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2,690 results on '"École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris"'

1. Right-left ventricular shape variations in tetralogy of Fallot: associations with pulmonary regurgitation

Author

Andrew D. McCulloch, Sachin Govil, Tarique Hussain, J. Omens, Radomir Chabiniok, Kuberan Pushparajah, James C. Perry, Alistair A. Young, Sanjeet Hegde, Charlene Mauger, Christopher J. Occleshaw, Liang Zhong, Kathleen Gilbert, Avan Suinesiaputra, University of Auckland [Auckland], Auckland Bioengineering Institute, University of California [San Diego] (UC San Diego), University of California (UC), King‘s College London, Czech Technical University in Prague (CTU), 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], Guy's and St Thomas' Hospital [London], Rady Children's Hospital San Diego, Department of Cardiology, Auckland District Health Board, Auckland, King's College London School of Medicine at Guy's, King's College and St Thomas' Hospitals, University of Leeds, Duke-NUS Medical School [Singapore], National Heart Centre Singapore (NHCS), University of California San Diego, La Jolla, CA, 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 University of California San Diego, La Jolla

Subjects
Adult, Multivariate statistics, medicine.medical_specialty, Adolescent, 030204 cardiovascular system & hematology, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, Young Adult, 0302 clinical medicine, Predictive Value of Tests, Bayesian multivariate linear regression, Internal medicine, Pulmonary Valve Replacement, Pulmonary regurgitation, Medicine, Humans, Diseases of the circulatory (Cardiovascular) system, Radiology, Nuclear Medicine and imaging, Wall motion, cardiovascular diseases, Child, Ventricular function, Tetralogy of Fallot, Angiology, Retrospective Studies, Radiological and Ultrasound Technology, medicine.diagnostic_test, business.industry, Myocardial deformation, Research, Magnetic resonance imaging, Atlases, medicine.disease, Pulmonary Valve Insufficiency, Cross-Sectional Studies, RC666-701, Cardiology, Ventricular Function, Right, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Cardiovascular magnetic resonance, Cardiology and Cardiovascular Medicine, business
Abstract

Background Relationships between right ventricular (RV) and left ventricular (LV) shape and function may be useful in determining optimal timing for pulmonary valve replacement in patients with repaired tetralogy of Fallot (rTOF). However, these are multivariate and difficult to quantify. We aimed to quantify variations in biventricular shape associated with pulmonary regurgitant volume (PRV) in rTOF using a biventricular atlas. Methods In this cross-sectional retrospective study, a biventricular shape model was customized to cardiovascular magnetic resonance (CMR) images from 88 rTOF patients (median age 16, inter-quartile range 11.8–24.3 years). Morphometric scores quantifying biventricular shape at end-diastole and end-systole were computed using principal component analysis. Multivariate linear regression was used to quantify biventricular shape associations with PRV, corrected for age, sex, height, and weight. Regional associations were confirmed by univariate correlations with distances and angles computed from the models, as well as global systolic strains computed from changes in arc length from end-diastole to end-systole. Results PRV was significantly associated with 5 biventricular morphometric scores, independent of covariates, and accounted for 12.3% of total shape variation (p Conclusion A biventricular atlas of rTOF patients quantified multivariate relationships between left–right ventricular morphometry and wall motion with pulmonary regurgitation. Regional RV dilation, LV reduction, LV septal-lateral flattening and increased RV strain were all associated with increased pulmonary regurgitant volume. Morphometric scores provide simple metrics linking mechanisms for structural and functional alteration with important clinical indices.

Published
2021

2. HARP-I: A Harmonic Phase Interpolation Method for the Estimation of Motion From Tagged MR Images

Author

Hui Wang, Sergio Uribe, Michael D. Taylor, Hernán Mella, Joaquín Mura, Jaroslav Tintera, Julio Sotelo, Radomir Chabiniok, Pontificia Universidad Católica de Chile (UC), Universidade Federal de Santa Maria (UFSM), Cincinnati Children's Hospital Medical Center, Department of Mathematics [Prague] (FNSPE), Czech Technical University in Prague (CTU), School of Biomedical Engineering & Imaging Sciences [London], Guy's and St Thomas' Hospital [London]-King‘s College London, 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], Institute for Clinical and Experimental Medicine (IKEM), Valparaiso University, Universidade Federal de Santa Maria = Federal University of Santa Maria [Santa Maria, RS, Brazil] (UFSM), King‘s College London-Guy's and St Thomas' Hospital [London], 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
Similarity (geometry), [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, Phase (waves), Harmonic (mathematics), 030204 cardiovascular system & hematology, 030218 nuclear medicine & medical imaging, Harmonic analysis, Motion, 03 medical and health sciences, 0302 clinical medicine, Motion estimation, Image Processing, Computer-Assisted, Cardiac Strain, Electrical and Electronic Engineering, Cardiac MRI, Tagged MRI, SPAMM, HARP, Physics, Radiological and Ultrasound Technology, Sine-wave Modeling, CSPAMM, Harmonic Phase Analysis, Magnetic Resonance Imaging, Computer Science Applications, Noise, Cytokines, Astrophysics::Earth and Planetary Astrophysics, Carrier Proteins, Algorithm, Motion Estimation, Algorithms, Software, Interpolation
Abstract

International audience; We proposed a novel method called HARP-I, which enhances the estimation of motion from tagged Magnetic Resonance Imaging (MRI). The harmonic phase of the images is unwrapped and treated as noisy measurements of reference coordinates on a deformed domain, obtaining motion with high accuracy using Radial Basis Functions interpolations. Results were compared against Shortest Path HARP Refinement (SP-HR) and Sine-wave Modeling (SinMod), two harmonic image-based techniques for motion estimation from tagged images. HARP-I showed a favorable similarity with both methods under noise-free conditions, whereas a more robust performance was found in the presence of noise. Cardiac strain was better estimated using HARP-I at almost any motion level, giving strain maps with less artifacts. Additionally, HARP-I showed better temporal consistency as a new method was developed to fix phase jumps between frames. In conclusion, HARP-I showed to be a robust method for the estimation of motion and strain under ideal and non-ideal conditions.

Published
2021

3. Brain fragility among middle-aged and elderly patients from electroencephalogram during induction of anaesthesia

Author

Cyril Touchard, Jerome Cartailler, Fabrice Vallée, Claire Paquet, Etienne Gayat, Pierre Parutto, Groupe Hospitalier Saint Louis - Lariboisière - Fernand Widal [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), Université de Paris (UP), UK Dementia Research Institute (UK DRI), University College of London [London] (UCL), Marqueurs cardiovasculaires en situation de stress (MASCOT (UMR_S_942 / U942)), Institut National de la Santé et de la Recherche Médicale (INSERM)-Groupe Hospitalier Saint Louis - Lariboisière - Fernand Widal [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Université Sorbonne Paris Nord, Centre de Neurologie Cognitive [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Université Paris Diderot - Paris 7 (UPD7)-Hôpitaux Universitaires Saint-Louis, Lariboisière, Fernand-Widal, Optimisation thérapeutique en Neuropsychopharmacologie (OPTeN (UMR_S_1144 / U1144)), Institut National de la Santé et de la Recherche Médicale (INSERM)-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 Cité (UPCité), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Université Sorbonne Paris Nord, Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris Cité (UPCité), 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 Zunara, Fatima

Subjects
2019-20 coronavirus outbreak, [SDV.MHEP] Life Sciences [q-bio]/Human health and pathology, Coronavirus disease 2019 (COVID-19), business.industry, Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), Brain, Electroencephalography, Middle Aged, 03 medical and health sciences, 0302 clinical medicine, Anesthesiology and Pain Medicine, Fragility, Anesthesiology, 030202 anesthesiology, Anesthesia, Humans, Medicine, business, Short scientific reports and Correspondence, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology, 030217 neurology & neurosurgery, Aged
Abstract

International audience; Cognitive decline (CD) is a common condition amongst elderly, affecting memory, language or thinking. Patients experiencing CD have a higher incidence rate of post-operative neurocognitive disorders 1. Moreover, for a fraction of these patients

Published
2021

4. A relaxed growth modeling framework for controlling growth-induced residual stresses

Author

Martin Genet, 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), 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
Relaxation, Finite element method, Computer science, Finite Element Analysis, Biophysics, [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], Decomposition analysis, Residual stresses, 03 medical and health sciences, 0302 clinical medicine, Residual stress, Humans, Orthopedics and Sports Medicine, Models, Cardiovascular, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Internal pressure, Arteries, 030229 sport sciences, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Elasticity, Biomechanical Phenomena, Transformation (function), Stress, Mechanical, Relaxation (approximation), Biological system, Finite growth, 030217 neurology & neurosurgery
Abstract

International audience; Background. Constitutive models of the mechanical response of soft tissues have been established and are widely accepted, but models of soft tissues remodeling are more controversial. Specifically for growth, one important question arises pertaining to residual stresses: existing growth models inevitably introduce residual stresses, but it is not entirely clear if this is physiological or merely an artifact of the modeling framework. As a consequence, in simulating growth, some authors have chosen to keep growth-induced residual stresses, and others have chosen to remove them.Methods. In this paper, we introduce a novel “relaxed growth” framework allowing for a fine control of the amount of residual stresses generated during tissue growth. It is a direct extension of the classical framework of the multiplicative decomposition of the transformation gradient, to which an additional sub-transformation is introduced in order to let the original unloaded configuration evolve, hence relieving some residual stresses. We provide multiple illustrations of the framework mechanical response, on time-driven constrained growth as well as the strain-driven growth problem of the artery under internal pressure, including the opening angle experiment.Findings. The novel relaxed growth modeling framework introduced in this paper allows for a better control of growth-induced residual stresses compared to standard growth models based on the multiplicative decomposition of the transformation gradient.Interpretation. Growth-induced residual stresses should 1 be better handled in soft tissues biomechanical models, especially in patient-specific models of diseased organs that are aimed at augmented diagnosis and treatment optimization.

Published
2019

5. Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials

Author

Barré, Mathieu, Grandmont, Céline, Moireau, Philippe, 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), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), 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), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, 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 (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Département de Mathématique [Bruxelles] (ULB), Faculté des Sciences [Bruxelles] (ULB), Université libre de Bruxelles (ULB)-Université libre de Bruxelles (ULB), 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), Sorbonne Université (SU), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Grandmont, Celine

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

International audience; In this paper, we thoroughly analyze the linearized version of a poromechanics model developed to simulate biological tissues perfusion. This is a fully dynamical model in which the fluid and solid equations are strongly coupled through the interstitial pressure. As such, it generalizes Darcy, Brinkman and Biot equations of poroelasticity. The mathematical and numerical analysis of this model was first performed for a compressible porous material. Here, we focus on the nearly incompressible case with a semigroup approach that also enables to prove the existence of weak solutions. We show the existence and uniqueness of strong and weak solutions in the incompressible limit, for which a non-standard divergence constraint arises. Due to the special form of the coupling, the underlying problem is not coercive. Nevertheless, by using the notion of T-coercivity, we obtain stability estimates and well-posedness results. Our study also provides guidelines to propose a stable and robust approximation of the problem with mixed finite elements. In particular, we recover an inf-sup condition independent of the phase field. Finally, we investigate numerically the elliptic regularity of the associated steady-state problem and illustrate the sensitivity of the solution with respect to the different model parameters.

