CARMEN

CARMEN - 2025

2025Activity‌‌ reportProject-TeamCARMEN

RNSR: 201121001J

Research center Inria‌ Centre at the University‌ of Bordeaux
In partnership‌‌ with:Université de Bordeaux, Bordeaux INP
Team name:‌ Modélisation et calculs pour‌ l'électrophysiologie cardiaque
In collaboration‌‌ with:Institut de Mathématiques de Bordeaux (IMB)

Creation‌ of the Project-Team: 2016‌ June 01

Each year,‌‌ Inria research teams publish an Activity Report presenting‌ their work and results‌ over the reporting period.‌‌ These reports follow a common structure, with some‌ optional sections depending on‌ the specific team. They‌‌ typically begin by outlining the overall objectives and‌ research programme, including the‌ main research themes, goals,‌‌ and methodological approaches. They also describe the application‌ domains targeted by the‌ team, highlighting the scientific‌‌ or societal contexts in which their work is‌ situated.

The reports then‌ present the highlights of‌‌ the year, covering major scientific achievements, software developments,‌ or teaching contributions. When‌ relevant, they include sections‌‌ on software, platforms, and open data, detailing the‌ tools developed and how‌ they are shared. A‌‌ substantial part is dedicated to new results, where‌ scientific contributions are described‌ in detail, often with‌‌ subsections specifying participants and‌ associated keywords.

Finally, the Activity Report addresses funding,‌ contracts, partnerships, and collaborations at various levels, from‌ industrial agreements to international cooperations. It also covers‌ dissemination and teaching activities, such as participation in‌ scientific events, outreach, and supervision. The document concludes‌ with a presentation of scientific production, including major‌ publications and those produced during the year.

Keywords‌

Computer Science and Digital Science

A6.1.1. Continuous Modeling‌ (PDE, ODE)
A6.1.2. Stochastic Modeling
A6.1.4. Multiscale modeling‌
A6.2.1. Numerical analysis of PDE and ODE
A6.2.4.‌ Statistical methods
A6.2.6. Optimization
A6.2.7. HPC for machine‌ learning
A6.2.8. Computational geometry and meshes
A6.3.1. Inverse‌ problems
A6.3.3. Data processing
A6.3.5. Uncertainty Quantification
A6.5.‌ Mathematical modeling for physical sciences

1 Team members, visitors, external collaborators‌

Research Scientists

Jacques Henry [INRIA, Emeritus‌, HDR]
Peter Langfield [INRIA,‌ Researcher]
Michael Leguebe [INRIA, Researcher‌]
Nejib Zemzemi [INRIA, Researcher]‌

Faculty Members

Yves Coudière [Team leader,‌ UNIV BORDEAUX, Professor Delegation, HDR]‌
Mostafa Bendahmane [UNIV BORDEAUX, Associate Professor‌, HDR]
Julien Moatti [BORDEAUX INP‌, Associate Professor, from Feb 2025]‌
Mark Potse [UNIV BORDEAUX, Professor,‌ Permanent contract with the UNIV BORDEAUX, without teaching‌ duties, HDR]
Lisl Weynans [UNIV‌ BORDEAUX, Professor, HDR]

Post-Doctoral Fellows‌

Safaa Al Ali [UNIV BORDEAUX, Post-Doctoral‌ Fellow, from Sep 2025]
Suraj Baloda‌ [INRIA, Post-Doctoral Fellow]
Delphine Deshors‌ [UNIV BORDEAUX, Post-Doctoral Fellow, until‌ Jun 2025]
Joyce Ghantous [UNIV BORDEAUX‌, Post-Doctoral Fellow, from Sep 2025]‌

PhD Students

Simon Bihoreau [INRIA, Member‌ of MONC, co-supervized by M. Leguèbe]
Dylan‌ Chapotte [INRIA, from Oct 2025]‌
Zeina Chehade [UNIV BORDEAUX, until Mar‌ 2025]
Sylvain Fourcade [INRIA]
Nour‌ Hamad [INRIA, from Oct 2025]‌
Emma Lagracie [UNIV BORDEAUX, until Sep‌ 2025]

Technical Staff

Loïc Calvez [UNIV‌ BORDEAUX, Engineer]
Zeina Chehade [UNIV‌ BORDEAUX, Engineer, from May 2025 until‌ Jul 2025]
Gengis Lourenco [UNIV BORDEAUX‌, Engineer]
Gwladys Ravon [INRIA,‌ Engineer]

Interns and Apprentices

Heloise Dudoignon [‌UNIV BORDEAUX, Intern, from Feb 2025‌ until Aug 2025]
Mohamed Ilyes Hachmi [‌UNIV BORDEAUX, Intern, from May 2025‌ until Sep 2025]
Kelcy Limeri [UNIV‌ BORDEAUX, Intern, from Mar 2025 until‌ Jul 2025]

Administrative Assistants

Flavie Blondel [‌INRIA]
Anne-Laure Gautier [INRIA]

Visiting‌ Scientists

Narjess Ben Abid [ENIT TUNIS,‌ from Aug 2025 until Nov 2025]
Mohamed Jebalia [UNIV TUNIS‌, from Dec 2025‌]

External Collaborators

Emma‌‌ Lagracie [University of Magdeburg, from Oct‌ 2025]
Xavier Muller‌ [INRIA, Member‌‌ of the Tadaam team involved in the MICROCARD-2‌ project]

2 Overall‌ objectives

The Carmen team‌‌ develops and uses models and numerical methods to‌ simulate the electrophysiology of‌ the heart from the‌‌ molecular to the whole-organ scale, and its relation‌ to measurable signals inside‌ the heart and on‌‌ the body surface. It aims at:

improving understanding‌ of normal and pathological‌ cardiac electrophysiology,
improving the‌‌ efficiency and accuracy of numerical models,
exploiting all‌ available electrical signals for‌ diagnosis,
improving understanding and‌‌ guidance of ablative treatment of cardiac arrhythmia.

The‌ numerical models developed, analyzed,‌ and used by the‌‌ team incorporate essentially the gating dynamics of the‌ ion channels in the‌ cardiac cell membranes and‌‌ the heterogeneities of the cardiac tissue, coupling processes‌ on the cellular scale‌ into macroscopic reaction-diffusion models.‌‌ The team also works on incorporating new biological‌ knowledge, at any scale,‌ that helps to understand‌‌ the mechanisms of arrhythmias, their diagnosis or treatment.‌ At the same time‌ we use simpler or‌‌ reduced models to solve the inverse problems related‌ to non-invasive electrical imaging‌ of the heart.

The‌‌ fields involved in our research are: ordinary and‌ partial differential equations (ODE‌ & PDE), inverse problems,‌‌ numerical analysis, high-performance computing, image segmentation, and mesh‌ construction.

A main goal‌ of the team is‌‌ to contribute to the work packages defined in‌ the project of IHU‌ Liryc, an institute‌‌ founded in 2011 that focuses on cardiac arrhythmia.‌

We cooperate with physiologists‌ and cardiologists on several‌‌ projects. The team is building new models and‌ powerful simulation tools that‌ will help to understand‌‌ the mechanisms behind cardiac arrhythmias and to establish‌ personalized and optimized treatments.‌ A particular challenge consists‌‌ in making the simulations reliable and accessible to‌ the medical community.

3‌ Research program

3.1 Complex‌‌ models for the propagation of cardiac action potentials‌

The contraction of the‌ heart is coordinated by‌‌ a complex electrical activation process which relies on‌ about a million ion‌ channels, pumps, and exchangers‌‌ of various kinds in the membrane of each‌ cardiac cell. Their interaction‌ results in a periodic‌‌ change in transmembrane potential called an action potential.‌ Action potentials in the‌ cardiac muscle propagate rapidly‌‌ from cell to cell, synchronizing the contraction of‌ the entire muscle to‌ achieve an efficient pump‌‌ function. The spatio-temporal pattern of this propagation is‌ related both to the‌ function of the cellular‌‌ membrane and to the structural organization of the‌ cells into tissues. Cardiac‌ arrhythmias originate from malfunctions‌‌ in this process. The field of cardiac electrophysiology‌ studies the multiscale organization‌ of the cardiac activation‌‌ process from the subcellular scale up to the‌ scale of the body.‌ It relates the molecular‌‌ processes in the cell membranes to the propagation‌ process through the multiscale‌ structure of the tissue‌‌ and organ, to measurable‌ signals in the heart and to the electrocardiogram,‌ an electrical signal on the torso surface.

Several‌ improvements of current models of the propagation of‌ action potentials are being developed in the Carmen‌ team, based on previous work 35 and on‌ the data available at IHU Liryc:

Enrichment of‌ the current monodomain and bidomain models 35,‌ 45 by accounting for structural heterogeneities of the‌ tissue at cellular and intermediate scales. Here we‌ focus on multiscale analysis techniques applied to the‌ various high-resolution structural data available at IHU Liryc.‌
Coupling of the tissues from the different cardiac‌ compartments and conduction systems. Here, we develop models‌ that couple 1D, 2D and 3D phenomena described‌ by reaction- diffusion PDEs.

These models are essential‌ to improve our understanding of cardiac electrical dysfunction.‌ To this aim, we use high-performance computing techniques‌ in order to explore numerically the complexity of‌ these models.

We use these model codes for‌ applied studies in two important areas of cardiac‌ electrophysiology: atrial fibrillation 37 and sudden-cardiac-death (SCD) syndromes‌ 8, 740. This work is‌ performed in collaboration with several physiologists and clinicians‌ both at IHU Liryc and abroad.

3.2 Simplified‌ models and inverse problems

The medical and clinical‌ exploration of the cardiac electric signals is based‌ on accurate reconstruction of the patterns of propagation‌ of the action potential. The correct detection of‌ these complex patterns by non-invasive electrical imaging techniques‌ has to be developed. This involves solving inverse‌ problems that cannot be addressed with the more‌ complex models. We want both to develop simple‌ and fast models of the propagation of cardiac‌ action potentials and improve the solutions to the‌ reconstruction questions of cardiac electrical imaging techniques.

These‌ questions concern the reconstruction of diverse information, such‌ as cardiac activation maps or, more generally, the‌ whole cardiac electrical activity, from high-density body surface‌ electrocardiograms. It is a potentially powerful diagnosis technique,‌ which success would be considered as a breakthrough.‌ Although widely studied during the last decade, the‌ reconstructed activation maps, for instance, are highly inaccurate‌ and have a poor clinical interest. It remains‌ a challenge for the scientific community to understand‌ how body surface signals can better inform on‌ the fine details of arrhythmic mechanisms.

The most‌ usual method consists in solving a Laplace equation‌ on the volume delimited by the body surface‌ and the epicardial surface, for which we contribute‌ by:

studying in depth the dependence of the‌ inverse problem on inhomogeneities in the torso, conductivity‌ values, the geometry, electrode positions, etc., and
improving‌ the solution to the inverse problem by using‌ new regularization strategies, factorization of boundary value problems,‌ and the theory of optimal control.

In addition,‌ we have started to explore many alternative approaches‌ including:

using complete propagation models in the inverse‌ problem, like the bidomain or monodomain equations, for‌ instance in order to localize electrical sources,
constructing‌ data-based models using e.g. statistical learning techniques, which would accurately represent some‌ families of well-identified pathologies,‌ or allow to combine‌‌ physics and biology-informed models and clinical data, and‌
constructing simpler models of‌ the propagation of the‌‌ activation front, based on eikonal or level-set equations.‌

3.3 Numerical techniques

We‌ want our numerical simulations‌‌ to be efficient, accurate, and reliable with respect‌ to the needs of‌ the medical community. Based‌‌ on previous work on solving the monodomain and‌ bidomain equations 5,‌ 4, 9,‌‌ 1, we will focus on:

high-order numerical‌ techniques with respect to‌ the variables with physiological‌‌ meaning, like velocity, AP duration and restitution properties‌ and
efficient, dedicated preconditioning‌ techniques coupled with parallel‌‌ computing.

Existing simulation tools used in our team‌ rely, among others, on‌ mixtures of explicit and‌‌ implicit integration methods for ODEs, hybrid MPI-OpenMP parallelization,‌ algebraic multigrid preconditioning, and‌ Krylov solvers. New developments‌‌ include high-order explicit integration methods and task-based dynamic‌ parallelism.

