3.1.1 Cardiovascular hemodynamics

We distinguish between cardiac hemodynamics (blood flow inside the four chambers of the heart) and vascular hemodynamics (blood flow in the vessels of the body).

Cardiac hemodynamics. The numerical simulation of cardiac hemodynamics presents many difficulties. We can mention, for instance, the large deformation of the cardiac chambers and the complex fluid-structure interaction (FSI) phenomena between blood, the valves and the myocardium. Blood flow can be described by the incompressible Navier-Stokes equations which have to be coupled with a bio-physical model of the myocardium electro-mechanics and a mechanical model of the valves. The coupling between the fluid and the solid media is enforced by kinematic and dynamic coupling conditions, which guarantee the continuity of velocity and stresses across the interface. In spite of the significant advances achieved since the beginning of this century (see, e.g., 62, 63, 60, 65, 53), the simulation of all the fluid-structure interaction phenomena involved in the heart hemodynamics remains a complex and challenging problem.

Heart valves are definitely a bottleneck of the problem, particularly due to their fast dynamics and the contact phenomena with high pressure-drops. Computational cost is recognized as one of the key difficulties, related to the efficiency of the FSI coupling method and the robustness of the contact algorithm. Furthermore, the numerical discretization of these coupled systems requires to deal with unfitted fluid and solid meshes, which are known to complicate the accuracy and/or the robustness of the numerical approximations (see Section 3.3.2 below).

The ultimate goal of the proposed research activity is the simulation of the complete fluid-structure-contact interaction phenomena involved within the heart. Most of this work will be carried out in close collaboration with the M3DISIM project-team, which has a wide expertise on the modeling, simulation and estimation of myocardium electro-mechanics. We will also consider simplified approaches for cardiac hemodynamics (see, e.g., 35, 48, 51). The objective is to develop mathematically sound models of reduced valve dynamics with the purpose of enhancing the description of the pressure dynamics right after the opening/closing of the valve (traditional models yield spurious pressure oscillations).

Vascular hemodynamics. The modeling and simulation of vascular hemodynamics in large vessels has been one of the core research topics of some members of COMMEDIA, notably as regards the fluid-structure interaction phenomena. Here we propose to investigate the modeling of pathological scenarios, such as the hemorrhage phenomena in smaller vessels. Modeling of hemorrhage is motivated by the medical constatation that, after a primary vessel wall rupture, secondary vessel wall ruptures are observed. Biologists postulate that the mechanical explanation of this phenomenon might be in the change of applied stress due to blood bleeding. We propose to model and simulate the underlying coupled system, blood vessel flow through the external tissue, to estimate the effect of the subsequent stress variation.

3.1.2 Respiratory flows

The motivation of the proposed research activities is to develop a hierarchy of easily parametrizable models allowing to describe and efficiently simulate the physical, mechanical and biological phenomena related to human respiration, namely, ventilation, particle deposition, gas diffusion and coupling with the circulatory system.

Ventilation. The current modeling approaches (either 3D–0D coupled models where the 3D Navier-Stokes equations are solved in truncated geometries of the bronchial tree with appropriate lumped boundary conditions, or 0D–3D coupled models where the lung parenchyma is described by a 3D elastic media irrigated by a simplified bronchial tree) provide satisfactory results in the case of mechanical ventilation or normal breathing. Realistic volume-flow phase portraits can also be simulated in the case of forced expiration (see 37, 45, 68), but the magnitude of the corresponding pressure is not physiological. The current models must be enriched since they do not yet correctly describe all the physiological phenomena at play. We hence propose to extend the 0D–3D (bronchial tree–parenchyma) model developed in the team, by considering a non-linear, viscoelastic and possibly poro-elastic description of the parenchyma with appropriate boundary conditions that describe ribs and adjacent organs and taking into account an appropriate resistive model.

So far, the motion of the trachea and proximal bronchi has been neglected in the ventilation models (see, e.g., 70). These features can be critical for the modeling of pathologic phenomena such as sleep apnea and occlusion of the airways. This would be a long-term goal where fluid-structure interaction and the possible contact phenomena will be taken into account, as in the simulation of cardiac hemodynamics (see Section 3.1.1).