Published
2021

6. 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

7. Estimation for dynamical systems using a population-based Kalman filter – Applications in computational biology

Author

Collin, Annabelle, Prague, Mélanie, Moireau, Philippe, 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), Statistics In System biology and Translational Medicine (SISTM), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)- Bordeaux population health (BPH), Université de Bordeaux (UB)-Institut de Santé Publique, d'Épidémiologie et de Développement (ISPED)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Bordeaux (UB)-Institut de Santé Publique, d'Épidémiologie et de Développement (ISPED)-Institut National de la Santé et de la Recherche Médicale (INSERM), 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, Institut Polytechnique de Bordeaux (Bordeaux INP), Centre National de la Recherche Scientifique (CNRS), Vaccine Research Institute (VRI), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), 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 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], 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, and Collin, Annabelle

Subjects
Epidemiology, Kalman Filters, COVID-19, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Mixed-effect estimation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Non linear mixed-effect models, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [SDV.SP.PHARMA] Life Sciences [q-bio]/Pharmaceutical sciences/Pharmacology, population-based sequential estimation, [SDV.SP.PHARMA]Life Sciences [q-bio]/Pharmaceutical sciences/Pharmacology, Pharmacokinetics, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], data assimilation
Abstract

International audience; Estimation of dynamical systems - in particular, identification of their parameters - is fundamental in computational biology, e.g., pharmacology, virology, or epidemiology, to reconcile model runs with available measurements. Unfortunately, the mean and variance priorities of the parameters must be chosen very appropriately to balance our distrust of the measurements when the data are sparse or corrupted by noise. Otherwise, the identification procedure fails. One option is to use repeated measurements collected in configurations with common priorities - for example, with multiple subjects in a clinical trial or clusters in an epidemiological investigation. This shared information is beneficial and is typically modeled in statistics using nonlinear mixed-effects models. In this paper, we present a data assimilation method that is compatible with such a mixed-effects strategy without being compromised by the potential curse of dimensionality. We define population-based estimators through maximum likelihood estimation. We then develop an equivalent robust sequential estimator for large populations based on filtering theory that sequentially integrates data. Finally, we limit the computational complexity by defining a reduced-order version of this population-based Kalman filter that clusters subpopulations with common observational backgrounds. The performance of the resulting algorithm is evaluated against classical pharmacokinetics benchmarks. Finally, the versatility of the proposed method is tested in an epidemiological study using real data on the hospitalisation of COVID-19 patients in the regions and departments of France.

Published
2021

8. 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

9. Exploitation conjointe d'un modèle biomécanique patient-spécifique de coeur et vaisseaux et de données mesurées au bloc opératoire pour augmenter le monitorage hémodynamique des patients sous anesthésie générale

Author

Le Gall, Arthur, 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), Hôpital Lariboisière-Fernand-Widal [APHP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), Institut Polytechnique de Paris (IP Paris), Institut polytechnique de Paris, Dominique Chapelle, Radomir Chabiniok, Etienne Gayat, 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), Institut Polytechnique de Paris, Étienne Gayat, and STAR, ABES

Subjects
Time-varying elastance, Monitorage cardiovasculaire, [PHYS.MECA.BIOM] Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Cardiac biomechanical modelling, Modélisation biomécanique cardiaque, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Relation pressionvolume en diastole (EDPVR), Calibration patient-spécifique, Élastance variable, Relation pression-volume en diastole (EDPVR), [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Noradrenaline haemodynamic effects, [SDV.MHEP.CSC] Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Effets hémodynamique de la Noradrénaline, Cardiovascular monitoring, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, End-diastolic pressure-volume relationship (EDPVR), [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, Patient-specific calibration, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph]
Abstract

Haemodynamic evaluation of anaesthetised patients in operating theatre or in intensive care units can be challenging. Indeed, monitoring devices can be inaccurate and/or invasive. Physicians have to evaluate the usefulness of the information given by the monitor, and its potential harms linked to its invasiveness before implementing the technique. Modelling methods may be an interesting alternative to improve the risk/benefit balance for the patients.Biomechanical modelling of heart and vessels as presented in this PhD thesis, when turned into patient-specific regime using patients' data measured in operating theatre, can allow simulation of cardiovascular physiology, including pressure-volume relationships through the cardiac cycle.In 45 patients undergoing general anaesthesia, we analysed the haemodynamic profile in terms of cardiac bioenergetics or ventricular arterial coupling, and we were able to evaluate the effects of Noradrenaline administered for 16 hypotensive patients, on cardiac efficiency, using pressure-volume loops estimated from a patient-specific biomechanical model.Our approach is original as it is based on a rigorous cardiovascular physiological description and on continuum mechanics theory allowing physical and physiological interpretation of the modelling results.This PhD thesis presents also original methods for model calibration, from limited data availability. We developed a passive constitutive law (end-diastolic pressure-volume relationship -- EDPVR) estimation method which reunites the biomechanical approach, usually difficult to implement in clinical settings, and the phenomenological approach, more efficient but less rigorous.We also explored the potentials of a time-varying elastance model, derived from the full biomechanical model. We demonstrated that for reasonable variation ranges, the time-varying elastance model could be used as a surrogate for the biomechanical model. This approach improves the computational time and resources, allowing to consider the transfer of our approach in real-time monitoring conditions.This PhD thesis is a proof of concept of the coupling between biomechanical modelling of heart and vessels and data measured in operating theatre to augment cardiovascular monitoring in anaesthetised patients. This is also the first step toward transfer of the method from bench to bedside., L'évaluation hémodynamique des patients sous anesthésie générale est une tache complexe pour les médecins anesthésistes et/ou réanimateurs. En effet, les techniques de monitorage sont imparfaites, imprécises et/ou invasives, et le choix de la technique de monitorage doit prendre en compte la délicate balance entre l'utilité attendue de l'information recueillie, et l'invasivité et l'imprécision de la méthode utilisée pour recueillir cette information. Les méthodes numériques peuvent représenter une alternative intéressante en améliorant ce rapport bénéfice/risque pour le patient.En particulier, la modélisation biomécanique de coeur et vaisseaux présentée dans cette thèse, une fois calibrée sur les données mesurées couramment au bloc opératoire, peuvent permettre de simuler, entre-autres, un cathétérisme cardiaque gauche. Nous avons ainsi pu analyser le profil hémodynamique de 45 patients sous anesthésie générale, et interpréter les effets de la Noradrénaline administré pour corriger une hypotension artérielle chez 16 patients, en termes de bioénergétique cardiaque, et de couplage ventriculo-aortique, à partir de boucles pression-volume ventriculaires simulées.Notre approche est originale car elle s'intègre dans une démarche rigoureuse basée sur la physiologie cardiovasculaire et la mécanique des milieux continus permettant ainsi de conserver une signification physique et physiologique aux résultats de la modélisation.Cette thèse présente également des méthodes originales, permettant de calibrer le modèle à partir d'une quantité limitée d'information mesurée chez les patients.Ainsi, nous avons mis au point des méthodes d'estimation des paramètres de la loi passive de comportement du coeur en diastole (relation pression-volume en diastole -- EDPVR), réunissant l'approche biomécanique, difficile à mettre en oeuvre en clinique, et l'approche phénoménologique, plus efficace mais moins rigoureuse.Nous avons également exploré les potentialités d'un modèle d'élastance variable, dérivé du modèle biomécanique. Nous avons pu montrer que dans une gamme de variation raisonnable, le modèle d'élastance variable pouvait être utilisé en lieu et place du modèle biomécanique, permettant d'envisager l'utilisation de notre approche dans des conditions de monitorage pour lesquelles l'estimation en temps réel est un enjeu important.Cette thèse représente une preuve de concept de l'exploitation conjointe des données mesurées couramment au bloc opératoire et d'un modèle biomécanique de coeur et vaisseaux pour augmenter le monitorage hémodynamique des patients sous anesthésie générale. Elle représente également la première étape du transfert de la méthode vers la pratique clinique.

Published
2021

10. Coupling reduced-order blood flow and cardiac models through energy-consistent strategies: modeling and discretization

Author

Sébastien Imperiale, François Kimmig, Federica Caforio, Philippe Moireau, Jessica Manganotti, 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), Karl-Franzens-Universität Graz, 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 Institute of Mathematics and Scientific Computing, University of Graz

Subjects
Work (thermodynamics), Reduced-order models, Heart models, Discretization, Quantitative Biology::Tissues and Organs, 0206 medical engineering, 02 engineering and technology, 030204 cardiovascular system & hematology, Energy-preserving time-scheme, Reduced order, Systems engineering, Cardiovascular modelling, 03 medical and health sciences, Arterial segment, TA168, 0302 clinical medicine, Computational Science and Engineering, Engineering (miscellaneous), Physics, Coupling, Applied Mathematics, Mechanics of engineering. Applied mechanics, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Mechanics, Blood flow, TA349-359, Dicrotic notch, 020601 biomedical engineering, Computer Science Applications, Shallow-water models, Ageing, Modeling and Simulation, Energy (signal processing), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

In this work we provide a novel energy-consistent formulation for the classical 1D formulation of blood flow in an arterial segment. The resulting reformulation is shown to be suitable for the coupling with a lumped (0D) model of the heart that incorporates a reduced formulation of the actin-myosin interaction. The coupling being consistent with energy balances, we provide a complete heart-circulation model compatible with thermodynamics hence stable numerically and informative physiologically. These latter two properties are verified by numerical experiments.

