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292 results on '"Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC"'

151. Stochastic spontaneous calcium release events and sodium channelopathies promote ventricular arrhythmias

Author

Yohannes Shiferaw, Edward J. Vigmond, Fernando O. Campos, Gernot Plank, Deutsches Herzzentrum Berlin, Medical University Graz, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), European Space Research and Technology Centre (ESTEC), European Space Agency (ESA), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], and Agence Spatiale Européenne = European Space Agency (ESA)

Subjects
0301 basic medicine, medicine.medical_specialty, Purkinje fibers, Sodium, Heart Ventricles, General Physics and Astronomy, chemistry.chemical_element, Action Potentials, 030204 cardiovascular system & hematology, Calcium, behavioral disciplines and activities, Purkinje Fibers, 03 medical and health sciences, 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Heart Conduction System, Internal medicine, medicine, Myocyte, Animals, Focus Issue: Complex Cardiac Dynamics, Computer Simulation, Myocytes, Cardiac, cardiovascular diseases, Mathematical Physics, Calcium metabolism, Stochastic Processes, business.industry, Applied Mathematics, Models, Cardiovascular, Statistical and Nonlinear Physics, Arrhythmias, Cardiac, Reentry, Ventricular Premature Complexes, Electrophysiology, 030104 developmental biology, medicine.anatomical_structure, chemistry, Cardiology, cardiovascular system, Channelopathies, Rabbits, Electrical conduction system of the heart, business
Abstract

International audience; Premature ventricular complexes (PVCs), the first initiating beats of a variety of cardiac arrhythmias, have been associated with spontaneous calcium release (SCR) events at the cell level. However, the mechanisms underlying the degeneration of such PVCs into arrhythmias are not fully understood. The objective of this study was to investigate the conditions under which SCR-mediated PVCs can lead to ventricular arrhythmias. In particular, we sought to determine whether sodium (Na+) current loss-of-function in the structurally normal ventricles provides a substrate for unidirectional conduction block and reentry initiated by SCR-mediated PVCs. To achieve this goal, a stochastic model of SCR was incorporated into an anatomically accurate compute model of the rabbit ventricles with the His-Purkinje system (HPS). Simulations with reduced Na+ current due to a negative-shift in the steady-state channel inactivation showed that SCR-mediated delayed afterdepolarizations led to PVC formation in the HPS, where the electrotonic load was lower, conduction block, and reentry in the 3D myocardium. Moreover, arrhythmia initiation was only possible when intrinsic electrophysiological heterogeneity in action potential within the ventricles was present. In conclusion, while benign in healthy individuals SCR-mediated PVCs can lead to life-threatening ventricular arrhythmias when combined with Na+ channelopathies.

Published
2017

152. On the identification of multiple space dependent ionic parameters in cardiac electrophysiology modelling

Author

ABIDI, Yassine, BELLASSOUED, Mourad, MAHJOUB, Moncef, ZEMZEMI, Nejib, Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] (LR-LAMSIN-ENIT), Ecole Nationale d'Ingénieurs de Tunis (ENIT), Université de Tunis El Manar (UTM)-Université de Tunis El Manar (UTM), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], INRIA, Epicard, LIRIMA, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Lipschitz stability estimate, cardiac electrophysiology modelling, Quantitative Biology::Neurons and Cognition, Quantitative Biology::Tissues and Organs, Physics::Medical Physics, ionic parameters identification, Carleman estimate, monodomain system, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Hodgkin-Huxley model
Abstract

In this paper, we consider the inverse problem of space dependent multiple ionic parameters identification in cardiac electrophysiology modelling from a set of observations. We use the monodomain system known as a state-of-the-art model in cardiac electrophysiology and we consider a general Hodgkin-Huxley formalism to describe the ionic exchanges at the microscopic level. This formalism covers many physiological transmembrane potential models including those in cardiac electrophysiology. Our main result is the proof of the uniqueness and a Lipschitz stability estimate of ion channels conductance parameters based on some observations on an arbitrary subdomain. The key idea is a Carleman estimate for a parabolic operator with multiple coefficients and an ordinary differential equation system.

Published
2017

153. Numerical Analysis of a Finite Element Method for an Optimal Control of Bidomain-bath Model

Author

Bendahmane, Mostafa, Chamakuri, Nagaiah, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences (OeAW), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
[SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Quantitative Biology::Tissues and Organs, Finite Element Method, First order optimality conditions, Cardiac electrophysiology, Weak solution, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Bidomain model, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Optimal control
Abstract

International audience; This work is concerned with the study of the convergence analysis for an optimal control of bidomain-bath model by using the finite element scheme. The bidomain-bath model equations describe the cardiac bioelectric activity at the tissue and bath volumes where the control acts at the boundary of the tissue domain. We establish the existence of the finite element scheme, and convergence of the unique weak solution of the direct bidomain-bath model. The convergence proof is based on deriving a series of a priori estimates and using a general L 2-compactness criterion. Moreover, the well-posedness of the adjoint problem and the first order necessary optimality conditions are shown. Comparing to the direct problem, the convergence proof of the adjoint problem is based on using a general L 1-compactness criterion. The numerical tests are demonstrated which achieve the successful cardiac defibrillation by utilizing less total current. Finally, the robustness of the Newton optimization algorithm is presented for different finer mesh geometries. 1. Introduction. The electrical behavior of the cardiac tissue surrounded by a nonconductive bath is described by a coupled partial and ordinary differential equations which are so called bidomain model equations [17, 22, 24]. The bidomain model equations consist of two parabolic partial differential equations (PDEs) which describe the dynamics of the intra and the extracellular potentials. The PDEs coupled with an ordinary differential equations which model the ionic currents associated with the reaction terms. Furthermore , an additional Poisson problem has to be solved when the cardiac tissue is immersed in a conductive fluid, e.g. tissue bath in an experimental context or a surrounding torso to model in vivo scenarios.

Published
2017

154. Inverse Problem of Electrocardiography: estimating the location of cardiac isquemia in a 3D geometry

Author

Chavez, C.E., Zemzemi, Nejib, Coudière, Yves, Alonso-Atienza, Felipe, Alvarez, Diegó, Universidad Carlos III de Madrid [Madrid] (UC3M), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), LIRIMA, Epicard, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Electrocardiography Imaging, Quantitative Biology::Tissues and Organs, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Inverse Problem
Abstract

International audience; The inverse problem in cardiology (IPC) has been formulated in different ways in order to non invasively obtain valuable infor-mations about the heart condition. Most of the formulations solve the IPC under a quasistatic assumption neglecting the dynamic behavior of the electrical wave propagation in the heart. In this work we take into account this dynamic behavior by constraining the cost function with the monodomain model. We use an iterative algorithm combined with a level set formulation allowing us to localize an ischemic region in the heart. The method has been presented by Alvarez et al in [1] and [4], in which the authors developed a method for localize ischemic regions using a simple phenomenological model in a 2D cardiac tissue. In this work, we analyze the performance of this method in different 3D geometries. The inverse procedure exploits the spatiotemporal correlations contained in the observed data, which is formulated as a parametric adjust of a mathematical model that minimizes the misfit between the simulated and the observed data. We start by testing this method on two concentric spheres and then analyze the performance in a 3D real anatomical geometry. Both for analytical and real life geometries, numerical results show that using this algorithm we are capable of identifying the position and, in most of the cases, approximate the size of the ischemic regions.

Published
2017

155. An in-silico analysis of the effect of changing activation wavefronts on voltage amplitudes in patients with heart failure

Author

Nguyên, Uyên Châu, Potse, Mark, Vernooy, Kevin, Krause, Rolf, Auricchio, Angelo, Prinzen, Frits W., Maastricht University [Maastricht], Center for Computational Medicine in Cardiology [Lugano], Università della Svizzera italiana = University of Italian Switzerland (USI), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Faculty of Informatics [Lugano], This work was granted access to the HPC resources of TGCC and CINES under the allocation 2016-A0010307379 made by GENCI, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system
Abstract

International audience; Background: Voltage amplitudes are commonly used for the detection of non-excitable tissue, but may be influenced by the propagation of the activation wavefront with respect to the recording electrode. Objective: The aim of this study was to investigate the influence of changing activation wavefronts on unipolar voltageamplitudes (UnipV) in-silico using tailored models of patients with heart failure.Methods: Five patient-tailored bidomain models were created. Propagating wavefronts and electrograms were computedwith state-of-the-art techniques. Simulations were performed with the Propag-5 software on 2304 cores of the Bullxcluster "Curie" (TGCC, CEA, France). The baseline simulation was fitted on geometrical and electro-anatomic mappingdata during intrinsic rhythm from heart failure patients. Fibrosis was not incorporated in the simulations allowing only onesource of variation on UnipV. UnipV from simulations of single point right ventricular (RV) pacing and left ventricular (LV)pacing were compared at the LV endocardium and epicardium with the baseline simulation (intrinsic rhythm) using pairedanalyses.Results: A total of 26,872 paired endocardial (5,374±1,165 per patient) and 51,756 epicardial electrograms(10,351±2,068 per patient) were analysed. At baseline, three patients had a left bundle branch block (LBBB) and twopatients a non-specific intraventricular conduction defect. The correlation of UnipV between baseline and pacing waspoor for both endocardial (RV pacing: R=0.38, LV pacing: R=0.30) as well as epicardial UnipV (RV pacing: R=0.30, LVpacing: R=0.13). The mean absolute change in UnipV between baseline and RV and LV pacing was respectively 3.9±1.2mV and 3.9±1.2 mV (both 31% of baseline) for the endocardium, and 5.8±5.8 mV and 6.4±5.4 (36% and 41% ofbaseline) for the epicardium. RV pacing resulted on average in lower endocardial UnipV in 1 patient, and higher UnipV in4 patients, while lower epicardial UnipV were observed in 4 patients, and higher UnipV in 1 patient (all p

Published
2017

156. Fast simulation of standard 12-lead ECG and 3D ventricular activation

Author

Pezzuto, Simone, Kaľavský, Peter, Potse, Mark, Prinzen, Frits W., Auricchio, Angelo, Krause, Rolf, Faculty of Informatics [Lugano], Università della Svizzera italiana = University of Italian Switzerland (USI), Center for Computational Medicine in Cardiology [Lugano], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Maastricht University [Maastricht], Cardiocentro Ticino [Lugano], Universität Zürich [Zürich] = University of Zurich (UZH), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
[SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2017

157. Improving the Spatial Solution of Electrocardiographic Imaging: A New Regularization Parameter Choice Technique for the Tikhonov Method

Author

Yves Coudière, Rémi Dubois, Mark Potse, Judit Chamorro-Servent, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre de recherche Cardio-Thoracique de Bordeaux [Bordeaux] (CRCTB), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut National de la Santé et de la Recherche Médicale (INSERM), This study received financial support from the French Government under the 'In-vestments of the Future' program managed by the National Research Agency (ANR), Grant reference ANR-10-IAHU-04 and from the Conseil Régional Aquitaine as part of the project 'Assimilation de données en cancérologie et cardiologie'. This work was granted access to the HPC resources of TGCC under the allocation x2016037379 made by GENCI., Mihaela Pop, Graham A. Wright, ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Chamorro Servent, Judit, and Instituts Hospitalo-Universitaires - L'Institut de Rythmologie et modélisation Cardiaque - - LIRYC2010 - ANR-10-IAHU-0004 - IAHU - VALID

Subjects
Mathematical optimization, Correlation coefficient, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, 0206 medical engineering, [INFO.INFO-IM] Computer Science [cs]/Medical Imaging, Regularization perspectives on support vector machines, [MATH] Mathematics [math], 02 engineering and technology, 030204 cardiovascular system & hematology, Ill-posed problems, Regularization (mathematics), Tikhonov regularization, ill-posed problems, 03 medical and health sciences, u-curve, 0302 clinical medicine, Regularization, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Applied mathematics, discrete picard condition, [MATH]Mathematics [math], Mathematics, po- tentials, Electrocardiographic imaging, Backus–Gilbert method, Inverse problem, 020601 biomedical engineering, regularization, [SDV.IB.IMA] Life Sciences [q-bio]/Bioengineering/Imaging, Spiral wave, electrocardiographic imaging, inverse problem, Potentials
Abstract

Comunicació presentada a: The 9th International Conference Proceedings, FIMH 2017, celebrat de l'11 al 13 de juny de 2017 a Toronto, Canadà The electrocardiographic imaging (ECGI) inverse problem is highly ill-posed and regularization is needed to stabilize the problem and to provide a unique solution. When Tikhonov regularization is used, choosing the regularization parameter is a challenging problem. Mathematically, a suitable value for this parameter needs to fulfill the Discrete Picard Condition (DPC). In this study, we propose two new methods to choose the regularization parameter for ECGI with the Tikhonov method: i) a new automatic technique based on the DPC, which we named ADPC, and ii) the U-curve method, introduced in other fields for cases where the well-known L-curve method fails or provides an over-regularized solution, and not tested yet in ECGI. We calculated the Tikhonov solution with the ADPC and U-curve parameters for in-silico data, and we compared them with the solution obtained with other automatic regularization choice methods widely used for the ECGI problem (CRESO and L-curve). ADPC provided a better correlation coefficient of the potentials in time and of the activation time (AT) maps, while less error was present in most of the cases compared to the other methods. Furthermore, we found that for in-silico spiral wave data, the L-curve method over-regularized the solution and the AT maps could not be solved for some of these cases. U-curve and ADPC provided the best solutions in these last cases. This study received financial support from the French Government under the “Investments of the Future” program managed by the National Research 12 Agency (ANR), Grant reference ANR-10-IAHU-04 and from the Conseil Régional Aquitaine as part of the project “Assimilation de données en cancérologie et cardiologie”. This work was granted access to the HPC resources of TGCC under the allocation x2016037379 made by GENCI.

