@inproceedings{CheginiFroehlyHuynhetal., author = {Chegini, Fatemeh and Froehly, Algiane and Huynh, Ngoc Mai Monica and Pavarino, Luca and Potse, Mark and Scacchi, Simone and Weiser, Martin}, title = {Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution}, series = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, booktitle = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, doi = {10.23967/c.coupled.2023.004}, abstract = {The cardiac extracellular-membrane-intracellular (EMI) model enables the precise geometrical representation and resolution of aggregates of individual myocytes. As a result, it not only yields more accurate simulations of cardiac excitation compared to homogenized models but also presents the challenge of solving much larger problems. In this paper, we introduce recent advancements in three key areas: (i) the creation of artificial, yet realistic grids, (ii) efficient higher-order time stepping achieved by combining low-overhead spatial adaptivity on the algebraic level with progressive spectral deferred correction methods, and (iii) substructuring domain decomposition preconditioners tailored to address the complexities of heterogeneous problem structures. The efficiency gains of these proposed methods are demonstrated through numerical results on cardiac meshes of different sizes.}, language = {en} } @article{CheginiKopanicakovaKrauseetal., author = {Chegini, Fatemeh and Kopanicakova, Alena and Krause, Rolf and Weiser, Martin}, title = {Efficient Identification of Scars using Heterogeneous Model Hierarchies}, series = {EP Europace}, volume = {23}, journal = {EP Europace}, doi = {10.1093/europace/euaa402}, pages = {i113 -- i122}, abstract = {Aims. Detection and quantification of myocardial scars are helpful both for diagnosis of heart diseases and for building personalized simulation models. Scar tissue is generally charac­terized by a different conduction of electrical excitation. We aim at estimating conductivity-related parameters from endocardial mapping data, in particular the conductivity tensor. Solving this inverse problem requires computationally expensive monodomain simulations on fine discretizations. Therefore, we aim at accelerating the estimation using a multilevel method combining electrophysiology models of different complexity, namely the mono­domain and the eikonal model. Methods. Distributed parameter estimation is performed by minimizing the misfit between simulated and measured electrical activity on the endocardial surface, subject to the mono­domain model and regularization, leading to a constrained optimization problem. We formulate this optimization problem, including the modeling of scar tissue and different regularizations, and design an efficient iterative solver. We consider monodomain grid hierarchies and monodomain-eikonal model hierarchies in a recursive multilevel trust-region method. Results. From several numerical examples, both the efficiency of the method and the estimation quality, depending on the data, are investigated. The multilevel solver is significantly faster than a comparable single level solver. Endocardial mapping data of realistic density appears to be just sufficient to provide quantitatively reasonable estimates of location, size, and shape of scars close to the endocardial surface. Conclusion. In several situations, scar reconstruction based on eikonal and monodomain models differ significantly, suggesting the use of the more accurate but more expensive monodomain model for this purpose. Still, eikonal models can be utilized to accelerate the computations considerably, enabling the use of complex electrophysiology models for estimating myocardial scars from endocardial mapping data.}, language = {en} } @inproceedings{CheginiKopanicakovaWeiseretal., author = {Chegini, Fatemeh and Kopanicakova, Alena and Weiser, Martin and Krause, Rolf}, title = {Quantitative Analysis of Nonlinear MultifidelityOptimization for Inverse Electrophysiology}, series = {Domain Decomposition Methods in Science and Engineering XXVI}, booktitle = {Domain Decomposition Methods in Science and Engineering XXVI}, publisher = {Springer}, pages = {65 -- 76}, abstract = {The electric conductivity of cardiac tissue determines excitation propagation and is important for quantifying ischemia and scar tissue and for building personalized models. Estimating conductivity distributions from endocardial mapping data is a challenging inverse problem due to the computational complexity of the monodomain equation, which describes the cardiac excitation. For computing a maximum posterior estimate, we investigate different optimization approaches based on adjoint gradient computation: steepest descent, limited memory BFGS, and recursive multilevel trust region methods, which are using mesh hierarchies or heterogeneous model hierarchies. We compare overall performance, asymptotic convergence rate, and pre-asymptotic progress on selected examples in order to assess the benefit of our multifidelity acceleration.}, language = {en} } @inproceedings{CheginiSteinkeWeiser, author = {Chegini, Fatemeh and Steinke, Thomas and Weiser, Martin}, title = {Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods}, abstract = {The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the computations. Here we investigate a different route to spatial adaptivity that is based on nested subset selection for algebraic degrees of freedom in spectral deferred correction methods. This combination of algebraic adaptivity and iterative solvers for higher order collocation time stepping realizes a multirate integration with minimal overhead. This leads to moderate but significant speedups in both monodomain and cell-by-cell models of cardiac excitation, as demonstrated at four numerical examples.