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1. Solving 2D linear isotropic elastodynamics by means of scalar potentials: a new challenge for finite elements

Author

Patrick Joly, Jerónimo Rodríguez, Sébastien Imperiale, Jorge Martínez, 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 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, 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), Universidade de Santiago de Compostela, 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 ), Propagation des Ondes : Étude Mathématique et Simulation ( POEMS ), 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 ( Univ. Paris-Saclay, ENSTA ParisTech ) -École Nationale Supérieure de Techniques Avancées ( Univ. Paris-Saclay, ENSTA ParisTech ) -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
Numerical Analysis, Applied Mathematics, Isotropy, Scalar (mathematics), Mathematical analysis, General Engineering, 010103 numerical & computational mathematics, [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], 01 natural sciences, Finite element method, Theoretical Computer Science, 010101 applied mathematics, Computational Mathematics, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], Computational Theory and Mathematics, Displacement field, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, Time domain, 0101 mathematics, Scalar field, Helmholtz decomposition, Software, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

International audience; In this work we present a method for the computation of numerical solutions of 2D homogeneous isotropic elastodynamics equations by solving scalar wave equations. These equations act on the potentials of a Helmholtz decomposition of the displacement field and are decoupled inside the propagation domain. We detail how these equations are coupled at the boundary depending on the nature of the boundary condition satisfied by the displacement field. After presenting the case of rigid boundary conditions, that presents no specific difficulty, we tackle the challenging case of free surface boundary conditions that presents severe stability issues if a straightforward approach is used. We introduce an adequate functional framework as well as a time domain mixed formulation to circumvent these issues. Numerical results confirm the stability of the proposed approach.

Published
2018
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2. Finite Strain Formulation of the Discrete Equilibrium Gap Principle: I-Mechanically Consistent Regularization for Large Motion Tracking

Author

Genet, Martin, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Inverse problems, Finite element method, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Motion tracking Mechanical regularization Equilibrium gap principle Finite element method Inverse problems, Mechanical regularization, [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], Motion tracking, Equilibrium gap principle
Abstract

The equilibrium gap principle offers a good trade-off between robustness & accuracy for regularizing motion tracking, as it simply enforces that the tracked motion corresponds to a body deforming under arbitrary loadings. This paper introduces an extension of the equilibrium gap principle in the large deformation setting, a novel regularization term to control surface tractions, both in the context of finite element motion tracking, and an inverse problem consistent reformulation of the tracking problem. Tracking performance of the proposed method, with displacement resolution down to the pixel size, is demonstrated on synthetic images representing various motions with various signal-to-noise ratios.

Published
2023

3. Numerical analysis of an incompressible soft material poromechanics model using T-coercivity

Author

Barré, Mathieu, Grandmont, Céline, Moireau, Philippe, 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), 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 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 Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), 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 Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Département de Mathématique [Bruxelles] (ULB), Faculté des Sciences [Bruxelles] (ULB), Université libre de Bruxelles (ULB)-Université libre de Bruxelles (ULB), and Sorbonne Université (SU)

Subjects
inf-sup stability, [PHYS.MECA.MEMA]Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph], mixture theory, energy preserving scheme, total discretization, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], incompressible limit
Abstract

This article is devoted to the numerical analysis of the full discretization of a generalized poromechanical model resulting from the linearization of an initial model fitted to soft tissue perfusion. Our strategy here is based on the use of energy-based estimates and T-coercivity methods, so that the numerical analysis benefits from the essential tools used in the existence analysis of the continuous-time and continuous-space formulation. In particular, our T-coercivity strategy allows us to obtain the necessary inf-sup condition for the global system from the inf-sup condition restricted to a subsystem having the same structure as the Stokes problem. This allows us to prove that any finite element pair adapted to the Stokes problem is also suitable for this global poromechanical model regardless of porosity and permeability, generalizing previous results from the literature studying this model.

Published
2023

4. Mortensen Observer for a class of variational inequalities - Lost equivalence with stochastic filtering approaches

Author

Chaintron, Louis-Pierre, Mateos González, Álvaro, Mertz, Laurent, Moireau, Philippe, Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS-PSL), 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), 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), New York University [Shanghai], NYU System (NYU), and City University of Hong Kong [Hong Kong] (CUHK)

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

We address the problem of deterministic sequential estimation for a nonsmooth dynamics governed by a variational inequality. An example of such dynamics is the Skorokhod problem with a reflective boundary condition. For smooth dynamics, Mortensen introduced in 1968 a nonlinear estimator based on likelihood maximisation. Then, starting with Hijab in 1980, several authors established a connection between Mortensen's approach and the vanishing noise limit of the robust form of the so-called Zakai equation. In this paper, we investigate to what extent these methods can be developed for dynamics governed by a variational inequality.On the one hand, we address this problem by relaxing the inequality constraint by penalization: this yields an approximate Mortensen estimator relying on an approximating smooth dynamics. We verify that the equivalence between the deterministic and stochastic approaches holds through a vanishing noise limit.On the other hand, inspired by the smooth dynamics approach, we study the vanishing viscosity limit of the Hamilton-Jacobi equation satisfied by the Hopf-Cole transform of the solution of the robust Zakai equation. In contrast to the case of smooth dynamics, the zero-noise limit of the robust form of the Zakai equation cannot be understood in our case from the Bellman equation on the value function arising in Mortensen's procedure. This unveils a violation of equivalence for dynamics governed by a variational inequality between the Mortensen approach and the low noise stochastic approach for nonsmooth dynamics.

Published
2023

5. A biomechanics-based parametrized cardiac end-diastolic pressure–volume relationship for accurate patient-specific calibration and estimation

Author

Chapelle, Dominique, 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 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), Service d'ophthalmologie [CHU Lariboisière], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital Lariboisière-Fernand-Widal [APHP], and Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Université Paris Cité (UPCité)

Subjects
cardiac passive behavior, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, cardiac biomechanical model, patient-specific modeling, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], EDPVR
Abstract

International audience; A simple power law has been proposed in the pioneering work of Klotz et al. (Am J Physiol Heart Circ Physiol 291(1):H403–H412, 2006) to approximate the end-diastolic pressure–volume relationship of the left cardiac ventricle, with limited inter-individual variability provided the volume is adequately normalized. Nevertheless, we use here a biomechanical model to investigate the sources of the remaining data dispersion observed in the normalized space, and we show that variations of the parameters of the biomechanical model realistically account for a substantial part of this dispersion. We therefore propose an alternative law based on the biomechanical model that embeds some intrinsic physical parameters, which directly enables personalization capabilities, and paves the way for related estimation approaches.

