RESEARCH CENTRE

Inria Paris Centre
at Sorbonne University

IN PARTNERSHIP WITH:

CNRS, Sorbonne Université

2023
ACTIVITY REPORT

Project-Team

COMMEDIA

Computational mathematics for
bio-medical applications

IN COLLABORATION WITH: Laboratoire Jacques-Louis Lions (LJLL)

DOMAIN

Digital Health, Biology and Earth

THEME

Modeling and Control for Life Sciences

Contents

Project-Team COMMEDIA

1 Team members, visitors, external collaborators

2 Overall objectives

3 Research program

3.1 Multi-physics modeling and simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Cardiovascular hemodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Respiratory flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Simulation with data interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Fluid flow reconstruction from medical imaging . . . . . . . . . . . . . . . . . . . . .
3.2.2 Safety pharmacology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Methodological core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Mathematical analysis of PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Numerical methods for multi-physics problems . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Statistical learning and mathematical modeling interactions . . . . . . . . . . . . . .
3.3.4 Tensor approximation and HPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Application domains

4.1 Cardiovascular hemodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Respiratory flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Safety pharmacology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 New software, platforms, open data

5.1 New software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 FELiScE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 FELiScE-NS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 DCIMaL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.4 ADAPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 New results

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6.1 Reduced Order modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6.2 Safety pharmacology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
6.3 Mathematical analysis of PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
6.4 Numerical methods for multi-physics problems . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7 Bilateral contracts and grants with industry

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7.1 Bilateral contracts with industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

8 Partnerships and cooperations

11
8.1 International initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.1.1 Associate Teams in the framework of an Inria International Lab or in the framework

8.2 European initiatives

of an Inria International Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.1.2 Visits of international scientists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
8.2.1 Horizon Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
8.3 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
8.3.1 ANR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

9 Dissemination

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9.1 Promoting scientific activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
9.1.1 Scientific events: organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
9.1.2 Journal
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
9.1.3 Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
9.1.4 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
9.2 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
9.2.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
9.2.2 Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
9.2.3 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
9.3 Popularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

10 Scientific production

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10.1 Major publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
10.2 Publications of the year
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10.3 Cited publications

Project COMMEDIA

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Project-Team COMMEDIA

Creation of the Project-Team: 2019 June 01

Keywords

Computer sciences and digital sciences

A6.1.1. – Continuous Modeling (PDE, ODE)

A6.1.4. – Multiscale modeling

A6.1.5. – Multiphysics modeling

A6.2.1. – Numerical analysis of PDE and ODE

A6.3.1. – Inverse problems

A6.3.2. – Data assimilation

A6.3.4. – Model reduction

Other research topics and application domains

B2.2.1. – Cardiovascular and respiratory diseases

B2.4.1. – Pharmaco kinetics and dynamics

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Inria Annual Report 2023

1 Team members, visitors, external collaborators

Research Scientists

• Miguel Angel Fernández Varela [Team leader, INRIA, Senior Researcher, HDR]

• Céline Grandmont [INRIA, Senior Researcher, HDR]

• Adrien Lefieux [INRIA, Advanced Research Position]

• Damiano Lombardi [INRIA, Researcher, HDR]

• Marina Vidrascu [INRIA, Emeritus]

Faculty Members

• Muriel Boulakia [USVQ, until Jun 2023, secondment , HDR]

• Guillaume Delay [SORBONNE UNIVERSITE, Associate Professor]

• Fabien Vergnet [SORBONNE UNIVERSITE, Associate Professor]

Post-Doctoral Fellows

• Cyril Karamaoun [CNRS, Post-Doctoral Fellow]

• Sébastien Riffaud [INRIA, Post-Doctoral Fellow, until Nov 2023]

PhD Students

• Marguerite Champion [CNRS]

• Daniele Carlo Corti [INRIA]

• Sara Costa Faya [INRIA]

• Maria Fuente Ruiz [INRIA, until Feb 2023]

• Corrie James [UVSQ, from Oct 2023]

• Gael Le Ruz [SORBONNE UNIVERSITE]

• Fabien Lespagnol [POLITECNICO DI MILANO]

• Haibo Liu [NOTOCORD]

• Oscar Ruz [ANID (BECAS CHILE)]

Interns and Apprentices

• Riccardo Bianchi [INRIA, Intern, from Oct 2023]

• Marloes Coolen [INRIA, Intern, from Mar 2023 until Jun 2023]

• Corrie James [INRIA, Intern, from Apr 2023 until Aug 2023]

Administrative Assistant

• Julien Guieu [INRIA]

Project COMMEDIA

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2 Overall objectives

COMMEDIA is a joint project-team of the Inria Research Center of Paris and the Jacques-Louis Lions
Laboratory (LJLL) of Sorbonne Université and CNRS (UMR7598). The research activity of COMMEDIA
focuses on the numerical simulation of bio-fluid flows in the human body, more specifically, blood flows
in the cardiovascular system and air flows in the respiratory system. These simulations are intended
to complement available clinical data with the following purpose: help clinicians or bio-engineers to
enhance the understanding of physiological phenomena, to improve diagnosis and therapy planning or
to optimize medical devices. The main main objectives of COMMEDIA are:

• the development of appropriate mathematical models and efficient numerical methods for the

simulations and for the interaction of simulations with measured data;

• the mathematical analysis of these models and numerical techniques;

• the development and validation of scientific computing software which implements these numer-

ical techniques.

A distinctive feature of the mathematical models considered in COMMEDIA is that they often couple
different types of partial differential equations (PDEs). This heterogeneous character in the models is a
mathematical manifestation of the multi-physics nature of the considered problems.

3 Research program

3.1 Multi-physics modeling and simulation

The research activity in terms of modeling and simulation (i.e., the so-called forward problem) is driven
by two application domains related to the cardiovascular and the respiratory systems.

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 diffi-
culties. 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 con-
ditions, 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., [69, 70, 67, 72, 60]), 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 at 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., [42, 55, 58]). 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).

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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 phenomena 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 [44, 52, 75]), but the magnitude of the corresponding pressure is not physiolo-
gical. 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 de-
veloped 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., [77]). 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 [71]). 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 Simulation with data interaction

The second research axis of COMMEDIA is devoted to the interaction of numerical simulations with
measured data. Several research directions related to two specific applications are described below: blood
flows and cardiac electrophysiology, for which the mathematical models have been validated against

Project COMMEDIA

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experimental data. This list is not exhaustive and additional problems (related to cardiac and respiratory
flows) shall be considered depending on the degree of maturity of the developed models.

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 [66]). 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 [65]). 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 [49]) 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 Methodological core

The work described in this section is aimed at investigating fundamental mathematical and numerical
problems which arise in the first two research axes.

