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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"'

1. A Patchwork Method to Improve the Performance of Current Methods for Solving the Inverse Problem of Electrocardiography

Author: Oumayma Bouhamama, Mark Potse, Laura Bear, Lisl Weynans, 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], 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: Biomedical Engineering, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; Objective: Noninvasive electrocardiographic imaging (ECGI) reconstructs cardiac electrical activity from body surface potential measurements. However, current methods have demonstrated inaccuracies in reconstructing sinus rhythm, and in particular breakthrough sites. This study aims to combine existing inverse algorithms, making the most of their advantages while minimizing their limitations. Method: The “patchwork method” (PM) combines two classical numerical methods for ECGI: the method of fundamental solutions (MFS) and the finite-element method (FEM). We assume that the method with the smallest residual in the predicted torso potentials, computed using the boundary element method (BEM), provides the most accurate solution. The PM selects for each heart node and time step the method whose estimated reconstruction error is smallest. The performance of the PM was evaluated using simulated ectopic and normal ventricular beats. Results: Cardiac potentials and activation maps obtained with the PM (CC = 0.63 ± 0.01 and 0.61 ± 0.05 respectively) were more accurate than MFS (CC = 0.61 ± 0.01 and 0.48 ± 0.05 respectively), FEM (CC = 0.58 ± 0.01 and 0.51 ± 0.02 respectively) or BEM (CC = 0.57 ± 0.02 and 0.49 ± 0.02 respectively). The PM also located all epicardial breakthrough sites, whereas the traditional numerical methods usually missed one. Furthermore, the PM showed its robustness and stability in the presence of Gaussian noise added to the torso potentials. Conclusion: The PM overcomes some of the limitations of classical numerical methods, improving the accuracy of mapping important features of activation during sinus rhythm and paced beats. Significance: This novel method for optimizing ECGI solutions opens a new avenue for improving not only ECGI but also other inverse problems.
Published: 2023

2. A numerical method for wave-structure interactions in the Boussinesq regime

Author: Beck, Geoffrey, Lannes, David, Weynans, Lisl, Multi-scale numerical geometric schemes (MINGUS), École normale supérieure - Rennes (ENS Rennes)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), 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], and ANR-18-CE40-0027,SingFlows,Ecoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure(2018)
Subjects: Boussinesq system, Mathematics - Analysis of PDEs, 35G61, 35Q35, 74F10, 65M08, FOS: Mathematics, Numerical Analysis (math.NA), Wave-structure interactions, Mathematics - Numerical Analysis, [MATH]Mathematics [math], Initial boundary value problems, Analysis of PDEs (math.AP), Numerical analysis
Abstract: The goal of this work is to study waves interacting with partially immersed objects allowed to move freely in the vertical direction, and in a regime in which the propagation of the waves is described by the one dimensional Boussinesq-Abbott system. The problem can be reduced to a transmission problem for this Boussinesq system, in which the transmission conditions between the components of the domain at the left and at the right of the object are determined through the resolution of coupled forced ODEs in time satisfied by the vertical displacement of the object and the average discharge in the portion of the fluid located under the object. We propose a new extended formulation in which these ODEs are complemented by two other forced ODEs satisfied by the trace of the surface elevation at the contact points. The interest of this new extended formulation is that the forcing terms are easy to compute numerically and that the surface elevation at the contact points is furnished for free. Based on this formulation, we propose a second order scheme that involves a generalization of the MacCormack scheme with nonlocal flux and a source term, which is coupled to a second order Heun scheme for the ODEs. In order to validate this scheme, several explicit solutions for this wave-structure interaction problem are derived and can serve as benchmark for future codes. As a byproduct, our method provides a second order scheme for the generation of waves at the entrance of the numerical domain for the Boussinesq-Abbott system.
Published: 2023

3. A continuous spatial and temporal mathematical model for assessing the distribution of dengue in Brazil with control

Author: FERNANDO LUIZ PIO DOS SANTOS, MOSTAFA BENDAHMANE, ELMAHDI ERRAJI, FAHD KARAMI, Universidade Estadual Paulista Júlio de Mesquita Filho = São Paulo State University (UNESP), 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], Ecole Supérieure de Technologie d'Essaouira, and Université Cadi Ayyad [Marrakech] (UCA)
Subjects: Ecology, Aedes, Optimal Control, Applied Mathematics, Epidemic Model, General Medicine, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Reaction-Diffusion System, Agricultural and Biological Sciences (miscellaneous)
Abstract: International audience; In this paper, we developed an optimal control of a reaction–diffusion mathematical model, describing the spatial spread of dengue infection. Compartments for human and vector populations are considered in the model, including a compartment for the aquatic phase of mosquitoes. This enabled us to discuss the vertical transmission effects on the spread of the disease in a two-dimensional domain, using demographic data for different scenarios. The model was analyzed, establishing the existence and convergence of the weak solution for the model. The convergence of the numerical scheme to the weak solution was proved. For numerical approximation, we adopted the finite element scheme to solve direct and adjoint state systems. We also used the nonlinear gradient descent method to solve the optimal control problem, where the optimal management of government investment was proposed and leads to more effective dengue fever infection control. These results may help us understand the complex dynamics driven by dengue and assess the public health policies in the control of the disease.
Published: 2023

4. Numerical Investigation of Methods Used In Commercial Clinical Devices for Solving the ECGI Inverse Problem

Author: Gassa, Narimane, Kalinin, Vitaly, 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], EP Solutions SA, ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), ANR-11-EQPX-0030,MUSIC,Plateforme multi-modale d'exploration en cardiologie(2011), and European Project: 860974,PersonalizeAF(2020)
Subjects: Electrocardiography, [SPI]Engineering Sciences [physics], Method of Fundamental Solutions, Inverse problem, Equivalent Single Layer
Abstract: Electrocardiographic Imaging (ECGI) is a promising tool to non-invasively map the electrical activity of the heart using body surface potentials (BSPs) combined with the patient specific anatomical data. In this work, we assess two ECGI algorithms used in commercial ECGI systems to solve the inverse problem; the Method of Fundamental Solutions (MFS) and the Equivalent Single Layer (ESL). We quantify the performance of these two methods in conjunction with two different activation maps to estimate the activation times and earliest activation sites. ESL provided more accurate reconstruction of the cardiac electrical activity, especially on the endocardial part of the heart. Nevertheless, both methods provided comparable results in terms of the derived activation maps and the localization of the focal origin as a clinically relevant parameter.
Published: 2023

5. Optimal control for a two-sidedly degenerate aggregation equation

Author: Bendahmane, Mostafa, Karami, Fahd, Erraji, Elmahdi, Atlas, Abdelghafour, Afraites, Abdelkbir, 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), Ecole Supérieure de Technologie d'Essaouira, Université Cadi Ayyad [Marrakech] (UCA), Ecole Nationale des Sciences Appliquées [Marrakech] (ENSA), and Université Sultan Moulay Slimane (USMS )
Subjects: Nonlocal models, Aggregation equation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Degenerate diffusion, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Finite volume, Adjoint problem, Optimal control
Abstract: International audience; In this paper, we are concerned with the study of the mathematical analysis for an optimal control of a nonlocal degenerate aggregation model. This model describes the aggregation of organisms such as pedestrian movements, chemotaxis, animal swarming. We establish the well-posedness (existence and uniqueness) for the weak solution of the direct problem by means of an auxiliary nondegenerate aggregation equation, the Faedo-Galerkin method (for the existence result) and duality method (for the uniqueness). Moreover, for the adjoint problem, we prove the existence result of minimizers and first order necessary conditions. The main novelty of this work concern the presence of a control to our nonlocal degenerate aggregation model. Our results are complemented with some numerical simulations.
Published: 2023

6. INTER-OPERATOR SEGMENTATION VARIABILITY INDUCES HIGH PREMATURE VENTRICULAR CONTRACTIONS LOCALIZATION UNCERTAINTY AT THE HEART BASE

Author: Gassa, Narimane, Zemzemi, Nejib, Boonstra, Machteld, Tate, Jess, Svehlikova, Jana, Ondrusova, Beata, 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], Institut de rythmologie et modélisation cardiaque [Pessac] (IHU Liryc), University Medical Center [Utrecht], Scientific Computing and Imaging Institute (SCI Institute), University of Utah, Slovak University of Technology in Bratislava, Slovak Academy of Sciences Institute of Measurement Science, Institute of Measurement Science (IMS), Slovak Academy of Sciences (SAS), and European Project: 860974,PersonalizeAF(2020)
Subjects: [SDV.IB]Life Sciences [q-bio]/Bioengineering
Abstract: BackgroundElectrocardiographic imaging (ECGI) is a promising tool for the treatment and diagnosis of cardiac arrhythmias. ECGI estimates non-invasively the electrical activity of the heart using body surface potentials (BSPs) obtained at the body surface in combination with a specific CT/MRI based anatomical models and defined electrode positions. In order to solve the ECGI inverse problem the first step to be considered is indeed the image segmentation and mesh generation.ObjectiveOur main purpose is to evaluate the effect of the inter-operator segmentation variability on the PVC localization.MethodsEight different cardiac segmentations from the same single subject CT-scans were performed by researchers within the consortium for Electrocardiographic Imaging. For all generated meshes, eight ventricular stimulation protocols were used; left and right ventricular free walls (LV, RV), apex, left and right ventricular outflow tract (LVOT, RVOT), septum, and two locations at the left and right heart base (LVB, RVB). BSPs were generated using computational models. We designed two test cases: with and without segmentation uncertainty. In test A, no segmentation uncertainty is considered. In test B, we solve the inverse problem for the eight geometries starting from one single BSP generated with a reference heart geometry. For each test case and for each stimulation protocol we computed the inverse solution using the Method of Fundamental Solutions and assessed the Localization Error (LE) of the pacing sites. In order to quantify the effect of segmentation uncertainty we also computed the difference between LEs obtained in tests B and A.ResultsIn test A, the mean LEs for LV, RV, apex, LVOT, RVOT, septum, LVB and RVB pacings are 7, 7, 5, 12, 14, 18, 13, 15 mm, respectively. In test B, the mean LEs are 7, 7, 5, 17, 23, 17, 16, 23 mm, respectively. The average differences between LEs are 0, 0, -1,5, 8, -1, 3, 8 mm, respectively.ConclusionThis study shows that the effect of the segmentation uncertainty on the localization of PVC is more important for RVOT, LVOT, RVB and LVB. We believe that the high uncertainty is due to the variability of segmentations at the base of the heart. These findings suggest that uncertainty in cardiac segmentation can have a significant impact on ECGI and its interpretability in clinical applications; therefore, careful segmentation is strongly recommended, especially at the base of the heart.
Published: 2023

7. Estimation des niveaux de potassium et calcium dans le sérum par caractérisation des formes d'onde de dépolarisation et de repolarisation de l'électrocardiogramme

Author: Bukhari, Syed Hassaan Ahmed, 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, Universidad de Zaragoza (Espagne), Mark Potse, Esther Pueyo, and Carlos Sánchez
Subjects: Électrophysiologie cardiaque, High-Performance computing, Numerical models, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], Cardiac electrophysiology, Calcul intensif, Équations aux dérivées partielles
Abstract: Chronic kidney disease (CKD), a condition defined by a gradual decline in kidney function over time, has become a global health concern affecting between 11 and 13% of the world population. As renal function declines, CKD patients gradually lose their ability to maintain normal values of potassium concentration ([K+]) in their blood. Elevated serum [K+], known as hyperkalemia, increases the risk for life-threatening arrhythmias and sudden cardiac death.An increase in serum [K+] outside the physiological range is commonly silent and is only detected when hyperkalemia is already very severe or when a blood test is performed. Maintenance and monitoring of [K+] in the blood is an important component in the treatment of CKD patients because therapies for hyperkalemia management in CKD patients are designed to prevent arrhythmias and to immediately lower serum [K+] to safe ranges. However, this is currently only possible by taking a blood sample and is associated with a long analysis time. Therefore it is useful to have a simple, noninvasive method to estimate serum [K+], particularly using the electrocardiogram (ECG). Indeed, variations in serum electrolyte levels have been shown to alter the electrical behavior of the heart and to induce changes in the ECG. However, large inter-individual variability exists in the relationship between ion concentrations and ECG features. Previous attempts to estimate serum [K+] from the ECG have therefore shown limitations, such as not being applicable to some common types of ECG waveforms or relying on specific ECG characteristics that may present large variations not necessarily associated with hyperkalemia.The aim of this thesis is to develop novel estimates of serum [K+] that are robust enough to detect hypokalemia (reduced [K+]) or hyperkalemia in a timely manner to provide life-saving treatment. Additionally, the effect of changes in other electrolyte levels, like calcium concentration ([Ca2+]), and in heart rate are investigated. These aims are achieved by combining novel ECG signal processing techniques with in silico modeling and simulation of cardiac electrophysiology.In conclusion, we identify several markers of ECG morphology, including depolarization and repolarization features, that are highly correlated with serum electrolyte (potassium and calcium) concentrations. ECG morphological variability markers vary significantly with [K+] and [Ca2+] in both simulated and measured ECGs, with a wide range of patterns observed for such relationships. The proportions of endocardial, midmyocardial and epicardial cells have a large impact on ECG markers, particularly for serum electrolyte concentrations out of their physiological levels. This suggests that transmural heterogeneities can modulate ECG responses to changes in electrolyte concentrations in CKD patients. Agreement between actual potassium and calcium levels and their estimates derived from the ECG is promising, with lower average errors than previously proposed markers in the literature. These findings can have major relevance for noninvasive monitoring of serum electrolyte levels and prediction of arrhythmic events in these patients.; L’insuffisance rénale chronique (IRC), caractérisée par un déclin graduel de la fonction rénale, est devenu un problème sanitaire important, affectant entre 11 et 13% de la population mondiale. Lorsque leur fonction rénale décline, les patients affectées d’IRC perdent graduellement leur capacité de maintenir une concentrations sanguine de potassium ([K+]) normale. Une [K+] sanguine élevée, nommée hyperkaliémie, augmente le risque d’arythmie cardiaque engageant le pronostic vital et de mort subite cardiaque.Une augmentation de la [K+] sanguine hors de sa plage physiologique reste le plus souvent inaper¸cue et n’est détectée que si elle est très sévère ou si un prélèvement sanguin est effectué. La maintenance et la surveillance de la [K+] sanguine est un élément important de la prise en charge des patients affectés d’IRC, les thérapies pour la maˆıtrise de l’hyperkaliémie dans ces patients visant la prévention des arythmies et la réduction immédiate de la [K+] vers des valeurs inoffensives. Cependant, de nos jours une telle surveillance n’est possible que par des prélèvements sanguins associées avec un temps d’analyse long. Il serait donc utile d’avoir une méthode simple et noninvasive pour l’estimation de la [K+], notamment en utilisant l’électrocardiogramme (ECG). En effet, il a été démontré que les variations des niveaux d’électrolytes dans le sérum sanguin modifient le comportement électrique du cœur et donc l’ECG. Malheureusement, la rélation entre les concentrations d’électrolytes et les caractéristiques de l’ECG est très variable d’une personne `a l’autre. Des travaux antérieurs ont donc montré des limitations, tels que l’exclusion de certains types d’ECG ou la dépendance sur des caractéristiques présentant une variabilité large et non nécessairement corrélée avec l’hyperkaliémie.L’objectif de cette thèse est de développer des nouveaux marqueurs de la [K+] sanguine suffisamment robustes pour détecter l’hypokaliémie ([K+] anormalement bas) et l’hyperkaliémie assez rapidement pour permettre des interventions potentiellement salvateures. En plus, les effets de changements d’autres concentrations d’électrolytes, tels que le calcium ([Ca2+]) et de la fréquence cardiaque sont étudiés. Ces objectifs sont atteints en combinant des nouvelles techniques de traitement de signal avec la modélisation in silico de l’électrophysiologie cardiaque.En conclusion, nous identifions plusieurs marqueurs morphologiques de l’ECG, incluant des caractéristiques de dépolarisation et de repolarisation, qui sont fortement corrélées avec [K+] et [Ca2+]. Cette corrélation est présente aussi bien dans les ECGs simulées que dans les ECGs mesurées, avec une gamme de morphologies telle qu’observée chez les patients. Les proportions de cellules de type endocardique, mi-myocardique, et épicardique ont un effet important sur les marqueurs de l’ECG, particulièrement pour des concentrations électrolytiques hors de leurs plages physiologiques. Cette observation suggère que ces hétérogénéités peuvent moduler la réponse de l’ECG aux changements des concentrations électrolytiques chez des patients atteints d’IRC. La concordance entre les concentrations estimées et celles mesurées est prometteuse, avec des erreurs moyennes moins grands que celles obtenues avec les méthodes de la littérature. Ces résultats peuvent avoir une grande importance pour la surveillance noninvasive des concentrations d’électrolytes dans le sang et pour la prévision d’arythmies chez les patients atteints d’IRC.
Published: 2023

