Author: "Dominique Chapelle" / Publisher: hal ccsd - Searchworks@Jio Institute Digital Library Search Results

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76 results on '"Dominique Chapelle"'

1. Reduced left ventricular dynamics modeling based on a cylindrical assumption

Author: Martin Genet, Jérôme Diaz, Dominique Chapelle, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: Computational Theory and Mathematics, Applied Mathematics, Modeling and Simulation, Computational mechanics, Continuum mechanics on manifold, Reduced-order modeling, Biomedical Engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Cardiac modeling, Molecular Biology, Software
Abstract: Biomechanical modeling and simulation is expected to play a significant role in the development of the next generation tools in many fields of medicine. However, full-fledged finite element models of complex organs such as the heart can be computationally very expensive, thus limiting their practical usability. Therefore, reduced models are much valuable to be used, e.g., for pre-calibration of full-fledged models, fast predictions, real-time applications, etc.. In this work, focused on the left ventricle, we develop a reduced model by defining reduced geometry & kinematics while keeping general motion and behavior laws, allowing to derive a reduced model where all variables & parameters have a strong physical meaning. More specifically, we propose a reduced ventricular model based on cylindrical geometry & kinematics, which allows to describe the myofiber orientation through the ventricular wall and to represent contraction patterns such as ventricular twist, two important features of ventricular mechanics. Our model is based on the original cylindrical model of [Guccione, McCulloch, & Waldman 1991; Guccione, Waldman, & McCulloch 1993], albeit with multiple differences: we propose a fully dynamical formulation, integrated into an open-loop lumped circulation model, and based on a material behavior that incorporates a fine description of contraction mechanisms; moreover, the issue of the cylinder closure has been completely reformulated; our numerical approach is novel as well, with consistent spatial (finite element) and time discretizations. Finally, we analyse the sensitivity of the model response to various numerical and physical parameters, and study its physiological response.
Published: 2023
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2. Varying thin filament activation in the framework of the Huxley'57 model

Author: François Kimmig, Matthieu Caruel, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Modélisation et Simulation Multi-Echelle (MSME), and Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel
Subjects: Sarcomeres, Applied Mathematics, Biomedical Engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Cardiac modeling, Actins, Actin Cytoskeleton, Computational Theory and Mathematics, Thick and thin filament activation, Modeling and Simulation, Huxley'57 model, Calcium, Mathematical modeling, Molecular Biology, Software, Muscle Contraction
Abstract: International audience; Muscle contraction is triggered by the activation of the actin sites of the thin filament by calcium ions. It results that the thin filament activation level varies over time. Moreover, this activation process is also used as a regulation mechanism of the developed force. Our objective is to build a model of varying actin site activation level within the classical Huxley'57 two-state framework. This new model is obtained as an enhancement of a previously proposed formulation of the varying thick filament activation within the same framework [1]. We assume that the state of an actin site depends on whether it is activated and whether it forms a cross-bridge with the associated myosin head, which results in four possible states. The transitions between the actin site states are controlled by the global actin sites activation level and the dynamics of these transitions is coupled with the attachment-detachment process. A preliminary calibration of the model with experimental twitch contraction data obtained at varying sarcomere lengths is performed.
Published: 2022
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3. Prediction of Ventricular Mechanics After Pulmonary Valve Replacement in Tetralogy of Fallot by Biomechanical Modeling: A Step Towards Precision Healthcare

Author: Camille Hancock Friesen, Gerald F. Greil, Radomir Chabiniok, Maria Gusseva, Dominique Chapelle, Tarique Hussain, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], University of Nebraska Medical Center, University of Nebraska System, Czech Technical University in Prague (CTU), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: medicine.medical_specialty, medicine.medical_treatment, 0206 medical engineering, Biomedical Engineering, 02 engineering and technology, 030204 cardiovascular system & hematology, Contractility, 03 medical and health sciences, 0302 clinical medicine, Afterload, Valve replacement, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Internal medicine, Pulmonary Valve Replacement, Medicine, ComputingMilieux_MISCELLANEOUS, Ventricular mechanics, Tetralogy of Fallot, business.industry, valvular heart disease, medicine.disease, 020601 biomedical engineering, 3. Good health, medicine.anatomical_structure, Ventricle, Cardiology, [SDV.IB]Life Sciences [q-bio]/Bioengineering, business, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology
Abstract: Clinical indicators of heart function are often limited in their ability to accurately evaluate the current mechanical state of the myocardium. Biomechanical modeling has been shown to be a promising tool in addition to clinical indicators. By providing a patient-specific measure of myocardial active stress (contractility), biomechanical modeling can enhance the precision of the description of patient’s pathophysiology at any given point in time. In this work we aim to explore the ability of biomechanical modeling to predict the response of ventricular mechanics to the progressively decreasing afterload in repaired tetralogy of Fallot (rTOF) patients undergoing pulmonary valve replacement (PVR) for significant residual right ventricular outflow tract obstruction (RVOTO). We used 19 patient-specific models of patients with rTOF prior to pulmonary valve replacement (PVR), denoted as PSMpre, and patient-specific models of the same patients created post-PVR (PSMpost)—both created in our previous published work. Using the PSMpre and assuming cessation of the pulmonary regurgitation and a progressive decrease of RVOT resistance, we built relationships between the contractility and RVOT resistance post-PVR. The predictive value of such in silico obtained relationships were tested against the PSMpost, i.e. the models created from the actual post-PVR datasets. Our results show a linear 1-dimensional relationship between the in silico predicted contractility post-PVR and the RVOT resistance. The predicted contractility was close to the contractility in the PSMpost model with a mean (± SD) difference of 6.5 (± 3.0)%. The relationships between the contractility predicted by in silico PVR vs. RVOT resistance have a potential to inform clinicians about hypothetical mechanical response of the ventricle based on the degree of pre-operative RVOTO.
Published: 2021
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4. Biomechanical Modeling to Inform Pulmonary Valve Replacement in Tetralogy of Fallot Patients after Complete Repair

Author: Gerald F. Greil, Radomir Chabiniok, Keren Hasbani, Dominique Chapelle, Camille L. Hancock Friesen, Maria Gusseva, Animesh Tandon, Cécile Patte, Philippe Moireau, Tarique Hussain, Martin Genet, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], University of Texas at Austin [Austin], Czech Technical University in Prague (CTU), King‘s College London, Guy's and St Thomas' Hospital [London], École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: Adult, Male, Reoperation, medicine.medical_specialty, Percutaneous, Heart Ventricles, 0206 medical engineering, Magnetic Resonance Imaging, Cine, 02 engineering and technology, 030204 cardiovascular system & hematology, Models, Biological, Article, Contractility, 03 medical and health sciences, 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Cardiovascular modeling, Pulmonary Valve Replacement, Internal medicine, medicine.artery, Humans, Medicine, Abnormalities, Multiple, Cardiac Surgical Procedures, Retrospective Studies, Tetralogy of Fallot, Heart Valve Prosthesis Implantation, Cardiovascular magnetic resonance imaging, Pulmonary Valve, medicine.diagnostic_test, business.industry, Hemodynamics, Magnetic resonance imaging, Retrospective cohort study, Translational research, medicine.disease, 020601 biomedical engineering, Personalized medicine, Pulmonary Valve Insufficiency, Pulmonary artery, Cardiology, Female, Biomechanical model, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Myocardial contractility, Cardiology and Cardiovascular Medicine, business, Follow-Up Studies
Abstract: BACKGROUND: A biomechanical model of the heart can be used to incorporate multiple data sources (electrocardiography, imaging, invasive hemodynamics). The purpose of this study was to use this approach in a cohort of patients with tetralogy of Fallot after complete repair (rTOF) to assess comparative influences of residual right ventricular outflow tract obstruction (RVOTO) and pulmonary regurgitation on ventricular health. METHODS: Twenty patients with rTOF who underwent percutaneous pulmonary valve replacement (PVR) and cardiovascular magnetic resonance imaging were included in this retrospective study. RESULTS: RV contractility before PVR (mean 66 ± kPa, mean ± standard deviation) was increased in patients with rTOF compared with normal RV (38–48 kPa) (P < 0.05). The contractility decreased significantly in all patients after PVR (P < 0.05). Patients with predominantly RVOTO demonstrated greater reduction in contractility (median decrease 35%) after PVR than those with predominant pulmonary regurgitation (median decrease 11%). The model simulated post-PVR decreased EDV for the majority and suggested an increase of Q(eff)—both in line with published data. CONCLUSIONS: This study used a biomechanical model to synthesize multiple clinical inputs and give an insight into RV health. Individualized modeling allows us to predict the RV response to PVR. Initial data suggest that residual RVOTO imposes greater ventricular work than isolated pulmonary regurgitation. Biomechanical models specific to individual patient and physiology (before and after PVR) were created and used to estimate the RV myocardial contractility. The ability of models to capture post-PVR changes of right ventricular (RV) end-diastolic volume (EDV) and effective flow in the pulmonary artery (Qeff) was also compared with expected values.
Published: 2021
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5. Hierarchical modeling of length-dependent force generation in cardiac muscles and associated thermodynamically-consistent numerical schemes

Author: Dominique Chapelle, Philippe Moireau, François Kimmig, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Computer science, Computational Mechanics, Ocean Engineering, Context (language use), multi-scale modeling, Sarcomere, biomechanics, 03 medical and health sciences, Myosin head, 0302 clinical medicine, numerical methods, 030304 developmental biology, 0303 health sciences, Frank–Starling law of the heart, Hierarchical modeling, Applied Mathematics, Mechanical Engineering, Numerical analysis, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Cardiac modeling, Multiscale modeling, multiscale modeling, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computational Mathematics, Computational Theory and Mathematics, Coupling (computer programming), Frank-Starling mechanism, sarcomere, Biological system, 030217 neurology & neurosurgery, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; In the context of cardiac muscle modeling, the availability of the myosin heads in the sarcomeres varies over the heart cycle contributing to the Frank-Starling mechanism at the organ level. In this paper, we propose a new approach that allows to extend the Huxley'57 muscle contraction model equations to incorporate this variation. This extension is built in a thermodynamically consistent manner, and we also propose adapted numerical methods that satisfy thermodynamical balances at the discrete level. Moreover, this whole approach-both for the model and the numerics-is devised within a hierarchical strategy enabling the coupling of the microscopic sarcomere-level equations with the macroscopic tissue-level description. As an important illustration, coupling our model with a previously proposed simplified heart model, we demonstrate the ability of the modeling and numerical framework to capture the essential features of the Frank-Starling mechanism.
Published: 2021
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6. Model-Assisted Time-Synchronization of Cardiac MR Image and Catheter Pressure Data