Published
2017

158. Image-Based Modeling of the Heterogeneity of Propagation of the Cardiac Action Potential. Example of Rat Heart High Resolution MRI

Author

Yves Coudière, Yves Bourgault, Anđela Davidović, Université de Bordeaux (UB), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], University of Ottawa [Ottawa], M. Pop, G. Wright, ANR-13-MONU-0004,HR-CEM,Modèles numériques haute résolution de l'électrophysiologie cardiaque(2013), ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
[SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, 0206 medical engineering, High resolution, Image processing, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, bidomain model, Optics, Nuclear magnetic resonance, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, 0101 mathematics, [MATH]Mathematics [math], heterogeneous conductivities, Wavefront, Physics, business.industry, fibrosis, Bidomain model, Depolarization, Cardiac action potential, Rat heart, 020601 biomedical engineering, image-based modelling, multiscale modelling, business, Image based
Abstract

International audience; In this paper we present a modified bidomain model, derived with homogenization technique from assumption of existence of diffusive inclusions in the cardiac tissue. The diffusive inclusions represent regions without electrically active myocytes, e.g. fat, fibrosis etc. We present the application of this model to a rat heart. Starting from high resolution (HR) MRI, geometry is built and meshed using image processing techniques. We perform a study on the effects of tissue heterogeneities induced with diffusive inclusions on the velocity and shape of the depolarization wavefront. We study several test cases with different geometries for diffusive inclusions, and we find that the velocity might be affected by 5% and up to 37% in some cases. Additionally, the shape of the wavefront is affected.

Published
2017

159. A Parameter Optimization to Solve the Inverse Problem in Electrocardiography

Author

Gwladys Ravon, Rémi Dubois, Mark Potse, Yves Coudière, Centre de recherche Cardio-Thoracique de Bordeaux [Bordeaux] (CRCTB), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut National de la Santé et de la Recherche Médicale (INSERM), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Plafrim, ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Ravon, Gwladys, and Instituts Hospitalo-Universitaires - L'Institut de Rythmologie et modélisation Cardiaque - - LIRYC2010 - ANR-10-IAHU-0004 - IAHU - VALID

Subjects
Mathematical optimization, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, 0206 medical engineering, Parameterized complexity, 02 engineering and technology, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, medicine, Repolarization, parameter optimization, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], ECGi, Mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Function (mathematics), Inverse problem, Torso, 020601 biomedical engineering, Action (physics), [SDV.MHEP.CSC] Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Parameter identification problem, Identification (information), [SDV.IB.IMA] Life Sciences [q-bio]/Bioengineering/Imaging, medicine.anatomical_structure, inverse problem, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Algorithm
Abstract

International audience; The main challenge of electrocardiography is to retrieve the best possible electrical information from body surface electrical potential maps. The most common methods reconstruct epicardial potentials. Here we propose a method based on a parameter identification problem to reconstruct both activation and repolarization times. The shape of an action potential (AP) is well known and can be described as a parameterized function. From the parameterized APs we compute the electrical potentials on the torso. The inverse problem is reduced to the identification of all the parameters. The method was tested on in silico and experimental data, for single ventricular pacing. We reconstructed activation and repolarization times with good accuracy accurate (CC between 0.71 and 0.9).

Published
2017

160. Very high order finite volume methods for cardiac electrophysiology

Author

Rodolphe Turpault, Yves Coudière, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Institut Polytechnique de Bordeaux (Bordeaux INP), ANR-13-MONU-0004,HR-CEM,Modèles numériques haute résolution de l'électrophysiologie cardiaque(2013), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Scheme (programming language), Finite volume method, Computer simulation, Computer science, Cardiac electrophysiology, Finite volumes, 010103 numerical & computational mathematics, Very high-order schemes, 01 natural sciences, 010101 applied mathematics, Computational Mathematics, Planar, Computational Theory and Mathematics, Modeling and Simulation, MOOD, Polygon mesh, 0101 mathematics, High order, Algorithm, computer, Spiral, Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], computer.programming_language
Abstract

International audience; Numerical simulation of the propagation of electrical signals in the heart is a very demanding application. In fact, very fine meshes and small time steps are currently required to capture the phenomena. In this paper, we propose and explore a very high-order scheme specifically designed for this application. Its numerical properties are detailed and the different choices on both the scheme’s definition and implementation are discussed and justified. Numerical results show the importance of considering very high-order schemes, even for classical tests such as the propagation of planar or spiral waves.

Published
2017

161. New approach for solving electrocardiography imaging inverse problem with missing data on the body surface

Author

Addouche, Mohammed, Bouarroudj, Nadra, Henry, Jacques, Jday, Fadhel, Zemzemi, Nejib, Université Aboubekr Belkaid - University of Belkaïd Abou Bekr [Tlemcen], Département de Mathématiques [Oran], Université d'Oran 1 Ahmed Ben Bella [Oran], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Umm Al-Qura University, Epicard, LIRIMA, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
missing data, incomplete data, optimal control, Factorization method, inverse problem, electrocardiography imaging, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; In this work, we provide a new mathematical formulation for the inverse problem in electrocardiography imaging. The novelty of this approach is that we take into account the missing measurements on the body surface. The electrocardiography imaging is formulated as a data completion problem for the Laplace equation. The Neumann boundary condition is given at the whole body surface. The difficulty comes from the fact that the Dirichlet boundary condition is only given on a part of the body surface. In order to construct the electrical potential on the heart surface, we use an optimal control approach where the unknown potential at the external boundary is also part of the control variables. We use the method of factorization of elliptic boundary value problems combined with the finite difference method. We illustrate the theoretical results by some numerical simulations in a cylindrical domain. We numerically study the effect of the size of the missing data zone on the accuracy of the inverse solution.

Published
2017

162. Evaluation of a Rapid Anisotropic Model for ECG Simulation

Author

Simone Pezzuto, Peter Kal'avský, Mark Potse, Frits W. Prinzen, Angelo Auricchio, Rolf Krause, Faculty of Informatics [Lugano], Università della Svizzera italiana = University of Italian Switzerland (USI), Center for Computational Medicine in Cardiology [Lugano], Institute of Measurement Science (IMS), Slovak Academy of Sciences (SAS), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Maastricht University [Maastricht], Cardiocentro Ticino [Lugano], Universität Zürich [Zürich] = University of Zurich (UZH), Swiss National Supercomputing Centre (CSCS) project IDs s397, s598, s669, Sciex-NMS fellowship 'CATION', project code 14.158, Theo Rossi de Montelera Foundation, Metis Foundation Sergio Mantegazza, Fidinam Foundation, Horten Foundation, PASC Initiative, Switzerland, Biologic Delivery Systems, a Division of Biosense Webster, a Johnson & Johnson Company, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), RS: CARIM - R2.08 - Electro mechanics, Fysiologie, CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], University of Zurich, and Pezzuto, Simone

Subjects
CARDIAC ELECTROPHYSIOLOGY, Computer science, Physiology, Interface (computing), 0206 medical engineering, 610 Medicine & health, 02 engineering and technology, 030204 cardiovascular system & hematology, 11171 Cardiocentro Ticino, lcsh:Physiology, Computational science, lead fields, ACTIVATION, 03 medical and health sciences, 2737 Physiology (medical), 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, eikonal model, Physiology (medical), Convergence (routing), EXCITATION, Methods, Graphics, MESH: Mathematical Computing, Simulation, Sequence, bidomain modeling, lcsh:QP1-981, Cardiac electrophysiology, Eikonal equation, ECG, Bidomain model, 1314 Physiology, electrophysiology, 020601 biomedical engineering, BIDOMAIN EQUATIONS, MESH: Cardiac Electrophysiology, TISSUE, Scalability, patient-specific modeling, HEART-FAILURE, OPTIMAL MONODOMAIN APPROXIMATIONS
Abstract

International audience; State-of-the-art cardiac electrophysiology models that are able to deliver physiologically motivated activation maps and electrocardiograms (ECGs) can only be solved on high-performance computing architectures. This makes it nearly impossible to adopt such models in clinical practice. ECG imaging tools typically rely on simplified models, but these neglect the anisotropic electric conductivity of the tissue in the forward problem. Moreover, their results are often confined to the heart-torso interface. We propose a forward model that fully accounts for the anisotropic tissue conductivity and produces the standard 12-lead ECG in a few seconds. The activation sequence is approximated with an eikonal model in the 3d myocardium, while the ECG is computed with the lead-field approach. Both solvers were implemented on graphics processing units and massively parallelized. We studied the numerical convergence and scalability of the approach. We also compared the method to the bidomain model in terms of ECGs and activation maps, using a simplified but physiologically motivated geometry and 6 patient-specific anatomies. The proposed methods provided a good approximation of activation maps and ECGs computed with a bidomain model, in only a few seconds. Both solvers scaled very well to high-end hardware. These methods are suitable for use in ECG imaging methods, and may soon become fast enough for use in interactive simulation tools.

Published
2017

163. Spatial Resolution Requirements for Accurate Identification of Drivers of Atrial Fibrillation

Author

Jennifer H Tweedy, Nicholas S. Peters, Jason D. Bayer, Prapa Kanagaratnam, Norman Qureshi, Fu Siong Ng, Phang Boon Lim, Chris D. Cantwell, Caroline H. Roney, Edward J. Vigmond, Imperial College London, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], British Heart Foundation, Rosetrees Trust, Medical Research Council (MRC), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Patient-Specific Modeling, computational modeling, Cardiac Catheterization, Cardiac & Cardiovascular Systems, Time Factors, reentry, Action Potentials, VELOCITY VECTOR-FIELDS, 030204 cardiovascular system & hematology, Cardiac Catheters, law.invention, Electrocardiography, 0302 clinical medicine, Heart Rate, law, Medicine, atrial fibrillation, ablation techniques, 1102 Cardiorespiratory Medicine and Haematology, Image resolution, Rotor (electric), Resolution (electron density), FOCAL IMPULSE, Models, Cardiovascular, Signal Processing, Computer-Assisted, Equipment Design, Reentry, 3. Good health, INSIGHTS, Identification (information), ComputingMethodologies_DOCUMENTANDTEXTPROCESSING, CONVENTIONAL ABLATION, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Electrophysiologic Techniques, Cardiac, Cardiology and Cardiovascular Medicine, Life Sciences & Biomedicine, arrhythmias, cardiac, Context (language use), Stability (probability), MECHANISMS, PERSISTENT, 03 medical and health sciences, ROTOR MODULATION, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Heart Conduction System, Predictive Value of Tests, Physiology (medical), Humans, ELIMINATION, Simulation, Wavefront, Science & Technology, business.industry, Reproducibility of Results, 1103 Clinical Sciences, Pattern recognition, Original Articles, arrhythmias, cardiac, MODEL, DOMINANT FREQUENCY, Cardiovascular System & Hematology, 1116 Medical Physiology, Cardiovascular System & Cardiology, rotor, Artificial intelligence, business, 030217 neurology & neurosurgery
Abstract

Supplemental Digital Content is available in the text., Background— Recent studies have demonstrated conflicting mechanisms underlying atrial fibrillation (AF), with the spatial resolution of data often cited as a potential reason for the disagreement. The purpose of this study was to investigate whether the variation in spatial resolution of mapping may lead to misinterpretation of the underlying mechanism in persistent AF. Methods and Results— Simulations of rotors and focal sources were performed to estimate the minimum number of recording points required to correctly identify the underlying AF mechanism. The effects of different data types (action potentials and unipolar or bipolar electrograms) and rotor stability on resolution requirements were investigated. We also determined the ability of clinically used endocardial catheters to identify AF mechanisms using clinically recorded and simulated data. The spatial resolution required for correct identification of rotors and focal sources is a linear function of spatial wavelength (the distance between wavefronts) of the arrhythmia. Rotor localization errors are larger for electrogram data than for action potential data. Stationary rotors are more reliably identified compared with meandering trajectories, for any given spatial resolution. All clinical high-resolution multipolar catheters are of sufficient resolution to accurately detect and track rotors when placed over the rotor core although the low-resolution basket catheter is prone to false detections and may incorrectly identify rotors that are not present. Conclusions— The spatial resolution of AF data can significantly affect the interpretation of the underlying AF mechanism. Therefore, the interpretation of human AF data must be taken in the context of the spatial resolution of the recordings.