Published
2021

11. Altered Aortic Hemodynamics and Relative Pressure in Patients with Dilated Cardiomyopathy

Author

David Marlevi, Jorge Mariscal-Harana, Nicholas S. Burris, Julio Sotelo, Bram Ruijsink, Myrianthi Hadjicharalambous, Liya Asner, Eva Sammut, Radomir Chabiniok, Sergio Uribe, Reidar Winter, Pablo Lamata, Jordi Alastruey, David Nordsletten, Massachusetts Institute of Technology (MIT), King‘s College London, Department of Mathematics - University of Michigan, University of Michigan [Ann Arbor], University of Michigan System-University of Michigan System, Universidad de Valparaiso [Chile], Pontificia Universidad Católica de Chile (UC), University of Cyprus (UCY), University of Bristol [Bristol], University of Texas Southwestern Medical Center [Dallas], 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), Karolinska Institutet, Department of Clinical Sciences, Danderyd Hospital, Division of Rehabilitation Medicine, Stockholm, Sweden, University of Michigan System, University of Cyprus [Nicosia] (UCY), 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 Danderyds sjukhus = Danderyd University Hospital

Subjects
4D flow MRI, Cardiomyopathy, Dilated, Aortic hemodynamics, Aortic relative pressure, Heart Ventricles, Dilated cardiomyopathy, Aortic stiffness, Hemodynamics, Pharmaceutical Science, 030204 cardiovascular system & hematology, Magnetic Resonance Imaging, Ventricular Function, Left, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, 0302 clinical medicine, Genetics, cardiovascular system, Molecular Medicine, Humans, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Cardiology and Cardiovascular Medicine, Genetics (clinical), Aorta
Abstract

Ventricular-vascular interaction is central in the adaptation to cardiovascular disease. However, cardiomyopathy patients are predominantly monitored using cardiac biomarkers. The aim of this study is therefore to explore aortic function in dilated cardiomyopathy (DCM). Fourteen idiopathic DCM patients and 16 controls underwent cardiac magnetic resonance imaging, with aortic relative pressure derived using physics-based image processing and a virtual cohort utilized to assess the impact of cardiovascular properties on aortic behaviour. Subjects with reduced left ventricular systolic function had significantly reduced aortic relative pressure, increased aortic stiffness, and significantly delayed time-to-pressure peak duration. From the virtual cohort, aortic stiffness and aortic volumetric size were identified as key determinants of aortic relative pressure. As such, this study shows how advanced flow imaging and aortic hemodynamic evaluation could provide novel insights into the manifestation of DCM, with signs of both altered aortic structure and function derived in DCM using our proposed imaging protocol. Graphic Abstractr

Published
2021

12. Asymptotic analysis of abstract two-scale wave propagation problems

Author

Imperiale, Sébastien, Université Paris-Saclay, 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
Asymptotic analysis, Operator theory, Wave equation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

This work addresses the mathematical analysis, by means of asymptotic analysis, of linear wave propagation problems involving two scales, represented by a single small parameter, and written in an abstract setting. This abstract setting is defined using linear operators in Hilbert spaces and also enters the framework of semi-group theory. In this setting, we show, under some assumptions on the structure of the wave propagation problems, weak and strong convergence of solutions with respect to the small parameter towards the solution of a well-defined limit problem.

Published
2021

13. 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

14. Multiscale experimental and theoretical investigation of the structure-property relationships in the myocardium

Author

Tueni, Nicole, 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), Institut Polytechnique de Paris, Jean-Marc Allain, Martin Genet, Ecole polytechnique, 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
Multiscale, Propriétés mécaniques, Mechanical properties, Etude multi échelle, Biomécanique, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], [PHYS.MECA.MSMECA]Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph], [PHYS.MECA.MEMA]Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph], Étude Multi-Échelle, Multiscale study, [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], Heart tissue, Biomechanics, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Microstructure, Tissu cardiaque, Cardiac tissue
Abstract

The myocardium is a complex tissue, primarily made of cardiac cells and extra-cellular collagenous matrix, arranged in a hierarchical microstructure. This microstructure evolves with time, either physiologically or pathologically, altering the macroscopic mechanical properties of heart, hence its function. The objective of this PhD thesis is to improve our understanding of the structure-properties relationships in the cardiac tissue by focusing on the role of mesostructure, called the sheetlet, on the macroscopic mechanical properties. In a first part, a literature review of the existing literature on the role of sheetlet is performed. In the second chapter, we present an experimental setup we developed, combining a full-field Mueller polarimetric imager and an in-situ traction device with a local measure of the deformation during sample stretch. We observe a global cohesion of the tissue apart on separation lines at the mesoscale, that tend to open under traction. We hypothesize that these lines are the collageneous layers separating the sheetles, bundles of cardiomyocytes surrounded by layers of perimysial collagen. In the third chapter, we propose a simple optical method combined with a fast image analysis to extract the sheetlet local orientation on left ventricle slices, in order to construct a 3D mapping of the sheetlet organization in the heart. In the second part of the PhD thesis (chapter four), we propose a multiscale model of the myocardium aiming at determining the structural origin of the observed macroscale mechanical anisotropy. Indeed, the observed orthotropy can be due either to the rotation of the cell orientation, or to the presence of the mesoscale collageneous layers. We design three mesostructures made of different configurations of cardiomyocytes and collagen. The mechanical response of these mesostructures are homogenized with numerical periodic homogenization, and the obtained material parameters are used in a macroscopic simulation of a shear experiment. The comparison between our results and the experimental data show that the collagen layers are necessary to reproduce the material orthotropy. The final chapter of this thesis presents some perspectives of this work.; Le myocarde est un tissu complexe, principalement constitué de cellules cardiaques et d'une matrice collagénique extracellulaire, disposés selon une microstructure hiérarchique. Cette microstructure évolue au cours du temps, de manière physiologique ou pathologique, altérant les propriétés mécaniques macroscopiques du cœur, donc sa fonction. L'objectif de cette thèse est d'améliorer notre compréhension des relations structure-propriétés dans le tissu cardiaque en s'intéressant au rôle de la mésostructure, appelée feuillet, sur les propriétés mécaniques macroscopiques. Dans une première partie, une revue de la littérature existante sur le rôle du feuillet est réalisée. Dans le deuxième chapitre, nous présentons un montage expérimental que nous avons développé, combinant un imageur polarimétrique Mueller plein champ et un dispositif de traction in-situ avec une mesure locale de la déformation lors de l'étirement de l'échantillon. On observe une cohésion globale des tissus à part sur des lignes de séparation à mésoéchelle, qui ont tendance à s'ouvrir sous traction. Nous émettons l'hypothèse que ces lignes sont les couches collagéniques séparant les feuillets, des faisceaux de cardiomyocytes entourés de couches de collagène périmysial. Dans le troisième chapitre, nous proposons une méthode optique simple combinée à une analyse d'image rapide pour extraire l'orientation locale des feuillets sur des coupes de ventricule gauche, afin de construire une cartographie 3D de l'organisation des feuillets dans le cœur. Dans la deuxième partie de la thèse (chapitre quatre), nous proposons un modèle multi-échelle du myocarde visant à déterminer l'origine structurale de l'anisotropie mécanique macro-échelle observée. En effet, l'orthotropie observée peut être due soit à la rotation de l'orientation des cellules, soit à la présence des couches collagéniques méso-échelle. Nous concevons trois mésostructures constituées de différentes configurations de cardiomyocytes et de collagène. La réponse mécanique de ces mésostructures est homogénéisée avec une homogénéisation périodique numérique, et les paramètres de matériau obtenus sont utilisés dans une simulation macroscopique d'une expérience de cisaillement. La comparaison entre nos résultats et les données expérimentales montre que les couches de collagène sont nécessaires pour reproduire l'orthotropie du matériau. Le dernier chapitre de ce manuscrit présente quelques perspectives de ce travail.

Published
2021

15. Modelling the fluid–structure interactions of a capsule using a nonlinear thin shell model: Effect of wall thickness

Author

Dupont, C., Vidrascu, M., Le Tallec, P., Barthès-Biesel, D., Salsac, A.-V., Biomécanique et Bioingénierie (BMBI), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, 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 (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de Mécanique des Structures (LMS), Université Tahri Mohamed Bechar [Bechar], 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), This work received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant agreement No. ERC-2017-COG -MultiphysMicroCaps)., Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), 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
Physics::Fluid Dynamics, Microcapsules, Mechanical Engineering, Numerical simulations, Shell, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Fluid-structure interactions
Abstract

International audience; We address the question of the modelling of the fluid-structure interactions for a microcapsule enclosed by a finite-thickness wall, and of the prediction of the buckling behaviour when it is subjected to large displacements and deformations. Specifically, we model the strong coupling between the solid (the wall dynamics) and fluid (the flow inside and outside the capsule) mechanics, for a wall material that can be strain-hardening or softening, while accounting for the bending resistance due to thickness. The fluid flow is assumed to be inertialess on the capsule scale, which allows the use of the boundary integral formulation for the fluid velocity. We discuss the different simplifications that are made when designing a fluid-shell interaction model for large deformations, and present a shear-membrane-bending (SMB) shell model that allows for a nonlinear wall stretching law. The performance of the model, as compared to a simple membrane model where bending resistance is neglected, is illustrated on a generic example: we consider an initially ellipsoidal capsule, freely suspended in a plane hyperbolic flow, that is subjected to such stringent deformation, that its short axis becomes the long one. We show that the simple membrane model predicts reasonably well the overall shape of the capsule, but cannot capture the detailed post buckling behaviour, for which a robust shell model is necessary. The SMB shell model complies with dominant membrane effects, remains stable even under large deformation and avoids numerical locking. It allows predicting post-buckling behaviour, which depends on the material constitutive law.

Published
2022

16. 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

17. A fully equilibrated microsphere model with damage for rubberlike materials

Author

Julie Diani, P. Le Tallec, 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), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), 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
Materials science, Styrene-butadiene, 02 engineering and technology, 01 natural sciences, [SPI.MAT]Engineering Sciences [physics]/Materials, 010305 fluids & plasmas, chemistry.chemical_compound, rubber material, Natural rubber, 0103 physical sciences, constitutive behavior, Composite material, Softening, Mechanical Engineering, Isotropy, anisotropic material, [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], 021001 nanoscience & nanotechnology, Condensed Matter Physics, Mullins softening, chemistry, finite strain, Mechanics of Materials, Hyperelastic material, Finite strain theory, visual_art, Weight distribution, visual_art.visual_art_medium, Affine transformation, 0210 nano-technology
Abstract

International audience; A non-affine microsphere model for rubberlike materials is proposed, based on a local minimization of the network free energy under a maximal advance path constraint. It accounts for any chain weight distribution and for damage such as Mullins softening observed in filled rubber materials. The non-affine equal-force model is compared to the common affine model and a hybrid equal-force model from the literature, when considering the isotropic hyperelastic behavior without damage of rubber materials presenting chains of various lengths. The non-affine model shows an improved deformability compared to the affine model limited by the maximal extension of the shorter chains and a significantly softer behavior. Possible damage is introduced by increasing the chain lengths according to the submitted maximal chain traction force. Each chain are impacted independently resulting in a directional softening that introduces the evolution of the stress-free configuration that needs to be assessed over the loadings. The model was successfully tested on the cyclic uniaxial tension stretch-stress responses of carbon-black filled styrene butadiene rubbers that were well fitted with three parameters only.

Published
2019

18. Stochastic modeling of chemical–mechanical coupling in striated muscles

Author

Dominique Chapelle, Philippe Moireau, Matthieu Caruel, 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), 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), Université Paris-Saclay, 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 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, 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
Mechanical Phenomena, power stroke, 0206 medical engineering, Probability density function, 02 engineering and technology, Myosins, Models, Biological, Sarcomere, Myosin head, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Isometric Contraction, [SDV.MHEP.PHY]Life Sciences [q-bio]/Human health and pathology/Tissues and Organs [q-bio.TO], muscle modeling, sliding filament, Statistical physics, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Power stroke, Physics, Coupling, Stochastic Processes, Partial differential equation, Viscosity, Mechanical Engineering, 020601 biomedical engineering, Muscle, Striated, Biomechanical Phenomena, Macroscopic scale, Modeling and Simulation, Calibration, Thermodynamics, cross-bridge, sarcomere, Langevin equations, Fokker-Planck equations, Biotechnology
Abstract

International audience; We propose a chemical-mechanical model of myosin heads in sarcomeres, within the classical description of rigid sliding filaments. In our case, myosin heads have two mechanical degrees-of-freedom (dofs) - one of which associated with the so-called power stroke - and two possible chemical states, i.e. bound to an actin site or not. Our major motivations are twofold: (1) to derive a multiscale coupled chemical-mechanical model, and (2) to thus account - at the macroscopic scale - for mechanical phenomena that are out of reach for classical muscle models. This model is first written in the form of Langevin stochastic equations, and we are then able to obtain the corresponding Fokker-Planck partial differential equations governing the probability density functions associated with the mechanical dofs and chemical states. This second form is important, as it allows to monitor muscle energetics, and also to compare our model with classical ones, such as the Huxley'57 model to which our equations are shown to reduce under two different types of simplifying assumptions. This provides insight, and gives a Langevin form for Huxley'57. We then show how we can calibrate our model based on experimental data - taken here for skeletal muscles - and numerical simulations demonstrate the adequacy of the model to represent complex physiological phenomena, in particular the fast isometric transients in which the power stroke is known to have a crucial role, thus circumventing a limitation of many classical models.