Author: Mohamed Abdelghafar Hussein, Maria Gusseva, Radomir Chabiniok, Surendranath R. Veeram Reddy, Gerald F. Greil, Daniel A. Castellanos, Joshua S. Greer, Tarique Hussain, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], Boston Children's Hospital, Pediatric department, Kafrelsheikh University, Kafrelsheikh University, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Faculty of Medicine, Kafrelsheikh University, Kafrelsheikh, Egypt
Subjects: Physics, cardiovascular modeling, time-synchronization of clinical data, medicine.diagnostic_test, Cardiac cycle, pressure volume loops, Image (category theory), Magnetic resonance imaging, personalized medicine, 030204 cardiovascular system & hematology, Type (model theory), 030218 nuclear medicine & medical imaging, 03 medical and health sciences, QRS complex, 0302 clinical medicine, Nuclear magnetic resonance, translational research, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Norm (mathematics), Ventricular pressure, medicine, [SDV.IB]Life Sciences [q-bio]/Bioengineering, interventional cardiovascular magnetic resonance imaging, Volume (compression)
Abstract: International audience; When combining cardiovascular magnetic resonance imaging (CMR) with pressure catheter measurements, the acquired imageand pressure data need to be synchronized in time. The time offset between the image and pressure data depends on a number of factors,such as the type and settings of the MR sequence, duration and shape of QRS complex or the type of catheter, and cannot be typically estimated beforehand. In the present work we propose using a biophysical heart model to synchronize the left ventricular (LV) pressure and volume (P-V) data. Ten patients, who underwent CMR and LV catheterization, were included. A biophysical model of reduced geometrical complexity with physiologically substantiated timing of each phase of the cardiac cycle was first adjusted to individual patients using basic morphological and functional indicators. The pressure and volume waveforms simulated by the patient-specific models were then used as templates to detect the time offset between the acquired ventricular pressure and volume waveforms. Time-varying ventricular elastance was derived from clinical data both as originally acquired as well as when time-synchronized, and normalized with respect to end-systolic time and maximum elastance value$E^N_\text {orig}(t)$, $E^N_\text {t-syn}(t)$, respectively). $E^N_\text {t-syn}(t)$ was significantly closer to the experimentally obtained $E^N_\text {exp}(t)$ published in the literature (p < 0.05, $L^2$ norm). The work concludes that the model-driven time-synchronization of P-V data obtained by catheter measurement and CMR allows to generate high quality P-V loops, which can then be used for clinical interpretation.
Published: 2021
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7. Sequential data assimilation for mechanical systems with complex image data: application to tagged-MRI in cardiac mechanics

Author: Philippe Moireau, Dominique Chapelle, Alexandre Imperiale, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Département Imagerie et Simulation pour le Contrôle (DISC), Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Laboratoire d'Intégration des Systèmes et des Technologies (LIST)
Subjects: Computer science, 0206 medical engineering, Image processing, 02 engineering and technology, Data type, Synthetic data, 030218 nuclear medicine & medical imaging, lcsh:TA168, 03 medical and health sciences, 0302 clinical medicine, Data assimilation, Medical imaging, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Engineering (miscellaneous), Flexibility (engineering), Measure (data warehouse), Tagged-MRI, business.industry, Applied Mathematics, Pattern recognition, Cardiac modeling, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computer Science Applications, lcsh:Systems engineering, Modeling and Simulation, Patient-specific model, Artificial intelligence, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Focus (optics), business, lcsh:Mechanics of engineering. Applied mechanics, lcsh:TA349-359, Estimation
Abstract: Tagged Magnetic Resonance images (tagged-MRI) are generally considered to be the gold standard of medical imaging in cardiology. By imaging spatially-modulated magnetizations of the deforming tissue, indeed, this modality enables an assessment of intra-myocardial deformations over the heart cycle. The objective of the present work is to incorporate the most valuable information contained in tagged-MRI in a data assimilation framework, in order to perform joint state-parameter estimation for a complete biomechanical model of the heart. This type of estimation is the second major step, after initial anatomical personalization, for obtaining a genuinely patient-specific model that integrates the individual characteristics of the patient, an essential prerequisite for benefitting from the model predictive capabilities. Here, we focus our attention on proposing adequate means of quantitatively comparing the cardiac model with various types of data that can be extracted from tagged-MRI after an initial image processing step, namely, 3D displacements fields, deforming tag planes or grids, or apparent 2D displacements. This quantitative comparison—called discrepancy measure—is then used to feed a sequential data assimilation procedure. In the state estimation stage of this procedure, we also propose a new algorithm based on the prediction–correction paradigm, which provides increased flexibility and effectiveness in the solution process. The complete estimation chain is eventually assessed with synthetic data, produced by running a realistic model simulation representing an infarcted heart characterized by increased stiffness and reduced contractility in a given region of the myocardium. From this simulation we extract the 3D displacements, tag planes and grids, and apparent 2D displacements, and we assess the estimation with each corresponding discrepancy measure. We demonstrate that—via regional estimation of the above parameters—the data assimilation procedure allows to quantitatively estimate the biophysical parameters with good accuracy, thus simultaneously providing the location of the infarct and characterizing its seriousness. This shows great potential for combining a biomechanical heart model with tagged-MRI in order to extract valuable new indices in clinical diagnosis.
Published: 2021
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8. A quasi-static poromechanical model of the lungs

Author: Cécile Patte, Martin Genet, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-10-EQPX-0037,MATMECA,MATériaux-MECAnique/Elaboration-Caractérisation-Observation-Modélisation-Simulation(2010), ANR-19-CE45-0007,LungManyScale,Biomécanique Computationnelle Pulmonaire: Modélisation Multi-échelle et Estimation(2019), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Mechanical Engineering, Respiration, 0206 medical engineering, Diaphragm, Poromechanics, Modeling, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], 02 engineering and technology, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, 0302 clinical medicine, Inverse Poromechanics, Modeling and Simulation, Finite Element Method, Pulmonary Mechanics, [SDV.MHEP.AHA]Life Sciences [q-bio]/Human health and pathology/Tissues and Organs [q-bio.TO], Lung, Biotechnology
Abstract: International audience; The lung vital function of providing oxygen to the body heavily relies on its mechanical behavior, and the interaction with its complex environment. In particular, the large compliance and the porosity of the pulmonary tissue are critical for lung inflation and air inhalation, and the diaphragm, the pleura, the rib cage and intercostal muscles all play a role in delivering and controlling the breathing driving forces. In this paper, we introduce a novel poromechanical model of the lungs. The constitutive law is derived within a general poromechanics theory via the formulation of lung-specific assumptions, leading to a hyperelastic potential reproducing the volume response of the pulmonary mixture to a change of pressure. Moreover, physiological boundary conditions are formulated to account for the interaction of the lungs with their surroundings, including a following pressure and bilateral frictionless contact. A strategy is established to estimate the unloaded configuration from a given loaded state, with a particular focus on ensuring a positive porosity. Finally, we illustrate through several realistic examples the relevance of our model and its potential clinical applications.
Published: 2021
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9. Personalized pulmonary poromechanics

Author: Pierre-Yves Brillet, Dominique Chapelle, Catalin Fetita, Cécile Patte, Martin Genet, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Polytechnique de Paris (IP Paris), Département Advanced Research And Techniques For Multidimensional Imaging Systems (TSP - ARTEMIS), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), ARMEDIA (ARMEDIA-SAMOVAR), Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux (SAMOVAR), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP)-Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), Hypoxie et Poumon : pneumopathologies fibrosantes, modulations ventilatoires et circulatoires (H&P), UFR SMBH-Université Sorbonne Paris Nord, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Département Advanced Research And Techniques For Multidimensional Imaging Systems (ARTEMIS)
Subjects: Computer science, 0206 medical engineering, Poromechanics, Biomedical Engineering, Bioengineering, 02 engineering and technology, [SDV.MHEP.PSR]Life Sciences [q-bio]/Human health and pathology/Pulmonology and respiratory tract, 03 medical and health sciences, 0302 clinical medicine, Pulmonary mechanics, Modeling, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Control engineering, 030229 sport sciences, General Medicine, respiratory system, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 3. Good health, Computer Science Applications, Human-Computer Interaction, Current (fluid), Estimation, Simulation
Abstract: International audience; Lung biomechanics has been extensively studied by physiologists, experimentally as well as theoretically, laying the ground for our current fundamental understanding of the relationship between function and mechanical behavior. However, many questions remain, notably in the intricate coupling between the multiple constituents. These fundamental questions represent real clinical challenges, as pulmonary diseases are an important health burden. Interstitial lung diseases, for instance, affect several million people globally. Idiopathic Pulmonary Fibrosis (IPF), notably, a progressive form of interstitial lung diseases where some alveolar septa get thicker and stiffer while others get completely damaged, remains poorly understood, poorly diagnosed, and poorly treated (Nunes et al. 2015).
Published: 2020
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10. Activation-CONTRACTION COUPLING IN A MULTISCALE HEART MODEL

Author: François Kimmig, Matthieu Caruel, Dominique Chapelle, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Modélisation et Simulation Multi Echelle (MSME), Université Paris-Est Marne-la-Vallée (UPEM)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Université Paris-Est Marne-la-Vallée (UPEM), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Caruel, Matthieu
Subjects: [PHYS.MECA.SOLID] Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], [PHYS.MECA.BIOM] Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph], ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2019

11. Cardiac displacement tracking with data assimilation combining a biomechanical model and an automatic contour detection

Author: Gautier Bureau, Dominique Chapelle, Jürgen Weese, Jaroslav Tintera, Radomir Chabiniok, Alexandra Groth, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), King‘s College London, Philips Research [Germany], Philips Research, Institute for Clinical and Experimental Medicine (IKEM), Zemzemi, Nejib, Ozenne, Valéry, Vigmond, Edward, Coudière, Yves, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Computational model, Computer science, business.industry, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, 0206 medical engineering, 02 engineering and technology, Tracking (particle physics), 020601 biomedical engineering, Biophysical heart modeling, cine MRI, Displacement (vector), Bottleneck, 030218 nuclear medicine & medical imaging, Term (time), Cine mri, 03 medical and health sciences, 0302 clinical medicine, Data assimilation, Computer vision, Artificial intelligence, business, [SDV.IB.BIO]Life Sciences [q-bio]/Bioengineering/Biomaterials, Cardiac imaging
Abstract: International audience; Data assimilation in computational models represents an essential step in building patient-specific simulations. This work aims at circumventing one major bottleneck in the practical use of data assimilation strategies in cardiac applications, namely, the difficulty of formulating and effectively computing adequate data-fitting term for cardiac imaging such as cine MRI. We here provide a proof-of-concept study of data assimilation based on automatic contour detection. The tissue motion simulated by the data assimilation framework is then assessed with displacements extracted from tagged MRI in six subjects, and the results illustrate the performance of the proposed method, including for circumferential displacements, which are not well extracted from cine MRI alone.
Published: 2019
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12. Minimally-invasive estimation of patient-specific end-systolic elastance using a biomechanical heart model

