64 results on '"Damiano Lombardi"'
Search Results
2. An Information-Theoretic Framework for Optimal Design: Analysis of Protocols for Estimating Soft Tissue Parameters in Biaxial Experiments
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Ankush Aggarwal, Damiano Lombardi, and Sanjay Pant
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optimal design ,soft tissue mechanics ,mutual information ,biaxial experiment ,inverse problems ,information theory ,Mathematics ,QA1-939 - Abstract
A new framework for optimal design based on the information-theoretic measures of mutual information, conditional mutual information and their combination is proposed. The framework is tested on the analysis of protocols—a combination of angles along which strain measurements can be acquired—in a biaxial experiment of soft tissues for the estimation of hyperelastic constitutive model parameters. The proposed framework considers the information gain about the parameters from the experiment as the key criterion to be maximised, which can be directly used for optimal design. Information gain is computed through k-nearest neighbour algorithms applied to the joint samples of the parameters and measurements produced by the forward and observation models. For biaxial experiments, the results show that low angles have a relatively low information content compared to high angles. The results also show that a smaller number of angles with suitably chosen combinations can result in higher information gains when compared to a larger number of angles which are poorly combined. Finally, it is shown that the proposed framework is consistent with classical approaches, particularly D-optimal design. more...
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- 2021
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3. Composite Biomarkers Derived from Micro-Electrode Array Measurements and Computer Simulations Improve the Classification of Drug-Induced Channel Block
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Eliott Tixier, Fabien Raphel, Damiano Lombardi, and Jean-Frédéric Gerbeau
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cardiac electrophysiology ,numerical simulations ,bidomain model ,micro-electrode array ,classification ,drug safety evaluation ,Physiology ,QP1-981 - Abstract
The Micro-Electrode Array (MEA) device enables high-throughput electrophysiology measurements that are less labor-intensive than patch-clamp based techniques. Combined with human-induced pluripotent stem cells cardiomyocytes (hiPSC-CM), it represents a new and promising paradigm for automated and accurate in vitro drug safety evaluation. In this article, the following question is addressed: which features of the MEA signals should be measured to better classify the effects of drugs? A framework for the classification of drugs using MEA measurements is proposed. The classification is based on the ion channels blockades induced by the drugs. It relies on an in silico electrophysiology model of the MEA, a feature selection algorithm and automatic classification tools. An in silico model of the MEA is developed and is used to generate synthetic measurements. An algorithm that extracts MEA measurements features designed to perform well in a classification context is described. These features are called composite biomarkers. A state-of-the-art machine learning program is used to carry out the classification of drugs using experimental MEA measurements. The experiments are carried out using five different drugs: mexiletine, flecainide, diltiazem, moxifloxacin, and dofetilide. We show that the composite biomarkers outperform the classical ones in different classification scenarios. We show that using both synthetic and experimental MEA measurements improves the robustness of the composite biomarkers and that the classification scores are increased. more...
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- 2018
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4. Conformal variational discretisation of infinite dimensional Hamiltonian systems with gradient flow dissipation.
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Damiano Lombardi and Cecilia Pagliantini
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- 2024
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5. A Low-Rank Solver for Parameter Estimation and Uncertainty Quantification in Time-Dependent Systems of Partial Differential Equations.
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Sébastien Riffaud, Miguel A. Fernández, and Damiano Lombardi
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- 2024
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6. In Silico Characterization of Repolarization Duration and Variability in the Long QT1 Syndrome Under β-Adrenergic Stimulation.
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David Adolfo Sampedro-Puente, Fabien Raphel, Jesus Fernandez-Bes, Pablo Laguna, Damiano Lombardi, and Esther Pueyo
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- 2020
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7. Adaptive Hierarchical Subtensor Partitioning for Tensor Compression.
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Virginie Ehrlacher, Laura Grigori, Damiano Lombardi, and Hao Song
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- 2021
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8. Characterization of Spatio-Temporal Cardiac Action Potential Variability at Baseline and Under $\beta$-Adrenergic Stimulation by Combined Unscented Kalman Filter and Double Greedy Dimension Reduction.
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David Adolfo Sampedro-Puente, Fabien Raphel, Jesus Fernandez-Bes, Pablo Laguna, Damiano Lombardi, and Esther Pueyo
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- 2021
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9. Approximation of optimal transport problems with marginal moments constraints.
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Aurélien Alfonsi, Rafaël Coyaud, Virginie Ehrlacher, and Damiano Lombardi
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- 2021
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10. Waserstein model reduction approach for parametrized flow problems in porous media.
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Beatrice Battisti, Tobias Blickhan, Guillaume Enchéry, Virginie Ehrlacher, Damiano Lombardi, and Olga Mula
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- 2022
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11. Numerical quadrature in the Brillouin zone for periodic Schrödinger operators.
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Eric Cancès, Virginie Ehrlacher, David Gontier, Antoine Levitt, and Damiano Lombardi
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- 2020
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12. State Estimation with Model Reduction and Shape Variability. Application to biomedical problems.
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Felipe Galarce, Damiano Lombardi, and Olga Mula
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- 2021
13. State Estimation with Model Reduction and Shape Variability. Application to biomedical problems.
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Felipe Galarce, Damiano Lombardi, and Olga Mula
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- 2022
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14. SOTT: Greedy Approximation of a Tensor as a Sum of Tensor Trains.
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Virginie Ehrlacher, Maria Fuente Ruiz, and Damiano Lombardi
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- 2022
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15. Reconstructing Haemodynamics Quantities of Interest from Doppler Ultrasound Imaging.
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Felipe Galarce, Damiano Lombardi, and Olga Mula
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- 2020
16. CP-TT: using TT-SVD to greedily construct a Canonical Polyadic tensor approximation.
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Virginie Ehrlacher, Maria Fuente Ruiz, and Damiano Lombardi
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- 2020
17. A dynamical adaptive tensor method for the Vlasov-Poisson system.
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Virginie Ehrlacher and Damiano Lombardi
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- 2017
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18. Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces.
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Virginie Ehrlacher, Damiano Lombardi, Olga Mula, and François-Xavier Vialard
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- 2019
19. A Moment-Matching Method to Study the Variability of Phenomena Described by Partial Differential Equations.
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Jean-Frédéric Gerbeau, Damiano Lombardi, and Eliott Tixier
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- 2018
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20. Reduced order model in cardiac electrophysiology with approximated Lax pairs.
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Jean-Frédéric Gerbeau, Damiano Lombardi, and Elisa Schenone
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- 2015
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21. Approximated Lax pairs for the reduced order integration of nonlinear evolution equations.
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Jean-Frédéric Gerbeau and Damiano Lombardi
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- 2014
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22. A lagrangian scheme for the solution of the optimal mass transfer problem.
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Angelo Iollo and Damiano Lombardi
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- 2011
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23. Fast semi-automatic segmentation based on reduced basis
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Yvon Maday, Damiano Lombardi, Lydie Uro, COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut des Sciences du Calcul et des Données (ISCD), 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), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité) more...