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 [64, 62]). 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 [54], which allows for nonlinear
constitutive behaviors and viscous effects, both in the fluid and the solid. Among the questions which will

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Inria Annual Report 2023

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 [46, 48]. 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 discretiza-
tion 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 an 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 [74, 45, 61, 43]) are known to be inaccurate in space. These difficulties have been
recently circumvented by a Nitsche-based cut-FEM methodolgy (see [40, 50]). 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
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., [59]). 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 interac-
tion 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., [71, 73,
47]). 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 [41]) build a relationship between the system observations and the predictions of the QoI based

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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
model 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 [68]). 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 [63]). 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 [76]). 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 (Université Paris-Dauphine) and
the ALPINES and MATHERIALS project-teams.

4 Application domains

4.1 Cardiovascular hemodynamics

The heart is a double pump whose purpose is to deliver blood to the tissue and organs of the body. This
function is made possible through the opening and closing of the heart valves. Cardiac diseases generally
manifest by affecting the pumping function of the heart. Numerical simulations of cardiac hemodynamics,
in normal and pathological conditions, are recognized as a tool of paramount importance for improving
the understanding, diagnosis and treatment of cardiac pathologies, and also for the development of
implantable devices (see, e.g., [72, 53]). As an example, we can mention the case of cardiac mitral valve
regurgitation, one of the most common heart valve diseases. For this pathology, clinical data are known
to be insufficient for determining the optimal timing for surgery, the best surgical strategy and the long-
term outcome of a surgical repair. Contrary to imaging techniques, numerical simulations provide local
information, such as pressure and stresses, which are of fundamental importance for the prediction of
the mechanical behavior of native valves and of implantable devices.

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Inria Annual Report 2023

4.2 Respiratory flows

Respiration involves the transport of air through the airways from the mouth to the alveoli of the lungs.
These units where diffusion of oxygen and carbon dioxide take place, are surrounded by a viscoelastic
medium (the parenchyma) consisting of blood vessels and collagen fibers. Air flows due to the displace-
ment of the diaphragm, which drives the pulmonary parenchyma. Accidental inhalations of foreign
bodies or pathologies such as asthma, emphysema and fibrosis might prevent the lung of fulfilling its
function. Therapies mostly use aerosols (set of small particles, solid or liquid), which must reach the
specific areas of the lung targeted for treatment. Understanding the airflow mechanisms within the
respiratory network is a fundamental ingredient for predicting the particles motion and their deposition
(see, e.g., [51]). Moreover, understanding of the gas diffusion in the lung is also of major importance since
the main fonction of this organ is to deliver oxygen to the blood.

4.3 Safety pharmacology

The problem of safety pharmacology can be summarized as follows: given a molecule which is a candidate
to become a drug, is its use dangerous due to side effects? Among all the different problems to be
addressed, one of the most relevant questions in pharmacology is cardio-toxicity (see [65]). More precisely,
the objective is to determine whether or not a molecule alters in a significant way the normal functioning
of the cardiac cells. To answer these questions, the CiPA initiative promotes the introduction of novel
techniques and their standardisation (see [57]). One of the proposed tests of the CiPA panel is to measure
the the electrical activity using Micro-Electrodes Array: these are microchips that record the electrical
activity of an ensemble of cells. The task is to infer the impact of a drug on the ionic currents of each cell
based on the electrical signal measured (electrograms) and, in perspective, to be able to assess whether a
molecule can induce arrhythmia (see [56]).

5 New software, platforms, open data

5.1 New software

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 code which the M3DISIM and REO project-teams
initially jointly develop in order to build up on their respective experiences concerning finite
element simulations. One specific objective of this code is to provide in a unified software environ-
ment 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: Daniele Carlo Corti, Miguel Angel Fernandez Varela, Marina Vidrascu, Sara Costa Faya,

Mocia Agbalessi, Mihai-simion Nechita, Oscar Ruz, Fabien Lespagnol, Vicente Mataix Ferrandiz

5.1.2 FELiScE-NS

Functional Description: FELiScE-NS is a set finite elements solvers for incompressible fluids (fractional-
step schemes) and non-linear thin-walled structures (3D shells, and 2D curved beams) developed in

Project COMMEDIA

9

the framework of the FELiScE library. FELiSCe-NS was registered in 2018 at the Agence pour la Pro-
tection des Programmes Inter Deposit Digital Number IDDN.FR.001.270015.000.S.A.2018.000.31200.

Contact: Miguel Angel Fernandez Varela

Participants: Miguel Angel Fernandez Varela, Marina Vidrascu, Daniele Carlo Corti, Mocia Agbalessi,

Sara Costa Faya, Vicente Mataix Ferrandiz, Mocia Agbalessi

5.1.3 DCIMaL

Functional Description: DCIMaL is a Python and C++ software for safety pharmacology studies and par-
ticularly field potentials signals measured with micro-electrode array (MEA). The software includes
a solver for field potential simulations and a dictionary of entries corresponding to features which
can be extracted from real or simulated potential signals. It also includes an algorithm for drug
classification (channel blockade or torsadogenic risk) and a tool for estimating ion channel activity
(based on the CMAES library). DCIMaL was registered in 2018 at the Agence pour la Protection des
Programmes Inter Deposit Digital Number IDDN.FR.001.270003.000.S.P.2018.000.31230

Contact: Damiano Lombardi

Participants: Fabien Raphel, Damiano Lombardi

5.1.4 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, Maria Fuente Ruiz, Damiano Lombardi, Sebastien Riffaud

6 New results

6.1 Reduced Order modelling

Participants: Muriel Boulakia, Céline Grandmont, Fabien Lespagnol, Sébas-

tien Riffaud.

In [32], we propose a reduced model associated to the Poisson problem in a domain with small holes.
The reduction method is based on a fictitious domain formulation combined with a projection of Dirichlet
boudary constraints on a finite dimensional approximation space. After analyzing the existence of a
solution for the reduced problem and its convergence towards the full problem, we propose a numerical
discretization which relies on augmented finite elements and allows to achieve optimal convergence
properties that are illustrated through numerical illustrations.

In [38], we introduce a hybrid approach that alternates between a high-fidelity model and a reduced-
order model to speedup numerical simulations while maintaining accurate approximations. In particular,
a residual-based error indicator is developed to determine when the reduced-order model is not suffi-
ciently accurate and the high-fidelity model needs to be solved. Then, we propose an adaptive-extended
version of the hybrid approach to update the reduced-order model with the solution snapshots generated
by the high-fidelity model when the reduced-order model was not sufficiently accurate. In this way, we

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Inria Annual Report 2023

expect the reduced-order model to become more robust for predicting new out-of-sample solutions. The
performance of the proposed method is evaluated on parametrized, time-dependent, nonlinear problems
governed by the 1D Burgers’ equation and 2D compressible Euler equations. The results demonstrate the
accuracy and computational efficiency of the adaptive hybrid approach with respect to the high-fidelity
model.