3.4 Cardiac electrophysiology‌ at the microscopic scale‌‌

Traditional numerical models of whole-heart physiology are based‌ on the approximation of‌ a perfect muscle using‌‌ homogenisation methods. However, due to aging and cardiomyopathies,‌ the cellular structure of‌ the tissue changes. These‌‌ modifications can give rise to life-threatening arrhythmias, the‌ mechanisms of which we‌ are investigating in collaboration‌‌ with cardiologists at the IHU Liryc. For this‌ research we are building‌ models that describe the‌‌ strong heterogeneity of the tissue at the cellular‌ level.

The literature on‌ this type of model‌‌ is still very limited 51. Existing models‌ are two-dimensional 41 or‌ limited to idealized geometries,‌‌ and use a linear (purely resistive) behaviour of‌ the gap-junction channels that‌ connect the cells. We‌‌ propose a three-dimensional approach using realistic cellular geometry‌ (Fig. 1), nonlinear‌ gap-junction behaviour, and a‌‌ numerical approach that can scale to hundreds of‌ cells while maintaining a‌ sub-micrometer spatial resolution (10‌‌ to 100 times smaller than the size of‌ a cardiomyocyte). Following preliminary‌ work in this area‌‌ by us 30, 29, 28 and‌ by others 51 we‌ proposed a European project‌‌ with 10 partner institutes and a 5.8M€ budget‌ to develop software that‌ can simulate such models,‌‌ with micrometer resolution, on the scale of millions‌ of cells, using future‌ exascale supercomputers (microcard.eu‌‌). This project ran from April 2021 to‌ October 2024, and involves‌ also the Inria teams‌‌ CAMUS, STORM and CARDAMOM as well as the‌ Inria-led MMG Consortium.

Figure 1: A: The cardiac muscle consists‌ of a branching network‌ of elongated muscle cells,‌‌ interspersed with other structures. Sheets of connective tissue‌ (blue) can grow between‌ the muscle cells and‌‌ become pathogenic. B: Current models can only represent‌ such alterations in a‌ coarse way by replacing‌‌ model elements with different types; each cube in‌ this illustration would represent‌ hundreds of cells. C:‌‌ This example from the‌ MICROCARD project 44 illustrates the type of geometric‌ model we are experimenting with. It represents $500‌ \times 400 \times 100$ µm of tissue (corresponding‌ to $5 \times 4$ blocks in panel B)‌ and contains 1600 cells, identified with different colours.‌ Each cell is here represented by hundreds of‌ elements.

The cell-by-cell bidomain model presents numerous mathematical‌ and computational challenges. First, mathematically, its unusual formulation‌ providing time dynamics as an ordinary differential equation‌ (ODE) at the cell- to-cell connections and cell-to-extracellular‌ matrix interfaces. Second, the ionic model coupled to‌ the nonstandard transmission conditions, introduce stiff non linear‌ dynamics. Third, the simulation would be performed for‌ billions of myocytes, leading to extremely large systems.‌ In the MICROCARD project, we simulate the micromodel‌ using finite volumes, finite elements and boundary element‌ methods. In November 2024 the project was succeeded‌ by the Centre of Excellence MICROCARD-2, in which‌ the Inria teams CARMEN, STORM, CAMUS and TADAAM‌ are involved.

3.5 Models and tools for ablative‌ therapies

Today, the most effective way to treat‌ arrhythmias is to ablate selected regions of the‌ cardiac tissue. The lesions are assumed electrically passive,‌ and consequently create conduction blocks that stop the‌ disorganized propagation of action potentials. The ablation procedure‌ consists in placing a catheter in contact with‌ the targeted site and deliver energy into the‌ tissue. The energy can be overheating by radio-frequency‌ current, electroporating electric pulses or temperature drop (cryotherapy).‌ In practice, the choice of the ablation site‌ is done by the clinician based on previous‌ signal measurements and imagery, and is also guided‌ during the procedure with real-time measurement of the‌ electric signal.

Our team works on several subjects‌ related to ablation techniques that may improve the‌ success rate of the treatments:

accurate computation of‌ electric fields generated by catheters: complex catheter shapes,‌ contact models, tissue heterogeneities;
models of creation of‌ the lesions, either through temperature rise (radio-frequency) or‌ electroporation; and
localization tools to help clinicians target‌ the optimal ablation sites, based on both data‌ of previously ablated patients and synthetic data.

4‌ Application domains

4.1 Scientific context: IHU Liryc

The‌ University Hospital of Bordeaux (CHU de Bordeaux‌) is equipped with a specialized cardiology hospital,‌ the Hôpital Cardiologique du Haut-Lévêque, where the‌ group of Professor Michel Haïssaguerre has established itself‌ as a global leader in the field of‌ cardiac electrophysiology 39, 38, 33.‌ Their discoveries in the area of atrial fibrillation‌ and sudden cardiac death syndromes are widely acclaimed,‌ and the group is a national and international‌ referral centre for treatment of cardiac arrhythmia. Thus‌ the group also sees large numbers of patients‌ with rare cardiac diseases.

In 2011 the group‌ was awarded a 40 million euro Investissements d'Avenir‌ grant for the establishment of IHU Liryc,‌ an institute that combines clinical, experimental, and numerical‌ research in the area of cardiac arrhythmia. The‌ institute works in all areas of modern cardiac electrophysiology: atrial arrhythmias, sudden‌ death due to ventricular‌ fibrillation, heart failure related‌‌ to ventricular dyssynchrony, and metabolic disorders. It is‌ recognized worldwide as one‌ of the most important‌‌ centres in this area.

The Carmen team was‌ founded as a part‌ of IHU Liryc. We‌‌ bring applied mathematics and scientific computing closer to‌ experimental and clinical cardiac‌ electrophysiology. In collaboration with‌‌ experimental and clinical researchers at Liryc we work‌ to enhance fundamental knowledge‌ of the normal and‌‌ abnormal cardiac electrical activity and of the patterns‌ of the electrocardiogram, and‌ we develop new simulation‌‌ tools for training, biological, and clinical applications.

4.2‌ Basic experimental electrophysiology

Our‌ modeling is carried out‌‌ in coordination with the experimental teams from IHU‌ Liryc. It helps to‌ write new concepts concerning‌‌ the multiscale organisation of the cardiac action potentials‌ that will serve our‌ understanding in many electrical‌‌ pathologies. For example, we model the structural heterogeneities‌ at the cellular scale‌ 31 (the MICROCARD‌‌ project), and at an intermediate scale between‌ the cellular and tissue‌ scales.

At the atrial‌‌ level, we apply our models to understand the‌ mechanisms of complex arrhythmias‌ and the relation with‌‌ the heterogeneities at the insertion of the pulmonary‌ veins. We will model‌ the heterogeneities specific to‌‌ the atria, like fibrosis or fatty infiltration 47‌, 37. These‌ heterogeneities are thought to‌‌ play a major role in the development of‌ atrial fibrillation.

At the‌ ventricular level, we focus‌‌ on (1) modeling the complex coupling between the‌ Purkinje network and the‌ ventricles, which is supposed‌‌ to play a major role in sudden cardiac‌ death, and (2) modeling‌ the heteogeneities related to‌‌ the complex organization and disorganization of the myocytes‌ and fibroblasts, which is‌ important in the study‌‌ of infarct scars for instance.

4.3 Clinical electrophysiology‌

Treatment of cardiac arrhythmia‌ is possible by pharmacological‌‌ means, by implantation of pacemakers and defibrillators, and‌ by curative ablation of‌ diseased tissue by local‌‌ heating, freezing or electroporation. In particular the ablative‌ therapies create challenges that‌ can be addressed by‌‌ numerical means. Cardiologists would like to know, preferably‌ by noninvasive means, where‌ an arrhythmia originates and‌‌ by what mechanism it is sustained.

We address‌ this issue in the‌ first place using inverse‌‌ models, which attempt to estimate the cardiac activity‌ from a (high-density) electrocardiogram.‌ A new project aims‌‌ to perform this estimation on-site in the catheterization‌ laboratory and presenting the‌ results, together with the‌‌ cardiac anatomy, on the screen that the cardiologist‌ uses to monitor the‌ catheter positions 42,‌‌ 27.

4.4 Application in Deep Brain Stimulation‌

Since 2017, we have‌ been working with neurosurgeons‌‌ from the Bordeaux University Hospital (Pr Cuny and‌ Dr. Engelhardt) on improving‌ the planning technique for‌‌ deep brain surgery (DBS) for Parkinson's and Essential‌ tremor diseases. DBS is‌ the last resort to‌‌ treat the symptoms of Parkinson's disease after the‌ drug Levodopa. The surgery‌ consists in placing electrodes‌‌ in very specific regions‌ of the patient's brain. These regions are unfortunately‌ not visible on the 1.5 Tesla MRI, the‌ most widely available MRI machines in hospitals. The‌ most effective solution to date is to introduce‌ 5 micro-electrodes (MER) to record the activity of‌ neurons in the patient's brain and to prospect‌ by moving the electrodes in order to find‌ the best location. However, this approach renders the‌ surgery very cumbersome because the patient must be‌ awake during the exploration phase. In addition, this‌ phase takes at least 3 hours and mobilizes‌ a neurologist with his staff. The total duration‌ of the operation is between 7 and 8‌ hours. Many elderly patients do not tolerate this‌ surgery. We have proposed an approach that avoids‌ the prospecting phase and performs surgery under general‌ anesthesia. The idea is to learn on pairs‌ of clinical landmarks and the position of active‌ electrodes in order to predict the optimal position‌ of the DBS from a pre-operative image. This‌ approach simplifies and standardizes surgery planning. We tested‌ several approaches, 6. We continue to seek‌ approaches to fully automate the targeting process. We‌ carried out a proof of concept by learning‌ on the clinical database of the Bordeaux University‌ Hospital. The clinical validation of our approach is‌ in progress through a clinical trial which includes‌ patients from the University Hospitals of Bordeaux and‌ Lyon. Pr Cuny has submitted a phase 3‌ national clinical research hospital project (PHRCN) including 11‌ CHUs in France which has been accepted by‌ the General Directorate for Care Offers (DGOS). The‌ aim is to compare our new approach to‌ the ones used in the other centres. Inria‌ Bordeaux is a partner in this project and‌ we maintain the OptimDBS software and solve any‌ technical problem related to the compatibility of the‌ MRIs exported by our software and the surgical‌ robots in the different centres.

5 Social and‌ environmental responsibility

5.1 Footprint of research activities

We‌ avoid flying whenever we can, and try to‌ keep computers for 7 years, despite the fact‌ that they are not supported by the DSI‌ that long.

In 2025, we choose not to‌ submit any article to the Computing in Cardiology‌ annual conference, because it was organized in Sao‌ Paolo (Brazil), and only one person traveled to‌ the bi-annual conference on Functional Imaging and Modeling‌ of the Heart (Dallas, US), presenting the contributions‌ of 2 PhD theses. Although major events in‌ our domain, these conferences take place in Europe‌ regularly.

Lisl Weynans is involved in the creation‌ of courses about environmental and social transition at‌ Bordeaux University.

5.2 Impact of research results

The‌ MICROCARD project and its successor MICROCARD-2, which we‌ coordinate, has energy efficiency as one of its‌ goals. To this end, our partners in the‌ STORM and CAMUS teams are developing methods to‌ increase the time- and energy-efficiency of cardiac simulation‌ codes.

6 Highlights of the year

Niami Nasr, former PhD student in‌ Carmen, obtained a permanent‌ position as Assistant Professor‌‌ at Rouen University.

We officially welcomed Julien Moatti‌ as a new permanent‌ member of the Carmen‌‌ team.

7 Latest software developments, platforms, open data‌

7.1 CEPS updates

This‌ year, CEPS has been‌‌ made available on the open-software platform Codeberg,‌ along with the publication‌ of a release paper‌‌ in the Journal of Open Source Software 16‌. This is a‌ major step for this‌‌ software since there was no document to refer‌ to when the team‌ used CEPS for its‌‌ research. An effort has been made to make‌ CEPS more user-friendly, with‌ a strong push to‌‌ the user guide, and providing a Docker‌ container in which people‌ can directly run CEPS‌‌ simulations, and evaluate its performance.

This has been‌ the opportunity to publish‌ a version of CEPS‌‌ which has been significantly optimized, thanks to the‌ work of Loïc Calvez‌ and Michael Leguèbe .‌‌ We encourage the readers of this report to‌ check the changelog for‌ more details on new‌‌ features.