Published
2017

164. Virtual electrodes around anatomical structures and their roles in defibrillation

Author

Connolly, Adam, Vigmond, Edward, Bishop, Martin, King‘s College London, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
Physiology, Science, Parabolas, Electric Countershock, Geometry, Surgical and Invasive Medical Procedures, Membrane Potential, Electricity, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Medicine and Health Sciences, Humans, Electrodes, Curvature, Functional Electrical Stimulation, Physics, Myocardium, Electric Conductivity, Biology and Life Sciences, Heart, Models, Theoretical, Body Fluids, Electrophysiology, Blood, Electric Field, Physical Sciences, Cardiovascular Anatomy, Medicine, Depolarization, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Anatomy, Mathematics, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology, Research Article
Abstract

BackgroundVirtual electrodes from structural/conductivity heterogeneities are known to elicit wavefront propagation, upon field-stimulation, and are thought to be important for defibrillation. In this work we investigate how the constitutive and geometrical parameters associated with such anatomical heterogeneities, represented by endo/epicardial surfaces and intramural surfaces in the form of blood-vessels, affect the virtual electrode patterns produced.Methods and resultsThe steady-state bidomain model is used to obtain, using analytical and numerical methods, the virtual electrode patterns created around idealized endocardial trabeculations and blood-vessels. The virtual electrode pattern around blood-vessels is shown to be composed of two dominant effects; current traversing the vessel surface and conductivity heterogeneity from the fibre-architecture. The relative magnitudes of these two effects explain the swapping of the virtual electrode polarity observed, as a function of the vessel radius, and aid in the understanding of the virtual electrode patterns predicted by numerical bidomain modelling. The relatively high conductivity of blood, compared to myocardium, is shown to cause stronger depolarizations in the endocardial trabeculae grooves than the protrusions.ConclusionsThe results provide additional quantitative understanding of the virtual electrodes produced by small-scale ventricular anatomy, and highlight the importance of faithfully representing the physiology and the physics in the context of computational modelling of field stimulation.

Published
2017

165. Interplay among distinct Ca 2+ conductances drives Ca 2+ sparks/spontaneous transient outward currents in rat cerebral arteries

Author

Anders Nygren, Ahmed M. Hashad, Donald G. Welsh, Kamran Bigdely-Shamloo, Sean M. Wilson, Jose L. Puglisi, Monica Romero, Edward J. Vigmond, Osama F. Harraz, Neil Mazumdar, University of Calgary, University of Western Ontario (UWO), Loma Linda University, University of Vermont [Burlington], California Northstate University (CNSU), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], School of Informatics [Edimbourg], University of Edinburgh, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
0301 basic medicine, Physiology, Myocytes, Smooth Muscle, Cerebral arteries, TRPV Cation Channels, Nanotechnology, cerebral arteries, Cardiovascular, Muscle, Smooth, Vascular, Sodium-Calcium Exchanger, Rats, Sprague-Dawley, 03 medical and health sciences, Ca2+ spark, BKCa channels, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Animals, Myocyte, Calcium Signaling, Cells, Cultured, Calcium signaling, Sodium-calcium exchanger, Voltage-dependent calcium channel, Chemistry, Conductance, Depolarization, Rats, Electrophysiology, 030104 developmental biology, Biophysics, Female, Calcium Channels, Ca2+ channels
Abstract

Ca2+ sparks are generated in a voltage dependent manner to initiate spontaneous transient outward currents (STOC), events that moderate arterial constriction. In this study, we defined the mechanisms by which membrane depolarization increases Ca2+ sparks and subsequent STOC production. Using perforated patch clamp electrophysiology and rat cerebral arterial myocytes, we monitored STOC in the presence and absence of agents that modulate Ca2+ entry. Beginning with CaV3.2 inhibition, Ni2+ was shown to decrease STOC frequency in cells held at hyperpolarized (−40 mV) but not depolarized (−20 mV) voltages. In contrast, nifedipine, a CaV1.2 inhibitor, markedly suppressed STOC frequency at −20 mV but not −40 mV. These findings aligned with the voltage-dependent profiles of L- and T-type Ca2+ channels. Furthermore, computational and experimental observations illustrated that Ca2+ spark production is intimately tied to the activity of both conductances. Intriguingly, this study observed residual STOC production at depolarized voltages that was independent of CaV1.2 and CaV3.2. This residual component was insensitive to TRPV4 channel modulation and was abolished by Na+/Ca2+ exchange blockade. In summary, our work highlights that the voltage-dependent triggering of Ca2+ sparks/STOCs is not tied to a single conductance but rather reflects an interplay among multiple Ca2+ permeable pores with distinct electrophysiological properties. This integrated orchestration enables smooth muscle to grade Ca2+ spark/STOC production and thus precisely tune negative electrical feedback. This article is protected by copyright. All rights reserved

Published
2017

166. A conduction velocity adapted eikonal model for electrophysiology problems with re-excitability evaluation

Author

Cesare Corrado, Nejib Zemzemi, King‘s College London, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
Scale (ratio), Computer science, Mitchell And Schaeffer model, Conduction velocity, 0206 medical engineering, Velocity, Action Potentials, Health Informatics, 02 engineering and technology, 030204 cardiovascular system & hematology, Conduction, 03 medical and health sciences, 0302 clinical medicine, Heart Conduction System, Dijkstra, Radiology, Nuclear Medicine and imaging, Variable (mathematics), Computational model, Clinical time scale, Radiological and Ultrasound Technology, Computer simulation, Series (mathematics), Eikonal equation, Cardiac electrophysiology, Multi-front eikonal model, Heart, Dijkstra algorithm, Models, Theoretical, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 020601 biomedical engineering, Computer Graphics and Computer-Aided Design, Algorithm, Catheter Ablation, Computer Vision and Pattern Recognition, Cardiac Electrophysiology, Dijkstra's algorithm, Algorithms
Abstract

International audience; Computational models of heart electrophysiology achieved a considerable interest in the medical community as they represent a novel framework for the study of the mechanisms underpinning heart pathologies. The high demand of computational resources and the long computational time required to evaluate the model solution hamper the use of detailed computational models in clinical applications. In this paper, we present a multi-front eikonal algorithm that adapts the conduction velocity (CV) to the activation frequency of the tissue substrate. We then couple the eikonal new algorithm with the Mitchell-Schaeffer (MS) ionic model to determine the tissue electrical state. Compared to the standard eikonal model, this model introduces three novelties: first, it evaluates the local value of the transmembrane potential and of the ionic variable solving an ionic model; second, it computes the action potential duration (APD) and the diastolic interval (DI) from the solution of the MS model and uses them to determine if the tissue is locally re-excitable; third, it adapts the CV to the underpinning electrophysiological state through an analytical expression of the CV restitution and the computed local DI. We conduct series of simulations on a 3D tissue slab and on a realistic heart geometry and compare the solutions with those obtained solving the monodomain equation. Our results show that the new model is significantly more accurate than the standard eikonal model. The proposed model enables the numerical simulation of the heart electrophys-iology on a clinical time scale and thus constitutes a viable model candidate for computer-guided radio-frequency ablation.

Published
2017

167. Convergence of a cartesian method for elliptic problems with immersed interfaces

Author

Weynans, Lisl, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), CPU, INRIA Bordeaux, Univ. Bordeaux, Memphis, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
Elliptic problem, Méthode cartésienne, Fonction de Green discrète, Discrete Green’s function, Inconnues sur l’interface, Interface unknowns, Finite-differences, Cartesian method, Interface discontinuity, Discontinuité au travers de l’interface, Différences finies, Convergence, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Problème elliptique
Abstract

We study in this report the convergence of a Cartesian method for elliptic problems with immersed interfaces that was presented in a previous paper. This method is based on additional unknowns located on the interface, used to express the jump conditions across the interface and discretize the elliptic operator in each subdomain separately. It is numerically second-order accurate in L¥-norm. This paper is a step toward the convergence proof of this method. We prove the convergence of the method in two cases: the original second-order method in one dimension, and a first-order version in two dimensions. The proof of convergence takes advantage of a discrete maximum principle to obtain estimates on the coefficients of the inverse matrix. More precisely, we obtain estimates for the sums of the coefficients of several blocks ofthe inverse matrix. Associated to the consistency error, which has different leading orders throughout the domain, these estimates lead to the convergence results.; Nous étudions dans ce rapport la convergence d’une méthode sur grille cartésienne pourdes problèmes elliptiques avec des interfaces immergées, introduite dans un article précédent. Cette méthode repose sur l’utilisation d’inconnues supplémentaires situées sur l’interface, qui servent à discrétiser séparémentl’opérateur elliptique dans chaque sous-domaine et à exprimer avec une précision suffisante les conditionsde saut au travers de l’interface. Il a été montré numériquement que cette méthode converge àl’ordre deux en norme L∞. Cet article est un pas en avant vers la preuve de la convergence de cetteméthode. En effet, nous prouvons la convergence dans deux cas: celui de la méthode originale en unedimension, et celui d’une version à l’ordre un, mais en deux dimensions. La preuve de convergence faitappel à des fonctions de Green discrètes et tire profit d’un principe du maximum discret pour obtenir desestimations des coefficients de la matrice inverse.

Published
2017

168. Efficient computation of electrograms and ECGs in human whole heart simulations using a reaction-eikonal model

Author

Gernot Plank, Martin J. Bishop, Steven A. Niederer, Aurel Neic, Anton J. Prassl, Fernando O. Campos, Edward J. Vigmond, Medical University Graz, Deutsches Herzzentrum Berlin, King‘s College London, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Karl-Franzens-Universität [Graz, Autriche], Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], and Karl-Franzens-Universität Graz

Subjects
Physics and Astronomy (miscellaneous), Computer science, Computation, 0206 medical engineering, Cardiac electrophysiology, Electrical activation and repolarization, 02 engineering and technology, 030204 cardiovascular system & hematology, Machine learning, computer.software_genre, Article, Rendering (computer graphics), Personalization, 03 medical and health sciences, 0302 clinical medicine, High fidelity, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Eikonal model, Numerical Analysis, Modality (human–computer interaction), business.industry, Eikonal equation, Applied Mathematics, Perspective (graphical), Bidomain model, 020601 biomedical engineering, Computer Science Applications, Computational Mathematics, Modeling and Simulation, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Artificial intelligence, business, computer
Abstract

International audience; Anatomically accurate and biophysically detailed bidomain models of the human heart have proven a powerful tool for gaining quantitative insight into the links between electrical sources in the myocardium and the concomitant current flow in the surrounding medium as they represent their relationship mechanistically based on first principles. Such models are increasingly considered as a clinical research tool with the perspective of being used, ultimately, as a complementary diagnostic modality. An important prerequisite in many clinical modeling applications is the ability of models to faithfully replicate potential maps and electrograms recorded from a given patient. However, while the personalization of electrophysiology models based on the gold standard bidomain formulation is in principle feasible, the associated computational expenses are significant, rendering their use incompatible with clinical time frames. In this study we report on the development of a novel computationally efficient reaction-eikonal (R-E) model for modeling extracellular potential maps and electrograms. Using a biventricular human electrophysiology model, which incorporates a topologically realistic His-Purkinje system (HPS), we demonstrate by comparing against a high-resolution reaction-diffusion (R-D) bidomain model that the R-E model predicts extracellular potential fields, electrograms as well as ECGs at the body surface with high fidelity and offers vast computational savings greater than three orders of magnitude. Due to their efficiency R-E models are ideally suitable for forward simulations in clinical modeling studies which attempt to personalize electrophysiological model features.