Published
2019

19. Multiscale mechanical model based on patient-specific geometry: Application to early keratoconus development

Author

C. Giraudet, J. Diaz, P. Le Tallec, J.-M. Allain, 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
Biomedical Engineering, FOS: Physical sciences, Keratoconus, Physics - Medical Physics, eye diseases, Cornea, Biomaterials, Tonometry, Ocular, Mechanics of Materials, Patient-specific, Humans, multiscale model, Collagen, sense organs, Medical Physics (physics.med-ph), [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Intraocular Pressure
Abstract

Keratoconus is a pathology of the cornea associated with a tissue thinning and a weakening of its mechanical properties. However, it remains elusive which aspect is the leading cause of the disease. To investigate this question, we combined a multiscale model with a patient-geometry in order to simulate the mechanical response of healthy and pathological corneas under intraocular pressure. The constitutive behavior of the cornea is described through an energy function which takes into account the isotropic matrix of the cornea, the geometric structure of collagen lamellae and the quasi-incompressibility of the tissue. A micro-sphere description is implemented to take into account the typical features of the collagen lamellae as obtained experimentally, namely their orientation, their stiffness and their dispersion, as well as the their unfolding stretch, at which they start to provide a significant force. A set of reference parameters is obtained to fit experimental inflation data of the literature. We show that the most sensitive parameter is the unfolding stretch, as a small variation of this parameter induces a major change in the corneal apex displacement. The keratoconus case is then studied by separating the impact of the geometry and the one of the mechanics. We computed the evolution of the SimK (a clinical indicator of cornea curvature) and elevation maps: we were able to reproduce the reported changes of SimK with pressure only by a mechanical weakening, and not by a change in geometry. More specifically, the weakening has to target the lamellae and not the matrix. The mechanical weakening leads to elevations close to early stage keratoconus, but our model lacks the remodeling component to couple the change in mechanics with changes in geometry. Still, these findings indicate that new methods for early diagnosis of keratoconus should focus on the detection of a mechanical weakening, and that stiffening treatments should be appropriate.

Published
2022

20. A discrete-time optimal filtering approach for non-linear systems as a stable discretization of the Mortensen observer

Author

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), Université Paris-Saclay, 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
time-discrete non-linear systems, Control and Optimization, Observer (quantum physics), Discretization, optimal filtering, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Estimator, Context (language use), 010103 numerical & computational mathematics, Filter (signal processing), Kalman filter, 01 natural sciences, 010101 applied mathematics, Dynamic programming, Computational Mathematics, Discrete time and continuous time, Control and Systems Engineering, deterministic observer, Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Hamilton-Jacobi-Bellman, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

International audience; In this work, we seek exact formulations of the optimal estimator and filter for a non-linear framework, as the Kalman filter is for a linear framework. The solution is well established with the Mortensen filter in a continuous-time setting, but we seek here its counterpart in a discrete-time context. We demonstrate that it is possible to pursue at the discrete-time level an exact dynamic programming strategy and we find an optimal estimator combining a prediction step using the model and a correction step using the data. This optimal estimator reduces to the discrete-time Kalman estimator when the operators are in fact linear. Furthermore, the strategy that consists of discretizing the least square criterion and then finding the exact estimator at the discrete level allows to determine a new time-scheme for the Mortensen filter which is proven to be consistent and unconditionally stable, with also a consistent and stable discretization of the underlying Hamilton-Jacobi-Bellman equation.

Published
2018

21. 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

22. 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

23. Perfusion Index: Physical Principles, Physiological Meanings and Clinical Implications in Anaesthesia and Critical Care

Author

Jona Joachim, Emmanuel Dudoignon, Etienne Gayat, Fabrice Vallée, François Dépret, Maxime Coutrot, Groupe Hospitalier Saint Louis - Lariboisière - Fernand Widal [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), Université de Paris (UP), Marqueurs cardiovasculaires en situation de stress (MASCOT (UMR_S_942 / U942)), Institut National de la Santé et de la Recherche Médicale (INSERM)-Groupe Hospitalier Saint Louis - Lariboisière - Fernand Widal [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Université Sorbonne Paris Nord, 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), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), 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), Cardiovascular and Renal Clinical Trialists [Vandoeuvre-les-Nancy] (INI-CRCT), Institut Lorrain du Coeur et des Vaisseaux Louis Mathieu [Nancy], Université Paris Cité (UPCité), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Université Sorbonne Paris Nord, 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 Zunara, Fatima

Subjects
Light absorbance, Critical Care, Perfusion index, Haemodynamic monitoring, Neuraxial blockade, Critical Care and Intensive Care Medicine, 03 medical and health sciences, 0302 clinical medicine, 030202 anesthesiology, Photoplethysmogram, Intensive care, Humans, Medicine, Anesthesia, Oximetry, [SDV.MHEP] Life Sciences [q-bio]/Human health and pathology, business.industry, Signal Processing, Computer-Assisted, 030208 emergency & critical care medicine, General Medicine, Perioperative, 3. Good health, Anesthesiology and Pain Medicine, non-invasive monitoring, Narrative review, photoplethysmography, business, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology
Abstract

Short title: Clinical Usefulness of Perfusion Index; International audience; Photoplethysmography (PPG) has been extensively used for pulse oximetry monitoring in anaesthesia, perioperative and intensive care. However, some components of PPG signal have been employed for other purposes, such as non-invasive haemodynamic monitoring. Perfusion index (PI) is derived from PPG signal and represents the ratio of pulsatile on non-pulsatile light absorbance or reflectance of the PPG signal. PI determinants are complex and interlinked, involving and reflecting the interaction between peripheral and central haemodynamic characteristics, such as vascular tone and stroke volume. Recently, several studies have shed light on the interesting performances of this variable, especially assessing regional or neuraxial block success, and haemodynamic monitoring in anaesthesia, perioperative and intensive care. Nevertheless, no review has yet been published concerning the interest of PI in these fields. In this narrative review will be exposed first the physiological and pathophysiological determinants of PI, and then the mean to measure this value as well as its potential limitations. In the second part, the existing data concerning usefulness of PI in different clinical settings such as operating theatres, intensive care units and emergency departments will be presented and discussed. Finally, the perspectives concerning the use of PI and mentioned aspects that should be explored regarding this tool will be underlined.

Published
2021

24. Personalized Pulmonary Poromechanics in Health and Idiopathic Pulmonary Fibrosis

Author

Genet, Martin, Patte, Cécile, Fetita, Catalin, Brillet, Pierre-Yves, Chapelle, Dominique, 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
[SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2021

25. Left ventricular torsion obtained using equilibrated warping in patients with repaired Tetralogy of Fallot

Author

Abhijit Bhattaru, Gerald F. Greil, Animesh Tandon, Jeanne Dillenbeck, Barbara Burkhardt, Radomir Chabiniok, Tarique Hussain, Daniel A. Castellanos, Martin Genet, Ezgi Berberoglu, Kateřina Škardová, Boston Children's Hospital, Harvard Medical School [Boston] (HMS), Czech Technical University in Prague (CTU), University of Texas Southwestern Medical Center [Dallas], The College of New Jersey (TCNJ), 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), Institute for Biomedical Engineering [ETH Zürich] (IBT), Universität Zürich [Zürich] = University of Zurich (UZH)-Department of Information Technology and Electrical Engineering [Zürich] (D-ITET), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich)- Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), University of Texas Southwestern Medical Center, University Children’s Hospital Zurich, 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, University of Zurich, and Castellanos, Daniel Alexander

Subjects
Torsion, medicine.medical_specialty, Intraclass correlation, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, 610 Medicine & health, 030204 cardiovascular system & hematology, Motion tracking, 2705 Cardiology and Cardiovascular Medicine, Article, 03 medical and health sciences, 0302 clinical medicine, Internal medicine, medicine, 2735 Pediatrics, Perinatology and Child Health, Image warping, Twist, Tetralogy of Fallot, Equilibrated warping, Reproducibility, Ejection fraction, business.industry, Torsion (mechanics), medicine.disease, Cardiac surgery, Early-stage heart failure, 030228 respiratory system, 10036 Medical Clinic, Heart failure, Pediatrics, Perinatology and Child Health, Cardiology, Cardiology and Cardiovascular Medicine, business
Abstract

International audience; Purpose:Patients after surgical repair of Tetralogy of Fallot (rTOF) may suffer a decrease in left ventricular (LV) function. The aim of our study is to evaluate a novel method of assessing LV torsion in patients with rTOF, as an early indicator of systolic LV dysfunction. Methods:Motion tracking based on image registration regularized by the equilibrium gap principle, known as equilibrated warping, was employed to assess LV torsion. Seventy-six cases of rTOF and ten normal controls were included. The group of controls was assessed for reproducibility using both equilibrated warping and standard clinical tissue tracking software (CVI42, version 5.10.1, Calgary, Canada). Patients were dichotomized into two groups: normal vs. loss of torsion.Results:Torsion by equilibrated warping was successfully obtained in 68 of 76 (89%) patients and 9 of 10 (90%) controls. For equilibrated warping, the intra- and inter-observer coefficients of variation were 0.095 and 0.117, respectively; compared to 0.260 and 0.831 for tissue tracking by standard clinical software. The intra- and inter-observer intraclass correlation coefficients for equilibrated warping were 0.862 and 0.831, respectively; compared to 0.992 and 0.648 for tissue tracking. Loss of torsion was noted in 32 of the 68 (47%) patients with rTOF. There was no difference in LV or RV volumes or ejection fraction between these groups.Conclusion:The assessment of LV torsion by equilibrated warping is feasible and shows good reliability. Loss of torsion is common in patients with rTOF and its robust assessment might contribute into uncovering heart failure in an earlier stage.