6.2 Safety pharmacology

Participants: Muriel Boulakia, Haibo Liu, Damiano Lombardi.

In [33], we study how to regularise, by means of a dataset of existing observations, parameter es-
timation problems in dynamical systems. Thanks to a representation of the dataset in the form of an
encoder-decoder pair, we are able to introduce a Lipschitz stable non-linear change of variables such that
the parameter estimation problem can be cast as an optimisation of a convex function. We prove that,
given a Hölder regularity C 1,β
of the composition of the encoder and the dynamical system equation,
we can have some theoretical guarantees on the convergence. Some encouraging numerical results are
shown on the Van der Pol and the FizHugh-Nagumo dynamical systems.

6.3 Mathematical analysis of PDEs

Participants: Marguerite Champion, Miguel Angel Fernández Varela, Céline Grand-

mont, Fabien Vergnet, Marina Vidrascu.

In [16], we propose and study a new continuum mechanics model for the fluid-structure interaction
problem involving active thin structures embedded in a Stokes flow. In particular, this model is able to
reproduce the behavior of cilia or flagella betting in a viscous flow. In the context of linear or nonlinear
elasticity, the model is based upon the definition of a suitable internal Piola-Kirchoff tensor , which mimics
the action of internal biological motors, inducing the motility of the structures. The well-posedness of this
coupled system is studied and, for the numerical resolution, an equivalent formulation using Lagrange
multipliers is introduced, allowing for the use of standard (fluid and structure) solvers, up to an iterative
procedure. Numerical simulations are presented, which illustrate the potential of the proposed active
elasticity model.

In [36] we analyse of the contact capabilities of the fluid-structure interaction (FSI) model with
seepage reported in [4]. In the case of a rigid disk moving over a fixed horizontal plane, we show that
this model encompasses contact and hence removes the non collision paradox of traditional FSI models
which rely on Dirichlet or Dirichlet/Navier boundary conditions. Numerical evidence on the theoretical
results is also provided.

6.4 Numerical methods for multi-physics problems

Participants: Daniele Corti, Guillaume Delay, Miguel Angel Fernández Varela,
Céline Grandmont, Fabien Lespagnol, Oscar Ruz, Fabien Vergnet, Mar-
ina Vidrascu.

One of the main difficulties that has to be faced with fictitious domain approximation of incom-
pressible flows with immersed interfaces is related to the potential lack of mass conservation across the
interface. In [15], we propose and analyze a low order fictitious domain stabilized finite element method
which mitigates this issue with the addition of a single velocity constraint. We provide a complete a priori
numerical analysis of the method under minimal regularity assumptions. A comprehensive numerical
study illustrates the capabilities of the proposed method, including comparisons with alternative fitted
and unfitted mesh methods.

Project COMMEDIA

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The numerical simulation of incompressible fluid-structure interaction systems with loosely coupled
schemes is a delicate problem. Indeed, the splitting method must both be stable for the full nonlinear sys-
tem and have sufficient accuracy to be of use in practice. In the case of the coupling of an incompressible
fluid with thick-walled solids the error analyses reported in the literature are limited to 1/2-order accuracy
in time. In [34] we introduce two important extensions of the analysis of the Robin-Robin loosely coupled
scheme recently reported in [Numer. Math., 151(4):807–840, 2022]. First, we give a formulation of the
scheme in a general non-linear setting and prove its unconditional energy stability. Then we show that
nearly-optimal accuracy can be achieved in the linear case. These theoretical findings are illustrated in a
series of numerical examples.

In [11] we analyse the convergence of the full discretization of a generalized poromechanical model
resulting from the linearization of an initial model fitted to soft tissue perfusion. Our strategy here is based
on the use of energy-based estimates and T-coercivity methods, so that the numerical analysis benefits
from the essential tools used in the existence analysis of the continuous-time and continuous-space
formulation.

[37] We consider the simulation of slender structures immersed in a three-dimensional (3D) flow.
By exploiting the special geometric configuration of the slender structures, this particular problem can
be modeled by mixed-dimensional coupled equations (3D for the fluid and 1D for the solid). Several
challenges must be faced when dealing with this type of problems. From a mathematical point of view,
these include defining wellposed trace operators of codimension two. On the computational standpoint,
the nonstandard mathematical formulation makes it difficult to ensure the accuracy of the solutions
obtained with the mixed-dimensional discrete formulation as compared to a fully resolved one. We
establish the continuous formulation using the Navier-Stokes equations for the fluid and a Timoshenko
beam model for the structure. We complement these models with a mixed-dimensional version of the
fluid-structure interface conditions, based on the projection of kinematic coupling conditions on a
finite-dimensional Fourier space. Furthermore, we develop a discrete formulation within the framework
of the finite element method, establish the energy stability of the scheme, provide extensive numerical
evidence of the accuracy of the discrete formulation, notably with respect to a fully resolved (ALE based)
model and a standard reduced modeling approach.

7 Bilateral contracts and grants with industry

7.1 Bilateral contracts with industry

Withings

Participants: Miguel Ángel Fernández Varela (coordinator), Adrien Lefieux, Dami-

ano 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.

8 Partnerships and cooperations

8.1 International initiatives

8.1.1 Associate Teams in the framework of an Inria International Lab or in the framework of an Inria

International Program

IMFIBIO: Innovative Methods for Forward and Inverse problems in BIO-medical applications

Participants: Muriel Boulakia, Daniele Carlo Corti, Guillaume Delay, Miguel Án-

gel Fernández Varela (coordinator).

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Inria Annual Report 2023

Title: Innovative Methods for Forward and Inverse problems in BIO-medical applications

Duration: 2022-2025

Coordinator: Miguel Angel Fernández Varela

Partner: University College London London (Royaume-Uni)

UCL contact: Erik Burman

Summary: The purpose of the IMFIBIO Associate Team is to exploit the complementary expertise of both
partners in mathematical analysis, numerical analysis, scientific computing and data assimilation
in order to develop innovative methods for the study of forward and inverse problems in the context
of bio-medical applications.

Web site: team.inria.fr/imfibio

8.1.2 Visits of international scientists

• Erik Burman (UCL), March and October 2023.

• Mihai Nechita (Tiberiu Popoviciu Institute of Numerical Analysis), May 2023.

• Cecilia Pagliantini (Università di Pisa), February and October 2023.

• Gianluca Ceruti (University of Innsbruck), February and October 2023.

