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 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 42 and on the data available at IHU Liryc:

• Enrichment of the current monodomain and bidomain models 42, 53 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 numerically explore the complexity of these models.

We use these model codes for applied studies in two important areas of cardiac electrophysiology: atrial fibrillation 46 and sudden-cardiac-death (SCD) syndromes 7, 649. 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 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:

• studying in depth the dependance 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 44, 43, 52, 34, 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 parallellization, algebraic multigrid preconditioning, and Krylov solvers. New developments include high-order explicit integration methods and task-based dynamic parallellism.

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 59. Existing models are two-dimensional  50 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  38, 37, 36 and by others 59 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.

Image of the microstructure from histology, current, insufficient, representation of microstructural defects, and foreseen geometry to be used in microscopic models.

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. 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:

• 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.

4.1 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 48, 47, 40. 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.

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  39 (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   55, 46. 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 51, 35.

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 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.

5.1 Footprint of research activities

We avoid flying whenever we can. For example, we used trains to travel to Nice (10 hours) and Budapest (2 days). One of us traveled to the 2022 CinC meeting in Tampere (Finland) by bicycle.

5.2 Impact of research results

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.

7.1 CEPS

No new feature of high relevance was added to CEPS this year. However, the software is currently being deeply rewritten for the H2020 SimCardioTest project. In this project, it will be used as the core computing engine of a cloud based platform for in silico trials, targeting the design of pacemakers.

• The pacemaker model that is derived (see section 8.3) requires to changes deeply the architecture of CEPS.
• In parallel, in order to comply with software quality criteria described by the FDA in the V&V40 standard, CEPS is now being monitored through the SonarQube platform of Inria, and a much more thorough testing suite is being written.

7.2 Mmg and ParMmg

Mmg and ParMmg are intensively used in the MICROCARD project to automatically generate 3D meshes of cardiac tissues from imaging data. The CARMEN teams contributes to Mmg, with the main objective of making the software robust when dealing with complex meshes provided by Orobix (italian partner company in MICROCARD).

ParMmg is a parallel unstructured mesh adaptation software using iterative remeshing and repartitionning. It uses the Mmg software to perform the sequential remeshing steps. A new version of Mmg (5.7.0) has been released this year, and improvement of the level-set discretization is being investigated. In addition, a new version of ParMmg is under development to be able to run on large heterogeneous supercomputers.

7.3 New software

7.4 New platforms

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 756, 46, 45, 41 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 58. The code scales excellently to large core counts 57 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, named after a famous model maker, 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 2), 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 54. 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. As of 2022, the segmentation work is mostly done with the MUSICardio software, but we still use Blender for finishing touches and high-quality visualization.

A 

B 

C 

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

8.1 Analysis of partial differential equations

• Global Lipschitz stability of multiple space dependent ionic parameters for the MEA/hiPSC-CM assays 9. The work is now published in Inverse Problems journal (DOI 10.1088/1361-6420/aca70d). This work is devoted to analyze the inverse problem of determining two space dependent ionic parameters of a nonlinear reaction diffusion system arainsing from MEA/hiPSC-CM assays model described in 33. We consider the classical phenomenological model in cardiac electrophysiology of FitzHugh-Nagumo to describe the ionic exchanges at the microscopic level. Our main result is the uniqueness and a Lipschitz stability estimate for two ionic parameters (k, γ) of the model using sub-boundary observations over an interval of time. The key ingredients are global Carleman-type estimates with a suitable observations acting on a part of the boundary.

8.2 Numerical analysis and development of numerical methods

• The foundations of several projects that use numerical continuation techniques have been established. Most notably, a method for computing isochrons in higher-dimensional models has been developed. To demonstrate the method, it has been applied to the four dimensional Hodgkin-Huxley model. The computed isochrons are consistent with previous depictions, but the method is also able to uncover complicated isochron geometry arising from numerical sensitivities in the model that were not previously resolved.

  Additionally, the development of a toolbox with the aim of studying propagating waves has started. In practice, this is a numerical continuation solver based on the Auto package, but with spatial domains that have appropriate discretizations and solution representations. The toolbox is implemented partially in Python as a prototype, where further detailed analysis and testing can be performed.