Author: Radomir Chabiniok, Dominique Chapelle, Fabrice Vallée, Arthur Le Gall, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), Centre National de la Recherche Scientifique (CNRS)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École polytechnique (X)-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), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École polytechnique (X), Service d'Anesthésie-Réanimation [AP-HP Hôpitaux Saint-Louis Lariboisière], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital Lariboisière-Fernand-Widal [APHP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), School of Biomedical Engineering & Imaging Sciences [London], Guy's and St Thomas' Hospital [London]-King‘s College London, ANAESTASSIST, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), King‘s College London-Guy's and St Thomas' Hospital [London], Coudière, Yves, Ozenne, Valéry, Vigmond, Edward, Zemzemi, Nejib, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS), Assistance publique - Hôpitaux de Paris (AP-HP) (APHP)-Hôpital Lariboisière-Université Paris Diderot - Paris 7 (UPD7), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Time-varying elastance, Linear function (calculus), [SDV]Life Sciences [q-bio], 0206 medical engineering, Patient-specific biophysical modelling, 02 engineering and technology, State (functional analysis), Function (mathematics), 030204 cardiovascular system & hematology, Patient specific, 020601 biomedical engineering, Confidence interval, [SHS]Humanities and Social Sciences, Combinatorics, 03 medical and health sciences, 0302 clinical medicine, End systolic elastance, Time-varying elastan, End-systolic elastance estimation, Sensitivity (control systems), Uniqueness, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology, Mathematics
Abstract: The end-systolic elastance ($E_{\text {es}}$) – the slope of the end-systolic pressure-volume relationship (ESPVR) at the end of ejection phase – has become a reliable indicator of myocardial functional state. The estimation of $E_{\text {es}}$ by the original multiple-beat method is invasive, which limits its routine usage. By contrast, non-invasive single-beat estimation methods, based on the assumption of the linearity of ESPVR and the uniqueness of the normalised time-varying elastance curve $E^N(t)$ across subjects and physiology states, have been applied in a number of clinical studies. It is however known that these two assumptions have a limited validity, as ESPVR can be approximated by a linear function only locally, and $E^N(t)$ obtained from a multi-subject experiment includes a confidence interval around the mean function. Using datasets of 3 patients undergoing general anaesthesia (each containing aortic flow and pressure measurements at baseline and after introducing a vasopressor noradrenaline), we first study the sensitivity of two single-beat methods—by Sensaki et al. and by Chen et al.—to the uncertainty of $E^N(t)$. Then, we propose a minimally-invasive method based on a patient-specific biophysical modelling to estimate the whole time-varying elastance curve $E^{\text {model}}(t)$. We compare $E^{\text {model}}_{\text {es}}$ with the two single-beat estimation methods, and the normalised varying elastance curve $E^{N,\text {model}}(t)$ with $E^{N}(t)$ from published physiological experiments.
Published: 2019
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13. Numerical analysis for an energy-stable total discretization of a poromechanics model with inf-sup stability

Author: Philippe Moireau, Dominique Chapelle, Bruno Burtschell, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Spacetime, Discretization, energy estimates, Applied Mathematics, Numerical analysis, Poromechanics, poromechanics, 010103 numerical & computational mathematics, incompressibility, 01 natural sciences, Stability (probability), 010101 applied mathematics, inf-sup, Nonlinear system, [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], Compressibility, Applied mathematics, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, total discretization, Energy (signal processing), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; We consider a previously proposed general nonlinear poromechanical formulation, and we derive a linearized version of this model. For this linearized model, we obtain an existence result and we propose a complete discretization strategy - in time and space - with a special concern for issues associated with incompressible or nearly-incompressible behavior. We provide a detailed mathematical analysis of this strategy, the main result being an error estimate uniform with respect to the compressibility parameter. We then illustrate our approach with detailed simulation results and we numerically investigate the importance of the assumptions made in the analysis, including the fulfillment of specific inf-sup conditions.
Published: 2019
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14. Thermodynamic properties of muscle contraction models and associated discrete-time principles

Author: Dominique Chapelle, Philippe Moireau, François Kimmig, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Large class, 74F25 ·74H15 · 65M12 ·35Q79 and 92C45, Discretization, 02 engineering and technology, Clausius–Duhem inequality, 01 natural sciences, lcsh:TA168, muscle contraction, 0203 mechanical engineering, medicine, Computational Science and Engineering, Statistical physics, 0101 mathematics, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Engineering (miscellaneous), thermodynamically consistent time-discretization, Mathematics, Clausius-Duhem inequality, Continuum mechanics, Applied Mathematics, sliding filaments, Computer Science Applications, 010101 applied mathematics, 020303 mechanical engineering & transports, Discrete time and continuous time, lcsh:Systems engineering, Modeling and Simulation, medicine.symptom, lcsh:Mechanics of engineering. Applied mechanics, lcsh:TA349-359, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Muscle contraction
Abstract: International audience; Considering a large class of muscle contraction models accounting for actin-myosin interaction, we present a mathematical setting in which solution properties can be established, including fundamental thermodynamic balances. Moreover, we propose a complete discretization strategy for which we are also able to obtain discrete versions of the thermodynamic balances and other properties. Our major objective is to show how the thermodynamics of such models can be tracked after discretization, including when they are coupled to a macroscopic muscle formulation in the realm of continuum mechanics. Our approach allows to carefully identify the sources of energy and entropy in the system, and to follow them up to the numerical applications.
Published: 2019
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15. Airborne ultrasound surface motion camera: application to seismocardiography

Author: Pavel Shirkovskiy, R.K. Ing, Dominique Chapelle, Mathias Fink, Nathan Jeger-Madiot, Alexandre Laurin, Institut Langevin - Ondes et Images (UMR7587) (IL), Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Synthetic aperture radar, Physics and Astronomy (miscellaneous), Computer science, Wave propagation, Acoustics, non-contact seismocardiography, 030204 cardiovascular system & hematology, Accelerometer, 01 natural sciences, cardiac mechanics, 03 medical and health sciences, Acceleration, 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Position (vector), [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Center frequency, surface motion, business.industry, 010401 analytical chemistry, Ultrasound, airborne ultrasound vibrometry, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], cardio-vascular signals, Non-contact ultrasonic imaging, 0104 chemical sciences, Identifiability, business
Abstract: International audience; The recent achievements in the accelerometer-based seismocardiography field indicate a strong potential for this technique to address wide variety of clinical needs. Recordings from different locations on the chest can give a more comprehensive observation and interpretation of wave propagation phenomena than a single-point recording, can validate existing modeling assumptions (such as the representation of the sternum as a single solid body), and provide better identifiability for models using richer recordings. Ultimately, the goal is to advance our physiological understanding of the processes to provide useful data to promote cardiovascular health. Accelerometer-based multichannel system is a contact method and laborious for use in practice, also even ultralight accelerometers can cause non-negligible loading effects. We propose a new contactless ultrasound imaging method to measure thoracic and abdominal surface motions, demonstrating that it is adequate for typical seismocardiogram use. The developed method extends non-contact surface-vibrometry to fast 2D mapping by originally combining multi-element airborne ultrasound arrays, a synthetic aperture implementation and pulsed-waves. Experimental results show the ability of the developed method to obtain 2D seismocardiographic maps of the body surface 30×40 cm 2 in dimension, with a temporal sampling rate of several hundred Hz, using ultrasound waves with the central frequency of 40 kHz. Our implementation was validated in-vivo on eight healthy human participants. The shape and position of the zone of maximal absolute acceleration and velocity during the cardiac cycle were also observed. This technology could potentially be used to obtain more complete cardio-vascular information than single-source SCG in and out of clinical environments, due to enhanced identifiability provided by distributed measurements, and observation of propagation phenomena.
Published: 2018
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16. Effective and energy-preserving time discretization for a general nonlinear poromechanical formulation

Author: Dominique Chapelle, Bruno Burtschell, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Centre National de la Recherche Scientifique (CNRS)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École polytechnique (X)-Inria Saclay - Ile de France
Subjects: Coupling, Mathematical optimization, Work (thermodynamics), Discretization, Mechanical Engineering, 010103 numerical & computational mathematics, Dissipation, 01 natural sciences, Computer Science Applications, 010101 applied mathematics, Nonlinear system, Modeling and Simulation, Component (UML), Applied mathematics, General Materials Science, 0101 mathematics, Energy (signal processing), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Civil and Structural Engineering, Free energy principle, Mathematics
Abstract: Proposed time discretization scheme for general two-phase poromechanical model.Discrete energy estimate with the total free energy of the mixture, in a general nonlinear framework.Numerical examples with representative test problems. We consider a general nonlinear poromechanical model, formulated based on fundamental thermodynamics principle, suitable for representing the coupling of rapid internal fluid flows with large deformations of the solid, and compatible with a wide class of constitutive behavior. The objective of the present work is to propose for this model a time discretization scheme of the partitioned type, to allow the use of existing time schemes and possibly separate solvers for each component of the model, i.e. for the fluid and the solid. To that purpose, we adapt and extend an earlier proposed approach devised for fluid-structure interaction in an Arbitrary Lagrangian-Eulerian framework. We then establish an energy estimate for the resulting time scheme, in a form that is consistent with the underlying energy principle in the poromechanical formulation, up to some numerical dissipation effects and some perturbations that we have carefully identified and assessed. In addition, we provide some numerical illustrations of our numerical strategy with test problems that present typical features of large strains and rapid fluid flows, and also a case of singular transition related to total drainage. An example of challenging application envisioned for this model and associated numerical coupling scheme concerns the perfusion of the heart.
Published: 2017
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17. Patient-Specific Biomechanical Modeling of Cardiac Amyloidosis – A Case Study

Author: Aziz Guellich, Radomir Chabiniok, Jean-François Deux, Dominique Chapelle, Thibaud Damy, Alessandro Felder, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Imaging Sciences and Biomedical Engineering Division [London], Guy's and St Thomas' Hospital [London]-King‘s College London, Unité fonctionnelle insuffisance cardiaque, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital Henri Mondor-Université Paris-Est (UPE), Institut Mondor de Recherche Biomédicale (IMRB), Institut National de la Santé et de la Recherche Médicale (INSERM)-IFR10-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), H. van Assen, P. Bovendeerd, T. Delhaas, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: amyloidosis, medicine.medical_specialty, Heartbeat, business.industry, Amyloidosis, heart failure, Patient specific, medicine.disease, Surgery, cardiac modeling, Physical medicine and rehabilitation, Cardiac amyloidosis, patient-specific, Heart failure, medicine, business, Passive stiffness, Venous return curve, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We present a patient-specific biomechanical modeling framework and an initial case study for investigating cardiac amyloidosis (CA). Our patient-specific heartbeat simulations are in good agreement with the data, and our model calibration indicates that the major effect of CA in the biophysical behavior lies in a dramatic increase of the passive stiffness. We also conducted a preliminary trial for predicting the effects of pharmacological treatments – which is an important clinical challenge – based on the model combined with a simple venous return representation. This requires further investigation and validation, albeit provides some valuable preliminary insight.
Published: 2015
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18. Sequential State Estimation for Electrophysiology Models with Front Level-Set Data Using Topological Gradient Derivations