7.2 cardiolib updates

The remodeling of cardiolib‌ has been completed and‌ the package is available‌‌ for all team members. The 3 standard models‌ are implemented, as well‌ as models developed in‌‌ the team.

Discussion have been initiated with Bordeaux‌ University to choose a‌ license in order to‌‌ release a first public version in 2026.

7.3‌ MICROCARD-2 updates

The HPC‌ cell-by-cell cardiac electrophysiology simulator‌‌ based on the openCARP code has become functional‌ and we have been‌ able to visualize simulated‌‌ cardiac activation at the cellular level. The code‌ is now being tested‌ on European-scale supercomputers. In‌‌ the context of this project the Carmen team‌ has also developed mesh‌ creation and parallel remeshing‌‌ code which now allows us to create synthetic‌ meshes of multiple cubic‌ millimetres of cardiac tissue,‌‌ representing many thousands of cells using nearly a‌ billion tetrahedra; for an‌ example, see the figure‌‌ below. Our previous improvements in the mmg3d code‌ (mmgtools.org), culminating in release‌ 5.8.0, have been crucial‌‌ for this.

Figure 2‌‌: An example of a mesh created using‌ the latest mesh-creation developments‌ in MICROCARD-2, representing a‌‌ tissue formed by a set of highly-detailed cells‌ with numerous internal boundaries.‌

7.4 Latest software developments‌‌

7.4.1 CEPS

Name:
Cardiac ElectroPhysiology Simulation
Keywords:
Simulation,‌ Health, Mesh, Cardiac, 3D,‌ Cardiac Electrophysiology
Scientific Description:‌‌
As compared to other existing softwares, CEPS aims‌ at providing a more‌ general framework of integration‌‌ for new methods or models of cardiac electrophysiology‌ and a better efficiency‌ in parallel. CEPS is‌‌ designed to run on massively parallel architectures, and‌ to make use of‌ state-of-the-art and well known‌‌ computing libraries to achieve realistic and complex heart‌ simulations. CEPS also includes‌ software engineering and validation‌‌ tools.
Functional Description:
CEPS‌ is a modular high-performance computing software for performing‌ numerical simulations in cardiac electrophysiology. It is based‌ on modules : - management of geometries represented‌ by meshes in 3D, 2D or 1D (volumes,‌ surfaces, trees), - model simulation of cellular electrophysiology,‌ - calculating the tissue propagation of the action‌ potentials in the cardiac geometries, - calculation of‌ extracardiac potentials, - time approximation methods in order‌ 2, 3 and 4 specific to electrocardiography.
URL:‌
https://carmen.gitlabpages.inria.fr/ceps/
Publication:
hal-05313674
Contact:
Ceps Dev Team
Participants:‌
Loïc Calvez, Yves Coudière, Michael Leguebe, Valentin Pannetier,‌ Pierre-Elliott Bécue, Andjela Davidovic, Charlie Douanla Lontsi, Mehdi‌ Juhoor, Nejib Zemzemi, 3 anonymous participants
Partners:
Université‌ de Bordeaux, Fondation Bordeaux Université, CHU de Bordeaux,‌ Inria

7.4.2 cardiolib

Keywords:
Cardiac Electrophysiology, Python
Functional‌ Description:
Python packages used to build and solve‌ various numerical models in cardiac electrophysiology.
Contact:
Yves‌ Coudière
Participants:
Lisl Weynans, Zeina Chehade, Emma Lagracie,‌ Valentin Pannetier, Yves Coudière, Gwladys Ravon

7.5 New‌ platforms

Participants: Mark Potse, Yves Coudière,‌ Gengis Lourenco, Xavier Muller.

OpenCARP

OpenCARP‌ is an open cardiac electrophysiology simulator for in-silico‌ experiments. Its source code is public and the‌ software is freely available for academic purposes. OpenCARP‌ is easy to use and offers single cell‌ as well as multiscale simulations from ion channel‌ to organ level. Additionally, openCARP includes a wide‌ variety of functions for pre- and post-processing of‌ data as well as visualization. The python-based CARPutils‌ framework enables the user to develop and share‌ simulation pipelines, i.e. automating in-silico experiments including all‌ modeling/simulation steps.

KIT and the company Numericor, the‌ main creators of openCARP, with the University of‌ Graz, are partners of the MICROCARD project. The‌ openCARP simulator is developed within the MICROCARD project‌ targeting the creation of a microscopic cardiac model.‌

We have been contributing by managing the MICROCARD-2‌ consortium and its contributions to openCARP, and by‌ adapting the partitioning scheme (based on parMETIS) to‌ the context of the microscopic model.

Mmg

Participants:‌ Mark Potse, Yves Coudière, Gengis Lourenco‌, Xavier Muller.

Mmg is an open‌ source software suite for simplicial remeshing and an‌ open source Consortium, which participates in the MICROCARD‌ project.

For the purposes of the MICROCARD project,‌ Mark Potse uses Mmg3d for the challenging task‌ of creating artificial models of cardiac muscle fibers‌ (Figure 1C).

In the MICROCARD project, tetrahedral‌ meshes are created using both segmented data and‌ synthetic models. Several improvements made this year in‌ mmg now allow us to 1) use these‌ segmented data to create valid meshes with much‌ fewer elements than in the initial data, 2)‌ improve the synthetic generation of cardiac tissue. Gengis‌ Lourenco , hired to work on the MICROCARD‌ project, has been working on postprocessing tools related‌ to these meshing activities, notably the ability to‌ construct images of cut planes of the 3D‌ domain for better visualisation.

CEMPACK

CEMPACK is a‌ collection of software that was previously archived in different places. It includes‌ the high-performance simulation code‌ Propag and a suite‌‌ of software to create geometric models, prepare inputs‌ for Propag, and analyse‌ its outputs. In 2017‌‌ the code was collected in an archive on‌ Inria's GitLab platform. The‌ main components of CEMPACK‌‌ are the following.

Propag-5.1
Applied modeling studies performed‌ by the Carmen team‌ in collaboration with IHU‌‌ Liryc and foreign partners 848, 37‌, 36, 34‌ rely on high-performance computations‌‌ on the national supercomputers Irene, Zay, and Adastra.‌ The Propag-5 code is‌ optimized for these systems.‌‌ It is the result of a decades-long development‌ first at the Université‌ de Montréal in Canada,‌‌ then at Maastricht University in the Netherlands, and‌ finally at the Institute‌ of Computational Science of‌‌ the Università della Svizzera italiana in Lugano, Switzerland.‌ Since 2016 most of‌ the development on Propag‌‌ has been done by M. Potse at the‌ Carmen team 50.‌ The code scales excellently‌‌ to large core counts 49 and, as it‌ is controlled completely with‌ command-line flags and configuration‌‌ files, it can be used by non-programmers. It‌ also features:
- a plugin‌ system for membrane models,‌‌
- a completely parallel workflow, including the initial anatomy‌ input and mesh partitioning,‌ which allows it to‌‌ work with meshes of more than $10^{9‌}$ nodes,
- a flexible output‌ scheme allowing hundreds of‌‌ different state variables and transient variables to be‌ output to file, when‌ desired, using any spatial‌‌ and temporal subsampling,
- a configurable, LUSTRE-aware parallel output‌ system in which groups‌ of processes write HDF5/netCDF‌‌ files, and
- CWEB documentation of the entire code‌ base.
The code has‌ been stable and reliable‌‌ for many years. It can be considered the‌ workhorse for our HPC‌ work until CEPS takes‌‌ over.
Gepetto
The Gepetto suite transforms a surface‌ mesh of the heart‌ into a set of‌‌ (semi-)structured meshes for use by the Propag software‌ or others. It creates‌ the different fiber orientations‌‌ in the model, including the transmurally rotating ventricular‌ fibers and the various‌ bundle structures in the‌‌ atria (figure 3), and creates layers with‌ possibly different electrophysiological properties‌ across the wall. A‌‌ practically important function is that it automatically builds‌ the matching heart and‌ torso meshes that Propag‌‌ uses to simulate potentials in the torso (at‌ a resolution of 1‌ mm) after projecting simulation‌‌ results from the heart model (at 0.1 to‌ 0.2 mm) on the‌ coarser torso mesh 46‌‌. Like Propag, the Gepetto software results from‌ a long-term development that‌ started in Montreal, Canada,‌‌ around 2002. The code for atrial fiber structure‌ was developed by our‌ team.
Blender plugins
Blender‌‌ is a free software package for the production‌ of 3-D models, renderings,‌ and animations, comparable to‌‌ commercial software such as Cinema4D. CEMPACK includes a‌ set of plugins for‌ Blender that facilitate the‌‌ production of anatomical models and the visualization of‌ measured and simulated data.‌ It uses the MMG‌‌ remeshing library, which is‌ developed by the CARDAMOM team at Inria Bordeaux.‌ Currently our segmentation work is mostly done with‌ the MUSICardio software, but we still use Blender‌ for finishing touches and high-quality visualization.

Figure 3.a — Figure 3: A and B:‌ Complete heart-torso geometries created with CEMPACK tools. C:‌ Bundle structures and different layers of fiber orientation‌ created by the Gepetto software and visualized using‌ Blender.

Figure 3.b — Figure 3: A and B:‌ Complete heart-torso geometries created with CEMPACK tools. C:‌ Bundle structures and different layers of fiber orientation‌ created by the Gepetto software and visualized using‌ Blender.

8 New results

Participants: Mostafa Bendahmane,‌ Yves Coudière, Jacques Henry, Peter Langfield‌, Michael Leguèbe, Julien Moatti, Mark‌ Potse, Lisl Weynans, Nejib Zemzemi.‌

8.1 Analysis of partial differential equations

In 23‌Julien Moattiet al. consider a stationary drift-diffusion‌ system with external generation of electron and hole‌ charge carriers, arising in the context of semiconductor‌ modeling for perovskite solar cells. Using iterative energy‌ estimates combined with truncation techniques, they show the‌ existence and uniform upper and lower bounds on‌ the solutions. The dependency of the bounds on‌ the various parameters of the model is then‌ investigated numerically.
Nonlocal Fractional Bidomain Model The bidomain‌ model is a fundamental mathematical description of cardiac‌ electrical activity, formulated as a system of coupled‌ partial differential equations for the intra- and extracellular‌ potentials. To account for tissue heterogeneity and long-range‌ electrical interactions, nonlocal and fractional extensions of the‌ bidomain model have been proposed. These models involve‌ fractional diffusion operators that better reflect anomalous conduction‌ phenomena. Under suitable assumptions on the fractional conductivities‌ and nonlinear ionic current terms, the existence of‌ weak solutions are established using variational formulations, compactness‌ methods, and monotone operator theory. This theoretical result,‌ obtained by Mostafa Bendahmane and collaborators, ensures the‌ mathematical well-posedness of the nonlocal bidomain model and‌ provides a solid basis for numerical simulations and‌ applications in electrcardiology.

8.2 Numerical analysis and development‌ of numerical methods

Phase resetting surfaces In collaboration‌ with Profs Hinke Osinga and Bernd Krauskopf (University‌ of Auckland), Peter Langfield further developed their novel‌ numerical-continuation approach for analysing phase shifts of higher-dimensional‌ oscillators, leading to phase resetting surfaces. The isochrons‌ that form such surfaces were shown to have‌ a specific geometrical arrangement. The mechanism underlying this‌ arrangement was further investigated, where critical level sets‌ were discovered that give rise to such arrangements.‌ Geometrical argumentation was used to show that these‌ critical sets were shown to be a geometrical‌ necessity 15.
In collaboration with David Lannes‌ (IMB, Bordeaux) and Geoffrey Beck (Inria Rennes), Lisl‌ Weynans proposed a new extended formulation and a‌ new second-order numerical scheme to simulate waves interacting‌ with partially immersed objects allowed to move freely‌ in the vertical direction, and in a regime‌ in which the propagation of the waves is‌ described by the one dimensional Boussinesq-Abbott system 12.
Very high order‌ three-dimensional finite volume methods‌ In collaboration with R.‌‌ Turpault and K. Khadra, Yves Coudière has been‌ running numerous tests using‌ the regional computing resources‌‌ MCIA. This on-going work aims at improving‌ cardiac solvers' accuracy, with‌ methods that scale efficiently‌‌ in parallel.
Zeina Chehade defended her PhD thesis‌ (part of the MICROCARD‌ project), including a new,‌‌ unpublished work on the development of a hybrid‌ finite volume method (inspired‌ by the SUSHI scheme)‌‌ for the EMI model of cardiac electrophysiology 21‌. The scheme could‌ be used on polytopal‌‌ meshes with very little geometrical assumptions.
It was‌ published a journal paper‌ that aims at referencing‌‌ the CEPS software code, in the Journal of‌ Open Source Software 16‌

8.3 Modeling and inverse‌‌ problems

Simon Bihoreau , with Michael Leguèbe ,‌ Annabelle Collin from Univ.‌ Nantes and Clair Poignard‌‌ from Inria Rennes, has submitted 24 his theoretical‌ work on the model‌ for cardiac electroporation which‌‌ was proposed in 2024 in the Dielectric project‌ : existence of solution,‌ theoretical and numerical proof‌‌ of convergence towards a homogeneized problem. Numerical results‌ illustrate the importance of‌ information at the cellular‌‌ scale in order to compute accurately lesion shapes.‌
Pacemaker modeling. In‌ the context of the‌‌ SimCardioTest H2020 project, Michael Leguèbe and Yves Coudière‌ used 3D and 0D‌ models of cardiac stimulation‌‌ by a pacemaker to compute Lapicque curves, and‌ compare them to experimental‌ curves, which are in‌‌ a quite good agreement for a non-calibrated model.‌ Experiments were conducted at‌ IHU Liryc. Yves Coudière‌‌ presented these results at FIMH 2025 19.‌

The plots show that‌ computed stimulation threshold fall‌‌ within the experimental range of thresholds, across multiple‌ tested sheep.