8. Data Assimilation with Machine Learning for Dynamical Systems: Modelling Indoor Ventilation

Author: Heaney, Claire, Tang, Jieyi, Yan, Jintao, Guo, Donghu, Ipock, Jamesson, Kaluvakollu, Sanjana, Lin, Yushen, Shao, Danhui, Chen, Boyang, Mottet, Laetitia, Kumar, Prashant, Pain, Christopher, Imperial College London, University of Manchester [Manchester], 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], and University of Surrey (UNIS)
Subjects: [PHYS]Physics [physics], machine learning, Adversarial neural networks, indoor fluid dynamics modelling, data assimilation
Abstract: Data assimilation is a method of combining physical observations with prior knowledge (for instance, a computational simulation) in order to produce an improved model; that is, improved over what thephysical observations or the computational simulation could offer in isolation. Recently, machine learning techniques have been deployed in order to address the significant computational burden that is associated with the procedures involved in data assimilation.In this paper we propose an approach that uses a non-intrusive reduced-order model (NIROM) as a surrogate for a high-resolution model thereby saving computational effort. The mismatch between observations and the surrogate model is propagated forwards and backwards in time in a manner similar to 4D-variational data assimilation methods. The observations and prior are reconciled in a new way which takes full advantage of the neural network used in the NIROM and also means that there is no need to form the sensitivities explicitly when propagating the mismatch. Instead, the observations are part of the input and output of the network.Modelling the air quality in a school classroom is the test case for our demonstration. Firstly, the data assimilation approach is shown to perform very well in a dual-twin type experiment, and secondly, theapproach is used to assimilate observations collected from a classroom in Houndsfield Primary School with predictions from the NIROM.
Published: 2023

9. Segmentation Uncertainty Quantification in Cardiac Propagation Models

Author: 'Jess Tate, Nejib Zemzemi, Shireen Elhabian, Beata Ondrusova, Machteld Boonstra, Peter van Dam, Dana Brooks, Akil Narayan, Rob MacLeod\\', Scientific Computing and Imaging Institute (SCI Institute), University of Utah, 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], Slovak University of Technology in Bratislava, University Medical Center [Utrecht], and Northeastern University [Boston]
Subjects: [SPI]Engineering Sciences [physics]
Abstract: International audience; A key part of patient-specific cardiac simulations is segmentation, yet the impact of this subjective and errorprone process hasn't been quantified in most simulation pipelines. In this study we quantify the dependence of a cardiac propagation model on from segmentation variability. We used statistical shape modeling and polynomial Chaos (PC) to capture segmentation variability dependence and applied its affects to a propagation model. We evaluated the predicted local activation times (LATs) an body surface potentials (BSPs) from two modeling pipelines: an EIkonal propagation model and a surfacebased fastest route model. The predicted uncertainty due to segmentation shape variability was distributed near the base of the heart and near high amplitude torso potential regions. Our results suggest that modeling pipelines may have to accommodate segmentation errors if regions of interest correspond to high segmentation error. Further, even small errors could proliferate if modeling results are used to to feed further computations, such as ECGI.
Published: 2022

10. The Effect of Segmentation Variability in Forward ECG Simulation

Author: 'Beata Ondrusova, Machteld Boonstra, Jana Svehlikova, Dana Brooks, Peter van Dam, Ali Rababah, Akil Narayan, Rob MacLeod, Nejib Zemzemi, Jess Tate\\', Institute of Measurement Science (IMS), Slovak Academy of Sciences (SAS), University Medical Center [Utrecht], Slovak University of Technology in Bratislava, Northeastern University [Boston], Jordanian Royal Medical Services, Scientific Computing and Imaging Institute (SCI Institute), University of Utah, 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, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]
Subjects: [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging
Abstract: International audience; Segmentation of patient-specific anatomical models is one of the first steps in Electrocardiographic imaging (ECGI). However, the effect of segmentation variability on ECGI remains unexplored. In this study, we assess the effect of heart segmentation variability on ECG simulation. We generated a statistical shape model from segmentations of the same patient and generated 262 cardiac geometries to run in an ECG forward computation of body surface potentials (BSPs) using an equivalent dipole layer cardiac source model and 5 ventricular stimulation protocols. Variability between simulated BSPs for all models and protocols was assessed using Pearson's correlation coefficient (CC). Compared to the BSPs of the mean cardiac shape model, the lowest variability (average CC = 0.98 ± 0.03) was found for apical pacing whereas the highest variability (average CC = 0.90 ± 0.23) was found for right ventricular free wall pacing. Furthermore, low amplitude BSPs show a larger variation in QRS morphology compared to high amplitude signals. The results indicate that the uncertainty in cardiac shape has a significant impact on ECGI.
Published: 2022

11. 'A comparison of multithreading, vectorization, and GPU computing for the acceleration of cardiac electrophysiology models'

Author: Sakka, Chiheb, Guermouche, Amina, Aumage, Olivier, Saillard, Emmanuelle, Potse, Mark, Coudière, Yves, Barthou, Denis, STatic Optimizations, Runtime Methods (STORM), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-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 de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-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-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], ANR-18-CE46-0010,Exacard,Simulation exascale de l'électrophysiologie cardiaque pour la recherche sur les arythmies(2018), and ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010)
Subjects: [INFO]Computer Science [cs]
Abstract: International audience; Realistic simulation of cardiac electrophysiology requires both high resolution and computationally expensive models of membrane dynamics. Optimization of membrane models can therefore have a large impact on time, hardware, and energy usage. We tested both CPU-based and GPU-based optimization techniques for a human heart model with Ten Tusscher-Panfilov 2006 dynamics. Compared to a multithreaded code running on 64 CPU cores, the tested NVIDIA Tesla P100 GPU proved about 3 times faster. Effective use of the CPU's SIMD capabilities allowed a similar performance gain. GPU performance was bounded by the data transfer rate between GPU and main memory. Optimal SIMD use required explicit vectorization and an adapted data structure. We conclude that on mixed CPU-GPU systems the best results are obtained by optimizing both CPU and GPU code and using a runtime system that balances CPU and GPU load.
Published: 2022

12. À quoi servent les ordinateurs les plus puissants au monde ? Un exemple en cardiologie

Author: Saillard, Emmanuelle, Potse, Mark, STatic Optimizations, Runtime Methods (STORM), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-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 de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-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), 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), ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), and European Project: 955495,MICROCARD
Subjects: [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract: International audience; Cardiac arrhythmia affect millions of people and cause 300 000 deaths each year in Europe. Their mechanisms are studied by numerical simulation but require computations at an unprecedented scale. The human heart has about 10 billion cells, each equipped with roughly a million ion channels, able to change their behaviour in less than a nanosecond. Computations at this level require a computational power that exceeds by far the capacities of present-day computers. In this article we outline future exascale supercomputers will help cardiac research.; Les arythmies cardiaques touchent des millions de personnes et provoquent 300 000 morts chaque année en Europe. Leurs mécanismes sont étudiés par simulation numérique mais nécessitent des calculs à une échelle encore jamais atteinte. En effet, le cœur humain comporte 10 milliards de cellules, chacune équipée d’un million de canaux ioniques capables de changer leur comportement en moins d’une nanoseconde. Faire des calculs au niveau de ces canaux représente une force de calculs dépassant de loin les capacités de calculs des ordinateurs actuels.; Hartritmestoornissen raken miljoenen mensen en veroorzaken zo'n 300 000 sterfgevallen per jaar in Europa. De onderliggende mechanismen worden onder andere bestudeerd doormiddel van computersimulaties, maar daarvoor zijn berekeningen nodig op een schaal die nog niet eerder is bereikt. Een menselijk hart bevat 10 miljard cellen, elk voorzien van een miljoen ionkanalen, die in staat zijn hun gedrag te veranderen in minder dan een nanoseconde. Simulaties op dit nivo vereisen een veel grotere rekenkracht dan nu beschikbaar is. In dit artikel beschrijven we hoe toekomstige exascalaire supercomputers het hartonderzoek verder kunnen helpen.
Published: 2022

13. Left-axis deviation in patients with nonischemic heart failure and left bundle branch block is a purely electrical phenomenon

Author: Michel Haïssaguerre, F. Daniel Ramirez, Romain Eschalier, Hubert Cochet, Peter Huntjens, Saer Abu-Alrub, Samuel Buliard, Hugo Marchand, Pierre Bordachar, Mark Potse, Marc Strik, Sylvain Ploux, CHU Bordeaux [Bordeaux], IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Washington University in Saint Louis (WUSTL), 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, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], 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), CHU Clermont-Ferrand, This work 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. FDR is supported by a Canadian Institutes of Health Research Banting Postdoctoral Fellowship., 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, 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: Male, medicine.medical_specialty, Heart Ventricles, Bundle-Branch Block, Block, 030204 cardiovascular system & hematology, Cardiac Resynchronization Therapy, Electrocardiography, 03 medical and health sciences, 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Physiology (medical), Internal medicine, medicine, Electrical mapping, Humans, Cardiac structure, In patient, cardiovascular diseases, 030212 general & internal medicine, Left bundle branch, ComputingMilieux_MISCELLANEOUS, Aged, Heart Failure, medicine.diagnostic_test, Left bundle branch block, Cardiac electrophysiology, business.industry, Computer modeling, Magnetic resonance imaging, Middle Aged, medicine.disease, Heart failure, cardiovascular system, Cardiology, Left axis deviation, Female, QRS axis, Cardiology and Cardiovascular Medicine, Qrs axis, business, Left-axis deviation, Electromagnetic Phenomena
Abstract: Possible mechanisms of left-axis deviation (LAD) in the setting of left bundle branch block (LBBB) include differences in cardiac electrophysiology, structure, or anatomic axis.The purpose of this study was to clarify the mechanism(s) responsible for LAD in patients with LBBB.Twenty-nine patients with nonischemic cardiomyopathies and LBBB underwent noninvasive electrocardiographic imaging (ECGi), cardiac computed tomography, and magnetic resonance imaging in order to define ventricular electrical activation, characterize cardiac structure, and determine the cardiac anatomic axis.Sixteen patients had a normal QRS axis (NA) (mean axis 8° ± 23°), whereas 13 patients had LAD (mean axis -48° ± 13°; P.001). Total activation times were longer in the LAD group (112 ± 25 ms vs 91 ± 14 ms; P = .01) due to delayed activation of the basal anterolateral region (107 ± 10 ms vs 81 ± 17 ms; P .001). Left ventricular (LV) activation in patients with LAD was from apex to base, in contrast to a circumferential pattern of activation in patients with NA. Apex-to-base delay was longer in the LA group (95 ± 13 ms vs 64 ± 21 ms; P.001) and correlated with QRS frontal axis (RLAD in LBBB appears to be due to electrophysiological abnormalities rather than structural factors or cardiac anatomic axis.
Published: 2021

14. Microscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 -- Derivation of the macroscopic tridomain model by unfolding homogenization method