Author: Annabelle Collin, Dominique Chapelle, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Modélisation Mathématique pour l'Oncologie (MONC), 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)-Institut Bergonié [Bordeaux], UNICANCER-UNICANCER-Inria Bordeaux - Sud-Ouest, H. van Assen, P. Bovendeerd, T. Delhaas, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, 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)-Institut Bergonié [Bordeaux]
Subjects: Sequential estimation, bidomain equations, Observer (quantum physics), estimation, topological gradient, Quantitative Biology::Tissues and Organs, Physics::Medical Physics, observer, Topology, electrophysiology modeling, Term (time), Electrophysiology, Data assimilation, Level set, shape derivative, State (computer science), data assimilation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; We propose a new sequential estimation method for making an electrophysiology model patient-specific, with data in the form of level sets of the electrical potential. Our method incorporates a novel correction term based on topological gradients, in order to track solutions of complex patterns. Our assessments demonstrate the effectiveness of this approach, including in a realistic case of atrial fibrillation.
Published: 2015
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19. Dimensional reductions of a cardiac model for effective validation and calibration

Author: Dominique Chapelle, Matthieu Caruel, Philippe Moireau, Yves Lecarpentier, Radomir Chabiniok, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Imaging Sciences and Biomedical Engineering Division [London], Guy's and St Thomas' Hospital [London]-King‘s College London, CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)
Subjects: Sarcomeres, Beating heart, Engineering, Calibration and validation, Heart Ventricles, 0206 medical engineering, Blood Pressure, Model parameters, 02 engineering and technology, 030204 cardiovascular system & hematology, Ventricular Function, Left, Elastance, cardiac modeling, 03 medical and health sciences, Imaging, Three-Dimensional, 0302 clinical medicine, Afterload, experimental validation, Animals, Computer Simulation, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Simulation, Frank–Starling law of the heart, length-dependence effects, business.industry, Myocardium, Mechanical Engineering, Models, Cardiovascular, Reproducibility of Results, Experimental data, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Heart, Myocardial Contraction, 020601 biomedical engineering, Elasticity, Rats, Preload, Modeling and Simulation, Calibration, Frank-Starling mechanism, hierarchical modeling, Biological system, business, Algorithms, Biotechnology
Abstract: International audience; Complex 3D beating heart models are now available, but their complexity makes calibration and validation very difficult tasks. We thus propose a systematic approach of deriving simplified reduced-dimen\-sional models, in ''0D'' --~typically, to represent a cardiac cavity, or several coupled cavities --~and in ''1D'' --~to model elongated structures such as muscle samples or myocytes. We apply this approach with an earlier-proposed 3D cardiac model designed to capture length-dependence effects in contraction, which we here complement by an additional modeling component devised to represent length-dependent relaxation. We then pre\-sent experimental data produced with rat papillary muscles samples when varying preload and afterload conditions, and we achieve some detailed validations of the 1D model with these data, including for the length-dependence effects that are accurately captured. Finally, when running simulations of the 0D model pre-calibrated with the 1D model parameters, we obtain pressure-volume indicators of the left ventricle in good agreement with some important features of cardiac physiology, including the so-called Frank-Starling mechanism, the End-Systolic Pres\-sure-Volume Relationship (ESPVR), as well as varying elastance properties. This integrated multi-dimensional modeling approach thus sheds new light on the relations between the phenomena observed at different scales and at the local vs. organ levels.
Published: 2014
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20. Direct finite element computation of non-linear modal coupling coefficients for reduced-order shell models

Author: Marina Vidrascu, Dominique Chapelle, Cyril Touzé, Unité de Mécanique (UME), École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: Discretization, Computational Mechanics, Shell (structure), Ocean Engineering, Geometry, Bifurcation diagram, Quadratic equation, [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph], stiffness evaluation, Mathematics, Coupling, MITC elements, bifurcation diagram, reduced-order models, Applied Mathematics, Mechanical Engineering, Mathematical analysis, geometric nonlinearity, Finite element method, Computational Mathematics, Nonlinear system, Computational Theory and Mathematics, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], finite elements, Reduction (mathematics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We propose a direct method for computing modal coupling coefficients - due to geometrically nonlinear effects - for thin shells vibrating at large amplitude and discretized by a finite element (FE) procedure. These coupling coefficients arise when considering a discrete expansion of the unknown displacement onto the eigenmodes of the linear operator. The evolution problem is thus projected onto the eigenmodes basis and expressed as an assembly of oscillators with quadratic and cubic nonlinearities. The nonlinear coupling coefficients are directly derived from the finite element formulation, with specificities pertaining to the shell elements considered, namely, here elements of the ''Mixed Interpolation of Tensorial Components'' family (MITC). Therefore, the computation of coupling coefficients, combined with an adequate selection of the significant eigenmodes, allows the derivation of effective reduced-order models for computing - with a continuation procedure - the stable and unstable vibratory states of any vibrating shell, up to large amplitudes. The procedure is illustrated on a hyperbolic paraboloid panel. Bifurcation diagrams in free and forced vibrations are obtained. Comparisons with direct time simulations of the full FE model are given. Finally, the computed coefficients are used for a maximal reduction based on asymptotic nonlinear normal modes (NNMs), and we find that the most important part of the dynamics can be predicted with a single oscillator equation.
Published: 2014
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21. General coupling of porous flows and hyperelastic formulations -- From thermodynamics principles to energy balance and compatible time schemes

Author: Philippe Moireau, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: thermomechanics, Spacetime, Computer science, Poromechanics, Energy balance, poromechanics, General Physics and Astronomy, Thermodynamics, Laws of thermodynamics, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Isothermal process, biomechanics, Mixture theory, thermodynamics, Classical mechanics, mixtures, Hyperelastic material, hyperelasticity, Porosity, Mathematical Physics
Abstract: Updated version of previously published research report; International audience; We formulate a general poromechanics model -- within the framework of a two-phase mixture theory -- compatible with large strains and without any simplification in the momentum expressions, in particular concerning the fluid flows. The only specific assumptions made are fluid incompressibility and isothermal conditions. Our formulation is based on fundamental physical principles -- namely, essential conservation and thermodynamics laws -- and we thus obtain a Clausius-Duhem inequality which is crucial for devising compatible constitutive laws. We then propose to model the solid behavior based on a generalized hyperelastic free energy potential -- with additional viscous effects -- which allows to represent a wide range of mechanical behaviors. The resulting formulation takes the form of a coupled system similar to a fluid-structure interaction problem written in an Arbitrary Lagrangian-Eulerian formalism, with additional volume-distributed interaction forces. We achieve another important objective by identifying the essential energy balance prevailing in the model, and this paves the way for further works on mathematical analyses, and time and space discretizations of the formulation.; Nous présentons, dans le cadre de la théorie des mélanges, un model poromécanique général valide en grands déplacements et sans simplification sur le bilan de conservation des moments, en particulier pour le système fluide. Les seules hypothèses faites sont l'incompressibilité du fluide et des conditions isothermes. Notre formulation s'appuie sur les principes de la thermodynamiques et nous obtenons une inégalité de Clausius-Duhem fondamentale pour l'obtention de lois de comportement adaptées. Nous proposons alors de modéliser le solide avec un potentiel d'énergie libre hyperélastique généralisé auquel s'ajoute un potentiel visqueux, permettant ainsi de représenter une large gamme de comportements mécaniques. La formulation résultante prend la forme d'un système couplé similaire à ceux rencontrés en interaction fluide-structure de type ALE comprenant un couplage volumique supplémentaire. Nous sommes alors en mesure d'écrire sur le modèle complet des estimations d'énergie qui seront à l'origine de travaux futurs, que ce soit pour l'analyse mathématique du système ou la formulation de discrétisations en temps et en espace adaptées.
Published: 2014
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22. Dimensional Reduction of Cardiac Models for Effective Validation and Calibration

Author: Radomir Chabiniok, Philippe Moireau, Yves Lecarpentier, Dominique Chapelle, Matthieu Caruel, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Imaging Sciences and Biomedical Engineering Division [London], Guy's and St Thomas' Hospital [London]-King‘s College London, Service d'Explorations Fonctionnelles Cardio-Respiratoires, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital de Bicêtre, Ourselin, Sebastien and Rueckert, Daniel and Smith, Nicolas, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: multi scale, 0303 health sciences, Beating heart, Calibration and validation, Hierarchical modeling, Computer science, Calibration (statistics), 0206 medical engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], 02 engineering and technology, Experimental validation, heart, 020601 biomedical engineering, Model validation, 03 medical and health sciences, Dimensional reduction, model reduction, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Algorithm, Simulation, 030304 developmental biology
Abstract: To be published as proceedings in: Functional Imaging and Modeling of the Heart 7th International Conference, FIMH 2013, London, UK, Lecture Notes in Computer Science 7945; International audience; Complex 3D beating heart models are now available, but their complexity makes calibration and validation very difficult tasks. We thus propose a systematic approach of deriving simplified reduced- dimensional models, in "0D" - typically, to represent a cardiac cavity, or several coupled cavities - and in "1D" - to model elongated structures such as fibers or myocytes. As illustrations of our approach, we demon- strate model validation based on experiments performed with papillary muscles, and calibration using patient-specific pressure-volume loops.
Published: 2013

23. Surface-based electrophysiology modeling and assessment of physiological simulations in atria

Author: Michel Haïssaguerre, Dominique Chapelle, Jean-Frédéric Gerbeau, Annabelle Collin, Mélèze Hocini, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Hôpital Haut-Lévêque, Université Sciences et Technologies - Bordeaux 1-CHU Bordeaux [Bordeaux], Sébastien Ourselin and Daniel Rueckert and Nicolas Smith, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Sciences et Technologies - Bordeaux 1 (UB)-CHU Bordeaux [Bordeaux]
Subjects: Surface (mathematics), Materials science, Asymptotic analysis, Left atrium, Bidomain model, Cardiology, 3d model, 030204 cardiovascular system & hematology, 01 natural sciences, 010101 applied mathematics, 03 medical and health sciences, Electrophysiology, 0302 clinical medicine, medicine.anatomical_structure, Electrophysiology modelling, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, medicine, 0101 mathematics, Wall thickness, Anisotropy, Biological system, Simulation
Abstract: International audience; The objective of this paper is to assess a previously-proposed surface-based electrophysiology model with detailed atrial simulations. This model - derived and substantiated by mathematical arguments - is specifically designed to address thin structures such as atria, and to take into account strong anisotropy effects related to fiber directions with possibly rapid variations across the wall thickness. The simulation results are in excellent adequacy with previous studies, and confirm the importance of anisotropy effects and variations thereof. Furthermore, this surface-based model provides dramatic computational benefits over 3D models with preserved accuracy.
Published: 2013
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24. Personalization of a Cardiac Electromechanical Model using Reduced Order Unscented Kalman Filtering from Regional Volumes