Figure 4‌: Comparison between experimental‌‌ and simulated stimulation threshold curves as part of‌ pacemaker modeling in the‌ SimCardioTest project.
Modeling the‌‌ noise in EIT measurements During the first year‌ of PhD of Sylvain‌ Fourcade , in collaboration‌‌ with Bénédicte Puig (LMAP, Pau) and under the‌ supervision of Lisl Weynans‌ , we validated a‌‌ new formalism to study the inverse problem of‌ EIT, based on the‌ complete electrode model for‌‌ EIT and the use of a Kohn-Vogelius functional‌ to minimize. The next‌ step is to associate‌‌ to this model the use of noise models‌ to account for multiple‌ measurements on the electrodes‌‌
In the context of the end of PhD‌ of Emma Lagracie ,‌ supervized by Yves Coudière‌‌ and Lisl Weynans , a TV regularization was‌ developed for the formerly‌ developed epicardial model. This‌‌ regularization improved significantly the reconstructions compared to the‌ classical Thikhonov L2 regularization‌ 22. The Epicardial‌‌ model was also used to evaluate the effects‌ of inserting a priori‌ information on electrical conductivities‌‌ in surface ECGi. The results of this study‌ were presented at the‌ FIMH conference in Dallas‌‌ 18.
In collaboration with L. de Montella‌ (Astral team), Emma Lagracie‌ proposed a low-dimensional representation‌‌ of the activation sequence‌ that enables the use of particle filtering, a‌ Bayesian filtering method that does not rely on‌ predefined assumptions regarding the shape of the posterior‌ distribution, in contrast to approaches like the Kalman‌ filter 26. This allows to produce not‌ only activation maps but also probabilistic maps indicating‌ the likelihood of activation at each point on‌ the heart over time, as well as pseudo-probability‌ maps reflecting the likelihood of a point being‌ part of an earliest activation site.
Joyce Ghantous‌ , with Yves Coudière and Michael Leguèbe ,‌ is developing a mechanics-based framework to map optical‌ mapping data onto MRI images of cardiac tissues.‌ This approach is formulated as an energy minimization‌ problem. It captures the large deformation between the‌ MRI resting configuration and the stretched/flattened optical mapping‌ setup. It relies on a nonlinear, anisotropic, quasi-incompressible‌ hyperelastic model (Holzapfel-Ogden type).
Safaa Al-Ali is working‌ with Yves Coudière , Michael Leguèbe , and‌ Gaël Poette on Sensitivity analysis and calibration of‌ an electrophysiological cardiac model. The first objective‌ is to calibrate a cardiac electrophysiology model using‌ experimental data obtained during the PhD thesis of‌ Valentin Pannetier . In particular, the focus is‌ on the calibration of Lapicque curves, which characterize‌ the stimulation threshold of cardiac tissue under pacing,‌ through Bayesian inference approaches. The second objective is‌ to perform a comprehensive sensitivity analysis of the‌ electrophysiological model in order to identify the most‌ influential parameters governing cardiac activation in the context‌ of pacemaker stimulation. To this end, both classical‌ global sensitivity analysis methods, such as Sobol, and‌ causal discovery approaches will be employed.
Radiofrequency Ablation‌ (RFA) in Electrophysiology Radiofrequency ablation (RFA) is a‌ widely used interventional therapy in cardiac electrophysiology for‌ the treatment of arrhythmias. Mostafa Bendahmane and collaborators‌ have developed and analyzed mathematical models describing the‌ electrical and thermal effects of RFA within cardiac‌ tissue, with a particular focus on the interaction‌ between ablation-induced lesions and electrical propagation. Using continuum‌ models of cardiac electrophysiology, they investigated how tissue‌ heterogeneities and conductivity changes induced by thermal damage‌ affect wave propagation and ablation efficacy. These studies‌ contribute to a better quantitative understanding of RFA‌ mechanisms and provide a reliable modeling framework for‌ the simulation and optimization of ablation procedures 32‌, 43.
In the SPIMCY project, Nejib‌ Zemzemi and collaborators studied in great details the‌ question of the Carleman estimate constants dependency on‌ the size of the observation boundary. This allows‌ to quantify the effect of measurements uncertainty with‌ respect to the size of the observation boundary‌ in many inverse and control problems. We take‌ an example of the inverse source problem for‌ a parabolic equation and explicitly calculate Lipschitz stability‌ constants that appears in the $L^{2}$ estimate‌ of the source function. We deliberately construct a‌ class of space dependent weight functions that depend‌ on the measurement boundary size. Then we identify‌ the optimal weight function that allows to minimize the stability constant. Using‌ our approach, we found‌ that when the measurement‌‌ boundary covers 80 % or more of the‌ domain boundary, we can‌ explicitly provide the formula‌‌ of the optimal constant. When the measurement boundary‌ is less than 80‌ %, we are not‌‌ able to find the explicit formula of the‌ optimal expression, but we‌ are able to numerically‌‌ approximate the optimal constant. It requires meticulous calculations‌ 11.
As part‌ of the ECOS Nord‌‌ collaboration with Prof. A. Fraguela in Puebla (Mexico),‌ Jacques Henry obtained new‌ results on the regularization‌‌ of the Cauchy problem (which can be considered‌ to solve the ECGi‌ problem), by considering the‌‌ factorized version of the direct problem which yields‌ an ill posed equation‌ for the inverse problem.‌‌ They proposed four regularizations that they analyze using‌ the Morozov principle 25‌.

8.4 Clinical applications‌‌

As part of the ATLAS-RVA project, led‌ by Peter Langfield ,‌ the left ventricle endocardium‌‌ contact-mapping datasets of a cohort of twenty patients‌ has been processed for‌ comparison, including the semi-automatic‌‌ annotation of unipolar and ECG signals, and surface‌ manipulations to a common‌ reference model. Spatial repolarization‌‌ time gradients have been detailed, and relations between‌ repolarization time and physiological‌ axes have been assessed‌‌ and quantified.
Peter Langfield with Ed Vigmond and‌ clinical researchers at the‌ Erasmus Medical Center, are‌‌ investigating the occurrence of an atypical biphasic T-wave‌ observed in human unipolar‌ electrograms, by way of‌‌ a biventricular modelling approach. This work has uncovered‌ mechanisms attributed to specific‌ spatial patterns of repolarization‌‌ time.
Deep brain stimulation (DBS) is an‌ effective treatment of essential‌ tremor (ET), but the‌‌ optimal target and how to reach it with‌ the best accuracy remain‌ controversial. The OptimDBS algorithm‌‌ is based on Kernel Ridge Regression and was‌ trained on a database‌ of patients who underwent‌‌ DBS with optimal postoperative outcomes. Using 3-dimensional T1-weighted‌ MRI as the only‌ input, it calculates the‌‌ stereotactic coordinates of an effective DBS target for‌ treating tremor. The aim‌ of the study 14‌‌ by Nejib Zemzemi and co-authors, was to evaluate‌ the efficacy and safety‌ of OptimDBS-guided asleep DBS‌‌ without peroperative clinical and electrophysiological controls in an‌ independent cohort of patients.‌
- Methods:
  The OPTIVIM study‌‌ was a prospective, single-arm, multicenter Phase 2 trial.‌ The primary outcome was‌ tremor reduction and improvement‌‌ in activities of daily living as assessed by‌ the Fahn-Tolosa-Marin scale 3‌ months after surgery. Secondary‌‌ outcomes included reduction in tremor amplitude on accelerometry,‌ quality of life (modified‌ Parkinson's Disease Questionnaire-39), ataxia‌‌ (Scale for the Assessment and Rating of Ataxia),‌ adverse events, and anatomic‌ location of active contacts‌‌ and the volume of tissue activated, all measured‌ 3 months after surgery.‌
- Results:
  Twenty-two patients from‌‌ 2 centers were enrolled. Fahn-Tolosa-Marin scores improved by‌ 61.3% (95% CI: 53.7%-68.9%).‌ Accelerometry (mean ± SD)‌‌ showed a reduction in postural tremor amplitude of‌ 81% ± 56% on‌ the right side and‌‌ 84% ± 35% on‌ the left side. Modified Parkinson's Disease Questionnaire-39 scores‌ (median [Q1-Q3]) improved by 55% [24.3%-77.8%]. Scale for‌ the Assessment and Rating of Ataxia scores remained‌ stable (median [Q1-Q3], preoperative vs postoperative: 4 [3-6]‌ vs 3 [2-6]). There were no serious adverse‌ events. Active contacts were located in the posterior‌ subthalamic area (59%) or the ventral-intermediate nucleus of‌ the thalamus (20%), with 100% of volume of‌ tissue activated overlapping the ventral-intermediate nucleus of the‌ thalamus or posterior subthalamic area.
- Conclusion:
  The results‌ of OptimDBS-guided asleep DBS seem to be comparable‌ with those reported in the literature for awake‌ and asleep DBS and ablative techniques. Long-term evaluations‌ with larger cohorts are needed to confirm these‌ results.
The study 20 by Nejib Zemzemi aims‌ to assess the accuracy of OptimDBS for ET-DBS‌ surgeries to improve electrode placement within the ventral‌ intermediate nucleus of the thalamus (VIM).
- Methods:
  Twenty-two‌ ET patients were enrolled from two university hospitals.‌ Preoperative planning was performed with the aid of‌ OptimDBS software, leveraging 18 anatomical landmarks. Lead-DBS software‌ played a central role in data processing, encompassing‌ tasks like CT to MRI coregistration and normalization.‌ It was also instrumental in 3D reconstruction of‌ the VIM structures, facilitating the precise calculation of‌ distances between preoperative markings ('white crosses') and the‌ VIM. The study employed rigorous statistical analyses to‌ evaluate targeting precision and compared these outcomes with‌ those obtained using GuideXT software, ensuring a comprehensive‌ examination of the research data.
- Results:
  The study's‌ forthcoming results, although awaiting publication, unveil promising insights‌ into the application of OptimDBS software for Essential‌ Tremor-Deep Brain Stimulation (ET-DBS) procedures. Preliminary data showcases‌ that all electrodes fell within the acceptable range,‌ adhering to the criterion of 2mm or less‌ to the VIM. The preoperative targeting was performed‌ with a mean distance of 0.4mm to the‌ VIM. Notably, 0 emerges as the most common‌ distance (25 out of 44), spanning from 0‌ to 1.92 (see the charts and a table).‌
- Conclusions:
  While the complete dataset and statistical analyses‌ are pending, these initial findings suggest the potential‌ for significant improvements in the precision and efficacy‌ of ET-DBS treatments. This study, integral to a‌ broader clinical trial, underscores the outstanding precision achieved‌ by the OptimDBS software in VIM targeting for‌ ET-DBS. With all 44 electrode placements well within‌ the acceptable range, averaging a mere 0.4 mm‌ from the calculated target to the VIM, this‌ technology emerges as a dependable tool for optimizing‌ DBS outcomes in ET patients and streamlining preoperative‌ processes, thereby widening access to ET-DBS for a‌ broader spectrum of surgeons. Future research may explore‌ precise stimulation site adjustments within the VIM and‌ investigate novel treatment avenues for ET and related‌ disorders.