Author: Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad, Raafat Talhouk, Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), 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), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ), Ecole Supérieure d'Ingénieurs Léonard de Vinci (ESILV), Ecole Doctorale des Sciences et de la Technologie (EDST), Lebanese University [Beirut] (LU), and ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011)
Subjects: Mathematics - Analysis of PDEs, General Mathematics, Tridomain model, FOS: Mathematics, homogenization theory, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], reaction-diffusion system, time-periodic unfolding method, cardiac electric field, gap junctions, Analysis of PDEs (math.AP)
Abstract: We study the homogenization of a novel microscopic tridomain system, allowing for a more detailed analysis of the properties of cardiac conduction than the classical bidomain and monodomain models. In (Acta Appl.Math. 179 (2022) 1--35), we detail this model in which gap junctions are considered as the connections between adjacent cells in cardiac muscle and could serve as alternative or supporting pathways for cell-to-cell electrical signal propagation. Departing from this microscopic cellular model, we apply the periodic unfolding method to derive the macroscopic tridomain model. Several difficulties prevent the application of unfolding homogenization results, including the degenerate temporal structure of the tridomain equations and a nonlinear dynamic boundary condition on the cellular membrane. To prove the convergence of the nonlinear terms, especially those defined on the microscopic interface, we use the boundary unfolding operator and a Kolmogorov--Riesz compactness's result., arXiv admin note: text overlap with arXiv:2201.03914
Published: 2022

15. Inter-individual differences in cell composition across the ventricular wall may explain variability in ECG response to serum potassium and calcium variations

Author: 'Syed Hassaan Ahmed Bukhari, Carlos Sánchez, Pablo Laguna, Mark Potse, Esther Pueyo\\', Aragón Institute of Engineering Research [Zaragoza] (I3A), University of Zaragoza - Universidad de Zaragoza [Zaragoza], Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Instituto de Salud Carlos III [Madrid] (ISC)-ministerio de ciencia e innovacion, 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), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), This work was granted access to the HPC resources of IDRIS under the allocation 2021-A0110307379 made by GENCI., ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), European Project: 764738,PIC, and European Project: 638284,H2020,ERC-2014-STG,MODELAGE(2015)
Subjects: [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, [INFO]Computer Science [cs]
Abstract: International audience; Non-invasive monitoring of serum potassium ([K + ]) and calcium ([Ca 2+ ]) concentration can help to prevent arrhythmia in kidney patients. Current electrocardiogram (ECG) markers, including the T wave width (T w) and its time-warped temporal morphological variability (d U w), correlate significantly with [K + ] and [Ca 2+ ] but these relations vary strongly between patients. We hypothesized that inter-individual differences in cell type distribution across the ventricular wall can explain this variability. We computed T w and d U w in simulated ECGs from a human heart-torso model at different proportions of endo-, mid-, and epicardial cells, while varying [K + ] (3 to 6.2 mM) and [Ca 2+ ] (1.4 to 3.2 mM). Electrical activity was simulated with a reaction-diffusion model with modified Ten Tusscher-Panfilov dynamics. Results were compared to data from 29 patients. T w and d U w correlated strongly with [K + ] (absolute median Pearson coefficient r = 0.70 to 0.93) and [Ca 2+ ] (r = 0.69 to 0.86) in simulations and in patients. Different cell type distributions reproduced inter-patient variability, with the same sign and magnitude of r. In conclusion, the inter-patient variability in the relation between serum electrolytes and their ECG markers can indeed be explained by inter-individual differences in cell type distribution across the ventricular wall.
Published: 2022

16. A Patient-Specific Equivalent Dipole Model

Author: Cardoso, Gabriel, Robin, Geneviève, Arrieula, Andony, Potse, Mark, Haïssaguerre, Michel, Moulines, Eric, Dubois, Rémi, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), 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), Université d'Évry-Val-d'Essonne (UEVE), 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), CHU Bordeaux [Bordeaux], Modélisation en pharmacologie de population (XPOP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), ANR-11-EQPX-0030,MUSIC,Plateforme multi-modale d'exploration en cardiologie(2011), and European Project: 715093,H2020,ERC-2016-STG,ECSTATIC(2017)
Subjects: [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, [MATH]Mathematics [math]
Abstract: International audience; Sophisticated models for the electrocardiographic inverse problem are available, but their reliance on imaging data and large numbers of electrodes limit their use. Simple models such as the equivalent dipole model (EDM) therefore remain relevant. We developed a probabilistic approach to the equivalent unbounded uniform single dipole problem and developed a natural extension to the bounded nonuniform case that relies on a patientspecific statistical inference of the propagation mechanism between the location of the dipole and the electrode locations. The two models were tested on data simulated with a detailed heart-torso model with four different activation sequences and three different sets of tissue characteristics. We observed a throughout enhancement of the ability to reconstruct the ECG of the patient-specific model when compared to the uniform unbounded dipole model.
Published: 2022

17. Accelerating stabilization of whole-heart models after changes in cycle length

Author: 'Syed Hassaan Ahmed Bukhari, Carlos Sánchez, Esther Pueyo, Mark Potse\\', Aragón Institute of Engineering Research [Zaragoza] (I3A), University of Zaragoza - Universidad de Zaragoza [Zaragoza], Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), 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), IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], This work was granted access to the HPC resources of IDRIS under the allocation 2021-A0110307379 made by GENCI., ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), European Project: 764738,PIC, and European Project: 638284,H2020,ERC-2014-STG,MODELAGE(2015)
Subjects: [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, [INFO]Computer Science [cs]
Abstract: International audience; Parameter changes can cause long-term drift in membrane models. To reduce the cost of whole-heart simulations with such changes the stabilization can be performed in isolated-cell models, but it can then still take many beats to stabilize the full model. We hypothesized that differences in activation time leading to cycle length (CL) variability before the first beat contribute to this. To remove this variability we froze most state variables of the model until the sodium current activated. Simulations were performed with CL 400, 500, 600 and 1000 ms and modified Ten Tusscher-Panfilov 2006 dynamics. Isolated endocardial, mid-myocardial, and epicardial cells were simulated for 1000 beats. Their final states were then copied to a model of the whole human ventricles, which was run for 5 beats, with and without freezing. Stabilization of the full model took three to four beats. Freezing of the membrane state accelerated stabilization in some cell types but caused opposite drifts in others. Drifts were largest in the epicardial and mid-myocardial layers, and not in particular at their interfaces. Freezing of membrane state may help to accelerate stabilization but in our scenarios other types of drift dominate and may be aggravated by freezing, as it inhibits electrotonic interactions.
Published: 2022

18. Activation Sites Estimation using a Fast Algorithm Based on an Eikonal Equation

Author: Fehrenbach, Jérôme, Weynans, Lisl, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), 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, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]
Subjects: [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience
Published: 2022

19. MUSIC: Cardiac Imaging, Modelling and Visualisation Software for Diagnosis and Therapy

Author: Mathilde Merle, Florent Collot, Julien Castelneau, Pauline Migerditichan, Mehdi Juhoor, Buntheng Ly, Valery Ozenne, Bruno Quesson, Nejib Zemzemi, Yves Coudière, Pierre Jaïs, Hubert Cochet, Maxime Sermesant, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Service Expérimentation et Développement [Bordeaux] (SED), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), 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], Cardiovasculaire, métabolisme, diabétologie et nutrition (CarMeN), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Hospices Civils de Lyon (HCL)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), E-Patient : Images, données & mOdèles pour la médeciNe numériquE (EPIONE), Inria Sophia Antipolis - Méditerranée (CRISAM), 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), Hôpital Haut-Lévêque - CHU de Bordeaux (Centre médico chirurgical Magellan), ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), ANR-11-EQPX-0030,MUSIC,Plateforme multi-modale d'exploration en cardiologie(2011), and European Project: 715093,H2020,ERC-2016-STG,ECSTATIC(2017)
Subjects: Fluid Flow and Transfer Processes, inverse problems, Process Chemistry and Technology, General Engineering, multimodal, deep learning, biophysical modelling, electrophysiology, cardiac imaging, Computer Science Applications, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, General Materials Science, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Instrumentation
Abstract: International audience; The tremendous advancement of cardiac imaging methods, the substantial progress in predictive modelling, along with the amount of new investigative multimodalities, challenge the current technologies in the cardiology field. Innovative, robust and multimodal tools need to be created in order to fuse imaging data (e.g., MR, CT) with mapped electrical activity and to integrate those into 3D biophysical models. In the past years, several cross-platform toolkits have been developed to provide image analysis tools to help build such software. The aim of this study is to introduce a novel multimodality software platform dedicated to cardiovascular diagnosis and therapy guidance: MUSIC. This platform was created to improve the image-guided cardiovascular interventional procedures and is a robust platform for AI/Deep Learning, image analysis and modelling in a newly created consortium with international hospitals. It also helps our researchers develop new techniques and have a better understanding of the cardiac tissue properties and physiological signals. Thus, this extraction of quantitative information from medical data leads to more repeatable and reliable medical diagnoses.
Published: 2022
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20. A practical algorithm to build geometric models of cardiac muscle structure

Author: Potse, Mark, Cirrottola, Luca, Froehly, Algiane, 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], 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 Polytechnique de Bordeaux (Bordeaux INP), Service Expérimentation et Développement [Bordeaux] (SED), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), This work was granted access to HPC resources of IDRIS under GENCI allocation 2021- A0110307379., and European Project: 955495,MICROCARD
Subjects: Biological systems, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, [INFO]Computer Science [cs], Mesh adaptation, Level-set Methods, Cardiac modeling
Abstract: International audience; Cardiac muscle tissue has a unique, network-like structure. Three-dimensional models of this structure are needed for simulations of cardiac electrophysiology and mechanics. We developed an algorithm to produce such models artificially, using an implicit surface expressed on a tailored unstructured multi-domain mesh to define the cell membranes. The algorithm first creates a random network of cell centers, observing angle and distance criteria inferred from real tissue. The space around the network edges is assigned to the cellular domains based on the nearest half-edge. The network is then immersed in a regular tetrahedral mesh which is refined to fit the domain boundaries and to offer sufficient density around the cell membrane. The refinements are alternated with basic mesh improvement operations to maintain an acceptable mesh quality. On the refined mesh a level-set function is expressed that defines the cell membrane. The remeshing code Mmg3d is then used to discretize the level set while retaining the domains, and to improve the quality of the final mesh. A serial implementation of the algorithm was able to produce meshes of a few hundreds of cardiac cells in 15 minutes, but we are still facing difficulties in the remesher, likely resulting from the unusual complexity of these meshes. It was still possible, however, to correctly mesh a small network of cells that was designed to be replicated by successive mirroring. This allowed us to build models of upto 1 cm 3 of tissue (11 million cells and 370 billion tetrahedra) that now serve in performance tests of a large-scale simulation code.
Published: 2022

21. Microscopic Tridomain Model of Electrical Activity in the Heart with Dynamical Gap Junctions. Part 1 -- Modeling and Well-Posedness

Author: Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad, Raafat Talhouk, Mathématiques, Image et Applications - EA 3165 (MIA), La Rochelle Université (ULR), 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], Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ), Ecole Doctorale des Sciences et de la Technologie (EDST), Lebanese University [Beirut] (LU), This research was supported by IEA-CNRS in the context of HIPHOP project., and ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011)
Subjects: Mathematics - Analysis of PDEs, Cardiac electro-physiology, Applied Mathematics, Tridomain model, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Weak solution, Uniqueness, Global existence, Gap junctions, Analysis of PDEs (math.AP)
Abstract: International audience; We present a novel microscopic tridomain model describing the electrical activity in cardiac tissue with dynamical gap junctions. The microscopic tridomain system consists of three PDEs modeling the tissue electrical conduction in the intra-and extra-cellular domains, supplemented by a nonlinear ODE system for the dynamics of the ion channels and the gap junctions. We establish the global existence and uniqueness of the weak solutions to our microscopic tridomain model. The global existence of solution, which constitutes the main result of this paper, is proved by means of an approximate non-degenerate system, the Faedo-Galerkin method, and an appropriate compactness argument.
Published: 2022

22. Reconstruction of three-dimensional biventricular activation based on the 12-lead electrocardiogram via patient-specific modelling

Author: Frits W. Prinzen, Giulio Conte, Rolf Krause, Simone Pezzuto, Mark Potse, Maria Luce Caputo, François Regoli, Angelo Auricchio, Francesco Maffessanti, Fysiologie, RS: Carim - H06 Electro mechanics, Clinical sciences, Center for Computational Medicine in Cardiology (CCMC), Università della Svizzera italiana = University of Italian Switzerland (USI), Cardiovascular Research Institute Maastricht (CARIM), Maastricht University [Maastricht], 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-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, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], 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), Cardiocentro Ticino [Lugano], Universität Zürich [Zürich] = University of Zurich (UZH), Theo Rossi di Montelera Foundation (Lausanne, Switzerland), Metis Foundation Sergio Mantegazza (Lugano, Switzerland), Fidinam Foundation (Lugano, Swizerland), Swiss Heart Foundation (Bern, Switzerland), SNSF project 32003B_165802 (Bern, Switzerland), Horten Foundation (Castelrotto, Switzerland), and CSCS—Swiss National Supercomputing Centre production grant s778 (Lugano, Switzerland)., University of Zurich, Pezzuto, Simone, 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, 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: CARDIAC ELECTROPHYSIOLOGY, medicine.medical_specialty, Patient-specific modelling, Heart Ventricles, 0206 medical engineering, 12 lead electrocardiogram, 610 Medicine & health, 02 engineering and technology, 030204 cardiovascular system & hematology, Heart Ventricles/diagnostic imaging, Techincal Issues, 11171 Cardiocentro Ticino, 2705 Cardiology and Cardiovascular Medicine, Nerve conduction velocity, VALIDATION, 03 medical and health sciences, QRS complex, Electrocardiography, 2737 Physiology (medical), 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Physiology (medical), Internal medicine, Eikonal model, medicine, Humans, magnetic resonance imaging, AcademicSubjects/MED00200, cardiovascular diseases, Endocardium, Coronary sinus, medicine.diagnostic_test, Ventricular activation • Three-dimensional activation, business.industry, Cardiac electrophysiology, Body Surface Potential Mapping, Magnetic resonance imaging, 020601 biomedical engineering, Three-dimensional activation, Ventricular activation, Twelve-lead electrocardiogram, Cardiology, cardiovascular system, patient-specific modeling, business, Cardiology and Cardiovascular Medicine
Abstract: Aims Non-invasive imaging of electrical activation requires high-density body surface potential mapping. The nine electrodes of the 12-lead electrocardiogram (ECG) are insufficient for a reliable reconstruction with standard inverse methods. Patient-specific modelling may offer an alternative route to physiologically constraint the reconstruction. The aim of the study was to assess the feasibility of reconstructing the fully 3D electrical activation map of the ventricles from the 12-lead ECG and cardiovascular magnetic resonance (CMR). Methods and results Ventricular activation was estimated by iteratively optimizing the parameters (conduction velocity and sites of earliest activation) of a patient-specific model to fit the simulated to the recorded ECG. Chest and cardiac anatomy of 11 patients (QRS duration 126–180 ms, documented scar in two) were segmented from CMR images. Scar presence was assessed by magnetic resonance (MR) contrast enhancement. Activation sequences were modelled with a physiologically based propagation model and ECGs with lead field theory. Validation was performed by comparing reconstructed activation maps with those acquired by invasive electroanatomical mapping of coronary sinus/veins (CS) and right ventricular (RV) and left ventricular (LV) endocardium. The QRS complex was correctly reproduced by the model (Pearson’s correlation r = 0.923). Reconstructions accurately located the earliest and latest activated LV regions (median barycentre distance 8.2 mm, IQR 8.8 mm). Correlation of simulated with recorded activation time was very good at LV endocardium (r = 0.83) and good at CS (r = 0.68) and RV endocardium (r = 0.58). Conclusion Non-invasive assessment of biventricular 3D activation using the 12-lead ECG and MR imaging is feasible. Potential applications include patient-specific modelling and pre-/per-procedural evaluation of ventricular activation.
Published: 2021