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Basis (linear algebra) ,business.industry ,General Mathematics ,Linear system ,Pattern recognition ,02 engineering and technology ,Object (computer science) ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,Grayscale ,030218 nuclear medicine & medical imaging ,Image (mathematics) ,03 medical and health sciences ,0302 clinical medicine ,0202 electrical engineering, electronic engineering, information engineering ,Medical imaging ,A priori and a posteriori ,020201 artificial intelligence & image processing ,Segmentation ,Artificial intelligence ,business ,Mathematics - Abstract
International audience; This note adresses the following segmentation problem in medical imaging : minimize expert intervention for semi-automatic segmentation process. Using a reduced basis, we have an a priori knowledge of the objet we want to identify on the images, like a muscle on a CT-Scan. We just have to identify the coefficients associated to the object of interest in the reduced basis, by solving a linear system taking as input the coordinates of some selected points in the image. An example implemented in 2D is shown. This method is independent of the grayscale of the image, and can therefore be applied to all objects and images. To cite this article: Y. Maday, D. Lombardi, L. Uro, C. R. Acad. Sci. Paris, Ser. I 340 (2019).; Résumé Méthode de segmentation semi-automatique fondée sur une base réduite Nous présentons ici une méthode de segmentation d'imagerie médicale semi-automatique minimisant l'interventions d'un expert. A l'aide d'une base réduite, nous connaissons a priori la forme de l'objetà identifier sur les images, comme un muscle sur un scanner. Il suffit d'identifier les coefficients associésà l'objet d'intéret dans la base rduite, via la résolution d'un système linéaire prenant en entrée les coordonnées de quelques points sélectionnés sur l'image. Un exemple implémenté en 2D est proposé.. Cette méthode est indépendante des niveaux de gris de l'image, et peut donĉ etre appliquées sur tous objets et toutes imageries. Pour citer cet article : Y. Maday, D. Lombardi, L. Uro, C. R. Acad. Sci. Paris, Ser. I 340 (2005). more...
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- 2021
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24. State estimation in nonlinear parametric time dependent systems using tensor train
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Damiano, Lombardi, primary
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- 2022
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25. A non-parametric k-nearest neighbour entropy estimator.
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Damiano Lombardi and Sanjay Pant
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- 2015
26. A method to enrich experimental datasets by means of numerical simulations in view of classification tasks
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Damiano Lombardi, Fabien Raphel, 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), and 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) more...
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Science and engineering ,02 engineering and technology ,Machine learning ,computer.software_genre ,01 natural sciences ,010305 fluids & plasmas ,Set (abstract data type) ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,1991 Mathematics Subject Classification. 60B10, 68T05 ,[MATH]Mathematics [math] ,Mathematics ,Numerical Analysis ,business.industry ,Statistical learning ,Hausdorff distance ,Applied Mathematics ,Construct (python library) ,Nearest Neighbors ,Classification ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,Variety (cybernetics) ,Computational Mathematics ,ComputingMethodologies_PATTERNRECOGNITION ,Mathematics Subject Classification. 60B10, 68T05 ,Modeling and Simulation ,A priori and a posteriori ,020201 artificial intelligence & image processing ,Artificial intelligence ,business ,Classifier (UML) ,computer ,Analysis - Abstract
International audience; Classification tasks are frequent in many applications in science and engineering. A wide variety of statistical learning methods exist to deal with these problems. However, in many industrial applications, the number of available samples to train and construct a classifier is scarce and this has an impact on the classifications performances. In this work, we consider the case in which some a priori information on the system is available in form of a mathematical model. In particular, a set of numerical simulations of the system can be integrated to the experimental dataset. The main question we address is how to integrate them systematically in order to improve the classification performances. The method proposed is based on Nearest Neighbours and on the notion of Hausdorff distance between sets. Some theoretical results and several numerical studies are proposed.; Les problèmes de classification sont fréquents dans de nombreuses applications de la science et de l'ingénierie. Une grande variété de méthodes d'apprentissages statistique existent pour répondrè a ces problématiques. Cependant, dans beaucoup d'applications industrielles, le nombre d'échantillons disponibles pour la base d'apprentissage et construire le classificateur est faible et impacte ainsi les preformances de classification. Dans ce travail, nous considérons le cas dans lequel nous avons un modèle mathématiques décrivant le système physique associé. En particulier, un ensemble de ces simulations du système peuventêtre intégréesà la base de données expérimentale. La principale question que nous abordons concerne l'intégration automatique de ces données dans le but d'améliorer les performances du classificateur. La méthode proposée utilise les plus proches voisins ainsi que la distance de Hausdorff entre ensembles. Des résultats théoriques et des exemples d'applications numériques sont montrés. more...
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- 2021
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27. Fast reconstruction of 3D blood flows from Doppler ultrasound images and reduced models
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Jean-Frédéric Gerbeau, Olga Mula, Damiano Lombardi, Felipe Galarce, 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), Inria Siège, Institut National de Recherche en Informatique et en Automatique (Inria), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), 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), Université Paris Dauphine-PSL, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) more...
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Computer science ,Mechanical Engineering ,3D reconstruction ,Computational Mechanics ,General Physics and Astronomy ,Numerical Analysis (math.NA) ,010103 numerical & computational mathematics ,01 natural sciences ,3. Good health ,Computer Science Applications ,Term (time) ,Task (project management) ,010101 applied mathematics ,Linear map ,Nonlinear system ,[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] ,Flow (mathematics) ,Mechanics of Materials ,FOS: Mathematics ,A priori and a posteriori ,Mathematics - Numerical Analysis ,0101 mathematics ,Greedy algorithm ,Algorithm ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
This paper deals with the problem of building fast and reliable 3D reconstruction methods for blood flows for which partial information is given by Doppler ultrasound measurements. This task is of interest in medicine since it could enrich the available information used in the diagnosis of certain diseases which is currently based essentially on the measurements coming from ultrasound devices. The fast reconstruction of the full flow can be performed with state estimation methods that have been introduced in recent years and that involve reduced order models. One simple and efficient strategy is the so-called Parametrized Background Data-Weak approach (PBDW, see Maday et al. (2015)). It is a linear mapping that consists in a least squares fit between the measurement data and a linear reduced model to which a certain correction term is added. However, in the original approach, the reduced model is built a priori and independently of the reconstruction task (typically with a proper orthogonal decomposition or a greedy algorithm). In this paper, we investigate the construction of other reduced spaces which are built to be better adapted to the reconstruction task and which result in mappings that are sometimes nonlinear. We compare the performance of the different algorithms on numerical experiments involving synthetic Doppler measurements. The results illustrate the superiority of the proposed alternatives to the classical linear PBDW approach. more...
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- 2021
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28. Adaptive Hierarchical Subtensor Partitioning for Tensor Compression
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Hao Song, Virginie Ehrlacher, Laura Grigori, Damiano Lombardi, Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), MATHematics for MatERIALS (MATHERIALS), École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Algorithms and parallel tools for integrated numerical simulations (ALPINES), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-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), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, ANR-18-CE46-0001,ADAPT,Méthodes tensorielles parallèles dynamiques et adaptatives(2018), European Project: 810367,EMC2(2019), 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), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC), and 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) more...
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Work (thermodynamics) ,Applied Mathematics ,Numerical analysis ,010102 general mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,Compression ,CP and Tucker formats ,Order (ring theory) ,010103 numerical & computational mathematics ,Tensors ,[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA] ,01 natural sciences ,Partition (database) ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,Computational Mathematics ,AMS subject classifications. 65F99, 65D15 ,Compression (functional analysis) ,A priori and a posteriori ,HOSVD ,Tensor ,0101 mathematics ,Algorithm ,Mathematics - Abstract
International audience In this work a numerical method is proposed to compress a tensor by constructing a piece-wise tensor approximation. This is defined by partitioning a tensor into sub-tensors and by computing a low-rank tensor approximation (in a given format) in each sub-tensor. Neither the partition nor the ranks are fixed a priori, but, instead, are obtained in order to fulfill a prescribed accuracy and optimize, to some extent, the storage. The different steps of the method are detailed and some numerical experiments are proposed to assess its performances. more...