Author: Alejandro F. Frangi, Stephanie Marchesseau, Nicholas Ayache, Christophe Leclercq, Simon G. Duckett, Karim Lekadir, Reza Razavi, Hervé Delingette, Philippe Moireau, Kawal Rhode, Erwan Donal, Christopher A. Rinaldi, R.M. Figueras i Ventura, Catalina Tobon-Gomez, Dominique Chapelle, Mireille Garreau, Alfredo Hernandez, Maxime Sermesant, Rocio Cabrera-Lozoya, Analysis and Simulation of Biomedical Images (ASCLEPIOS), 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), Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB), Universitat Pompeu Fabra [Barcelona] (UPF), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Laboratoire Traitement du Signal et de l'Image (LTSI), Université de Rennes (UR)-Institut National de la Santé et de la Recherche Médicale (INSERM), Division of Imaging Sciences, King‘s College London, Department of cardiology [Guy's and St. Thomas ' hospitals] [London], Guy's and St Thomas' Hospital [London]-Guy's Hospital [London], NIHR Biomedical Research Centre [London], Guy's and St Thomas' NHS Foundation Trust-King‘s College London, European Project: 291080,EC:FP7:ERC,ERC-2011-ADG_20110209,MEDYMA(2012), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université de Rennes 1 (UR1), and Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de la Santé et de la Recherche Médicale (INSERM)
Subjects: Matching (graph theory), Computer science, Heart Ventricles, 0206 medical engineering, Magnetic Resonance Imaging, Cine, Health Informatics, 02 engineering and technology, Kinematics, Sensitivity and Specificity, Ventricular Function, Left, 030218 nuclear medicine & medical imaging, Reduced order, Personalization, 03 medical and health sciences, Imaging, Three-Dimensional, 0302 clinical medicine, Heart Conduction System, Image Interpretation, Computer-Assisted, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Humans, Computer Simulation, Radiology, Nuclear Medicine and imaging, Segmentation, Computer vision, Unscented transform, Precision Medicine, Excitation Contraction Coupling, Radiological and Ultrasound Technology, Estimation theory, business.industry, Models, Cardiovascular, Reproducibility of Results, Organ Size, Image Enhancement, Myocardial Contraction, 020601 biomedical engineering, Computer Graphics and Computer-Aided Design, Unscented kalman filtering, Computer Vision and Pattern Recognition, Artificial intelligence, business, Algorithms
Abstract: International audience; Patient-specific cardiac modelling can help in understanding pathophysiology and therapy planning. However it requires to combine functional and anatomical data in order to build accurate models and to personalize the model geometry, kinematics, electrophysiology and mechanics. Personalizing the electromechanical coupling from medical images is a challenging task. We use the Bestel-Clément-Sorine (BCS) electromechanical model of the heart, which provides reasonable accuracy with a reasonable number of parameters (14 for each ventricle) compared to the available clinical data at the organ level. We propose a personalization strategy from cine MRI data in two steps. We first estimate global parameters with an automatic calibration algorithm based on the Unscented Transform which allows to initialize the parameters while matching the volume and pressure curves. In a second step we locally personalize the contractilities of all AHA (American Heart Association) zones of the left ventricle using the Reduced Order Unscented Kalman Filtering on Regional Volumes. This personalization strategy was validated synthetically and tested successfully on eight healthy and three pathological cases.
Published: 2013
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25. State observers of a vascular fluid-structure interaction model through measurements in the solid

Author: Jean-Frédéric Gerbeau, Miguel Angel Fernández, Cristóbal Bertoglio, Dominique Chapelle, Philippe Moireau, Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Modeling, analysis and control in computational structural dynamics (MACS), Inria Saclay - Ile de France, European Project: 224495,ICT,FP7-ICT-2007-2,EUHEART(2008), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: Observer (quantum physics), 0206 medical engineering, Computational Mechanics, General Physics and Astronomy, fluid-structure interaction, 02 engineering and technology, hemodynamics, 01 natural sciences, Control theory, Fluid–structure interaction, Fluid dynamics, State observer, Boundary value problem, 0101 mathematics, Added mass, Mathematics, observers, estimation, Mechanical Engineering, Interaction model, 020601 biomedical engineering, Computer Science Applications, 010101 applied mathematics, Mechanics of Materials, Displacement (fluid), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We analyze the performances of two types of Luenberger observers -- namely, the so-called Direct Velocity Feedback and Schur Displacement Feedback procedures, originally devised for elasto-dynamics -- to estimate the state of a fluid-structure interaction model for hemodynamics, when the measurements are assumed to be restricted to displacements or velocities in the solid. We first assess the observers using hemodynamics-inspired test problems with the complete model, including the Navier-Stokes equations in Arbitrary Lagrangian-Eulerian formulation, in particular. Then, in order to obtain more detailed insight we consider several well-chosen simplified models, each of which allowing a thorough analysis -- emphasizing spectral considerations -- while illustrating a major phenomenon of interest for the observer performance, namely, the added mass effect for the structure, the coupling with a lumped-parameter boundary condition model for the fluid flow, and the fluid dynamics effect per se. Whereas improvements can be sought when additional measurements are available in the fluid domain in order to more effectively deal with strong uncertainties in the fluid state, in the present framework this establishes Luenberger observer methods as very attractive strategies -- compared, e.g., to classical variational techniques -- to perform state estimation, and more generally for uncertainty estimation since other observer procedures can be conveniently combined to estimate uncertain parameters.
Published: 2013
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26. A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems -- Analysis, assessments and applications to parameter estimation

Author: Jacques Sainte-Marie, Dominique Chapelle, Philippe Moireau, Asven Gariah, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Numerical Analysis, Geophysics and Ecology (ANGE), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Centre d'Études Techniques Maritimes et Fluviales (CETMEF), Avant création Cerema, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Mathematical optimization, Proper Orthogonal Decomposition, FitzHugh-Nagumo equations, 010103 numerical & computational mathematics, 01 natural sciences, Applied mathematics, 0101 mathematics, Remainder, Galerkin method, Mathematics, Numerical Analysis, Sequential estimation, Estimation theory, Applied Mathematics, Cardiac modeling, Real image, 010101 applied mathematics, Computational Mathematics, Modeling and Simulation, Parameter variations, Proper orthogonal decomposition, A priori and a posteriori, Estimation, Mathematics Subject Classification: 65M60, 35A35, 35B45, 93E10, Analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Interpolation
Abstract: We address the issue of parameter variations in POD approximations of time-dependent problems, without any specific restriction on the form of parameter dependence. Considering a parabolic model problem, we propose a POD construction strategy allowing us to obtain some a priori error estimates controlled by the POD remainder – in the construction procedure – and some parameter-wise interpolation errors for the model solutions. We provide a thorough numerical assessment of this strategy with the FitzHugh − Nagumo 1D model. Finally, we give detailed illustrations of the approach in two parameter estimation applications, the first in a variational estimation framework with the FitzHugh − Nagumo model, and the second with a beating heart mechanical model for which we employ a sequential estimation method to characterize model parameters using real image data in a clinical case.
Published: 2013
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27. A surface-based electrophysiology model relying on asymptotic analysis and motivated by cardiac atria modeling

Author: Annabelle Collin, Dominique Chapelle, Jean-Frédéric Gerbeau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Surface (mathematics), 0303 health sciences, Asymptotic analysis, Mathematical optimization, Computational model, Field (physics), Computer science, Computational electrophysiology, Applied Mathematics, Thin domains, Cardiac modeling, 01 natural sciences, 010101 applied mathematics, 03 medical and health sciences, Modeling and Simulation, Convergence (routing), Statistical physics, Limit (mathematics), 0101 mathematics, AMS Subject Classification: 22E46, 53C35, 57S20, Anisotropy, Representation (mathematics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], 030304 developmental biology
Abstract: International audience; Computational electrophysiology is a very active field with tremendous potential in medical applications, albeit leads to highly intensive simulations. We here propose a surface-based electrophysiology formulation, motivated by the modeling of thin structures such as cardiac atria, which greatly reduces the size of the computational models. Moreover, our model is specifically devised to retain the key features associated with the anisotropy in the diffusion effects induced by the fiber architecture, with rapid variations across the thickness which cannot be adequately represented by naive averaging strategies. Our proposed model relies on a detailed asymptotic analysis in which we identify a limit model and establish strong convergence results. We also provide detailed numerical assessments which confirm an excellent accuracy of the surface-based model -- compared with the reference 3D model -- including in the representation of a complex phenomenon, namely, spiral waves.
Published: 2013
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28. Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart

Author: Dominique Chapelle, Philippe Moireau, Vivien Mallet, Marc Fragu, Modeling, analysis and control in computational structural dynamics (MACS), 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), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Centre d'Enseignement et de Recherche en Environnement Atmosphérique (CEREA), École des Ponts ParisTech (ENPC)-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Coupling environmental data and simulation models for software integration (Clime), Inria Paris-Rocquencourt, European Project: 224495,ICT,FP7-ICT-2007-2,EUHEART(2008), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: Databases, Factual, Computer science, 0206 medical engineering, Biomedical Engineering, 02 engineering and technology, 01 natural sciences, Personalization, Data assimilation, Software, Software library, Personalized modeling, Humans, 0101 mathematics, Computer Applications, business.industry, Models, Cardiovascular, Human physiology, Modular architecture, 020601 biomedical engineering, Data science, Computer Science Applications, 010101 applied mathematics, Cardiac models, Clinical diagnosis, Model simulation, Database Management Systems, business, Algorithms, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience We present the fundamental principles of data assimilation underlying the Verdandi library, and how they are articulated with the modular architecture of the library. This translates -- in particular -- into the definition of standardized interfaces through which the data assimilation library interoperates with the model simulation software and the so-called observation manager. We also survey various examples of data assimilation applied to the personalization of biophysical models, in particular for cardiac modeling applications within the euHeart European project. This illustrates the power of data assimilation concepts in such novel applications, with tremendous potential in clinical diagnosis assistance.
Published: 2013
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29. Exponential convergence of an observer based on partial field measurements for the wave equation

Author: Dominique Chapelle, Maya de Buhan, Philippe Moireau, Nicolae Cîndea, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: 0209 industrial biotechnology, Observer (quantum physics), Article Subject, exponential stability, General Mathematics, observability condition, 02 engineering and technology, 01 natural sciences, Partial field, 020901 industrial engineering & automation, Exponential stability, Observability, 0101 mathematics, Mathematics, Exponential convergence, lcsh:Mathematics, Mathematical analysis, General Engineering, observer, Order (ring theory), filtering, Wave equation, lcsh:QA1-939, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 010101 applied mathematics, lcsh:TA1-2040, Time derivative, nudging, wave equation, lcsh:Engineering (General). Civil engineering (General), second-order evolution equation
Abstract: International audience; We analyze an observer strategy based on partial --~i.e.~in a subdomain --~measurements of the solution of a wave equation, in order to compensate for unknown initial conditions. We prove the exponential convergence of this observer under a non-standard observability condition, whereas using measurements of the time-derivative of the solution would lead to a standard observability condition arising in stabilization and exact controlability. Nevertheless, we directly relate our specific condition to the classical geometric control condition. Finally, we provide some numerical illustrations of the effectiveness of the approach.; Nous analysons un observateur formulé pour l'équation des ondes et utilisant des mesures de la solution dans un sous-domaine afin de compenser des conditions initiales inconnues. Nous démontrons la convergence exponentielle de cet observateur moyennant une condition d'observabilité non-standard, alors qu'une mesure de la dérivée en temps de la solution conduirait à la forme standard de la condition d'observabilité apparaissant en stabilisation et contrôla\-bilité exacte. Néanmoins, nous établissons un lien direct entre notre condition spécifique et la condition de contrôle géométrique classique.
Published: 2012
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30. Sequential identification of boundary support parameters in a fluid-structure vascular model using patient image data