Published
2017

169. An asymptotic two-layer monodomain model of cardiac electrophysiology in the atria: derivation and convergence *

Author

Simon Labarthe, Yves Coudière, Jacques Henry, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Région Aquitaine, ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and ANR-10-IAHU-04/10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010)

Subjects
Asymptotic analysis, surface model, Cardiac electrophysiology, Applied Mathematics, Quantitative Biology::Tissues and Organs, Mathematical analysis, Physics::Medical Physics, Two layer, Geometry, 030204 cardiovascular system & hematology, atrial model, 01 natural sciences, Manifold, cardiac modeling, 010101 applied mathematics, 03 medical and health sciences, asymptotic analysis, 0302 clinical medicine, Dimensional reduction, Convergence (routing), [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], AMS subject classifications 92C30 - 92C50 - 35Q92, 0101 mathematics, Monodomain model, Mathematics
Abstract

Research Report] RR-8593, INRIA. 2014, pp.32.; International audience; We investigate a dimensional reduction problem of a reaction-diffusion system related to cardiac electrophysiology modeling in the atria. The atrial tissues are very thin. The physical problem is then routinely stated on a two-dimensional manifold. However, some electrophysiological heterogeneities are located through the thickness of the tissue. Despite their biomedical significance, the usual dimensional reduction techniques tend to average and erase their influence on the two-dimensional propagation. We introduce a two-dimensional model with two coupled superimposed layers that allows us to take into account three-dimensional phenomena, but retains a reasonable computational cost. We present its mathematical derivation, show its convergence toward the three-dimensional model, and check numerically its convergence speed.

Published
2017

170. Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology

Author

Charlie Douanla Lontsi, Charles Pierre, Yves Coudière, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), This work was supported by the ANR, INRIA, the Lyric and the CNRS, ANR-13-MONU-0004,HR-CEM,Modèles numériques haute résolution de l'électrophysiologie cardiaque(2013), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), and This work was supported by the ANR, Inria, LIRYC (grant ANR-10-IAHU-04), and CNRS.

Subjects
Cardiac electrophysiology, Numerical Analysis (math.NA), 65L04, 65L06, 65L20, 65L99, Exponential integrator, stiff equations, Exponential function, Time stepping, explicit high-order multistep methods, Integrator, FOS: Mathematics, Dahlquist stability, Applied mathematics, Mathematics - Numerical Analysis, stability and convergence, High order, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Analysis, exponential integrators, Mathematics
Abstract

International audience; To address the issues of stability and accuracy for reaction-diffusion equations, the development of high order and stable time-stepping methods is necessary. This is particularly true in the context of cardiac electrophysiology, where reaction-diffusion equations are coupled with stiff ODE systems. Many research have been led in that way in the past 15 years concerning implicit-explicit methods and exponential integrators. In 2009, Perego and Veneziani proposed an innovative time-stepping method of order 2. In this paper we present the extension of this method to the orders 3 and 4 and introduce the Rush-Larsen schemes of order k (shortly denoted RL_k). The RL_k schemes are explicit multistep exponential integrators. They display a simple general formulation and an easy implementation. The RL_k schemes are shown to be stable under perturbation and convergent of order k. Their Dahlquist stability analysis is performed. They have a very large stability domain provided that the stabilizer associated with the method captures well enough the stiff modes of the problem. The RL_k method is numerically studied as applied to the membrane equation in cardiac electrophysiology. The RL k schemes are shown to be stable under perturbation and convergent oforder k. Their Dahlquist stability analysis is performed. They have a very large stability domain provided that the stabilizer associated with the method captures well enough the stiff modes of the problem. The RL k method is numerically studied as applied to the membrane equation in cardiac electrophysiology.

Published
2017
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171. Modélisation mathématique multi-échelle des hétérogénéités structurelles en électrophysiologie cardiaque

Author

DAVIDOVIĆ, Andjela, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Université de Bordeaux, Yves Coudière, Clair Poignard, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Magali Ribot [Président], Piero Colli Franzone [Rapporteur], Maxime Sermesant [Rapporteur], Muriel Boulakia, Pierre Jais, Coudière, Yves, Poignard, Clair, Ribot, Magali, Colli Franzone, Piero, Sermesant, Maxime, Boulakia, Muriel, and Jais, Pierre

Subjects
Homogenization, Électrophysiologie cardiaque, Modélisation multi-échelle, Asymptotic analysis, Jonctions communicantes, Modélisation basée sur des images, Cardiac electrophysiology, Modèle bidomaine, Analyse asymptotique, Bidomain model, Two-scale convergence, Image-based modelling, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Homogénéisation, Convergence à deux échelles, Numerical simulations, Multi-scale modelling, Gap junctions, Simulations numériques
Abstract

In this thesis we addressed two problems in mathematical modelling of propagation of electrical signals in the heart: tissue scale propagation with presence of tissue heterogeneities and cell scale propagation with non-linear gap junctions. Diffusive inclusions. The standard model used in cardiac electrophysiology is the bidomain model. It is an averaged model derived from the microscopic properties of the tissue.The bidomain model assumes that the electrically active myocytes are present uniformly everywhere in the heart. While this is a reasonable assumption for healthy hearts, it fails insome pathological cases where significant changes in the tissue structure occur, for examplein ischaemic and rheumatic heart disease, inflammation, hypertrophy, or infarction. These tissue heterogeneities are often taken into account through an ad-hoc tuning of model parameters. The first aim of this thesis consisted in generalizing the bidomain equations to the case of structural heart diseases.We assumed a periodic alternation of healthy (bidomain model) and altered (diffusive inclusion) tissue patches. Such a model may be simulated directly, at the high computational cost of a very fine discretisation. Instead we derived a homogenized model at the macroscopic scale, using a rigorous two-scale analysis. We recovered a bidomain-type model with modified conductivity coefficients, and performed a 2D numerical verificationof the convergence of the microscopic model towards the homogenized one.In the second part we quantified the effects of different shapes and sizes of diffusive inclusions on the effective conductivity coefficients and their anisotropy ratios in 2D and3D. Additionally, we ran simulations on 2D patches of tissue with modified conductivity coefficients. We observed changes in the propagation velocity as well as in the shape of the depolarization wave-front.In the third part, based on high-resolution MR images of a rat heart we simulated 3D propagations with the homogenized model. Using image analysis software tools we assessed the structural properties of the tissue, that we used afterwards as parameters inthe homogenized model. Non-linear gap junctions. In the last part of this thesis, we studied the effects of nonlineargap junction channels on the signal propagation at the cell scale. In existing models, the gap junction channels, if modelled, are assumed to have a linear behaviour, while from experimental data we know that they have a time- and voltage-dependent non-linear behaviour. Firstly, we stated a non-linear 0D model for the gap junctional current, and secondly fitted the model to available experimental data. Finally, we proposed a 2D mathematical model that describes the electrical interaction of cardiac myocytes on the cell scale. It accounts for the gap junctional current as "the direct link" between the adjacent cells.; Dans cette thèse, nous avons abordé deux problèmes de modélisation mathématique pour la propagation des signaux électriques cardiaques : la propagation à l’échelle tissulaire en présence d’hétérogénéités et la propagation à l’échelle cellulaire avec des jonctions communicantes non linéaires. Inclusions diffusives. Le modèle standard utilisé en électrocardiologie est le modèle bidomaine. Il est déduit par homogénéisation des propriétés microscopiques du tissu. Pour cela, on suppose que les myocytes électriquement actifs sont uniformément répartis dans le coeur. Bien que ce soit une hypothèse raisonnable pour des coeurs sains, ce n’est plus vrai dans certains cas pathologiques où des changements importants dans la structure tissulaire se produisent. C’est le cas, par exemple des maladies cardiaques ischémiques, rhumatismales et inflammatoires, de l’hypertrophie ou de l’infarctus. Ces hétérogénéités tissulaires sont souvent prises en compte à l’aide d’un ajustement ad hoc des paramètres du modèle. Le premier objectif de cette thèse consistait à généraliser les équations du modèle bidomaine au cas des pathologies cardiaques structurelles.Nous avons supposé une alternance périodique d’éléments de tissus sains (modèle bidomaine) et modifiées (inclusions diffusives). La simulation numérique directe d’un tel modèle nécessite une discrétisation très fine, et entraîne un coût de calcul élevé. Pour éviter cela, nous avons construit un modèle homogénéisé à l’échelle macroscopique en utilisant une analyse à deux échelles. Nous avons retrouvé un modèle de type bidomaine avec des coefficients de conductivité modifiés, dits effectifs. En complément, nous avons effectué une vérification numérique de la convergence du modèle microscopique vers celui homogénéisé, dans une situation bidimensionnelle.Dans la deuxième partie, nous avons quantifié les effets de différentes formes d’inclusions diffusives sur les coefficients de conductivité effectifs et leur anisotropie en 2D et 3D. De plus, nous avons effectué des simulations sur des domaines représentant des morceaux de tissu 2D avec ces coefficients de conductivité modifiés. Nous avons observé des changements de la vitesse de propagation et de la forme du front de l’onde de dépolarisation. Dans la troisième partie, nous avons simulé le modèle homogénéisé en 3D, à partir d’images par résonance magnétique (IRM) à haute résolution d’un coeur de rat. Nous avons évalué les propriétés structurelles du tissu en utilisant des outils d’analyse d’image.Nous avons ensuite utilisés ces évaluations pour construire les paramètres dans le modèle homogénéisé. Jonctions communicantes non linéaires. Dans la dernière partie de cette thèse, nous avons étudié les effets du comportement non linéaires des jonctions communicantes sur la propagation du signal à l’échelle cellulaire. Dans les modèles existants, les jonctions communicantes sont supposées avoir un comportement linéaire, lorsqu’elles sont modélisées.Cependant les données provenant des expériences montrent que ceux-ci ont un comportement non linéaire dépendant du temps et de la différence de potentiel entre cellules voisines. D’abord, nous avons présenté un modèle non linéaire 0D du courant dans les jonctions communicantes. Ensuite, nous avons recalé le modèle sur les données expérimentales.Enfin, nous avons proposé un modèle mathématique 2D qui décrit l’interaction électrique des myocytes cardiaques à l’échelle cellulaire. Ce modèle utilise le courant dans les jonctions communicantes comme une liaison directe entre des cellules adjacentes.

Published
2016

172. The effects of the diffusive inclusions in the bidomain model: theoretical and numerical study. Application to the rat heart

Author

Davidović, Anđela, Coudière, Yves, Poignard, Clair, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université de Bordeaux (UB), Modélisation Mathématique pour l'Oncologie (MONC), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux], UNICANCER-UNICANCER-Inria Bordeaux - Sud-Ouest, ANR-13-MONU-0004,HR-CEM,Modèles numériques haute résolution de l'électrophysiologie cardiaque(2013), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux]

Subjects
Rat heart, Cardiac Electrophisiology, Homogenisation, Bidomain model, [MATH]Mathematics [math], Multiscale Modeling
Abstract

International audience; The standard bidomain model is based on the fact that electrically active cardiomyocytes are present uniformly everywhere in the heart. While this is a reasonable assumption for healthy hearts, it fails in some pathological cases where significant alterations in the tissue structure occur, for example fibrosis in infarct scars, or due to ageing. The effects of the non-excitable regions, that we call the inclusions, are often taken into account through ad-hoc rough tuning of the model. In this work, we introduce a mathematically rigorous way to derive the modified model from a microscopic description of the inclusions. More precisely we show that both shape and volume fraction of the inclusions affect the conductivity tensors in the bidomain model. We develop a numerical toolkit for determining the modified conductivities, based on shape and size of the diffusive inclusions. We perform 2D and 3D numerical studies of the effects of the inclusions on the conductivities by testing several basic shapes for the inclusions and varying their volume fraction. We observe the change in the anisotropy ratios for both intracellular and extracellular conductivity tensors. Additionally, in some cases we observe the change in the principal direction of the propagation. Finally, we apply our model to a rat heart model desgined from HiResMRI. Using image analysis softwares we asses the structural properties of the tissue, that we use then as parameters in the modified model. Simulating both the standard and modified model in the whole heart, we observe the differences in the the signal propagation.