23. Optimal control for nonlocal reaction‐diffusion system describing calcium dynamics in cardiac cell

Author: Mostafa Bendahmane, Fahd Karami, Elmahdi Erraji, 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], Ecole Supérieure de Technologie d'Essaouira, Université Cadi Ayyad [Marrakech] (UCA), and the research program PPR supported by CNRST (Morocco), project 'Modèles Mathématiques appliquées l’environnement, à l’imagerie médicale et aux biosystèmes'
Subjects: calcium model, Computer simulation, [SDV]Life Sciences [q-bio], General Mathematics, Weak solution, finite element method, General Engineering, nonlocal diffusion, weak solution, Mechanics, Optimal control, first order optimality conditions, Cardiac cell, Finite element method, Calcium dynamics, numerical simulation, Reaction–diffusion system, [MATH]Mathematics [math], Mathematics
Abstract: International audience; The purpose of this paper is to introduce an optimal control for a nonlocal calcium dynamic model in a cardiac cell acting on ryanodine receptors. The optimal control problem is considered as a coupled nonlocal reaction-diffusion system with a transmission boundary condition covering the sarcoplasmic reticulum and cytosolic domain. We establish the well-posedness result of the adjoint problem using Faedo-Galerkin approximation, a priori estimates and compactness arguments. The numerical discretization of direct and adjoint problems is realized by using the implicit Euler method in time and the finite element for spatial discretization. Moreover, we obtain the stability result in the 2-norm for the direct and the adjoint discrete problems. Finally, in order to illustrate the control of our calcium dynamic model, we present some numerical experiments devoted to constant and nonlocal diffusions using the proposed numerical scheme.
Published: 2020

24. Méthodes numériques pour la résolution du problème inverse en électrocardiographie dans le cas d’anomalies structurelles du tissu cardiaque

Author: Bouhamama, Oumayma, 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), Université de Bordeaux, Lisl Weynans, Laura Bear, and STAR, ABES
Subjects: Arythmie ventriculaire, Inverse Problems, Calcul scientifique, Myocardial Infarction, Algorithmes de Monte Carlo, Infarctus du myocarde, Scientific Computing, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Electrocardiography Imaging, Imagerie électrocardiaque, Problèmes inverses, Ventricular Arrhythmia, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, Monte-Carlo Algorithms
Abstract: The continued development of non invasive methods of mapping the electri-cal activity of the heart is motivated by the general hope that they may be clinically useful in the diagnosis and treatment of cardiac rhythm disorders, responsible for 80% of the 350,000 sudden cardiac arrest deaths that occur each year in Europe [LZ06]. Non-invasive electrocardiographic imaging (ECGI) provides real-time panoramic images of epicardial electrical activity from potential measurements on the surface of the torso. Though several methods have been developped for ECGI, recent validation studies have demonstrated that current implementations are inaccurate in reconstructing electrical activity in the presence of conduction anomalies and in structurally heterogeneous hearts. ECGI is known to produce artificial lines of block in healthy tissue, raising doubts about the ability of these methods to detect the presence of regions of true conduction slowly in structurally abnormal hearts.The objective of this thesis is to develop a new method in order to improve ECGI and its ability to detect regions of slow conduction in the presence of structural abnormalities.First, we presented a new method for solving the inverse problem of electro-cardiography. The idea of the method is to combine the solutions obtained with classical formulations in order to select the most accurate method in each area and at each time step, based on their residuals of the torso surface. This new approach, named the Patchwork Method (PM), is evaluated, along with other classical inverse methods, using simulated and experimental data. The stability and robustness of this new approach are also tested by adding Gaussian measurement noise to the torso surface potentials.Secondly, we focused on the detection of areas with damaged cardiac tissue. The different ECGI methods were evaluated based on the caracteristics of bipolar signals associated with structural abnormalities : amplitude, QRS duration and fragmentation. Being unable to detect the damaged areas using these features, we have developed a new method to detect slow conduction areas using the activation time gradient. Subsequently, we evaluated the ability of the standard ECGI methods, as well as the Patchwork method, to locate slow conduction areas and reduce the frequency of artificial lines of block.The main contribution of this thesis is the development of a new ECGI ap-proach to reconstruct electrical information on the surface of the heart. The Patchwork method has demonstrated a higher level of accuracy in recons-tructing activation maps and locating breakthrough sites than standard ECGI methods. This method is an effective tool to help overcome some of the limi-tations of conventional numerical methods in structurally abnormal hearts, showing its ability to detect regions of slow conduction using the activation time gradient. Importantly, these improvements include a reduction in the frequency of artificial lines of block. This has important clinical implications as it may help reduce false diagnosis of conduction disorders., Le développement continu des méthodes non invasives de cartographie de l’activité électrique du cœur est motivé par l’espoir général qu’elles puissent être cliniquement utiles dans le diagnostic et le traitement des troubles du rythme cardiaque, responsables de 80 % des 350 000 décès par arrêt cardiaque soudain qui surviennent chaque année en Europe [LZ06]. L’imagerie électrocardiographique non invasive (ECGI) fournit des images panoramiques en temps réel de l’activité électrique épicardique à partir de mesures de poten-tiel à la surface du torse. Bien que plusieurs méthodes aient été développées pour l’ECGI, des études de validation récentes ont démontré que les implémentations actuelles sont imprécises dans la reconstruction de l’activité électrique en présence d’anomalies de conduction et dans les cœurs structurellement hétérogènes. L’ECGI est connue pour produire des lignes de bloc artificielles dans les tissus sains, ce qui fait douter de la capacité de ces méthodes à détecter la présence de régions de véritable conduction lente dans les cœurs structurellement anormaux.L’objectif de cette thèse est de développer une nouvelle méthode afin d’améliorer l’ECGI et sa capacité à détecter les régions de conduction lente en présence d’anomalies structurelles.Tout d’abord, nous avons présenté une nouvelle méthode pour résoudre le problème inverse de l’électrocardiographie. L’idée de la méthode est de combiner les solutions obtenues avec les formulations classiques afin de sélectionner la méthode la plus précise dans chaque zone et à chaque pas de temps, en fonction de leurs résidus de la surface du torse. Cette nouvelle approche, appelée la méthode Patchwork (PM), est évaluée, avec d’autres méthodes inverses classiques, à l’aide des données simulées et expérimentales. La stabilité et la robustesse de cette nouvelle approche sont également testées en ajoutant un bruit de mesure Gaussien aux potentiels de la surface du torse.Deuxièmement, nous nous sommes concentrés sur la détection de zones pré-sentant des tissus cardiaques endommagés. Les différentes méthodes d’ECGI ont été évaluées sur la base des caractéristiques des signaux bipolaires associés aux anomalies structurelles : amplitude, durée du QRS et fragmentation. N’étant pas en mesure de détecter les zones endommagées à l’aide de ces caractéristiques, nous avons développé une nouvelle méthode pour détecter les zones de conduction lente en utilisant le gradient de temps d’activation. Par la suite, nous avons évalué la capacité des méthodes ECGI standard, ainsi que de la méthode Patchwork, à localiser les zones de conduction lente et à réduire la fréquence des lignes de bloc artificielles.La principale contribution de cette thèse est le développement d’une nouvelle approche ECGI pour reconstruire les informations électriques à la surface du cœur. La méthode Patchwork a démontré un niveau de précision plus élevé dans la reconstruction des cartes d’activation et la localisation des sites de percée que les méthodes ECGI standard. Cette méthode est un outil efficace pour aider à surmonter certaines des limites des méthodes numériques conventionnelles dans les cœurs structurellement anormaux, montrant sa capacité à détecter les régions de conduction lente en utilisant le gradient de temps d’activation. Il est important de noter que ces améliorations incluent une réduction de la fréquence des lignes de bloc artificielles. Cela a des implications cliniques importantes car cela peut contribuer à réduire les faux diagnostics de troubles de la conduction.
Published: 2022

25. Impact of intraventricular septal fiber orientation on cardiac electromechanical function

Author: Jairo Rodríguez-Padilla, Argyrios Petras, Julie Magat, Jason Bayer, Yann Bihan-Poudec, Dounia El Hamrani, Girish Ramlugun, Aurel Neic, Christoph M. Augustin, Fanny Vaillant, Marion Constantin, David Benoist, Line Pourtau, Virginie Dubes, Julien Rogier, Louis Labrousse, Olivier Bernus, Bruno Quesson, Michel Haïssaguerre, Matthias Gsell, Gernot Plank, Valéry Ozenne, Edward Vigmond, E-Patient : Images, données & mOdèles pour la médeciNe numériquE (EPIONE), 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), Austrian Academy of Sciences (OeAW), 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], 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), Medical University Graz, Medical University of Graz, BioTechMed-Graz, Graz University of Technology [Graz] (TU Graz)-Karl-Franzens-Universität Graz-Medical University Graz, Biologie des maladies cardiovasculaires = Biology of Cardiovascular Diseases, Université de Bordeaux (UB)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Institut de rythmologie et modélisation cardiaque [Pessac] (IHU Liryc), Hôpital Haut-Lévêque [CHU Bordeaux], CHU Bordeaux [Bordeaux], Graz University of Technology [Graz] (TU Graz), Centre de résonance magnétique des systèmes biologiques (CRMSB), 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), ANR-17-CE19-0007,CARTLOVE,Contrôle des Ablations Radiofréquence par Thermométrie (IRM) pour Les Oreillettes et VEntricules(2017), ANR-19-ECVD-0006,SICVALVES,Multiscale Modeling of Valvular Heart Diseases - Understanding the Mechanisms of Adverse Remodeling to Improve Precision Medicine(2019), and European Project: 680969,H2020,H2020-HCO-2015,ERA-CVD(2015)
Subjects: Mammals, fiber orientation, Sheep, Physiology, Swine, Heart Ventricles, Myocardium, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Ventricular Septum, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Rats, Diffusion Tensor Imaging, Dogs, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Physiology (medical), intraventricular septum, normal structural discontinuities, electromechanical models, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Animals, Diamond, Cardiology and Cardiovascular Medicine, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: Cardiac fiber direction is an important factor determining the propagation of electrical activity, as well as the development of mechanical force. In this article, we imaged the ventricles of several species with special attention to the intraventricular septum to determine the functional consequences of septal fiber organization. First, we identified a dual-layer organization of the fiber orientation in the intraventricular septum of ex vivo sheep hearts using diffusion tensor imaging at high field MRI. To expand the scope of the results, we investigated the presence of a similar fiber organization in five mammalian species (rat, canine, pig, sheep, and human) and highlighted the continuity of the layer with the moderator band in large mammalian species. We implemented the measured septal fiber fields in three-dimensional electromechanical computer models to assess the impact of the fiber orientation. The downward fibers produced a diamond activation pattern superficially in the right ventricle. Electromechanically, there was very little change in pressure volume loops although the stress distribution was altered. In conclusion, we clarified that the right ventricular septum has a downwardly directed superficial layer in larger mammalian species, which can have modest effects on stress distribution.
Published: 2022