8.5 High performance computing and Microscopic models‌

In 17, Julien Moattiet al. introduce‌ a numerical framework in order to simulate Aluminium‌ gallium nitride based UV-C LEDs. The model used‌ takes into account optical polarization and relies on an extracted tight-binding energy‌ landscape injected into a‌ drift-diffusion system. Results show‌‌ the influence of the quantum well's size on‌ the turn-on voltage and‌ on the internal efficiency.‌‌

9 Bilateral contracts and grants with industry

Participants:‌ Nejib Zemzemi.

9.1‌ Bilateral Grants with Industry‌‌

RebrAIn and Inria contracted an agreement allowing Nejib‌ Zemzemi to pass 90‌ % of his time‌‌ working at RebrAIn. The startup RebrAIn has been‌ co-founded by N. Zemzemi‌ and E. Cuny.

10‌‌ Partnerships and cooperations

10.1 International initiatives

10.1.1 Associate‌ Teams in the framework‌ of an Inria International‌‌ Lab or in the framework of an Inria‌ International Program

SPIMCY

Title:‌
Stochastic forward and inverse‌‌ Problems In electrical and Mechanical Cardiac physiologY
Duration:‌
2024 – 2026
Coordinator:‌
Mahjoub Moncef (moncef.mahjoub@enit.utm.tn)
Partners:‌‌
- Université de Tunis El Manar Tunis (Tunisie)
Inria‌ contact:
Mostafa Bendahmane
Summary:‌
The electrocardiography imaging inverse‌‌ problem is frequently solved using the deterministic quasi-static‌ models. These models don't‌ take into account the‌‌ heart dynamic in time, channel noise and external‌ random perturbations acting in‌ the torso. Recent numerical‌‌ studies in the direct problem have shown that‌ such randomness cannot be‌ suppressed. Occasionally deterministic equations‌‌ give qualitatively incorrect results. Therefore, it is important‌ to quantify the nature‌ of the noise and‌‌ choose an appropriate model incorporating randomness. In our‌ project, we study the‌ inverse problem constrained by‌‌ the stochastic monodomain or bidomain equations in electrocardiology.‌ The state equations consist‌ in a coupled stochastic‌‌ reaction-diffusion system modelling the propagation of the intracellular‌ and extracellular electrical potentials,‌ and stochastic ionic currents‌‌ in the heart. These equations are coupled to‌ the stochastic quasi-static elliptic‌ equation in the torso.‌‌ Thus, we will demonstrate that the novel concept‌ of applying the stochastic‌ model will be useful‌‌ to improve noninvasive reconstruction of electrical and mechanical‌ heart activity. Moreover, we‌ will study the stability‌‌ result for the conductivities and numerically solve the‌ parameter estimation problem in‌ the stochastic model.

ECOS‌‌ Nord

Participants: Jacques Henry, Yves Coudière.‌

Title:
Qualitative and numerical‌ analysis of inverse problems‌‌ in cardiology
Partner Institution(s):
Cuerpo Academico de Ecuaciones‌ Diferenciales y Modelacion Matematica,‌ Facultad de Ciencias Fisico‌‌ Matematicas
- Benemerita Universidad Autonoma de Puebla, Mexico
Date/Duration:‌
2021–2025 (prolonged due to‌ Covid)
Additionnal info/keywords:

ARISE‌‌

Participants: Julien Moatti.

Title:
Analysis of Robust‌ Numerical Solvers for Innovative‌ Semiconductors in View of‌‌ Energy Transition
Partner Institution(s):
- NUMSEMIC team at WIAS‌, Berlin
- RAPSODI team‌, Inria centre at‌‌ the University of Lille
Date/Duration:
2025–2027
Additionnal info/keywords:‌
An Inria associate team‌ about transport charge modelling‌‌ and simulation, see the page of the project‌ for more information.

10.2‌ European initiatives

10.2.1 Horizon‌‌ Europe - EuroHPC

MICROCARD-2

Participants: Mark Potse,‌ Yves Coudière.

MICROCARD-2‌ on the EuroHPC website‌‌

Title:
MICROCARD-2: numerical modeling of cardiac electrophysiology at‌ the cellular scale
Date/Duration:‌
From November 1, 2024‌‌ to April 30, 2027
Partners:
- Université de Bordeaux,‌ France
- Inria, France
- Karlsruher‌ Institut Für Technologie, Germany‌‌
- Megware, Germany
- Simula Research‌ Laboratory (Simula), Norway
- Technical University München (TUM), Germany‌
- Università degli Studi di Pavia, Italy
- Università di‌ Trento (UTrento), Italy
- Université de Strasbourg, France
- Zuse‌ Institute Berlin (ZIB), Germany
Inria contact:
Olivier Aumage‌ (Storm)
Coordinator:
Mark Potse, Université de Bordeaux‌
Summary:

The MICROCARD-2 project is coordinated by Université‌ de Bordeaux and involves the Inria teams Carmen,‌ Storm, and Tadaam in Bordeaux and CAMUS in‌ Strasbourg, among a total of ten partner institutions‌ in France, Germany, Italy, and Norway. This Centre‌ of Excellence for numerical modeling of cardiac electrophysiology‌ at the cellular scale builds on the MICROCARD‌ project (2021–2024) and has the same website.‌

The modelling of cardiac electrophysiology at the cellular‌ scale requires thousands of model elements per cell,‌ of which there are billions in a human‌ heart. Even for small tissue samples such models‌ require at least exascale supercomputers. In addition the‌ production of meshes of the complex tissue structure‌ is extremely challenging, even more so at this‌ scale. MICROCARD-2 works, in concert, on every aspect‌ of this problem: tailored numerical schemes, linear-system solvers,‌ and preconditioners; dedicated compilers to produce efficient system‌ code for different CPU and GPU architectures (including‌ the EPI and other ARM architectures); mitigation of‌ energy usage; mesh production and partitioning; simulation workflows;‌ and benchmarking.

10.2.2 H2020 projects

SimCardioTest

Participants: Yves‌ Coudière, Michael Leguèbe, Valentin Pannetier,‌ Delphine Deshors, Loïc Calvez.

SimCardioTest on‌ the EuroHPC website

Title:
Simulation of Cardiac Devices‌ & Drugs for in-silico Testing and Certification
Date/Duration:‌
From January 1, 2021 to June 30, 2025‌
Partners:
- Université de Bordeaux, France
- Universidad Pompeu Fabra,‌ Spain
- Universitat Politècnica de València, Spain
- Simula Research‌ Laboratory AS, Norway
- InSilicoTrials Technologies S.p.A., Italy
- Sorin‌ CRM SAS, France
- ExactCure, France
- Virtual Physiological Human‌ Institute for Integrative Biomedical Research VZW, Belgium
- Institut‌ National de Recherche en Informatique et Automatique (INRIA),‌ France
Inria contact:
Maxime Sermesant
Coordinator:
Inria
Summary:‌
Computer modelling and simulation have the power to‌ increase speed and reduce costs in most product‌ development pipelines. The EU-funded SimCardioTest project aims to‌ implement computer modelling, simulation and artificial intelligence to‌ design and test cardiac drugs and medical devices.‌ Scientists will establish a platform for running in‌ silico trials and obtaining scientific evidence based on‌ controlled investigations. The simulation of disease conditions and‌ cohort characteristics has the potential to overcome clinical‌ trial limitations, such as under-representation of groups. It‌ also reduces the size and duration of human‌ clinical trials as well as animal testing, and‌ offers robust, personalised information. Leveraging in silico technology‌ in healthcare will expedite product and drug certification‌ and offer patients the best possible care.

10.3‌ National initiatives

Dielectric (FFC project)

The Dielectric project,‌ co-funded by the Federation Française de Cardiologie and‌ Inria, started in January 2023, and is co-piloted‌ by Pr. Pierre Jaïs (IHU Liryc) and Clair‌ Poignard (Inria MONC). It aims at a better‌ understanding of cardiac ablation by electroporation. Both Inria teams MONC and CARMEN‌ are involved, with the‌ PhD of Simon Bihoreau,‌‌ co-directed by Annabelle Collin (MONC) and Michael Leguèbe‌ (CARMEN).

ANR Mire4VTach

PI‌ Annabelle Collin (Inria MONC),‌‌ started late 2023. Michael Leguèbe contributes in Mire4VTach,‌ another project on cardiac‌ electroporation which is more‌‌ focused on the application and confrontation with data‌ than the work in‌ the Dielectric project. Mire4Tach‌‌ also involves people from Inria MONC, CARMEN and‌ IHU Liryc.

PEPS JCJC‌

Julien Moatti is a‌‌ member of a project funded by a PEPS-JCJC‌ grant (2.5k€) of the‌ INSMI section of the‌‌ CNRS, together with Quentin Chauleur (PI) and Guillaume‌ Ferriere from Inria Lille.‌ The project is dedicated‌‌ to the developpement and analysis of numerical scheme‌ for Gross-Pitaevskii equation with‌ complex geometries.

REALPRIOREIT (Action‌‌ Exploratoire Inria)

A project (exploratory action) funded by‌ Inria, coordinated by Lisl‌ Weynans and Jing-Rebecca Li‌‌ (Saclay). This project aims at developing bayesian inference‌ tools for EIT (see‌ the "new results" section).‌‌

ATLAS-RVA (IHU Liryc internal call)

The ATLAS-RVA project‌ was funded by IHU‌ Liryc. It is coordinated‌‌ by Peter Langfield and Karim Benali (IHU Liryc),‌ and aims to investigate‌ repolarization patterns in the‌‌ cardiac ventricles via in-vivo clinical datasets. The main‌ goals are to describe‌ typical repolarization patterns in‌‌ humans, from which localized variablility of such patterns‌ can be assessed, and‌ in turn, how particular‌‌ pathologies manifest.

10.3.1 GENCI

Nejib Zemzemi has an‌ allocation of compute time‌ at GENCI to work‌‌ on deep learning methods for segmenting brain structure,‌ and also to predict‌ stimulation zones for deep‌‌ brain stimulation surgery.

10.4 Regional initiatives

R-EITCardio

A‌ grant from the Science‌ and Technologies Department of‌‌ Bordeaux University to support meetings between collaborators of‌ the hereafter described EIT‌ project, during the year‌‌ 2025.

EITCardio

Participants:
Laura Bear , Yves Coudière‌ , Charles Pierre ,‌ Bénédicte Puig , Lisl‌‌ Weynans
Duration:
From September 2023 to September 2027‌
Partners:
- Centre Inria de‌ l'université de Bordeaux
- IHU‌‌ Liryc
- Université de Pau et des Pays de‌ l'Adour
Coordinator:
Lisl Weynans‌
Summary:
The objective of‌‌ this project is to develop mathematical methods for‌ solving Electrical Impedance Tomography‌ (EIT) to enhance the‌‌ resolution of the ECGi (Electrocardiographic Imaging) problem and‌ validate them experimentally. Specifically,‌ the project consists of‌‌ two parts:
- Development of mathematical and numerical methods‌ to solve the inverse‌ problem of EIT in‌‌ the torso and identify influential parameters for the‌ propagation of the electric‌ field, such as conductivities‌‌ and organ movements.
- Experimental validation of the ECGi‌ + EIT coupling. This‌ experimental validation will be‌‌ conducted first within the experimental setup, the torso‌ tank, currently available at‌ Liryc, which allows measurements‌‌ for ECGi in a controlled environment. Subsequently, it‌ will be conducted as‌ in-vivo experiments, meaning a‌‌ context closer to clinical reality.

11 Dissemination

11.1‌ Scientific Journals (selection)

11.1.1‌ Editorial activities

Mark Potse‌‌ is associate editor for Frontiers in Cardiac Electrophysiology‌ and Journal of Electrocardiology.‌

11.1.2 Review activities

Yves‌‌ Coudière was reviewer for‌ journal in applied mathematics, and in particular the‌ Journal of Applied Mathematics and Physics (ZAMP).‌

Safaa Al-Ali was a reviewer for the journals‌ "Computers in Biology and Medicine" and "IEEE Transactions‌ on Neural Systems and Rehabilitation Engineering"

Julien Moatti‌ was a reviewer for various scientific computing and‌ numerical analysis journals, including Calcolo, aJournal‌ of Computational Physics, IMA Journal of Numerical‌ Analysis and Computer & Mathematics with Applications.‌

Michael Leguèbe was a reviewer for Bionanoscience.‌

11.2 Scientific events (selection)

11.2.1 Scientific events: organisation‌

Julien Moatti co-organizes the scientific computing and modelisation‌ seminar of the Institut de Mathématiques de Bordeaux.‌

The MICROCARD-2 project had its kick-off meeting in‌ July and organized a summer school in Oslo‌ in June.