Published
2016

173. Propagation of two independent sources of uncertainty in the electrocardiography imaging inverse solution

Author

Najib Fikal, Nejib Zemzemi, Rajae Aboulaich, El Mahdi El Guarmah, Laboratoire d'Etudes et Recherche en Mathématiques Appliquées (LERMA), Ecole Mohammadia d'Ingénieurs (EMI), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), EPICARD, LIRIMA, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
Ill posed problem, Computer science, 0206 medical engineering, Inverse, Probability density function, 02 engineering and technology, 01 natural sciences, Electrocardiography imaging forward and inverse problems, medicine, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Applied mathematics, Stochastic finite elements, Boundary value problem, 0101 mathematics, Uncertainty quantification, Randomness, Stochastic control, Random field, Applied Mathematics, Mathematics Subject Classification. 65N20, 65N21, 65N22, 65N25, 65N30, 60H35, Torso, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 020601 biomedical engineering, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010101 applied mathematics, medicine.anatomical_structure, Modeling and Simulation, [SDV.IB]Life Sciences [q-bio]/Bioengineering, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

This study investigates the effects of the input parameter uncertainties (organ conductivities, boundary data, etc.) on the electrocardiography (ECG) imaging problem. These inputs are very important for the construction of the torso potential for the forward problem and for the non-invasive electrical potential on the heart surface in the case of the inverse problem. We propose a new stochastic formulation that allows us to combine both sources of errors. We formulate the forward and inverse stochastic problems by considering the input parameters as random fields and a stochastic optimal control formulation. In order to quantify multiple independent sources of uncertainties on the forward and inverse solutions, we attribute suitable probability density functions for each randomness source and apply stochastic finite elements based on generalized polynomial chaos method. The efficiency of this approach to solve the forward and inverse ECG problems and the usability to quantify the effect of organ conductivity and epicardial boundary data uncertainties in the torso are demonstrated by a number of numerical simulations on a two-dimensional computational mesh of a realistic torso geometry.

Published
2019

174. Analysis of the ECGI inverse problem solution with respect to the measurement boundary size and the distribution of noise

Author

Fadhel Jday, Mohammed Addouche, Jacques Henry, Nadra Bouarroudj, Nejib Zemzemi, Université Aboubekr Belkaid - University of Belkaïd Abou Bekr [Tlemcen], Département de Mathématiques [Oran], Université d'Oran 1 Ahmed Ben Bella [Oran], Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] (LR-LAMSIN-ENIT), Ecole Nationale d'Ingénieurs de Tunis (ENIT), Université de Tunis El Manar (UTM)-Université de Tunis El Manar (UTM), Umm Al-Qura University, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], LIRIMA, EPICARD, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
Mathematics Subject Classification. 12A34, 56B78, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, Boundary (topology), 01 natural sciences, 010305 fluids & plasmas, symbols.namesake, Eectrocardiography imaging, 0103 physical sciences, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, 0101 mathematics, Mathematics, Factorization method, Applied Mathematics, Mathematical analysis, Cauchy distribution, Inverse problem, Optimal control, Missing data, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Finite element method, 010101 applied mathematics, Modeling and Simulation, Dirichlet boundary condition, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Riccati equations
Abstract

International audience; In this work, we analyze the influence of adding a body surface missing data on the solution of the electrocardiographic imaging inverse problem. The difficulty comes from the fact that the measured Cauchy data is provided only on a part of the body surface and thus a missing data boundary is adjacent to a measured boundary. In order to construct the electrical potential on the heart surface, we use an optimal control approach where the unknown potential at the external boundary is also part of the control variables. We theoretically compare this case to the case where the Dirichlet boundary condition is given on the full accessible surface. We then compare both cases and based on the distribution of noise in the measurements, we conclude whether or not it is worth to use all the data. We use the method of factorization of elliptic boundary value problems combined with the finite element method. We illustrate the theoretical results by some numerical simulations in a cylindrical domain. We numerically study the effect of the size of the missing data zone on the accuracy of the inverse solution.

Published
2019

175. A Parallel Second Order Cartesian Method for Elliptic Interface Problems

Author

Marco Cisternino, Lisl Weynans, Dipartimento di Ingegneria Aeronautica e Spaziale [Torino] (DIASP), Politecnico di Torino = Polytechnic of Turin (Polito), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), PLAFRIM, Politecnico di Torino [Torino] (Polito), Modélisation, contrôle et calcul (MC2), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
Mathematical optimization, Physics and Astronomy (miscellaneous), Discretization, Interface (Java), 010103 numerical & computational mathematics, ACM: G.: Mathematics of Computing/G.1: NUMERICAL ANALYSIS/G.1.8: Partial Differential Equations/G.1.8.2: Finite difference methods, 01 natural sciences, Second order scheme, Domain (mathematical analysis), Computational science, law.invention, law, Cartesian method, Point (geometry), Cartesian coordinate system, 0101 mathematics, AMS subject classifications: 65N06, 65N12, 65Y05, Mathematics, Grid, 010101 applied mathematics, Elliptic operator, Interface unknowns, Elliptic interface problem, Transmission (telecommunications), ACM: G.: Mathematics of Computing/G.1: NUMERICAL ANALYSIS/G.1.8: Partial Differential Equations/G.1.8.1: Elliptic equations, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; We present in this paper a parallel Cartesian method to solve elliptic problems with complex immersed interfaces. This method is based on a finite difference scheme and second order accurate in the whole domain. We use a standard five point scheme for the discretization of the elliptic operator on all grid points, coupled with the discretization of transmission conditions across the interface. The originality of the method lies in the use of additional unknowns located on the interface, where the transmission conditions are imposed. We firstly describe the method itself and the details of its parallelization performed with the PETSc library. Then we present numerical validations in two dimensions, assorted with comparisons to other related methods, and a numerical study of the parallelized method.; Nous présentons dans ce rapport une méthode cartésienne parallèle pour résoudre des problèmes elliptiques avec des interfaces complexes. Cette méthode est basée sur un schéma aux différences finies et est d'ordre deux dans tout le domaine. Nous utilisons un schéma standart à cinq points pour la discrétisation de l'opérateur elliptique sur tous les points de grille, couplé à une discrétisation des conditions de transmission à travers l'interface. L'originalité de la méthode consiste en l'utilisation d'inconnues additionnelles situées sur l'interface, là où sont imposées les conditions de transmission. Nous décrivons d'abord la méthode elle-même et les détails de sa parallélisation réalisée avec la librairie PETSc. Puis nous présentons des validations numériques en deux dimensions, accompagnées de comparaisons avec d'autres méthodes du même type, et une étude numérique de sa version parallèle.

Published
2012

176. Sensitivity of the electrocardiographic forward problem to the heart potential measuement noise and conductivity uncertainties

Author

Aboulaich, Rajae, Fikal, Najib, Guarmah, El Mahdi, Zemzemi, Nejib, Laboratoire d'Etudes et Recherche en Mathématiques Appliquées (LERMA), Ecole Mohammadia d'Ingénieurs (EMI), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Epicard, LIRIMA, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
stochastic finite elements, stochastic Galerkin, uncertainty quantification, electrocardiographic forward problem, Physics::Medical Physics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], stochastic processes, polynomial chaos, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In this work we are interested in quantifying the conductivity and epicardial potential boundary data uncertainties for the forward problem of electrocardiography (ECG). Indeed these input data are very important for the computation of the torso potential and consequently for the computation of the ECG. We use a stochastic approach for two dimensional torso geometry. We attribute probability density functions for the various source of randomness, and apply stochastic finite elements based on generalized polynomial chaos method. This work is the first step in order to quantify the uncertainties in inverse problem, which the goal is to complete the epicardial data. The efficiency of this approach to solve the forward ECG problem and the usability to quantify the effect of organs conductivity and epicardial boundary data uncertainties in the torso are demonstrated through a number of numerical simulations on a 2D computational mesh of the torso geometry.

Published
2016

177. Identification of sources for the bidomain equation using topological gradient

Author

Lassoued, Jamila, Mahjoub, Moncef, Zemzemi, Nejib, Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] (LR-LAMSIN-ENIT), Ecole Nationale d'Ingénieurs de Tunis (ENIT), Université de Tunis El Manar (UTM)-Université de Tunis El Manar (UTM), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Epicard, LIRIMA, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
problème adjoint, Gradient topologique, Analyse de sensibilité, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Topological gradient, Modèle bidomaine, Bidomain model, Adjoint problem, Analysis sensibility, Electrophysiologie cardiaque, Cardiac electrophsiology, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; An approach for estimating electrical sources within the heart area from noninvasive measurements recorded on the outer surface of the thorax is proposed. The approach uses a topo-logical gradient method. This method consists in studying the behavior of a cost function during a disturbance within the domain. We show that our proposed approach based on the topological gradient method has actually been able to perfectly adapt to the identification of the source term for obtaining very interesting results, and a particularly low computational cost.; Une approche pour estimer les sources électriques dans le coeur à partir de mesures non invasives enregistrés sur la surface externe du thorax est proposé. L'approche est basé sur la méthode du gradient topologique. Cette méthode consiste à étudier le comportement d'une fonction coût au cours d'une perturbation dans le domaine. Nous montrons que notre approche proposée a effectivement été capable d'identifier le terme source et obtenir des résultats intéressants, et avec un coût de calcul particulièrement faible.

Published
2016

178. Possible improvements of the method of fundamental solution to solve the ECGI problem

Author

Chamorro-Servent, Judit, Bear, Laura, Duchateau, Josselin, Potse, Mark, Dubois, Rémi, Coudière, Yves, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Santé et de la Recherche Médicale (INSERM), Centre de recherche Cardio-Thoracique de Bordeaux [Bordeaux] (CRCTB), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut National de la Santé et de la Recherche Médicale (INSERM), This study received financial support from the French Government as part of the 'Investments of the Future' program managed by the National Research Agency (ANR), Grant reference ANR-10-IAHU-04 and from the Conseil Régional Aquitaine as part of the project 'Assimilation de données en cancérologie et cardiologie', ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Chamorro Servent, Judit, and Instituts Hospitalo-Universitaires - L'Institut de Rythmologie et modélisation Cardiaque - - LIRYC2010 - ANR-10-IAHU-0004 - IAHU - VALID

Subjects
[SPI]Engineering Sciences [physics], method of fundamental solutions, [SPI] Engineering Sciences [physics], boundary conditions, virtual sources, electrocardiographic imaging, [MATH] Mathematics [math], [MATH]Mathematics [math], ill-posedness
Abstract

International audience; Despite all the success of electrocardiographic imaging (ECGi), the understanding and treatment of many cardiac diseases is not feasible yet without an improvement of the inverse problem. A meshless method based on the method of fundamental solution (MFS) was adapted to ECGi. In the MFS, the potential is expressed as summation over a discrete set of virtual point sources placed outside of the domain of interest. This formulation yields to a linear system, which involves contributions of the Dirichlet and the homogenous Neumann (HN) conditions at torso surface in an equivalent manner. HN conditions requires accurate computation of the normals at the torso surface, and due to the meshing, non-physiological conditions are applied to the top, bottom of torso and arms. Finally, the virtual sources are placed by inflating and deflating the heart and torso surfaces with respect to the heart’s geometric center. However, for some heart-torso geometries, this geometrical center is a poor reference.First, we studied the effect of weighting the MFS objective function in consideration of the Dirichlet and HN conditions respectively. Second, we proposed a new distribution of torso sources by projecting for each electrode the closest heart’s point. Finally, we compared the solution from both modifications with the standard MFS one, using both in-silico and experimental data.A small quotient between the norms of the HN part of the MFS matrix and its respective Dirichlet part (~10-3) was found, indicating the negligibility of the HN conditions in the standard MFS method. Not including HN conditions in the reconstruction had significantly higher CCs (p

Published
2016

179. Integration of data and model in cardiac electrophysiology

Author

Juhoor, Mehdi, Fuentes, Marc, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Liryc, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
numerical simulation:cardiac imaging, [INFO]Computer Science [cs], cardiac electrophysiology, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; The Carmen team plans to build realistic numerical models of the electrical activity of the heart.To solve these models, the team is developing the numerical solver CEPS, an open source simulationpackage.Its purpose is to integrate a broad range of multiscale novel models in a generic extensible and efficient platform.Additionally, numerical solvers like CEPS require anatomical and distributed electrophysical information representing the geometrical domain and the parameters of a simulation.Building complete cardiac models directly from imaging data and expert knowledge is time-consuming and error-prone: specific expertise and multiple softwares are often needed to process data stemming from medical imaging into realistic meshes and parameter distribution.Furthermore, visualization and analysis of simulation results are performed in software that are not specific to cardiac applications.On the whole, this makes it difficult to confront numerical models to experimental data.The goal of the IDAM project is twofold:- ease the preprocess and postprocess stages of any cardiac numerical simulation;- improve the CEPS numerical solver to allow the integration of more complex models;To achieve this, we rely on MUSIC, the multimodal platform for cardiac imaging developed by the Imaging team at Liryc.By using the toolbox and pipeline architecture in MUSIC, we aim to streamline the workflow of a complete cardiac simulation: anatomical mesh generation from patient specific data, description of simulation parameters, running and analysing the simulations.