Aerosol and gas diffusion. The dynamics of aerosols in the lung have been widely studied from the mathematical modeling standpoint. They can be described by models at different scales: the microscopic one for which each particle is described individually, the mesoscopic (or kinetic) one for which a density of probability is considered, or the macroscopic one where reaction-diffusion equations describing the behavior of the constituant concentration are considered. The objective of COMMEDIA will mainly be to develop the kinetic approach that allows a precise description of the deposition area at controlled computational costs. Part of this study could be done in collaboration with colleagues from the Research Center for Respiratory Diseases at Inserm Tours (UMR1100).

The macroscopic description is also appropriate for the diffusion of gases (oxygen and carbon dioxide) in the bronchial tree (see 64). Regarding the influence of the carrier gas, if the patient inhales a different mixture of air such as a Helium-Oxygen mixture, the diffusion mechanisms could be modified. In this context, the goal is to evaluate if the cross-diffusion (and thus the carrier gas) modifies the quantities of oxygen diffused. Part of this work will be carried out in collaboration with members of the LJLL and of the MAP5.

As a long term goal, we propose to investigate the coupling of these models to models of diffusion in the blood or to perfusion models of the parenchyma, and thus, have access thanks to numerical simulations to new indices of ventilation efficiency (such as dissolved oxygen levels), depending on the pathology considered or the resting or exercise condition of the patient.

3.2.1 Fluid flow reconstruction from medical imaging

A first problem which is currently under study at COMMEDIA is the reconstruction of the flow state from Doppler ultrasound measurements. This is a cheap and largely available imaging modality where the measure can be interpreted as the average on a voxel of the velocity along the direction of the ultrasound beam. The goal is to perform a full-state estimation in a time compatible with a realistic application.

A second problem which is relevant is the flow and wall dynamics reconstruction using 4D-flow MRI. This imaging modality is richer than Doppler ultrasound and provides directly a measure of the 3D velocity field in the voxels. This enables the use of direct estimation methods at a reduced computational cost with respect to the traditional variational data assimilation approaches. Yet, the sensitivity of the results to subsampling and noise is still not well understood.

We also propose to address the issues related to uncertainty quantification. Indeed, measurements are corrupted by noise and the parameters as well as the available data of the system are either hidden or not known exactly (see 59). This uncertainty makes the estimation difficult and has a large impact on the precision of the reconstruction, to be quantified in order to provide a reliable tool.

3.2.2 Safety pharmacology

One of the the most important problems in pharmacology is cardio-toxicity (see 58). The objective is to predict whether or not a molecule alters in a significant way the normal functioning of the cardiac cells. This problem can be formulated as inferring the impact of a drug on the ionic currents of each cell based on the measured electrical signal (e.g., electrograms from Micro-Electrodes Arrays). The proposed approach in collaboration with two industrial partners (NOTOCORD and Ncardia) consists in combining available realistic data with virtual ones obtained by numerical simulations. These two datasets can be used to construct efficient classifiers and regressors using machine learning tools (see 42) and hence providing a rapid way to estimate the impact of a molecule on the electrical activity. The methodological aspects of this work are addressed in Section 3.3.3.

3.3.1 Mathematical analysis of PDEs

The mathematical analysis of the multi-scale and multi-physics models are a fundamental tool of the simulation chain. Indeed, well-posedness results provide precious insights on the properties of solutions of the systems which can, for instance, guide the design of the numerical methods or help to discriminate between different modeling options.

Fluid-structure interaction. Most of the existing results concern the existence of solutions locally in time or away from contacts. One fundamental problem, related to the modeling and simulation of valve dynamics (see Sections 3.1.1 and 3.3.2), is the question of whether or not the model allows for contact (see 57, 55). The proposed research activity is aimed at investigating the case of both immersed rigid or elastic structures and explore if the considered model allows for contact and if existence can be proved beyond contact. The question of the choice of the model is crucial and considering different types of fluid (Newtonian or non-Newtonian), structure (smooth or rough, elastic, viscoelastic, poro-elastic), or various interface conditions has an influence on whether the model allows contact or not.

Fluid–structure mixture. The main motivation to study fluid-solid mixtures (i.e., porous media consisting of a skeleton and connecting pores filled with fluid) comes from the modeling of the lung parenchyma and cerebral hemorrhages (see Sections 3.1.1–3.1.2). The Biot model is the most widely used in the literature for the modeling of poro-elastic effects in the arterial wall. Here, we propose to investigate the recent model proposed by the M3DISIM project-team in 47, which allows for nonlinear constitutive behaviors and viscous effects, both in the fluid and the solid. Among the questions which will be addressed, some of them in collaboration with M3DISIM, we mention the justification of the model (or its linearized version) by means of homogenization techniques and its well-posedness.