Published
2021

26. Quantification of Left Ventricular Strain by Joint Analysis of 3D Tagging and Cine MR Images

Author

Berberoglu, Ezgi, Stoeck, Christian, Kozerke, Sebastian, Genet, Martin, Institute for Biomedical Engineering [ETH Zürich] (IBT), Universität Zürich [Zürich] = University of Zurich (UZH)-Department of Information Technology and Electrical Engineering [Zürich] (D-ITET), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich)- Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), 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
[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2021

27. Combining data assimilation and machine learning to build data-driven models for unknown long time dynamics—Applications in cardiovascular modeling

Author

Francesco Regazzoni, Philippe Moireau, Dominique Chapelle, Modeling and Scientific Computing [Milano] (MOX), Politecnico di Milano [Milan] (POLIMI), 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), 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
cardiovascular modeling, Computer science, Differential equation, data‐driven modeling, 0206 medical engineering, Biomedical Engineering, Context (language use), 02 engineering and technology, 030204 cardiovascular system & hematology, Machine learning, computer.software_genre, Field (computer science), Data-driven, 03 medical and health sciences, 0302 clinical medicine, multiscale problems, Molecular Biology, data assimilation, Interpretability, Parametric statistics, Research Article ‐ Fundamental, Artificial neural network, business.industry, Applied Mathematics, Models, Theoretical, 020601 biomedical engineering, Test case, machine learning, Computational Theory and Mathematics, data-driven modeling, Modeling and Simulation, Artificial intelligence, business, computer, artificial neural networks, Algorithms, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Software
Abstract

We propose a method to discover differential equations describing the long‐term dynamics of phenomena featuring a multiscale behavior in time, starting from measurements taken at the fast‐scale. Our methodology is based on a synergetic combination of data assimilation (DA), used to estimate the parameters associated with the known fast‐scale dynamics, and machine learning (ML), used to infer the laws underlying the slow‐scale dynamics. Specifically, by exploiting the scale separation between the fast and the slow dynamics, we propose a decoupling of time scales that allows to drastically lower the computational burden. Then, we propose a ML algorithm that learns a parametric mathematical model from a collection of time series coming from the phenomenon to be modeled. Moreover, we study the interpretability of the data‐driven models obtained within the black‐box learning framework proposed in this paper. In particular, we show that every model can be rewritten in infinitely many different equivalent ways, thus making intrinsically ill‐posed the problem of learning a parametric differential equation starting from time series. Hence, we propose a strategy that allows to select a unique representative model in each equivalence class, thus enhancing the interpretability of the results. We demonstrate the effectiveness and noise‐robustness of the proposed methods through several test cases, in which we reconstruct several differential models starting from time series generated through the models themselves. Finally, we show the results obtained for a test case in the cardiovascular modeling context, which sheds light on a promising field of application of the proposed methods., We propose a method to discover differential equations describing the long‐term dynamics of phenomena featuring a multiscale behavior in time, starting from measurements taken at the fast‐scale. Our methodology is based on a synergetic combination of data assimilation, used to estimate the parameters associated with the known fast‐scale dynamics, and machine learning, used to infer the laws underlying the slow‐scale dynamics. By exploiting the scale separation between the fast and the slow dynamics, we propose a decoupling of time scales that allows to drastically lower the computational burden.

Published
2021

28. Numerical Analysis of a Method for Solving 2D Linear Isotropic Elastodynamics with Free Boundary Condition using Potentials and Finite Elements

Author

Albella Martínez, Jorge, Imperiale, Sébastien, Joly, Patrick, Rodríguez, Jerónimo, Departamento de Matemática Aplicada, Universidade de Santiago de Compostela [Spain] (USC ), 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), Institut Polytechnique de Paris (IP Paris), Propagation des Ondes : Étude Mathématique et Simulation (POEMS), 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)-Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-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
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; When solving 2D linear elastodynamic equations in a homogeneous isotropic media, a Helmholtz decomposition of the displacement field decouples the equations into two scalar wave equations that only interact at the boundary. It is then natural to look for numerical schemes that independently solve the scalar equations and couple the solutions at the boundary. The case of rigid boundary condition was treated In [3, 2]. However in [4] the case of free surface boundary condition was proven to be unstable if a straight- forward approach is used. Then an adequate functional framework as well as a time domain mixed formulation to circumvent these issues was presented. In this work we first review the formulation presented in [4] and propose a subsequent discretised formulation. We provide the complete stability analysis of the corresponding numerical scheme. Numerical results that illustrate the theory are also shown.

Published
2021

29. Translational Cardiovascular Modeling: Tetralogy of Fallot and Modeling of Diseases

Author

Radomír Chabiniok, Kateřina Škardová, Radek Galabov, Pavel Eichler, Maria Gusseva, Jan Janoušek, Radek Fučík, Jaroslav Tintěra, Tomáš Oberhuber, Tarique Hussain, King‘s College London, Czech Technical University in Prague (CTU), 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], Guy's and St Thomas' Hospital [London], Faculty of Nuclear Sciences and Physical Engineering [Prague] (FJFI CTU), Institute for Clinical and Experimental Medicine (IKEM), University Hospital Motol, 2nd Faculty of Medicine, Charles University Prague, 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
[SDV.IB]Life Sciences [q-bio]/Bioengineering
Abstract

International audience; Translational cardiovascular modeling (TCM) combines clinical data with physiologically and biophysically based models of the heart, vessels or circulation, while aiming to contribute to diagnosis or optimal clinical management. Models of heart mechanics and electromechanical models are applicable when assessing ventricular function, contributing to planning of optimal intervention. During a pe- rioperative period or acute exacerbation of heart failure, close to real time running models can be coupled with signals monitoring cardiovascular physiology. Blood flow assessed by combining phase contrast magnetic resonance imaging with flow models can contribute to the decision about a possible intervention e.g. on heart valves or large vessels. Furthermore, advanced imaging and image processing con- strained by biophysical models allows for the study of distinct patterns, which could contribute to early detection or mapping a disease progress. In this chapter we demonstrate applicability of some TCM methods on tetralogy of Fallot (TOF) – the most common cyanotic congenital heart disease. A number of already existing modeling techniques can be applied on the cohort of TOF. Likewise, some novel techniques developed specifically for the group of TOF patients could serve in some other pathologies. This whole approach leads to an acronym TOFMOD, standing for Tetralogy of Fallot and Modeling of Diseases.

Published
2021

30. In-silico study of accuracy and precision of left-ventricular strain quantification from 3D tagged MRI

Author

Ezgi Berberoglu, Christian T. Stoeck, Philippe Moireau, Sebastian Kozerke, Martin Genet, Institute for Biomedical Engineering [ETH Zürich] (IBT), Universität Zürich [Zürich] = University of Zurich (UZH)-Department of Information Technology and Electrical Engineering [Zürich] (D-ITET), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich)- Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), 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), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), French National Research Agency Research Grant Nr. ANR-10-EQPX-37 received by Martin Genet. • Swiss National Science Foundation(SNF) Research Grants Nr. CR23I3_166485 received by Sebastian Kozerke. Ezgi Berberoğlu’s salary was paid by this grant. • Swiss NationalScience Foundation (SNF) Research Grants Nr. PZ00P2_174144 received by Christian T. Stoeck., 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
[SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, Physics::Medical Physics, 030204 cardiovascular system & hematology, Signal-To-Noise Ratio, Ventricular Function, Left, 030218 nuclear medicine & medical imaging, Diagnostic Radiology, 0302 clinical medicine, Medicine and Health Sciences, Biomechanics, Image resolution, Physics, Ground truth, Multidisciplinary, medicine.diagnostic_test, Radiology and Imaging, Classical Mechanics, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Condensed Matter Physics, Magnetic Resonance Imaging, Deformation, Biomechanical Phenomena, In Vivo Imaging, Physical Sciences, Engineering and Technology, Medicine, Radial stress, Research Article, Accuracy and precision, Imaging Techniques, Heart Ventricles, Science, Materials Science, Material Properties, Image processing, Image Analysis, Research and Analysis Methods, 03 medical and health sciences, Imaging, Three-Dimensional, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Cardiac magnetic resonance imaging, Diagnostic Medicine, Image Interpretation, Computer-Assisted, medicine, Humans, Computer Simulation, Image warping, Signal to Noise Ratio, Damage Mechanics, Reproducibility of Results, Biology and Life Sciences, Magnetic resonance imaging, Signal Processing, Anisotropy, Biomedical engineering
Abstract

Cardiac Magnetic Resonance Imaging (MRI) allows quantifying myocardial tissue deformation and strain based on the tagging principle. In this work, we investigate accuracy and precision of strain quantification from synthetic 3D tagged MRI using equilibrated warping. To this end, synthetic biomechanical left-ventricular tagged MRI data with varying tag distance, spatial resolution and signal-to-noise ratio (SNR) were generated and processed to quantify errors in radial, circumferential and longitudinal strains relative to ground truth. Results reveal that radial strain is more sensitive to image resolution and noise than the other strain components. The study also shows robustness of quantifying circumferential and longitudinal strain in the presence of geometrical inconsistencies of 3D tagged data. In conclusion, our study points to the need for higher-resolution 3D tagged MRI than currently available in practice in order to achieve sufficient accuracy of radial strain quantification., PLoS ONE, 16 (11), ISSN:1932-6203

Published
2021

31. Cellular transduction of mechanical oscillations in plants by the plasma-membrane mechanosensitive channel MSL10

Author

Nathalie Leblanc-Fournier, Emmanuel de Langre, Jean-Marie Frachisse, Bruno Moulia, Tiffanie Girault, Marjorie Guichard, Sébastien Thomine, Daniel Tran, Jean-Marc Allain, Agroscope, Institut de Biologie Intégrative de la Cellule (I2BC), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique et Physiologie Intégratives de l’Arbre en environnement Fluctuant (PIAF), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire d'hydrodynamique (LadHyX), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), 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), ANR-09-BLAN-0245,Senzo(2009), ANR-11-BSV7-0010,CAROLS,Canaux ioniques et espèces actives de l'oxygène dans le poil absorbant de légumineuse: rôle dans la symbiose avec Rhizobium(2011), ANR-10-LABX-0040,SPS,Saclay Plant Sciences(2010), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Clermont Auvergne (UCA), 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
0106 biological sciences, Materials science, Arabidopsis, 01 natural sciences, Mechanotransduction, Cellular, Ion Channels, 03 medical and health sciences, Passive movements, vibration modes, wind, [SDV.BV]Life Sciences [q-bio]/Vegetal Biology, Mechanotransduction, 030304 developmental biology, mechanotransduction, mechanosensitive channel, 0303 health sciences, Multidisciplinary, Ion Transport, Oscillation, Arabidopsis Proteins, atmsl10 wind, Cell Membrane, Membrane Proteins, Plasma, oscillation, Biological Sciences, Plants, Genetically Modified, Membrane, frequency, ion-channel, Biophysics, Mechanosensitive channels, Transduction (physiology), Mechanoreceptors, 010606 plant biology & botany, Communication channel, Signal Transduction
Abstract

International audience; Plants spend most of their life oscillating around 1–3 Hz due to the effect of the wind. Therefore, stems and foliage experience repetitive mechanical stresses through these passive movements. However, the mechanism of the cellular perception and transduction of such recurring mechanical signals remains an open question. Multimeric protein complexes forming mechanosensitive (MS) channels embedded in the membrane provide an efficient system to rapidly convert mechanical tension into an electrical signal. So far, studies have mostly focused on nonoscillatory stretching of these channels. Here, we show that the plasma-membrane MS channel MscS-LIKE 10 (MSL10) from the model plant Arabidopsis thaliana responds to pulsed membrane stretching with rapid activation and relaxation kinetics in the range of 1 s. Under sinusoidal membrane stretching MSL10 presents a greater activity than under static stimulation. We observed this amplification mostly in the range of 0.3–3 Hz. Above these frequencies the channel activity is very close to that under static conditions. With a localization in aerial organs naturally submitted to wind-driven oscillations, our results suggest that the MS channel MSL10, and by extension MS channels sharing similar properties, represents a molecular component allowing the perception of oscillatory mechanical stimulations by plants.