Published
2016

180. Front observer for data assimilation of electroanatomical mapping data for a numerical atrial model

Author

Gérard, A, Collin, Annabelle, Bayer, J, Frontera, A, Moireau, Philippe, Coudière, Yves, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Université de Bordeaux (UB), Modélisation Mathématique pour l'Oncologie (MONC), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux], UNICANCER-UNICANCER-Inria Bordeaux - Sud-Ouest, CHU Bordeaux [Bordeaux], Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux], École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
Data assimilation, Patient-specific method, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; The purpose of our work is to personalize an atrial model of the propagation of the action potential, based on electrical catheter data with the help of the data assimilation approach introduced in [Collin & Al, Journal of Computational Physics 2015]. The originality of the approach is to indroduce a Luenberger observer of a surface atrial model of the propagation which can pursue - like in classical Kalman filtering approach - the actual activation front reconstructed from catheter data. Moreover, this approach may account for the breakthrough of new activation fronts at anytime with an additional topological gradient term. In the present work, we adapt this approach to the bilayer surface atrial model of th propagation of action potentials [Labarthe & Al, Europace 2014], and evaluated for the first time on a real patient's dataset. First, the model was geometrically fit to the patient's data. A fiber architecture was added to the geometry. Then an initial electrophysiological state was guessed, and the model was run with the Luenberger filter for some catheter data acquired during a CARTO procedure. All along the simulation, the filter corrects the action potential so as to track CARTO local activation times, while preserving a biophysical behavior. With this technique, we are able to reconstruct smooth activation maps over the whole atrial surfaces. This promising technique may also allow to reconstruct velocity fields and directions, phase map and possibly give information on repolarization. This work results from a collaborative project carried out during a training session at CEMRACS 2016 in Marseille, Luminy.

Published
2016

181. Regional conduction slowing can explain inferolateral J waves and their attenuation by sodium channel blockers

Author

Potse, Mark, Meijborg, Veronique, Belterman, Charly, de Bakker, Jacques, Conrath, Chantal, Coronel, Ruben, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Academic Medical Center - Academisch Medisch Centrum [Amsterdam] (AMC), University of Amsterdam [Amsterdam] (UvA), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
[SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system
Abstract

International audience; J waves in inferolateral leads are associated with an increased risk for idiopathic ventricular fibrillation. The mechanism behind such J waves is unknown. A similarity with Brugada syndrome (BS) exists but while administration of sodium (Na) channel blockers increases J waves in BS it attenuates inferolateral J waves. We hypothesized that regionally reduced conduction velocity in the lateral wall can explain both inferolateral J waves and their attenuation by Na-channel blockers.METHODS The effects of Na-channel block, reduced coupling, and increased transient outward current were evaluated with computer simulations using a detailed model of the human heart and torso. As far as possible findings were backed up with experiments in explanted pig hearts.RESULTS Reduced Na current in lateral but not in other regions induced inferolateral J waves. Increased transient outward current and cellular uncoupling caused only subthreshold J-point elevations. Administration of Na-channel blockers deformed and prolonged the QRS complex, masking the inferolateral J waves.CONCLUSION Regionally reduced Na current can explain inferolateral J waves. The fact that the lateral region is normally late-activated is crucial for the development of J waves and may explain the special importance of the inferolateral leads. The proposed mechanism also explains attenuation of J waves by Na-channel blockers.

Published
2016

182. High order time-stepping methods for cardiac electrophysiology models

Author

Douanla Lontsi, Charlie, Coudière, Yves, Pierre, Charles, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH]Mathematics [math], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2016

183. Parameters estimation approach for the MEA/hiPSC-CM assays

Author

Bouyssier, Julien, Bendahmane, Mostafa, Coudière, Yves, Gerbeau, Jean-Frédéric, Pedron, Julien, Zitoun, Philippe, Zemzemi, Nejib, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), NOTOCORD Systems, ANR-13-LAB1-0007,CardioXcomp,Modélisation, simulation et traitement du signal en électrophysiologie cardiaque(2013), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Zemzemi, Nejib, Laboratoires communs organismes de recherche publics – PME/ETI - Modélisation, simulation et traitement du signal en électrophysiologie cardiaque - - CardioXcomp2013 - ANR-13-LAB1-0007 - LabCom - VALID, and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; We propose a mathematical approach for the analysis of drugs effects on the electrical activity of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) based on multi-electrode array (MEA) experiments. Our goal is to produce an in silico tool able to simulate drugs action in MEA/hiPSC-CM assays and to fit the drug model parameters to the experimental data. The electrical activity of the stem cells at the ion-channel level is modelled using the Paci et.al. (2013) transmembrane potential model. We use the bidomain model in order to describe the propagation of the electrical wave in the stem cells preparation. The field potential (FP) measured by the MEA is modeled by the extra-cellular potential of the bidomain equations. First, we propose a strategy allowing us to generate a FP in good agreement with the experimental data. Second, we introduce a drug/ion channels interaction based on a pore block model. We conduct different simulations for five drugs. Results show that the model reflects properly the main effects of these drugs on the FP. In order to estimate the parameters of the drug model, we define a cost function minimizing the distance between the simulated and the experimental FPs. We use an optimization procedure based on a gradient descent method where the cost function gradient is computed using an adjoint approach. Results, based on simulated observations, show that this procedure is able to estimate either the drug doze or its IC50 value.

Published
2016

184. Probìeme inverse en électrocardiographie : Théorie de la factorisation

Author

Moussitou, Ronald, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA, Université de nantes, Nejib.Zemzmi, Jacques Henry, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

National audience; Le problème inverse en électrocardiographie consiste à déterminer la cause du potentielélectrique gééeré sur la surface du torse. On cherche à relier l'activité électrique ducoeur à partir du potentiel qu'il génère au potentiel qui s'est propaée sur le thorax parconduction dans tout le torse. C'est un domaine de recherche en plein expansion et quia des nombreuses applications cliniques importantes (par exemples : aide aux cliniciensdans leurs diagnostiques d'arrhythmie cardiaque, aide aux chirurgiens en leur donnantdes informations supplémentaires avant les interventions).

Published
2016

185. Do we need to enforce the homogeneous Neumann condition on the torso for solving the inverse electrocardiographic problem?

Author

Judit Chamorro Servent, Bear, L., Duchateau, J., Potse, M., Dubois, R., Coudiere, Y., IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Centre de recherche Cardio-Thoracique de Bordeaux [Bordeaux] (CRCTB), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut National de la Santé et de la Recherche Médicale (INSERM), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SPI]Engineering Sciences [physics], [MATH]Mathematics [math]
Abstract

Robust calculations of the inverse electrocardiographic problem may require accurate specification of boundary conditions at the torso and cardiac surfaces. In particular, the numerical specification of the no-flux condition on the torso is difficult because surface normals must be computed, and because the torso may alternatively be considered infinitely far away from the heart. Using the method of fundamental solutions (MFS) proposed in [1], this boundary conditions can be taken into account in different manners. Specifically, the no-flux condition on the torso can be ignored, or weighted with respect to the Dirichlet boundary condition associated to the torso data, or can be strongly enforced through a saddle-point problem. In this article, we compare these approaches. In this work we provide a preliminary comparison of these different strategies. This study received financial support from the French Government as part of the “Investissements d’avenir” program managed by the National Research Agency (ANR), Grant reference ANR-10-IAHU-04 and from the Conseil R´egional Aquitaine as part of the project “Assimilation de donn´ees en canc´erologie et cardiologie”.

Published
2016

186. Epicardial Fibrosis Explains Increased Transmural Conduction in a Computer Model of Atrial Fibrillation

Author

Mark Potse, Ali Gharaviri, Ulrich Schotten, Angelo Auricchio, Rolf Krause, Sander Verheule, Center for Computational Medicine in Cardiology [Lugano], Università della Svizzera italiana = University of Italian Switzerland (USI), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Maastricht University [Maastricht], European Project: 261057,EC:FP7:HEALTH,FP7-HEALTH-2010-single-stage,EUTRAF(2010), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
medicine.medical_specialty, Materials science, Atrium (architecture), Fiber orientation, 0206 medical engineering, Atrial fibrillation, 02 engineering and technology, 030204 cardiovascular system & hematology, Atrial wall, Thermal conduction, medicine.disease, 020601 biomedical engineering, 03 medical and health sciences, 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Fibrosis, Internal medicine, medicine, Cardiology
Abstract

International audience; Introduction Recent work has shown that the transition from persistent to permanent AF in goats coincides with an increase in fibrosis in the outer millimeter of the atrial wall. Macroscopically this leads to reduced electrical conductivity orthogonal to the dominant fiber orientation. A causal relation has not been established yet. Our purpose was to test if epicardial fibrosis can explain the increased incidence of transmural conduction (breakthroughs), which is also observed in permanent AF. Methods We constructed a detailed geometry of the human atria including epicardial layer and all major endocardial bundle structures. The model also includes realistic one to three layers of fiber orientations, corresponding to their location in the atrium. Computer simulations were run with a mesh of 0.2 mm resolution and Courtemanche human atrial cell model. Epicardial fibrosis was modeled by assigning zero transverse conductivity to a random selection of model elements in the epicardial layer. Simulations were performed with 0, 50, and 70% affected elements. Results The numbers of waves, phase singularities, and breakthroughs (BTs) were quantified at different degrees of fibrotic tissue. Increase in the “fibrotic” volume from zero (Control) to moderate (50% Fibrotic), and severe (70% Fibrotic) increased both the number of waves and the number of phase singularities. Along with the increase in fibrosis, the endo-epicardial electrical activity dyssynchrony increased from 8.6% to 18.6%, and 38.4%. Fibrosis increased the incidence of BTs. Conclusion: This model is the first anatomical atrial model to display BTs, a common and conspicuous feature in experimental studies on AF. Epicardial fibrosis in this model increases the degree of endo-epicardial electrical activity dyssynchrony and the incidence of BTs, thus increasing the complexity of fibrillatory conduction. The model offers the opportunity to study transmural conduction, which frequently occurs during AF, in more detail.