11.2.2 Member of conference program committees‌

Yves Coudière was a member of the program‌ committee of the FIMH 2025 conference in Dallas,‌ Texas.

11.2.3 Review activities

Yves Coudière was a‌ reviewer for the FIMH 2025 and CINC 2025‌ conferences.

Safaa Al-Ali was a reviewer for ISPOR‌ international conference.

11.2.4 Invited talks

Lisl Weynans was‌ a plenary speaker at the PICOF conference held‌ in Hammamet, Tunisia, october 2025.

Joyce Ghantous was‌ invited to give talks at the Scientific Computation‌ Seminar at the University of Leeds (UK, 27‌ November 2025) and at the IDEFIX team seminar‌ at Inria Saclay (13 November 2025).

Safaa Al-Ali‌ was invited as a speaker at the Séminaire‌ du Calcul Scientifique et Modélisation, Institut de Mathématiques‌ de Bordeaux (Bordeaux, 4 December 2025), and at‌ the Meditwin Workshop - Sensitivity Analysis and Uncertainty‌ Quantification (online, 24 November 2025).

Julien Moatti gave‌ a talk at the seminar of the "analysis‌ pole" of the CMAP (Palaiseau), as well a‌ talk in the Laboratoire Paul Painleve (Lille) for‌ the mini-workshop ARISE on charge transport models, and‌ a talk at the WIAS (Berlin, Germany) for‌ the starting workshop of the associate team ARISE‌.

Yves Coudière gave a conference at the‌ Journée horizon-calcul : Prospectives autour du calcul pour‌ les mathématiques, 2025-10-14, where he presented challenges‌ from the MICROCARD project; and presented work done‌ in the SIMCARDIOTEST project at the Innovaheart workshop‌, 2025-03-26, in Paris-Santé-Campus.

11.2.5 Leadership within the‌ scientific community

Lisl Weynans was elected at the‌ Commission de La Recherche of Bordeaux University, wich‌ is part of the Conseil académique (CAc) de‌ l'université de Bordeaux.

Emma Lagracie was selected as‌ a leader of a working group of the‌ International Consortium on ECGi.

Yves Coudière was‌ a co-author in an article published in the‌ Project Repository Journal, a dissemination journal of the‌ European Commission, dedicated to showcasing funded science and‌ research throughout Europe 13

11.2.6 Scientific expertise

Safaa‌ Al-Ali was a member of the FC3R scientific‌ committee.

Yves Coudière provided expertise for ANRT on‌ Cifre Phd Theses projects, for Inserm on the‌ MESSIDORE call, for CNRS-INSMI on the call for‌ international research labs, and for ANR of research proposals.

11.2.7 Research administration‌

Yves Coudière is the‌ co-responsible of the modeling‌‌ group at the Liryc Institute, part of‌ the Comcos committee, and‌ the scientific committee.

Mark‌‌ Potse is a member of the user committee‌ of GENCI.

Yves‌ Coudière is in charge‌‌ of International relations for the math laboratory, Institut‌ de Mathématiques de Bordeaux‌

11.3 Teaching - Supervision‌‌ - Juries - Educational and pedagogical outreach

11.3.1‌ Teaching

The 2 assistant‌ professors and 2 professors‌‌ teach at several levels of the Bordeaux University‌ programs in Mathematics, Neurosciences,‌ and Medicine (respectively, 192,‌‌ 192 and 96 h/year on average), and EINSERB-MATMECA‌ engineering school of Bordeaux-INP.‌ The researchers also have‌‌ a regular teaching activity, contributing to several courses‌ in the Applied Mathematics‌ at the Bachelor and‌‌ Master levels (between 16 and 72 h/year).

The‌ PhD students who ask‌ for it are used‌‌ to teach between 32 and 64 h/year, usually‌ courses of general mathematics‌ in L1 or mathematics‌‌ for biologists in L1 or L2.

Typical courses‌ taught by team members‌ (L for Bachelor level,‌‌ M for Master level, E for Engineering school‌ – E1 is equivalent‌ to L3, and E2-3‌‌ are equivalent to M1-2):

Numerical analysis (L2)
Programming‌ for scientific computing with‌ C++ (L3) and Modern‌‌ Fortran (M1)
Solving sparse linear systems (L3)
Differential‌ calculus and ordinary differential‌ equations
Numerical approximation of‌‌ PDEs: Finite Differences, Finite Elements, Finite Volumes (M1,‌ M2)
Supervision of programming‌ projects (L3, M1)
Analysis,‌‌ L2
Computational Neurosciences, M2
Neuropsychology and Psychophysiology, L3‌
Physics for students in‌ medicine, one lecture on‌‌ cardiac modelling

In addition to the recurrent activities,‌ for 2024:

Mark Potse‌ gave a lecture on‌‌ « Modeling cardiac electrophysiology at the micrometer scale:‌ an exascale challenge »‌ at the Intensive Summer‌‌ School on Computational Cardiology 2025. Milano, Italy,‌ June 2025.

11.3.2 Teaching‌ administration

Lisl Weynans: in‌‌ charge of the Bachelor track Licence Mathématique parcours‌ ingénierie mathématique,
Yves Coudière‌ is an elected member‌‌ of the Conseil du Collège Sciences et Techniques‌ of the University of‌ Bordeaux
Yves Coudière is‌‌ an elected member of the Conseil de l'UF‌ Mathématiques et Interactions of‌ the University of Bordeaux‌‌

11.3.3 Juries

Lisl Weynans was president of the‌ PhD jury of Kilian‌ Vuillemot (Montpellier Univ.) and‌‌ Kylian Desier (Bordeaux Univ.).
Yves Coudière was president‌ of the PhD jury‌ of Vincent Alba (université‌‌ de Bordeaux) in informatics.
Nejib Zemzemi was a‌ member of the HDR‌ jury of Julien Engelhardt‌‌ PhD, MD. Université de Bordeaux, 2025-12-10.
Nejib Zemzemi‌ was a member of‌ the PhD Jury of‌‌ the thesis of Hamza Ammar, Université de Bordeaux,‌ 2025-10-27.

11.3.4 Educational and‌ pedagogical outreach

Julien Moatti‌‌ gave a talk to the first years Matmeca‌ student ( $\sim$ 100‌ students) about his research‌‌ activity in the framework of the "Parcours ingénieur-docteur"‌ of the ENSEIRB-MATMECA. He‌ also gave an outreach‌‌ talk about numerical simulation to the student of‌ second years of Bordeaux‌ INP ( $\sim$ 600‌‌ students) for the "Journée‌ scientifique" of Bordeaux INP.

11.4 Popularization

Recurrent‌ actions that were pursued in 2025

Receiving schoolchildren‌ visits (élèves de 3e): whole team
Participation to‌ the Chiche action: Yves Coudière
Participation to «‌ La Nuit de la Recherche » (2025-09-29): Yves‌ Coudière
Participation to Moi informaticienne, moi mathématicienne:‌ Emma Lagracie

Other actions specific to 2025

Animation‌ of hands-on session for the « Circuit scientifique‌ Bordelais », one day in Terrasson-Laviledieu, with TV‌ interview on France 3, Yves Coudière
Participation to‌ the « journée portes ouvertes » at IHU‌ Liryc, 2025-10-4: Yves Coudière
Digest, 2025-12-04: feedback on‌ popularization of science by Yves Coudière

A news‌ article promoting the MICROCARD and MICROCARD-2 projects was‌ published publicly on the Inria news platform.‌

12 Scientific production

12.1 Major publications

1 article‌B.Boris Andreianov, M.Mostafa Bendahmane,‌ K. H.Kenneth H. Karlsen and C.Charles‌ Pierre. Convergence of discrete duality finite volume‌ schemes for the cardiac bidomain model.Networks‌ and Heterogeneous Media622011, 195-240‌HAL back to text
2 articleA.Adnane‌ Azzouzi, Y.Yves Coudière, R.Rodolphe‌ Turpault and N.Nejib Zemzemi. A mathematical‌ model of Purkinje-Muscle Junctions.Mathematical Biosciences and‌ Engineering842011, 915-930
3 article‌Y.Yves Bourgault, Y.Yves Coudière and‌ C.Charles Pierre. Existence And Uniqueness Of‌ The Solution For The Bidomain Model Used In‌ Cardiac Electrophysiology.Nonlinear Anal. Real World Appl.‌1012009, 458-482URL: http://hal.archives-ouvertes.fr/hal-00101458/fr
4‌ articleY.Yves Coudière, C.Charles Pierre‌, O.Olivier Rousseau and R.Rodolphe Turpault‌. A 2D/3D Discrete Duality Finite Volume Scheme.‌ Application to ECG simulation.International Journal on‌ Finite Volumes612009, URL: http://hal.archives-ouvertes.fr/hal-00328251/fr‌back to text
5 articleY.Yves Coudière‌ and C.Charles Pierre. Stability And Convergence‌ Of A Finite Volume Method For Two Systems‌ Of Reaction-Diffusion Equations In Electro-Cardiology.Nonlinear Anal.‌ Real World Appl.742006, 916--935‌URL: http://hal.archives-ouvertes.fr/hal-00016816/frback to text
6 articleJ.‌Julien Engelhardt, E.Emmanuel Cuny, D.‌Dominique Guehl, P.Pierre Burbaud, N.‌Nathalie Damon-Perrière, C.Camille Dallies-Labourdette, J.‌Juliette Thomas, O.Olivier Branchard, L.-A.‌Louise-Amélie Schmitt, N.Narimane Gassa and N.‌Nejib Zemzemi. Prediction of Clinical Deep Brain‌ Stimulation Target for Essential Tremor From 1.5 Tesla‌ MRI Anatomical Landmarks.Frontiers in Neurology12‌October 2021HAL DOIback to text
7‌ articleP. W.Peter W. Macfarlane, C.‌Charles Antzelevitch, M.Michel Haïssaguerre, H.‌ V.Heikki V. Huikuri, M.Mark Potse‌, R.Raphael Rosso, F.Frederic Sacher‌, J. T.Jani T. Tikkanen, H.‌Hein Wellens and G.-X.Gan-Xin Yan. The‌ Early Repolarization Pattern; A Consensus Paper.Journal‌ of the American College of Cardiology66resulting‌ from the Symposium on J Wave Patterns and a J Wave Syndrome,‌ Glasgow, August 2013. Defines‌ terminology for the J‌‌ point: Jo, Jp, Jt. Provisionally accepted 19 May‌ 2015.2015, 470-477‌URL: http://dx.doi.org/10.1016/j.jacc.2015.05.033back to‌‌ text
8 articleV. M.Veronique M F‌ Meijborg, M.Mark‌ Potse, C. E.‌‌Chantal E Conrath, C. N.Charly N‌ W Belterman, J.‌ M.Jacques M T‌‌ de Bakker and R.Ruben Coronel. Reduced‌ Sodium Current in the‌ Lateral Ventricular Wall Induces‌‌ Inferolateral J-Waves.Front Physiol7365August‌ 2016HAL DOI back‌ to text back to‌‌ text
9 articleC.Charles Pierre. Preconditioning‌ the bidomain model with‌ almost linear complexity.‌‌Journal of Computational Physics2311January 2012‌, 82--97URL: http://www.sciencedirect.com/science/article/pii/S0021999111005122‌DOI back to text‌‌
10 articleJ.Job Stoks, P.Peter‌ Langfield and M. J.‌Matthijs J.M. Cluitmans.‌‌ Methodological and Mechanistic Considerations in Local Repolarization Mapping‌.JACC: Clinical Electrophysiology‌102February 2024‌‌, 376-377HAL DOI

