The team Carmen is part the the Liryc Institute
(http://

The team Carmen plans to develop some models and numerical methods in order to simulate the propagation of the cardiac action potential, from the cellular scale to the scale of the body. It aims at improving:

our knowledge and the treatment of electrical cardiac pathologies;

the exploitation of all available electrical signals.

Therefore, we want to incorporate the heterogeneities and coupling processes from the intermediate scales into the macroscopic PDE models. They play a primary role in the cardiac electrical arrhythmias. Meanwhile, we want to use the models to solve the inverse problems related to non-invasive electrical imaging of the heart.

The mathematical fields involved in our research are: PDE modeling and in particular reaction-diffusion equations, inverse problems, numerical analysis and scientific computing.

A main goal of the team is to contribute to the work-packages defined in the IHU Liryc, which focuses on electrical arrhythmias and how heart failure relates to electrical asynchrony.

A cooperation with physiology, physiopathology and medicine is being developed. the team will build 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.

S. Labarthe was awarded the poster price for the theoretical and applied aspects of his work on atrial modeling by to distinct communities:

poster award by the medical community after at the « printemps de la cardiologie 2012 »;

poster award by the applied mathematics community at the CANUM 2012.

N. Zemzemi: best poster presentation award at the international conference Computing in Cardiology 2012 (CINC'2012), .

Cardiac arrythmias originates from the multiscale organisation of the cardiac action potential from the cellular scale up to the scale of the body. It relates the molecular processes from the cell membranes to the electrocardiogram, an electrical signal on the torso. The spatio-temporal patterns of this propagation is related both to the function of the cellular membrane and of the structural organisation of the cells into tissues, into the organ and final within the body.

Several improvements of current models of the propagation of the action potential will be developped, based on previous work , , and on the data available at the Liryc:

Enrichment of the current monodomain and bidomain models by accounting for structural heterogeneities of the tissue at an intermediate scale. Here we focus on multiscale analysis techniques applied to the various high-resolution structural data available at the Liryc.

Coupling of the tissues from the different cardiac compartments and conduction systems. Here, we want to develop model that couples 1D, 2D and 3D phenomena described by reaction-diffusion PDEs.

These models are essential to improve our in-depth understanding of cardiac electrical dysfunction. To this aim, we will use high-performance computing techniques in order to explore numerically the complexity of these models and check that they are reliable experimental tools.

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

The cardiac inverse problem consists in finding the cardiac activation maps or, more generally the whole cardiac electrical activity, from high density body surface electrocardiograms. It is a new and a powerful diagnosis technique, which success would be considered as a breakthrough in the cardiac diagnosis. Although widely studied during the last years, it remains a challenge for the scientific community. In many cases the quality of reconstructed electrical potential is not sufficiently accurate. The methods used consist in solving the Laplace equation on the volume delimited by the body surface and the epicardial surface.We plan to

study in depth the dependance of this inverse problem inhomogeneities in the torso, conductivity values, the geometry, electrode placements...

improve the solution to the inverse problem be using new regularization strategies and the theory of optimal control, both in the quasistatic and in the dynamic contexts.

Of cours we will use our models as a basis to regularize these inverse problems. We will conside the follwong strategies:

using complete propagation models in the inverse problem, like the bidomain equations; for instance in order to localize some electrical sources;

construct some families of reduced order models, using e.g. statistical learning techniques, which would accurately represent some families of well-identified pathologies;

construct some simple models of the propagation of the activation front, based on eikonal or level-sets equations, but which would incorporate the representation of complex activation patterns.

Additionnaly, we will need to develop numerical techniques dedicated to our simplified eikonal/levl-sets equations.

We want the numerical simulations of the previous direct or inverse models to be efficient and reliable with respect to the need of the medical community. It needs to qualify and guarantee the accuracy and robustness of the numerical techniques and the efficiency of the resolution algorithms.

Based on previous work on solving the monodomain and bidomain equations , and and , we will focus on

High-order numerical techniques with respect to the variables with physiological meaning, like velocity, AP duration and restitution properties;

Efficient, dedicated preconditionning techniques coupled with parallel computing.

Our fields of application are naturally: electrophysiology and cardiac physiopathology at the tissue scale on one side; medical and clinical cardiology on the other side.