Published
2023
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6. Modeling acto-myosin interaction: beyond the Huxley–Hill framework

Author

Chaintron, Louis-Pierre, Caruel, Matthieu, Kimmig, François, Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS-PSL), 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), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Muscle contraction, Thermodynamics, Jump-diffusion process, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Molecular motors, Poisson random measures, Applied mathematics, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Applied probability
Abstract

Contractile force in muscle tissue is produced by the interaction of myosin molecular motors that bind and pull on specific sites located on surrounding actin filaments. The classical framework set by the landmark works of A.F. Huxley and T.L. Hill to model this active system is build on the central assumption that thermal fluctuations of a given myosin motor are sufficiently small so that it cannot interact with more than one binding site at any time. In this paper we present the physiological and mathematical limitations of this approach to motivate a new formulation that circumvent them without resorting to the more complex multi-site model paradigm. The acto-myosin system is now described as a Markov process combining Langevin driftdiffusion and Poisson jumps dynamics. We show that the corresponding system of Stochastic Differential Equation is well-posed and derive its Partial Differential Equation analog in order to obtain the thermodynamic balance laws. We finally show that by applying standard elimination procedures, a modified version of the original Huxley-Hill framework can be obtained as a reduced version of our model. Theoretical results are supported by numerical simulations where the model outputs are compared to benchmark experimental data.

Published
2023

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

Author

Martin Genet, Jérôme Diaz, Dominique Chapelle, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Computational Theory and Mathematics, Applied Mathematics, Modeling and Simulation, Computational mechanics, Continuum mechanics on manifold, Reduced-order modeling, Biomedical Engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Cardiac modeling, Molecular Biology, Software
Abstract

Biomechanical modeling and simulation is expected to play a significant role in the development of the next generation tools in many fields of medicine. However, full-fledged finite element models of complex organs such as the heart can be computationally very expensive, thus limiting their practical usability. Therefore, reduced models are much valuable to be used, e.g., for pre-calibration of full-fledged models, fast predictions, real-time applications, etc.. In this work, focused on the left ventricle, we develop a reduced model by defining reduced geometry & kinematics while keeping general motion and behavior laws, allowing to derive a reduced model where all variables & parameters have a strong physical meaning. More specifically, we propose a reduced ventricular model based on cylindrical geometry & kinematics, which allows to describe the myofiber orientation through the ventricular wall and to represent contraction patterns such as ventricular twist, two important features of ventricular mechanics. Our model is based on the original cylindrical model of [Guccione, McCulloch, & Waldman 1991; Guccione, Waldman, & McCulloch 1993], albeit with multiple differences: we propose a fully dynamical formulation, integrated into an open-loop lumped circulation model, and based on a material behavior that incorporates a fine description of contraction mechanisms; moreover, the issue of the cylinder closure has been completely reformulated; our numerical approach is novel as well, with consistent spatial (finite element) and time discretizations. Finally, we analyse the sensitivity of the model response to various numerical and physical parameters, and study its physiological response.

Published
2023
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8. De la décomposition de domaine à la réduction de modèle pour les grandes structures non linéaires

Author

Bertrand Leturcq, Patrick Le Tallec, Laboratoire de Mécanique Systèmes et Simulation (LM2S), Service d'Etudes Mécaniques et Thermiques (SEMT), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Département de Modélisation des Systèmes et Structures (DM2S), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-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 Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
[SPI]Engineering Sciences [physics], Réduction de modèle, Mechanics of Materials, Model reduction, Assemblage de combustible, fluage, General Materials Science, Domain decomposition, Décomposition de domaines, Nuclear fuel assemblies, creep, contact
Abstract

International audience; The numerical simulation of multiscale and multiphysics problems requires efficient tools for spatial localization and model reduction. A general strategy combining Domain Decomposition and Nonuniform Transformation Field Analysis (NTFA) is proposed herein for the simulation of nuclear fuel assembliesat the scale of a full nuclear reactor. The model at subdomain level solves the full elastic problem but witha reduced nonlinear loading, based on simplified boundary conditions, reduced creep flow rules, projected sign preserving contact conditions, and a NTFA like reduced friction law to get the evolution of each slipping mode. With this loading reduction, the local solution can be explicitly obtained from a small set of precomputed elementary elastic solutions. The numerical tests indicate that considerable cost reduction (a factor of 50 to 1000) can be achieved while preserving engineering accuracy; . La simulation numérique de problèmes multi-échelles et multi-physiques nécessite des outils performants de localisation spatiale et de réduction de modèle. Une stratégie générale combinant la décomposition de domaine et l’analyse de champ de transformation non uniforme (NTFA) est proposée ici pour la simulation d’assemblages de combustible nucléaire à l’échelle d’un réacteur nucléaire complet. Le modèle au niveau du sous-domaine résout le problème élastique complet mais avec un chargement non linéaire réduit, basé sur des conditions aux limites simplifiées, des règles d’écoulement de fluage réduites, des conditions de contact préservant le signe projeté et une loi de frottement réduit de type NTFA pour obtenir l’évolution de chaque mode de glissement. Avec cette réduction de chargement, la solution locale peut être obtenue explicitement à partir d’un petit ensemble de solutions élastiques élémentaires précalculées. Les tests numériques indiquent qu’une réduction considérable des coûts (un facteur de 50 à 1000) peut être obtenue tout en préservant la précision du calcul

Published
2023
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9. Acoustic and gravity waves in the ocean: a new derivation of a linear model from the compressible Euler equation

Author

Dubois, Juliette, Imperiale, Sébastien, Mangeney, Anne, Bouchut, François, Sainte-Marie, Jacques, Dubois, Juliette, Numerical Analysis, Geophysics and Ecology (ANGE), 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 Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), 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 de Physique du Globe de Paris (IPG Paris), Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, and This work was supported by grants from Région Ile-de-France and the project ERC-CG-2013-PE10-617472 SLIDEQUAKES

Subjects
[SDU.OCEAN]Sciences of the Universe [physics]/Ocean, Atmosphere, [SDU.OCEAN] Sciences of the Universe [physics]/Ocean, Atmosphere, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

In this paper we construct an accurate linear model describing the propagation of both acoustic and gravity waves in water. This original model is obtainedby the linearization of the compressible Euler equations, written in Lagrangian coordinates. The system is studied in the isentropic case, with a free surface, an arbitrary bathymetry, and vertical variations of the background temperature and density. We show that our model is an extension of some models from the litterature to the case of a non-barotropic fluid with a variable sound speed.Other models from the literature are recovered from our model through two asymptotic analysis, one for the incompressible regime and one for the acoustic regime. We also propose a method to write the model in Eulerian coordinates. Our model includes many physical properties, such as the existence of internal gravity waves or the variation of the sound speed with depth.