Fluid–particle interaction. Mathematical analysis studies on the Navier-Stokes-Vlasov system for fluid-particle interaction in aerosols can be found in 39, 41. We propose to extend these studies to more realistic models which take into account, for instance, changes in the volume of the particles due to humidity.

3.3.2 Numerical methods for multi-physics problems

In this section we describe the main research directions that we propose to explore as regards the numerical approximation of multi-physics problems.

Fluid-structure interaction. The spatial discretization of fluid-structure interaction (FSI) problems generally depends on the amount of solid displacement within the fluid. Problems featuring moderate interface displacements can be successfully simulated using (moving) fitted meshes with an arbitrary Lagrangian-Eulerian (ALE) description of the fluid. This facilitates, in particular, the accurate discretization of the interface conditions. Nevertheless, for problems involving large structural deflections, with solids that might come into contact or that might break up, the ALE formalism becomes cumbersome. A preferred approach in this case is to combine a Eulerian formalism in the fluid with an unfitted mesh discretization, in which the fluid-structure interface deforms independently of a background fluid mesh. In general, traditional unfitted mesh approaches (such as the immersed boundary and the fictitious domain methods 67, 38, 54, 36) are known to be inaccurate in space. These difficulties have been recently circumvented by a Nitsche-based cut-FEM methodology (see 33, 43). The superior accuracy properties of cut-FEM approaches comes at a price: these methods demand a much more involved computer implementation and require a specific evaluation of the interface intersections.

As regards the time discretization, significant advances have been achieved over the last decade in the development and the analysis of time-splitting schemes that avoid strong coupling (fully implicit treatment of the interface coupling), without compromising stability and accuracy. In the vast majority of these studies, the spatial discretization is based on body fitted fluid meshes and the problem of accuracy remains practically open for the coupling with thick-walled structures (see, e.g., 52). Within the unfitted mesh framework, splitting schemes which avoid strong coupling are much more rare in the literature.

Computational efficiency is a major bottleneck in the numerical simulation of fluid-structure interaction problems with unfitted meshes. The proposed research activity is aimed at addressing these issues. Another fundamental problem that we propose to face is the case of topology changes in the fluid, due to contact or fracture of immersed solids. This challenging problem (fluid-structure-contact-fracture interaction) has major role in many applications (e.g., heart valves repair or replacement, break-up of drug-loaded micro-capsules) but most of the available studies are still merely illustrative. Indeed, besides the numerical issues discussed above, the stability and the accuracy properties of the numerical approximations in such a singular setting are not known.

Fluid–particle interaction and gas diffusion. Aerosols can be described through mesoscopic equations of kinetic type, which provide a trade-off between model complexity and accuracy. The strongly coupled fluid-particle system involves the incompressible Navier-Stokes equations and the Vlasov equation. The proposed research activity is aimed at investigating the theoretical stability of time-splitting schemes for this system. We also propose to extend these studies to more complex models that take into account the radius growth of the particles due to humidity, and for which stable, accurate and mass conservative schemes have to be developed.

As regards gas diffusion, the mathematical models are generally highly non-linear (see, e.g., 64, 66, 40). Numerical difficulties arise from these strong non linearities and we propose to develop numerical schemes able to deal with the stiff geometrical terms and that guarantee mass conservation. Moreover, numerical diffusion must be limited in order to correctly capture the time scales and the cross-diffusion effects.

3.3.3 Statistical learning and mathematical modeling interactions

Machine learning and in general statistical learning methods (currently intensively developed and used, see 34) build a relationship between the system observations and the predictions of the QoI (quantities of interest) based on the a posteriori knowledge of a large amount of data. When dealing with biomedical applications, the available observations are signals (think for instance to images or electro-cardiograms, pressure and Doppler measurements). These data are high dimensional and the number of available individuals to set up precise classification/regression tools could be prohibitively large. To overcome this major problem and still try to exploit the advantages of statistical learning approaches, we try to add, to the a posteriori knowledge of the available data an a priori knowledge, based on the mathematical modeling of the system. A large number of numerical simulations is performed in order to explore a set of meaningful scenarios, potentially missing in the dataset. This in silico database of virtual experiments is added to the real dataset: the number of individuals is increased and, moreover, this larger dataset can be used to compute semi-empirical functions to reduce the dimension of the observed signals.