• In the context of Electrical Impedance Tomography, we proposed a new system of equations to obtain a unique solution for the Complete Electrode Model and proved the convergence of an immersed boundary method to solve numerically this model.
• In the context of the MICROCARD project, we have extended the standard two point flux approximation finite volume method to the microscopic bidomain equations, proved its convergence, and obtained some error estimate. A prototype code is currently being implemented. The work was presented at the DDFV workshop in Marseille, October 17th-21st, 2022.

8.3 Modeling and inverse problems

• The Ph.D. thesis of Bachar Tarraf was defended in February 2022 29. We extended our simple model of cardiac mitochondria to include ROS production and mPTP opening. We tried several machine learning techniques to generate a classification of mitochondria in different respiratory media and try to reproduce data from our collaborators within the Mitocard ANR project. However, the data were hardly exploitable to establish a reference classification from the start, and we were not able to determine specifically any parameter from our extended model.

• Modeling pacemakers: in the context of the H2020 SimCardioTest European project, we derived a simple model of electric stimulation by a pacemaker, in collaboration with Microport CRM, manufacturer. To our knowledge, the study of cardiac stimulation is done along two research axes that are dissociated. On one hand, extensive literature can be found on the polarization phenomena that occur at the surface of an electrode when it delivers current into an electrolyte. On the other hand, stimulation of cardiac tissue is generally made through a simple rectangle function that acts as source term of the monodomain or bidomain equations, representing a direct injection of current into the tissue.

  We are now coupling a model of pacemaker and a model of electrode contact to a stimulation model. In order to determine the parameters of the contact, that depend on the shape and material of each pacemaker electrode, we used data from bench tests performed at Microport. The model represents the contact by a simple capacitance in parallel with a resistance. Even if the model is quite simple, we already faced difficulties to calibrate the parameters. Even if all the physics could not be explained by this model, we obtained fits that differ by $\sim$2% (in L2 relative error) from the data, which is suitable for using them as input to a cardiac model.

  We have coupled this contact model to a 0D model a cardiac cell stimulation in order to determine the parameters of the complete model that influence the voltage and duration of stimulation that are required to excite the cells, determining the so-called Lapicque curve. The results of this study will be submitted to FIMH 2023. We are also currentlty implementing a coupled 3D pacemaker/bidomain model.

• In the framework of the international ECGI consortium, we continue the work on the assessement of the Effect of the segmentation uncertanties on the ECGI forward and inverse problem solutions.

  This year we had many publications at the international conference of Computing in Cardiology 2022 that hold in Tampere. In the first study 26 we quantify the dependence of a cardiac propagation model on segmentation variability. We used statistical shape modeling and polynomial Chaos (PC) to capture segmentation variability dependence and applied its affects to a propagation model. We evaluated the predicted local activation times (LATs) an body surface potentials (BSPs) from two modeling pipelines: an Eikonal propagation model and a surface-based fastest route model. The predicted uncertainty due to segmentation shape variability was distributed near the base of the heart and near high amplitude torso potential regions. Our results suggest that modeling pipelines may have to accommodate segmentation errors if regions of interest correspond to high segmentation error. Further, even small errors could proliferate if modeling results are used to to feed further computations, such as ECGI.

  In the second study 18, we generated a statistical shape model from segmentations of the same patient and generated 262 cardiac geometries to run in an ECG forward computation of body surface potentials (BSPs) using an equivalent dipole layer cardiac source model and 5 ventricular stimulation protocols. Variability between simulated BSPs for all models and protocols was assessed using Pearson's correlation coefficient (CC). Compared to the BSPs of the mean cardiac shape model, the lowest variability (average CC = 0.98 ± 0.03) was found for apical pacing whereas the highest variability (average CC = 0.90 ± 0.23) was found for right ventricular free wall pacing. Furthermore, low amplitude BSPs show a larger variation in QRS morphology compared to high amplitude signals. The results indicate that the uncertainty in cardiac shape has a significant impact on ECGI.

  In the third study 17, we analysed the effect of segmentation variability on the ECGI estimation of the cardiac activity with 262 shape models generated from fifteen different segmentations. Therefore, we designed two test cases: with and without shape model uncertainty. Moreover, we used four cases for ectopic ventricular excitation and compared the ECGI results in terms of reconstructed activation times and excitation origins. The preliminary results indicate that a small variation of the activation maps can be observed with a model uncertainty but no significant effect on the source localization is observed.