The team's research project is part of the IHU Liryc project, initiated by Pr. M. Haissaguerre. It is concerned by the major issues of modern electrocardiology: atrial arrhythmias, sudden death due to ventricular fibrillation and heart failure related to ventricular dyssynchrony.

We aim at bringing applied mathematics and scientific computing closer to biomedical research applied to cardiac rhythmology and clinical cardiology. It aims at enhancing our fundamental knowledge of the normal and abnormal cardiac electrical activity, of the patterns of the electrocardiogram; and we will develop new simulation tools for training, biological and clinical applications.

Our modeling is carried out in coordination with the experimental teams from the Liryc. It will help to write new concepts concerning the multiscale organisation of the cardiac action potentials and will serve our understanding in many electrical pathologies:

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 vein.

At the ventricula level, we focus on (1) modeling the complex coupling between the Purkinje network and the ventricles and (2) modeling the structural heterogeneities at the cellular scale, taking into account the complex organisation and disorganisation of the myocytes and fibroblasts. Point (1) is supposed to play a major role in sudden cardiac death and point (2) is important in the study of infarct scars for instance.

The Liryc use, on a daily basis and in the clinical context, complex electrical imaging systems, like intracardiac catheters and the CardioInsight vest with 252 body syrface electrodes.

The numerical models can guide the analysis of these signals and conversely, the models can be guided by the signals.

Other applied questions can be addressed by modeling, like the nature of the various electrical signals measured by catheters, that heavily depends on the nature and spatial localisation of the electrodes.

: we explain the links between the solutions of the bidomain and monodomain models using some analytical arguments. The result is partially based on the theory of the bidomain operator explained in .

: We computed some bidomain solutions for use by M. Pop and M. Sermesant in the STACOM'11 challenge from the MICCAI 2011 conference and derived collaborative article .

Project *Modélisation pour les données multimodales*
(2012-2015) funded by the *Conseil Regional
Aquitaine*. Coordinator J.-F. Aujol (Pr University Bordeaux
1). The PhD of G. ravon is funded within this project: 3D
reconstruction by inverse problem in cardiac optical mapping.

Our work is partially funded by the Liryc project.

For 2012-2015: 1/2 PhD thesis associated to the project *Modélisation pour les données multimodales* (see section Regional
Initiaves).

Partner 1: CNR, IMATI (Italie) – G. Manzini.

Finite volume discretization on general, distorted meshes, for second order operators with anisotropy and discontinuities. Applications to the simulation of ECG.

Partner 2: Computational Biology Group, University of Oxford. Department of Computer Science (United Kingdom).

Our work with the computational biology group concerns the development of multi-scale models of the drugs and their effect on the electrical activity of the heart. The main goal is to assess the drug−induced effects on the electrocardiogram, using a computational model describing the physiology from ion channel to body surface potentials.

Collaboration with the Pr. Y. Bourgault
(http://

*Subject:* models and numerical methods for cardiac
electrophysiology.

*Support:* for the last years the collaboration was
supported by the ANR project Momme (ANR-JCJC-07-0141), the *Region des Pays de la Loire* and the Natural Sciences and
Engineering of Research council of Canada

Equipe Problèmes Inverses et Contrôle (EPIC), University Tunis Al Manar. Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur (LAMSIN), Tunisia.

The EPIC team has an important experience in dealing with ill-posed inverse problems for static and evolution problems. The goal of this collaboration is to apply the methods developed in this team to inverse problems in electrocardiography.

Y. Bourgault, Pr. Univeristy of Ottawa, Department of mathematics and statistics. 22/10/2012 to 26/10/2012.

Comparison between the monodomain and bidomain models for cardiac electrophysiology.

Moncef Mahjoub, Teaching assistant at University of Tunis Al Manar (ENIT-LAMSIN), Tunisia. 01/10/2012 to 06/10/2012.

Inverse problems.

Fadhel Jeday. Teaching assistant at University of Sousse, Tunisia. 03/12/2012 to 07/12/2012.

Inverse problems.

Nicolas Claude (from July 2012 until September 2012)

Subject: Real-time simulation of ECGs based on the finite element Sofa library developed at Inria Lille.

Institution: ENSEIRB-MATMECA, Bordeaux (Master 1 student).

