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1. Numerical analysis of an incompressible soft material poromechanics model using $\protect \tt {T}$-coercivity

Author

Barré, Mathieu, Grandmont, Céline, and Moireau, Philippe

Subjects
Poromechanics, mixture theory, incompressible limit, total discretization, inf-sup stability, energy preserving time-scheme, Materials of engineering and construction. Mechanics of materials, TA401-492
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 $\tt {T}$-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 $\tt {T}$-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
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5. INSPIRE: A European training network to foster research and training in cardiovascular safety pharmacology

Author

Guns, Pieter-Jan D., Guth, Brian D., Braam, Stefan, Kosmidis, Georgios, Matsa, Elena, Delaunois, Annie, Gryshkova, Vitalina, Bernasconi, Sylvain, Knot, Harm J., Shemesh, Yair, Chen, Alon, Markert, Michael, Fernández, Miguel A., Lombardi, Damiano, Grandmont, Céline, Cillero-Pastor, Berta, Heeren, Ron M.A., Martinet, Wim, Woolard, Jeanette, Skinner, Matt, Segers, Vincent F.M., Franssen, Constantijn, Van Craenenbroeck, Emeline M., Volders, Paul G.A., Pauwelyn, Thomas, Braeken, Dries, Yanez, Paz, Correll, Krystle, Yang, Xi, Prior, Helen, Kismihók, Gábor, De Meyer, Guido R.Y., and Valentin, Jean-Pierre

Published
2020
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7. On the analysis of a mechanically consistent model of fluid-structure-contact interaction.

Author

Champion, Marguerite, Fernández, Miguel A., Grandmont, Céline, Vergnet, Fabien, and Vidrascu, Marina

Subjects
FLUID dynamics, DIRICHLET problem, STOKES flow, MATHEMATICAL models of engineering, SEEPAGE
Abstract

This paper is devoted to the mathematical analysis of the contact capabilities of the fluid-structure interaction (FSI) model with seepage reported in [Comput. Methods Appl. Mech., 392:114637, 2022]. In the case of a rigid disk moving over a fixed horizontal plane, we show that this model encompasses contact and hence removes the non collision paradox of traditional FSI models which rely on Dirichlet or Dirichlet/Navier boundary conditions. Numerical evidence on the theoretical results is also provided. [ABSTRACT FROM AUTHOR]

Published
2024
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10. 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

12. Numerical approximation of the Poisson problem with small holes, using augmented finite elements and defective boundary conditions

Author

Boulakia, Muriel, Grandmont, Céline, Lespagnol, Fabien, Zunino, Paolo, Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Sorbonne Université (SU), 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), Laboratorio di Modellistica e Calcolo Scientifico MOX (Dipartimento di Matematica 'Francesco Brioschi'), Politecnico di Milano [Milan] (POLIMI), and Fabien Lespagnol is supported by the project A new computational approach for the fluid-structure in-teraction of slender bodies immersed in three-dimensional flows granted by the Università Italo-Francese, in the framework Vinci 2019.

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

We consider the Poisson problem in a domain with small holes, as a template for developing efficient and accurate numerical approximation schemes for partial differential equations defined on domains with low-dimensional inclusions, such as embedded fibers. We propose a reduced model based on the projection of Dirichlet boundary constraints on a finite dimensional approximation space, obtaining in this way a Poisson problem with defective interface conditions. We analyze the existence of the solution of the reduced problem and for arbitrarily small holes we prove its convergence towards the original problem, the rate of which depends on the size of the inclusion and on the number of modes of the finite dimensional space. The numerical discretization of the reduced problem is addressed by the finite element method, using a computational mesh that does not fit to the holes in the framework of a fictitious domain approach. We propose a stable, optimally convergent and robust formulation with respect to the hole size that exploits an augmented Galerkin formulation based on the addition of suitable non-polynomial functions to the finite element approximation space. The properties of the discretization method are supported by numerical experiments.

Published
2023

13. A coupled model for the dynamics of gas exchanges in the human lung with Haldane and Bohr's effects

Author

Boudin, Laurent, Grandmont, Céline, Grec, Bérénice, Martin, Sébastien, 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), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), and Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [SDV.MHEP.PSR]Life Sciences [q-bio]/Human health and pathology/Pulmonology and respiratory tract
Abstract

We propose an integrated dynamical model for oxygen and carbon dioxide transfer from the lung into the blood, coupled with a lumped mechanical model for the ventilation process, for healthy patients as well as in pathological cases. In particular, we focus on the Bohr and Haldane effects, which induce a nonlinear coupling between the oxygen and the carbon dioxide. We also take into account the dead space volume, which requires a special attention in the pathological cases.