26. Mathematical modeling of the cardiac mitochondrial activity

Author: Tarraf, Bachar, 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, and Michael Leguebe
Subjects: Experimental validation, Analyse de sensibilité, Mitochondries, Scientific Computing, Classification, Équations différentielles ordinaires, Mitochondria, Estimation des paramètres, Parameters estimation, Validation expérimentale, Sensitivity analysis, Ordinary differential equations, Modélisation biologique, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: Cardiac mitochondria are intracellular organelles that have many crucial roles, including energy metabolism and cellular calcium regulation. They are thus linked to the excitation-contraction cycle of the heart cell. A large number of mathematical models have been proposed to better understand the cardiac mitochondrial dynamics, but they generally show a high level of complexity, and their parameters are very hard to fit to experimental data. In this work, we first derive a model, that includes the basic mitochondrial mechanisms, based on thermodynamics free energy-transduction principles and results from the literature. We propose simple expressions for the mitochondrial regulated ionic exchanges and reaction rates, that allow reducing the number of parameters to a minimum. Using experimental data of mitochondrial respiration, we proceed with global sensitivity analysis on the model parameters in order to quantify their influence on the output of the model. The influential parameters are then calibrated using a genetic algorithm. Results show that the model is able to reproduce respiration rates of mitochondria with very low variability of the parameters between the different experiments. In a second part, we incorporate into the model a complex mechanism known as the mitochondrial permeability transition pore (mPTP). The functioning of this pore is poorly understood to our days and is thought to behave either physiologically or pathologically depending on its opening state. Next, since a model evaluation is time-consuming, we use a machine learning supervised classification algorithm to build a meta-model that is able to classify the output of the model without evaluating it. We then use this meta-model to perform parameter inference using a maximum likelihood iterative algorithm. Using experimental data on the mPTP opening type, we compute adequate statistical distributions for some of the parameters of the model.Overall, the utility of such a model in itself is that it can be used to make predictions of mechanisms of interest related to mitochondrial respiration, or even to perform simulations of some unfeasible experiments of interest. The model guarantees, at least qualitatively, the ability to represent population of cardiac mitochondria. It could also be interesting to eventually incorporate this model into cardiac excitation-contraction models. That is because the potential model could make it possible to explore the involvement of mitochondrial ROS and mPTP in the regulation of the excitation-contraction coupling in cardiomyocytes, under physiological and pathological conditions.; Les mitochondries cardiaques sont des organites intracellulaires qui ont de nombreux rôles cruciaux, notamment le métabolisme énergétique et la régulation du calcium cellulaire. Elles sont ainsi liées au cycle d’excitation-contraction de la cellule cardiaque. Un grand nombre de modèles mathématiques ont été proposés pour mieux comprendre la dynamique mitochondriale cardiaque, mais ils montrent généralement un haut niveau de complexité, et leurs paramètres sont très difficiles à recaler aux données expérimentales.Dans ce travail, nous écrivons d’abord un modèle, qui inclut les mécanismes mitochondriaux de base, basé sur des principes thermodynamiques de transduction d’énergie libre et des résultats de la littérature. Nous proposons des expressions simples pour les réactions et les échanges ioniques gérés par la mitochondrie, qui permettent de réduire le nombre de paramètres au minimum. A partir de données expérimentales de respiration mitochondriale,nous procédons à une analyse de sensibilité globale sur les paramètres du modèle afin de quantifier leur influence sur la sortie du modèle. Les paramètres influents sont ensuite recalés à l’aide d’un algorithme génétique. Les résultats montrent que le modèle est capable de reproduire les taux de respiration des mitochondries avec une très faible variabilité des paramètres entre les différentes expériences.Dans une seconde partie, nous incorporons au modèle un mécanisme complexe connu sous le nom de pore de transition de perméabilité mitochondriale (mPTP). Le fonctionnement de ce pore est mal connu de nos jours et on pense qu’il peut se comporter physiologiquement ou pathologiquement en fonction de son état d’ouverture. Ensuite, comme l’évaluation du modèle est coûteuse, nous utilisons un algorithme de classification supervisé par apprentissage automatique pour construire un méta-modèle capable de caractériser la sortie du modèle sans l’évaluer.Nous utilisons ensuite ce méta-modèle pour effectuer une inférence de paramètres à l’aide d’un algorithme itératif à maximum de vraisemblance. En utilisant des données expérimentales sur le type d’ouverture du mPTP, nous calculons des distributions statistiques adéquates pour certains des paramètres du modèle.Dans l'ensemble, l'utilité d'un tel modèle en soi est qu'il peut être utilisé pour faire des prédictions de mécanismes d'intérêt liés à la respiration mitochondriale, ou encore pour effectuer des simulations de quelques expériences d'intérêt irréalisables. Le modèle garantit, au moins qualitativement, la capacité de représenter la population de mitochondries cardiaques. Il pourrait également être intéressant d'intégrer à terme ce modèle aux modèles d'excitation-contraction cardiaque. En effet, le modèle potentiel pourrait permettre d'explorer l'implication de ROS mitochondriaux et mPTP dans la régulation du couplage excitation-contraction en cardiomyocytes, dans des conditions physiologiques et pathologiques.
Published: 2022

27. A positive cell vertex Godunov scheme for a Beeler–Reuter based model of cardiac electrical activity

Author: Mostafa Bendahmane, Fatima Mroue, Mazen Saad, 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), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria), 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 Libanaise, Ecole Doctorale des Sciences et de Technologie, and École Centrale de Nantes (ECN)
Subjects: Vertex (graph theory), Numerical Analysis, Finite volume method, [SDV]Life Sciences [q-bio], Applied Mathematics, Godunov's scheme, Finite Element, Finite element method, Godunov Scheme, Computational Mathematics, Maximum principle, Monodomain model, Applied mathematics, [MATH]Mathematics [math], Finite volume, Convergence, Analysis, Mathematics
Abstract: International audience; The monodomain model is a widely used model in electrocardiology to simulate the propagation of electrical potential in the myocardium. In this paper, we investigate a positive nonlinear control volume finite element (CVFE) scheme, based on Godunov's flux approximation of the diffusion term, for the monodomain model coupled to a physiological ionic model (the Beeler-Reuter model) and using an anisotropic diffusion tensor. In this scheme, degrees of freedom are assigned to vertices of a primal triangular mesh, as in conforming finite element methods. The diffusion term which involves an anisotropic tensor is discretized on a dual mesh using the diffusion fluxes provided by the conforming finite element reconstruction on the primal mesh and the other terms are discretized by means of an upwind finite volume method on the dual mesh. The scheme ensures the validity of the discrete maximum principle without any restriction on the transmissibility coefficients. By using a compactness argument, we obtain the convergence of the discrete solution and as a consequence, we get the existence of a weak solution of the original model. Finally, we illustrate the efficiency of the proposed scheme by exhibiting some numerical results.
Published: 2020

28. Inferring characteristics of bacterial swimming in biofilm matrix from time-lapse confocal laser scanning microscopy

Author: Guillaume Ravel, Michel Bergmann, Alain Trubuil, Julien Deschamps, Romain Briandet, Simon Labarthe, from patterns to models in computational biodiversity and biotechnology (PLEIADE), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-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)-Biodiversité, Gènes & Communautés (BioGeCo), Université de Bordeaux (UB)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Biodiversité, Gènes & Communautés (BioGeCo), Université de Bordeaux (UB)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Modeling Enablers for Multi-PHysics and InteractionS (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), Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), MICrobiologie de l'ALImentation au Service de la Santé (MICALIS), AgroParisTech-Université Paris-Saclay-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Financial support was provided by the French National Research Agency ANR-12-ALID-0006., ANR-12-ALID-0006,GreenSwimmers,Sensibilisation de biofilms industriels à l'action de désinfectants par l'infiltration de bactéries hyper-motiles(2012), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Inria Bordeaux - Sud-Ouest, 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, 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 National de la Recherche Agronomique (INRA), Institut de Chimie de la Matière Condensée de Bordeaux (ICMCB), Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux-Institut de Chimie du CNRS (INC)-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), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), 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 Paris-Saclay
Subjects: [SDV]Life Sciences [q-bio], confocal microscopy, Time-Lapse Imaging, Quantitative Biology - Quantitative Methods, General Biochemistry, Genetics and Molecular Biology, biofilm, modelling, computational biology, [MATH]Mathematics [math], Ecosystem, Swimming, Quantitative Methods (q-bio.QM), Microscopy, Confocal, General Immunology and Microbiology, Bacteria, Extracellular Polymeric Substance Matrix, General Neuroscience, systems biology, General Medicine, bacterial swimmers, biochemical phenomena, metabolism, and nutrition, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [SDV.BIBS]Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], biofilm + microswimmer + image processing + inferrence + system dynamics, microswinner : image processing, Biofilms, FOS: Biological sciences, inferrence, system dynamics
Abstract: Biofilms are spatially organized communities of microorganisms embedded in a self-produced organic matrix, conferring to the population emerging properties such as an increased tolerance to the action of antimicrobials. It was shown that some bacilli were able to swim in the exogenous matrix of pathogenic biofilms and to counterbalance these properties. Swimming bacteria can deliver antimicrobial agents in situ, or potentiate the activity of antimicrobial by creating a transient vascularization network in the matrix. Hence, characterizing swimmer trajectories in the biofilm matrix is of particular interest to understand and optimize this new biocontrol strategy in particular, but also more generally to decipher ecological drivers of population spatial structure in natural biofilms ecosystems. In this study, a new methodology is developed to analyze time-lapse confocal laser scanning images to describe and compare the swimming trajectories of bacilli swimmers populations and their adaptations to the biofilm structure. The method is based on the inference of a kinetic model of swimmer populations including mechanistic interactions with the host biofilm. After validation on synthetic data, the methodology is implemented on images of three different species of motile bacillus species swimming in aAnyone who has ever cleaned a bathroom probably faced biofilms, the dark, slimy deposits that lurk around taps and pipes. These structures are created by bacteria which abandon their solitary lifestyle to work together as a community, secreting various substances that allow the cells to organise themselves in 3D and to better resist external aggression. Unwanted biofilms can impair industrial operations or endanger health, for example when they form inside medical equipment or water supplies. Removing these structures usually involves massive application of substances which can cause long-term damage to the environment. Recently, researchers have observed that a range of small rod-shaped bacteria – or ‘bacilli’ – can penetrate a harmful biofilm and dig transient tunnels in its 3D structure. These ‘swimmers’ can enhance the penetration of anti-microbial agents, or could even be modified to deliver these molecules right inside the biofilm. However, little is known about how the various types of bacilli, which have very different shapes and propelling systems, can navigate the complex environment that is a biofilm. This knowledge would be essential for scientists to select which swimmers could be the best to harness for industrial and medical applications. To investigate this question, Ravel et al. established a way to track how three species of bacilli swim inside a biofilm compared to in a simple fluid. A mathematical model was created which integrated several swimming behaviors such as speed adaptation and direction changes in response to the structure and density of the biofilm. This modelling was then fitted on microscopy images of the different species navigating the two types of environments. Different motion patterns for the three bacilli emerged, each showing different degrees of adapting to moving inside a biofilm. One species, in particular, was able to run straight in and out of this environment because it could adapt its speed to the biofilm density as well as randomly change direction. The new method developed by Ravel et al. can be redeployed to systematically study swimmer candidates in different types of biofilms. This would allow scientists to examine how various swimming characteristics impact how bacteria-killing chemicals can penetrate the altered biofilms. In addition, as the mathematical model can predict trajectories, it could be used in computational studies to examine which species of bacilli would be best suited in industrial settings.
Published: 2022

29. Three Scale Unfolding Homogenization Method Applied to Cardiac Bidomain Model

Author: Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad, Raafat Talhouk, Mathématiques, Image et Applications - EA 3165 (MIA), La Rochelle Université (ULR), 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], Laboratoire de Mathématiques Jean Leray (LMJL), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS), Ecole Doctorale des Sciences et de la Technologie (EDST), Lebanese University [Beirut] (LU), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Université de La Rochelle (ULR), 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)-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, Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Université de Nantes (UN)-Université de Nantes (UN)
Subjects: convergence, Applied Mathematics, Quantitative Biology::Tissues and Organs, 010102 general mathematics, homogenization theory, Bidomain model, reaction-diffusion system, 16. Peace & justice, periodic unfolding method, 01 natural sciences, Quantitative Biology::Cell Behavior, 010101 applied mathematics, Quantitative Biology::Subcellular Processes, Mathematics - Analysis of PDEs, double periodic media, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, doubleperiodic media, Analysis of PDEs (math.AP)
Abstract: In this paper, we are dealing with a rigorous homogenization result at two different levels for the bidomain model of cardiac electro-physiology. The first level associated with the mesoscopic structure such that the cardiac tissue consists of extracellular and intracellular domains separated by an interface (the sarcolemma). The second one related to the microscopic structure in such a way that the intracellular medium can only be viewed as a periodical layout of unit cells (mitochondria). At the interface between intra-and extracellular media, the fluxes are given by nonlinear functions of ionic and applied currents. A rigorous homogenization process based on unfolding operators is applied to derive the macroscopic (homogenized) model from our meso-microscopic bidomain model. We apply a three-scale unfolding method in the intracellular problem to obtain its homogenized equation at two levels. The first level upscaling of the intracellular structure yields the mesoscopic equation. The second step of the homogenization leads to obtain the intracellular homogenized equation. To prove the convergence of the nonlinear terms, especially those defined on the microscopic interface, we use the boundary unfolding method and a Kolmogorov-Riesz compactness's result. Next, we use the standard unfolding method to homogenize the extracellular problem. Finally, we obtain, at the limit, a reaction-diffusion system on a single domain (the superposition of the intracellular and extracellular media) which contains the homogenized equations depending on three scales. Such a model is widely used for describing the macroscopic behavior of the cardiac tissue, which is recognized to be an important messengers between the cytoplasm (intracellular) and the other extracellular inside the biological cells. Contents 2020 Mathematics Subject Classification. 65N55 and 35A01 and 35B27 and 35K57 and 65M.., arXiv admin note: substantial text overlap with arXiv:2201.03412
Published: 2022

30. Estimation of potassium levels in hemodialysis patients by T wave nonlinear dynamics and morphology markers

Author: Hassaan A. Bukhari, Carlos Sánchez, Sabarathinam Srinivasan, Flavio Palmieri, Mark Potse, Pablo Laguna, Esther Pueyo, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Aragón Institute of Engineering Research [Zaragoza] (I3A), University of Zaragoza - Universidad de Zaragoza [Zaragoza], Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Instituto de Salud Carlos III [Madrid] (ISC)-ministerio de ciencia e innovacion, 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), Centre de Recerca en Enginyeria Biomèdica [Catalunya] (CREB), Universitat Politècnica de Catalunya [Barcelona] (UPC), ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), European Project: 638284,H2020,ERC-2014-STG,MODELAGE(2015), European Project: 764738,PIC, and Universitat Politècnica de Catalunya. Doctorat en Enginyeria Biomèdica
Subjects: Ronyons -- Malalties, Kidneys -- Diseases, Enginyeria biomèdica [Àrees temàtiques de la UPC], Lyapunov exponents, Health Informatics, Potassi, Hemodiàlisi, 3. Good health, Computer Science Applications, Electrocardiogram, Electrocardiography, Potassium estimation, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Electrocardiografia, Hemodialysis, Potassium, T wave morphology, ComputingMilieux_MISCELLANEOUS
Abstract: Objective: Noninvasive screening of hypo- and hyperkalemia can prevent fatal arrhythmia in end-stage renal disease (ESRD) patients, but current methods for monitoring of serum potassium ([K+]) have important limita-tions. We investigated changes in nonlinear dynamics and morphology of the T wave in the electrocardiogram (ECG) of ESRD patients during hemodialysis (HD), assessing their relationship with [K+]and designing a [K+]estimator. Methods: ECG recordings from twenty-nine ESRD patients undergoing HD were processed. T waves in 2-min windows were extracted at each hour during an HD session as well as at 48 h after HD start. T wave nonlinear dynamics were characterized by two indices related to the maximum Lyapunov exponent (¿t, ¿wt) and a divergence-related index (¿). Morphological variability in the T wave was evaluated by three time warping- based indices (dw, reflecting morphological variability in the time domain, and da and dNLa, in the amplitude domain). [K+]was measured from blood samples extracted during and after HD. Stage-specific and patient- specific [K+]estimators were built based on the quantified indices and leave-one-out cross-validation was per-formed separately for each of the estimators. Results: The analyzed indices showed high inter-individual variability in their relationship with [K+]. Never-theless, all of them had higher values at the HD start and 48 h after it, corresponding to the highest [K+]. The indices ¿ and dw were the most strongly correlated with [K+](median Pearson correlation coefficient of 0.78 and 0.83, respectively) and were used in univariable and multivariable linear [K+]estimators. Agreement between actual and estimated [K+]was confirmed, with averaged errors over patients and time points being 0.000 ±0.875 mM and 0.046 ±0.690 mM for stage-specific and patient-specific multivariable [K+]estimators, respectively. Conclusion: ECG descriptors of T wave nonlinear dynamics and morphological variability allow noninvasive monitoring of [K+]in ESRD patients. Significance: ECG markers have the potential to be used for hypo- and hyperkalemia screening in ESRD patients.
Published: 2022