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- 2021
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29. INSPIRE
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Dries Braeken, Guido R.Y. De Meyer, Ron M. A. Heeren, Matt Skinner, Sylvain Bernasconi, Yair Shemesh, Xi Yang, Elena Matsa, Helen Prior, Vincent F.M. Segers, Paz Yanez, Harm J. Knot, Michael Markert, Vitalina Gryshkova, Wim Martinet, Brian Guth, Krystle Correll, Damiano Lombardi, Jean-Pierre Valentin, Jeanette Woolard, Georgios Kosmidis, Annie Delaunois, Pieter-Jan Guns, Constantijn Franssen, Emeline M. Van Craenenbroeck, Alon Chen, Berta Cillero-Pastor, Miguel Angel Fernández, Thomas Pauwelyn, Gábor Kismihók, Paul G.A. Volders, Céline Grandmont, Stefan R. Braam, Imaging Mass Spectrometry (IMS), RS: M4I - Imaging Mass Spectrometry (IMS), Cardiologie, MUMC+: MA Med Staf Spec Cardiologie (9), and RS: Carim - H04 Arrhythmogenesis and cardiogenetics more...
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Drug-Related Side Effects and Adverse Reactions ,Marie Sklodowska-curie actions ,Drug development ,030204 cardiovascular system & hematology ,PRESSURE ,Toxicology ,Cardiovascular System ,030226 pharmacology & pharmacy ,03 medical and health sciences ,0302 clinical medicine ,Political science ,Methods ,Humans ,Cardiovascular safety liabilities ,RODENTS ,European commission ,Drug reaction ,Cardio oncology ,Pharmacology ,Cardiovascular safety ,CELL-DERIVED CARDIOMYOCYTES ,Pharmacology. Therapy ,Safety pharmacology ,Pillar ,3. Good health ,Clinical trial ,Cardio-oncology ,PARADIGM ,Engineering ethics ,Safety ,Training and education ,CLINICAL-TRIALS - Abstract
Safety pharmacology is an essential part of drug development aiming to identify, evaluate and investigate undesirable pharmacodynamic properties of a drug primarily prior to clinical trials. In particular, cardiovascular adverse drug reactions (ADR) have halted many drug development programs. Safety pharmacology has successfully implemented a screening strategy to detect cardiovascular liabilities, but there is room for further refinement. In this setting, we present the INSPIRE project, a European Training Network in safety pharmacology for Early Stage Researchers (ESRs), funded by the European Commission's H2020-MSCA-ITN programme. INSPIRE has recruited 15 ESR fellows that will conduct an individual PhD-research project for a period of 36 months. INSPIRE aims to be complementary to ongoing research initiatives. With this as a goal, an inventory of collaborative research initiatives in safety pharmacology was created and the ESR projects have been designed to be complementary to this roadmap. Overall, INSPIRE aims to improve cardiovascular safety evaluation, either by investigating technological innovations or by adding mechanistic insight in emerging safety concerns, as observed in the field of cardio-oncology. Finally, in addition to its hands-on research pillar, INSPIRE will organize a number of summer schools and workshops that will be open to the wider community as well. In summary, INSPIRE aims to foster both research and training in safety pharmacology and hopes to inspire the future generation of safety scientists. more...
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- 2020
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30. Prediction of the Evolution of Thyroidal Lung Nodules Using a Mathematical Model.
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Thierry Colin, Angelo Iollo, Damiano Lombardi, and Olivier Saut
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- 2010
31. In Silico Characterization of Repolarization Duration and Variability in the LQT1 Syndrome Under β-Adrenergic Stimulation
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Pablo Laguna, Fabien Raphel, Jesus Fernandez-Bes, David Adolfo Sampedro-Puente, Esther Pueyo, and Damiano Lombardi
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0301 basic medicine ,education.field_of_study ,In silico ,Population ,Model parameters ,030204 cardiovascular system & hematology ,03 medical and health sciences ,030104 developmental biology ,0302 clinical medicine ,Duration (music) ,Repolarization ,β adrenergic stimulation ,education ,Neuroscience - Abstract
Enhanced temporal repolarization variability facilitates ventricular arrhythmias in the long QT 1 (LQT1) syndrome, particularly under β-adrenergic stimulation β-AS). The underlying mechanisms are, however, not fully elucidated. In silico investigation of such mechanisms first requires methods able to reproduce the experimental observations. Here, we describe a method for identification of in silico action potential (AP) models from input voltage traces and we apply it to investigate repolarization variability in LQT1. A combination of Double Greedy Dimension Reduction (DGDR) Unscented Kalman Filter (UKF) was used to estimate the ionic conductances and phosphorylation levels of coupled AP and β-AS models. Over synthetic AP traces from an experimentally-calibrated population of LQT1 cells, combined DGDR-UKF accurately estimated the model parameters, with reduced estimation uncertainty and convergence time. Importantly, combined DGDR-UKF was able to reliably replicate the statistical distributions of AP duration and short-term variability, both at baseline and underβ-AS, with relative errors below 4%. Arrhythmogenic AP alternans were reproduced too. In conclusion, our method allows characterization of repolarization duration and variability in LQT1, which is expected to help disentangling the mechanisms underlying adrenergic-induced arrhythmias in this syndrome. more...
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- 2020
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32. Reducing Hypermuscularization of the Transitional Segment Between Arterioles and Capillaries Protects Against Spontaneous Intracerebral Hemorrhage
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Monara Kaelle Servulo Cruz Angelim, Nicholas R. Klug, Julien Ratelade, Mark T. Nelson, Valérie Domenga-Denier, Fabrice Dabertrand, Anne Joutel, Damiano Lombardi, Rustam Al-Shahi Salman, Colin Smith, Jean-Frédéric Gerbeau, Institut de psychiatrie et neurosciences de Paris (IPNP - U1266 Inserm), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Paris (UP), University of Vermont [Burlington], 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), University of Colorado Anschutz [Aurora], University of Edinburgh, Inria Siège, Institut National de Recherche en Informatique et en Automatique (Inria), University of Manchester [Manchester], Université Sorbonne Paris Cité (USPC), This work was supported by Fondation Leducq (Transatlantic Network of Excellence on the Pathogenesis of Small Vessel Disease of the Brain) to AJ and MTN, the European Union (Horizon 2020 Research and Innovation Programme SVDs@target under the grant agreement n° 666881), the French National Agency of Research (ANR I-Can) and the French Fondation for Rare Diseases to AJ, the National Institute of Neurological Disorders and Stroke (NINDS) and National Institute of Aging (NIA) (R01NS110656), the National Institutes of Health under Award Number R35HL140027 and the Henry M. Jackson Foundation for the Advancement of Military Medicine (HU0001-18-2-0016) to MTN. The LINCHPIN study was funded by UK Medical Research Council (MRC) and The Stroke Association. The Edinburgh Brain Bank, part of the MRC UK Brain Bank Network, curates the brain tissue from LINCHPIN study tissue donors and controls who died suddenly from non-neurological conditions. The Edinburgh Brain Bank is funded by both MRC and The Stroke Association., Institut National de la Santé et de la Recherche Médicale (INSERM)-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), Martinez Rico, Clara, Institute of Psychiatry and Neurosciences of Paris, INSERM U1266, University of Paris, Paris, France., Department of Pharmacology, College of Medicine, University of Vermont, Burlington, VT., Inria Paris, Sorbonne University, Laboratory Jacques-Louis Lions, Paris, France, Institute of Psychiatry and Neurosciences of Paris, INSERM U1266, University of Paris, Paris, France, Department of Pharmacology, College of Medicine, University of Vermont, Burlington, VT, Department of Anesthesiology, Department of Pharmacology, Anschutz Medical Campus, University of Colorado, Aurora, CO, Institute of Psychiatry and Neurosciences of Paris, INSERM U1266, University of Paris, Paris, Centre for Clinical Brain Sciences, University of Edinburgh, Edinburgh, UK, Division of Cardiovascular Sciences, University of Manchester, Manchester, UK, DHU NeuroVasc, Sorbonne Paris Cité, Paris, France., Institut de psychiatrie et neurosciences de Paris (IPNP - U1266 Inserm - Paris Descartes), Université Paris Descartes - Paris 5 (UPD5)-Institut National de la Santé et de la Recherche Médicale (INSERM), and 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) more...