12.2 Publications of the‌ year

International journals

11‌ article H.Hamza Ammar‌‌, M.Mahjoub Moncef and N.Néjib Zemzemi‌. How does the‌ optimal constant of the‌‌ Carleman estimate depend on the size of the‌ observation boundary ? Inverse‌ Problems October 2025 HAL‌‌ DOI back to text
12 articleG.Geoffrey‌ Beck, D.David‌ Lannes and L.Lisl‌‌ Weynans. A numerical method for wave-structure interactions‌ in the boussinesq regime‌.ESAIM: Mathematical Modelling‌‌ and Numerical Analysis596November 2025,‌ 2895-2931HAL DOI back‌ to text
13 article‌‌V.Vincenzo Carbone, I.Irene Balelli,‌ Y.Yves Coudière,‌ O.Oscar Camara,‌‌ B.Beatriz Trenor, M.Michèle Barbier and‌ M.Maxime Sermesant.‌ A cloud-based platform for‌‌ seamless digital testing of cardiac medical devices and‌ drugs.The Project‌ Repository Journal241‌‌August 2025, 144-148HAL DOI back to‌ text
14 articleJ.‌Julien Engelhardt, E.‌‌Emile Simon, N.Nejib Zemzemi, C.‌Camille Dallies-Labourdette, E.‌Edouard Courtin, R.‌‌Remi Sitta, A.Antoine Benard, O.‌Olivier Branchard, M.‌Michel Goillandeau, H.‌‌Helene Gervais-Bernard, C.Catherine Caire, S.‌Stephane Thobois, T.‌Thomas Tourdias, F.‌‌Fanny Munsch, D.Dominique Guehl and E.‌Emmanuel Cuny. Enhancing‌ Asleep Deep Brain Stimulation‌‌ Targeting for Essential Tremor Using Machine Learning: The‌ OPTIVIM Phase 2 Study‌.NeurosurgeryDecember 2025‌‌HAL DOI back to text
15 articleP.‌Peter Langfield, B.‌Bernd Krauskopf, K.‌‌ H.Kyoung Hyun Lee and H. M.Hinke‌ M Osinga. The‌ global geometry of phase-resetting‌‌ surfaces: The role of critical level sets and‌ isochrons.Communications in‌ Nonlinear Science and Numerical‌‌ Simulation1512025, 109043HAL DOI back‌ to text
16 article‌M.Michael Leguèbe,‌‌ Y.Yves Coudière, L.Loïc Calvez,‌ V.Valentin Pannetier,‌ C.Charlie Douanla-Lontsi,‌‌ A.Anđela Davidović,‌ P.-E.Pierre-Elliott Bécue, M.Mehdi Juhoor and‌ N.Nejib Zemzemi. CEPS: a cardiac electrophysiology‌ exploration tool for new mathematical models and methods‌.Journal of Open Source Software10114‌October 2025, 8910HAL DOI back to‌ text back to text
17 articleM.Michael‌ O’donovan, R.Robert Finn, P.Patricio‌ Farrell, T.Timo Streckenbach, J.Julien‌ Moatti, S.Stefan Schulz and T.Thomas‌ Koprucki. Developing a hybrid single band carrier‌ transport model for (Al,Ga)N heterostructures.Journal of‌ Computational Electronics244June 2025, 114‌HAL DOI back to text

International peer-reviewed conferences‌

18 inproceedingsE.Emma Lagracie, L.Lisl‌ Weynans and Y.Yves Coudière. Effects of‌ the Insertion of Epicardial Anisotropy Versus Isotropy in‌ the Inverse Problem of Electrocardiography.Functional Imaging‌ and Modeling of the HeartFIMH 2025 -‌ 13th Functional Imaging and Modeling of the Heart‌ International ConferenceLNCSLecture Notes in Computer Science‌15672Dallas (Texas), United StatesSpringer Nature Switzerland‌June 2025, 83-93HAL DOI back to‌ text
19 inproceedingsV.Valentin Pannetier, M.‌Michael Leguèbe, Y.Yves Coudière, R.‌Richard Walton, G.Guilhem Fauré and R.‌Romano Setzu. Towards Validation of Two Computational‌ Models of Artificial Pacemakers.Functional Imaging and‌ Modeling of the Heart 13th International Conference, FIMH‌ 2025, Dallas, TX, USA, June 1–5, 2025, Proceedings,‌ Part IFIMH 2025 - Functional Imaging and‌ Modeling of the HeartLNCS-15672Lecture Notes in‌ Computer ScienceDallax, TX, United StatesSpringer Nature‌ Switzerland2025, 127-137HAL DOI back to‌ text
20 inproceedingsN.Nana Tchantchaleishvili, N.‌Nejib Zemzemi and E.Emmanuel Cuny. Precision‌ Validation of AI-Enhanced Preoperative Targeting for Essential Tremor‌ DBS.EANS2025 - European Association of Neurosurgical‌ Societies Congress5Vienna, Austria2025, 105182‌HAL DOI back to text

Doctoral dissertations and‌ habilitation theses

21 thesisZ.Zeina Chehade.‌ Finite volume methods on unstructured meshes for the‌ microscopic bidomain model in cardiac electrophysiology.Université‌ de BordeauxJune 2025HAL back to text‌
22 thesisE.Emma Lagracie. Reconstruction of‌ the electrical activation sequence of the heart from‌ non-invasive measurements.Université de BordeauxSeptember 2025‌HAL back to text

Reports & preprints

23‌ miscD.Dilara Abdel, A.Alain Blaustein‌, C.Claire Chainais-Hillairet, M.Maxime Herda‌ and J.Julien Moatti. Existence of solutions‌ and uniform bounds for the stationary semiconductor equations‌ with generation and ionic carriers.November 2025‌HAL back to text
24 miscS.Simon‌ Bihoreau-Duchemin, A.Annabelle Collin, M.Michael‌ Leguèbe and C.Clair Poignard. Mathematical Derivation‌ of a Homogenized Bidomain Model for Pulsed Field‌ Ablation.September 2025HAL back to text‌
25 miscJ.Jacques Henry and A.Andrès‌ Fraguela Collar. Solving the Cauchy problem in‌ a cylinder by using regularizations of the factorized formulation.June 2025‌HAL back to text‌
26 miscE.Emma‌‌ Lagracie and L.Luc de Montella. Particle‌ Filtering for Non-Deterministic Electrocardiographic‌ Imaging.September 2025‌‌HAL back to text

12.3 Cited publications

27‌ inproceedingsA.Andony Arrieula‌, H.Hubert Cochet‌‌, P.Pierre Jaïs, M.Michel Haïssaguerre‌ and M.Mark Potse‌. An Improved Iterative‌‌ Pace-Mapping Algorithm to Detect the Origin of Premature‌ Ventricular Contractions.Computing‌ in Cardiology47abstract‌‌ nr 62, really early. Oral presentation.RiminiComputing‌ in Cardiology2020,‌ 62HAL DOI back‌‌ to text
28 inproceedingsP.-E.Pierre-Elliott Bécue,‌ F.Florian Caro,‌ M.Mostafa Bendahmane and‌‌ M.Mark Potse. Modélisation et simulation de‌ l'électrophysiologie cardiaque à l'échelle‌ microscopique.43e Congrès‌‌ National d'Analyse Numérique (CANUM)oral presentationSMAIObernai,‌ Alsace, FranceMay 2016‌, URL: http://smai.emath.fr/canum2016/resumesPDF/peb/Abstract.pdfback‌‌ to text
29 miscP.-E.Pierre-Elliott Bécue,‌ F.Florian Caro,‌ M.Mark Potse and‌‌ Y.Yves Coudière. Theoretical and Numerical Study‌ of Cardiac Electrophysiology Problems‌ at the Microscopic Scale.‌‌.PosterJuly 2016HAL back to text‌
30 inproceedingsP.-E.Pierre-Elliott‌ Bécue, M.Mark‌‌ Potse and Y.Yves Coudière. A Three-Dimensional‌ Computational Model of Action‌ Potential Propagation Through a‌‌ Network of Individual Cells.Computing in Cardiology‌ 2017Rennes, FranceSeptember‌ 2017, 1-4HAL‌‌back to text
31 inproceedingsP.-E.Pierre-Elliott Bécue‌, M.Mark Potse‌ and Y.Yves Coudière‌‌. Microscopic Simulation of the Cardiac Electrophysiology: A‌ Study of the Influence‌ of Different Gap Junctions‌‌ Models.Computing in CardiologyMaastricht, NetherlandsSeptember‌ 2018HAL back to‌ text
32 articleM.‌‌Mostafa Bendahmane, Y.Youssef Ouakrim, Y.‌Yassine Ouzrour and M.‌Mohamed Zagour. Mathematical‌‌ analysis and numerical simulation of a nonlinear radiofrequency‌ ablation model in cardiac‌ tissue.Nonlinear Analysis:‌‌ Real World Applications872026, 104412back‌ to text
33 article‌B.Benjamin Berte,‌‌ F.Frederic Sacher, S.Saagar Mahida,‌ S.Seigo Yamashita,‌ H. S.Han S.‌‌ Lim, A.Arnaud Denis, N.Nicolas‌ Derval, M.Mélèze‌ Hocini, M.Michel‌‌ Haïssaguerre, H.Hubert Cochet and P.Pierre‌ Jaïs. Impact of‌ Septal Radiofrequency Ventricular Tachycardia‌‌ Ablation; Insights From Magnetic Resonance Imaging.Circulation‌1302014, 716-718‌URL: https://www.ahajournals.org/doi/10.1161/CIRCULATIONAHA.114.010175back to‌‌ text
34 inproceedingsJ.Judit Chamorro Servent,‌ L.Laura Bear,‌ J.Josselin Duchateau,‌‌ M.Mark Potse, R.Rémi Dubois and‌ Y.Yves Coudière.‌ Do we need to‌‌ enforce the homogeneous Neuman condition on the Torso‌ for solving the inverse‌ electrocardiographic problem by using‌‌ the method of fundamental solution ?Computing in‌ Cardiology 201643Computing‌ in Cardiology 2016Vancouver,‌‌ CanadaSeptember 2016, 425-428HAL back to‌ text
35 articleY.‌Yves Coudière, Y.‌‌Yves Bourgault and M.Myriam Rioux. Optimal‌ monodomain approximations of the‌ bidomain equations used in‌‌ cardiac electrophysiology.Mathematical‌ Models and Methods in Applied Sciences246‌February 2014, 1115-1140HAL back to text‌back to text
36 articleJ.Josselin Duchateau‌, M.Mark Potse and R.Remi Dubois‌. Spatially Coherent Activation Maps for Electrocardiographic Imaging‌.IEEE Transactions on Biomedical Engineering64May‌ 2017, 1149-1156HALDOI back to text‌
37 inproceedingsA.Ali Gharaviri, M.Mark‌ Potse, S.Sander Verheule, R.Rolf‌ Krause, A.Angelo Auricchio and U.Ulrich‌ Schotten. Epicardial Fibrosis Explains Increased Transmural Conduction‌ in a Computer Model of Atrial Fibrillation .‌Computing in CardiologyVancouver, CanadaSeptember 2016HAL‌back to text back to text back to‌ text
38 articleM.Michel Haïssaguerre, N.‌N. Derval, F.F. Sacher, L.‌L. Jesel, I.I. Deisenhofer, L.‌L. de Roy, J. L.J. L.‌ Pasquié, A.A. Nogami, D.D.‌ Babuty, S.S. Yli-Mayry, C.C.‌ De Chillou, P.P. Scanu, P.‌P. Mabo, S.S. Matsuo, V.‌V. Probst, S.S. Le Scouarnec,‌ P.P. Defaye, J.J. Schlaepfer,‌ T.T. Rostock, D.D. Lacroix,‌ D.D. Lamaison, T.T. Lavergne,‌ Y.Y. Aizawa, A.A. Englund,‌ F.F. Anselme, M.M. O'Neill,‌ M.M. Hocini, K. T.K. T.‌ Lim, S.S. Knecht, G. D.‌G. D. Veenhuyzen, P.P. Bordachar,‌ M.M. Chauvin, P.P. Jaïs,‌ G.G. Coureau, G.G. Chene,‌ G. J.G. J. Klein and J.J.‌ Clémenty. Sudden cardiac arrest associated with early‌ repolarization.N. Engl. J. Med.3582008‌, 2016--2023back to text
39 articleM.‌M. Haïssaguerre, P.P. Jaïs, D.‌ C.D. C. Shah, S.S. Garrigue‌, A.A. Takahashi, T.T. Lavergne‌, M.M. Hocini, J. T.J.‌ T. Peng, R.R. Roudaut and J.‌J Clémenty. Spontaneous initiation of atrial fibrillation‌ by ectopic beats originating in the pulmonary veins‌.N. Engl. J. Med.3391998,‌ 659-666URL: https://www.nejm.org/doi/full/10.1056/NEJM199809033391003back to text
40 article‌M. G.Mark G. Hoogendijk, M.Mark‌ Potse, A. C.André C. Linnenbank,‌ A. O.Arie O. Verkerk, H. M.‌Hester M. den Ruijter, S. C.Shirley‌ C. M. van Amersfoorth, E. C.Eva‌ C. Klaver, L.Leander Beekman, C.‌ R.Connie R. Bezzina, P. G.Pieter‌ G. Postema, H. L.Hanno L. Tan‌, A. G.Annette G. Reimer, A.‌ C.Allard C. van der Wal, A.‌ D.Arend D. J. ten Harkel, M.‌Michiel Dalinghaus, A.Alain Vinet, A.‌ A.Arthur A. M. Wilde, J. M.‌Jacques M. T. de Bakker and R.Ruben Coronel. Mechanism of‌ Right Precordial ST-Segment Elevation‌ in Structural Heart Disease:‌‌ Excitation Failure by Current-to-Load Mismatch.Heart Rhythm‌72010, 238-248‌URL: http://dx.doi.org/10.1016/j.hrthm.2009.10.007back to‌‌ text
41 articleM. L.Marjorie Letitia Hubbard‌ and C. S.Craig‌ S. Henriquez. A‌‌ microstructural model of reentry arising from focal breakthrough‌ at sites of source-load‌ mismatch in a central‌‌ region of slow conduction.Am. J. Physiol.‌ Heart Circ. Physiol.306‌2014, H1341-1352back‌‌ to text
42 inproceedingsM.Michal Kania,‌ Y.Yves Coudière,‌ H.Hubert Cochet,‌‌ M.Michel Haissaguerre, P.Pierre Ja\"is and‌ M.Mark Potse.‌ A new ECG-based method‌‌ to guide catheter ablation of ventricular tachycardia.‌iMAging and eLectrical Technologies‌Uppsala, SwedenApril 2018‌‌HAL back to text
43 articleY.Y‌ Ouzrour, M.M‌ Bendahmane, Y.Y‌‌ Ouakrim and M.M Zagour. Well-posedness analysis‌ and numerical simulation of‌ a radiofrequency ablation model‌‌ in a porous medium: Y. Ouzrour et al.‌.Journal of Engineering‌ Mathematics15412025‌‌, 2back to text
44 inproceedingsM.‌Mark Potse, L.‌Luca Cirrottola and A.‌‌Algiane Froehly. A practical algorithm to build‌ geometric models of cardiac‌ muscle structure.ECCOMAS‌‌ 2022 - The 8th European Congress on Computational‌ Methods in Applied Sciences‌ and EngineeringOslo, Norway‌‌June 2022HAL back to text
45 article‌M.Mark Potse,‌ B.Bruno Dubé,‌‌ J.Jacques Richer, A.Alain Vinet and‌ R. M.Ramesh M.‌ Gulrajani. A Comparison‌‌ of monodomain and bidomain reaction-diffusion.IEEE Transactions‌ on Biomedical Engineering53‌122006, 2425-2435‌‌URL: http://dx.doi.org/10.1109/TBME.2006.880875back to text
46 articleM.‌Mark Potse, B.‌Bruno Dubé and A.‌‌Alain Vinet. Cardiac Anisotropy in Boundary-Element Models‌ for the Electrocardiogram.‌Medical and Biological Engineering‌‌ and Computing472009, 719--729URL: http://dx.doi.org/10.1007/s11517-009-0472-x‌back to text
47‌ inproceedingsM.Mark Potse‌‌, A.Ali Gharaviri, S.Simone Pezzuto‌, A.Angelo Auricchio‌, R.Rolf Krause‌‌, S.Sander Verheule and U.Ulrich Schotten‌. Anatomically-induced Fibrillation in‌ a 3D model of‌‌ the Human Atria.Computing in CardiologyMaastricht,‌ NetherlandsSeptember 2018HAL‌back to text
48‌‌ miscM.Mark Potse, V. M.Veronique‌ M F Meijborg,‌ C. N.Charly N‌‌ W Belterman, J. M.Jacques M T‌ de Bakker, C.‌ E.Chantal E Conrath‌‌ and R.Ruben Coronel. Regional conduction slowing‌ can explain inferolateral J‌ waves and their attenuation‌‌ by sodium channel blockers.PosterSeptember 2016‌HAL back to text‌
49 inproceedingsM.Mark‌‌ Potse, E.Emmanuelle Saillard, D.Denis‌ Barthou and Y.Yves‌ Coudière. Feasibility of‌‌ Whole-Heart Electrophysiological Models With Near-Cellular Resolution.CinC‌ 2020 - Computing in‌ CardiologyRimini / Virtual,‌‌ ItalySeptember 2020HALDOI back to text‌
50 articleM.Mark‌ Potse. Scalable and‌‌ Accurate ECG Simulation for‌ Reaction-Diffusion Models of the Human Heart.Frontiers‌ in Physiology9April 2018, 370HAL‌DOI back to text
51 articleA.Aslak‌ Tveito, K. H.Karoline H. J\ae}ger,‌ M.Miroslav Kuchta, K.-A.Kent-Andre Mardal and‌ M. E.Marie E. Rognes. A Cell-Based‌ Framework for Numerical Modeling of Electrical Conduction in‌ Cardiac Tissue.Front. Phys.5This is‌ very very similar to what we were doing‌ with PEB... Looks like we're scooped at least‌ for the approach, but we do have a‌ few abstracts ([becue:cinc17], [becue16a], MMCE meeting in Ottawa‌ November 2017). Note it's in Frontiers in (Biomedical)‌ Physics, not Physiology.2017, 48back to‌ text back to text