Published
2022

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

Author

Barré, Mathieu, Grandmont, Céline, and Moireau, Philippe

Subjects
POROUS materials, NUMERICAL analysis, POROELASTICITY, MATHEMATICAL analysis, POROSITY
Abstract

In this work, we thoroughly analyze the linearized version of a poromechanics model developed to simulate soft tissues perfusion. This is a fully unsteady 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 initially performed for a compressible porous material. Here, we focus on the nearly incompressible case with a semigroup approach, which also allows us to prove the existence of weak solutions. We show the existence and uniqueness of strong and weak solutions in the incompressible limit case, for which a divergence constraint on the mixture velocity appears. 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 stable and robust approximations of the problem with mixed finite elements. In particular, we recover an inf-sup condition that is independent of the porosity. Finally, we numerically investigate the elliptic regularity of the associated steady-state problem and illustrate the sensitivity of the solution with respect to the different model parameters. [ABSTRACT FROM AUTHOR]

Published
2023
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16. Reduced models for the Poisson problem in perforated domains

Author

Boulakia, Muriel, Grandmont, Céline, Lespagnol, Fabien, Zunino, Paolo, Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), 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), Laboratorio di Modellistica e Calcolo Scientifico MOX (Dipartimento di Matematica 'Francesco Brioschi'), Politecnico di Milano [Milan] (POLIMI), and Fabien Lespagnol is supported by the project A new computational approach for the fluid-structure in-teraction of slender bodies immersed in three-dimensional flows granted by the Università Italo-Francese, in the framework Vinci 2019.

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

We develop a fictitious domain method to approximate a Dirichlet problem on a domain with small circular holes (simply called a perforated domain). To address the case of many small inclusions or exclusions, we propose a reduced model based on the projection of the homogeneous Dirichlet boundary constraint on a finite dimensional approximation space. We analyze the existence of the solution of this reduced problem and prove its convergence towards the limit problem without holes. We next obtain an estimate of the gap between the solution of the reduced model and the solution of the full initial model with small holes, the convergence rate depending on the size of the inclusion and on the number of modes of the finite dimensional space. The numerical discretization of the reduced problem is addressed by the finite element method, using a computational mesh that does not fit to the holes. The approximation properties of the finite element method are analyzed by a-priori estimates and confirmed by numerical experiments. elliptic differential equations, small inclusions, asymptotic analysis, approximated numerical method.

Published
2021

17. 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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19. Existence and uniqueness for a quasi-static interaction problem between a viscous fluid and an active structure

Author

Grandmont, Céline, Vergnet, Fabien, 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)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), 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), 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), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
Fluid-structure interaction, Strong solution, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Existence result, Active structure
Abstract

International audience; We consider a quasi-static fluid-structure interaction problem where the fluid is modeled by theStokes equations and the structure is an active and elastic medium. More precisely, the displacementof the structure verifies the equations of elasticity with an active stress, which models the presenceof internal biological motors in the structure. Under smallness assumptions on the data, we provethe existence of a unique solution for this strongly coupled system.

Published
2020
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22. Editorial CEMRACS 2018

Author

Calvez Vincent, Grandmont Céline, Lochërbach Eva, Poignard Clair, Ribot Magali, and Vauchelet Nicolas

Subjects
T57-57.97, Applied mathematics. Quantitative methods, QA1-939, Mathematics
Published
2020

24. Existence of solutions and continuous and semi-discrete stability estimates for 3D/0D coupled systems modelling airflows and blood flows.

Author

Grandmont, Céline and Martin, Sébastien

Subjects
*AIR flow, *NEUMANN boundary conditions, *MULTISCALE modeling, *BLOOD flow, *GEOMETRIC modeling
Abstract

In this paper we analyse geometric multiscale models arising in the description of physiological flows such as blood flow in arteries or air flow in the bronchial tree. The geometrical complexity of the networks in which air/blood flows lead to a classical decomposition in two areas: a truncated 3D geometry corresponding to the largest contribution of the domain, and a 0D part connected to the 3D part, modelling air/blood flows in smaller airways/vessels. The fluid in the 3D part is described by the Stokes or the Navier–Stokes system which is coupled to 0D models or so-called Windkessel models. The resulting Navier–Stokes–Windkessel coupled system involves Neumann non-local boundary conditions that depends on the considered applications. We first show that the different types of Windkessel models share a similar formalism. Next we derive existence results and stability estimates for the continuous coupled Stokes–Windkessel or Navier–Stokes–Windkessel problem as well as stability estimates for the semi-discretized systems with either implicit or explicit treatment of the boundary conditions. In all the calculations, we pay a special attention to the dependency of the various constants and smallness conditions on the data with respect to the physical and numerical parameters. In particular we exhibit different kinds of behavior depending on the considered 0D model. Moreover even if no energy estimates can be derived in energy norms for the Navier–Stokes–Windkessel system, leading to possible and observed numerical instabilities for large applied pressures, we show that stability estimates for both the continuous and semi-discrete problems, can be obtained in appropriate norms for small enough data by introducing a new well chosen Stokes-like operator. These sufficient stability conditions on the data may give a hint on the order of magnitude of the data enabling stable computations without stabilization method for the problem. Numerical simulations illustrate some of the theoretical results. [ABSTRACT FROM AUTHOR]

