkin discretizations of multicompartment parabolic reaction–diffusion equations, where the solution can exhibit natural discontinuities across the domain. We prove that the resulting preconditioned operator for the solution of the discrete system arising at each time step converges with a scalable and quasi-optimal upper bound for the condition number. The GDSW preconditioner is then applied to the EMI (Extracellular - Membrane - Intracellular) reaction–diffusion system, recently proposed to model microscopically the spatiotemporal evolution of cardiac bioelectrical potentials. Numerical tests validate the scalability and quasi-optimality of the EMI-GDSW preconditioner, and investigate its robustness with respect to the time-step size as well as jumps in the diffusion coefficients
-VEM for some variants of the Cahn-Hilliard equation: A numerical exploration
No full textWe consider the C1-Virtual Element Method (VEM) for the conforming numerical approximation of some variants of the Cahn-Hilliard equation on polygonal meshes. In particular, we focus on the discretization of the advective Cahn-Hilliard problem and the Cahn-Hilliard inpainting problem. We present the numerical approximation and several numerical results to assess the efficacy of the proposed methodology
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