Several investigations have to be carried out to systematically set up this framework. First, often there is not a single mathematical model describing a physiological phenomenon, but hierarchies of models of different complexity. Every model is characterized by a model error. How can this be accounted for? Moreover, several statistical estimators can be set up and eventually combined together in order to improve the estimations (see 61). Other issues have an actual impact and has to be investigated: what is the optimal number of in silico experiments to be added? What are the most relevant scenarios to be simulated in relation to the statistical learning approach considered in order to obtain reliable results? In order to answer to these questions, discussions and collaborations with statistics and machine learning groups have to be developed.

3.3.4 Tensor approximation and HPC

Tensor methods have a recent significant development because of their pertinence in providing a compact representation of large, high-dimensional data. Their applications range from applied mathematics and numerical analysis to machine learning and computational physics. Several tensor decompositions and methods are currently available (see 56). Contrary to matrices, for tensors of order higher or equal to three, there does not exist, in general, a best low rank approximation, the problem being ill posed (see 69). Two main points will be addressed: (i) The tensor construction and the multi-linear algebra operations involved when solving high-dimensional problems are still sequential in most of the cases. The objective is to design efficient parallel methods for tensor construction and computations; (ii) When solving high-dimensional problems, the tensor is not assigned; instead, it is specified through a set of equations and tensor data. Our goal is to devise numerical methods able to (dynamically) adapt the rank and the discretization (possibly even the tensor format) to respect the chosen error criterion. This could, in turn, improve the efficiency and reduce the computational burden.

These sought improvements could make the definition of parsimonious discretizations for kinetic theory and uncertainty quantification problems (see Section 3.2.1) more efficient and suitable for a HPC paradigm. This work will be carried out in collaboration with Olga Mula (TU Eindhoven) and MATHERIALS project-teams.

5.1.1 FELiScE

• Name:
  Finite Elements for Life SCiences and Engineering problems
• Keywords:
  Finite element modelling, Cardiac Electrophysiology, Cardiovascular and respiratory systems
• Functional Description:
  FELiScE is a finite element developed by COMMEDIA project-team. One specific objective of this code is to provide in a unified software environment all the state-of-the-art tools needed to perform simulations of the complex respiratory and cardiovascular models considered in the two teams – namely involving fluid and solid mechanics, electrophysiology, and the various associated coupling phenomena. FELISCE is written in C++ and open source, and may be later released as an opensource library. FELiScE was registered in July 2014 at the Agence pour la Protection des Programmes under the Inter Deposit Digital Number IDDN.FR.001.350015.000.S.P.2014.000.10000.
• URL:
  https://­team.­inria.­fr/­commedia/­software/­felisce/
• Contact:
  Miguel Angel Fernandez Varela
• Participants:
  Romain Lemore, Marguerite Champion, Daniele Carlo Corti, Miguel Angel Fernandez Varela, Marina Vidrascu, Sara Costa Faya, Oscar Ruz, Fabien Lespagnol, Carlos Brito Pacheco

5.1.2 FELiScE-NS

• Keywords:
  Thin-walled solids, Incompressible flows
• Functional Description:
  FELiScE-NS is a set of finite elements solvers for incompressible fluids (fractional-step schemes) and non-linear thin-walled structures (3D shells, and 2D curved beams) developed in the framework of the FELiScE library. FELiSCe-NS was registered in 2018 at the Agence pour la Protection des Programmes Inter Deposit Digital Number IDDN.FR.001.270015.000.S.A.2018.000.31200.
• Contact:
  Miguel Angel Fernandez Varela
• Participants:
  Oscar Ruz, Fabien Lespagnol, Miguel Angel Fernandez Varela, Marina Vidrascu, Daniele Carlo Corti, Sara Costa Faya

5.1.3 ADAPT

• Name:
  Adaptive Dynamical Approximation via Parallel Tensor methods
• Keywords:
  Scientific computing, Tensor decomposition, Partial differential equation
• Functional Description:
  ADAPT is a library containing methods for scientific computing based on tensors. In many fields of science and engineering we need to approximate the solution of high-dimensional problems. In this library we propose a collection of methods to parsimoniously discretise high-dimensional problems. These methods are mainly based on tensors.
• Contact:
  Damiano Lombardi
• Participants:
  Virginie Ehrlacher, Damiano Lombardi, Sebastien Riffaud

Withings

Participants: Miguel Ángel Fernández Varela [coordinator], Adrien Lefieux, Damiano Lombardi, Marina Vidrascu, Fabien Vergent.