31. Source and metric estimation in the eikonal equation using optimization on a manifold

Author: Fehrenbach, Jérôme, Weynans, Lisl, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), 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), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-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), and Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3)
Subjects: eikonal equation, Control and Optimization, Modeling and Simulation, Inverse problem, electrocardiographic imaging, Discrete Mathematics and Combinatorics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Analysis
Abstract: We address the estimation of the source(s) location in the eikonal equation on a Riemann surface, as well as the determination of the metric when it depends on a few parameters. The available observations are the arrival times or are obtained indirectly from the arrival times by an observation operator, this frame is intended to describe electro-cardiographic imaging. The sensitivity of the arrival times is computed from \begin{document}$ {{{\rm{Log}}}}_x $\end{document} the log map wrt to the source \begin{document}$ x $\end{document} on the surface. The \begin{document}$ {{{\rm{Log}}}}_x $\end{document} map is approximated by solving an elliptic vectorial equation, using the Vector Heat Method. The \begin{document}$ L^2 $\end{document}-error function between the model predictions and the observations is minimized using Gauss-Newton optimization on the Riemann surface. This allows to obtain fast convergence. We present numerical results, where coefficients describing the metric are also recovered like anisotropy and global orientation.
Published: 2021

32. A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios

Author: Michel Bergmann, Lisl Weynans, Modeling Enablers for Multi-PHysics and InteractionS (MEMPHIS), 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), Modélisation et calculs pour l'électrophysiologie cardiaque (CARMEN), 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], This study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the Investments for the future Programme IdEx Bordeaux (ANR-10-IDEX-03-02)., 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, and ANR-10-IDEX-0003,IDEX BORDEAUX,Initiative d'excellence de l'Université de Bordeaux(2010)
Subjects: Discretization, finite differences, incompressible Navier–Stokes equations, 010103 numerical & computational mathematics, 01 natural sciences, law.invention, Regular grid, immersed interfaces, Physics::Fluid Dynamics, law, Projection method, Applied mathematics, Cartesian coordinate system, level-set, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, interface unknowns, Mathematics, Fluid Flow and Transfer Processes, QC120-168.85, projection method, Mechanical Engineering, Finite difference, Function (mathematics), Solver, Condensed Matter Physics, 010101 applied mathematics, Cartesian grid, Descriptive and experimental mechanics, incompressible Navier-Stokes equations, Compressibility, Thermodynamics, QC310.15-319
Abstract: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY); International audience; An Eulerian method to numerically solve incompressible bifluid problems with high density ratio is presented. This method can be considered as an improvement of the Ghost Fluid method, with the specificity of a sharp second-order numerical scheme for the spatial resolution of the discontinuous elliptic problem for the pressure. The Navier–Stokes equations are integrated in time with a fractional step method based on the Chorin scheme and discretized in space on a Cartesian mesh. The bifluid interface is implicitly represented using a level-set function. The advantage of this method is its simplicity to implement in a standard monofluid Navier–Stokes solver while being more accurate and conservative than other simple classical bifluid methods. The numerical tests highlight the improvements obtained with this sharp method compared to the reference standard first-order methods.
Published: 2021
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33. Global Lipschitz stability of multiple space dependent ionic parameters for the MEA/hiPSC-CM assays

Author: MAHJOUB Moncef, Nejib Zemzemi, Hamza Ammar, 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], SPICY, and LIRIMA
Subjects: [SDV]Life Sciences [q-bio], Applied Mathematics, Signal Processing, [MATH]Mathematics [math], Mathematical Physics, Computer Science Applications, Theoretical Computer Science
Abstract: In this paper, we consider an inverse problem of determining two space dependent ionic parameters of a strongly coupled parabolic-elliptic reaction–diffusion system arising in cardiac electrophysiology modeling when simulating drugs action with multi-electrode array/human induced pluripotent stem cells-cardiomyocytes assays. We use the bidomain model coupled to an ordinary differential equation and we consider the classical phenomenological model in cardiac electrophysiology of FitzHugh–Nagumo to describe the ionic exchanges at the microscopic level. Our main result is the uniqueness and a Lipschitz stability estimate for two ionic parameters ( k , γ ) of the model using sub-boundary observations over an interval of time. The key ingredients are a global Carleman-type estimates with a suitable observations acting on a part of the boundary.
Published: 2022

34. Prediction of Clinical Deep Brain Stimulation Target for Essential Tremor From 1.5 Tesla MRI Anatomical Landmarks

Author: Engelhardt, Julien, Cuny, Emmanuel, Guehl, Dominique, Burbaud, Pierre, Damon-Perrière, Nathalie, Dallies-Labourdette, Camille, Thomas, Juliette, Branchard, Olivier, Schmitt, Louise-Amélie, Gassa, Narimane, Zemzemi, Nejib, CHU Bordeaux [Bordeaux], Institut des Maladies Neurodégénératives [Bordeaux] (IMN), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), 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, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Université de Bordeaux (UB), 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, 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: Brain surgery, Deep brain stimulation (DBS) surgery, Machine learning, Neurosurgery, Vim nucleus, Essential tremor, [INFO.INFO-NE]Computer Science [cs]/Neural and Evolutionary Computing [cs.NE], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Neural network applications, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract: International audience; Background: Deep brain stimulation is an efficacious treatment for refractory essential tremor, though targeting the intra-thalamic nuclei remains challenging. Objectives: We sought to develop an inverse approach to retrieve the position of the leads in a cohort of patients operated on with optimal clinical outcomes from anatomical landmarks identifiable by 1.5 Tesla magnetic resonance imaging. Methods: The learning database included clinical outcomes and post-operative imaging from which the coordinates of the active contacts and those of anatomical landmarks were extracted. We used machine learning regression methods to build three different prediction models. External validation was performed according to a leave-one-out cross-validation. Results: Fifteen patients (29 leads) were included, with a median tremor improvement of 72% on the Fahn-Tolosa-Marin scale. Kernel ridge regression, deep neural networks, and support vector regression (SVR) were used. SVR gave the best results with a mean error of 1.33 ± 1.64 mm between the predicted target and the active contact position. Conclusion: We report an original method for the targeting in deep brain stimulation for essential tremor based on patients' radio-anatomical features. This approach will be tested in a prospective clinical trial.
Published: 2021

35. Derivation of a new macroscopic bidomain model including three scales for the electrical activity of cardiac tissue

Author: Fakhrielddine Bader, Raafat Talhouk, Mostafa Bendahmane, Mazen Saad, Mathématiques, Image et Applications - EA 3165 (MIA), La Rochelle Université (ULR), 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), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria), 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], Laboratoire de Mathématiques Jean Leray (LMJL), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS), Ecole Doctorale des Sciences et de la Technologie (EDST), Lebanese University [Beirut] (LU), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Université de La Rochelle (ULR), 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 National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Université de Nantes (UN)-Université de Nantes (UN)
Subjects: Physics, Power series, Mesoscopic physics, Structural level, Quantitative Biology::Tissues and Organs, General Mathematics, 010102 general mathematics, General Engineering, Bidomain model, 01 natural sciences, Homogenization (chemistry), Domain (mathematical analysis), Quantitative Biology::Cell Behavior, 010101 applied mathematics, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Asymptotic expansion, Biological system, Asymptotic homogenization, Analysis of PDEs (math.AP)
Abstract: International audience; In the present paper, a new three-scale asymptotic homogenization method is proposed to study the electrical behavior of the cardiac tissue structure with multiple heterogeneities at two different levels. The first level is associated with the mesoscopic structure such that the cardiac tissue is composed of extracellular and intracellular domains. The second level is associated with the microscopic structure in such a way the intracellular medium can only be viewed as a periodical layout of unit cells (mitochondria). Then, we define two kinds of local cells that are obtained by upscaling methods. The homogenization method is based on a power series expansion which allows determining the macroscopic (homogenized) bidomain model from the microscopic bidomain problem at each structural level. First, we use the two-scale asymptotic expansion to homogenize the extracellular problem. Then, we apply a three-scale asymptotic expansion in the intracellular problem to obtain its homogenized equation at two levels. The first upscaling level of the intracellular structure yields the mesoscopic equation and the second step of the homogenization leads to obtain the intracellular homogenized equation. Both the mesoscopic and microscopic information is obtained by homogenization to capture local characteristics inside the cardiac tissue structure. Finally, we obtain the macroscopic bidomain model and the heart domain coincides with the intracellular medium and extracellular one, which are two inter-penetrating and superimposed continua connected at each point by the cardiac cellular membrane. The interest of the proposed method comes from the fact that it combines microscopic and mesoscopic characteristics to obtain a macroscopic description of the electrical behavior of the heart.
Published: 2021

36. A Cardiac Shape Model for Segmentation Uncertainty Quantification

Author: Tate, Jess, Elhabian, Shireen, Zemzemi, Nejib, Good, Wilson, van Dam, Peter, Brooks, Dana, Macleod, Rob, University of Utah, 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], UMC Utrecht, University Medical Center [Utrecht], and Northeastern University [Boston]
Subjects: [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract: International audience; Segmentation of cardiac images is a variable component of many patient specific computational pipelines, yet its impact on simulated results are still not fully understood. A hurdle to to exploring the impact of the segmentation variability is the technical challenge of building a statistical shape model of the ventricles. In this study, we improved open our previous shape analysis by creating a unified shape model including both the epicardium and endocardium. We tested four techniques within ShapeWorks to generate a ventricular shape model: standard, multidomain, hybrid multidomain, and geodesic distance. The multidomain and hybrid multidomain generated a shape model using all eleven segmentations, and the geodesic distance method generated a shape model using a subset of four segmentations. Each of the shape models captured spatially dependent characteristics of the segmentation variability, including wall thickness, annular diameter, and basal truncation. While each of the three methods have benefits, the hybrid multidomain approach provided the most accurate shape model with fewest points and may be most useful in a majority of applications.
Published: 2021

37. QRS Slopes for Potassium and Calcium Monitoring in End-Stage Renal Disease Patients

Author: Hassaan A Bukhari, Pablo Laguna, Mark Potse, Carlos Sanchez, Esther Pueyo, 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, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], Aragón Institute of Engineering Research [Zaragoza] (I3A), University of Zaragoza - Universidad de Zaragoza [Zaragoza], 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), Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Instituto de Salud Carlos III [Madrid] (ISC)-ministerio de ciencia e innovacion, Institut de rythmologie et modélisation cardiaque [Pessac] (IHU Liryc), This work was supported by projects ERC-StG 638284 (ERC), PID2019-105674RB-I00 and PID2019-104881RB-I00 (Ministerio de Ciencia e Innovacion), Marie Skłodowska-Curie grant 764738 (European Commission) and European Social Fund (EU) and Aragon Government through BSICoS group T39 20R and project LMP124-18. Computations were performed by ICTS NANBIOSIS (HPC Unit, Univ. Zaragoza)., 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, 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 CHU Bordeaux [Bordeaux]-Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]
Subjects: [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2021

38. Cardiac Activation Maps Reconstruction: A Comparative Study Between Data-Driven and Physics-Based Methods

Author: KAROUI, Amel, BENDAHMANE, Mostafa, ZEMZEMI, Nejib, 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), Université de Bordeaux (UB), This project has received funding from the French National Research Agency, grant references ANR-10-IAHU04- LIRYC and ANR-11-EQPX-0030., plafrim, LIRIMA, Epicard, Spicy, ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), ANR-11-EQPX-0030,MUSIC,Plateforme multi-modale d'exploration en cardiologie(2011), 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: Physics-based approaches, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Data-driven approaches, Deep learning, ECGI inverse problem, Cardiac activation mapping, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Neural networks, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract: International audience; One of the essential diagnostic tools of cardiac arrhythmia is activation mapping. Noninvasive current mapping procedures include electrocardiographic imaging. It allows reconstructing heart surface potentials from measured body surface potentials. Then, activation maps are generated using the heart surface potentials. Recently, a study suggests to deploy artificial neural networks to estimate activation maps directly from body surface potential measurements. Here we carry out a comparative study between the data-driven approach DirectMap and noninvasive classic technique based on reconstructed heart surface potentials using both Finite element method combined with L1-norm regularization (FEM-L1) and the spatial adaptation of Time-delay neural networks (SATDNN-AT). In this work, we assess the performance of the three approaches using a synthetic single paced-rhythm dataset generated on the atria surface. The results show that data-driven approach DirectMap quantitatively outperforms the two other methods. In fact, we observe an absolute activation time error and a correlation coefficient, respectively, equal to 7.20 ms , 93.2% using DirectMap, 14.60 ms , 76.2% using FEM-L1 and 13.58 ms , 79.6% using SATDNN-AT. In addition, results show that data-driven approaches (DirectMap and SATDNN-AT) are strongly robust against additive gaussian noise compared to FEM-L1.
Published: 2021

39. Analysis of the heart-torso conductivity parameters recovery inverse problem in cardiac electrophysiology ECG modelling