Published
2023

10. Measure of the hygroscopic expansion of human dentin

Author

Gharbi, Hakim, Wenlong, Wang, Giraudet, Chloé, Allain, Jean-Marc, Vennat, Elsa, 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), Laboratoire de Mécanique Paris-Saclay (LMPS), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay), 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 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), Unité de Recherche Biomatériaux Innovants et Interfaces (URB2i (URP_4462)), Université Paris Cité (UPCité)-Université Sorbonne Paris Nord, This work has benefited from the financial support of the LabeX LaSIPS (ANR-10-LABX-0040-LaSIPS) managed by the French National Research Agency under the 'Investissements d'avenir' program (n°ANR-11-IDEX-0003-02)., and ANR-11-IDEX-0003,IPS,Idex Paris-Saclay(2011)

Subjects
DIC, Dentin, humidity, microscopy, FOS: Physical sciences, Medical Physics (physics.med-ph), strain measurement, mechanical properties, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Physics - Medical Physics, compression
Abstract

Background: Direct dental restoration implies a drying of the dentin substrate. This drying may induce significant strain in the dentin, affecting the bonding efficiency of the restoration. Objective: We measure the dilatation of dentine under changes of relative humidity as well as the impact of humidity on dentin elastic properties. This investigates the role of relative humidity variation during dental surgery on restoration lifetime. Methods: We have coupled an environmental chamber to control both temperature and humidity on the sample, with an optical microscope to measure precisely the strain on the sample surface, after a quantification of the measurement noise. This set-up is used on carefully prepared samples placed on a compression device to measure the elastic parameters. Results: Dentin dilates when the relative humidity increases, with a coefficient of hygroscopic expansion of typically 6.10-3 %.(%RH)-1. This dilatation occurs in about ten minutes. Young modulus and Poisson's ratio are not modified by the variation of relative humidity. Conclusions: Hygroscopic expansion is an order of magnitude larger than thermal expansion during dental surgery: around 0.3% with respect to 0.03%. These levels are low with respect to dental rupture, but may induce a significant decrease of the life-expectancy of a restoration.

Published
2022

11. 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
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12. T-coercivité et problèmes mixtes

Author

Barré, Mathieu, Ciarlet, Patrick, 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), 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 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), and École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

Classically, the well-posedness of variational formulations of mixed linear problems is achieved through the inf-sup condition. In this note, we propose an alternative framework to study such problems by using the T-coercivity approach. This is a constructive approach that leads to the design of suitable approximations in a simple way. In general, the derivation of the uniform discrete inf-sup condition for the approximate problems stems straightforwardly from the study of the original problem. To support our view, we solve a series of classical mixed problems with the T-coercivity approach. Among others, the celebrated Fortin Lemma appears naturally in the numerical analysis of the approximate problems.; Classiquement, le caractère bien posé des formulations variationnelles de problèmes linéaires mixtes est obtenu à l'aide de la condition inf-sup. Dans cette note, nous proposons un cadre alternatif pour étudier de tels problèmes en utilisant la notion de T-coercivité. Il s'agit d'une approche constructive qui permet en outre de concevoir simplement des approximations numériques adaptées car la dérivation de la condition inf-sup discrète uniforme découle en général directement de l'étude du problème continu. Pour appuyer notre propos, nous résolvons une série de problèmes mixtes classiques grâce à la notion de Tcoercivité. Entre autres, le lemme de Fortin apparaît naturellement dans l'analyse numérique des problèmes discrets.

Published
2022

13. Varying thin filament activation in the framework of the Huxley'57 model

Author

François Kimmig, Matthieu Caruel, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Modélisation et Simulation Multi-Echelle (MSME), and Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel

Subjects
Sarcomeres, Applied Mathematics, Biomedical Engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Cardiac modeling, Actins, Actin Cytoskeleton, Computational Theory and Mathematics, Thick and thin filament activation, Modeling and Simulation, Huxley'57 model, Calcium, Mathematical modeling, Molecular Biology, Software, Muscle Contraction
Abstract

International audience; Muscle contraction is triggered by the activation of the actin sites of the thin filament by calcium ions. It results that the thin filament activation level varies over time. Moreover, this activation process is also used as a regulation mechanism of the developed force. Our objective is to build a model of varying actin site activation level within the classical Huxley'57 two-state framework. This new model is obtained as an enhancement of a previously proposed formulation of the varying thick filament activation within the same framework [1]. We assume that the state of an actin site depends on whether it is activated and whether it forms a cross-bridge with the associated myosin head, which results in four possible states. The transitions between the actin site states are controlled by the global actin sites activation level and the dynamics of these transitions is coupled with the attachment-detachment process. A preliminary calibration of the model with experimental twitch contraction data obtained at varying sarcomere lengths is performed.

Published
2022
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14. A generic numerical solver for modeling the influence of stress conditions on guided wave propagation for SHM applications

Author

Dalmora, Andre, Imperiale, Alexandre, Imperiale, Sébastien, Moireau, Philippe, 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, Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria), 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), European Project: 860104,H2020-MSCA-ITN-2019,GW4SHM, 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 Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
EOCs, 3D Shell Elements, Spectral Finite Elements, Prestresses, [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], Wave Propagation, Guided Waves, Numerical Simulation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Struc- tural Health Monitoring
Abstract

In leading-edge industrial applications, assessing structure integrity is an important aspect of safety requirements. Structural Health Monitoring (SHM) proposes to use sensors and signal processing units in situ. One of the most attractive SHM techniques relies on ultrasonic guided waves. Modeling and simulation can be helpful tools for the design or the reliability assessment of SHM solutions. Currently available models developed for that purpose do not take into account effects of operational conditions such as internal stresses. These conditions can change wave propagation and therefore affect the interpretation of recorded signals. The objective of this work is to propose a model that fills this gap, and to derive corresponding numerical methods for elastic wave propagation in an arbitrarily deformed medium. Any hyperelastic constitutive law can be considered. As the structures considered are usually thin, we avoid shear-locking by using a shell formulation to solve the quasi-static problem representing the effects of structure loading. The computed displacement is then fed into a spectral elements method (SFEM) kernel to solve the time-domain linearized 3D elastodynamics problem representing the wave propagation. We validate our model against experimental data in the literature for an isotropic aluminium plate under tensile forces. Additionally, we apply these numerical procedures to a realistic bending experiment of a steel pipe. These validations steps show that our generic approach is able to capture the effects of stresses on ultrasonic guided wave propagation such as changes in wave velocity and induced anisotropy.