This research project has the objective of developing mathematical models of photoplethysmography (PPG) measurements in the wrist and their connection to blood pressure estimation.

CASIS

Participants: Miguel Ángel Fernández Varela [coordinator], Damiano Lombardi, Romain Lemore.

Calibration of vascular fluid-structure interaction simulations from 4D-flow MRI data.

8.1.1 Inria associate team not involved in an IIL or an international program

8.1.2 Visits of international scientists

• Erik Burman (UCL), April, October, Decmber 2024.
• Rodolfo Araya (Universidad de Concepción), April-June 2024.
• Hessam Sam Babaee (University of Pittsburgh), September-October 2024.

8.2.1 Horizon Europe

SIMR: Simulation and Imaging for Mitral Regurgitation

Participants: Daniele Carlo Corti, Miguel Angel Fernández Varela, Marina Vidrascu, Céline Grandmont.

• Funding:
  ANR PRC
• Duration:
  2020-2024
• Coordinator:
  Miguel Angel Fernández Varela
• Partners:
  CREATIS, HCL, LGEF, M3DISIM, TIMC
• Summary:
  The SIMR project aims at evaluating the physical consequences of mitral repair using efficient numerical simulations, advanced imaging techniques and an innovative measurement tools in a clinical study

CoCop: Heart-Lung Coupling: aid to monitor cardio-respiratory functions in intensive care

Participants: Céline Grandmont, Frédérique Noël, Fabien Vergnet, Romain Lopez-Surjus.

• Funding:
  Inria Exploratory Actions
• Duration:
  2024–2027
• Coordinator:
  Céline Grandmont
• Partners:
  MEDISIM project-team (D. Chapelle, P. Moireau), APHP Lariboisière Hospital (F. Vallée)
• Summary:
  The project seeks to respond to the clinical need for a better understanding of cardio-respiratory functions for patients placed under mechanical ventilation. It aims in particular to propose ventilatory maneuvers or minimally invasive measurements that can be carried out at the bedside of patients, making it possible to estimate the condition of the lung, the level of blood perfusion and help optimize ventilator settings in order to minimize damage to the lungs.

MediTwin

Participants: Carlos Brito Pacheco, Miguel Angel Fernandez Varela, Damiano Lombardi, Marina Vidrascu.

• Funding:
  BPI
• Duration:
  2024-2029
• Local coordinator:
  Miguel Angel Fernández Varela
• Partners:
  Dassault Systems, SIMBIOTX projec-team, M3DISIM project-team
• Summary:
  3D modeling and simulation of cardiac hemodynamics, notably of patohological scenarios such as the Hypoplastic Left Heart Syndrome (HLHS), whith the purpose of assesing different surgicals options.

9.1.1 Scientific events: organisation

• Guillaume Delay
  • Co-organizer of the scientific computing seminar, joint event between Inria and Laboratoire Jacques-Louis Lions.
  • Mini-symposium co-organizer, Immersed boundary methods, in CANUM 2024, Ile de Ré, May 2024.
• Miguel Angel Fernández Varela
  • Co-organizer of Mini-symposium New trends in the Mathematical and Numerical aspects of Fluid-Structure Interaction, ECCOMAS Congress 2024, Lisbon, June 2024.
• Céline Grandmont
  • Member of organizing comitte of a Workshop on fluid-structure interaction, Janvier 2024, ULB
• Damiano Lombardi
  • Co-organizer of the scientific computing seminar, joint event between Inria and Laboratoire Jacques-Louis Lions.
  • Mini-symposium co-organizer (with F. Nobile, EPFL) Low Rank Methods for Random Dynamical Systems and Sequential Data Assimilation., SIAM UQ 2024, Trieste, 02-2024.
  • Co-president of CES (Commission Emploi Scientifique), INRIA.
  • Scientific committee of Journées Lions-Magenes 2024, Pavia, 05-2024.
• Fabien Vergnet
  • Mini-symposium co-organizer, Immersed boundary methods, in CANUM 2024, Ile de Ré, May 2024.
• Marina Vidrascu
  • Co-organizer of Mini-symposium New trends in the Mathematical and Numerical aspects of Fluid-Structure Interaction, ECCOMAS Congress 2024, Lisbon, June 2024.