Published
2016

187. Reduced Sodium Current in the Lateral Ventricular Wall Induces Inferolateral J-Waves

Author

Veronique Marlinde Frederica Meijborg, Mark Potse, Chantal E Conrath, Charly NW Belterman, Jacques MT De Bakker, Ruben Coronel, Academic Medical Center - Academisch Medisch Centrum [Amsterdam] (AMC), University of Amsterdam [Amsterdam] (UvA), Center for Computational Medicine in Cardiology [Lugano], Università della Svizzera italiana = University of Italian Switzerland (USI), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Support from Fundació Marató de TV3 grant (project 080632), Barcelona, Spain and from Fondation LeDucqgrant (ShapeHeart, project10801). This work was granted access to the HPC resources of IDRIS under the allocation x2015037379 made by GENCI., Cardiology, ACS - Amsterdam Cardiovascular Sciences, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
medicine.medical_specialty, conduction, Benign early repolarization, Physiology, early repolarization, 030204 cardiovascular system & hematology, lcsh:Physiology, 03 medical and health sciences, QRS complex, 0302 clinical medicine, Sodium channel blocker, depolarization, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Physiology (medical), Internal medicine, medicine, Repolarization, 030212 general & internal medicine, cardiovascular diseases, J wave, Original Research, Cardiac transient outward potassium current, sodium current, lcsh:QP1-981, Chemistry, Sodium channel, Depolarization, J-wave, Cardiology, cellular uncoupling
Abstract

International audience; Background: J-waves in inferolateral leads are associated with a higher risk for idiopathic ventricular fibrillation. We aimed to test potential mechanisms (depolarization or repolarization dependent) responsible for inferolateral J-waves. We hypothesized that inferolateral J-waves can be caused by regional delayed activation of myocardium that is activated late during normal conditions.Methods: Computer simulations were performed to evaluate how J-point elevation is influenced by reducing sodium current conductivity (GNa), increasing transient outward current conductivity (Gto), or cellular uncoupling in three predefined ventricular regions (lateral, anterior, or septal). Two pig hearts were Langendorff-perfused with selective perfusion with a sodium channel blocker of lateral or anterior/septal regions. Volume-conducted pseudo-electrocardiograms (ECG) were recorded to detect the presence of J-waves. Epicardial unipolar electrograms were simultaneously recorded to obtain activation times (AT).Results: Simulation data showed that conduction slowing, caused by reduced sodium current, in lateral, but not in other regions induced inferolateral J-waves. An increase in transient outward potassium current or cellular uncoupling in the lateral zone elicited slight J-point elevations which did not meet J-wave criteria. Additional conduction slowing in the entire heart attenuated J-waves and J-point elevations on the ECG, because of masking by the QRS. Experimental data confirmed that conduction slowing attributed to sodium channel blockade in the left lateral but not in the anterior/septal ventricular region induced inferolateral J-waves. J-waves coincided with the delayed activation.Conclusion: Reduced sodium current in the left lateral ventricular myocardium can cause inferolateral J-waves on the ECG.

Published
2016

188. Spatially Coherent Activation Maps for Electrocardiographic Imaging

Author

Rémi Dubois, Josselin Duchateau, Mark Potse, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Centre de recherche Cardio-Thoracique de Bordeaux [Bordeaux] (CRCTB), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut National de la Santé et de la Recherche Médicale (INSERM), Institut National de la Santé et de la Recherche Médicale (INSERM), Center for Computational Medicine in Cardiology [Lugano], Università della Svizzera italiana = University of Italian Switzerland (USI), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI Paris), Université Paris sciences et lettres (PSL), This work was granted access to the HPC resources of IDRIS under the allocation x2015037379 made by GENCI., Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Inverse problems, Computer science, 0206 medical engineering, Biomedical Engineering, 02 engineering and technology, 030204 cardiovascular system & hematology, Sensitivity and Specificity, 03 medical and health sciences, Electrocardiography, 0302 clinical medicine, Spatio-Temporal Analysis, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Heart Conduction System, Electronic engineering, Humans, Computer Simulation, Diagnosis, Computer-Assisted, Sequence, Cardiac electrophysiology, business.industry, Body Surface Potential Mapping, Models, Cardiovascular, Reproducibility of Results, Pattern recognition, 020601 biomedical engineering, Electrophysiology, Electrocardiographic imaging, Artificial intelligence, business, Algorithms
Abstract

Objective : Cardiac mapping is an important diagnostic step in cardiac electrophysiology. One of its purposes is to generate a map of the depolarization sequence. This map is constructed in clinical routine either by directly analyzing cardiac electrograms (EGMs) recorded invasively or an estimate of these EGMs obtained by a noninvasive technique. Activation maps based on noninvasively estimated EGMs often show artefactual jumps in activation times. To overcome this problem, we present a new method to construct the activation maps from reconstructed unipolar EGMs. Methods : On top of the standard estimation of local activation time from unipolar intrinsic deflections, we propose to mutually compare the EGMs in order to estimate the delays in activation for neighboring recording locations. We then describe a workflow to construct a spatially coherent activation map from local activation times and delay estimates in order to create more accurate maps. The method is optimized using simulated data and evaluated on clinical data from 12 different activation sequences. Results : We found that the standard methodology created lines of artificially strong activation time gradient. The proposed workflow enhanced these maps significantly. Conclusion : Estimating delays between neighbors is an interesting option for activation map computation in electrocardiographic imaging.

Published
2016

189. Theoretical and Numerical Study of Cardiac Electrophysiology Problems at the Microscopic Scale

Author

Bécue, Pierre-Elliott, Caro, Florian, Potse, Mark, Coudière, Yves, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Quantitative Biology::Tissues and Organs, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

International audience; The bidomain model efficiently represents macroscopic cardiac electrophysiology but neglects inhomogeneities on the cellular scale. Furthermore, it cannot represent gap junctions accurately. We introduce a microscopic model. We prove the existence of a solution of this model.

Published
2016

190. Decentralized Strategies for Ill Posed Inverse Problems

Author

Habbal, Abderrahmane, Kallel, Moez, Chamekh, Rabeb, Zemzemi, Nejib, Analysis and Control of Unsteady Models for Engineering Sciences (ACUMES), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] (LR-LAMSIN-ENIT), Ecole Nationale d'Ingénieurs de Tunis (ENIT), Université de Tunis El Manar (UTM)-Université de Tunis El Manar (UTM), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2016

191. Rapid estimation of 3D ventricular activation from electroanatomic mapping

Author

Pezzuto, Simone, Kalavsky, Peter, Potse, Mark, Regoli, François, Caputo, Maria Luce, Conte, Giulio, Moccetti, Tiziano, Prinzen, Frits W., Auricchio, Angelo, Krause, Rolf, Center for Computational Medicine in Cardiology [Lugano], Università della Svizzera italiana = University of Italian Switzerland (USI), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Cardiocentro Ticino [Lugano], Universität Zürich [Zürich] = University of Zurich (UZH), Maastricht University [Maastricht], Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
[SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system
Abstract

International audience; Purpose Heart failure patients are often affected by a ventricular conduction disorder. Accurate characterization of the tridimensional (3D) activation sequence of the ventricles is fundamental for an effective personalized therapy. Electroanatomical mapping provides the activation times at the endocardium, with limited coverage due to anatomical constraints. Our aim is to develop a robust tool to generate a complete 3D, biventricular activation map from a limited number of endocardial measurements.Method In 6 candidates to cardiac resynchronization therapy a high density endocardial activation map of the right and left ventricle was obtained. High resolution propagating activation was simulated in patient-tailored anatomical heart models using the anisotropic eikonal equation and realistic fiber orientation. Subsequently, the mean square error between the measured and simulated activation times was minimized by varying early activation site(s) and local anisotropic conduction velocities.Results. A close correlation was achieved between the simulated and measured activation time for a single patient (Panel A) while detailed 3D activation maps were achieved (panel B and C). In all cases, the optimal parameters were identified within few minutes and the full activation sequence was computed in less than 2 seconds. A 0.9 to 0.95 Pearson correlation between measured and simulated activation times was obtained in all cases. The mathematical formulation is flexible in terms of the number of activation sites and a possible delay between them, in order to mimic the presence of a partially working Purkinje network.Conclusion Our methodology is able to generate in a clinically affordable computational time (few minutes) reliable, patient-specific, fully volumetric activation map of both ventricles using a local workstation or a laptop.

Published
2016

192. Stability results for the parameter identification inverse problem in cardiac electrophysiology

Author

Nejib Zemzemi, Jamila Lassoued, Moncef Mahjoub, Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] (LR-LAMSIN-ENIT), Ecole Nationale d'Ingénieurs de Tunis (ENIT), Université de Tunis El Manar (UTM)-Université de Tunis El Manar (UTM), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Epicard, LIRIMA, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], and Equipe associée Epicard

Subjects
State variable, Carleman inequality, Parameter identification, stability result, Ionic parameters Submitted to: Inverse Problems, 01 natural sciences, Domain (mathematical analysis), Theoretical Computer Science, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, 0101 mathematics, Monodomain model, Mathematical Physics, Mathematics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Monodomain system, Ode, Inverse problem, Computer Science Applications, 010101 applied mathematics, Parameter identification problem, Mitchell-Schaeffer model, Ordinary differential equation, Signal Processing, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In this paper we prove a stability estimate of the parameter identification problem in cardiac electrophysiology modeling. We use the monodomain model which is a reaction diffusion parabolic equation where the reaction term is obtained by solving an ordinary differential equation. We are interested in proving the stability of the identification of the parameter τ in which is the parameter that multiplies the cubic term in the reaction term. The proof of the result is based on a new Carleman-type estimate for both the PDE and ODE problems. As a consequence of the stability result we prove the uniqueness of the parameter τ in giving some observations of both state variables at a given time t 0 in the whole domain and the PDE variable in a non empty open subset w 0 of the domain.

Published
2016

193. A Nash-game approach to solve the Coupled problem of conductivity identification and data completion

Author

Chamekh, Rabeb, Habbal, Abderrahmane, Kallel, Moez, Zemzemi, Nejib, Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] (LR-LAMSIN-ENIT), Ecole Nationale d'Ingénieurs de Tunis (ENIT), Université de Tunis El Manar (UTM)-Université de Tunis El Manar (UTM), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Epicard, LIRIMA, Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
conductivity identification, Computer Science::Computer Science and Game Theory, data completion, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Nash games
Abstract

International audience; We consider the identification problem of the conductivity coefficient for an elliptic operator using an incomplete over-specified measurements on the surface (Cauchy data). Data completion problems are widely discussed in literature by several methods (see, e.g., for control and game oriented approaches [1, 2], and references therein). The identification of conductivity and permit-tivity parameters has also been investigated in many studies (see, e.g., [3, 4]). In this work, our purpose is to extend the method introduced in [1], based on a game theory approach, to develop a new algorithm for the simultaneous identification of conductivity coefficient and missing boundary data. We shall say that there are three players and we define three objective functions. Each player controls one variable and minimizes his own cost function in order to seek a Nash equilibrium which is expected to approximate the inverse problem solution. The first player solves the elliptic equation (div(k.(u)) = 0) with the Dirichlet part of the Cauchy data prescribed over the accessible boundary and a variable Neumann condition (which we call first player's strategy) prescribed over the inaccessible part of the boundary. The second player makes use correspondingly of the Neumann part of the Cauchy data, with a variable Dirichlet condition prescribed over the inaccessible part of the boundary. The first player then minimizes the gap related to the non used Neumann part of the Cauchy data, and so does the second player with a corresponding Dirichlet gap. The two players consider a response of the unknown conductivity of the third player. The third player controls the conductivity coefficient, and uses the over specified Dirichlet condition as well as the second's player Dirichlet condition strategy prescribed over the inaccessible part of the boundary.

Published
2016

194. Étude d'un modèle microscopique de l'électrophysiologie cardiaque

Author

Bécue, Pierre-Elliott, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
[SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

National audience; Les modèles monodomaine et bidomaine permettent de représenter l’électrophysiologie cardiaque dans certaines situations. Néanmoins, ces modèles ne sont pas en mesure de prendre en compte les affections microscopiques qui peuvent survenir au sein du cœur (présence de graisses, cellules nécrosées, etc . . . ).Un modèle ”microscopique” issu du modèle bidomaine est proposé afin de représenter séparément le milieu intracellulaire du milieu extracellulaire. Ce modèle peut s’étendre à N cellules naturellement et c’est le but de notre activité de recherche : explorer numériquement les pathologies cardiaques liées à des hétérogénéités à l’échelle du tissu cellulaire.Nous montrons l’existence d’une solution faible de ce système d’équations par compacité après discrétisation en temps. Les points délicats sont la gestion des termes ioniques non-linéaires indispensables pour la stimulation cardiaque ainsi que les termes de bords au niveau de la cellule.