Published
2021
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27. A multi-scale epidemic model of Salmonella infection with heterogeneous shedding.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Labarthe, Simon, Laroche, Béatrice, Nguyen, Thi Nhu Tao, Polizzi, Bastien, Patout, Florian, and Stegmaier, Tabea

Subjects
*SALMONELLA, *MULTISCALE modeling, *PATHOGENIC bacteria, *VETERINARY bacteriology, *COMPUTER simulation
Abstract

Salmonella strains colonize the digestive tract of farm livestock, such as chickens or pigs, without affecting them, and potentially infect food products, representing a threat for human health ranging from food poisoning to typhoid fever. It has been shown that the ability to excrete the pathogen in the environment and contaminate other animals is variable. This heterogeneity in pathogen carriage and shedding results from interactions between the host's immune response, the pathogen and the commensal intestinal microbiota. In this paper we propose a novel generic multiscale modeling framework of heterogeneous pathogen transmission in an animal population. At the intra-host level, the model describes the interaction between the commensal microbiota, the pathogen and the inflammatory response. Random fluctuations in the ecological dynamics of the individual microbiota and transmission at between-host scale are added to obtain a drift-diffusion PDE model of the pathogen distribution at the population level. The model is further extended to represent transmission between several populations. The asymptotic behavior as well as the impact of control strategies including cleaning and antimicrobial administration are investigated through numerical simulation. [ABSTRACT FROM AUTHOR]

Published
2020
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28. Opinion propagation on social networks: a mathematical standpoint.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Lavenant, H., and Maury, B.

Subjects
*STOCHASTIC analysis, *PARTIAL differential equations, *NONLINEAR analysis, *GAUSSIAN function, *EVOLUTION equations
Abstract

These lecture notes address mathematical issues related to the modeling of opinion propagation on networks of the social type. Starting from the behavior of the simplest discrete linear model, we develop various standpoints and describe some extensions: stochastic interpretation, monitoring of a network, time continuous evolution problem, charismatic networks, links with discretized Partial Differential Equations, nonlinear models, inertial version and stability issues. These developments rely on basic mathematical tools, which makes them accessible at an undergraduate level. In a last section, we propose a new model of opinion propagation, where the opinion of an agent is described by a Gaussian density, and the (discrete) evolution equation is based on barycenters with respect to the Fisher metric. [ABSTRACT FROM AUTHOR]

Published
2020
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29. Comparison and calibration of different electroporation models. Application to rabbit livers experiments.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Jankowiak, Gaspard, Taing, Cécile, and Collin, Annabelle

Subjects
*ELECTROPORATION, *TUMORS, *ELECTRIC fields, *ELECTROPHYSIOLOGY, *COMPUTER simulation of biological systems
Abstract

Electroporation is a complex phenomenon that occurs when biological tissues are subjected to electric pulses. The clinical interest for the phenomenon has constantly increased for the last decades. Indeed, electroporation makes it possible to either kill directly the cells in the target region (tumor) or to introduce molecules into living cells. However, one of the main limitation of using electroporation in the clinical routine comes from the technical difficulties raised by such therapies, in particular it is difficult to well determine the treated zone. Numerical modeling of the electric field magnitude could provide a powerful strategy to assess the treatment efficacy: thanks to well-designed models, the computation of the distribution of the electric field is achievable, providing a numerical evaluation of the treatment. The main objective of this work is to go further on the patient-adapted numerical modeling of the electric field magnitude by laying the ground of the possible electroporation models - which will be compared qualitatively - and their calibrations. This will be done in the framework of bioelectrical measurements on rabbit livers that come from the literature. [ABSTRACT FROM AUTHOR]

Published
2020
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30. Cell migration in complex environments: chemotaxis and topographical obstacles.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Cucchi, Alessandro, Etchegaray, Christèle, Meunier, Nicolas, Navoret, Laurent, and Sabbagh, Lamis

Subjects
*CELL migration, *CELL motility, *TWO-dimensional models, *STOCHASTIC differential equations, *DISCRETE systems
Abstract

Cell migration is a complex phenomenon that plays an important role in many biological processes. Our aim here is to build and study models of reduced complexity to describe some aspects of cell motility in tissues. Precisely, we study the impact of some biochemical and mechanical cues on the cell dynamics in a 2D framework. For that purpose, we model the cell as an active particle with a velocity solution to a particular Stochastic Differential Equation that describes the intracellular dynamics as well as the presence of some biochemical cues. In the 1D case, an asymptotic analysis puts to light a transition between migration dominated by the cell's internal activity and migration dominated by an external signal. In a second step, we use the contact algorithm introduced in [15,18] to describe the cell dynamics in an environment with obstacles. In the 2D case, we study how a cell submitted to a constant directional force that mimics the action of chemoattractant, behaves in the presence of obstacles. We numerically observe the existence of a velocity value that the cell can not exceed even if the directional force intensity increases. We find that this threshold value depends on the number of obstacles. Our result confirms a result that was already observed in a discrete framework in [3,4]. [ABSTRACT FROM AUTHOR]