Author: Nan Xiao, Jean-Frédéric Gerbeau, Charles A. Taylor, C. A. Figueroa, Dominique Chapelle, Philippe Moireau, Cristóbal Bertoglio, Modeling, analysis and control in computational structural dynamics (MACS), 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), Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Department of Bioengineering [Stanford], Stanford University, Biomedical Engineering Department, King‘s College London, Department of Surgery [Stanford], Stanford Medicine, Stanford University-Stanford University, and Team Cardio
Subjects: Diagnostic Imaging, Time Factors, Calibration (statistics), Computation, 0206 medical engineering, Boundary (topology), Aorta, Thoracic, 02 engineering and technology, 01 natural sciences, Image (mathematics), Operator (computer programming), Data assimilation, Imaging, Three-Dimensional, Humans, Computer vision, Computer Simulation, 0101 mathematics, Mathematics, Estimation theory, business.industry, Mechanical Engineering, Hemodynamics, Models, Cardiovascular, Nonlinear fluid-structure interaction Patient-specific hemodynamics Image-based data assimilation Parameter identification Support boundary conditions, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 010101 applied mathematics, Identification (information), Modeling and Simulation, Artificial intelligence, business, Algorithm, Algorithms, Biotechnology
Abstract: International audience; Viscoelastic support has been previously established as a valuable modeling ingredient to represent the effect of surrounding tissues and organs in a fluid-structure vascular model. In this paper, we propose a complete methodological chain for the identification of the corresponding boundary support parameters, using patient image data. We consider distance maps of model to image contours as the discrepancy driving the data assimilation approach, which then relies on a combination of (1) state estimation based on the so-called SDF filtering method, designed within the realm of Luenberger observers and well adapted to handling measurements provided by image sequences, and (2) parameter estimation based on a reduced-order UKF filtering method which has no need for tangent operator computations and features natural parallelism to a high degree. Implementation issues are discussed, and we show that the resulting computational effectiveness of the complete estimation chain is comparable to that of a direct simulation. Furthermore, we demonstrate the use of this framework in a realistic application case involving hemodynamics in the thoracic aorta. The estimation of the boundary support parameters proves successful, in particular in that direct modeling simulations based on the estimated parameters are more accurate than with a previous manual expert calibration. This paves the way for complete patient-specific fluid-structure vascular modeling in which all types of available measurements could be used to estimate additional uncertain parameters of biophysical and clinical relevance.
Published: 2012
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31. Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model

Author: Philippe Moireau, Radomir Chabiniok, Jean-François Deux, Dominique Chapelle, Pierre-François Lesault, Alain Rahmouni, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Hôpital Henri Mondor, and Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital Henri Mondor-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)
Subjects: Models, Anatomic, Engineering, Medical knowledge, Beating heart, 0206 medical engineering, Magnetic Resonance Imaging, Cine, 02 engineering and technology, 030204 cardiovascular system & hematology, Synthetic data, Contractility, 03 medical and health sciences, 0302 clinical medicine, Data assimilation, Patient-specific cardiac modeling, Humans, Subdivision, Estimation, business.industry, Mechanical Engineering, State and parameter estimation, Pattern recognition, 020601 biomedical engineering, Myocardial Contraction, Cine mri, Biomechanical Phenomena, Modeling and Simulation, Clinical data, Artificial intelligence, business, Filtering, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Biotechnology, Biomedical engineering
Abstract: International audience; The objective of this paper is to propose and assess an estimation procedure - based on data assimilation principles - well-suited to obtain some regional values of key biophysical parameters in a beating heart model, using actual Cine-MR images. The motivation is twofold: (1) to provide an automatic tool for personalizing the characteristics of a cardiac model in order to achieve predictivity in patient-specific modeling, and (2) to obtain some useful information for diagnosis purposes in the estimated quantities themselves. In order to assess the global methodology we specifically devised an animal experiment in which a controlled infarct was produced and data acquired before and after infarction, with an estimation of regional tissue contractility - a key parameter directly affected by the pathology - performed for every measured stage. After performing a preliminary assessment of our proposed methodology using synthetic data, we then demonstrate a full-scale application by first estimating contractility values associated with 6 regions based on the AHA subdivision, before running a more detailed estimation using the actual AHA segments. The estimation results are assessed by comparison with the medical knowledge of the specific infarct, and with late enhancement MR images. We discuss their accuracy at the various subdivision levels, in the light of the inherent modeling limitations and of the intrinsic information contents featured in the data.
Published: 2012
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32. Galerkin approximation with Proper Orthogonal Decomposition: new error estimates and illustrative examples

Author: Dominique Chapelle, Asven Gariah, Jacques Sainte-Marie, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre d'Études Techniques Maritimes et Fluviales (CETMEF), and Avant création Cerema
Subjects: Numerical Analysis, Complex differential equation, Applied Mathematics, Numerical analysis, Mathematical analysis, Complex system, 010103 numerical & computational mathematics, Lipschitz continuity, 01 natural sciences, 010101 applied mathematics, Computational Mathematics, Uniform continuity, Modeling and Simulation, Norm (mathematics), A priori and a posteriori, 0101 mathematics, Galerkin method, Analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; We propose a numerical analysis of Proper Orthogonal Decomposition (POD) model reductions in which a priori error estimates are expressed in terms of the projection errors that are controlled in the construction of POD bases. These error estimates are derived for generic parabolic evolution PDEs, including with non-linear Lipschitz right-hand sides, and for wave-like equations. A specific projection continuity norm appears in the estimates and -- whereas a general uniform continuity bound seems out of reach -- we prove that such a bound holds in a variety of Galerkin bases choices. Furthermore, we directly numerically assess this bound -- and the effectiveness of the POD approach altogether -- for test problems of the type considered in the numerical analysis, and also for more complex equations. Namely, the numerical assessment includes a parabolic equation with super-linear reaction terms, inspired from the FitzHugh-Nagumo electrophysiology model, and a 3D biomechanical heart model. This shows that the effectiveness established for the simpler models is also achieved in the reduced-order simulation of these highly complex systems.
Published: 2012
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33. Improving convergence in numerical analysis using observers - The wave-like equation case

Author: Dominique Chapelle, Philippe Moireau, Nicolae Cîndea, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: 0209 industrial biotechnology, Discretization, Observer (quantum physics), Applied Mathematics, Numerical analysis, Mathematical analysis, Luenberger observers, 02 engineering and technology, 01 natural sciences, Stability (probability), 010101 applied mathematics, Discrete system, 020901 industrial engineering & automation, Exponential stability, Modeling and Simulation, Bounded function, Observability, 0101 mathematics, numerical analysis with measurements, data assimilation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics, stabilization of conservative systems
Abstract: International audience; We propose an observer-based approach to circumvent the issue of unbounded approximation errors -- with respect to the length of the time window considered -- in the discretization of wave-like equations in bounded domains, which covers the cases of the wave equation per se and of linear elasticity as well as beam, plate and shell formulations, and so on. Namely, taking advantage of some measurements available on the system over time, we adopt a strategy inspired from sequential data assimilation and by which the discrete system is dynamically corrected using the discrepancy between the solution and the measurements. In addition to the classical cornerstones of numerical analysis made up by stability and consistency, we are thus led to incorporating a third crucial requirement pertaining to observability -- to be preserved through discretization. The latter property warrants exponential stability for the corrected dynamics, hence provides bounded approximation errors over time. Special care is needed to establish the required observability at the discrete level, in particular due to the fact that we focus on an original observer method adapted to measurements of the main variable, whereas measurements of the time-derivative -- admissible, of course, albeit less frequent in practical systems -- lead to a stability analysis in which existing results can be more directly applied. We also provide some detailed application examples with several such wave-like equations, and the corresponding numerical assessments illustrate the performance of our approach.
Published: 2012
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34. External tissue support and fluid-structure simulation in blood flows

Author: Nan Xiao, Dominique Chapelle, Charles A. Taylor, Jean-Frédéric Gerbeau, Philippe Moireau, C. A. Figueroa, Matteo Astorino, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Bioengineering [Stanford], Stanford University, Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Department of Surgery [Stanford], Stanford Medicine, and Stanford University-Stanford University
Subjects: Adult, Male, Work (thermodynamics), Engineering, 0206 medical engineering, Blood flows, 02 engineering and technology, Patient-specific geometry, 01 natural sciences, Viscoelasticity, Domain (mathematical analysis), Motion, Region of interest, Fluid–structure interaction, Fluid-structure interaction, Humans, Computer Simulation, Boundary value problem, 0101 mathematics, Simulation, Boundary conditions, business.industry, Mechanical Engineering, Models, Cardiovascular, Mechanics, Middle Aged, 020601 biomedical engineering, Arterial tree, Biomechanical Phenomena, 010101 applied mathematics, Flow (mathematics), Organ Specificity, Modeling and Simulation, Tissue support, Calibration, Hemorheology, Aorta modeling, business, Tomography, X-Ray Computed, Blood Flow Velocity, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Biotechnology
Abstract: International audience; The objective of this work is to address the formulation of an adequate model of the external tissue environment when studying a portion of the arterial tree with fluid-structure interaction. Whereas much work has already been accomplished concerning flow and pressure boundary conditions associated with truncations in the fluid domain, very few studies take into account the tissues surrounding the region of interest to derive adequate boundary conditions for the solid domain. In this paper, we propose to model the effect of external tissues by introducing viscoelastic support conditions along the artery wall, with two--possibly distributed--parameters that can be adjusted to mimic the response of various physiological tissues. In order to illustrate the versatility and effectiveness of our approach, we apply this strategy to perform patient-specific modeling of thoracic aortae based on clinical data, in two different cases and using a distinct fluid-structure interaction methodology for each, namely an Arbitrary Lagrangian-Eulerian (ALE) approach with prescribed inlet motion in the first case and the coupled momentum method in the second case. In both cases, the resulting simulations are quantitatively assessed by detailed comparisons with dynamic image sequences, and the model results are shown to be in very good adequacy with the data.
Published: 2012
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35. Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems

Author: Philippe Moireau, Dominique Chapelle, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: Control and Optimization, Discretization, Dynamical systems theory, 0206 medical engineering, 02 engineering and technology, 020601 biomedical engineering, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, Computational Mathematics, Nonlinear system, Extended Kalman filter, 0302 clinical medicine, Discrete time and continuous time, Control and Systems Engineering, Control theory, Unscented transform, State observer, Equations for a falling body, Algorithm, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: See also erratum DOI:10.1051/cocv/2011001; International audience; We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered. The algorithms are derived in discrete time as in the classical UKF formalism - well-adapted to time discretized dynamical equations - and then extended into consistent continuous-time versions. This reduced-order filtering approach can be used in particular for the estimation of parameters in large dynamical systems arising from the discretization of partial differential equations, when state estimation can be handled by an adequate Luenberger observer inspired from feedback control. In this case, we give an analysis of the joint state-parameter estimation procedure based on linearized error, and we illustrate the effectiveness of the approach using a test problem inspired from cardiac biomechanics.
Published: 2011
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36. On the ellipticity condition for model-parameter dependent mixed formulations