}, language = {en} } @article{HuynhCheginiPavarinoetal., author = {Huynh, Ngoc and Chegini, Fatemeh and Pavarino, Luca and Weiser, Martin and Scacchi, Simone}, title = {Convergence analysis of BDDC preconditioners for hybrid DG discretizations of the cardiac cell-by-cell model}, series = {SIAM Journal on Scientific Computing}, volume = {45}, journal = {SIAM Journal on Scientific Computing}, number = {6}, pages = {A2836 -- A2857}, abstract = {A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of hybrid Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. The latter are different from the classical Bidomain and Monodomain cardiac models based on homogenized descriptions of the cardiac tissue at the macroscopic level, and therefore they allow the representation of individual cardiac cells, cell aggregates, damaged tissues and nonuniform distributions of ion channels on the cell membrane. The resulting discrete cell-by-cell models have discontinuous global solutions across the cell boundaries, hence the proposed BDDC preconditioner is based on appropriate dual and primal spaces with additional constraints which transfer information between cells (subdomains) without influencing the overall discontinuity of the global solution. A scalable convergence rate bound is proved for the resulting BDDC cell-by-cell preconditioned operator, while numerical tests validate this bound and investigate its dependence on the discretization parameters.}, language = {en} } @inproceedings{SteyerCheginiPotseetal., author = {Steyer, Joshua and Chegini, Fatemeh and Potse, Mark and Loewe, Axel and Weiser, Martin}, title = {Continuity of Microscopic Cardiac Conduction in a Computational Cell-by-Cell Model}, series = {2023 Computing in Cardiology Conference (CinC)}, volume = {50}, booktitle = {2023 Computing in Cardiology Conference (CinC)}, publisher = {Computing in Cardiology}, issn = {2325-887X}, doi = {10.22489/CinC.2023.385}, abstract = {Conduction velocity in cardiac tissue is a crucial electrophysiological parameter for arrhythmia vulnerability. Pathologically reduced conduction velocity facilitates arrhythmogenesis because such conduction velocities decrease the wavelength with which re-entry may occur. Computational studies on CV and how it changes regionally in models at spatial scales multiple times larger than actual cardiac cells exist. However, microscopic conduction within cells and between them have been studied less in simulations. In this work, we study the relation of microscopic conduction patterns and clinically observable macroscopic conduction using an extracellular-membrane-intracellular model which represents cardiac tissue with these subdomains at subcellular resolution. By considering cell arrangement and non-uniform gap junction distribution, it yields anisotropic excitation propagation. This novel kind of model can for example be used to understand how discontinuous conduction on the microscopic level affects fractionation of electrograms in healthy and fibrotic tissue. Along the membrane of a cell, we observed a continuously propagating activation wavefront. When transitioning from one cell to the neighbouring one, jumps in local activation times occurred, which led to lower global conduction velocities than locally within each cell.}, language = {en} } @inproceedings{SteyerCheginiStaryetal., author = {Steyer, Joshua and Chegini, Fatemeh and Star{\´y}, Tomas and Potse, Mark and Weiser, Martin and Loewe, Axel}, title = {Electrograms in a Cardiac Cell-by-Cell Model}, abstract = {Cardiac electrograms are an important tool to study the spread of excitation waves inside the heart, which in turn underlie muscle contraction. Electrograms can be used to analyse the dynamics of these waves, e.g. in fibrotic tissue. In computational models, these analyses can be done with greater detail than during minimally invasive in vivo procedures. Whilst homogenised models have been used to study electrogram genesis, such analyses have not yet been done in cellularly resolved models. Such high resolution may be required to develop a thorough understanding of the mechanisms behind abnormal excitation patterns leading to arrhythmias. In this study, we derived electrograms from an excitation propagation simulation in the Extracellular, Membrane, Intracellular (EMI) model, which represents these three domains explicitly in the mesh. We studied the effects of the microstructural excitation dynamics on electrogram genesis and morphology. We found that electrograms are sensitive to the myocyte alignment and connectivity, which translates into micro-fractionations in the electrograms.}, language = {en} } @inproceedings{WeiserChegini, author = {Weiser, Martin and Chegini, Fatemeh}, title = {Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods}, series = {CMBE22 - 7th International Conference on Computational \& Mathematical Biomedical Engineering}, booktitle = {CMBE22 - 7th International Conference on Computational \& Mathematical Biomedical Engineering}, pages = {528 -- 531}, abstract = {The highly localized dynamics of cardiac electrophysiology models call for adaptive simulation methods. Unfortunately, the overhead incurred by classical mesh adaptivity turns out to outweigh the performance improvements achieved by reducing the problem size. Here, we explore a different approach to adaptivity based on algebraic degree of freedom subset selection during spectral deferred correction sweeps, which realizes a kind of multirate higher order integration. Numerical experience indicates a significant performance increase compared to uniform simulations.}, language = {en} } @misc{WeiserChegini, author = {Weiser, Martin and Chegini, Fatemeh}, title = {Higher-order time integration using spectral deferred correction method (SDC) in a cell by cell discretization of cardiac excitation}, doi = {10.35097/716}, abstract = {This C++ code implements a cell-by-cell model of cardiac excitation using a piecewise-continuous finite element discretization and spectral deferred correction time stepping. The code is based on the Kaskade 7 finite element toolbox and forms a prototype for the µCarp code to be implemented in the Microcard project.}, language = {en} }