Published
2020
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31. Modeling and analysis of adipocytes dynamic with a differentiation process.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Gilleron, Jérôme, Goudon, Thierry, Lagoutière, Frédéric, Martin, Hugo, Mauroy, Benjamin, Millet, Pascal, and Vaghi, Cristina

Subjects
*FAT cells, *MESENCHYMAL stem cells, *ADVECTION, *DIFFERENTIAL equations
Abstract

We propose in this article a model describing the dynamic of a system of adipocytes, structured by their sizes. This model takes into account the differentiation of a population of mesenchymal cells into preadipocytes and of preadipocytes into adipocytes; the differentiation rates depend on the mean adipocyte radius. The considered equations are therefore ordinary differential equations, coupled with an advection equation, the growth rate of which depends on food availability and on the total surface of adipocytes. Since this velocity is discontinuous, we need to introduce a convenient notion of solutions coming from Filippov theory. We are consequently able to determine the stationary solutions of the system, to prove the existence and uniqueness of solutions and to describe the asymptotic behavior of solutions in some simple cases. Finally, the parameters of the model are fitted thanks to some experimental data and numerical simulations are displayed; a spatial extension of the model is studied numerically. [ABSTRACT FROM AUTHOR]

Published
2020
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32. Curved interface reconstruction for 2D compressible multi-material flows.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Chollet, Igor, Lissoni, Giulia, Corot, Théo, Hoch, Philippe, Leroy, Thomas, and Dumas, Laurent

Subjects
*DYNAMIC programming, *TWO-dimensional models, *COMPRESSIBLE flow, *ROBUST control
Abstract

In this paper, we describe an interface reconstruction method in two dimension. This method is an extension of DPIR [1], which reconstructs continuous interfaces and preserves partial volumes using dynamic programming. First we extend the method to curved interfaces. Then, we present tools to improve its robustness in order to apply it to unstructured grid. Finally, we describe an extension to three materials. [ABSTRACT FROM AUTHOR]

Published
2020
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33. Horizontal gene transfer: numerical comparison between stochastic and deterministic approaches.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Figueroa Iglesias, Susely, Hivert, Hélène, Méléard, Sylvie, Melnykova, Anna, and Nordmann, Samuel

Subjects
*HORIZONTAL gene transfer, *GENETIC transformation, *DRUG resistance in bacteria, *INTEGRO-differential equations, *HAMILTON-Jacobi equations, *COMPUTER simulation of biological systems
Abstract

Horizontal gene Transfer (HT) denotes the transmission of genetic material between two living organisms, while the vertical transmission refers to a DNA transfer from parents to their offspring. Consistent experimental evidence report that this phenomenon plays an essential role in the evolution of certain bacterias. In particular, HT is believed to be the main instrument of developing the antibiotic resistance. In this work, we consider several models which describe this phenomenon: a stochastic jump process (individual-based) and the deterministic nonlinear integrodifferential equation obtained as a limit for large populations. We also consider a Hamilton-Jacobi equation, obtained as a limit of the deterministic model under the assumption of small mutations. The goal of this paper is to compare these models with the help of numerical simulations. More specifically, our goal is to understand to which extent the Hamilton-Jacobi model reproduces the qualitative behavior of the stochastic model and the phenomenon of evolutionary rescue in particular. [ABSTRACT FROM AUTHOR]

Published
2020
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34. Fluid-kinetic modelling for respiratory aerosols with variable size and temperature.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Boudin, Laurent, Grec, Bérénice, Martin, Sébastien, Mecherbet, Amina, and Noël, Frédérique

Subjects
*AIR flow, *PARTICLES, *RESPIRATORY organs, *NAVIER-Stokes equations, *VLASOV equation, *COMPUTER simulation of biological systems
Abstract

In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Twodimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics. [ABSTRACT FROM AUTHOR]

Published
2020
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35. Construction of a statistical learning tool based on ordinary differential equations to model the digestive behaviour of ross chickens.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Bloyet, Nicolas, Flourent, Hélène, Frénod, Emmanuel, Handa, Marouan, Moundoyi, Harold, and Phuong, Thuy Vo Thi

Subjects
*DOMESTIC animals, *DATA modeling, *ANIMAL feeds, *CHICKENS, *STATISTICAL learning, *APPROXIMATION theory
Abstract