Author: Mourad Bellassoued, Nejib Zemzemi, Moncef Mahjoub, Abir Amri, Ecole Nationale d'Ingénieurs de Tunis (ENIT), Université de Tunis El Manar (UTM), 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), This work has been supported by EPICARD cooperative research program, funded by INRIA international laboratory LIRIMA. The LAMSIN researcher’s work is supported on a regular basis by the Tunisian Ministry ofHigher Education, Scientific Research and Technology. This work was also supported by the Agence Nationale de la Recherche (grant number IHU LIRYC ANR-10-IAHU-04)., Epicard, Lirima, SPICY, 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, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]
Subjects: Quantitative Biology::Tissues and Organs, Physics::Medical Physics, Conductivity parameters, Cardiac electrophysiology, Carleman estimate, 01 natural sciences, Stability (probability), Computer Science::Robotics, 2010 Mathematics Subject Classification.Primary 35Q92, Secondary: 35R30, medicine, 0101 mathematics, Stability estimate, Monodomain model, Mathematics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Inverse problem, Torso, Lipschitz continuity, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 010101 applied mathematics, Parameter identification problem, Elliptic curve, medicine.anatomical_structure, Analysis
Abstract: International audience; In this paper, we prove a stability estimate of the conductivity parameters identification problem in cardiac electrophysiology. The propagation of the electrical wave in the heart is described by the monodomain model coupled to an elliptic equation describing the diffusion of the electrical wave in the whole body. Our result concerns both heart and torso conductivity parameters. The main difficulty that we solve in this paper is related to the transmission conditions between the heart and the torso. We first, establish Carleman estimates for the coupled heart-torso system. Then, using these estimates and the Bukhgeim and Klibanov approach, we prove a Lipschitz stability estimate of cardiac and torso conductivity parameters.
Published: 2021

40. A Volume Source Method for Solving ECGI Inverse Problem

Author: Yves Coudière, Mohamadou Malal Diallo, Rémi Dubois, IHU Liryc, Electrophysiology and Heart Modeling Institute, Hopital Xavier Arnozan, 33600, Pessac, France, 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, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], 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), ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), European Project, 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-Université Sciences et Technologies - Bordeaux 1 (UB)-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], Institut de rythmologie et modélisation cardiaque [Pessac] (IHU Liryc), Daniel B. Ennis, Luigi E. Perotti, Vicky Y. Wang, Diallo, Mohamadou Malal, Instituts Hospitalo-Universitaires - L'Institut de Rythmologie et modélisation Cardiaque - - LIRYC2010 - ANR-10-IAHU-0004 - IAHU - VALID, and ERC Grant ECSTATIC 715093 - INCOMING
Subjects: 010103 numerical & computational mathematics, Inverse problem, Torso, 01 natural sciences, 010101 applied mathematics, Tikhonov regularization, Noise, Electrocardiography, medicine.anatomical_structure, Scar, Approximation error, medicine, Method of fundamental solutions, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Sensitivity (control systems), [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, ECGI, Algorithm, Mathematics, Volume (compression)
Abstract: International audience; Electrocardiographic Imaging (ECGI) is a non-invasive procedure that allows to reconstruct the electrical activity of the heart from body surface potential map (BSPM). In this paper, we present a volume model to solve the electrocardiography inverse problem capable to take into account structural informations obtained by imaging techniques. The direct problem maps a volume current in the cardiac muscle (ventricles) to the body surface electrical measures. The model is based on coupling bidomain heart model with torso conduction. The corresponding inverse problem is solved with the Tikhonov regularization. Simulated database are used for the evaluation of this method and we compared them to standard method of fundamental solutions (MFS). The sensitivity to noise is also assessed. The correlation coefficients (CC) and the relative error (RE) of activation times were computed. Results show that the CC (respectively RE) median is respectively 0.75 for the volume model and 0.4 for the MFS (respectively 0.31 vs 0.35) on the epicardium. On the endocardium, the CC and the RE median are 0.65 and 0.33 for the volume method. In conclusion, the volume method performs better than the method of fundamental solutions (MFS) for any noise level, and reconstruct in addition endocardial information.
Published: 2021

41. A simple model of cardiac mitochondrial respiration with experimental validation

Author: Bachar, Tarraf, Emmanuel, Suraniti, Camille, Colin, Stéphane, Arbault, Philippe, Diolez, Michael, Leguèbe, Yves, Coudière, 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, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux], 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], Institut des Sciences Moléculaires (ISM), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Institut de rythmologie et modélisation cardiaque [Pessac] (IHU Liryc), Université de Bordeaux (UB), 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 Agence Nationale de la Recherche grant ANR-10-IAHU-04 and also from the project MITOCARD (ANR-17-CE11-0041)., ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), ANR-17-CE11-0041,MITOCARD,Electrophysiologie de la Mitochondrie Cardiaque(2017), 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-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 Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1 (UB)-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), LEGUEBE, Michael, Instituts Hospitalo-Universitaires - L'Institut de Rythmologie et modélisation Cardiaque - - LIRYC2010 - ANR-10-IAHU-0004 - IAHU - VALID, and Electrophysiologie de la Mitochondrie Cardiaque - - MITOCARD2017 - ANR-17-CE11-0041 - AAPG2017 - VALID
Subjects: Biological modeling, Experimental validation, Respiration, Heart, [MATH] Mathematics [math], [SDV.BC]Life Sciences [q-bio]/Cellular Biology, Mitochondria, Heart, Mitochondria, QA1-939, [MATH]Mathematics [math], Energy Metabolism, Sensitivity analysis, [SDV.BC] Life Sciences [q-bio]/Cellular Biology, TP248.13-248.65, Mathematics, Ordinary differential equations, Biotechnology
Abstract: International audience; Cardiac mitochondria are intracellular organelles that play an important role in energy metabolism and cellular calcium regulation. In particular, they influence the excitation-contraction cycle of the heart cell. A large number of mathematical models have been proposed to better understand the mitochondrial dynamics, but they generally show a high level of complexity, and their parameters are very hard to fit to experimental data.We derived a model based on historical free energy-transduction principles, and results from the literature. We proposed simple expressions that allow to reduce the number of parameters to a minimum with respect to the mitochondrial behavior of interest for us. The resulting model has thirty-two parameters, which are reduced to twenty-three after a global sensitivity analysis of its expressions based on Sobol indices.We calibrated our model to experimental data that consists of measurements of mitochondrial respiration rates controlled by external ADP additions. A sensitivity analysis of the respiration rates showed that only seven parameters can be identified using these observations. We calibrated them using a genetic algorithm, with five experimental data sets. At last, we used the calibration results to verify the ability of the model to accurately predict the values of a sixth dataset.Results show that our model is able to reproduce both respiration rates of mitochondria and transitions between those states, with very low variability of the parameters between each experiment. The same methodology may apply to recover all the parameters of the model, if corresponding experimental data were available.
Published: 2021

42. Towards the modeling of the Purkinje/myocardium coupled problem: A well-posedness analysis

Author: S. Mani Aouadi, W. Mbarki, Nejib Zemzemi, Université de Tunis El Manar (UTM), 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), 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: Discretization, Purkinje fibers, Quantitative Biology::Tissues and Organs, Physics::Medical Physics, 030204 cardiovascular system & hematology, Space (mathematics), Discrete problem, 03 medical and health sciences, 0302 clinical medicine, medicine, Weighted Sobolev spaces, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, [MATH]Mathematics [math], Purkinje/myocardium, 030304 developmental biology, Mathematics, 0303 health sciences, Applied Mathematics, Mathematical analysis, Semi-implicit scheme, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Finite element method, Coupling (electronics), Sobolev space, Computational Mathematics, medicine.anatomical_structure, 2010 MSC: 92B05, 35K55, 35K57, 65N38, Electrical conduction system of the heart, Monodomain/bidomain
Abstract: The Purkinje network is the specialized conduction system in the heart. It ensures the physiological spread of the electrical wave in the ventricles. In this work, in an insulated heart framework, we model the free running Purkinje system, using the monodomain equation. The intra-myocardium part of the Purkinje fiber is coupled to the ventricular tissue using the bidomain equation. The coupling is performed through the extracellular potential. We discretize the problem in time using a semi-implicit scheme. Then, we write a variational formulation of the semi discrete problem in a non standard weighted Sobolev functional spaces. We prove the existence and uniqueness of the solution of the Purkinje/myocardium semi-discretized problem. We discretize in space by the finite element P 1 − L a g r a n g e and conduct some numerical tests showing the anterograde and retrograde propagation of the electrical wave between the tissue and the Purkinje fibers.
Published: 2019

43. Méthodes numériques pour la résolution de problèmes inverses en électrocardiographie

Author: Karoui, Amel, 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, Néjib Zemzemi, Mostafa Bendahmane, STAR, ABES, 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, and Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux]-CHU Bordeaux [Bordeaux]
Subjects: Problème inverse, Artificial neural networks, Cardiac activation, Activation cardiaque, Numerical simulation, Apprentissage automatique, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Electrocardiography, Simulation numérique, Inverse problem, Machine learning, Réseaux de neurones, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Électrocardiographie
Abstract: In this thesis, we are interested in the mathematical modeling of cardiac electrophysiology and more precisely, the numerical study of the electrical activity of the heart. One of the challenges of this scientific theme is to reconstruct the electrical information on the cardiac surface from measurements taken on the thoracic surface. Such a problem is called the inverse problem. First, we analyze several methods of solving the inverse problem present in the literature and we propose a new approach of regularization based on the flow of electric current at the cardiac surface. The results are illustrated using simulated and experimental data. Next, we are interested in machine learning methods. Several models of artificial neural networks are created and developed to solve the inverse problem. We show that this approach improves the results of reconstruction of the cardiac electrical potential compared to classical inverse methods. Then, the greatest contribution of this thesis consists in the development of an artificial neural network model for cardiac activation mapping. The latter is characterized by a very great robustness against the noise previously present in the thoracic electrical signals. The last part is devoted to the comparison between the different models developed previously in order to determine the best numerical approach for cardiac activation mapping. The study is conducted using a simulated data set. We prove that methods based on machine learning provide the best results., Dans cette thèse, nous nous intéressons à la modélisation mathématique de l’électrophysiologie cardiaque et plus précisément, l’étude numérique de l’activité électrique du coeur. L’un des défis de cette thématique scientifique consiste à reconstruire l’information électrique à la surface cardiaque à partir des mesures réalisées à la surface thoracique. Un tel problème est appelé problème inverse. Dans un premier temps, nous analysons plusieurs méthodes de résolution du problème inverse présentes dans la littérature et nous proposons une nouvelle approche de régularisation basée sur le flux du courant électrique à la surface cardiaque. Les résultats sont illustrés moyennant des données simulées et expérimentales. Ensuite, nous nous intéressons aux méthodes d’apprentissage automatique. Plusieurs modèles de réseaux de neurones artificiels sont créés et développés pour résoudre le problème inverse. Nous montrons que cette approche améliore les résultats de reconstruction du potentiel électrique cardiaque par rapport aux méthodes inverses classiques. Puis, Le plus grand apport de cette thèse consiste au développement d’un modèle de réseau neuronal artificiel de cartographie d’activation cardiaque. Ce dernier se caractérise par une très grande robustesse face au bruit préalablement présent dans les signaux électriques thoraciques. La dernière partie est consacrée à la comparaison entre les différents modèles développés auparavant afin de déterminer la meilleure approche numérique de cartographie de l’activation cardiaque. L’étude est menée en utilisant un jeu de données simulées. Nous prouvons que les méthodes basées sur l’apprentissage automatique fournissent les meilleurs résultats.
Published: 2021

44. Human ventricular activation sequence and the simulation of the electrocardiographic QRS complex and its variability in healthy and intraventricular block conditions

Author: Cardone-Noott, Louie, Bueno-Orovio, Alfonso, Mincholé, Ana, Zemzemi, Nejib, Rodriguez, Blanca, Computing Science Laboratory - Oxford University, University of Oxford [Oxford], 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 Oxford, 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: cardiovascular system, cardiovascular diseases, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract: Aims To investigate how variability in activation sequence and passive conduction properties translates into clinical variability in QRS biomarkers, and gain novel physiological knowledge on the information contained in the human QRS complex. Methods and results Multiscale bidomain simulations using a detailed heart-torso human anatomical model are performed to investigatethe impact of activation sequence characteristics on clinical QRS biomarkers. Activation sequences are built and validated against experimentally-derived ex vivo and in vivo human activation data. R-peak amplitude exhibits the largest variability in terms of QRS morphology, due to its simultaneous modulation by activation sequence speed, myocardial intracellular and extracellular conductivities, and propagation through the human torso. QRS width, however, is regulated by endocardial activation speed and intracellular myocardial conductivities, whereas QR intervals are only affected by the endocardial activation profile. Variability in the apico-basal location of activation sites on the anterior and posterior left ventricular wall is associated with S-wave progression in limb and precordial leads, respectively, and occasional notched QRS complexes in precordial derivations. Variability in the number ofearly activation sites successfully reproduces pathological abnormalities of the human conduction system in the QRS complex. Conclusion Variability in activation sequence and passive conduction properties captures and explains a large part of the clinical variability observed in the human QRS complex. Our physiological insights allow for a deeper interpretation of human QRS biomarkers in terms of QRS morphology and location of early endocardial activation sites. This mightbe used to attain a better patient-specific knowledge of activation sequence from routine body-surface electrocardiograms.
Published: 2021

