A parallel solver for reaction-diffusion systems in computational electrocardiology

In this work, a parallel three-dimensional solver for numerical simulations in computational electrocardiology is introduced and studied. The solver is based on the anisotropic Bidomain %(AB) cardiac model, consisting of a system of two degenerate parabolic reaction-diffusion equations describing the intra and extracellular potentials of the myocardial tissue. This model includes intramural fiber rotation and anisotropic conductivity coefficients that can be fully orthotropic or axially symmetric around the fiber direction. %In case of equal anisotropy ratio, this system reduces to The solver also includes the simpler anisotropic Monodomain model, consisting of only one reaction-diffusion equation. These cardiac models are coupled with a membrane model for the ionic currents, consisting of a system of ordinary differential equations that can vary from the simple FitzHugh-Nagumo (FHN) model to the more complex phase-I Luo-Rudy model (LR1). The solver employs structured isoparametric $Q_1$ finite elements in space and a semi-implicit adaptive method in time. Parallelization and portability are based on the PETSc parallel library. Large-scale computations with up to $O(10^7)$ unknowns have been run on parallel computers, simulating excitation and repolarization phenomena in three-dimensional domains

Parallel inexact Newton-Krylov and quasi-Newton solvers for nonlinear elasticity

In this work, we address the implementation and performance of inexact Newton-Krylov and quasi-Newton algorithms, more specifically the BFGS method, for the solution of the nonlinear elasticity equations, and compare them to a standard Newton-Krylov method. This is done through a systematic analysis of the performance of the solvers with respect to the problem size, the magnitude of the data and the number of processors in both almost incompressible and incompressible mechanics. We consider three test cases: Cook's membrane (static, almost incompressible), a twist test (static, incompressible) and a cardiac model (complex material, time dependent, almost incompressible). Our results suggest that quasi-Newton methods should be preferred for compressible mechanics, whereas inexact Newton-Krylov methods should be preferred for incompressible problems. We show that these claims are also backed up by the convergence analysis of the methods. In any case, all methods present adequate performance, and provide a significant speed-up over the standard Newton-Krylov method, with a CPU time reduction exceeding 50% in the best cases

Overlapping Schwarz methods for Fekete and Gauss-Lobatto spectral elements

The classical overlapping Schwarz algorithm is here extended to the triangular/tetrahedral spectral element (TSEM) discretization of elliptic problems. This discretization, based on Fekete nodes, is a generalization to nontensorial elements of the tensorial Gauss–Lobatto–Legendre quadrilateral spectral elements (QSEM). The overlapping Schwarz preconditioners are based on partitioning the domain of the problem into overlapping subdomains, solving local problems on these subdomains, and solving an additional coarse problem associated with either the subdomain mesh or the spectral element mesh. The overlap size is generous, i.e., one element wide, in the TSEM case, while it is minimal or variable in the QSEM case. The results of several numerical experiments show that the convergence rate of the proposed preconditioning algorithm is independent of the number of subdomains $N$ and the spectral degree $p$ in case of generous overlap; otherwise it depends inversely on the overlap size. The proposed preconditioners are also robust with respect to arbitrary jumps of the coefficients of the elliptic operator across subdomains

Robust parallel nonlinear solvers for implicit time discretizations of the Bidomain equations

In this work, we study the convergence and performance of nonlinear solvers for the Bidomain equations after decoupling the ordinary and partial differential equations of the cardiac system. Firstly, we provide a rigorous proof of the global convergence of Quasi-Newton methods, such as BFGS, and nonlinear Conjugate-Gradient methods, such as Fletcher--Reeves, for the Bidomain system, by analyzing an auxiliary variational problem under physically reasonable hypotheses. Secondly, we compare several nonlinear Bidomain solvers in terms of execution time, robustness with respect to the data and parallel scalability. Our findings indicate that Quasi-Newton methods are the best choice for nonlinear Bidomain systems, since they exhibit faster convergence rates compared to standard Newton-Krylov methods, while maintaining robustness and scalability. Furthermore, first-order methods also demonstrate competitiveness and serve as a viable alternative, particularly for matrix-free implementations that are well-suited for GPU computing

A clinical-in silico study on the effectiveness of multipoint bicathodic and cathodic-anodal pacing in cardiac resynchronization therapy.