• In the context of the project about electrical impedance tomography, we developed a method to reconstruct not only the conductivities inside the domain of interest, but also the shape of the domain itself and the location of the electrodes. The code for the inverse problem of Electrical Impedance Tomography was validated in sequential 2D, and parallelized.
• In collaboration with Jérôme Fehrenbach (Univ. Toulouse), we developed a fast algorithm to estimate the location of activation based on an eikonal equation.

8.4 Clinical electrophysiology

• Andony Arrieula defended his PhD thesis in October 2022 27. In this thesis he developed two methods to help find suitable ablation sites for premature ventricular beats during a cardiac catheterization procedure. The first method uses ECG data from beats stimulated with the catheter at known positions, accurately measured with the clinical catheter localization system. Using linear interpolation it can subsequently infer the location of a premature beat from a measured ECG. The main challenge here was to deal with both underdetermined and overdetermined linear systems. The second method is entirely noninvasive: after training with thousands of simulated ECGs, a machine-learning technique predicts the site of origin from an ECG and with help from an anatomical model of the heart extracted from clinical imaging data. Both methods were tested extensively on simulated data and on clinical data.

8.5 High performance computing

• We used high-performance computing resources principally for the work described in section 8.4.
• We provided simulated data to test machine-learning and signal analysis methods 23, 21.
• We used simulations to investigate whether inter-individual differences in cell composition across the ventricular wall may explain variability in the ECG response to serum potassium and calcium variations 19.
• We tested a method aimed to accelerate the initialization of whole-heart models with strongly abnormal parameter settings 20.

8.6 Microscopic models

• Within the MICROCARD project the CARMEN team is also involved in the construction of synthetic models of the cardiac muscle at the cellular scale. These models are to complement the imaging-derived models, which will be very limited in size. We reported a first method for this purpose at the ECCOMAS meeting in June 24. At the time of the meeting we were still limited to models of a few dozen cells. Thanks to the improvements in the Mmg software, released in version 5.7.0 in December 2022, we have leaped to thousands of cells in the last few days of the year.
• As detailed above, a finite volume numerical method was defined and analyzed to wolve the microscopic bidomain esuations on these geometries.

9.1 Bilateral Grants with Industry

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

Lisl Weynans obtained a grant from EDF Foundation to found a research project about Electrical Impedance Tomography.

10.1 International initiatives

10.2 European initiatives

10.3 National initiatives

11.1 Promoting scientific activities

11.2 Teaching - Supervision - Juries

11.3 Popularization

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, 195-240
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• 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/fr
• 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/fr
• 6 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.2015.05.033
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• 7 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 2016
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• 8 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/S0021999111005122
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12.2 Publications of the year

12.3 Other

12.4 Cited publications

• 33 articleE.Emanuela Abbate, M.Muriel Boulakia, Y.Yves Coudière, J.-F.Jean-Frédéric Gerbeau, P.Philippe Zitoun and N.Nejib Zemzemi. In silico assessment of the effects of various compounds in MEA/hiPSC-CM assays: Modelling and numerical simulations.Journal of Pharmacological and Toxicological Methods892018, 59-72
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• 34 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, 195-240
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• 35 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, 62
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• 36 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.pdf
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• 37 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 2016
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• 38 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, 1-4
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• 39 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 2018
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• 40 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.114.010175
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• 41 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, 425-428
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• 42 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, 1115-1140
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• 43 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/fr
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• 44 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/fr
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• 45 articleJ.Josselin Duchateau, M.Mark Potse and R.Remi Dubois. Spatially Coherent Activation Maps for Electrocardiographic Imaging.IEEE Transactions on Biomedical Engineering64May 2017, 1149-1156
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• 46 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 2016
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• 47 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--2023
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• 48 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/NEJM199809033391003
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• 49 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.2009.10.007
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• 50 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, H1341-1352
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• 51 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 2018
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• 52 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/S0021999111005122
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• 53 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.2006.880875
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• 54 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-x
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• 55 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 2018
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• 56 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 2016
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• 57 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 2020
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• 58 articleM.Mark Potse. Scalable and Accurate ECG Simulation for Reaction-Diffusion Models of the Human Heart.Frontiers in Physiology9April 2018, 370
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• 59 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, 48
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