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Pathology ,[SDV]Life Sciences [q-bio] ,Gene Expression ,Retinal Neovascularization ,Hypermuscularization ,Muscle, Smooth, Vascular ,Mice ,0302 clinical medicine ,Transitional segment ,Receptor, Notch3 ,Mice, Knockout ,Collagen IV ,0303 health sciences ,[SDV.MHEP] Life Sciences [q-bio]/Human health and pathology ,Hyperplasia ,Immunohistochemistry ,Molecular Imaging ,3. Good health ,[SDV] Life Sciences [q-bio] ,medicine.anatomical_structure ,cardiovascular system ,[SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC] ,Disease Susceptibility ,Cardiology and Cardiovascular Medicine ,Collagen Type IV ,medicine.medical_specialty ,Genotype ,Myocytes, Smooth Muscle ,Retina ,Article ,Mural cell ,Contractility ,03 medical and health sciences ,Downregulation and upregulation ,Arteriole ,Physiology (medical) ,medicine.artery ,Genetic model ,[SDV.BBM] Life Sciences [q-bio]/Biochemistry, Molecular Biology ,medicine ,Animals ,Humans ,[SDV.BBM]Life Sciences [q-bio]/Biochemistry, Molecular Biology ,[SDV.NEU] Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC] ,cardiovascular diseases ,Cerebral Hemorrhage ,030304 developmental biology ,Intracerebral hemorrhage ,business.industry ,Notch3 ,medicine.disease ,Disease Models, Animal ,Microvessels ,Mutation ,business ,Biomarkers ,[SDV.MHEP]Life Sciences [q-bio]/Human health and pathology ,030217 neurology & neurosurgery - Abstract
Background: Spontaneous deep intracerebral hemorrhage (ICH) is a devastating subtype of stroke without specific treatments. It has been thought that smooth muscle cell (SMC) degeneration at the site of arteriolar wall rupture may be sufficient to cause hemorrhage. However, deep ICHs are rare in some aggressive small vessel diseases that are characterized by significant arteriolar SMC degeneration. Here we hypothesized that a second cellular defect may be required for the occurrence of ICH. Methods: We studied a genetic model of spontaneous deep ICH using Col4a1 +/G498V and Col4a1 +/G1064D mouse lines that are mutated for the α1 chain of collagen type IV. We analyzed cerebroretinal microvessels, performed genetic rescue experiments, vascular reactivity analysis, and computational modeling. We examined postmortem brain tissues from patients with sporadic deep ICH. Results: We identified in the normal cerebroretinal vasculature a novel segment between arterioles and capillaries, herein called the transitional segment (TS), which is covered by mural cells distinct from SMCs and pericytes. In Col4a1 mutant mice, this TS was hypermuscularized, with a hyperplasia of mural cells expressing more contractile proteins, whereas the upstream arteriole exhibited a loss of SMCs. TSs mechanistically showed a transient increase in proliferation of mural cells during postnatal maturation. Mutant brain microvessels, unlike mutant arteries, displayed a significant upregulation of SM genes and Notch3 target genes, and genetic reduction of Notch3 in Col4a1 +/G498V mice protected against ICH. Retina analysis showed that hypermuscularization of the TS was attenuated, but arteriolar SMC loss was unchanged in Col4a1 +/G498V , Notch3 +/− mice. Moreover, hypermuscularization of the retinal TS increased its contractility and tone and raised the intravascular pressure in the upstream feeding arteriole. We similarly found hypermuscularization of the TS and focal arteriolar SMC loss in brain tissues from patients with sporadic deep ICH. Conclusions: Our results suggest that hypermuscularization of the TS, through increased Notch3 activity, is involved in the occurrence of ICH in Col4a1 mutant mice, by raising the intravascular pressure in the upstream feeding arteriole and promoting its rupture at the site of SMC loss. Our human data indicate that these 2 mutually reinforcing vascular defects may represent a general mechanism of deep ICH. more...
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- 2020
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33. A reduced-order representation of the Poincaré-Steklov operator: an application to coupled multi-physics problems
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Matteo Aletti and Damiano Lombardi
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Numerical Analysis ,Basis (linear algebra) ,Interface (Java) ,Applied Mathematics ,Computation ,Mathematical analysis ,General Engineering ,010103 numerical & computational mathematics ,Eigenfunction ,01 natural sciences ,Poincaré–Steklov operator ,010101 applied mathematics ,Reduction (complexity) ,Operator (computer programming) ,Applied mathematics ,0101 mathematics ,Representation (mathematics) ,Mathematics - Abstract
This work investigates a model reduction method applied to coupled multi-physics systems. The case in which a system of interest interacts with an external system is considered. An approximation of the \PoinSte operator is computed by simulating, in an offline phase, the external problem when the inputs are the Laplace-Beltrami eigenfunctions defined at the interface. In the online phase, only the reduced representation of the operator is needed to account for the influence of the external problem on the main system. An online basis enrichment is proposed in order to guarantee a precise reduced-order computation. Several test-cases are proposed on different fluid-structure couplings. more...
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- 2017
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34. Combining field potential data and in silico simulated data to improve machine learning approaches and better assess drug cardiotoxicity
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Fabien Raphel, Tessa de Korte, Sylvain Bernasconi, Stefan R. Braam, Christophe Bleunven, Jean-Frédéric Gerbeau, and Damiano Lombardi
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Pharmacology ,Cardiotoxicity ,business.industry ,Computer science ,In silico ,Simulated data ,Artificial intelligence ,Toxicology ,business ,Machine learning ,computer.software_genre ,computer ,Field (computer science) - Published
- 2020
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35. How to choose biomarkers in view of parameter estimation
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Eliott Tixier, Damiano Lombardi, Jean-Frédéric Gerbeau, Gerbeau, Jean-Frédéric, 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 de Paris, 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 ) -Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Université Paris Diderot - Paris 7 ( UPD7 ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Paris-Rocquencourt, Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Université Paris Diderot - Paris 7 ( UPD7 ) -Centre National de la Recherche Scientifique ( CNRS ), Numerical simulation of biological flows (REO), Sorbonne Université (SU)-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)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), and Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS) more...