9.1.2 Journal

9.1.3 Invited talks

• Marguerite Champion
  • Invited speaker, Lions-Magenes days, Pavia, May 2024.
  • Contributed talk in minisymposium, ECCOMAS Congress 2024, Lisbon, June 2024.
• Guillaume Delay
  • Seminar laboratoire Paul Painlevé, Lille, December 2024
  • Invited talk in POEMS: POlytopal Element Methods in Mathematics and Engineering, Paris December 3-6 2024
  • Invited talk in workshop Computational methods for Inverse and Ill-posed problems November 7-8, 2024, London
  • Invited speaker, Workshop on Frontiers in Finite Element Methods and Applications, June 10-14, 2024, Suzhou, China
• Miguel Angel Fernández Varela
  • Invited speaker, Mathematical Models and Numerical Methods for Multiphysics Systems Conference, May 1-3, 2024, University of Pittsburgh, USA
  • Invited speaker, Workshop on Frontiers in Finite Element Methods and Applications, June 10-14, 2024, Suzhou, China
• Sara Costa Faya
  • Talk in workshop 16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics, July 21-26, 2024, Vancouver, Canada
• Céline Grandmont
  • Plenary speaker Canum 2024
• Damiano Lombardi
  • Talk in mini-symposium: SIAM UQ 2024, Trieste, 02-2024.
  • Talk in workshop: Conformal variational discretisation for infinite dimensional Hamiltonian systems with gradient flow dissipation., SNS, Pisa, 04-2024.
  • Talk in workshop: Uncertainty Quantification for High-Dimensional problems, CWI Amsterdam, 12-2024.
• Frédérique Noël
  • Invited talk Third Summer School on Economic principles in cell biology, Paris, July 2024.
  • Talk European Conference on Mathematical and Theoretical Biology, Toledo, July 2024
• Marina Vidrascu
  • Invited talk in minisymposium in the 16th French Romanian Colloquium, Bucharest 26-30 August 2024

9.1.4 Scientific expertise

• Miguel Angel Fernández Varela
  • Member of the Project-Teams Committee Bureau, Inria Paris
• Céline Grandmont
  • Member of the Scientific Committee of the thematic network "Math Bio Santé" and of de axis "Mathématiques, Santé, Sciences du Vivant

9.2.1 Teaching

• Licence:
  • Marguerite ChampionToggle sub-subsection view
    • Numerical analysis, 248h, L3, Sorbonne University
    • Python, 32h, L2, Sorbonne University
  • Guillaume DelayToggle sub-subsection view
    • Remise à Niveau en Math à PolyTech Sorbonne L3, (12h)
  • Corrie JamesToggle sub-subsection view
    • Math Tutoring, 9h, L1, Université de Versailles Saint-Quentin-en-Yvelines
  • Gaël le RuzToggle sub-subsection view
    • Linear algebra and ODE, 30h, L3, Polytech Sorbonne, Sorbonne Université.
    • Numerical Analysis for PDE, 12h, L3, Polytech Sorbonne, Sorbonne Université.
  • Fabien VergnetToggle sub-subsection view
    • Numerical analysis and ODE, 56h, L3, Polytech Sorbonne, Sorbonne Université.
    • Fourier Analysis 15h, L3, Polytech Sorbonne, Sorbonne Université.
    • Dynamical Systems 6h, L3, Polytech Sorbonne, Sorbonne Université.
• Master:
  • Guillaume DelayToggle sub-subsection view
    • Preparation to Agrégation, 34h, M2, Sorbonne Université
    • Numerical analysis for PDE, 18h, M1,PolyTech Sorbonne
    • Initiation to C++, 27h, M2, Sorbonne Université.
    • C++ projet, 21h, M2, Sorbonne Université.
  • Miguel Angel Fernández VarelaToggle sub-subsection view
    • Mathematical models and numerical methods for hemodynamics simulations, 20h, M2, Sorbonne Université.
  • Damiano LombardiToggle sub-subsection view
    • Lecture, 1.5h, Modeling the electro-physiology of heart, November 2023, Ecole des Mines Paristech.
  • Frédérique NoëlToggle sub-subsection view
    • Programming in C++, 28h, M1, Sorbonne Université