8.2 European initiatives

8.2.1 Horizon Europe

INSPIRE: INnovation in Safety Pharmacology for Integrated cardiovascular safety assessment to
REduce adverse events and late stage drug attrition

Participants:

Sara Costa, Miguel Ángel Fernández Varela, Haibo Liu, Damiano Lom-
bardi (coordinator).

Funding: Horizon 2020 - MSCA-ITN

Duration: 2020-2024

Coordinator: University of Antwerp

Local coordinator: Damiano Lombardi

Summary: INSPIRE is an European Training Network (ETN) projet funding 15 Early Stage Researchers
(ESRs) aimed to exploit innovative techniques for better assessment and prediction of cardiovascu-
lar safety liabilities.

Web site: www.uantwerpen.be/en/projects/inspire-safety-pharmacology

8.3 National initiatives

8.3.1 ANR

ADAPT: Adaptive Dynamical Approximations by Parallel Tensor methods

Project COMMEDIA

13

Participants: Maria Fuente-Ruiz, Damiano Lombardi

(coordinator), Sébas-

tien Riffaud
.

Funding: ANR JCJC

Duration: 2018-2023

Coordinator: Damiano Lombardi

Summary: The main goal of the ANR is to investigate the numerical approximation of the solution
of high-dimensional problems. In particular, the applications that motivate this study are the
Uncertainty Quantification and the Kinetic theory. The main objective is to construct in an adaptive
way parsimonious discretisations starting from arbitrarily chosen separated discretisations.

Web site: project.inria.fr/adapt

SIMR: Simulation and Imaging for Mitral Regurgitation

Participants: Daniele Carlo Corti, Miguel Ángel Fernández Varela (coordinator),

Céline Grandmont, Marina Vidrascu.

Funding: ANR PRC

Duration: 2020-2024

Coordinator: Miguel Ángel 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.

Web site: project.inria.fr/simr

9 Dissemination

9.1 Promoting scientific activities

9.1.1 Scientific events: organisation

• Guillaume Delay

– Co-organiser of the scientific computing seminar, joint event between Inria and Laboratoire

Jacques-Louis Lions.

– Organizer of the Workshop on data assimilation, Sorbonne Université, November 2023.

• Miguel Ángel Fernández Varela

– Co-organizer of an FIMH sateltite workshop, Simulation and Imaging for Mitral Regurgitation,

Lyon, June 2023.

• Damiano Lombardi

– Co-organiser of the scientific computing seminar, joint event between Inria and Laboratoire

Jacques-Louis Lions.

– Mini-symposium organiser, High-Dimensional Approximation and Reduced-Order Models,

in SIAM CSE, Amsterdam, March 2023.

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Inria Annual Report 2023

9.1.2 Journal

Member of the editorial boards

• Céline Grandmont

– Mathematical Modelling of Natural Phenomena

– Journal of Mathematical Fluid Mechanics

– ESAIM: Mathematical Modelling and Numerical Analysis

9.1.3 Invited talks

• Muriel Boulakia

– Invited speaker, Workshop ANR Trecos, ENS Rennes, June 2023

– Invited speaker, Conference Optimization and Control in Burgundy, Dijon, May 2023

– Mini-symposium keynote speaker, CFC 2023, Cannes, April 2023

• Miguel Angel Fernández Varela

– Invited talk in MS, ICIAM, Tokyo, August, 2023

• Céline Grandmont

– Conference in honnor pf Grigory Panasenko, Saint Etienne University, Octobre 2023.

– Séminaire EDP, Grenoble Rhone Alpes Univ., Sept. 2023.

– Colloquium Nantes, April 2023

• Damiano Lombardi

– Keynote speaker, Biophysics-based modeling and data assimilation in medical imaging, Berlin,

August 2023.

– Invited talk in MS, ICIAM, Tokyo, August, 2023

• Fabien Vergnet

– European Conference on Numerical Mathematics and Advanced Applications (ENUMATH),

September 2023, Lisbon, Portugal

9.1.4 Research administration

• Muriel Boulakia

– Member of the committee of the doctoral school FMJH/LMH Paris-Saclay for the thematics

Mathematics of Scientific Computing and Engineering

• Miguel Fernández Varela

– Head of Science,Inria Paris

– Member of the Inria Evaluation Committee

• Céline Grandmont

– Member of the Inria Evaluation Commitee

– Member of the Inria Parity

– Member of the scientific commitee of the doctoral school EDMH, Paris-Saclay.

– Member of the scientific commitee of GDR MathSAv: Mathématiques, Santé, Sciences de la

Vie. Commitee

• Damiano lombardi

– Co-president of CES (Commission Emploi Scientifique), Inria Paris.

Project COMMEDIA

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9.2 Teaching - Supervision - Juries

9.2.1 Teaching

• Licence:

– Marguerite Champion

* Numerical analysis, 24h, L3, Sorbonne University
* Python, 32h, L2, Sorbonne University

– Guillaume Delay

* Analyse Numérique L3, (48h)
* Remise à Niveau en Math à PolyTech Sorbonne L3, (12h)

– Corrie James

* Math Tutoring, 9h, L1, Université de Versailles Saint-Quentin-en-Yvelines

– Gaël le Ruz

* Linear algebra and ODE, 30h, L3, Polytech Sorbonne, Sorbonne Université.
* Fourier Analysis, 24h, L3, Polytech Sorbonne, Sorbonne Université.
* Numerical Analysis for PDE, 12h, L3, Polytech Sorbonne, Sorbonne Université.

– Fabien Vergnet

* Numerical analysis and ODE, 58h, L3, Polytech Sorbonne, Sorbonne Université.
* Nonlinear systems and optimization, 30h, L3, Polytech Sorbonne, Sorbonne Université.

• Master:

– Guillaume Delay

* 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 Ángel Fernández Varela

* Mathematical models and numerical methods for hemodynamics simulations, 20h, M2,

Sorbonne Université.

– Damiano Lombardi

* Lecture, 1.5h, Modelling the heart, June 2023, ENPC.
* Lecture, 1.5h, Modeling the electro-physiology of heart, November 2023, Ecole des Mines

Paristech.

9.2.2 Supervision

• PhD Mathieu Barré, Mathematical and numerical study of a poroelastic model.Supevisors: C.

Grandmont & P. Moireau (M3DISIM, Inria Saclay defended in October 2023).

• 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: Daniele Corti, Modeling and numerical simulation of the mitral apparatus.Since

October 2020. Supervisors: M.A. Fernández Varela, G. Delay , F. Vergnet & M. Vidrascu.