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0301 basic medicine ,Statistics and Probability ,Inverse problems ,[ INFO.INFO-MO ] Computer Science [cs]/Modeling and Simulation ,Optimization problem ,Computer science ,Feature selection ,Sparse optimization ,010103 numerical & computational mathematics ,Pulse Wave Analysis ,computer.software_genre ,01 natural sciences ,Models, Biological ,General Biochemistry, Genetics and Molecular Biology ,03 medical and health sciences ,Animals ,Humans ,Computer Simulation ,Myocytes, Cardiac ,0101 mathematics ,General Immunology and Microbiology ,Estimation theory ,Applied Mathematics ,Hemodynamics ,General Medicine ,[ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA] ,Mathematical Concepts ,Inverse problem ,[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA] ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,3. Good health ,Electrophysiological Phenomena ,Electrophysiology ,030104 developmental biology ,ComputingMethodologies_PATTERNRECOGNITION ,Nonlinear Dynamics ,Modeling and Simulation ,Data mining ,[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation ,General Agricultural and Biological Sciences ,computer ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] ,Algorithms ,Biomarkers - Abstract
In numerous applications in biophysics, physiology and medicine, the system of interest is studied by monitoring quantities, called biomarkers, extracted from measurements. These biomarkers convey some information about relevant hidden quantities, which can be seen as parameters of an underlying model. In this paper we propose a strategy to automatically design biomarkers to estimate a given parameter. Such biomarkers are chosen as the solution of a sparse optimization problem given a user-supplied dictionary of candidate features. The method is in particular illustrated with two realistic applications, one in electrophysiology and the other in hemodynamics. In both cases, our algorithm provides composite biomarkers which improve the parameter estimation problem. more...
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- 2018
36. An a posteriori error estimator based on shifts for positive hermitian eigenvalue problems
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Athmane Bakhta, Damiano Lombardi, Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), 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 de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Lombardi, Damiano more...
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Spectrum (functional analysis) ,Mathematical properties ,Estimator ,010103 numerical & computational mathematics ,General Medicine ,[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA] ,Residual ,01 natural sciences ,Hermitian matrix ,hermitian eigenvalue problems ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,a posteriori error estimation ,010101 applied mathematics ,Matrix (mathematics) ,Applied mathematics ,A priori and a posteriori ,[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation ,0101 mathematics ,Eigenvalues and eigenvectors ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] ,Mathematics - Abstract
This work deals with an a posteriori error estimator for hermitian positive eigenvalue problems. The proposed estimator is based on the residual and the definition of suitable shifts in the matrix spectrum. The mathematical properties (certification and sharpness) are investigated and some numerical experiments are proposed. more...
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- 2017
37. Inverse problems in 1D hemodynamics on systemic networks: A sequential approach
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Damiano Lombardi
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Applied Mathematics ,Work (physics) ,Perspective (graphical) ,Biomedical Engineering ,Kalman filter ,Inverse problem ,medicine.disease ,Circulation (fluid dynamics) ,Computational Theory and Mathematics ,Terminal (electronics) ,Control theory ,Modeling and Simulation ,Arterial stiffness ,medicine ,Molecular Biology ,Pulse wave velocity ,Algorithm ,Software ,Mathematics - Abstract
In this work a sequential approach based on the Unscented Kalman Filter is applied to solve inverse problems in 1D hemodynamics, on a systemic network. For instance, the arterial stiffness is estimated by exploiting cross sectional area and mean speed observations in several locations of the arteries. The results are compared to those ones obtained by estimating the Pulse Wave Velocity and the Moens-Korteweg formula. In the last section, a perspective concerning the identification of the terminal models parameters and peripheral circulation (modeled by a Windkessel circuit) is presented. more...
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- 2013
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38. In vivo mathematical modeling of tumor growth from imaging data: Soon to come in the future?
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Olivier Saut, François Cornelis, Angelo Iollo, Damiano Lombardi, Jean Palussière, Thierry Colin, Patricio Cumsille, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modélisation, contrôle et calcul (MC2), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Service d'imagerie diagnostique et interventionnelle de l'adulte, CHU Bordeaux [Bordeaux], Centro de Modelamiento Matemático [Santiago] (CMM), Universidad de Santiago de Chile [Santiago] (USACH)-Centre National de la Recherche Scientifique (CNRS), departement imagerie, Institut Bergonié [Bordeaux], UNICANCER-UNICANCER, plafrim, cpu, and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS) more...
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Diagnostic Imaging ,medicine.medical_specialty ,Pathology ,medicine.medical_treatment ,Imaging data ,Imaging ,Targeted therapy ,Medium term ,03 medical and health sciences ,Imaging, Three-Dimensional ,0302 clinical medicine ,In vivo ,Neoplasms ,Image Interpretation, Computer-Assisted ,medicine ,Radiology, Nuclear Medicine and imaging ,Tumor growth ,Medical physics ,Evaluation ,ComputingMilieux_MISCELLANEOUS ,Cell Proliferation ,Neoplasm Staging ,030304 developmental biology ,0303 health sciences ,Tumor ,Radiological and Ultrasound Technology ,business.industry ,Modeling ,General Medicine ,Models, Theoretical ,Prognosis ,Survival Analysis ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,Response to treatment ,3. Good health ,Functional imaging ,Radiation therapy ,Treatment Outcome ,030220 oncology & carcinogenesis ,Disease Progression ,Tomography, X-Ray Computed ,business - Abstract
The future challenges in oncology imaging are to assess the response to treatment even earlier. As an addition to functional imaging, mathematical modeling based on the imaging is an alternative, cross-disciplinary area of development. Modeling was developed in oncology not only in order to understand and predict tumor growth, but also to anticipate the effects of targeted and untargeted therapies. A very wide range of these models exist, involving many stages in the progression of tumors. Few models, however, have been proposed to reproduce in vivo tumor growth because of the complexity of the mechanisms involved. Morphological imaging combined with ''spatial'' models appears to perform well although functioning imaging could still provide further information on metabolism and the micro-architecture. The combina- tion of imaging and modeling can resolve complex problems and describe many facets of tumor growth or response to treatment. It is now possible to consider its clinical use in the medium term. This review describes the basic principles of mathematical modeling and describes the advantages, limitations and future prospects for this in vivo approach based on imaging data. © 2013 Editions francaises de radiologie. Published by Elsevier Masson SAS. All rights reserved. Nowadays, imaging lies at the heart of patient management, particularly in oncology. Apart from the time when a disease is diagnosed, the different imaging methods are used to assess the effectiveness of both local (surgery, radiotherapy, heat ablation) and systemic (chemotherapy, targeted therapy) treatments during follow-up. The protocols usually rec- ommend assessment criteria such as the RECIST, WHO or CHOI, although these are less than perfect (1). more...
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- 2013
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39. Automatic ionic profiling on iPSC-CM from MEA signals using mathematical modeling and machine learning
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Jean-Frédéric Gerbeau, Philippe Zitoun, Damiano Lombardi, Fabien Raphel, and Eliott Tixier
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Pharmacology ,Computer science ,Ionic bonding ,Profiling (information science) ,Toxicology ,Biological system - Published
- 2018
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40. Eulerian models and algorithms for unbalanced optimal transport
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Emmanuel Maitre, Damiano Lombardi, 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), Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), ANR-11-BS01-0014,TOMMI,Transport Optimal et Modèles Multiphysiques de l'Image(2011), and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF) more...