Being able to monitor and forecast farm animal performances is a strategic problem in the agronomy industry. We use a Data-Model Coupling approach to build a biomimetic Statistical Learning tool taking into account some aspects of the biological dynamics of the animal body. The objective is to build a tool which is able to assimilate data about daily feed consumption and measured performances. The model encompasses several sub-models corresponding to compartments and permitting to mimic a kinetic process divided into several steps. Each sub-model contains parameters which can be learnt by using an optimization algorithm and data. The goal of the first application of the model on field data was to simulate and predict the growth of chickens. An experiment was performed during 70 days to collect every day the feed consumption and the weight gain of a male and a female chickens. After the learning of the model parameters, the model shows a very good approximation of the chicken's weight evolution over time. [ABSTRACT FROM AUTHOR]

Published
2020
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36. Geometry description and mesh construction from medical imaging.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Carlino, Michele Giuliano, Ricka, Philippe, Phan, Minh, Bertoluzza, Silvia, Pennacchio, Micol, Patanè, Giuseppe, and Spagnuolo, Michela

Subjects
*IMAGE segmentation, *MESH networks, *ALGORITHMS, *MEDICAL imaging systems, *COMPUTER simulation
Abstract

We present a new method for defining and meshing patient-specific domains from medical images. Our approach is based on an atlas image segmentation technique, and relies on the modular registration algorithm of S. Bertoluzza et al. [25]. The mesh of the patient-specific domain is generated by deforming the corresponding mesh on an a priori segmented and meshed reference image (the atlas). Our method aims at automating the process at the interface of medical imaging and numerical simulation, thus reducing the computational cost in those situations where simulations have to be managed on numerous medical images of similar patients. [ABSTRACT FROM AUTHOR]

Published
2020
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37. Swimming at low Reynolds number.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Berti, Luca, Giraldi, Laetitia, and Prud'homme, Christophe

Subjects
*SWIMMING, *RIGID bodies, *REYNOLDS number, *STOKES equations, *QUATERNIONS
Abstract

We address the swimming problem at low Reynolds number. This regime, which is typically used for micro-swimmers, is described by Stokes equations. We couple a PDE solver of Stokes equations, derived from the Feel++ finite elements library, to a quaternion-based rigid-body solver. We validate our numerical results both on a 2D exact solution and on an exact solution for a rotating rigid body respectively. Finally, we apply them to simulate the motion of a one-hinged swimmer, which obeys to the scallop theorem. [ABSTRACT FROM AUTHOR]

Published
2020
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38. Influence of the mode of reproduction on dispersal evolution during species invasion.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Crevat, Joachim, Dekens, Léonard, Fabrèges, Benoit, Kuczma, Frédéric, Lavigne, Florian, and Raoul, Gaël

Subjects
*REACTION-diffusion equations, *ASEXUAL reproduction, *REPRODUCTION, *HEURISTIC
Abstract

We consider a reaction-diffusion-reproduction equation, modeling a population which is spatially heterogeneous. The dispersion of each individuals is influenced by its phenotype. In the literature, the asymptotic propagation speed of an asexual population has already been rigorously determined. In this paper we focus on the difference between the asexual reproduction case, and the sexual reproduction case, involving a non-local term modeling the reproduction. This comparison leads to a different invasion speed according to the reproduction. After a formal analysis of both cases, leading to a heuristic of the asymptotic behaviour of the invasion fronts, we give some numerical evidence that the acceleration rate of the spatial spreading of a sexual population is slower than the acceleration rate of an asexual one. The main difficulty to get sharper results on a transient comes from the non-local sexual reproduction term. [ABSTRACT FROM AUTHOR]

Published
2020
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39. Multiscale population dynamics in reproductive biology: singular perturbation reduction in deterministic and stochastic models.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Bonnet, Celine, Chahour, Keltoum, Clément, Frédérique, Postel, Marie, and Yvinec, Romain

Subjects
*OVARIAN follicle, *DIFFERENTIAL equations, *TIMESCALE number, *SINGULAR perturbations
Abstract

In this study, we describe different modeling approaches for ovarian follicle population dynamics, based on either ordinary (ODE), partial (PDE) or stochastic (SDE) differential equations, and accounting for interactions between follicles. We put a special focus on representing the population-level feedback exerted by growing ovarian follicles onto the activation of quiescent follicles. We take advantage of the timescale difference existing between the growth and activation processes to apply model reduction techniques in the framework of singular perturbations. We first study the linear versions of the models to derive theoretical results on the convergence to the limit models. In the nonlinear cases, we provide detailed numerical evidence of convergence to the limit behavior. We reproduce the main semi-quantitative features characterizing the ovarian follicle pool, namely a bimodal distribution of the whole population, and a slope break in the decay of the quiescent pool with aging. [ABSTRACT FROM AUTHOR]

Published
2020
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40. Optimal release of mosquitoes to control dengue transmission.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Almeida, Luis, Haddon, Antoine, Kermorvant, Claire, Léculier, Alexis, Privat, Yannick, Strugarek, Martin, and Zubelli, Jorge P.