• PhD in progress: Sara Costa Faya, An in silico approach to monitor and predict haemodynamics
during safety pharmacology studies. Since September 2020. Supervisors: M.A. Fernández Varela,
D.Lombardi.

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Inria Annual Report 2023

• PhD in progress: Fabien Lespagnol, A new computational approach for fluid-structure interaction
of slender bodies immersed in three-dimensional flow. Since September 2020. Supervisors: M.
Boulakia, M.A. Fernández Varela, C. Grandmont & Paolo Zunino (MOX, Politecnico de Milano).

• PhD in progress: Haibo Liu, Data assimilation for high-throughputs creening in safety pharmaco-

logy. Since September 2020. Supervisors: D. Lombardi & M. Boulakia.

• PhD in progress: Gaël le Ruz, Observer theory in general constrained spaces – from formulations to

applications. Since September 2020. Supervisors: D. Lombardi & P. Moireau.

• PhD defended (March 2023): Maria Fuente Ruiz, Adaptive tensor methods for scientific computing.

Supervisors: D. Lombardi & V. Ehrlacher.

• PostDoc: Cyril Karamaoun (CNRS, Sorbonne Université), Until dec 2023, Modelling of gas transport

and exchange in the lung. Supervisors: L. Boudin (Sorbonne Univ.) & C. Grandmont.

• PostDoc: Sebastien Riffaud. Tensor methods for parametric fluid-structure interaction and data

assimilation. Supervisors: D. Lombardi & M.A. Fernández Varela.

• PostDoc in progress: Lamis Sabbagh (ARC-ULB, hosted by ULB), Mathematical analysis of fluid-

structure interactions problems. Supervisor: C. Grandmont.

• Internship Marloes Coolen. Supervisor: M.A. Fernández Varela.

• Internship Corrie James. Supervisors: M. Boulakia & D. Lombardi.

• Internship Riccardo Bianchi. Supervisors: D. Lombardi & Stefano Pagani (Politecnico di Milano)

9.2.3 Juries

• Muriel Boulakia

– Hiring committees: MdC at GEMaC laboratory, UVSQ ; Professor at Laboratoire de Math-

ématiques, Université du Littoral Côte d’Opale

• Céline Grandmont

– Member of the PhD thesis prize SMAI-Gamni 2023

– Member of the scientific commitee of SMAI 2023.

– Hiring committees: Inria CR/IFSP Nancy, "Repyramidage PR" La Rochelle University, Inria

DR2, and "Chaire de Professeur Junior", Sorbonne Université.

• Miguel Ángel Fernández Varela

– Hiring committe: Inria CR/IFSP Saclay.

9.3 Popularization

• Marguerite Champion

– Co-organizer of "Rencontres Jeunes Mathématiciennes et Informaticiennes", Inria Paris,

October 2023

Project COMMEDIA

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10 Scientific production

10.1 Major publications

[1] M. Barré, C. Grandmont and P. Moireau. ‘Analysis of a linearized poromechanics model for incom-
pressible and nearly incompressible materials’. In: Evolution Equations and Control Theory (2022).
URL: https://hal.inria.fr/hal-03501526.

[2] E. Burman, R. Durst, M. A. Fernández and J. Guzmán. ‘Fully discrete loosely coupled Robin-Robin
scheme for incompressible fluid-structure interaction: stability and error analysis’. In: Numerische
Mathematik (5th July 2022). DOI: 10.1007/s00211-022-01295-y. URL: https://hal.science
/hal-02893444.

[3] V. Ehrlacher, M. Fuente-Ruiz and D. Lombardi. ‘SoTT: greedy approximation of a tensor as a sum of
Tensor Trains’. In: SIAM Journal on Scientific Computing (2021). URL: https://hal.inria.fr/ha
l-03018646.

[4] S. Frei, F. Gerosa, E. Burman and M. A. Fernández. ‘A mechanically consistent model for fluid-
structure interactions with contact including seepage’. In: Computer Methods in Applied Mechanics
and Engineering (2022). DOI: 10.1016/j.cma.2022.114637. URL: https://hal.science/hal-
03174087.

[5] C. Grandmont and F. Vergnet. ‘Existence and uniqueness for a quasi-static interaction problem
between a viscous fluid and an active structure’. In: Journal of Mathematical Fluid Mechanics 23.45
(27th Mar. 2021). DOI: 10.1007/s00021-020-00552-0. URL: https://hal.archives-ouverte
s.fr/hal-02493384.

[6] D. Lombardi. ‘State estimation in nonlinear parametric time dependent systems using Tensor Train’.
In: International Journal for Numerical Methods in Engineering (2022). DOI: 10.1002/nme.7067.
URL: https://hal.inria.fr/hal-03375811.

[7] D. Lombardi and F. Raphel. ‘A method to enrich experimental datasets by means of numerical
simulations in view of classification tasks’. In: ESAIM: Mathematical Modelling and Numerical
Analysis 55.5 (Sept. 2021), pp. 2259–2291. DOI: 10.1051/m2an/2021060. URL: https://hal.sci
ence/hal-03377036.

[8] A. This, L. Boilevin-Kayl, M. A. Fernández and J.-F. Gerbeau. ‘Augmented Resistive Immersed
Surfaces valve model for the simulation of cardiac hemodynamics with isovolumetric phases’. In:
International Journal for Numerical Methods in Biomedical Engineering 36.3 (Feb. 2020), e3223.
DOI: 10.1002/cnm.3223. URL: https://hal.inria.fr/hal-01944798.

10.2 Publications of the year

International journals

[9] M. Agbalessi, A. Lalande, O. Bouchot, T. Hayase, J.-J. Christophe, M. A. Fernández and D. Lombardi.
‘Tracking of blood vessels motion from 4D-flow MRI data’. In: Cardiovascular Engineering and
Technology 14 (14th Aug. 2023), pp. 577–604. DOI: 10.1007/s13239-023-00677-z. URL: https:
//inria.hal.science/hal-03349442.

[10] M. Annese, M. A. Fernández and L. Gastaldi. ‘Splitting schemes for a Lagrange multiplier formu-
lation of FSI with immersed thin-walled structure: stability and convergence analysis’. In: IMA
Journal of Numerical Analysis 43.2 (2023), pp. 881–919. DOI: 10.1093/imanum/drac004. URL:
https://hal.science/hal-02893508.

[11] M. Barré, C. Grandmont and P. Moireau. ‘Numerical analysis of an incompressible soft material
poromechanics model using T-coercivity’. In: Comptes Rendus. Mécanique 351.S1 (2023), pp. 1–36.
DOI: 10.5802/crmeca.194. URL: https://hal.science/hal-04098153.