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Numerical Analysis ,Unbalanced ,Tumor ,Applied Mathematics ,Trilinear interpolation ,Bilinear interpolation ,Stairstep interpolation ,Linear interpolation ,Interpolation ,Algorithm ,Computational Mathematics ,Nearest-neighbor interpolation ,Modeling and Simulation ,49-XX, 35-XX, 49MXX, 65-XX, 62H35 ,Optimal transport ,Image ,Bicubic interpolation ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Spline interpolation ,Analysis ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] ,Mathematics - Abstract
International audience; Benamou and Brenier formulation of Monge transportation problem (Numer. Math. 84:375-393, 2000) has proven to be of great interest in image processing to compute warpings and distances between pair of images (SIAM J. Math. Analysis, 35:61-97, 2003). One requirement for the algorithm to work is to interpolate densities of same mass. In most applications to image interpolation, this is a serious limitation. Existing approaches to overcome this caveat are reviewed, and discussed. Due to the mix between transport and $L^2$ interpolation, these models can produce instantaneous motion at finite range. In this paper we propose new methods, parameter-free, for interpolating unbalanced densities. One of our motivations is the application to interpolation of growing tumor images. more...
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- 2015
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41. An information-theoretic approach to assess practical identifiability of parametric dynamical systems
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Damiano Lombardi, Sanjay Pant, 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, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) more...
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Statistics and Probability ,Mathematical optimization ,Dynamical systems theory ,uncertainty quantification ,0206 medical engineering ,Information Theory ,010103 numerical & computational mathematics ,02 engineering and technology ,non-parametric estimation ,Information theory ,01 natural sciences ,General Biochemistry, Genetics and Molecular Biology ,Linear dynamical system ,Applied mathematics ,Entropy (information theory) ,0101 mathematics ,mutual information ,Mathematics ,Parametric statistics ,General Immunology and Microbiology ,Applied Mathematics ,Conditional mutual information ,General Medicine ,Mutual information ,Models, Theoretical ,dynamical systems ,identifiability ,020601 biomedical engineering ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,Modeling and Simulation ,Identifiability ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,General Agricultural and Biological Sciences ,entropy ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
International audience; A new approach for assessing parameter identifiability of dynamical systems in a Bayesian setting is presented. The concept of Shannon entropy is employed to measure the inherent uncertainty in the parameters. The expected reduction in this uncertainty is seen as the amount of information one expects to gain about the parameters due to the availability of noisy measurements of the dynamical system. Such expected information gain is interpreted in terms of the variance of a hypothetical measurement device that can measure the parameters directly, and is related to practical identifiability of the parameters. If the individual parameters are unidentifiable, correlation between parameter combinations is assessed through conditional mutual information to determine which sets of parameters can be identified together. The information theoretic quantities of entropy and information are evaluated numerically through a combination of Monte Carlo and k-nearest neighbour methods in a non-parametric fashion. Unlike many methods to evaluate identifiability proposed in the literature, the proposed approach takes the measurement-noise into account and is not restricted to any particular noise-structure. Whilst computationally intensive for large dynamical systems, it is easily parallelisable and is non-intrusive as it does not necessitate re-writing of the numerical solvers of the dynamical system. The application of such an approach is presented for a variety of dynamical systems – ranging from systems governed by ordinary differential equations to partial differential equations – and, where possible, validated against results previously published in the literature. more...
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- 2015
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42. A non-parametric k-nearest neighbour entropy estimator
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Sanjay Pant, Damiano Lombardi, 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 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 de Paris more...
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FOS: Computer and information sciences ,Computer Science - Information Theory ,Information Theory (cs.IT) ,Entropy ,Estimator ,020206 networking & telecommunications ,Numerical Analysis (math.NA) ,02 engineering and technology ,Trimmed estimator ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,Minimum-variance unbiased estimator ,Efficient estimator ,Non-parametric Estimation ,Bias of an estimator ,k-nearest neighbours ,Consistent estimator ,Statistics ,Stein's unbiased risk estimate ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Mathematics - Numerical Analysis ,Invariant estimator ,Mathematics - Abstract
International audience; A non-parametric k-nearest neighbor based entropy estimator is proposed a. It improves on the classical Kozachenko-Leonenko estimator by considering non-uniform probability densities in the region of k-nearest neighbors around each sample point. It aims at improving the classical estimators in three situations: first, when the dimensionality of the random variable is large; second, when near-functional relationships leading to high correlation between components of the random variable are present; and third, when the marginal variances of random variable components vary significantly with respect to each other. Heuristics on the error of the proposed and classical estimators are presented. Finally, the proposed estimator is tested for a variety of distributions in successively increasing dimensions and in the presence of a near-functional relationship. Its performance is compared with a classical estimator and shown to be a significant improvement. more...
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- 2015
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43. Reduced order model in cardiac electrophysiology with approximated Lax pairs
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Elisa Schenone, Damiano Lombardi, Jean-Frédéric Gerbeau, 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 Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS) more...
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Cardiac electrophysiology ,Applied Mathematics ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,Finite element method ,Reduced order ,Visualization ,cardiac electro-physiology ,Reduction (complexity) ,Approximated Lax Pairs ,Computational Mathematics ,Reduced-Order Modeling ,Computational Science and Engineering ,Cardiac Electrophysiology ,Parametric equation ,Reduced-Order Modeling ROM ,Algorithm ,Mathematics - Abstract
International audience; A reduced-order method based on Approximated Lax Pairs (ALP) is applied to the integration of electrophysiology models. These are often high- dimensional parametric equation systems, challenging from a model reduction stand- point. The method is tested on two and three dimensional test-cases, of increasing complexity. The solutions are compared to the ones obtained by a finite element. The reduced-order simulation of pseudo-electrocardiograms based on ALP is proposed in the last part. more...
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- 2015
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44. Advection modes by optimal mass transfer
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Angelo Iollo, Damiano Lombardi, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modélisation, contrôle et calcul (MC2), Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, CPU, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS) more...
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Classical mechanics ,Scattering ,Advection ,Mass transfer ,Mathematical analysis ,Representation (mathematics) ,Reduction (mathematics) ,Stability (probability) ,Fourier series ,ComputingMilieux_MISCELLANEOUS ,Mathematics ,Vortex - Abstract
Classical model reduction techniques approximate the solution of a physical model by a limited number of global modes. These modes are usually determined by variants of principal component analysis. Global modes can lead to reduced models that perform well in terms of stability and accuracy. However, when the physics of the model is mainly characterized by advection, the nonlocal representation of the solution by global modes essentially reduces to a Fourier expansion. In this paper we describe a method to determine a low-order representation of advection. This method is based on the solution of Monge-Kantorovich mass transfer problems. Examples of application to point vortex scattering, Korteweg--de Vries equation, and hurricane Dean advection are discussed. more...