Published
2016

195. Intermittent drivers anchoring to structural heterogeneities as a major pathophysiological mechanism of human persistent atrial fibrillation

Author

HAÏSSAGUERRE, Michel, SHAH, Ashok, COCHET, Hubert, HOCINI, Mélèze, DUBOIS, Rémi, EFIMOV, Igor, VIGMOND, Edward, BERNUS, Olivier, TRAYANOVA, Natalia, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Département de cardiologie, CHU Bordeaux [Bordeaux]-Hôpital Haut-Lévêque [CHU Bordeaux], CHU Bordeaux [Bordeaux], AgroParisTech, Washington University in Saint Louis (WUSTL), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Johns Hopkins University (JHU), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
[SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Atrial Fibrillation, cardiovascular system, Reviews, Animals, Humans, Heart Atria, Magnetic Resonance Imaging
Abstract

International audience; The mechanisms responsible for perpetuation of human persistent atrial fibrillation (AF) are controversial and probably vary between individuals. A wide spectrum of mechanisms have been described in experimental studies, ranging from a single localized stable (focal/reentrant) source, to multiple sources, up to diffuse bi-atrial wavelets. We characterized AF drivers in patients with persistent AF (lasting less than 1 year) using novel high resolution mapping, imaging and modelling approaches with the objective of evaluating their relationship to atrial structural heterogeneities. Using panoramic non-invasive mapping in humans, focal or reentrant sources driving AF waves were identified, originating from multiple distinct regions and exhibiting short lifespans and periodic recurrences in the same locations. The reentrant driver regions harboured long, fractionated electrograms covering most of the fibrillatory cycle lengths with varying beat-to-beat sequences suggestive of unstable trajectories attached to slow conducting heterogeneous tissue. MRI atrial imaging demonstrated that such drivers preferentially clustered at the borders of fibrotic atrial regions. In patient-specific computer simulations, sustained AF was shown to be driven by meandering transitory reentries attached to fibrosis borders expressing specific metrics in density and extent. Finally, random microstructural alterations devoid of cellular electrical changes were modelled, showing that a percolation mechanism could also explain atrial reentries and complex fractionated electrograms. These data from clinical, imaging and computational studies strongly suggest that intermittent and spatially unstable drivers anchoring to structural heterogeneities are a major pathophysiological mechanism in human persistent atrial fibrillation.

Published
2016

196. Novel Radiofrequency Ablation Strategies for Terminating Atrial Fibrillation in the Left Atrium: A Simulation Study

Author

Jason D Bayer, Caroline H Roney, Ali ePashaei, Pierre eJaïs, Edward Joseph Vigmond, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), King‘s College London, Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB), Universitat Pompeu Fabra [Barcelona] (UPF), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
0301 basic medicine, medicine.medical_specialty, Physiology, Radiofrequency ablation, medicine.medical_treatment, Left atrium, phase singularity mapping, Phase singularity, Ablation, 030204 cardiovascular system & hematology, ablation, lcsh:Physiology, law.invention, Pulmonary vein, 03 medical and health sciences, 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, law, Physiology (medical), Internal medicine, medicine, Sinus rhythm, Cycle length, computer modeling, Original Research, lcsh:QP1-981, Phase singularity mapping, business.industry, fibrosis, Atrial fibrillation, medicine.disease, Fibrosis, persistent atrial fibrillation, Surgery, surgical procedures, operative, 030104 developmental biology, medicine.anatomical_structure, Cardiology, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Persistent atrial fibrillation, business
Abstract

International audience; Pulmonary vein isolation (PVI) with radiofrequency ablation (RFA) is the cornerstone of atrial fibrillation (AF) therapy, but few strategies exist for when it fails. To guide RFA, phase singularity (PS) mapping locates reentrant electrical waves (rotors) that perpetuate AF. The goal of this study was to test existing and develop new RFA strategies for terminating rotors identified with PS mapping. It is unsafe to test experimental RFA strategies in patients, so they were evaluated in silico using a bilayer computer model of the human atria with persistent AF (pAF) electrical (ionic) and structural (fibrosis) remodeling. pAF was initiated by rapidly pacing the right (RSPV) and left (LSPV) superior pulmonary veins during sinus rhythm, and rotor dynamics quantified by PS analysis. Three RFA strategies were studied: (i) PVI, roof, and mitral lines; (ii) circles, perforated circles, lines, and crosses 0.5-1.5 cm in diameter/length administered near rotor locations/pathways identified by PS mapping; and (iii) 4-8 lines streamlining the sequence of electrical activation during sinus rhythm. As in pAF patients, 2 ± 1 rotors with cycle length 185 ± 4 ms and short PS duration 452 ± 401 ms perpetuated simulated pAF. Spatially, PS density had weak to moderate positive correlations with fibrosis density (RSPV: r = 0.38, p = 0.35, LSPV: r = 0.77, p = 0.02). RFA PVI, mitral, and roof lines failed to terminate pAF, but RFA perforated circles and lines 1.5 cm in diameter/length terminated meandering rotors from RSPV pacing when placed at locations with high PS density. Similarly, RFA circles, perforated circles, and crosses 1.5 cm in diameter/length terminated stationary rotors from LSPV pacing. The most effective strategy for terminating pAF was to streamline the sequence of activation during sinus rhythm with >4 RFA lines. These results demonstrate that co-localizing 1.5 cm RFA lesions with locations of high PS density is a promising strategy for terminating pAF rotors. For patients immune to PVI, roof, mitral, and PS guided RFA strategies, streamlining patient-specific activation sequences during sinus rhythm is a robust but challenging alternative.

Published
2016

197. Theoretical connections between mathematical neuronal models corresponding to different expressions of noise

Author

Grégory Dumont, Carmen Oana Tarniceriu, Jacques Henry, Group for Neural Theory [Paris], Laboratoire de Neurosciences Cognitives & Computationnelles (LNC2), Département d'Etudes Cognitives - ENS Paris (DEC), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Département d'Etudes Cognitives - ENS Paris (DEC), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Labex Institut d'étude de la cognition (IEC), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Faculty of Computer Science [Iași], Alexandru Ioan Cuza University of Iași [Romania], École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0301 basic medicine, Statistics and Probability, Process (engineering), Stochastic modelling, Models, Neurological, Probability density function, General Biochemistry, Genetics and Molecular Biology, 03 medical and health sciences, symbols.namesake, Theoretical physics, Age structured model, 0302 clinical medicine, Wiener process, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Computer Simulation, Statistical physics, Randomness, Mathematics, Neurons, Stochastic Processes, Computational neuroscience, General Immunology and Microbiology, Stochastic process, Neural noise, Applied Mathematics, Fokker-Planck equation, General Medicine, 030104 developmental biology, Quantitative Biology - Neurons and Cognition, FOS: Biological sciences, Modeling and Simulation, symbols, Neurons and Cognition (q-bio.NC), Fokker–Planck equation, Noisy Leaky Integrate-and-Fire model, Escape rate, General Agricultural and Biological Sciences, 030217 neurology & neurosurgery
Abstract

International audience; Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability are strikingly similar.

Published
2016

198. From Single Myocyte to Whole Heart

Author

DESPA, Sanda, VIGMOND, Edward, University of Kentucky, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Kentucky (UK), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]

Subjects
action potential, Editorial, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, intact heart, modeling, L-type Ca2+ channels, electrophysiology, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2016

199. Modelling methodology of atrial fibrosis affects rotor dynamics and electrograms

Author

RONEY, Caroline, BAYER, Jason, ZAHID, Sohail, MEO, Marianna, BOYLE, Patrick, TRAYANOVA, Natalia, HAÏSSAGUERRE, Michel, DUBOIS, Rémi, COCHET, Hubert, VIGMOND, Edward, BOYLE, Patrick M.J., IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Johns Hopkins University (JHU), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
0301 basic medicine, Patient-Specific Modeling, Pathology, medicine.medical_treatment, Action Potentials, 030204 cardiovascular system & hematology, Electrocardiography, 0302 clinical medicine, Fibrosis, Heart Rate, Atrial Fibrillation, medicine.diagnostic_test, Models, Cardiovascular, Atrial fibrillation, Signal Processing, Computer-Assisted, Reentry, Mechanics, Supplement: Reviews, Ablation, Atrial Function, Prognosis, Magnetic Resonance Imaging, Reentrancy, cardiovascular system, [SDV.IB]Life Sciences [q-bio]/Bioengineering, medicine.symptom, Cardiology and Cardiovascular Medicine, Electrophysiologic Techniques, Cardiac, medicine.medical_specialty, Catheter ablation, macromolecular substances, 03 medical and health sciences, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Non-invasive electrocardiographic imaging, Predictive Value of Tests, Physiology (medical), medicine, Humans, Heart Atria, Fibrillation, Electrogram fractionation, business.industry, Phase singularity mapping, Magnetic resonance imaging, Atrial fibrosis, medicine.disease, 030104 developmental biology, Computer modelling, business
Abstract

Aims Catheter ablation is an effective technique for terminating atrial arrhythmia. However, given a high atrial fibrillation (AF) recurrence rate, optimal ablation strategies have yet to be defined. Computer modelling can be a powerful aid but modelling of fibrosis, a major factor associated with AF, is an open question. Several groups have proposed methodologies based on imaging data, but no comparison to determine which methodology best corroborates clinically observed reentrant behaviour has been performed. We examined several methodologies to determine the best method for capturing fibrillation dynamics. Methods and results Patient late gadolinium-enhanced magnetic resonance imaging data were transferred onto a bilayer atrial computer model and used to assign fibrosis distributions. Fibrosis was modelled as conduction disturbances (lower conductivity, edge splitting, or percolation), transforming growth factor-β1 ionic channel effects, myocyte-fibroblast coupling, and combinations of the preceding. Reentry was induced through pulmonary vein ectopy and the ensuing rotor dynamics characterized. Non-invasive electrocardiographic imaging data of the patients in AF was used for comparison. Electrograms were computed and the fractionation durations measured over the surface. Edge splitting produced more phase singularities from wavebreaks than the other representations. The number of phase singularities seen with percolation was closer to the clinical values. Addition of fibroblast coupling had an organizing effect on rotor dynamics. Simple tissue conductivity changes with ionic changes localized rotors over fibrosis which was not observed with clinical data. Conclusion The specific representation of fibrosis has a large effect on rotor dynamics and needs to be carefully considered for patient specific modelling.

Published
2016

200. Do we need to enforce the homogeneous Neuman condition on the Torso forsolving the inverse electrocardiographic problem by using the method of fundamental solution ?

Author

Chamorro-Servent, Judit, Bear, Laura, Duchateau, Josselin, Potse, Mark, Dubois, Rémi, Coudière, Yves, Chamorro Servent, Judit, Instituts Hospitalo-Universitaires - L'Institut de Rythmologie et modélisation Cardiaque - - LIRYC2010 - ANR-10-IAHU-0004 - IAHU - VALID, Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Centre de recherche Cardio-Thoracique de Bordeaux [Bordeaux] (CRCTB), Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-Institut National de la Santé et de la Recherche Médicale (INSERM), This study received financial support from the FrenchGovernment as part of the 'Investissements d’avenir' programmanaged by the National Research Agency (ANR),Grant reference ANR-10-IAHU-04 and from the ConseilR´egional Aquitaine as part of the project 'Assimilation dedonn´ees en canc´erologie et cardiologie'., ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SPI]Engineering Sciences [physics], method of fundamental solutions, [SPI] Engineering Sciences [physics], boundary conditions, electrocardiographic imaging, inverse problem, [MATH] Mathematics [math], [MATH]Mathematics [math], ill-posed, Neumann
Abstract

International audience; Robust calculations of the inverse electrocardiographicproblem may require accurate specification of boundaryconditions at the torso and cardiac surfaces. In particular,the numerical specification of the no-flux condition onthe torso is difficult because surface normals must be computed,and because the torso may alternatively be consideredinfinitely far away from the heart. Using the method offundamental solutions (MFS), this boundaryconditions can be taken into account in different manners.Specifically, the no-flux condition on the torso can beignored, or weighted with respect to the Dirichlet boundarycondition associated to the torso data, or can bestrongly enforced through a saddle-point problem. In this work we provide a preliminary comparison ofthese different strategies.

Published
2016

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