[12] L. Boudin, C. Grandmont, B. Grec and S. Martin. ‘A coupled model for the dynamics of gas ex-
changes in the human lung with Haldane and Bohr’s effects’. In: Journal of Theoretical Biology
(2023), p. 111590. DOI: 10.1016/j.jtbi.2023.111590. URL: https://hal.science/hal-0388
3301.

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Inria Annual Report 2023

[13] E. Burman, R. Durst, M. A. Fernández and J. Guzmán. ‘Loosely coupled, non-iterative time-
splitting scheme based on Robin-Robin coupling: Unified analysis for Parabolic/Parabolic and
Parabolic/Hyperbolic problems’. In: Journal of Numerical Mathematics 31.1 (2023), pp. 59–77. DOI:
10.1515/jnma-2021-0119. URL: https://hal.science/hal-03381765.

[14] E. Burman, M. A. Fernández and F. Gerosa. ‘Convergence analysis of an unfitted mesh semi-
implicit coupling scheme for incompressible fluid-structure interaction’. In: Vietnam Journal of
Mathematics 51 (2023), pp. 37–69. DOI: 10.1007/s10013-022-00589-w. URL: https://inria.h
al.science/hal-03065803.

[15] D. Corti, G. Delay, M. A. Fernández, F. Vergnet and M. Vidrascu. ‘Low-order fictitious domain
method with enhanced mass conservation for an interface Stokes problem’. In: ESAIM: Mathem-
atical Modelling and Numerical Analysis (18th Dec. 2023). DOI: 10.1051/m2an/2023103. URL:
https://inria.hal.science/hal-04084162.

[16] A. Decoene, S. Martin and F. Vergnet. ‘A continuum active structure model for the interaction
of cilia with a viscous fluid’. In: Journal of Applied Mathematics and Mechanics / Zeitschrift für
Angewandte Mathematik und Mechanik (5th Oct. 2023). DOI: 10.1002/zamm.202100534. URL:
https://hal.science/hal-02493513.

[17] F. Noël and B. Mauroy. ‘Propagation of an idealized infection in an airway tree, consequences of
the inflammation on the oxygen transfer to blood’. In: Journal of Theoretical Biology (Jan. 2023).
DOI: 10.1016/j.jtbi.2023.111405. URL: https://hal.science/hal-03669474.

Invited conferences

[18] D. Lombardi. ‘Data assimilation problems in haemodynamics’. In: Workshop on Biophysics-based
modeling and data assimilation in medical imaging. Berlin, Germany, 30th Aug. 2023. URL: https:
//inria.hal.science/hal-04392374.

[19] D. Lombardi, V. Ehrlacher and M. Fuente-Ruiz. ‘SoTT: a greedy construction of a sum of Tensor
Trains’. In: ICOSAHOM 2023 - International Conference on Spectral and High Order Methods.
Seoul, South Korea, 14th Aug. 2023. URL: https://inria.hal.science/hal-04392369.

International peer-reviewed conferences

[20] M. A. Fernández, D. Lombardi and S. Riffaud. ‘Parametric solvers for simulation of blood flows’.
In: CFC 2023 - IACM Computational Fluids Conference. Cannes, France, 25th Apr. 2023. URL:
https://inria.hal.science/hal-04010559.

Conferences without proceedings

[21] M. Boulakia, M. A. Fernández, D. Lombardi, M. Nechita and M. Agbalessi. ‘Fluid-structure interac-
tion calibration from 4D-flow MRI data’. In: CFC 2023 - IACM Computational Fluids Conference.
Cannes, France, 25th Apr. 2023. URL: https://inria.hal.science/hal-04397115.

[22] H. Liu, D. Lombardi and M. Boulakia. ‘Lipschitz Stabilised Autoencoders in Parameter Identification
of Dynamical Systems’. In: 10th International Congress on Industrial and Applied Mathematics
(ICIAM 2023). Tokyo, Japan, 20th Aug. 2023. URL: https://hal.science/hal-04398536.

[23] H. Liu, D. Lombardi and M. Boulakia. ‘Lipschitz Stabilised Autoencoders to Study the Intrinsic
Dimensionality of Dynamical Systems and Build Data-driven Models’. In: Math 2 Product (M2P):
Emerging Technologies in Computational Science for Industry, Sustainability and Innovation.
Taormina, Italy, 30th May 2023. URL: https://hal.science/hal-04398549.

[24] D. Lombardi, O. Mula and F. Galarce Marin. ‘An optimal recovery formulation of data assimilation
in haemodynamics’. In: Data Assimilation. Paris, France, Nov. 2023. URL: https://inria.hal.sc
ience/hal-04392385.

[25] D. Lombardi, S. Riffaud and M. A. Fernández. ‘Parametric FSI solvers for haemodynamics’. In:
ICIAM 2023 - 10th International Congress on Industrial and Applied Mathematics. Tokyo, Japan,
20th Aug. 2023. URL: https://inria.hal.science/hal-04392371.

Project COMMEDIA

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[26] D. Lombardi, S. Riffaud and M. A. Fernández. ‘Parametric PDE solvers for parameter estimation
and Uncertainty Quantification’. In: ENUMATH 2023 - European Conference on Numerical Math-
ematics and Advanced Applications. Lisboa, Portugal, 4th Sept. 2023. URL: https://inria.hal.s
cience/hal-04392378.

[27]

[28]

S. Riffaud, D. Lombardi and M. A. Fernández. ‘Parametric PDEs solvers, uncertainty quantification
and parameter estimation’. In: First International Conference Math 2 Product - M2P 2023. Taormina,
Italy, 30th May 2023. URL: https://inria.hal.science/hal-04012237.

S. Riffaud, D. Lombardi and M. A. Fernández. ‘Solving parametric PDEs via parsimonious discretiz-
ations: application to Uncertainty Quantification and Data Assimilation’. In: 5th International Con-
ference on Uncertainty Quantification in Computational Science and Engineering - UNCECOMP
2023. Athens, Greece, 12th June 2023. URL: https://inria.hal.science/hal-04012274.

Edition (books, proceedings, special issue of a journal)

[29] B. Battisti, T. Blickhan, G. Enchery, V. Ehrlacher, D. Lombardi and O. Mula, eds. Wasserstein model
reduction approach for parametrized flow problems in porous media. CEMRACS 2021 - Data Assim-
ilation and Reduced Modeling for High Dimensional Problems. Vol. 73. EDP Sciences, 30th Aug.
2023, pp. 28–47. DOI: 10.1051/proc/202373028. URL: https://hal.science/hal-04390131.

Doctoral dissertations and habilitation theses

[30] M. Agbalessi. ‘State estimation in fluid-structure interaction from 4D-flow MRI data’. Sorbonne

Université, 3rd Apr. 2023. URL: https://inria.hal.science/tel-04072648.