Up to one-third of patients undergoing cardiac resynchronization therapy (CRT) are nonresponders. Multipoint bicathodic and cathodic-anodal left ventricle (LV) stimulations could overcome this clinical challenge, but their effectiveness remains controversial. Here we evaluate the performance of such stimulations through both in vivo and in silico experiments, the latter based on computer electromechanical modeling. Seven patients, all candidates for CRT, received a quadripolar LV lead. Four stimulations were tested: right ventricular (RVS); conventional single point biventricular (S-BS); multipoint biventricular bicathodic (CC-BS) and multipoint biventricular cathodic-anodal (CA-BS). The following parameters were processed: QRS duration; maximal time derivative of arterial pressure (dPdtmax); systolic arterial pressure (Psys); and stroke volume (SV). Echocardiographic data of each patient were then obtained to create an LV geometric model. Numerical simulations were based on a strongly coupled Bidomain electromechanical coupling model. Considering the in vivo parameters, when comparing S-BS to RVS, there was no significant decrease in SV (from 45 ± 11 to 44 ± 20 ml) and 6% and 4% increases of dPdtmax and Psys, respectively. Focusing on in silico parameters, with respect to RVS, S-BS exhibited a significant increase of SV, dPdtmax and Psys. Neither the in vivo nor in silico results showed any significant hemodynamic and electrical difference among S-BS, CC-BS and CA-BS configurations. These results show that CC-BS and CA-BS yield a comparable CRT performance, but they do not always yield improvement in terms of hemodynamic parameters with respect to S-BS. The computational results confirmed the in vivo observations, thus providing theoretical support to the clinical experiments

Unexpected impairment of INa underpins reentrant arrhythmias in a knock-in swine model of Timothy syndrome

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Genetic polymorphisms modulate the folate metabolism of Brazilian individuals with Down syndrome

Individuals with Down syndrome (DS) carry three copies of the Cystathionine beta-synthase (C beta S) gene. The increase in the dosage of this gene results in an altered profile of metabolites involved in the folate pathway, including reduced homocysteine (Hcy), methionine, S-adenosylhomocysteine (SAH) and S-adenosylmethionine (SAM). Furthermore, previous studies in individuals with DS have shown that genetic variants in genes involved in the folate pathway influence the concentrations of this metabolism's products. The purpose of this study is to investigate whether polymorphisms in genes involved in folate metabolism affect the plasma concentrations of Hcy and methylmalonic acid (MMA) along with the concentration of serum folate in individuals with DS. Twelve genetic polymorphisms were investigated in 90 individuals with DS (median age 1.29 years, range 0.07-30.35 years; 49 male and 41 female). Genotyping for the polymorphisms was performed either by polymerase chain reaction (PCR) based techniques or by direct sequencing. Plasma concentrations of Hcy and MMA were measured by liquid chromatography-tandem mass spectrometry as previously described, and serum folate was quantified using a competitive immunoassay. Our results indicate that the MTHFR C677T, MTR A2756G, TC2 C776G and BHMT G742A polymorphisms along with MMA concentration are predictors of Hcy concentration. They also show that age and Hcy concentration are predictors of MMA concentration. These findings could help to understand how genetic variation impacts folate metabolism and what metabolic consequences these variants have in individuals with trisomy 21.Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [04/15944-5, 03/09931-5]Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) [302157/2008-5]Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES) [CGPP 046/2006

Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes

In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polygonal/polyhedral meshes. We prove that the two-level method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the number of smoothing steps, which depends on p, is chosen sufficiently large. An analogous result is obtained for the W-cycle multigrid algorithm, which is proved to be uniformly convergent with respect to the mesh size, the polynomial approximation degree, and the number of levels, provided the latter remains bounded and the number of smoothing steps is chosen sufficiently large. Numerical experiments are presented which underpin the theoretical predictions; moreover, the proposed multilevel solvers are shown to be convergent in practice, even when some of the theoretical assumptions are not fully satisfied