Author: Dominique Chapelle, Klaus-Jürgen Bathe, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Massachusetts Institute of Technology (MIT)
Subjects: Mixed model, Mathematical optimization, Discretization, Mechanical Engineering, Zero (complex analysis), 02 engineering and technology, 01 natural sciences, Finite element method, Computer Science Applications, 010101 applied mathematics, 020303 mechanical engineering & transports, Model parameter, 0203 mechanical engineering, Modeling and Simulation, Applied mathematics, General Materials Science, Limit (mathematics), Numerical tests, 0101 mathematics, Problem solution, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Civil and Structural Engineering, Mathematics
Abstract: International audience; When establishing and analyzing model-parameter dependent mixed formulations, it is common to consider required ellipticity and inf-sup conditions for the continuous and discrete problems. However, in the modeling of some important categories of problems, like in the analysis of plates and shells, the ellipticity condition usually considered does not naturally hold, and the inf-sup condition can only be stated in an abstract form and can hardly be evaluated analytically. In this paper we present a new and practical ellipticity condition which together with the inf-sup condition guarantees that (i) when the model parameter goes to zero, the limit problem solution is uniformly approached, and (ii) an optimal finite element discretization has been established (for the interpolations used). In practice, a numerical test might be performed to see whether the proposed ellipticity condition is satisfied.
Published: 2010
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37. A poroelastic model valid in large strains with applications to perfusion in cardiac modeling

Author: Dominique Chapelle, Irene E. Vignon-Clementel, Jacques Sainte-Marie, Jean-Frédéric Gerbeau, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Laboratoire d'Hydraulique Saint-Venant / Saint-Venant Laboratory for Hydraulics (LHSV), École des Ponts ParisTech (ENPC)-PRES Université Paris-Est-EDF (EDF)-Avant création Cerema, and Laboratoire d'Hydraulique Saint-Venant / Saint-Venant Laboratory for Hydraulics (Saint-Venant)
Subjects: Cardiac perfusion, Computer science, Quantitative Biology::Tissues and Organs, 0206 medical engineering, Poromechanics, Physics::Medical Physics, Computational Mechanics, Porous media, Ocean Engineering, 02 engineering and technology, 01 natural sciences, Porous flow, Biomechanics, Incompressibility limit, 0101 mathematics, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Large deformation, business.industry, Applied Mathematics, Mechanical Engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Mechanics, Structural engineering, [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], 020601 biomedical engineering, 010101 applied mathematics, Computational Mathematics, Nonlinear system, Computational Theory and Mathematics, Flow (mathematics), Compressibility, Porous medium, business, Perfusion, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; This paper is motivated by the modeling of blood flows through the beating myocardium, namely cardiac perfusion. As in other works, perfusion is modeled here as a flow through a poroelastic medium. The main contribution of this study is the derivation of a general poroelastic model valid for a nearly incompressible medium which experiences finite deformations. A numerical procedure is proposed to iteratively solve the porous flow and the nonlinear poroviscoelastic problems. Three-dimensional numerical experiments are presented to illustrate the model. The first test cases consist of typical poroelastic configurations: swelling and complete drainage. Finally, a simulation of cardiac perfusion is presented in an idealized left ventricle embedded with active fibers. Results show the complex temporal and spatial interactions of the muscle and blood, reproducing several key phenomena observed in cardiac perfusion.
Published: 2010
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38. Cardiac motion extraction from images by filtering estimation based on a biomechanical model

Author: Dominique Chapelle, Mariette Yvinec, Philippe Moireau, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Geometric computing (GEOMETRICA), 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)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria), and Nicholas Ayache and Hervé Delingette and Maxime Sermesant
Subjects: business.industry, Computer science, Binary image, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, 010103 numerical & computational mathematics, 01 natural sciences, Synthetic data, 010101 applied mathematics, Data assimilation, Cardiac motion, Snapshot (computer storage), Segmentation, Biomechanical model, Polygon mesh, Computer vision, Artificial intelligence, 0101 mathematics, business, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], ComputingMethodologies_COMPUTERGRAPHICS
Abstract: International audience; Starting from the presentation of a unified perspective of segmentation with deformable models and data assimilation with images, we propose a data assimilation procedure designed to dynamically estimate 3D positions and velocities of the myocardium along the heart cycle, using data consisting of contours extracted from image sequences. We assess this procedure with a test problem based on a realistic computational heart model, and with synthetic data produced from reference simulations by creating binary images of the myocardium. The automatic meshing library CGAL is then employed to create contour meshes for each snapshot, and these meshes are directly used in the model measurement comparisons. This approach gives very satisfactory qualitativeand quantitative results.
Published: 2009
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39. Personalised Electromechanical Model of the Heart for the Prediction of the Acute Effects of Cardiac Resynchronisation Therapy

Author: Matthew Ginks, Reza Razavi, Simon R. Arridge, Radomir Chabiniok, Hervé Delingette, Dominique Chapelle, Nicholas Ayache, Jean-Marc Peyrat, Michel Sorine, Philippe Moireau, Phani Chinchapatnam, Florence Billet, C. Aldo Rinaldi, Maxime Sermesant, Kawal Rhode, Pier D. Lambiase, Tommaso Mansi, Analysis and Simulation of Biomedical Images (ASCLEPIOS), 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), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Centre for Medical Image Computing (CMIC), University College of London [London] (UCL), Division of Imaging Sciences, King‘s College London, The Heart Hospital [London], SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Department of cardiology [Guy's and St. Thomas ' hospitals] [London], Guy's and St Thomas' Hospital [London]-Guy's Hospital [London], NIHR Biomedical Research Centre [London], Guy's and St Thomas' NHS Foundation Trust-King‘s College London, and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)
Subjects: Acute effects, Cardiac function curve, medicine.medical_specialty, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, 0206 medical engineering, Therapy planning, 02 engineering and technology, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, 0302 clinical medicine, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Internal medicine, medicine, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Simulation, business.industry, Left bundle branch block, medicine.disease, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 3. Good health, Clinical trial, Heart failure, Adjunctive treatment, Cardiology, cardiovascular system, Clinical case, business, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract: International audience; Cardiac resynchronisation therapy (CRT) has been shown to be an effective adjunctive treatment for patients with dyssynchronous ventricular contraction and symptoms of the heart failure. However, clinical trials have also demonstrated that up to 30% of patients may be classified as non-responders. In this article, we present how the personalisation of an electromechanical model of the myocardium could help the therapy planning for CRT. We describe the four main components of our myocardial model, namely the anatomy, the electrophysiology, the kinematics and the mechanics. For each of these components we combine prior knowledge and observable parameters in order to personalise these models to patient data. Then the acute effects of a pacemaker on the cardiac function are predicted with the in silico model on a clinical case. This is a proof of concept of the potential of virtual physiological models to better select and plan the therapy.
Published: 2009
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40. Numerical simulation of the electromechanical activity of the heart

Author: Nejib Zemzemi, Miguel Angel Fernández, Jean-Frédéric Gerbeau, Philippe Moireau, Dominique Chapelle, Jacques Sainte-Marie, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Ayache, Nicholas and Delingette, Hervé and Sermesant, Maxime, Fernández, Miguel Angel, and Ayache, Nicholas and Delingette, Hervé and Sermesant, Maxime
Subjects: Laplace's equation, Continuum mechanics, Computer simulation, 0206 medical engineering, 02 engineering and technology, Mechanics, Torso, 020601 biomedical engineering, 01 natural sciences, Normal case, 010101 applied mathematics, medicine.anatomical_structure, medicine, 0101 mathematics, Physiological values, Contraction (operator theory), Mathematics
Abstract: International audience; We present numerical results obtained with a three-dimensional electromechanical model of the heart with a complete realistic anatomy. The electrical activity of the heart-torso domain is described by the bidomain equations in the heart and a Laplace equation in the torso. The mechanical model is based on a chemically-controlled contraction law of the myofibres integrated in a 3D continuum mechanics description accounting for large displacements and strains, and the main cardiovascular blood compartments are represented by simplified lumped models. We considered a normal case and a pathological condition and the medical indicators resulting from the simulations show physiological values, both for mechanical and electrical quantities of interest, in particular pressures, volumes and ECGs.
Published: 2009

41. Filtering for distributed mechanical systems using position measurements: perspectives in medical imaging

Author: Patrick Le Tallec, Philippe Moireau, Dominique Chapelle, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), and École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Applied Mathematics, 0206 medical engineering, 02 engineering and technology, Filter (signal processing), [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], Inverse problem, [PHYS.MECA.MSMECA]Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph], 020601 biomedical engineering, 01 natural sciences, Computer Science Applications, Theoretical Computer Science, 010101 applied mathematics, Mechanical system, Nonlinear system, Robustness (computer science), Control theory, Signal Processing, Medical imaging, 0101 mathematics, Robust control, Medical diagnosis, Algorithm, Mathematical Physics, Mathematics
Abstract: International audience; We propose an effective filtering methodology designed to perform estimation in a distributed mechanical system using position measurements. As in a previously introduced method, the filter is inspired from robust control feedback, but here we take full advantage of the estimation specificity to choose a feedback law that can act on displacements instead of velocities and still retain the same kind of dissipativity property which guarantees robustness. This is very valuable in many applications for which positions are more readily available than velocities, as in medical imaging. We provide an in-depth analysis of the proposed procedure, as well as detailed numerical assessments using a test problem inspired from cardiac biomechanics, as medical diagnosis assistance is an important perspective for this approach. The method is formulated first for measurements based on Lagrangian displacements, but we then derive a nonlinear extension allowing to instead consider segmented images, which of course is even more relevant in medical applications.
Published: 2009
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42. Robust filtering for joint state parameter estimation for distributed mechanical systems

Author: Patrick Le Tallec, Philippe Moireau, Dominique Chapelle, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), and École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: 0209 industrial biotechnology, State variable, numerical analysis, Boundary (topology), solid continuum mechanics, 02 engineering and technology, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], Type (model theory), 01 natural sciences, robust filtering, 020901 industrial engineering & automation, Control theory, Discrete Mathematics and Combinatorics, 0101 mathematics, Mathematics, Observational error, estimation, Applied Mathematics, Numerical analysis, 010102 general mathematics, Filter (signal processing), Kalman filter, [PHYS.MECA.MSMECA]Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph], Mechanical system, 35R30, 93B36, 74H15, Analysis
Abstract: International audience; We present an effective filtering procedure for jointly estimating state variables and parameters in a distributed mechanical system. This method is based on a robust, low-cost filter related to collocated feedback and used to estimate state variables, and an $H^\infty$ setting is then employed to formulate a joint state-parameter estimation filter. In addition to providing a tractable filtering approach for an infinite-dimensional mechanical system, the $H^\infty$ setting allows to consider measurement errors that cannot be handled by Kalman type filters, e.g. for measurements only available on the boundary. For this estimation strategy a complete error analysis is given, and a detailed numerical assessment - using a test problem inspired from cardiac biomechanics - demonstrates the effectiveness of our approach.
Published: 2009
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43. Towards improving the MITC6 triangular shell element

