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:
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 work on incorporating any new biological knowledge, at any scale, that helps to understand the mechanisms of arrythmias, 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.
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 arrythmias 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 39 and on the data available at IHU Liryc:
These models are essential to improve our understanding of cardiac electrical dysfunction. To this aim, we use high-performance computing techniques in order to numerically explore the complexity of these models.
We use these model codes for applied studies in two important areas of cardiac electrophysiology: atrial fibrillation 41 and sudden-cardiac-death (SCD) syndromes 7, 644. This work is performed in collaboration with several physiologists and clinicians both at IHU Liryc and abroad.
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 possibly 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 inacurate 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:
In addition, we have started to explore many alternative approaches including:
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, 8, 1, we will focus on:
Existing simulation tools used in our team rely, among others, on mixtures of explicit and implicit integration methods for ODEs, hybrid MPI-OpenMP parallellization, algebraic multigrid preconditioning, and Krylov solvers. New developments include high-order explicit integration methods and task-based dynamic parallellism.
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 54. Existing models are two-dimensional 45 or limited to idealized geometries, and use a linear (purely resistive) behaviour of the gap-juction 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 35, 34, 33 and by others 54 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 runs from April 2021 to October 2024, and involves also the Inria teams CAMUS, STORM and CARDAMOM as well as the Inria-led MMG Consortium.
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 non standard transmission conditions, introduce stiff non linear dynamics. Third, the simulation would performing for a billions of myocytes, that can lead to a significantly large system. In the MICROCARD project, we simulate the micromodel using finite volumes, finite elements and boundary element methods.
Today, the most effective way to treat arrhythmias is to ablate selected regions of the cardiac tissue. As the lesions have no particular electric property, this creates 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:
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 43, 42, 37. 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 center for treatment of cardiac arrhythmia. Thus
the group also sees large numbers of patients with rare cardiac diseases.
In 2011 the group has won the competition for 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 centers 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.
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 36 (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 arrythmias 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 50, 41. 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.
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 46, 31.
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 doi:10.3389/fneur.2021.620360. 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 centers. 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 centers.
We avoid flying whenever we can.
The MICROCARD project, 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.
Project EITCardio co-funded by the Région Nouvelle Aquitaine, Inria and the Fondation EDF on electrical impedance tomography for the detection of cardiac arhythmia, also in collaboration with Inria Saclay.
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:
The project involves researchers from the Inria CARMEN team, specializing in modeling the electrical activity of the heart, IHU-Liryc, and LMAP in Pau, experts in scientific computing and uncertainty consideration.
We added to CEPS the pacemaker models derived for the SimCardioTest project. These models required a complete rewriting of most of CEPS source code, which is now over. We developed new code according the high Software Quality standards, using Inria's sonarQube platform to monitor the issues.
We took advantage of this rewriting to perform a global overhaul of the code in terms of accessibility, be it in the API or the documentation.
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 microscopiv cardiac model.
We have been contributing by managing the MICROCARD consortium and its contributions to openCARP, and by adapting the partitionning scheme (based on parMETIS) to the context of the microscopic model.
Mmg is an open source software suite for simplicial remeshing and an open source Consortium, which participates in the MICROCARD project.
In this context we have been active developers of the Mmg software.
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 less elements than in the initial data, 2) improve the synthetic generation of cardiac tissue.
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.
Applied modeling studies performed by the Carmen team in
collaboration with IHU Liryc and foreign partners
751, 41, 40, 38
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 53.
The code scales excellently to large
core counts 52 and, as it is controlled completely with command-line
flags and configuration files, it can be used by non-programmers. It
also features:
The code has been stable and reliable for many years. It can be considered the workhorse for our HPC work until CEPS takes over.
MICROCARD project on cordis.europa.eu
Cardiovascular diseases are the most frequent cause of death worldwide and half of these deaths are due to cardiac arrhythmia, a disorder of the heart's electrical synchronization system. Numerical models of this complex system are highly sophisticated and widely used, but to match observations in aging and diseased hearts they need to move from a continuum approach to a representation of individual cells and their interconnections. This implies a different, harder numerical problem and a 10,000-fold increase in problem size. Exascale computers will be needed to run such models.