[31] M. Fuente Ruiz. ‘Adaptive tensor methods for high dimensional problems’. Sorbonne Université,

31st Mar. 2023. URL: https://theses.hal.science/tel-04082601.

Reports & preprints

[32] M. Boulakia, C. Grandmont, F. Lespagnol and P. Zunino. Numerical approximation of the Poisson
problem with small holes, using augmented finite elements and defective boundary conditions.
30th Jan. 2023. URL: https://inria.hal.science/hal-03501521.

[33] M. Boulakia, H. Liu and D. Lombardi. Parameter identification through gradient flow on latent

variables. 26th Dec. 2023. URL: https://inria.hal.science/hal-04364114.

[34] E. Burman, R. Durst, M. A. Fernández, J. Guzmán and O. Ruz. Robin-Robin loose coupling for
incompressible fluid-structure interaction: non-linear setting and nearly-optimal error analysis.
25th Oct. 2023. URL: https://inria.hal.science/hal-04258861.

[35] A. Canteaut, M. Serrano, C. Grandmont, G. Pallez, V. Perrier, X. Rival and E. Thomé. Bilan de la
mandature 2019-2023 de la Commission d’Évaluation Inria. Inria, 31st Aug. 2023. URL: https://i
nria.hal.science/hal-04193082.

[36] M. Champion, M. A. Fernández, C. Grandmont, F. Vergnet and M. Vidrascu. On the analysis of a
mechanically consistent model of fluid-structure-contact interaction. 4th Oct. 2023. URL: https:
//hal.science/hal-04229012.

[37] F. Lespagnol, C. Grandmont, P. Zunino and M. A. Fernández. A mixed-dimensional formulation
for the simulation of slender structures immersed in an incompressible flow. 1st Dec. 2023. URL:
https://inria.hal.science/hal-04318526.

[38] S. Riffaud. Accurate and robust predictions for model order reduction via an adaptive, hybrid
FOM/ROM approach. 22nd Dec. 2023. URL: https://inria.hal.science/hal-04361506.

Other scientific publications

[39]

S. C. Faya, M. Coolen, C. Wesley, M. Vidrascu, P.-J. Guns, M. A. Fernández and D. Lombardi. ‘An in
silico approach to monitor and predict haemodynamics during safety pharmacology studies’. In:
SPS Annual Meeting. Brussels, Belgium, 18th Sept. 2023. URL: https://hal.science/hal-0439
4917.

20

Inria Annual Report 2023

10.3 Cited publications

[40] F. Alauzet, B. Fabrèges, M. A. Fernández and M. Landajuela. ‘Nitsche-XFEM for the coupling of
an incompressible fluid with immersed thin-walled structures’. In: Comput. Methods Appl. Mech.
Engrg. 301 (2016), pp. 300–335.

[41] E. Alpaydin. Introduction to machine learning. MIT press, 2009.

[42] M. Astorino, J. Hamers, S. C. Shadden and J.-F. Gerbeau. ‘A robust and efficient valve model based
on resistive immersed surfaces’. In: Int. J. Numer. Meth. Biomed. Engng. 28.9 (2012), pp. 937–959.

[43] F. Baaijens. ‘A fictitious domain/mortar element method for fluid-structure interaction’. In: Int.

Jour. Num. Meth. Fluids 35 (2001), pp. 743–761.

[44] L. Baffico, C. Grandmont and B. Maury. ‘Multiscale modeling of the respiratory tract’. In: Math.

Models Methods Appl. Sci. 20.1 (2010), pp. 59–93.

[45] D. Boffi, N. Cavallini and L. Gastaldi. ‘Finite element approach to immersed boundary method with
different fluid and solid densities’. In: Math. Models Methods Appl. Sci. 21.12 (2011), pp. 2523–2550.

[46] L. Boudin, L. Desvillettes, C. Grandmont and A. Moussa. ‘Global existence of solutions for the
coupled Vlasov and Navier-Stokes equations’. In: Differential Integral Equations 22.11-12 (2009),
pp. 1247–1271.

[47] L. Boudin, D. Götz and B. Grec. ‘Diffusion models of multicomponent mixtures in the lung’. In:
CEMRACS 2009: Mathematical modelling in medicine. Vol. 30. ESAIM Proc. EDP Sci., Les Ulis, 2010,
pp. 90–103.

[48] L. Boudin, C. Grandmont and A. Moussa. ‘Global existence of solutions to the incompressible
Navier-Stokes-Vlasov equations in a time-dependent domain’. In: J. Differential Equations 262.3
(2017), pp. 1317–1340.

[49] L. Breiman. Classification and regression trees. Routledge, 2017.

[50] E. Burman and M. A. Fernández. ‘An unfitted Nitsche method for incompressible fluid-structure
interaction using overlapping meshes’. In: Comput. Methods Appl. Mech. Engrg. 279 (2014), pp. 497–
514.

[51] R. K. Calay, J. Kurujareon and A. E. Holdo. ‘Numerical simulation of respiratory flow patterns within

human lung’. In: Respir. Physiol. Neurobiol. 130.2 (2002), pp. 201–221.

[52] P. Cazeaux and C. Grandmont. ‘Homogenization of a multiscale viscoelastic model with non-
local damping, application to the human lungs’. In: Math. Models Methods Appl. Sci. 25.6 (2015),
pp. 1125–1177.

[53] K. B. Chandran. ‘Role of Computational Simulations in Heart Valve Dynamics and Design of Valvular

Prostheses’. In: Cardiovasc. Eng. Technol. 1.1 (2010), pp. 18–38.

[54] D. Chapelle and P. Moireau. ‘General coupling of porous flows and hyperelastic formulations—
From thermodynamics principles to energy balance and compatible time schemes’. In: Eur. J. Mech.
B Fluids. 46 (2014), pp. 82–96.

[55] C. Chnafa, S. Mendez and F. Nicoud. ‘Image-Based Simulations Show Important Flow Fluctuations
in a Normal Left Ventricle: What Could be the Implications?’ In: Ann. Biomed. Eng. 44.11 (2016),
pp. 3346–3358.

[56] T. Colatsky, B. Fermini, G. Gintant, J. B. Pierson, P. Sager, Y. Sekino, D. G. Strauss and N. Stockbridge.
‘The comprehensive in vitro proarrhythmia assay (CiPA) initiative—update on progress’. In: J.
Pharmacol. Toxicol. Methods 81 (2016), pp. 15–20.

[57] W. J. Crumb, J. Vicente, L. Johannesen and D. G. Strauss. ‘An evaluation of 30 clinical drugs against
the comprehensive in vitro proarrhythmia assay (CiPA) proposed ion channel panel’. In: J. Phar-
macol. Toxicol. Methods 81 (2016), pp. 251–262.