CARMEN - 2025

CARMEN - 2025

2025Activity﻿‌​‌ reportProject-TeamCARMEN

Keywords​‌﻿﻿

Computer Science and Digital​​﻿﻿ Science

Other Research Topics​​​‌ and Application Domains

1 Team﻿​﻿﻿ members, visitors, external collaborators​‌﻿﻿

Research Scientists

Faculty Members

Post-Doctoral Fellows​​​‌

PhD Students

Technical Staff​​﻿﻿

Interns and﻿​﻿﻿ Apprentices

Administrative﻿​﻿﻿ Assistants

Visiting​​​‌ Scientists

External Collaborators

2 Overall﻿﻿﻿‌ objectives

3﻿﻿﻿‌ Research program

3.1 Complex﻿‌​‌ models for the propagation﻿​​﻿ of cardiac action potentials​​​‌

3.2 Simplified​​​‌ models and inverse problems﻿​﻿﻿

3.3 Numerical techniques

3.4 Cardiac electrophysiology﻿﻿﻿‌ at the microscopic scale﻿‌​‌

3.5 Models​​﻿﻿ and tools for ablative​​​‌ therapies

4​​​‌ Application domains

4.1 Scientific﻿​﻿﻿ context: IHU Liryc

4.2​​​‌ Basic experimental electrophysiology

4.3 Clinical electrophysiology​​​‌

4.4 Application﻿​​﻿ in Deep Brain Stimulation​​​‌

5 Social and​‌﻿﻿ environmental responsibility

5.1 Footprint​​﻿﻿ of research activities

5.2 Impact​​﻿﻿ of research results

6 Highlights of​​﻿﻿ the year

7 Latest software﻿​​﻿ developments, platforms, open data​​​‌

7.1 CEPS updates

7.2 cardiolib updates﻿​​﻿

7.3​​​‌ MICROCARD-2 updates

7.4 Latest software developments﻿‌​‌

7.4.1 CEPS

7.4.2 cardiolib

7.5 New​‌﻿﻿ platforms

OpenCARP

Mmg

CEMPACK

8 New results﻿​﻿﻿

8.1 Analysis of partial﻿​﻿﻿ differential equations

8.2﻿​﻿﻿ Numerical analysis and development​‌﻿﻿ of numerical methods

8.3 Modeling and inverse﻿‌​‌ problems

8.4 Clinical applications﻿‌​‌

8.5 High performance​​﻿﻿ computing and Microscopic models​​​‌

9 Bilateral contracts and﻿​​﻿ grants with industry

9.1﻿﻿﻿‌ Bilateral Grants with Industry﻿‌​‌

10﻿‌​‌ Partnerships and cooperations

10.1﻿​​﻿ International initiatives

10.1.1 Associate​​​‌ Teams in the framework﻿﻿﻿‌ of an Inria International﻿‌​‌ Lab or in the﻿​​﻿ framework of an Inria​​​‌ International Program

SPIMCY

ECOS﻿‌​‌ Nord

ARISE﻿‌​‌

10.2﻿﻿﻿‌ European initiatives

10.2.1 Horizon﻿‌​‌ Europe - EuroHPC

MICROCARD-2﻿​​﻿

10.2.2 H2020﻿​﻿﻿ projects

SimCardioTest

10.3​​​‌ National initiatives

Dielectric (FFC﻿​﻿﻿ project)

ANR Mire4VTach

PEPS JCJC﻿﻿﻿‌

REALPRIOREIT (Action﻿‌​‌ Exploratoire Inria)

ATLAS-RVA (IHU Liryc internal﻿​​﻿ call)

10.3.1 GENCI﻿​​﻿

10.4﻿​​﻿ Regional initiatives

R-EITCardio

EITCardio

11 Dissemination

11.1​​​‌ Scientific Journals (selection)

11.1.1﻿﻿﻿‌ Editorial activities

11.1.2 Review activities

11.2 Scientific events (selection)﻿​﻿﻿

11.2.1 Scientific events: organisation​‌﻿﻿

11.2.2 Member​​﻿﻿ of conference program committees​​​‌

11.2.3 Review activities﻿​﻿﻿

2025Activity‌‌ reportProject-TeamCARMEN

Keywords‌

Computer Science and Digital Science

Other Research Topics‌ and Application Domains

1 Team members, visitors, external collaborators‌

Post-Doctoral Fellows‌

Technical Staff

Interns and Apprentices

Administrative Assistants

Visiting‌ Scientists

2 Overall‌ objectives

3‌ Research program

3.1 Complex‌‌ models for the propagation of cardiac action potentials‌

3.2 Simplified‌ models and inverse problems

3.4 Cardiac electrophysiology‌ at the microscopic scale‌‌

3.5 Models and tools for ablative‌ therapies

4‌ Application domains

4.1 Scientific context: IHU Liryc

4.2‌ Basic experimental electrophysiology

4.3 Clinical electrophysiology‌

4.4 Application in Deep Brain Stimulation‌

5 Social and‌ environmental responsibility

5.1 Footprint of research activities

5.2 Impact of research results

6 Highlights of the year

7 Latest software developments, platforms, open data‌

7.2 cardiolib updates

7.3‌ MICROCARD-2 updates

7.4 Latest software developments‌‌

7.5 New‌ platforms

8 New results

8.1 Analysis of partial differential equations

8.2 Numerical analysis and development‌ of numerical methods

8.3 Modeling and inverse‌‌ problems

8.4 Clinical applications‌‌

8.5 High performance computing and Microscopic models‌

9 Bilateral contracts and grants with industry

9.1‌ Bilateral Grants with Industry‌‌

10‌‌ Partnerships and cooperations

10.1 International initiatives

10.1.1 Associate‌ Teams in the framework‌ of an Inria International‌‌ Lab or in the framework of an Inria‌ International Program

ECOS‌‌ Nord

ARISE‌‌

10.2‌ European initiatives

10.2.1 Horizon‌‌ Europe - EuroHPC

MICROCARD-2

10.2.2 H2020 projects

10.3‌ National initiatives

Dielectric (FFC project)

PEPS JCJC‌

REALPRIOREIT (Action‌‌ Exploratoire Inria)

ATLAS-RVA (IHU Liryc internal call)

10.3.1 GENCI

10.4 Regional initiatives

11.1‌ Scientific Journals (selection)

11.1.1‌ Editorial activities

11.2 Scientific events (selection)

11.2.1 Scientific events: organisation‌

11.2.2 Member of conference program committees‌

11.2.3 Review activities

11.2.4 Invited talks

11.2.5 Leadership within the‌ scientific community

11.2.7 Research administration‌

11.3 Teaching - Supervision‌‌ - Juries - Educational and pedagogical outreach

11.3.1‌ Teaching

11.3.2 Teaching‌ administration

11.3.4 Educational and‌ pedagogical outreach

12.1 Major publications

12.2 Publications of the‌ year

International peer-reviewed conferences‌

Doctoral dissertations and‌ habilitation theses