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- 2014
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45. Reduced Order Models at Work in Aeronautics and Medicine
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Angelo Iollo, Michel Bergmann, Olivier Saut, Thierry Colin, Haysam Telib, and Damiano Lombardi
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Engineering ,Work (thermodynamics) ,Partial differential equation ,Aeronautics ,business.industry ,Delaunay triangulation ,Small number ,business ,Space (mathematics) ,Complex problems ,Reduced model ,Reduced order - Abstract
We review a few applications of reduced-order modeling in aeronautics and medicine. The common idea is to determine an empirical approximation space for a model described by partial differential equations. The empirical approximation space is usually spanned by a small number of global modes. In case of time-periodic or mainly diffusive phenomena it is shown that this approach can lead to accurate fast simulations of complex problems. In other cases, models based on definition of transport modes significantly improve the accuracy of the reduced model. more...
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- 2014
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46. Some Models for the Prediction of Tumor Growth: General Framework and Applications to Metastases in the Lung
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Damiano Lombardi, Angelo Iollo, Jean Palussière, Olivier Saut, Françoise Bonichon, Thierry Colin, 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), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modélisation, contrôle et calcul (MC2), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Plateforme de génétique moléculaire des cancers d'Aquitaine, Institut Bergonié [Bordeaux], UNICANCER-UNICANCER, UNICANCER, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-Inria Bordeaux - Sud-Ouest more...
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Oncology ,medicine.medical_specialty ,Computer science ,clinical applications ,Machine learning ,computer.software_genre ,01 natural sciences ,Reduced model ,lung metastasis growth prediction ,010305 fluids & plasmas ,Tumor growth modeling ,Spatial model ,Internal medicine ,0103 physical sciences ,medicine ,Tumor growth ,Sensitivity (control systems) ,0101 mathematics ,data assimilation ,ComputingMilieux_MISCELLANEOUS ,business.industry ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,3. Good health ,010101 applied mathematics ,Artificial intelligence ,business ,computer - Abstract
This chapter presents an example of an application of a mathematical model: the goal is here to help clinicians evaluate the aggressiveness of some metastases to the lung. For this matter, an adequate spatial model is described and two algorithms (one using a reduced model approach and the other one a sensitivity technique) are shown. They allow us to find reasonable values of the parameters of this model for a given patient with a sequence of medical images. The quality of the prognosis obtained through the calibrated model is then illustrated with several clinical cases. more...
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- 2013
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47. Mucus dynamics subject to air and wall motion
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Marc Thiriet, Damiano Lombardi, Philippe Poncet, Sébastien Enault, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), 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, 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 - Lyon (ENS Lyon), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), and Institut National des Sciences Appliquées (INSA) more...
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Work (thermodynamics) ,T57-57.97 ,Materials science ,Applied mathematics. Quantitative methods ,Computer simulation ,Dynamics (mechanics) ,[SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph] ,010103 numerical & computational mathematics ,Mechanics ,Propulsion ,01 natural sciences ,Mucus ,010305 fluids & plasmas ,Vibration ,Momentum diffusion ,0103 physical sciences ,QA1-939 ,0101 mathematics ,[PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph] ,Dimensioning ,Simulation ,Mathematics ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
This study presents a numerical investigation of basic interactions between respiratory mucus motion, air circulation and epithelium ciliated cells vibration. One focuses on identification of meaningful rheological parameters, physiological and numerical simulation dimensioning. These preliminary results are crucial before the study of more general configurations of respiratory mucus motion. The numerical study presented in this work aims at providing a first numerical tool able to simulate the effects of mucus mobility and its ability to carry out pathogens or to deliver aerosol therapy to membrane wall cells. Momentum diffusion is identified as the dominant effect, as expected in this micrometer scale configuration, and its associate momentum diffusion operator is shown to be extremely stiff. Furthermore, epithelium vibration is shown to be much more efficient than air circulation for mucus propulsion. Ce travail présente une étude numérique des interactions élémentaires entre le mucus de l’appareil respiratoire, la circulation de l’air et le mouvement vibratoire des cellules épithéliales ciliées tapissant la membrane pulmonaire. On s’intéresse en particulier à l’identification des paramètres les plus importants parmi les données rhéologiques, le dimensionnement physiologique et la configuration numérique. Ces résultats préliminaires sont cruciaux afin d’envisager l’étude de cas plus généraux de transport du mucus respiratoire. Un tel outil numérique aura pour but de quantifier la mobilité du mucus et sa capacité à expulser les pathogènes ou à délivrer un aérosol à travers membrane. La diffusion a été identifiée comme étant le phénomène dominant, comme attendu à l’échelle du micromètre, et son opérateur de diffusion associé a été observé comme étant extrêmement raide. D’autre part, il a été montré que la vibration de l’épithélium est bien plus efficace que la circulation de l’air pour assurer le transport du mucus. more...
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- 2010
48. State estimation in fluid-structure interaction from 4D-flow MRI data
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Agbalessi, Mocia, 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), Sorbonne Université, Miguel A. Fernández, Jean-Joseph Christophe, and Damiano Lombardi more...
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Filtre de Kalman ,Unique Continuation ,Observateur d'état de Luenberger ,[SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging ,Continuation unique ,FSI ,4D Flow MRI ,Kalman Filter ,Luenberger observer ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] ,IRM de flux 4D - Abstract
This thesis is devoted to the development of FSI state estimation algorithms using the 4D Flow MRI data. It is motivated by the increasing demand for patient-specific blood flow simulations for the assessment of predictive Wall Shear Stress (WSS) related biomarkers. However, patient- specific simulations raise major technical concerns such as the imposition of inflow/outflow boundary conditions, the way to use efficiently the medical data available. In the first chapter we leverage the richness of the 4D Flow data to develop a method that extracts the time-resolved wall displacement and velocity from 4D MRI, using a Kalman filter approach. The estimation of the wall displacement and velocity from 4D MRI with the tracking is tested for the reconstruction of the motion of an immersed vesicle with synthetic 4D Flow MRI data. An application to the tracking of the aorta wall of a patient is presented as a response to the need for non-static semi-automatic segmentation of the aortic wall using 4D MRI. The second and third chapters tackle the FSI state estimation on the academic FSI setting of a pressure wave propagating in a 3D tube. We propose novel approach for FSI state estimation in which no inflow and outflow boundary conditions are imposed. In the second chapter, small vibrations of the solid are assumed and with suitable kinematic assumptions, the FSI problem is simplified for a FSI fixed- domain problem, in which the solid state is expressed in terms of the fluid state. A first fluid-structure interaction state estimation algorithm is proposed based on unique continuation using fluid velocity measurements. The FSI state estimation algorithm is formulated as a PDE-constraint optimization problem in a L2 distance between simulation and measured data is minimized. Without specifying inflow and outflow boundary conditions, the problem is ill-posed, and the solvability is ensured at the discrete level by weakly consistent stabilization terms. It results in the resolution of a system in the primal variables and associated dual variables. Another FSI state algorithm is proposed in which non-parametric inflow and outflow boundary conditions are estimated using a unique continuation and imposed on a Luenberger state observer