Author: L. Beirão da Veiga, I. Paris Suarez, Dominique Chapelle, Dipartimento di Matematica 'F. Enriques', Universit' degli Studi di Milano, Department of Mathematics 'Federigo Enriques', Università degli Studi di Milano [Milano] (UNIMI)-Università degli Studi di Milano [Milano] (UNIMI), Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), BEIRAO DA VEIGA, L, Paris, I, Chapelle, D, and Università degli Studi di Milano = University of Milan (UNIMI)-Università degli Studi di Milano = University of Milan (UNIMI)
Subjects: Engineering, Shell (structure), 02 engineering and technology, Bending, Bilinear form, 01 natural sciences, Displacement (vector), Strain energy, Triangular MITC element, 0203 mechanical engineering, Shell, General Materials Science, Boundary value problem, 0101 mathematics, Boundary element method, Civil and Structural Engineering, business.industry, Mechanical Engineering, Mathematical analysis, Structural engineering, Stabilization, Finite element method, Computer Science Applications, Spurious mode, 010101 applied mathematics, 020303 mechanical engineering & transports, Locking, Modeling and Simulation, Mixed formulation, business, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; Effective triangular shell elements are of utmost interest in engineering practice, and the MITC6a element - a 6 node quadratic general shell element of the MITC family - has been shown to significantly reduce the locking phenomena arising in bending dominated behaviours. However, for some specific combinations of midsurface geometry and boundary conditions, the MITC6a element features some non-physical displacement modes with vanishing membrane strain energy. This phenomenon is thoroughly analyzed, and a remedy based on a stabilized bilinear form is proposed. Detailed numerical tests are included and the results demonstrate the good performance of the proposed method both for membrane and bending dominated problems.
Published: 2007
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44. CardioSense3D: Patient-Specific Cardiac Simulation

Author: Reza Razavi, Ph. Moireau, Dominique Chapelle, N. Ayache, Jacques Sainte-Marie, Elliot R. McVeigh, Miguel Angel Fernández, Hervé Delingette, Maxime Sermesant, K. Djabella, Jean-Frédéric Gerbeau, K. S. Rhode, Jean-Marc Peyrat, Q. Zhang, Michel Sorine, Analysis and Simulation of Biomedical Images (ASCLEPIOS), 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), Division of Imaging Sciences, King‘s College London, NIHR Biomedical Research Centre [London], Guy's and St Thomas' NHS Foundation Trust-King‘s College London, Department of Biomedical Engineering [Baltimore] (DBE), Johns Hopkins University (JHU), Laboratory of Cardiac Energetics (LCE), National Heart-Lung, and Blood Institute-National Institutes of Health, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Laboratoire d'Hydraulique Saint-Venant / Saint-Venant Laboratory for Hydraulics (LHSV), École des Ponts ParisTech (ENPC)-PRES Université Paris-Est-EDF (EDF)-Avant création Cerema, Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS), Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC), Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Centre d'Etudes Nucléaires de Bordeaux Gradignan (CENBG), Université Sciences et Technologies - Bordeaux 1 (UB)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Laboratoire d'Hydraulique Saint-Venant / Saint-Venant Laboratory for Hydraulics (Saint-Venant), and Université Sciences et Technologies - Bordeaux 1-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)
Subjects: medicine.medical_specialty, medicine.diagnostic_test, business.industry, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, 0206 medical engineering, 02 engineering and technology, Patient specific, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, 0302 clinical medicine, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Internal medicine, Cardiology, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Medicine, Medical physics, business, Electrocardiography, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Cardiac imaging
Abstract: In this paper, we overview the objectives and achievements of the CardioSense3D project dedicated to the construction of an electro-mechanical model of the heart.
Published: 2007

45. Modeling and estimation of the cardiac electromechanical activity

Author: Jacques Sainte-Marie, Dominique Chapelle, Michel Sorine, Robert Cimrman, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), New Technologies Research Centre [Plzeň] (NTC), University of West Bohemia [Plzeň ], and SIgnals and SYstems in PHysiology & Engineering (SISYPHE)
Subjects: Engineering, business.industry, Mechanical Engineering, 0206 medical engineering, System identification, Control engineering, 02 engineering and technology, 020601 biomedical engineering, 01 natural sciences, Computer Science Applications, 010101 applied mathematics, Data assimilation, Modeling and Simulation, General Materials Science, 0101 mathematics, business, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Civil and Structural Engineering
Abstract: International audience; We describe an approach that we propose to model the electromechanical behavior of the heart, and to use the model in a data assimilation procedure in order to perform an identification of the parameters and state. The modeling of the heart tissue is based on an electrically-activated contraction law formulated via multiscale considerations and is consistent with various physiological and thermomechanical key requirements. The global heart system also incorporates a simplified lumped modeling of the blood compartments. We report on numerical simulations and on validations of our model in reference and pathological conditions. Furthermore, the data assimilation procedure is intended to give access to quantities of interest for diagnosis purposes, and we present some promising results in this direction.
Published: 2006
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46. Asymptotic considerations shedding light on incompressible shell models

Author: Arnaud Münch, Cristinel Mardare, Dominique Chapelle, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Jacques-Louis Lions (LJLL), and Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Mechanical Engineering, Mathematical analysis, Geometry, 02 engineering and technology, incompressibility, Poisson distribution, 01 natural sciences, Incompressible material, 010101 applied mathematics, symbols.namesake, shell models, asymptotic analysis, 020303 mechanical engineering & transports, Singularity, 0203 mechanical engineering, Mechanics of Materials, Compressibility, symbols, General Materials Science, 0101 mathematics, Elasticity (economics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; The incompressible singularity found in 3D elasticity when Poisson's ratio approaches 1/2 is not present in classical shell models, nor in the limit models obtained from 3D elasticity when performing an asymptotic analysis with respect to the thickness parameter. However, some specific shell models - such as the 3D-shell model - do retain the incompressible singularity. These observations raise the issue of how adequately shell models can represent incompressible conditions, which this paper aims at investigating. We first perform a combined asymptotic analysis of 3D elasticity with respect to both the thickness parameter and Poisson's ratio and we obtain a commuting property, which is very valuable as a justification of the concept of an "incompressible shell", and substantiates the use of classical shell models with incompressible materials.We then show that the 3D-shell model does not enjoy a similar commuting property; nevertheless we propose a simple modification of this model for which commuting is obtained, hence consistency with incompressibility is recovered. We also illustrate our discussions with some numerical results.
Published: 2004
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47. 3D-shell elements and their underlying mathematical model

Author: Anca Ferent, Klaus-Jürgen Bathe, Dominique Chapelle, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Massachusetts Institute of Technology (MIT)
Subjects: Discretization, Generalization, Nuclear Theory, Shell (structure), Geometry, 02 engineering and technology, 01 natural sciences, Shells, 0203 mechanical engineering, Physics::Atomic and Molecular Clusters, Point (geometry), asymptotic behaviors, 0101 mathematics, Mathematics, Applied Mathematics, Mathematical analysis, general shell elements, 16. Peace & justice, locking, Finite element method, 010101 applied mathematics, 020303 mechanical engineering & transports, Modeling and Simulation, Scheme (mathematics), Focus (optics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Interpolation
Abstract: International audience; We focus on a family of shell elements which are a direct generalization of the shell elements most commonly used in engineering practice. The elements in the family include the effects of the through-the-thickness normal stress and can be employed to couple directly with surrounding media on either surfaces of the shell. We establish the "underlying" mathematical model of the shell discretization scheme, and we show that this mathematical model features the same asymptotic behaviors "when the shell thickness becomes increasingly smaller" as classical shell models. The question of "locking" of the finite element discretization is also briefly addressed and we point out that, for an effective finite element scheme, the MITC approach of interpolation is available.
Published: 2004
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48. The treatment of 'pinching locking' in 3D-shell elements

Author: Dominique Chapelle, Anca Ferent, Patrick Le Tallec, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), and École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Shell (structure), Geometry, 02 engineering and technology, 01 natural sciences, Numerical locking, Quadratic equation, 0203 mechanical engineering, shell finite elements, mixed formulation, 0101 mathematics, Mathematics, Numerical Analysis, Partial differential equation, Computer simulation, Applied Mathematics, Numerical analysis, Mathematical analysis, Finite element method, 010101 applied mathematics, Shear (sheet metal), Computational Mathematics, 020303 mechanical engineering & transports, Modeling and Simulation, Face (geometry), Analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon - that we call ''pinching locking'' - is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific source of locking is present, we are able to obtain error estimates independent of the thickness parameter, which shows that pinching locking is effectively treated. This is also confirmed by some numerical experiments of which we give an account.
Published: 2003
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49. A shell problem 'highly sensitive' to thickness changes

Author: Phill-Seung Lee, Dominique Chapelle, Klaus-Jürgen Bathe, Massachusetts Institute of Technology (MIT), Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: Asymptotic analysis, Nuclear Theory, Shell (structure), 02 engineering and technology, Bending, 01 natural sciences, 0203 mechanical engineering, Convergence (routing), Physics::Atomic and Molecular Clusters, finite element solution, 0101 mathematics, Physics, Numerical Analysis, business.industry, Applied Mathematics, General Engineering, Mechanics, Structural engineering, Finite element solution, Finite element method, Highly sensitive, 010101 applied mathematics, shells, asymptotic analysis, 020303 mechanical engineering & transports, business, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; In general, shell structural problems can be identified to fall into one of the categories of membrane-dominated, bending-dominated and mixed shell problems. The asymptotic behaviour with a well-defined load-scaling factor shows distinctly into which category a given shell problem falls. The objective of this paper is to present a shell problem and its solution for which there is no convergence to a well-defined load-scaling factor as the thickness of the shell decreases. Such shells are unduly sensitive in their behaviour because the ratio of membrane to bending energy stored changes significantly and indeed can fluctuate with changes in shell thickness. We briefly review the different asymptotic behaviours that shell problems can display, and then present the specific problem considered and its numerical solution using finite element analysis.
Published: 2003
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50. MITC elements for a classical shell model

Author: Miguel Luiz Bucalem, D.L. Oliveira, Dominique Chapelle, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Universidade de São Paulo (USP), and Universidade de São Paulo = University of São Paulo (USP)
Subjects: Asymptotic behaviour, General shell elements, SHELL model, Finite elements, Shell theory, 02 engineering and technology, 01 natural sciences, 0203 mechanical engineering, General Materials Science, Covariant transformation, 0101 mathematics, Civil and Structural Engineering, Mathematics, business.industry, Mechanical Engineering, Shell structures, Mathematical analysis, Structural engineering, Finite element method, Computer Science Applications, 010101 applied mathematics, 020303 mechanical engineering & transports, Locking, Modeling and Simulation, business, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; The formulation of nine-node mixed-interpolated shell elements based on a classical mathematical shell theory is presented, taking into account some fundamental considerations for the finite element analysis of shells. The elements are based on the Mixed Interpolation of Tensorial Components (MITC) approach, but the assumed covariant strain fields are applied only for the membrane and shear components. Two different types of elements are considered, depending on whether or not geometric approximations are included in the formulation. The performance of the proposed elements is illustrated with a well-established test problem - the Scordelis-Lo roof.
Published: 2003
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