Subjects
*DENGUE, *PREVENTION of infectious disease transmission, *INFECTIOUS disease transmission, *DISEASE progression, *MOSQUITO vectors, *WOLBACHIA, *INFECTION
Abstract

In order to prevent the propagation of human diseases transmitted by mosquitoes (as dengue or zika), a solution is to release mosquitoes infected by Wolbachia. In this study, we model the release and the propagation over time and space of such infected mosquitoes in a population of uninfected ones. The aim of this study is to investigate the best location in space of the release to ensure invasion by the infected mosquitoes. [ABSTRACT FROM AUTHOR]

Published
2020
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41. Phase transitions in a two-species model for cell segregation and logistic growth.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Almeida, Luis, Atsou, Kevin, Marulli, Marta, Peurichard, Diane, and Tesson, Rémi

Subjects
*CELL separation, *BROWNIAN motion, *MULTIAGENT systems, *MATHEMATICAL continuum, *COMPUTER simulation
Abstract

We study a model of cell segregation in a population composed of two cell types. Starting from a model initially proposed in [3], we aim to understand the impact of a cell division process on the system's segregation abilities. The original model describes a population of spherical cells interacting with their close neighbors by means of a repulsion potential and which centers are subject to Brownian motion. Here, we add a stochastic birth-death process in the agent-based model, that approaches a logistic growth term in the continuum limit. We address the linear stability of the spatially homogeneous steady states of the macroscopic model and obtain a precise criterion for the phase transition, which links the system segregation ability to the model parameters. By comparing the criterion with the one obtained without logistic growth, we show that the system's segregation ability is the result of a complex interplay between logistic growth, diffusion and mechanical repulsive interactions. Numerical simulations are presented to illustrate the results obtained at the microscopic scale. [ABSTRACT FROM AUTHOR]

Published
2020
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42. Modeling the spatial propagation of Aβ oligomers in Alzheimer's Disease.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Andrade-Restrepo, Martin, Lemarre, Paul, Pujo-Menjouet, Laurent, Tine, Leon Matar, and Ciuperca, Sorin Ionel

Subjects
*ALZHEIMER'S disease, *AMYLOID beta-protein precursor, *OLIGOMERS, *NEUROTOXICOLOGY, *DISEASE progression, *COMPUTER simulation of biological systems
Abstract

Recent advances in the study of Alzheimer's Disease and the role of Aβ amyloid formation have caused the focus of biologists to progressively shift towards the smaller protein assemblies, the oligomers. These appear very early on in the disease progression and they seem to be the most infectious species for the neurons. We suggest a model of spatial propagation of Aβ oligomers in the vicinity of a few neurons, without considering the formation of large fibrils or plaques. We also include a simple representation of the oligomers neurotoxic effect. A numerical study reveals that the oligomers spatial dynamics are very sensitive to the balance between their diffusion and their replication, and that the outcome in terms of the progression of AD strongly depends on it. [ABSTRACT FROM AUTHOR]

Published
2020
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43. Aerosol Transport Throughout Inspiration and Expiration in the Pulmonary Airways

Author

Oakes, Jessica M., Shadden, Shawn C., Grandmont, Céline, Vignon-Clementel, Irene, Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Mechanical Engineering [Berkeley], INRIA International Postdoctoral Grant (J.M. Oakes), University of California Presidential Postdoctoral Fellowship (J.M. Oakes), and ANR-11-TECS-0006,OxHelease,Impact de l'inhalation de l'hélium-oxygène sur la ventilation, l'oxygénation sanguine, le dépôt d'aérosol dans les maladies respiratoires chroniques obstructives: étude des cas de l'asthme et de l'emphysème(2011)

Subjects
[PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], particle deposition, whole lung modeling, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], respiratory tract, inhalation and exhalation, computational fluid dynamics (CFD)
Abstract

International audience; Little is known about transport throughout the respiration cycle in the conducting airways. It is challenging to appropriately describe the time-dependent number of particles entering back into the model during exhalation. Modeling the entire lung is not feasible; therefore multi-domain methods must be employed. Here, we present a new framework that is designed to simulate particles throughout the respiration cycle, incorporating realistic airway geometry and respiration. This framework is applied for a healthy rat lung exposed to 1 micron diameter particles to facilitate parameterization and validation. The flow field is calculated in the conducting airways (3D domain) by solving the incompressible Navier-Stokes equations with experimentally derived boundary conditions. Particles are tracked throughout inspiration by solving a modified Maxey-Riley equation. Next, we pass the time-dependent particle concentrations exiting the 3D model to the 1D volume conservation and advection-diffusion models (1D domain). Once the 1D models are solved, we prescribe the time-dependent number of particles entering back into the 3D airways to again solve for 3D transport. The coupled simulations highlight that about twice as many particles deposit during inhalation compared to exhalation for the entire lung. In contrast to inhalation, where the majority of particles deposit at the bifurcation zones, particles deposit relatively uniformly on the gravitationally dependent side of the 3D airways during exhalation. Strong agreement to previously collected regional experimental data is shown, as the 1D models account for lobe-dependent morphology. This framework may be applied to investigate dosimetry in other species and pathological lungs.