We propose to develop an exascale application platform for cardiac electrophysiology simulations that is usable for cell-by-cell simulations. The platform will be co-designed by HPC experts, numerical scientists, biomedical engineers, and biomedical scientists, from academia and industry. We will develop, in concert, numerical schemes suitable for exascale parallelism, problem-tailored linear-system solvers and preconditioners, and a compiler to translate high-level model descriptions into optimized, energy-efficient system code for heterogeneous computing systems. The code will be parallelized with a recently developed runtime system that is resilient to hardware failures and will use an energy-aware task placement strategy.
The platform will be applied in real-life use cases with high impact in the biomedical domain and will showcase HPC in this area where it is painfully underused. It will be made accessible for a wide range of users both as code and through a web interface.
We will further employ our HPC and biomedical expertise to accelerate the development of parallel segmentation and (re)meshing software, necessary to create the extremely large and complex meshes needed from available large volumes of microscopy data.
The platform will be adaptable to similar biological systems such as nerves, and components of the platform will be reusable in a wide range of applications.
SimCardioTest project on cordis.europa.eu
PersonalizeAF project on cordis.europa.eu
Atrial Fibrillation (AF) is the most common cardiac arrhythmia affecting more than 6 million Europeans with a cost exceeding 1
PersonalizeAF addresses this challenge by delivering an innovative multinational, multi-sectorial, and multidisciplinary research and training programme in new technologies and novel strategies for individualized characterization of AF substrate to and increase treatments efficiency.
From the research point of view, PersonalizeAF will integrate data and knowledge from in-vitro, in silico, ex vivo and in vivo animal and human models to: 1) generate an individual description of the state of the atrial muscle identifying the disease mechanisms and characteristics; 2) understand the potential effect that different therapies have on different atrial substrates; and 3) combine this information to generate a specific profile of the patient and the best therapy for each patient.
With this purpose, PersonalizeAF partnership aggregates relevant scientific staff from the academic and clinical world with highly specialised biomedical companies which will be involved in a high-level personalised training programme that will train a new generation of highly skilled professionals and guarantee ESRs and future PhD students outstanding Career Opportunities in the biomedical engineering, cardiology services and medical devices sectors. PersonalizeAF will disseminate results to a wide spectrum of stakeholders, create awareness in the general public about atrial fibrillation and encourage vocational careers among young students.
The ANR project MAESTRO (Magnetic Signal detection of ventricular arrhythmOgenic substrates), coordinated by Prof. Michel Haïssaguerre (IHU Liryc), has a computational component for which we recruited a postdoc from December 2022 to mid-November 2023, directed by Mark Potse.
GENCI project A0130307379, Interaction between tissue structure and ion-channel function in cardiac arrhythmia, coordinated by Mark Potse, comprises 2.35 million core-hours on the national supercomputers Zay and Joliot-Curie. Compared to previous years it is a modest allocation. This is because most of our computational needs in 2023 are either smaller or larger than the national scale.
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).
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.
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.
The project aims to study the variability of patterns of ventricular repolarization times in healty and unhealthy patients, and explore the role of such patterns.
The main objective of the project is to perform a statistical assessment of patterns of ventricular repolarization time via unipolar electrogram annotations from CARTO datasets, from roughly two hundred datasets from data centers across France. The cruicial difference between this project and previous work, is that specific filtering settings were imposed for the data acquisition that make the annotations reliable. The project will exploit this particular setting and the large volumes of data, to exlpore and assess alternative methods of repolarization time annotation. Finally, the project will study cases of ventricular tachycardia with the aim of ellucidating the role of repolarization time patterns and also the associated resitituion properties of the tissue.
Mark Potse is leading the H2020-EuroHPC MICROCARD project, strengthening his role as a European leader in the scientific community.
The 2 assistant professors and 1 professor of the team teach at several levels of the Bordeaux University programs in Mathematics, Neurosciences, and Medicine (respectively, 192, 192 and 96 h/year on average). 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):