Published
2020

32. Personalized pulmonary mechanics : modeling, estimation and application to pulmonary fibrosis

Author

Patte, Cécile, 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), Institut Polytechnique de Paris, Dominique Chapelle, Martin Genet, 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
Lung modeling, Estimation à partir d'images, Biomécanique, Poromechanics, Médecine numérique, Modélisation pulmonaire, Biomechanics, Image-Based estimation, In Silico medicine, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Poromécanique
Abstract

Idiopathic pulmonary fibrosis (IPF), an interstitial lung disease, strongly impacts lung mechanics, which raises clinical issues. The objective of this work is to improve the understanding and diagnosis of IPF based on poromechanical modeling of the lung, personalized with clinical imaging data. In a first part, a literature review analyzes the state of the art of pulmonary physiology in relation to the existing mechanical models, insisting on the multi-scale, multi-phase and multi-physics characteristics of the organ. We then propose a poromechanical model of the lung at the organ spatial scale and breathing time scale, derived from a general poromechanical theory formulated recently in the MΞDISIM team. The constitutive law proposed reproduces mainly the pressure-volume behaviour of the lung as well as the quasi-incompressiblity of the solid phase. The boundary conditions take into account the lung environment (thoracic cage, diaphragm, pleura) and distinguish between free and ventilated breathing. The unloaded configuration, non observed during a breathing cycle, is estimated, with a special attention given to maintain a positive porosity. Various elements of the model are then personalized with standard clinical data, i.e., two 3DCT images acquired at end-exhalation and end-inhalation. In particular, an inverse problem is formulated to estimate the pulmonary compliance of the healthy and fibrotic regions, since the poromechanical formulation allows to distinguish the effect of the porosity from that of the absolute compliance of the interstitial tissue. Applied to three patients suffering from IPF, the personalized model allows to find the foreseen properties of IPF, i.e., the stiffening of the diseased region. Stress concentrations are also observed at the diseased region interface, supporting the hypothesis of a mechanical vicious circle governing the IPF progress, where fibrosis induces large stresses, which in turn favors fibrosis. This numerical tool could later be used for objective and quantitative diagnosis of IPF and, with longitudinal data, to study the mechanics-induced remodeling.; Les poumons réalisent leur fonction vitale d'échanges gazeux grâce notamment à leur élasticité et leur porosité. La fibrose pulmonaire idiopathique (FPI), une maladie pulmonaire interstitielle, impacte fortement la mécanique pulmonaire, soulevant des problématiques cliniques. L'objectif de ce travail est d'améliorer la compréhension et le diagnostic de la FPI en s'appuyant sur une modélisation poromécanique du poumon, personnalisée grâce à des données d'imagerie médicale. Dans une première partie, une analyse bibliographique fait l'état de l'art de la physiologie pulmonaire en relation avec les modélisations mécaniques existantes, en insistant sur les caractères multiéchelle, multiphasique et multiphysique de l'organe. Nous proposons ensuite un modèle poromécanique du poumon à l'échelle spatiale de l'organe et à l'échelle temporelle de la respiration, dérivé d'une théorie générale de poromécanique récemment formulée dans l'équipe MΞDISIM. La loi de comportement proposée reproduit notamment le comportement pression-volume du poumon ainsi que la quasi-incompressiblité de la phase solide. Les conditions aux limites prennent en compte l'environnement du poumon (cage thoracique, diaphragme, plèvre) et distinguent les cas de la respiration libre vs ventilée. La configuration déchargée, non observée au cours d'un cycle respiratoire, est estimée, avec une attention particulière apportée pour contraindre la positivité de la porosité. Plusieurs éléments du modèle sont ensuite personnalisés à partir de données cliniques standards, i.e., deux images 3DCT prises en début et en fin d'inspiration. Un problème inverse est notamment formulé pour estimer la compliance pulmonaire en zones saines et fibrosées, la formulation poromécanique permettant de distinguer l’effet de la porosité de celui de la compliance du tissu interstitiel. Appliqué sur trois patients atteints de FPI, le modèle personnalisé permet de retrouver les propriétés pressenties de la FPI, i.e., la rigidification des zones malades. Des surcontraintes sont aussi observées en bordure de la région malade, corroborant ainsi l'hypothèse d'un cercle vicieux mécanique régissant l'évolution de la FPI, où la fibrose entraînerait des contraintes importantes, qui à leur tour favoriseraient la fibrose. Cet outil numérique pourrait servir par la suite au diagnostic objectif et quantitatif de la FPI et, avec des données longitudinales, à l'étude de son remodelage induit par la mécanique.

Published
2020

33. Mécanique pulmonaire personnalisée : modélisation, estimation et application à la fibrose pulmonaire

Author

Patte, Cécile, 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), Institut Polytechnique de Paris, Dominique Chapelle, and Martin Genet

Subjects
Lung modeling, Estimation à partir d'images, Biomécanique, Poromechanics, Médecine numérique, Modélisation pulmonaire, Biomechanics, Image-Based estimation, In Silico medicine, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Poromécanique
Abstract

Idiopathic pulmonary fibrosis (IPF), an interstitial lung disease, strongly impacts lung mechanics, which raises clinical issues. The objective of this work is to improve the understanding and diagnosis of IPF based on poromechanical modeling of the lung, personalized with clinical imaging data. In a first part, a literature review analyzes the state of the art of pulmonary physiology in relation to the existing mechanical models, insisting on the multi-scale, multi-phase and multi-physics characteristics of the organ. We then propose a poromechanical model of the lung at the organ spatial scale and breathing time scale, derived from a general poromechanical theory formulated recently in the MΞDISIM team. The constitutive law proposed reproduces mainly the pressure-volume behaviour of the lung as well as the quasi-incompressiblity of the solid phase. The boundary conditions take into account the lung environment (thoracic cage, diaphragm, pleura) and distinguish between free and ventilated breathing. The unloaded configuration, non observed during a breathing cycle, is estimated, with a special attention given to maintain a positive porosity. Various elements of the model are then personalized with standard clinical data, i.e., two 3DCT images acquired at end-exhalation and end-inhalation. In particular, an inverse problem is formulated to estimate the pulmonary compliance of the healthy and fibrotic regions, since the poromechanical formulation allows to distinguish the effect of the porosity from that of the absolute compliance of the interstitial tissue. Applied to three patients suffering from IPF, the personalized model allows to find the foreseen properties of IPF, i.e., the stiffening of the diseased region. Stress concentrations are also observed at the diseased region interface, supporting the hypothesis of a mechanical vicious circle governing the IPF progress, where fibrosis induces large stresses, which in turn favors fibrosis. This numerical tool could later be used for objective and quantitative diagnosis of IPF and, with longitudinal data, to study the mechanics-induced remodeling.; Les poumons réalisent leur fonction vitale d'échanges gazeux grâce notamment à leur élasticité et leur porosité. La fibrose pulmonaire idiopathique (FPI), une maladie pulmonaire interstitielle, impacte fortement la mécanique pulmonaire, soulevant des problématiques cliniques. L'objectif de ce travail est d'améliorer la compréhension et le diagnostic de la FPI en s'appuyant sur une modélisation poromécanique du poumon, personnalisée grâce à des données d'imagerie médicale. Dans une première partie, une analyse bibliographique fait l'état de l'art de la physiologie pulmonaire en relation avec les modélisations mécaniques existantes, en insistant sur les caractères multiéchelle, multiphasique et multiphysique de l'organe. Nous proposons ensuite un modèle poromécanique du poumon à l'échelle spatiale de l'organe et à l'échelle temporelle de la respiration, dérivé d'une théorie générale de poromécanique récemment formulée dans l'équipe MΞDISIM. La loi de comportement proposée reproduit notamment le comportement pression-volume du poumon ainsi que la quasi-incompressiblité de la phase solide. Les conditions aux limites prennent en compte l'environnement du poumon (cage thoracique, diaphragme, plèvre) et distinguent les cas de la respiration libre vs ventilée. La configuration déchargée, non observée au cours d'un cycle respiratoire, est estimée, avec une attention particulière apportée pour contraindre la positivité de la porosité. Plusieurs éléments du modèle sont ensuite personnalisés à partir de données cliniques standards, i.e., deux images 3DCT prises en début et en fin d'inspiration. Un problème inverse est notamment formulé pour estimer la compliance pulmonaire en zones saines et fibrosées, la formulation poromécanique permettant de distinguer l’effet de la porosité de celui de la compliance du tissu interstitiel. Appliqué sur trois patients atteints de FPI, le modèle personnalisé permet de retrouver les propriétés pressenties de la FPI, i.e., la rigidification des zones malades. Des surcontraintes sont aussi observées en bordure de la région malade, corroborant ainsi l'hypothèse d'un cercle vicieux mécanique régissant l'évolution de la FPI, où la fibrose entraînerait des contraintes importantes, qui à leur tour favoriseraient la fibrose. Cet outil numérique pourrait servir par la suite au diagnostic objectif et quantitatif de la FPI et, avec des données longitudinales, à l'étude de son remodelage induit par la mécanique.

Published
2020

34. Multipatch isogeometric mortar methods for thick shells

Author

Malek Zarroug, Nicolas Adam, Patrick Le Tallec, 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), PSA Peugeot - Citroën (PSA), PSA Peugeot Citroën (PSA), 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
Coupling, Augmented Lagrangian method, Computer science, Mechanical Engineering, Mathematical analysis, Computational Mechanics, General Physics and Astronomy, 010103 numerical & computational mathematics, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], 01 natural sciences, Computer Science Applications, 010101 applied mathematics, Set (abstract data type), Mechanics of Materials, 0101 mathematics, Mortar, Mortar methods
Abstract

International audience; This paper introduces, analyzes and validates isogeometric mortar methods for the solution of thick shells problems which are set on a multipatch geometry. A particular attention will be devoted to the introduction of a proper formulation of the coupling conditions, with a particular interest on augmented lagrangian formulations, to the choice and validation of mortar spaces, and to the derivation of adequate integration rules. The relevance of the proposed approach is assessed numerically on various significative examples.

Published
2020

35. A flexible framework for sequential estimation of model parameters in computational hemodynamics

Author

Christopher J. Arthurs, Tobias Schaeffter, C. Alberto Figueroa, Philippe Moireau, Nan Xiao, Imaging Sciences and Biomedical Engineering Division [London], Guy's and St Thomas' Hospital [London]-King‘s College London, 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), Technical University of Berlin / Technische Universität Berlin (TU), Physikalisch-Technische Bundesanstalt [Berlin] (PTB), Depts. of Surgery and Biomedical Engineering, University of Michigan, 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 Technical University Berlin

Subjects
Computer science, Calibration (statistics), 0206 medical engineering, Computational hemodynamics, 02 engineering and technology, Patient specific modeling, Synthetic data, lcsh:TA168, Stiffness, 03 medical and health sciences, 0302 clinical medicine, Data assimilation, Parameter estimation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Engineering (miscellaneous), Sequential estimation, Boundary conditions, Estimation theory, Applied Mathematics, Kalman filter, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computer Science Applications, Flow (mathematics), lcsh:Systems engineering, Modeling and Simulation, Netlist, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], lcsh:Mechanics of engineering. Applied mechanics, lcsh:TA349-359, Algorithm, Kalman filtering, 030217 neurology & neurosurgery, Research Article
Abstract

A major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A “Netlist” implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.