Published
2016

44. Aerosols in the lung: multi-domain transport and coupling

Author

Oakes, Jessica M., Shadden, Shawn C., Grandmont, Céline, Vignon-Clementel, Irene, Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Department of Mechanical Engineering [Berkeley]

Subjects
particles, computational fluid dynamics, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], respiratory tract, inspiration and expiration
Abstract

International audience; In this paper, we present a framework that couples three-dimensional (3D) to one-dimensional (1D) transport models to predict particle deposition in the respiratory airways throughout respiration. During respiration, the time dependent flow rate and particle concentration can be passed between the domains (inspiration: 3D to 1D, expiration: 1D to 3D). This framework enables us to predict particle transport and deposition in the whole lung and throughout both inspiration and expiration.

Published
2015

45. Numerical stability of coupling schemes in the 3d/0d modelling ofairflows and blood flows

Author

Fouchet-Incaux, Justine, Grandmont, Céline, Martin, Sebastien, Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), ANR-11-TECS-0006,OxHelease,Impact de l'inhalation de l'hélium-oxygène sur la ventilation, l'oxygénation sanguine, le dépôt d'aérosol dans les maladies respiratoires chroniques obstructives: étude des cas de l'asthme et de l'emphysème(2011), Numerical simulation of biological flows ( REO ), Laboratoire Jacques-Louis Lions ( LJLL ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Université Paris Diderot - Paris 7 ( UPD7 ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Université Paris Diderot - Paris 7 ( UPD7 ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), ANR-11-TECS-0006,OxHelease,Impact de l'inhalation de l'hélium-oxygène sur la ventilation, l'oxygénation sanguine, le dépôt d'aérosol dans les maladies respiratoires chroniques obstructives: étude des cas de l'asthme et de l'emphysème ( 2011 ), Grandmont, Celine, and Technologie pour la santé et l'autonomie - Impact de l'inhalation de l'hélium-oxygène sur la ventilation, l'oxygénation sanguine, le dépôt d'aérosol dans les maladies respiratoires chroniques obstructives: étude des cas de l'asthme et de l'emphysème - - OxHelease2011 - ANR-11-TECS-0006 - TecSan - VALID

Subjects
[ MATH ] Mathematics [math], [ INFO.INFO-MO ] Computer Science [cs]/Modeling and Simulation, [ SDV ] Life Sciences [q-bio], MESH: Numerical Analysis, [SDV]Life Sciences [q-bio], [MATH] Mathematics [math], [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], MESH : Fluid equations, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [SDV] Life Sciences [q-bio], MESH : Numerical Analysis, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, MESH: Fluid equations, [MATH]Mathematics [math], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

We consider models which are classically used in the simulation of airflows and blood flows andinvestigate the numerical stability of some discretization strategies. The geometrical complexity of the networksin which air/blood flows leads to a classical decomposition of two areas: a truncated 3D geometry correspondingto the largest contribution of the domain and a 0D part connected to the 3D part, modelling air/blood flowsin smaller airways/vessels. The resulting Navier-Stokes system in the 3D truncated part may involve non-local boundary conditions, deriving from a mechanical model. For various 3D/0D coupled models, differentdiscretization processes are presented and analyzed in terms of numerical stability, highlighting strong differencesaccording to the regimes that are considered. In particular, two main stability issues are investigated: first thecoupling between the 3D and the 0D part for which implicit or explicit strategies are studied and, second, thequestion of estimating the amount of kinetic energy entering the 3D domain because of the artificial boundaries.In particular, we prove new estimates in appropriate norms for the discretized-in-time Navier-Stokes system.These estimates are derived under conditions on the smallness of the data, enlighting the intrinsic difficultyencountered with such systems to perform realistic simulations. We illustrate some of the theoretical resultswith numerical simulations, firstly in a single tube, then in a bifurcation geometry and finally in real geometries.Finally, we discuss the difference between airflows and blood flows in terms of numerical stability related tothe magnitude of the physiological and physical parameters. Stokes and Navier-Stokes equations; coupling ofmodels; numerical stability; numerical computations; finite element method

Published
2014

46. Development of a 3D to 1D Particle Transport Model to Predict Deposition in the Lungs

Author

Oakes, Jessica M., Grandmont, Céline, Shadden, Shawn C., Vignon-Clementel, Irene, Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Department of Mechanical Engineering [Berkeley]