Jamila Lassoued (from August 2012 until November 2012)

Subject: application of model reduction techniques to the inverse problems in cardiac electrophysiology.

Institution: Ecole Nationale d'Ingénieurs de Tunis (Tunisia – Master 2 student)

Sinda Ben Khalfalla (from 04/12/2012 to 21/12/2012)

Subject: Inverse problems for the quasistatic inverse problem in electrocardiology.

Institution: Ecole Nationale d'Ingénieurs de Tunis (Tunisia – PhD student)

Mohammed Addouche (from 08/12/2012 to 05/01/2013)

Subject: On using factorisation methods for the quasistatic inverse problems of electrocardiology.

Institution: University of Tlemcen (Algeria – PhD student)

reviewing for (many) applied mathematics journals

N. Zemzemi was an Invited speaker in *Workshop on
Efficient Solvers in Biomedical Applications*. July 2-5, 2012
Graz, Austria.

Leading the cardiac challenge group in *the 3rd VPH NoE
Study Group*. Plenary session on Cardiac modeling challenges
(1h) + 4 hours course (cardiac modeling, mathematical methods in
cardiac elec- trphysiology, drug modeling and computational tools
in cardiac electrophysiology). May 7-11, 2012. Barcelona, Spain.

Invitation to give a presentation at the *Inria-Bcam
workshop*, Bilbao, 2012.

LAMSIN Seminar: 6 hours course on cardiac modeling for the
EPIC groupe (*Équipe Problèmes Inverses et Contrôle*), Forward
and inverse problem in cardiac electrophysiology. June 18-21,
2012, Tunis, Tunisia.

*Partial list of presentations given by the team
members* (besides the invitations above).

*Printemps de la cardiologie*, March 2012.

*Congrès d'Analyse Numérique* (CANUM), May 2012.

*21st International Conference on Domain Decomposition
Methods*. June 25-29 2012, Inria Rennes, Bretagne-Atlantique,
France.

*Computing in Cardiology 2012* conference. September 9-12
2012, Krakow, Poland.

Licence : Y. Coudière, Calcul scientifique : résolution des grands systèmes creux, 34.66 h eq. TD, L3, Université Bordeaux 1.

Master : Y. Coudière, Analyse numérique avancée, 36 h eq. TD, M2 Enseignant, titre du cours, nombre d'heures en équivalent TD, niveau (M1, M2), Université Bordeaux 1.

Licence : Simon Labarthe, probabilité et statistique, 22 h eq. TD, première année IUT, IUT HSE, Université Bordeaux 1.

Licence : Simon Labarthe, introduction aux bases de données, 24h eq. TD, première année IUT, IUT HSE, Université Bordeaux 1.

Licence : Enseignant, titre du cours, nombre d'heures en équivalent TD, niveau (L1, L2, L3), université, pays

Master : Enseignant, titre du cours, nombre d'heures en équivalent TD, niveau (M1, M2), université, pays

Doctorat : Enseignant, titre du cours, nombre d'heures en équivalent TD, université, pays

PhD in progress : A. Davidovic, *Modelling the cardiac
ventricular structural heterogeneities*, started on October 2012,
supervised by M. Bendahmane and Y. Coudière.

PhD in progress : S. Labarthe, *Modélisation de l'activité
électrique cardiaque dans les oreillettes et les veines
pulmonaires*, started on October 2010, supervised by Y. Coudière
and J. Henry.

PhD in progress : G. Ravon, *An inverse problem for cardiac
optical mapping*, started on October 2012, supervised by
Y. Coudière and A. Iollo.

Y. Coudière Reviewer and member of the jury for defense of the
PhD of J. Relan, *Personalised Electrophysiological Models of
Ventricular Tachycardia for Radio Frequency Ablation Therapy
Planning*, June 2012.

Y. Coudière, supervisor and member of the jury for defense of
the PhD of A. Uzureau, *Modélisations et calculs de la
cicatrisation osseuse. Application à la modélisation d'un
bioréacteur*, December 2012.

Recruitment commitee for an associate professor position, University of Nice, June 2012.

Reception of the students from *Ecole Nationale des Ponts
et Chaussées*, September 2012.

Exposé *Unithé ou café*, June 12, 2012. Inria Bordeaux
Sud-Ouest. France.