[58] M. Fedele, E. Faggiano, L. Dedè and A. Quarteroni. ‘A patient-specific aortic valve model based
on moving resistive immersed implicit surfaces’. In: Biomech. Model. Mechanobiol. 16.5 (2017),
pp. 1779–1803.

Project COMMEDIA

21

[59] M. A. Fernández and J. Mullaert. ‘Convergence and error analysis for a class of splitting schemes in

incompressible fluid-structure interaction’. In: IMA J. Numer. Anal. 36.4 (2016), pp. 1748–1782.

[60] H. Gao, L. Feng, N. Qi, C. Berry, B. Griffith and X. Luo. ‘A coupled mitral valve-left ventricle model

with fluid-structure interaction’. In: Med. Eng. Phys. 47 (Sept. 2017), pp. 128–136.

[61] R. Glowinski, T. Pan, T. Hesla and D. Joseph. ‘A distributed Lagrange mutiplier/fictitious domain

method for particulate flows’. In: Int. J. of Multiphase Flow 25 (1999), pp. 755–794.

[62] C. Grandmont and M. Hillairet. ‘Existence of global strong solutions to a beam-fluid interaction

system’. In: Arch. Ration. Mech. Anal. 220.3 (2016), pp. 1283–1333.

[63] L. Grasedyck, D. Kressner and C. Tobler. ‘A literature survey of low-rank tensor approximation

techniques’. In: GAMM-Mitt. 36.1 (2013), pp. 53–78.

[64] M. Hillairet. ‘Lack of collision between solid bodies in a 2D incompressible viscous flow’. In: Comm.

Partial Differential Equations 32.7-9 (2007), pp. 1345–1371.

[65] H. M. Himmel. ‘Drug-induced functional cardiotoxicity screening in stem cell-derived human and
mouse cardiomyocytes: effects of reference compounds’. In: J. Pharmacol. Toxicol. Methods 68.1
(2013), pp. 97–111.

[66]

J. Kaipio and E. Somersalo. Statistical and computational inverse problems. Vol. 160. Applied
Mathematical Sciences. Springer-Verlag, New York, 2005.

[67] D. Kamensky, M.-C. Hsu, Y. Yu, J. A. Evans, M. S. Sacks and T. J. R. Hughes. ‘Immersogeometric
cardiovascular fluid-structure interaction analysis with divergence-conforming B-splines’. In:
Comput. Methods Appl. Mech. Engrg. 314 (2017), pp. 408–472.

[68] M. J. van der Laan and S. Rose. Targeted learning. Springer Series in Statistics. Springer, New York,

2011.

[69] M. C. Lai and C. S. Peskin. ‘An immersed boundary method with formal second-order accuracy

and reduced numerical viscosity’. In: J. Comp. Phys. 160.2 (2000), pp. 705–719.

[70] R. van Loon, P. D. Anderson, J. de Hart and F. P. T. Baaijens. ‘A combined fictitious domain/adaptive
meshing method for fluid–structure interaction in heart valves’. In: International Journal for
Numerical Methods in Fluids 46.5 (2004), pp. 533–544.

[71] S. Martin and B. Maury. ‘Modeling of the oxygen transfer in the respiratory process’. In: ESAIM

Math. Model. Numer. Anal. 47.4 (2013), pp. 935–960.

[72] R. Mittal, J. H. Seo, V. Vedula, Y. J. Choi, H. Liu, H. H. Huang, S. Jain, L. Younes, T. Abraham and R. T.
George. ‘Computational modeling of cardiac hemodynamics: current status and future outlook’.
In: J. Comput. Phys. 305 (2016), pp. 1065–1082.

[73]

J. M. Oakes, S. C. Shadden, C. Grandmont and I. E. Vignon-Clementel. ‘Aerosol transport throughout
inspiration and expiration in the pulmonary airways’. In: Int. J. Numer. Methods Biomed. Eng. 33.9
(2017).

[74] C. S. Peskin. ‘The immersed boundary method’. In: Acta Numer. 11 (2002), pp. 479–517.

[75] C. J. Roth, M. Ismail, L. Yoshihara and W. A. Wall. ‘A comprehensive computational human lung
model incorporating inter-acinar dependencies: Application to spontaneous breathing and mech-
anical ventilation’. In: Int. J. Numer. Method. Biomed. Eng. 33.1 (2016). e02787.

[76] V. de Silva and L.-H. Lim. ‘Tensor rank and the ill-posedness of the best low-rank approximation

problem’. In: SIAM J. Matrix Anal. Appl. 30.3 (2008), pp. 1084–1127.

[77] L. Yoshihara, C. J. Roth and W. A. Wall. ‘Fluid-structure interaction including volumetric coupling
with homogenised subdomains for modeling respiratory mechanics’. In: Int. J. Numer. Method.
Biomed. Eng. 33.4 (2016). e2812.
<scratchpad>
- Main topic: Research Centre COMMEDIA
- Key points:
  - Focus on numerical simulation of bio-fluid flows in the human body
  - Research areas: cardiovascular hemodynamics, respiratory flows, and safety pharmacology
  - Methodological core includes mathematical analysis of PDEs, numerical methods for multi-physics problems, and tensor approximation
  - Application domains: cardiovascular diseases, respiratory diseases, and safety pharmacology
- Structure: The document is divided into sections, including Project-Team, Activity Report, Contents, Project COMMEDIA, and Dissemination
- Potential artifacts to ignore: Links, HTML tags, and unnecessary web-related elements
</scratchpad>

<final_summary>
The COMMEDIA research centre focuses on numerical simulation of bio-fluid flows in the human body, with a strong emphasis on cardiovascular hemodynamics, respiratory flows, and safety pharmacology. The centre's research activities involve the development of mathematical models, numerical methods, and tensor approximation techniques to simulate complex biological systems. The centre's work has applications in cardiovascular diseases, respiratory diseases, and safety pharmacology, and has led to the development of new software, platforms, and open data. The centre's research has been recognized through various awards and publications, and has contributed to the advancement of scientific knowledge in the field of biomedical engineering.
The COMMEDIA research centre focuses on numerical simulation of bio-fluid flows in the human body, with a strong emphasis on cardiovascular hemodynamics, respiratory flows, and safety pharmacology. The centre's research activities involve the development of mathematical models, numerical methods, and tensor approximation techniques to simulate complex biological systems. The centre's work has applications in cardiovascular diseases, respiratory diseases, and safety pharmacology, and has led to the development of new software, platforms, and open data. The centre's research has been recognized through various awards and publications, and has contributed to the advancement of scientific knowledge in the field of biomedical engineering.