with fluid velocity measurements. Numerical studies illustrate the performance of the two FSI algorithm for fixed domain FSI state estimation. In the third chapter, the FSI state estimation combining unique continuation with Luenberger observer for the fluid sub-problem is extended to moving domain FSI. We no longer consider a monolithic formulation of the FSI problem but a partitioned resolution. The fluid sub-problem and the solid sub-problem are solved independently and the FSI coupling is ensured by interface coupling conditions. A fourth algorithm is proposed to leverage displacements and velocity in the solid, by adding data feedback terms in the solid sub-problem in the form of a Luenberger state observer. A series of numerical tests are performed to illustrate the two algorithms.; Cette thèse est dédiée au développement d’algorithmes d’estimation d’état FSI en utilisant des données d’IRM de flux 4D. Elle est motivée par la demande croissante de simulations d’écoulement sanguin patient-spécifique pour l’évaluation de paramètres prédictives calculés à partir du Wall-Shear Stress (WSS). Cependant, les simulations patient-spécifiques soulève des difficultés techniques majeures comme l’imposition des conditions aux bords de flux entrants/sortants. Dans le premier chapitre, nous proposons une méthode d’extraction du déplacement et de la vitesse de la paroi du vaisseau, en utilisant un filtrage de Kalman. Le but est de tirer profit au maximum de la richesse des données contenues dans les IRM 4D pour réaliser une reconstruction non-statique et semi-automatique de la paroi de l’aorte dans son mouvement. Un filtre de Kalman est conçu pour corriger une prédiction du mouvement de la paroi issue d’un modèle dynamique simplifié avec des observations provenant d’un opérateur d’observation de position et des données de vitesse de l'IRM 4D. L’observation de position est complétée par les données de vitesse locale sur les images IRM 4D. L’estimation du déplacement de la paroi du vaisseau et de sa vitesse est appliquée à la reconstruction du mouvement d’une vésicule immergée dans un fluide visqueux, pour laquelle des données imitant l’IRM 4D ont été générées. Une application au tracking de la paroi de l’aorte d’un patient est finalement présentée, sous forme d’une segmentation semi-automatique et non-statique de la paroi de l’aorte à partir d’IRM 4D. Les second et troisième chapitres traitent de l’estimation d’état FSI sur un cas académique, celui de la propagation d’une onde de pression dans un tube. Nous proposons une approche nouvelle pour estimer l’état FSI sans imposer des conditions aux bords en entrée et en sortie de la géométrique. Dans le second chapitre, on suppose que l’onde de pression provoque des variations infinitésimales du tube et avec des approximations cinématiques bien choisies, le problème FSI est réduit à un problème sur domaine fixe, dans lequel la variation de déformation solide est exprimée au moyen des variables d’état fluides. Un premier algorithme d’estimation FSI est alors présenté, basé uniquement sur une méthode de continuation unique en utilisant les mesures de vitesse du fluide. L’algorithme d’estimation d’état FSI est formulée comme une optimisation de l’écart en norme L2 entre la simulation et les données mesurées, sous d’une équation différentielle partielle. Sans spécifier les conditions de flux entrant ou sortant, le problème est mal posé, et la solvabilité est assurée au niveau discret par des termes de stabilisation faiblement consistants. On se ramène ainsi à la résolution d’un système en variables primales et duales. Un second algorithme d’estimation FSI, très similaire à un observateur d’état de Luenberger, est proposée en utilisant le premier algorithme d’estimation d’état FSI pour estimer des conditions aux bords non paramétriques de flux entrains et sortants. Des études numériques illustrent la performance des 2 algorithmes sur domaine fixe. Dans le troisième chapitre, l’estimateur d’état FSI combinant l’étape d’estimation des conditions de flux entrants et sortant par continuation unique et l’observateur de Luenberger est étendue à des problèmes FSI sur domaine mobile. Au lieu d’une résolution monolithique, on utilise des solveurs fluide et solide partitionnés et couplés via des conditions d’interface. En profitant de mesures de déplacement et de vitesse de la paroi du tube, un dernier algorithme est proposé. Une série de tests numériques est effectuée pour illustrer le potentiel de ces nouvelles méthodes. more...
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- 2023
49. Méthodes tensorielles adaptatives pour problèmes haute dimensionnelles
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Fuente Ruiz, María, 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), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université, Damiano Lombardi, and Virginie Ehrlacher more...
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Neural Networks ,Singulary Perturbed Problems ,Canonical Polyadic ,PINNs ,[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA] ,High dimension ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,Polyadique canonique ,Tensor methods ,Méthodes numériques ,Réseaux neuronaux ,Modèles d'ordre réduit ,Méthodes tensorielles ,Numerical methods ,Model Order Reduction ,Problèmes perturbés singuliers ,Haute dimension - Abstract
This thesis aims to find numerical methods for approximating multivariate functions (tensors). It covers three different perspectives: a tensor approximation method (Sum of Tensor Trains), a local tensor approximation method based on clustering (local HOSVD), and a deep learning-based method for approximating a solution of a convection diffusion PDE. The first part of the work proposes a method for approximating a tensor as a sum of Tensor Trains, which is based on a greedy algorithm and TT-SVD. The second part proposes a local tensor approximation method that retrieves an approximated solution in the local HOSVD format, based on clustering and a search between possible partition combinations to minimize memory needed to store the approximation. The results show good compression rate compared to HOSVD.; Cette thèse vise à trouver des méthodes numériques pour approximer des fonctions multivariées. Elle couvre trois perspectives différentes: une méthode d'approximation de tenseur (Somme de Tensor Trains), une méthode d'approximation de tenseur locale basée sur le regroupement (HOSVD local), et une méthode basée sur l'apprentissage profond pour approximer une solution d'une EDP de convection diffusion. La première partie du travail propose une méthode pour approximer un tenseur en tant que somme de Tensor Trains, basée sur un algorithme gourmand et le TT-SVD. La seconde partie propose une méthode d'approximation de tenseur locale qui récupère une solution approximée au format HOSVD local, basée sur le regroupement et une recherche entre les combinaisons de partitions possibles pour minimiser la mémoire nécessaire pour stocker l'approximation. Les résultats montrent un bon taux de compression par rapport à HOSVD. more...
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- 2023
50. Inverse problems in hemodynamics. Fast estimation of blood flows from medical data
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Galarce Marin, Felipe, 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), Inria Paris, Sorbonne Universite, Laboratoire Jacques-Louis Lions, Jean-Frédéric Gerbeau, Damiano Lombardi, Olga Mula Hernandez, and 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) more...
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Inverse problems ,Inter-patient variability ,Model reduction ,Problèmes inverses ,Réduction de modèle ,Domaines non paramétriques ,Variabilité inter-patient ,Quantities of Interest ,Estimation d’état ,State estimation ,Non-parametric domains ,Quantités d’intérêt ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
This thesis presents a work at the interface between applied mathematics and biomedical engineering. The work’s main subject is the estimation of blood flows and quantities of medical interest in diagnosing certain diseases concerning the cardiovascular system. We propose a complete pipeline, providing the theoretical foundations for state estimation from medical data using reduced-order models, and addressing inter-patient variability. Extensive numerical tests are shown in realistic 3D scenarios that verify the potential impact of the work in the medical comunnity.; Cette thèse présente un travail à l’interface entre les mathématiques appliquées et l’ingénierie biomedicale. Le sujet principal en est l’estimation des écoulements sanguins et de quantités d’intérêt pour le diagnostic de certaines maladies cardiovasculaires. Nous proposons une procédure complète, dont nous détaillons les fondements théoriques, permettant l’estimation d’état à partir de données médicales en utilisant des techniques de réduction de modèle, et en prenant en compte la problématique de la variabilité inter-patients. De nombreux test numériques en 3D sont exposés afin de vérifier le potentiel de cette étude dans le domaine médical. more...
- Published
- 2021
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