Published
2022
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15. Some contributions to cardiac and pulmonary biomechanical modeling, simulation & estimation

Author

Genet, Martin, 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, and Patrick Le Tallec

Subjects
Growth & remodeling, Cœur, Modeling & Simulation, Biomécanique, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Heart, Motion tracking, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Poumon, Suivi de mouvement, Biomechanics, Modélisation & Simulation, Lung, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Croissance & remodelage
Published
2022

16. A new reduced order model to represent the creep induced fuel assembly bow in PWR cores

Author

Leturcq, Bertrand, Le Tallec, Patrick, Pascal, Serge, Fandeur, Olivier, Lamorte, Nicolas, Laboratoire de Mécanique Systèmes et Simulation (LM2S), Service d'Etudes Mécaniques et Thermiques (SEMT), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Département de Modélisation des Systèmes et Structures (DM2S), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, 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), Laboratoire Technologie d'Assemblage (LTA), FRAMATOME, 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 Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Nuclear and High Energy Physics, Mechanical Engineering, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], [PHYS.MECA.MSMECA]Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph], creep, [SPI]Engineering Sciences [physics], [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph], Nuclear Energy and Engineering, PWR assembly bow, model reduction, General Materials Science, PWR assembly bow model reduction NTFA creep, Safety, Risk, Reliability and Quality, NTFA, Waste Management and Disposal, ComputingMilieux_MISCELLANEOUS
Abstract

International audience; Progressive deformation of nuclear fuel assemblies that occurs during a succession of irradiation cycles within PWR is at the core of numerous interactions. Progresses in the study of this phenomenon resulted from more and more complex models. To date, in the more advanced models, a mechanical model is combined to a hydraulic model of the core to address the fluid-structure interaction. A complete mechanical model of the core is generally built with a simplified finite element representation of each assembly using beam or simpler elements. The simplifying approach is required due to the high complexity of the multi-body multi-physics calculations. In order to improve the representativeness of the core model without penalizing the computational cost of the coupled simulations, a new method of model order reduction is proposed. It is specially adapted to this context and borrows the concepts of NTFA non-linear homogenization. The theoretical foundations and the application to a slender structure are presented. First, the method is validated on a simple case with spatially homogeneous characteristics. Finally, the case of the creep response of a fuel assembly under realistic heterogeneous loads is demonstrated.

Published
2022
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17. Modélisation biomécanique cardiovasculaire personnalisée pour améliorer l'interprétation des données cliniques et aider à planifier les interventions chez les patients atteints de cardiopathie congénitale

Author

Gusseva, Maria, 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, Dominique Chapelle, and Radomir Chabiniok

Subjects
Ventricular overload, Time-Synchronization of clinical data, [SPI.OTHER]Engineering Sciences [physics]/Other, [SDV.OT]Life Sciences [q-bio]/Other [q-bio.OT], [PHYS.PHYS]Physics [physics]/Physics [physics], Contractilité du myocarde, Médecine personnalisée, Valvular heart disease, Personalized medicine, Surcharge ventriculaire, Cardiopathie valvulaire, Synchronisation temporelle des données cliniques, Modélisation biomécanique, Biomechanical modeling, Myocardial contractility, Cardiopathie congénitale, Congenital heart disease
Abstract

This PhD thesis is an interdisciplinary research that deals with applied biomechanical modeling of the cardiovascular system in patients with congenital heart diseases . The aim is to explore the potential of biomechanical modeling to assist in clinical decision-making.First, we explored the ability of a previously developed biomechanical model to augment the interpretation of clinical data for patients with tetralogy of Fallot after repair (rTOF) prior to and after pulmonary valve replacement (PVR). Patient-specific models of the right ventricle (RV) and pulmonary circulation were built for 20 subjects pre- and post-PVR using cardiovascular magnetic resonance (CMR) and pressure catheter data. These models were subjected to the effects of pulmonary valve (PV) regurgitation and/or RV outflow tract (RVOT) obstruction. The models provided patient-specific indices of myocardial contractility pre- and post-PVR. The results showed a decrease of contractility in all patients post-PVR. Patients with predominantly RVOT obstruction experienced a higher level of contractility decrease whereas ceasing the regurgitation itself did not lead to a significant reduction in contractility. After this detailed study of pathophysiology of the overloaded RVs pre- and post-PVR, we explored the ability of the model to predict the response of ventricular mechanics when progressively decreasing the afterload of the RVs in patients with rTOF. Pre-PVR patient-specific models were used and cessation of PV regurgitation and progressive decrease of RVOT resistance were assumed. The resulting in silico relationships between the contractility and RVOT resistance post-PVR appeared to be linear, and consistent with that given by the patient-specific post-PVR models.For patients with single-ventricle hearts undergoing CMR combined with a pressure catheter (as part of planning for complex surgery), the model was used to synchronize in time the catheter-pressure data and the ventricular volumes obtained by CMR. This model-assisted time-synchronization produces high quality P-V loops that yield more accurate indices of myocardial energetics (maximum value of time-varying elastance (E_max) and stroke work) and hence could be used to ameliorate the clinical interpretation.Finally, we compared the indices of E_max and maximum time derivative of ventricular pressure, max(dP/dt), when obtained directly from the clinical measurements vs. model-derived contractility and max(dP/dt). All data- and model-derived indices showed a good agreement. In addition, a potential application of model-derived max⁡(dP/dt) as a model-based data filter was emphasized.Overall, this thesis demonstrated (1) an ability of biomechanical modeling to provide additional mechanical indices of ventricular function and their evolution under different loading conditions, which has the potential to contribute into the planning of optimal therapy; (2) an application of the model to provide robust clinical data processing of a variety of data acquisition protocols; and (3) a correspondence of model-derived indices with clinically accepted surrogate measures of contractility. In conclusion, this thesis showed that biomechanical modeling could be deployed in a clinical environment to address various types of problems towards the delivery of personalized healthcare solutions.; Cette thèse de doctorat est une recherche interdisciplinaire qui porte sur la modélisation biomécanique appliquée du système cardiovasculaire chez les patients atteints de cardiopathies congénitales. L'objectif est d'explorer le potentiel de la modélisation biomécanique pour aider à la prise de décision clinique.Tout d'abord, nous avons exploré la capacité d'un modèle biomécanique précédemment développé à améliorer l'interprétation des données cliniques pour les patients atteints de tétralogie de Fallot après réparation (TOFr) avant et après le remplacement de la valve pulmonaire (RVP). Des modèles personnalisés du ventricule droit (VD) et de la circulation pulmonaire ont été construits pour 20 sujets avant et après le RVP à l'aide de données obtenues par résonance magnétique cardiovasculaire (RMC) et par cathéter de pression. Ces modèles ont été soumis aux effets de la régurgitation de la valve pulmonaire (VP) et/ou de l'obstruction du canal de sortie du VD (RVOT). Les modèles ont fourni des indices de contractilité myocardique personnalisés avant et après la RPV. Les résultats ont montré une diminution de la contractilité chez tous les patients après la RVP. Les patients présentant une obstruction prédominante de l'RVOT ont connu une diminution plus importante de la contractilité, alors que l'arrêt de la régurgitation elle-même n'a pas entraîné de réduction significative de la contractilité. Après cette étude détaillée de la pathophysiologie des VD surchargés avant et après la RVP, nous avons exploré la capacité du modèle à prédire la réponse de la mécanique ventriculaire lors de la diminution progressive de la post-charge des VD chez les patients atteints de TOFr. Des modèles pré-PVR personnalisés ont été utilisés et l'arrêt de la régurgitation PV et la diminution progressive de la résistance RVOT ont été supposés. Les relations in silico résultantes entre la contractilité et la résistance de l'RVOT après la RVP sont apparues linéaires et cohérentes avec celles données par les modèles post-RVP spécifiques aux patients.Pour les patients dont le cœur est constitué d'un seul ventricule et qui subissent une RMC combinée à un cathéter de pression (dans le cadre de la planification d'une chirurgie complexe), le modèle a été utilisé pour synchroniser dans le temps les données de pression du cathéter et les volumes ventriculaires obtenus par RMC. Cette synchronisation temporelle assistée par le modèle produit des boucles P-V de haute qualité qui donnent des indices plus précis de l'énergétique cardiaque (valeur maximale de l'élastance variable dans le temps (E_max) et du travail systémique) et qui pourraient donc être utilisés pour améliorer l'interprétation clinique.Enfin, nous avons comparé les indices de E_max et de la dérivée temporelle maximale de la pression ventriculaire, max(dP/dt), obtenus directement à partir des mesures cliniques, avec la contractilité et le max(dP/dt) dérivés du modèle. Tous les indices dérivés des données et du modèle ont montré une bonne concordance. De plus, une application potentielle du max(dP/dt) dérivé du modèle comme filtre de données basé sur le modèle a été soulignée.Dans l'ensemble, cette thèse a démontré (1) la capacité de la modélisation biomécanique à fournir des indices mécaniques supplémentaires de la fonction ventriculaire et leur évolution dans différentes conditions de charge, ce qui pourrait contribuer à la planification d'une thérapie optimale ; (2) une application du modèle pour fournir un traitement robuste des données cliniques d'une variété de protocoles d'acquisition de données ; et (3) une correspondance des indices dérivés du modèle avec des mesures de substitution de la contractilité acceptées cliniquement. En conclusion, cette thèse a montré que la modélisation biomécanique pouvait être déployée dans un environnement clinique pour résoudre divers types de problèmes en médecine personnalisée.