9.2.2 Supervision

• PhD in progress: Oscar Ruz, Mathematical modeling and numerical simulation of left heart hemodynamics with fluid–structure interactions. Supervisors: D. Chapelle, M.A. Fernández Varela & M. Vidrascu.
• PhD in progress: Marguerite Champion, Modeling, analysis and simulation of fluid-structure-contact interaction. Supervisors: M.A. Fernández Varela, C. Grandmont, F. Vergnet & M. Vidrascu.
• PhD in progress: Gaël le Ruz, Observer theory in general constrained spaces – from formulations to applications. Since October 2022. Supervisors: D. Lombardi & P. Moireau.
• PhD in progress: Corrie James, Data-Modeling interaction for biomedical applications. Since October 2023. Supervisors: M. Boulakia & D. Lombardi.
• PhD in progress: Romain Lemore, Modeling and patient specific fluid-structure interaction simulations of aortic pathological configurations. Since July 2024. Supervisors: M.A. Fernández Varela & D. Lombardi.
• PhD in progress: Romain Lopez-Surjus, Mathematical and numerical modelling of the cardio respiratory system. Since October 2024. Supervisors: C. Grandmont, F. Noël & F. Vergnet
• PhD in progress: Davide Duva, A 4D-var method for blood pressure reconstruction. Since December 2024. Supervisors: G. Delay & M.A. Fernández Varela.
• PostDoc in progress: Lamis Sabbagh (ARC-ULB, hosted by ULB), Mathematical analysis of fluid-structure interactions problems. Supervisor: C. Grandmont.
• PhD defended on December 16, 2024: Sara Costa Faya, An in silico approach to monitor and predict haemodynamics during safety pharmacology studies. Supervisors: M.A. Fernández Varela, D.Lombardi.
• PhD defended on June 27, 2024: Daniele Corti, Modeling and numerical simulation of the mitral apparatus. Supervisors: M.A. Fernández Varela, G. Delay , F. Vergnet & M. Vidrascu.
• PhD defended on June 26, 2024: Fabien Lespagnol, A new computational approach for fluid-structure interaction of slender bodies immersed in three-dimensional flow. Supervisors: M. Boulakia, M.A. Fernández Varela, C. Grandmont & Paolo Zunino (MOX, Politecnico de Milano).
• PhD defended on May 2, 2024: Haibo Liu, Data assimilation for high-throughputs creening in safety pharmacology. Supervisors: D. Lombardi & M. Boulakia.
• Internship Riccardo Bianchi. Supervisors: Damiano Lombardi, Stefano Pagani, Politecnico di Milano
• Internship Romain Lopez-Surjus. Supervisors: Frédérique Noël,Fabien Vergnet
• Internship David Duva. Supervisors: G. Delay, M.A. Fernández Varela.
• Internship Leo-Paul Baudet. Supervisors: G. Delay, M.A. Fernández Varela.

9.2.3 Juries

• Céline Grandmont
  • Selection Committee: Professor position Nantes Univ.

9.3.1 Participation in Live events

• Céline Grandmont
  • « 1 scientifique, 1 classe : chiche ! » program, 2h, students from Lycée Jeanne d'Albret (Saint-Germain en Laye), December 3, 2024, Rocquencourt
• Miguel Angel Fernández Varela
  • « 1 scientifique, 1 classe : chiche ! » program, 2h, students from Lycée Jeanne d'Albret (Saint-Germain en Laye), December 3, 2024, Rocquencourt

International journals

• 10 articleM.Muriel Boulakia, C.Céline Grandmont, F.Fabien Lespagnol and P.Paolo Zunino. Mathematical and numerical analysis of reduced order interface conditions and augmented finite elements for mixed dimensional problems.Computers & Mathematics with Applications175December 2024, 536-569HALDOI
• 11 articleE.Erik Burman, R.Rebecca Durst, M. A.Miguel Angel Fernández, J.Johnny Guzmán and S.Sijing Liu. A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems.IMA Journal of Numerical AnalysisSeptember 2024. In press. HALback to text
• 12 articleE.Erik Burman, R.Rebecca Durst, M. A.Miguel Angel Fernández, J.Johnny Guzmán and S.Sijing Liu. Estimates of discrete time derivatives for the parabolic-parabolic Robin-Robin coupling method.Numerical AlgorithmsAugust 2024HALDOIback to text
• 13 articleM.Marguerite Champion, M. A.Miguel Angel Fernández, C.Céline Grandmont, F.Fabien Vergnet and M.Marina Vidrascu. On the analysis of a mechanically consistent model of fluid-structure-contact interaction.Mathematics in Engineering632024, 425-467HALDOI
• 14 articleD.Daniele Corti, G.Guillaume Delay, M. A.Miguel Angel Fernández, F.Fabien Vergnet and M.Marina Vidrascu. Low-order fictitious domain method with enhanced mass conservation for an interface Stokes problem.ESAIM: Mathematical Modelling and Numerical Analysis581February 2024, 303-333HALDOI
• 15 articleF.Fabien Lespagnol, C.Céline Grandmont, P.Paolo Zunino and M. A.Miguel Angel Fernández. A mixed-dimensional formulation for the simulation of slender structures immersed in an incompressible flow.Computer Methods in Applied Mechanics and Engineering432August 2024, 117316HALDOI
• 16 articleS.Sébastien Riffaud. Accurate and robust predictions for model order reduction via an adaptive, hybrid FOM/ROM approach.Journal of Computational Physics5232024, 113677HALDOI
• 17 articleS.Sébastien Riffaud, M. A.Miguel Angel Fernández and D.Damiano Lombardi. A low-rank solver for parameter estimation and uncertainty quantification in linear time dependent systems of Partial Differential Equations.Journal of Scientific Computing9922024, 34HALDOI