Subjects
[PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph]
Abstract

International audience; Aerosolized particles are commonly used for therapeutic drug delivery as they can be delivered to the body systemically or be used to treat lung diseases. Recent advances in computational resources have allowed for sophisticated pulmonary simulations, however it is currently impossible to solve for airflow and particle transport for all length and time scales of the lung. Instead, multi-scale methods must be used. In our recent work, where computational methods were employed to solve for airflow and particle transport in the rat airways (Oakes et al. (2014), Annals of Biomedical Engineering, 42: 899-914), the number of particles to exit downstream of the 3D domain was determined. In this current work, the time-dependent Lagrangian description of particles was used to numerically solve a 1D convection-diffusion model (trumpet model, Taulbee and Yu (1975), Journal of Applied Physiology, 38: 77-85) parameterized specifically for the lung. The expansion of the airway dimensions was determined based on data collected from our aerosol exposure experiments (Oakes et al. (2014), Journal of Applied Physiology, 116: 1561-8). This 3D-1D framework enables us to predict the fate of particles in the whole lung.

Published
2014

47. Modeling of flow limitation phenomena in the human respiratory tract during forced expiration

Author

Fouchet-Incaux, Justine, Grandmont, Céline, Martin, Sebastien, Maury, Bertrand, Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Numerical simulation of biological flows ( REO ), Laboratoire Jacques-Louis Lions ( LJLL ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Université Paris Diderot - Paris 7 ( UPD7 ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Université Paris Diderot - Paris 7 ( UPD7 ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques d'Orsay ( LM-Orsay ), Université Paris-Sud - Paris 11 ( UP11 ) -Centre National de la Recherche Scientifique ( CNRS ), and Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)

Subjects
[ MATH ] Mathematics [math], [ SDV ] Life Sciences [q-bio], [SDV]Life Sciences [q-bio], [MATH]Mathematics [math], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2014

48. Mathematical and Numerical Analysis of some fluid-structure interaction problems

Author

Grandmont, Céline, Necasová, Sárka, Lukacova-Medvid'Ova, Maria, Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Mathematical Institute [Praha] - Academy of Sciences, Czech Academy of Sciences [Prague] (CAS), Technical University Hamburg Harburg [Hamburg], Bodnár, Tomáš and Galdi, Giovanni P. and Nečasová, Šárka, Grandmont, Celine, and Bodnár, Tomáš and Galdi, Giovanni P. and Nečasová, Šárka

Subjects
[SPI.MECA.BIOM] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], [PHYS.MECA.BIOM] Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], 35Q35, 74F10, 76Z05, 76M10, 76M12, 74S05, 74S10, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In this chapter we deal with some specific existence and numerical results applied to a 2D/1D fluid-structure coupled model, for an incompressible fluid and a thin elastic structure. We will try to underline some of the mathematical and numeri- cal difficulties that one may face when studying this kind of problems such as the geometrical nonlinearities or the added mass effect. In particular we will try to underline the link between the strategies of proof of weak or strong solutions and the possible algorithms to discretize these type of coupled problems

Published
2014

49. Spatial distribution of aerosols in healthy rat lungs: findings from numerical and experimental models

Author

Oakes, Jessica, Darquenne, Chantal, Grandmont, Céline, Scadeng, Miriam, Breen, Ellen, Vignon-Clementel, Irene, Marsden, Alison, Department of Mechanical and Aerospace Engineering [La Jolla] (UCSD), University of California [San Diego] (UC San Diego), University of California-University of California, Department of Medicine [San Diego], Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Radiology [San Diego], EA Cardio, Department of Mechanical and Aerospace Engineering [Univ California San Diego] (MAE - UC San Diego), University of California (UC)-University of California (UC), Department of Medicine [Univ California San Diego] (MED - UC San Diego), School of Medicine [Univ California San Diego] (UC San Diego), University of California (UC)-University of California (UC)-University of California [San Diego] (UC San Diego), and Department of Radiology [Univ California San Diego] (UC San Diego)

Subjects
[SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph]
Abstract

WOS:000317040000096; International audience

Published
2013

50. Stability estimates for the unique continuation property of the Stokes system. Application to an inverse problem

Author

Boulakia, Muriel, Egloffe, Anne-Claire, Grandmont, Céline, Egloffe, Anne-Claire, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Numerical simulation of biological flows (REO), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Stokes system, Robin boundary conditions, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Stability estimates, Local Carleman inequalities, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Inverse boundary coefficient problem
Abstract

International audience; In the first part of this paper, we prove hölderian and logarithmic stability estimates associated to the unique continuation property for the Stokes system. The proof of these results is based on local Carleman inequalities. In the second part, these estimates on the fluid velocity and on the fluid pressure are applied to solve an inverse problem: we consider the Stokes system completed with mixed Neumann and Robin boundary conditions and we want to recover the Robin coefficient (and obtain stability estimate for it) from measurements available on a part of the boundary where Neumann conditions are prescribed. For this identification parameter problem, we obtain a logarithmic stability estimate under the assumption that the velocity of a given reference solution stays far from 0 on a part of the boundary where Robin conditions are prescribed.

Published
2013

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