Published
2022

18. Discrete time formulations as time discretization strategies in data assimilation

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, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Mortensen estimator, Least squares minimization, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Kalman filtering, Luenberger observer, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; Data assimilation combines control theory and scientific computing to propose a set of methods for coupling dynamic models and data sequences for estimation and prediction in all engineering domains. Data assimilation naturally raises the question of how the developed control and optimization methods interact with the discretization of the underlying physical models, in particular their temporal discretization. We would like to present here some of the best known techniques developed for discrete-time models, which are essentially based on a mechanism involving model prediction on the one hand and data correction on the other. We show that they can be considered as specific discretizations of the data assimilation strategies proposed for continuous-time models in the sense of a discretization-and-then-control approach. This paradigm justifies the stability of these prediction-correction schemes, paving the way for convergence properties and justifying their popularity in practice.

Published
2022
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19. An efficient numerical method for time domain electromagnetic wave propagation in co-axial cables

Author

Akram Beni-Hamad, Geoffrey Beck, Sébastien Imperiale, Patrick Joly, Beck, Geoffrey, Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), 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 normale supérieure - Paris (ENS-PSL), 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), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)

Subjects
Computational Mathematics, Numerical Analysis, Edge elements, Hybrid numerical method, Applied Mathematics, Coaxial cables, Telegrapher's models, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Maxwell's equation, Numerical simulation, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

In this work, we construct an efficient numerical method to solve 3D Maxwell’s equations in coaxial cables. Our strategy is based upon a hybrid explicit-implicit time discretization combined with edge elements on prisms and numerical quadrature. One of the objectives is to validate numerically generalized telegrapher’s models that are used to simplify the 3D Maxwell equations into a 1D problem. This is the object of the second part of the article.

Published
2022
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20. On the structural origin of the anisotropy in the myocardium: Multiscale modeling and analysis

Author

Nicole Tueni, Jean-Marc Allain, 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, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Biomaterials, Mechanics of Materials, Biomedical Engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph]
Abstract

International audience; Due to structural heterogeneities within the tissue, the myocardium displays an orthotropic material behavior. However, the link between the microstructure and the macroscopic mechanical properties is still not fully established. In particular, if it is admitted that the cardiomyocyte organization induces a transversely isotropic symmetry, the relative role in the observed orthotropic symmetry of cardiomyocyte orientation variation and perimysium collagen "sheetlet" structure, two mechanisms occurring at different scales, is still a matter of debate. In order to shed light on this question, we designed a multiscale model of the myocardium, bridging the cell, sheetlet and tissue scales. More precisely, we compared the macroscopic anisotropy obtained by homogenization of different mesostructures consisting in cardiomyocytes and extracellular collageneous layers, also taking into account the variation of cardiomyocyte and sheetlet orientations on the macroscale, to available experimental data. This study confirms the importance of sheetlets layers in assuring the tissue's anisotropic response, as cardiomyocytes-only mesostructures cannot reproduce the observed anisotropy. Moreover, our model shows the existence of a size effect in the myocardial tissue shear properties, which will require further experimental analysis.