Published
2020

36. Efficacy of Almitrine in the Treatment of Hypoxemia in Sars-Cov-2 Acute Respiratory Distress Syndrome

Author

Arthur Le Gall, Ambre Tiepolo, Louis Morisson, Claire Mayeur, Romain Barthélémy, Alexandre Mebazaa, Samuel Gaugain, Pierre-Louis Blot, Benjamin G. Chousterman, Etienne Gayat, Marqueurs cardiovasculaires en situation de stress (MASCOT (UMR_S_942 / U942)), Institut National de la Santé et de la Recherche Médicale (INSERM)-Groupe Hospitalier Saint Louis - Lariboisière - Fernand Widal [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Université Sorbonne Paris Nord, Hôpital Lariboisière-Fernand-Widal [APHP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), 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), CCSD, Accord Elsevier, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Université Sorbonne Paris Nord, 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
Male, Almitrine, medicine.medical_treatment, [SDV]Life Sciences [q-bio], Respiratory System Agents, Critical Care and Intensive Care Medicine, Hypoxemia, Positive-Pressure Respiration, 0302 clinical medicine, 030202 anesthesiology, PEEP, Positive End Expiratory Pressure, FiO2, Fraction of Inspired Oxygen, Hypoxia, Respiratory Distress Syndrome, PvO2, Venous Oxygen Partial Pressure, ARDS, Acute Respiratory Distress Syndrome, Middle Aged, [SDV] Life Sciences [q-bio], Treatment Outcome, Anesthesia, PaO2, Arterial Oxygen Partial Pressure, Female, medicine.symptom, Coronavirus Infections, Cardiology and Cardiovascular Medicine, medicine.drug, Pulmonary and Respiratory Medicine, 2019-20 coronavirus outbreak, Coronavirus disease 2019 (COVID-19), ECMO, Extracorporeal Membrane Oxygenation, Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), Partial Pressure, Pneumonia, Viral, HPV, Hypoxic Pulmonary Vasoconstriction, Acute respiratory distress, Patient Positioning, Article, 03 medical and health sciences, Betacoronavirus, Extracorporeal Membrane Oxygenation, ICU, Intensive Care Unit, medicine, Extracorporeal membrane oxygenation, Prone Position, Humans, Pandemics, Aged, Retrospective Studies, iNO, Inhaled Nitric Oxid, business.industry, SARS-CoV-2, Oxygen Inhalation Therapy, RAP, Right Atrial Pressure, COVID-19, 030208 emergency & critical care medicine, medicine.disease, Respiration, Artificial, Oxygen, Pneumonia, Blood Gas Analysis, business, MV, Mechanical Ventilation
Abstract

International audience; No abstract available

Published
2020

37. Variational upscaling for modeling state of strain-dependent behavior and stress-induced crystallization in rubber-like materials

Author

Patrick Le Tallec, Julie Diani, 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), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), 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
Physics, Structural material, General Physics and Astronomy, 02 engineering and technology, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], 01 natural sciences, 010305 fluids & plasmas, law.invention, 020303 mechanical engineering & transports, Distribution (mathematics), 0203 mechanical engineering, Natural rubber, Mechanics of Materials, Position (vector), law, visual_art, 0103 physical sciences, visual_art.visual_art_medium, General Materials Science, Affine transformation, Boundary value problem, Statistical physics, Crystallization, Energy (signal processing)
Abstract

International audience; The purpose of this paper is to present a general upscaling strategy for deriving macroscopic constitutive laws for rubber-like materials from the knowledge of the network distribution and a mechanical description of the individual chains and of their free energy. The microscopic configuration is described by the position of the cross-links and is not obtained by an affine assumption but by minimizing the corresponding free energy on stochastic large representative volume elements with adequate boundary conditions. This general framework is then approximated by using a microsphere (directional) description of the network. It is presented in a global setting and is extended in order to handle situations with tube-like constraints and stress-induced crystallization.

Published
2020

38. Microstructural deformation observed by Mueller polarimetry during traction assay on myocardium samples

Author

Jean-Marc Allain, Angelo Pierangelo, Nicole Tueni, Jérémy Vizet, 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), Laboratoire de physique des interfaces et des couches minces [Palaiseau] (LPICM), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), 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
Materials science, Swine, Science, 0206 medical engineering, Polarimetry, 02 engineering and technology, 01 natural sciences, Article, Microscopic scale, 010309 optics, 0103 physical sciences, medicine, Animals, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Anisotropy, Perimysium, Multidisciplinary, Scattering, Myocardium, Polarization (waves), 020601 biomedical engineering, Tissues, medicine.anatomical_structure, Scanning Laser Polarimetry, Medicine, Biological Assay, Biophotonics, Stress, Mechanical, Affine transformation, Biological system, Biological physics, Coherence (physics)
Abstract

Despite recent advances, the myocardial microstructure remains imperfectly understood. In particular, bundles of cardiomyocytes have been observed but their three-dimensional organisation remains debated and the associated mechanical consequences unknown. One of the major challenges remains to perform multiscale observations of the mechanical response of the heart wall. For this purpose, in this study, a full-field Mueller polarimetric imager (MPI) was combined, for the first time, with an in-situ traction device. The full-field MPI enables to obtain a macroscopic image of the explored tissue, while providing detailed information about its structure on a microscopic scale. Specifically it exploits the polarization of the light to determine various biophysical quantities related to the tissue scattering or anisotropy properties. Combined with a mechanical traction device, the full-field MPI allows to measure the evolution of such biophysical quantities during tissue stretch. We observe separation lines on the tissue, which are associated with a fast variation of the fiber orientation, and have the size of cardiomyocyte bundles. Thus, we hypothesize that these lines are the perimysium, the collagen layer surrounding these bundles. During the mechanical traction, we observe two mechanisms simultaneously. On one hand, the azimuth shows an affine behavior, meaning the orientation changes according to the tissue deformation, and showing coherence in the tissue. On the other hand, the separation lines appear to be resistant in shear and compression but weak against traction, with a forming of gaps in the tissue.

Published
2020

39. A 3D personalized cardiac myocyte aggregate orientation model using MRI data-driven low-rank basis functions

Author

Johanna Stimm, Sebastian Kozerke, Stefano Buoso, Ezgi Berberoglu, Christian T. Stoeck, Martin Genet, Institute for Biomedical Engineering [ETH Zürich] (IBT), Universität Zürich [Zürich] = University of Zurich (UZH)-Department of Information Technology and Electrical Engineering [Zürich] (D-ITET), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich)- Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), 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
Proper generalized decomposition, Computer science, Swine, Heart Ventricles, Health Informatics, Basis function, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, 0302 clinical medicine, Data-driven parametric model, Singular value decomposition, Animals, Humans, Radiology, Nuclear Medicine and imaging, Myocytes, Cardiac, ComputingMilieux_MISCELLANEOUS, Computational model, Radiological and Ultrasound Technology, Cardiac cycle, 3D cardiac microstructure, Dimensionality reduction, Personalized modelling, Proper orthogonal decomposition, Cardiac electrophysiology, Orientation (computer vision), Cardiac myocyte, Computer Graphics and Computer-Aided Design, Magnetic Resonance Imaging, Diffusion Tensor Imaging, Parametric model, Computer Vision and Pattern Recognition, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Algorithm, 030217 neurology & neurosurgery
Abstract

Cardiac myocyte aggregate orientation has a strong impact on cardiac electrophysiology and mechanics. Studying the link between structural characteristics, strain, and stresses over the cardiac cycle and cardiac function requires a full volumetric representation of the microstructure. In this work, we exploit the structural similarity across hearts to extract a low-rank representation of predominant myocyte orientation in the left ventricle from high-resolution magnetic resonance ex-vivo cardiac diffusion tensor imaging (cDTI) in porcine hearts. We compared two reduction methods, Proper Generalized Decomposition combined with Singular Value Decomposition and Proper Orthogonal Decomposition. We demonstrate the existence of a general set of basis functions of aggregated myocyte orientation which defines a data-driven, personalizable, parametric model featuring higher flexibility than existing atlas and rule-based approaches. A more detailed representation of microstructure matching the available patient data can improve the accuracy of personalized computational models. Additionally, we approximate the myocyte orientation of one ex-vivo human heart and demonstrate the feasibility of transferring the basis functions to humans., Medical Image Analysis, 71, ISSN:1361-8415, ISSN:1361-8423

Published
2020

40. Computation of the exact discrete transparent boundary condition for 1D linear equations

Author

Fliss, Sonia, Imperiale, Sébastien, Tonnoir, Antoine, Propagation des Ondes : Étude Mathématique et Simulation (POEMS), 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)-Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS), 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), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), 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
Unbounded domain, Discrete transparent boundary conditions, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], periodic media
Abstract

In this work, we are interested in the construction of the exact transparent boundary conditions for a semi-discretized and fully discretized 1D linear PDE. The proposed method is quite general and is based on the computation of a family of canonical functions. Several examples and numerical results to illustrate the method are presented.

Published
2020

41. 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

42. Investigation of microstructure evolution and mechanical properties in cardiac tissue

Author

Angelo Pierangelo, Jean-Marc Allain, Martin Genet, N. Tueni, Jérémy Vizet, 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), 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), Laboratoire de physique des interfaces et des couches minces [Palaiseau] (LPICM), and École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Materials science, 0206 medical engineering, Biomedical Engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Bioengineering, 030229 sport sciences, 02 engineering and technology, General Medicine, Microstructure, 020601 biomedical engineering, Computer Science Applications, Human-Computer Interaction, 03 medical and health sciences, Matrix (mathematics), 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Composite material, ComputingMilieux_MISCELLANEOUS
Abstract

Cardiac tissue is made of cardiomyocytes, extra-cellular collagenous matrix, vasculature, etc., arranged in a highly hierarchical microstructure (Kanzaki et al. 2010). Despite the advances made in ...

Published
2020

43. Construction and convergence analysis of conservative second order local time discretisation for linear wave equations

Author

Juliette Chabassier, Sébastien Imperiale, Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Université Paris-Saclay, Modélisation et simulation de la propagation des ondes fondées sur des mesures expérimentales pour caractériser des milieux géophysiques et héliophysiques et concevoir des objets complexes (MAKUTU), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Polytechnique de Bordeaux (Bordeaux INP), 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
Discretization, 010103 numerical & computational mathematics, Time step, Mathematics Subject Classification.35L05, 65M12, 65M22, 65M60, 01 natural sciences, Applied mathematics, 0101 mathematics, [MATH]Mathematics [math], Mathematics, Numerical Analysis, Applied Mathematics, Domain decomposition methods, [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], Wave equation, 010101 applied mathematics, Wave equations, Computational Mathematics, Local implicit scheme, Test case, Modeling and Simulation, Local time, Norm (mathematics), Time discretisation, Local time stepping, Converge analysis, Analysis
Abstract

International audience; In this work we present and analyse a time discretisation strategy for linear wave equations t hat aims at using locally in space the most adapted time discretisation among a family of implicit or explicit centered second order schemes. The proposed family of schemes is adapted to domain decomposition methods such as the mortar element method. They correspond in that case to local implicit schemes and to local time stepping. We show that, if some regularity properties of the solution are satisfied and if the time step verifies a stability condition, then the family of proposed time discretisations provides, in a strong norm, second order space-time convergence. Finally, we provide 1D and 2D numerical illustrations that confirm the obtained theoretical results and we compare our approach on 1D test cases to other existing local time stepping strategies for wave equations.