45. Left Atrial Appendage Electrical Isolation Reduces Atrial Fibrillation Recurrences A Simulation Study

Author: Rolf Krause, Sander Verheule, Ali Gharaviri, Ulrich Schotten, Simone Pezzuto, Giulio Conte, Mark Potse, Angelo Auricchio, Center for Computational Medicine in Cardiology (CCMC), 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], Department of Physiology [Maastricht], Maastricht University [Maastricht], Fondazione Cardiocentro Ticino, This work was supported by the Swiss National Supercomputing Centre (CSCS project ID s778), by grants to US from the Netherlands Heart Foundation (CVON2014-09, RACE V), and the EU (ERACoSysMED H2020 ERA-NET). Dr Conte is supported by the Swiss National Foundation (SNF) (Ambizione grant no PZ00P3_180055 / 1)., European Project: 643271,H2020,H2020-HCO-2014,ERACoSysMed(2015), 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 Zurich, and Clinical sciences
Subjects: medicine.medical_specialty, left atrial appendage, medicine.medical_treatment, 610 Medicine & health, Catheter ablation, 030204 cardiovascular system & hematology, 11171 Cardiocentro Ticino, Heart Conduction System/physiopathology, Electrical isolation, 03 medical and health sciences, 0302 clinical medicine, Left atrial appendage electrical isolation, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Heart Conduction System, Recurrence, Left atrial, Physiology (medical), Internal medicine, Humans, Medicine, Atrial Appendage, Computer Simulation, atrial fibrillation, Atrial Appendage/surgery, Atrial Fibrillation recurrence, ComputingMilieux_MISCELLANEOUS, in-silico study, pulmonary vein isolation, 030304 developmental biology, Appendage, CATHETER ABLATION, 0303 health sciences, business.industry, fibrosis, Atrial fibrillation, medicine.disease, Catheter Ablation/methods, 3. Good health, Atrial Fibrillation/physiopathology, Treatment Outcome, Cardiology, Catheter ablation Fibrosis, Cardiology and Cardiovascular Medicine, business, Arrhythmia
Abstract: Supplemental Digital Content is available in the text.
Published: 2021

46. Uncertainty Quantification of the Effects of Segmentation Variability in ECGI

Author: Rob S. MacLeod, Wilson W. Good, Machteld J Boonstra, Jess D. Tate, Dana H. Brooks, Akil Narayan, Nejib Zemzemi, Peter M. van Dam, University of Utah, 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], Utrecht Brain Center [UMC], University Medical Center [Utrecht], Northeastern University [Boston], Supported by the National Institutes of Health, P41GM103545, R24GM136986, U24EB029012, U24EB029011, R01AR076120, and R01HL135568, Daniel B. Ennis, Luigi E. Perotti, and Vicky Y. Wang
Subjects: Electrocardiographic Imaging, Shape Analysis, Polynomial chaos, business.industry, Computer science, Pipeline (computing), High variability, Pattern recognition, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Article, Standard deviation, Electrocardiographic imaging, Uncertainty Quantification, Segmentation, Artificial intelligence, Uncertainty quantification, business, Shape analysis (digital geometry)
Abstract: International audience; Despite advances in many of the techniques used in Electrocardiographic Imaging (ECGI), uncertainty remains insufficiently quantified for many aspects of the pipeline. The effect of geometric uncertainty, particularly due to segmentation variability, may be the least explored to date. We use statistical shape modeling and uncertainty quantification (UQ) to compute the effect of segmentation variability on ECGI solutions. The shape model was made with Shapeworks from nine segmentations of the same patient and incorporated into an ECGI pipeline. We computed uncertainty of the pericardial potentials and local activation times (LATs) using polynomial chaos expansion (PCE) implemented in UncertainSCI. Uncertainty in pericardial potentials from segmentation variation mirrored areas of high variability in the shape model, near the base of the heart and the right ventricular outflow tract, and that ECGI was less sensitive to uncertainty in the posterior region of the heart. Subsequently LAT calculations could vary dramatically due to segmentation variability, with a standard deviation as high as 126ms, yet mainly in regions with low conduction velocity. Our shape modeling and UQ pipeline presented possible uncertainty in ECGI due to segmentation variability and can be used by researchers to reduce said uncertainty or mitigate its effects. The demonstrated use of statistical shape modeling and UQ can also be extended to other types of modeling pipelines.
Published: 2021

47. Characterization of t wave amplitude, duration and morphology changes during hemodialysis: Relationship with serum electrolyte levels and heart rate

Author: Julia Ramirez, Carlos Sánchez, José Esteban Ruiz, Esther Pueyo, Dina Ferreira, Pablo Laguna, Mark Potse, Hassaan A. Bukhari, Flavio Palmieri, Aragón Institute of Engineering Research [Zaragoza] (I3A), University of Zaragoza - Universidad de Zaragoza [Zaragoza], Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Instituto de Salud Carlos III [Madrid] (ISC)-ministerio de ciencia e innovacion, 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], Centre de Recerca en Enginyeria Biomèdica [Catalunya] (CREB), Universitat Politècnica de Catalunya [Barcelona] (UPC), William Harvey Research Institute, Barts and the London Medical School, Hospital Clínico Universitario 'Lozano Blesa' [Zaragoza, Spain], Laboratorios Rubió, IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], Centro Universitario de la Defensa de Zaragoza (CUD), General Military Academy of Zaragoza, This work was supported by projects ERC-StG 638284(ERC), PID2019-105674RB-I00 and PID2019-104881RB-I00 (Ministerio de Ciencia e Innovacion), Marie Skłodowska-Curie grants 786833 and 764738 (European Commission) and by European Social Fund (EU) and Aragon Government through BSICoS group T3920R and project LMP124-18. Computations were performed by the ICTS NANBIOSIS (HPC Unit at University of Zaragoza)., European Project: 282085,EC:FP7:ERC,ERC-2011-StG_20101109,RETGENTX(2012), Universitat Politècnica de Catalunya. Departament d'Enginyeria de Sistemes, Automàtica i Informàtica Industrial, 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: [SPI.OTHER]Engineering Sciences [physics]/Other, Morphology (linguistics), medicine.medical_treatment, 0206 medical engineering, Heart rate, Biomedical Engineering, 02 engineering and technology, in silico modelling, in silico modeling, T wave amplitude, Electrocardiography, Electrolytes, Nuclear magnetic resonance, Serum electrolyte levels, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Renal Dialysis, medicine, heart rate, T wave morphology, Humans, time warping, calcium, hemodialysis, Chemistry, ECG, potassium, Transmural heterogeneity, Arrhythmias, Cardiac, Time warping, 020601 biomedical engineering, Hemodiàlisi, Serum potassium, Hemodialysis, transmural heterogeneity, Potassium, Kidney Failure, Chronic, Calcium
Abstract: Objective: Chronic kidney disease affects more than 10% of the world population. Changes in serum ion concentrations increase the risk for ventricular arrhythmias and sudden cardiac death, particularly in end-stage renal disease (ESRD) patients. We characterized how T wave amplitude, duration and morphology descriptors change with variations in serum levels of potassium and calcium and in heart rate, both in ESRD patients and in simulated ventricular fibers. Methods: Electrocardiogram (ECG) recordings from twenty ESRD patients undergoing hemodialysis (HD) and pseudo-ECGs (pECGs) calculated from twenty-two simulated ventricular fibers at varying transmural heterogeneity levels were processed to quantify T wave width ( $T_{\mathrm{w}}$ ), T wave slope-to-amplitude ratio ( $T_{\text{S/A}}$ ) and four indices of T wave morphological variability based on time warping ( $d_{\mathrm{w}}$ , $d^{\text{NL}}_{\mathrm{w}}$ , $d_{\mathrm{a}}$ and $d^{\text{NL}}_{\mathrm{a}}$ ). Serum potassium and calcium levels and heart rate were measured along HD. Results: $d^{\text{NL}}_{\mathrm{a}}$ was the marker most strongly correlated with serum potassium, $d_{\mathrm{w}}$ with calcium and $d_{\mathrm{a}}$ with heart rate, after correction for covariates. Median values of partial correlation coefficients were 0.75, $-$ 0.74 and $-$ 0.90, respectively. For all analyzed T wave descriptors, high inter-patient variability was observed in the pattern of such relationships. This variability, accentuated during the first HD time points, was reproduced in the simulations and shown to be influenced by differences in transmural heterogeneity. Conclusion: Changes in serum potassium and calcium levels and in heart rate strongly affect T wave descriptors, particularly those quantifying morphological variability. Significance: ECG markers have the potential to be used for monitoring serum ion concentrations in ESRD patients.
Published: 2021

48. Global Sensitivity Analysis for Uncertain Parameters Applied to a Cardiac Mitochondrial Model

Author: Yves Coudière, Michael Leguèbe, Camille Colin, Philippe Diolez, Bachar Tarraf, Stéphane Arbault, Emmanuel Suraniti, IHU-LIRYC, 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), 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 (UB), Institut des Sciences Moléculaires (ISM), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1 (UB)-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-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 French Government as part of the 'Investments of the Future' program managed by the Agence Nationale de la Recherchegrant ANR-10-IAHU-04 and also from the project MITOCARD (ANR-17-CE11-0041), ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), ANR-17-CE11-0041,MITOCARD,Electrophysiologie de la Mitochondrie Cardiaque(2017), 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)-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, Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Tarraf, Bachar, Instituts Hospitalo-Universitaires - L'Institut de Rythmologie et modélisation Cardiaque - - LIRYC2010 - ANR-10-IAHU-0004 - IAHU - VALID, and Electrophysiologie de la Mitochondrie Cardiaque - - MITOCARD2017 - ANR-17-CE11-0041 - AAPG2017 - VALID
Subjects: 0303 health sciences, Mathematical model, Computer science, Ode, Experimental data, [MATH] Mathematics [math], 01 natural sciences, 03 medical and health sciences, Order (biology), Global sensitivity analysis, Ordinary differential equation, 0103 physical sciences, Genetic algorithm, Trajectory, [MATH]Mathematics [math], Biological system, 010303 astronomy & astrophysics, 030304 developmental biology
Abstract: International audience; Cardiac mitochondria are intracellular organelles that have several important roles. For instance, they ensure energy metabolism and calcium regulation, thus are linked to the excitation-contraction cycle of the heart cell. Mathematical models are useful to better understand the complexity of mitochondrial dynamics within a cardiac cell, and we are specifically interested in the dynamics of calcium. Litterature models reflect this complexity, especially in terms of number of equations and parameters, which makes them impossible to calibrate to experimental data. In this paper, we apply a global sensitivity analysis on our previously discussed simple mitochondria model [1], in order to quantify the uncertainty of the parameters. This analysis is done in two steps. First we eliminate non-influential parameters of the internal fluxes governing the activity of the mitochondria. Then we perform this analysis on the outputs of our ODE (ordinary differential equation) model, which are the respiratory rates. Finally, we calibrate the remaining influential parameters using a genetic algorithm with respect to experimental respiratory data.
Published: 2020

49. Prédiction de l'affluence journalière dans un réseau de transports urbains

Author: Louvet, Apolline, Arrieula, Andony, Prost, Jean, Freulon, Paul, Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut de rythmologie et modélisation cardiaque [Pessac] (IHU Liryc), 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), AMIES, Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), 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: [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Published: 2020

50. Monitoring of Serum Potassium and Calcium Levels in End-Stage Renal Disease Patients by ECG Depolarization Morphology Analysis

Author: Hassaan A. Bukhari, Carlos Sánchez, José Esteban Ruiz, Mark Potse, Pablo Laguna, Esther Pueyo, Aragón Institute of Engineering Research [Zaragoza] (I3A), University of Zaragoza - Universidad de Zaragoza [Zaragoza], Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), 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), Hospital Clínico Universitario 'Lozano Blesa' [Zaragoza, Spain], IHU-LIRYC, Université Bordeaux Segalen - Bordeaux 2-CHU Bordeaux [Bordeaux], This work was funded by projects PID2019-105674RB-I00 and PID2019-104881RB-I00 (Ministerio de Ciencia e Innovación), ERC-StG 638284 (ERC), Marie Skłodowska-Curie grant 764738 (European Commission) and by European Social Fund (EU) and Aragón Government through project LMP94_21 and BSICoS group T39_20R. M. Potse was funded by the French National Research Agency, grant reference ANR-10-IAHU04-LIRYC. Computations were performed by the ICTS NANBIOSIS (HPC Unit at University of Zaragoza)., ANR-10-IAHU-0004,LIRYC,L'Institut de Rythmologie et modélisation Cardiaque(2010), and European Project: 764738,PIC
Subjects: Male, QRS complex morphology, electrocardiogram, Biochemistry, Analytical Chemistry, Electrocardiography, Electrolytes, T wave morphology, Humans, cardiovascular diseases, Electrical and Electronic Engineering, calcium estimation, Instrumentation, time warping, potassium estimation, hemodialysis, regression, Arrhythmias, Cardiac, Atomic and Molecular Physics, and Optics, Potassium, cardiovascular system, Kidney Failure, Chronic, Calcium, Female, [SDV.IB]Life Sciences [q-bio]/Bioengineering
Abstract: International audience; Objective: Non-invasive estimation of serum potassium, [K + ], and calcium, [Ca 2+ ], can help to prevent life-threatening ventricular arrhythmias in patients with advanced renal disease, but current methods for estimation of electrolyte levels have limitations. We aimed to develop new markers based on the morphology of the QRS complex of the electrocardiogram (ECG). Methods: ECG recordings from 29 patients undergoing hemodialysis (HD) were processed. Mean warped QRS complexes were computed in two-minute windows at the start of an HD session, at the end of each HD hour and 48 h after it. We quantified QRS width, amplitude and the proposed QRS morphology-based markers that were computed by warping techniques. Reference [K + ] and [Ca 2+ ] were determined from blood samples acquired at the time points where the markers were estimated. Linear regression models were used to estimate electrolyte levels from the QRS markers individually and in combination with T wave morphology markers. Leave-one-out cross-validation was used to assess the performance of the estimators. Results: All markers, except for QRS width, strongly correlated with [K + ] (median Pearson correlation coefficients, r, ranging from 0.81 to 0.87) and with [Ca 2+ ] (r ranging from 0.61 to 0.76). QRS morphology markers showed very low sensitivity to heart rate (HR). Actual and estimated serum electrolyte levels differed, on average, by less than 0.035 mM (relative error of 0.018) for [K + ] and 0.010 mM (relative error of 0.004) for [Ca 2+ ] when patient-specific multivariable estimators combining QRS and T wave markers were used. Conclusion: QRS morphological markers allow non-invasive estimation of [K + ] and [Ca 2+ ] with low sensitivity to HR. The estimation performance is improved when multivariable models, including T wave markers, are considered. Significance: Markers based on the QRS complex of the ECG could contribute to non-invasive monitoring of serum electrolyte levels and arrhythmia risk prediction in patients with renal disease.
Published: 2022

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