Published
2022
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21. Kernel representation of Kalman observer and associated H-matrix based discretization

Author

Matthieu Aussal, Philippe Moireau, Inversion of Differential Equations For Imaging and physiX (IDEFIX), 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)-EDF (EDF), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Computational Mathematics, Riccati equation, Control and Optimization, Control and Systems Engineering, [MATH]Mathematics [math], Infinte dimensional systems, data assimilation
Abstract

In deterministic estimation, applying a Kalman filter to a dynamical model based on partial differential equations is theoretically seducing but solving the associated Riccati equation leads to a so-called curse of dimensionality for its numerical implementation. In this work, we propose to entirely revisit the theory of Kalman filters for parabolic problems where additional regularity results proves that the Riccati equation solution belongs to the class of Hilbert-Schmidt operators. The regularity of the associated kernel then allows to proceed to the numerical analysis of the Kalman full space-time discretization in adapted norms, hence justifying the implementation of the related Kalman filter numerical algorithm with H-matrices typically developed for integral equations discretization.

Published
2022
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22. 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
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23. Using Population Based Kalman Estimator to Model COVID-19 Epidemic in France: Estimating the Effects of Non-Pharmaceutical Interventions on the Dynamics of Epidemic

Author

Collin, Annabelle, Hejblum, Boris P., Vignals, Carole, Lehot, Laurent, Thiébaut, Rodolphe, Moireau, Philippe, Prague, MéLanie, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), 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), 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), Vaccine Research Institute (VRI), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), CHU de Bordeaux Pellegrin [Bordeaux], 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), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modélisation Mathématique pour l'Oncologie (MONC), Université Bordeaux Segalen - Bordeaux 2-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 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), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and Hejblum, Boris

Subjects
[SDV.MHEP.ME]Life Sciences [q-bio]/Human health and pathology/Emerging diseases, [STAT.AP]Statistics [stat]/Applications [stat.AP], Epidemic modeling, [SDV.MHEP.MI]Life Sciences [q-bio]/Human health and pathology/Infectious diseases, [SDV.SPEE] Life Sciences [q-bio]/Santé publique et épidémiologie, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Non-pharmaceutical interventions, COVID-19, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, Population estimation, COVID-19 Epidemic modeling Non-pharmaceutical interventions Kalman filters Population estimation, Kalman filters, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]
Abstract

International audience; In response to the ongoing COVID-19 pandemic caused by SARS-CoV-2, governments are taking a wide range of non-pharmaceutical interventions (NPI). These measures include interventions as stringent as strict lockdown but also school closure, bar and restaurant closure, curfews and barrier gestures i.e . social distancing. Disentangling the effectiveness of each NPI is crucial to inform response to future outbreaks. To this end, we first develop a multi-level estimation of the French COVID-19 epidemic over a period of one year. We rely on a global extended Susceptible-Infectious-Recovered (SIR) mechanistic model of the infection including a dynamical (over time) transmission rate containing a Wiener process accounting for modeling error. Random effects are integrated following an innovative population approach based on a Kalman-type filter where the log-likelihood functional couples data across French regions. We then fit the estimated time-varying transmission rate using a regression model depending on NPI, while accounting for vaccination coverage, apparition of variants of concern (VoC) and seasonal weather conditions. We show that all NPI considered have an independent significant effect on the transmission rate. We additionally demonstrate a strong effect from weather conditions which decrease transmission during the summer period, and also estimate increased transmissibility of VoCs.

Published
2021
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24. Prediction of Ventricular Mechanics After Pulmonary Valve Replacement in Tetralogy of Fallot by Biomechanical Modeling: A Step Towards Precision Healthcare

Author

Camille Hancock Friesen, Gerald F. Greil, Radomir Chabiniok, Maria Gusseva, Dominique Chapelle, Tarique Hussain, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], University of Nebraska Medical Center, University of Nebraska System, Czech Technical University in Prague (CTU), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
medicine.medical_specialty, medicine.medical_treatment, 0206 medical engineering, Biomedical Engineering, 02 engineering and technology, 030204 cardiovascular system & hematology, Contractility, 03 medical and health sciences, 0302 clinical medicine, Afterload, Valve replacement, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Internal medicine, Pulmonary Valve Replacement, Medicine, ComputingMilieux_MISCELLANEOUS, Ventricular mechanics, Tetralogy of Fallot, business.industry, valvular heart disease, medicine.disease, 020601 biomedical engineering, 3. Good health, medicine.anatomical_structure, Ventricle, Cardiology, [SDV.IB]Life Sciences [q-bio]/Bioengineering, business, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology
Abstract

Clinical indicators of heart function are often limited in their ability to accurately evaluate the current mechanical state of the myocardium. Biomechanical modeling has been shown to be a promising tool in addition to clinical indicators. By providing a patient-specific measure of myocardial active stress (contractility), biomechanical modeling can enhance the precision of the description of patient’s pathophysiology at any given point in time. In this work we aim to explore the ability of biomechanical modeling to predict the response of ventricular mechanics to the progressively decreasing afterload in repaired tetralogy of Fallot (rTOF) patients undergoing pulmonary valve replacement (PVR) for significant residual right ventricular outflow tract obstruction (RVOTO). We used 19 patient-specific models of patients with rTOF prior to pulmonary valve replacement (PVR), denoted as PSMpre, and patient-specific models of the same patients created post-PVR (PSMpost)—both created in our previous published work. Using the PSMpre and assuming cessation of the pulmonary regurgitation and a progressive decrease of RVOT resistance, we built relationships between the contractility and RVOT resistance post-PVR. The predictive value of such in silico obtained relationships were tested against the PSMpost, i.e. the models created from the actual post-PVR datasets. Our results show a linear 1-dimensional relationship between the in silico predicted contractility post-PVR and the RVOT resistance. The predicted contractility was close to the contractility in the PSMpost model with a mean (± SD) difference of 6.5 (± 3.0)%. The relationships between the contractility predicted by in silico PVR vs. RVOT resistance have a potential to inform clinicians about hypothetical mechanical response of the ventricle based on the degree of pre-operative RVOTO.

Published
2021
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25. 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
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26. Biomechanical Modeling to Inform Pulmonary Valve Replacement in Tetralogy of Fallot Patients after Complete Repair

Author

Gerald F. Greil, Radomir Chabiniok, Keren Hasbani, Dominique Chapelle, Camille L. Hancock Friesen, Maria Gusseva, Animesh Tandon, Cécile Patte, Philippe Moireau, Tarique Hussain, Martin Genet, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], University of Texas at Austin [Austin], Czech Technical University in Prague (CTU), King‘s College London, Guy's and St Thomas' Hospital [London], École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris

Subjects
Adult, Male, Reoperation, medicine.medical_specialty, Percutaneous, Heart Ventricles, 0206 medical engineering, Magnetic Resonance Imaging, Cine, 02 engineering and technology, 030204 cardiovascular system & hematology, Models, Biological, Article, Contractility, 03 medical and health sciences, 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Cardiovascular modeling, Pulmonary Valve Replacement, Internal medicine, medicine.artery, Humans, Medicine, Abnormalities, Multiple, Cardiac Surgical Procedures, Retrospective Studies, Tetralogy of Fallot, Heart Valve Prosthesis Implantation, Cardiovascular magnetic resonance imaging, Pulmonary Valve, medicine.diagnostic_test, business.industry, Hemodynamics, Magnetic resonance imaging, Retrospective cohort study, Translational research, medicine.disease, 020601 biomedical engineering, Personalized medicine, Pulmonary Valve Insufficiency, Pulmonary artery, Cardiology, Female, Biomechanical model, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Myocardial contractility, Cardiology and Cardiovascular Medicine, business, Follow-Up Studies
Abstract

BACKGROUND: A biomechanical model of the heart can be used to incorporate multiple data sources (electrocardiography, imaging, invasive hemodynamics). The purpose of this study was to use this approach in a cohort of patients with tetralogy of Fallot after complete repair (rTOF) to assess comparative influences of residual right ventricular outflow tract obstruction (RVOTO) and pulmonary regurgitation on ventricular health. METHODS: Twenty patients with rTOF who underwent percutaneous pulmonary valve replacement (PVR) and cardiovascular magnetic resonance imaging were included in this retrospective study. RESULTS: RV contractility before PVR (mean 66 ± kPa, mean ± standard deviation) was increased in patients with rTOF compared with normal RV (38–48 kPa) (P < 0.05). The contractility decreased significantly in all patients after PVR (P < 0.05). Patients with predominantly RVOTO demonstrated greater reduction in contractility (median decrease 35%) after PVR than those with predominant pulmonary regurgitation (median decrease 11%). The model simulated post-PVR decreased EDV for the majority and suggested an increase of Q(eff)—both in line with published data. CONCLUSIONS: This study used a biomechanical model to synthesize multiple clinical inputs and give an insight into RV health. Individualized modeling allows us to predict the RV response to PVR. Initial data suggest that residual RVOTO imposes greater ventricular work than isolated pulmonary regurgitation. Biomechanical models specific to individual patient and physiology (before and after PVR) were created and used to estimate the RV myocardial contractility. The ability of models to capture post-PVR changes of right ventricular (RV) end-diastolic volume (EDV) and effective flow in the pulmonary artery (Qeff) was also compared with expected values.

Published
2021
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27. 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

28. 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
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29. 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

30. Hierarchical modeling of length-dependent force generation in cardiac muscles and associated thermodynamically-consistent numerical schemes

Author

Dominique Chapelle, Philippe Moireau, François Kimmig, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
Computer science, Computational Mechanics, Ocean Engineering, Context (language use), multi-scale modeling, Sarcomere, biomechanics, 03 medical and health sciences, Myosin head, 0302 clinical medicine, numerical methods, 030304 developmental biology, 0303 health sciences, Frank–Starling law of the heart, Hierarchical modeling, Applied Mathematics, Mechanical Engineering, Numerical analysis, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Cardiac modeling, Multiscale modeling, multiscale modeling, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computational Mathematics, Computational Theory and Mathematics, Coupling (computer programming), Frank-Starling mechanism, sarcomere, Biological system, 030217 neurology & neurosurgery, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In the context of cardiac muscle modeling, the availability of the myosin heads in the sarcomeres varies over the heart cycle contributing to the Frank-Starling mechanism at the organ level. In this paper, we propose a new approach that allows to extend the Huxley'57 muscle contraction model equations to incorporate this variation. This extension is built in a thermodynamically consistent manner, and we also propose adapted numerical methods that satisfy thermodynamical balances at the discrete level. Moreover, this whole approach-both for the model and the numerics-is devised within a hierarchical strategy enabling the coupling of the microscopic sarcomere-level equations with the macroscopic tissue-level description. As an important illustration, coupling our model with a previously proposed simplified heart model, we demonstrate the ability of the modeling and numerical framework to capture the essential features of the Frank-Starling mechanism.

Published
2021
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31. 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

32. Model-Assisted Time-Synchronization of Cardiac MR Image and Catheter Pressure Data

Author

Mohamed Abdelghafar Hussein, Maria Gusseva, Radomir Chabiniok, Surendranath R. Veeram Reddy, Gerald F. Greil, Daniel A. Castellanos, Joshua S. Greer, Tarique Hussain, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], Boston Children's Hospital, Pediatric department, Kafrelsheikh University, Kafrelsheikh University, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Faculty of Medicine, Kafrelsheikh University, Kafrelsheikh, Egypt

Subjects
Physics, cardiovascular modeling, time-synchronization of clinical data, medicine.diagnostic_test, Cardiac cycle, pressure volume loops, Image (category theory), Magnetic resonance imaging, personalized medicine, 030204 cardiovascular system & hematology, Type (model theory), 030218 nuclear medicine & medical imaging, 03 medical and health sciences, QRS complex, 0302 clinical medicine, Nuclear magnetic resonance, translational research, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Norm (mathematics), Ventricular pressure, medicine, [SDV.IB]Life Sciences [q-bio]/Bioengineering, interventional cardiovascular magnetic resonance imaging, Volume (compression)
Abstract

International audience; When combining cardiovascular magnetic resonance imaging (CMR) with pressure catheter measurements, the acquired imageand pressure data need to be synchronized in time. The time offset between the image and pressure data depends on a number of factors,such as the type and settings of the MR sequence, duration and shape of QRS complex or the type of catheter, and cannot be typically estimated beforehand. In the present work we propose using a biophysical heart model to synchronize the left ventricular (LV) pressure and volume (P-V) data. Ten patients, who underwent CMR and LV catheterization, were included. A biophysical model of reduced geometrical complexity with physiologically substantiated timing of each phase of the cardiac cycle was first adjusted to individual patients using basic morphological and functional indicators. The pressure and volume waveforms simulated by the patient-specific models were then used as templates to detect the time offset between the acquired ventricular pressure and volume waveforms. Time-varying ventricular elastance was derived from clinical data both as originally acquired as well as when time-synchronized, and normalized with respect to end-systolic time and maximum elastance value$E^N_\text {orig}(t)$, $E^N_\text {t-syn}(t)$, respectively). $E^N_\text {t-syn}(t)$ was significantly closer to the experimentally obtained $E^N_\text {exp}(t)$ published in the literature (p < 0.05, $L^2$ norm). The work concludes that the model-driven time-synchronization of P-V data obtained by catheter measurement and CMR allows to generate high quality P-V loops, which can then be used for clinical interpretation.