Published
2020

44. Asymptotic modelling of Skin-effects in coaxial cables

Author

Sébastien Imperiale, Geoffrey Beck, Patrick Joly, 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), 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), Propagation des Ondes : Étude Mathématique et Simulation (POEMS), 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)-Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-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), 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), Propagation des Ondes : Etude Mathématique et Simulation (POEMS), 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, 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)-Inria Saclay - Ile de France, and École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)

Subjects
Physics, Work (thermodynamics), Asymptotic analysis, Partial differential equation, Numerical analysis, Mathematical analysis, 010103 numerical & computational mathematics, 01 natural sciences, Magnetic field, 010101 applied mathematics, symbols.namesake, [SPI.ELEC]Engineering Sciences [physics]/Electromagnetism, Maxwell's equations, symbols, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Coaxial, Reconstruction procedure
Abstract

International audience; In this work we tackle the modeling of non-perfectly conducting thin coaxial cables. From the non-dimensionnalised 3D Maxwells equations, we derive, by asymptotic analysis with respect to the (small) transverse dimension of the cable, a simplified effective 1D model and an effective reconstruction procedure of the electric and magnetic fields. The derived effective model involves a fractional time derivatives that accounts for the so-called skin effects in highly conducting regions.

Published
2020

45. Combined Estimation of Material Law and Unloaded Configuration (Application to Pulmonary Poro-Mechanics)

Author

Manoochehrtayebi, Mahdi, Département de Mécanique de l'École polytechnique (X-DEP-MECA), École polytechnique (X), 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), Ecole Polytechnique, Martin GENET, 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
[SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], ComputingMilieux_MISCELLANEOUS, [SPI.MECA.GEME]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanical engineering [physics.class-ph]
Abstract

International audience

Published
2020

46. Estimation of patient-specific mechanical parameters in pulmonary diseases

Author

Patte, Cécile, Brillet, Pierre-Yves, Fetita, Catalin, Gille, Thomas, Bernaudin, Jean-François, Nunes, Hilario, Chapelle, Dominique, Genet, Martin, 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), Hôpital Avicenne [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), Institut National de la Santé et de la Recherche Médicale (INSERM), Département Advanced Research And Techniques For Multidimensional Imaging Systems (ARTEMIS), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), Institut Polytechnique de Paris (IP Paris), 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), Université de Paris - UFR Médecine Paris Centre [Santé] (UP Médecine Paris Centre), Université de Paris (UP), 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), Département Advanced Research And Techniques For Multidimensional Imaging Systems (TSP - ARTEMIS), UFR Médecine [Santé] - Université Paris Cité (UFR Médecine UPCité), Université Paris Cité (UPCité), Patte, Cécile, and Université Paris Cité - UFR Médecine [Santé] (UPCité UFR Médecine)

Subjects
[SPI.MECA.BIOM] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Pulmonary mechanics, Finite Element Method, Poromechanics, Modeling, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Estimation, ComputingMilieux_MISCELLANEOUS, Simulation
Abstract

International audience

Published
2020

47. Intrinsic regulation of muscle contraction

Author

François Kimmig, Matthieu Caruel, Chapelle, D., 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), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Caruel, Matthieu, 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
[PHYS.MECA.SOLID] Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], length-dependence effects, contraction regulation, [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], muscle modelling, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2020

48. Estimation for dynamical systems using a population-based Kalman filter - Applications to pharmacokinetics models

Author

Collin, Annabelle, Prague, Mélanie, Moireau, Philippe, 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), Statistics In System biology and Translational Medicine (SISTM), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)- Bordeaux population health (BPH), Université de Bordeaux (UB)-Institut de Santé Publique, d'Épidémiologie et de Développement (ISPED)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Bordeaux (UB)-Institut de Santé Publique, d'Épidémiologie et de Développement (ISPED)-Institut National de la Santé et de la Recherche Médicale (INSERM), and Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Santé Publique, d'Épidémiologie et de Développement (ISPED)-Université de Bordeaux (UB)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Santé Publique, d'Épidémiologie et de Développement (ISPED)-Université de Bordeaux (UB)

Subjects
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [SDV.SP.PHARMA]Life Sciences [q-bio]/Pharmaceutical sciences/Pharmacology, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

Many methods exist to identify parameters of dynamical systems. Unfortunately, in addition to the classical measurement noise and under-sampling drawbacks, mean and variance priors of the estimated parameters can be very vague. These difficulties can lead the estimation procedure to underfitting. In clinical studies, a circumvention consists in using the fact that multiple independent patients are observed as proposed by nonlinear mixed-effect models. However, these very effective approaches can turn to be time-consuming or even intractable when the model complexity increases. Here, we propose an alternative strategy of controlled complexity. We first formulate a population least square estimator and its associated a Kalman based filter, hence defining a robust large population sequential estimator. Then, to reduce and control the computational complexity, we propose a reduced-order version of this population Kalman filter based on a clustering technique applied to the observations. Using simulated pharmacokinetics data and the theophylline pharmacokinetics data, we compare the proposed approach with literature methods. We show that using the population filter improves the estimation performance compared to the classical and fast patient-by-patient Kalman filter and leads to estimation results comparable to state-of-the-art population-based approaches. Then, the reduced-order version allows to drastically reduce the computational time for equivalent estimation and prediction.

Published
2020

49. Monitoring of cardiovascular physiology augmented by a patient-specific biomechanical model during general anesthesia. A proof of concept study

Author

Le Gall, Arthur, Vallée, Fabrice, Pushparajah, Kuberan, Hussain, Tarique, Mebazaa, Alexandre, Chapelle, Dominique, Gayat, Étienne, Chabiniok, Radomír, Service d'Anesthésie-Réanimation [AP-HP Hôpitaux Saint-Louis Lariboisière], Université de Paris-Assistance publique - Hôpitaux de Paris (AP-HP) (APHP)-Hôpital Lariboisière, 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-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, 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, University of Texas Southwestern Medical Center [Dallas], School of Biomedical Engineering & Imaging Sciences [London], Department of Mathematics [Prague] (FNSPE), Czech Technical University in Prague (CTU), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital Lariboisière-Fernand-Widal [APHP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Université de Paris (UP), 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, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Université Paris Cité (UPCité), 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 ANAESTASSIST

Subjects
Male, Blood Pressure, Vascular Medicine, Biochemistry, Stiffness, Norepinephrine, Catecholamines, Medicine and Health Sciences, Vasoconstrictor Agents, Prospective Studies, Amines, Cardiac Output, Aorta, Organic Compounds, Simulation and Modeling, Models, Cardiovascular, Heart, Neurochemistry, Neurotransmitters, Middle Aged, Systolic Pressure, Biomechanical Phenomena, Chemistry, Physical Sciences, Medicine, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Female, Anatomy, Hypotension, Algorithms, Research Article, Biogenic Amines, Science, Materials Science, Material Properties, Bioenergetics, Anesthesia, General, Research and Analysis Methods, Proof of Concept Study, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Mechanical Properties, Humans, Arterial Pressure, Organic Chemistry, Hemodynamic Monitoring, Chemical Compounds, Biology and Life Sciences, Stroke Volume, Hormones, Cardiovascular Anatomy, Blood Vessels, Neuroscience
Abstract

International audience; During general anesthesia (GA), direct analysis of arterial pressure or aortic flow waveforms may be inconclusive in complex situations. Patient-specific biomechanical models, based on data obtained during GA and capable to perform fast simulations of cardiac cycles, have the potential to augment hemodynamic monitoring. Such models allow to simulate Pressure-Volume (PV) loops and estimate functional indicators of cardiovascular (CV) system, e.g. ventricular-arterial coupling (Vva), cardiac efficiency (CE) or myocardial contractility, evolving throughout GA. In this prospective observational study, we created patient-specific biomechanical models of heart and vasculature of a reduced geometric complexity for n=45 patients undergoing GA, while using transthoracic echocardiography and aortic pressure and flow signals acquired in the beginning of GA (baseline condition). If intraoperative hypotension (IOH) appeared, diluted norepinephrine (NOR) was administered and the model readjusted according to the measured aortic pressure and flow signals. Such patients were a posteriori assigned into a so-called hypotensive group. The accuracy of simulated mean aortic pressure (MAP) and stroke volume (SV) at baseline were in accordance with the guidelines for the validation of new devices or reference measurement methods in all patients. After NOR administration in the hypotensive group, the percentage of concordance with 10% exclusion zone between measurement and simulation was > 95% for both MAP and SV. The modeling results showed a decreased Vva (0.64±0.37 vs 0.88±0.43; p=0.039) and an increased CE (0.8±0.1 vs 0.73±0.11; p=0.042) in hypotensive vs normotensive patients. Furthermore, Vva increased by 92±101%, CE decreased by 13±11% (p < 0.001 for both) and contractility increased by 14±11% (p = 0.002) in the hypotensive group post-NOR administration. In this work we demonstrated the application of fast-running patient-specific biophysical models to estimate PV loops and functional indicators of CV system using clinical data available during GA. The work paves the way for model-augmented hemodynamic monitoring at operating theatres or intensive care units to enhance the information on patient-specific physiology.

Published
2020

50. Construction and analysis of fourth order, energy consistent, family of explicit time discretizations for dissipative linear wave equations

Author

Julien Diaz, Juliette Chabassier, Sébastien Imperiale, Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Université 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
Numerical Analysis, Helmholtz equation, Applied Mathematics, Dissipative linear wave equation, Inverse, 010103 numerical & computational mathematics, [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], Space (mathematics), Wave equation, 01 natural sciences, Stability (probability), Energy analysis, 010101 applied mathematics, Computational Mathematics, Matrix (mathematics), Modeling and Simulation, Convergence (routing), Dissipative system, Applied mathematics, High order time discretisation, 0101 mathematics, 1991 Mathematics Subject Classification. 00A71, 35L05, 85A20, 33C55, 65M60, Analysis, Mathematics
Abstract

International audience; This paper deals with the construction of a family of fourth order, energy consistent, explicit time discretizations for dissipative linear wave equations. The schemes are obtained by replacing the inversion of a matrix, that comes naturally after using the technique of the Modified Equation on the second order Leap Frog scheme applied to dissipative linear wave equations, by explicit approximations of its inverse. The stability of the schemes are studied using an energy analysis and a convergence analysis is carried out. Numerical results in 1D illustrate the space/time convergence properties of the schemes and their efficiency is compared to more classical time discretizations.

Published
2020

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