Doctoral dissertations and habilitation theses

• 18 thesisD.Daniele Corti. Numerical methods for immersed fluid-structure interaction with enhanced interfacial mass conservation.Sorbonne UniversitéJune 2024HAL
• 19 thesisS. C.Sara Costa Faya. Modeling and numerical simulation applied to the prediction of the effect of drugs in the cardiovascular system.INRIADecember 2024HAL
• 20 thesisF.Fabien Lespagnol. A new computational approach for fluid-structure interaction of slender bodies immersed in three-dimensional flows.Politecnico di Milano. Dipartimento di mathematica (Milano, Italie); Sorbonne Université - Laboratoire Jacques-Louis LionsJune 2024HAL
• 21 thesisH.Haibo Liu. Empowering Predictivity and Speed of hiPSC CM Assays by Machine Learning Approach.Sorbonne UniversitéMay 2024HAL

Reports & preprints

• 22 miscR.Rodolfo Araya and M. A.Miguel Angel Fernández. Fractional-step methods and PSPG stabilized finite elements for the transient Stokes equations.June 2024HALback to text
• 23 miscM.Mathieu Barré, C.Céline Grandmont and P.Philippe Moireau. A projection scheme for an incompressible soft material poromechanics model.June 2024HALback to text
• 24 miscM.Muriel Boulakia, C.Corrie James and D.Damiano Lombardi. Numerical approximation of the unique continuation problem enriched by a database for the Stokes equations.October 2024HALback to text
• 25 miscE.Erik Burman, G.Guillaume Delay and A.Alexandre Ern. The unique continuation problem for the wave equation discretized with a high-order space-time nonconforming method.July 2024HALDOIback to text
• 26 miscD.Daniele Corti, J.Jérôme Diaz, M.Marina Vidrascu, D.Dominique Chapelle, P.Philippe Moireau and M. A.Miguel Angel Fernández. A fictitious domain method with enhanced interfacial mass conservation for immersed FSI with thin-walled solids.September 2024HALback to text
• 27 miscS. C.Sara Costa Faya, W.Wesley Callan, M.Marina Vidrascu, M. A.Miguel Angel Fernández, P.-J.Pieter-Jan Guns and D.Damiano Lombardi. Validation of a mathematical model of arterial wall mechanics with drug induced vasoconstriction against ex vivo measurements.December 2024HALback to text
• 28 miscC.Céline Grandmont and L.Lamis Sabbagh. Existence and Uniqueness of Strong Solutions to a Bi-dimensional Fluid-Structure Interaction System.June 2024HALback to text
• 29 miscD.Damiano Lombardi. A non-linear manifold reduction based on ridge regression.January 2024HALback to text
• 30 miscD.Damiano Lombardi and C.Cecilia Pagliantini. Conformal variational discretisation of infinite dimensional Hamiltonian systems with gradient flow dissipation.December 2024HALback to text
• 31 miscD.Damiano Lombardi and S.Sébastien Riffaud. Preconditioners for multilinear problems arising in parametric Partial Differential Equations.January 2024HALback to text
• 32 miscO.Oscar Ruz, J.Jérôme Diaz, M.Marina Vidrascu, P.Philippe Moireau, D.Dominique Chapelle and M. A.Miguel Angel Fernández. Left heart hemodynamics simulations with fluid-structure interaction and reduced valve modeling.October 2024HALback to text