Published
2021
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33. Sequential data assimilation for mechanical systems with complex image data: application to tagged-MRI in cardiac mechanics

Author

Philippe Moireau, Dominique Chapelle, Alexandre Imperiale, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Département Imagerie et Simulation pour le Contrôle (DISC), Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Laboratoire d'Intégration des Systèmes et des Technologies (LIST)

Subjects
Computer science, 0206 medical engineering, Image processing, 02 engineering and technology, Data type, Synthetic data, 030218 nuclear medicine & medical imaging, lcsh:TA168, 03 medical and health sciences, 0302 clinical medicine, Data assimilation, Medical imaging, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Engineering (miscellaneous), Flexibility (engineering), Measure (data warehouse), Tagged-MRI, business.industry, Applied Mathematics, Pattern recognition, Cardiac modeling, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computer Science Applications, lcsh:Systems engineering, Modeling and Simulation, Patient-specific model, Artificial intelligence, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Focus (optics), business, lcsh:Mechanics of engineering. Applied mechanics, lcsh:TA349-359, Estimation
Abstract

Tagged Magnetic Resonance images (tagged-MRI) are generally considered to be the gold standard of medical imaging in cardiology. By imaging spatially-modulated magnetizations of the deforming tissue, indeed, this modality enables an assessment of intra-myocardial deformations over the heart cycle. The objective of the present work is to incorporate the most valuable information contained in tagged-MRI in a data assimilation framework, in order to perform joint state-parameter estimation for a complete biomechanical model of the heart. This type of estimation is the second major step, after initial anatomical personalization, for obtaining a genuinely patient-specific model that integrates the individual characteristics of the patient, an essential prerequisite for benefitting from the model predictive capabilities. Here, we focus our attention on proposing adequate means of quantitatively comparing the cardiac model with various types of data that can be extracted from tagged-MRI after an initial image processing step, namely, 3D displacements fields, deforming tag planes or grids, or apparent 2D displacements. This quantitative comparison—called discrepancy measure—is then used to feed a sequential data assimilation procedure. In the state estimation stage of this procedure, we also propose a new algorithm based on the prediction–correction paradigm, which provides increased flexibility and effectiveness in the solution process. The complete estimation chain is eventually assessed with synthetic data, produced by running a realistic model simulation representing an infarcted heart characterized by increased stiffness and reduced contractility in a given region of the myocardium. From this simulation we extract the 3D displacements, tag planes and grids, and apparent 2D displacements, and we assess the estimation with each corresponding discrepancy measure. We demonstrate that—via regional estimation of the above parameters—the data assimilation procedure allows to quantitatively estimate the biophysical parameters with good accuracy, thus simultaneously providing the location of the infarct and characterizing its seriousness. This shows great potential for combining a biomechanical heart model with tagged-MRI in order to extract valuable new indices in clinical diagnosis.

Published
2021
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34. 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
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35. A quasi-static poromechanical model of the lungs

Author

Cécile Patte, Martin Genet, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-10-EQPX-0037,MATMECA,MATériaux-MECAnique/Elaboration-Caractérisation-Observation-Modélisation-Simulation(2010), ANR-19-CE45-0007,LungManyScale,Biomécanique Computationnelle Pulmonaire: Modélisation Multi-échelle et Estimation(2019), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
Mechanical Engineering, Respiration, 0206 medical engineering, Diaphragm, Poromechanics, Modeling, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], 02 engineering and technology, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, 0302 clinical medicine, Inverse Poromechanics, Modeling and Simulation, Finite Element Method, Pulmonary Mechanics, [SDV.MHEP.AHA]Life Sciences [q-bio]/Human health and pathology/Tissues and Organs [q-bio.TO], Lung, Biotechnology
Abstract

International audience; The lung vital function of providing oxygen to the body heavily relies on its mechanical behavior, and the interaction with its complex environment. In particular, the large compliance and the porosity of the pulmonary tissue are critical for lung inflation and air inhalation, and the diaphragm, the pleura, the rib cage and intercostal muscles all play a role in delivering and controlling the breathing driving forces. In this paper, we introduce a novel poromechanical model of the lungs. The constitutive law is derived within a general poromechanics theory via the formulation of lung-specific assumptions, leading to a hyperelastic potential reproducing the volume response of the pulmonary mixture to a change of pressure. Moreover, physiological boundary conditions are formulated to account for the interaction of the lungs with their surroundings, including a following pressure and bilateral frictionless contact. A strategy is established to estimate the unloaded configuration from a given loaded state, with a particular focus on ensuring a positive porosity. Finally, we illustrate through several realistic examples the relevance of our model and its potential clinical applications.

Published
2021
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36. 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

37. 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

38. 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
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39. 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

40. 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
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41. 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
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42. 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
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43. 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

44. 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

45. 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
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46. 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
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47. 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
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48. 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
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49. 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

50. Personalized pulmonary poromechanics

Author

Pierre-Yves Brillet, Dominique Chapelle, Catalin Fetita, Cécile Patte, Martin Genet, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Polytechnique de Paris (IP Paris), Département Advanced Research And Techniques For Multidimensional Imaging Systems (TSP - ARTEMIS), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), ARMEDIA (ARMEDIA-SAMOVAR), Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux (SAMOVAR), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP)-Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), Hypoxie et Poumon : pneumopathologies fibrosantes, modulations ventilatoires et circulatoires (H&P), UFR SMBH-Université Sorbonne Paris Nord, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Département Advanced Research And Techniques For Multidimensional Imaging Systems (ARTEMIS)

Subjects
Computer science, 0206 medical engineering, Poromechanics, Biomedical Engineering, Bioengineering, 02 engineering and technology, [SDV.MHEP.PSR]Life Sciences [q-bio]/Human health and pathology/Pulmonology and respiratory tract, 03 medical and health sciences, 0302 clinical medicine, Pulmonary mechanics, Modeling, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Control engineering, 030229 sport sciences, General Medicine, respiratory system, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 3. Good health, Computer Science Applications, Human-Computer Interaction, Current (fluid), Estimation, Simulation
Abstract

International audience; Lung biomechanics has been extensively studied by physiologists, experimentally as well as theoretically, laying the ground for our current fundamental understanding of the relationship between function and mechanical behavior. However, many questions remain, notably in the intricate coupling between the multiple constituents. These fundamental questions represent real clinical challenges, as pulmonary diseases are an important health burden. Interstitial lung diseases, for instance, affect several million people globally. Idiopathic Pulmonary Fibrosis (IPF), notably, a progressive form of interstitial lung diseases where some alveolar septa get thicker and stiffer while others get completely damaged, remains poorly understood, poorly diagnosed, and poorly treated (Nunes et al. 2015).

Published
2020
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