2023Activity reportProject-TeamCARMEN

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 39 and on the data available at IHU Liryc:

• Enrichment of the current monodomain and bidomain models 39, 48 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 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.

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 5, 4, 8, 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 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 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.

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

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.

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 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.

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  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.

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 46, 31.

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.

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 Evolution of existing software

7.2 New software

7.3 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 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:

  • 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 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 49. 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.

A 

B 

C 

An image of a torso model including the heart, the ribs, the lungs, the livers, and the location of torso electrodes, and a detailed image of an atrial anatomical model including fiber directions.

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

8.1 Numerical analysis and development of numerical methods

• Isochrone computation There has been ongoing development of a numerical continuation-based method to compute higher-dimensional isochrones. The method had been previously applied to the Hodgkin-Huxley model. During this year, a region of extremely low sensitivity of phase response to stimuli was identified, which is a property supportive of synchroniziation between cells. This region was studied and we have hypothesized an underlying mechanism that gives rise to it. These results form a manuscript that is currently in preparation, which will be submitted within the first few months of this year. We also started to use the method to study isochrones in more cardiac-related models, namely, the Beeler-Reuter model and a model of a sinoatrial node cell.
• Immersed boundary method for cardiac EIT We proposed an immersed boundary scheme for the numerical resolution of the Complete Electrode Model in Electrical Impedance Tomography, that we use as a main ingredient in the resolution of inverse problems in medical imaging. Such method allows to use a Cartesian mesh without accurate discretization of the boundary, which is useful in situations where the boundary is complicated and/or changing. We proved the convergence of the method 13.
• Immersed boundary method for some wave equations Besides the issue of cardiac electrophysiology, we also studied numerical schemes to study 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 23. The problem can be reduced to a transmission problem for this Boussinesq system, in which the transmission conditions between the components of the domain at the left and at the right of the object are determined through the resolution of coupled forced ODEs in time satisfied by the vertical displacement of the object and the average discharge in the portion of the fluid located under the object. We propose a new extended formulation in which these ODEs are complemented by two other forced ODEs satisfied by the trace of the surface elevation at the contact points. The interest of this new extended formulation is that the forcing terms are easy to compute numerically and that the surface elevation at the contact points is furnished for free. Based on this formulation, we propose a second order scheme that involves a generalization of the MacCormack scheme with nonlocal flux and a source term, which is coupled to a second order Heun scheme for the ODEs. In order to validate this scheme, several explicit solutions for this wave-structure interaction problem are derived and can serve as benchmark for future codes. As a byproduct, our method provides a second order scheme for the generation of waves at the entrance of the numerical domain for the Boussinesq-Abbott system.

8.2 Modeling and inverse problems

• Modeling and in-silico trial for pacemakers We pursued our work within the H2020 SimCardioTest European project, by using both 0D and 3D models of cardiac stimulation by a pacemaker, which were derived in collaboration with Microport CRM, manufacturer. The models couple a model of the pacemaker circuitry with cardiac tissue through boundary conditions which model the polarization of the electrodes. First results were presented at FIMH 2023 18. The implementation of the 3D model was made following high quality standards in order to match the Verification and Validation standards of the V&V40 document 32, which gives a list a software requirements for the Verification aspects. We are currently using data from bench experiments of optical mapping to comply with the Validation items. In particular, we are calibrating parameters of the ionic models using measured activation maps. This verification and validation process following the V& V40 guidelines was presented at the RICAM workshop on Cardiovascular Modeling and simulation in 2023 20. Finally, we designed a first in-silico clinical trial, that is described in a deliverable of the European project (still not published). the question of interest for this trial concerns the changes of the electrical capture properties of a pacemaker bradychardia lead with respect to some design parameters, in the context where fibrosis develops at the tip lf the lead.
• The patchwork method for ECGi We propose a novel “patchwork method” (PM) 10, which combines two classical numerical approaches for ECGI: the method of fundamental solutions (MFS) and the finite-element method (FEM). We assume that the method with the smallest residual in the predicted torso potentials provides the most accurate solution. These residuals were computed using the boundaryelement method, and projected onto the heart surface using an orthogonal projection. The PM then selects for each heart node and each time step the method whose estimated reconstruction error is smallest. The performance of the PM was compared to both FEM and MFS alone using simulated ectopic and normal ventricular activation beats. Results: Cardiac potentials and activation maps obtained with the PM (CC=0.63±0.004 and 0.61±0.05 respectively) were more accurate than MFS (CC=0.61± 0.005 and 0.48±0.05 respectively) or FEM (CC=0.58±0.009 and 0.51±0.02 respectively). The PM also succeeded in locating all epicardial activation breakthrough sites, whereas the individual numerical methods usually missed one. Moreover, the PM outperformed the other methods in the presence of Gaussian measurement noise added to the torso surface potential distribution, showing its robustness and stability with respect to noise. Conclusions: The PM overcomes some of the limitations of classical numerical methods, improving the accuracy of mapping important features of activation during sinus rhythm and paced beats.
• Electrical Impedance Tomography (EIT) We applied the immersed boundary scheme evocated hereabove to the resolution of the inverse problem of Electrical Impedance Tomography. We performed reconstructions of conductivites, contact impedances on electrodes and shape of the considered domain of interest 13.
• A model for cardiac electroporation In the Dielectric project in collaboration with Inria Team MONC and IHU Liryc, we derived formally a bidomain model at the tissue scale that takes into account the specificity of electroporation, which involves different time scales than the classical bidomain model. This model was presented at the 2023 RICAM workshop 26.
• Comparison of different formulations for ECG computations We compared and numerically studied two formulations that map the body surface potential maps from the transmembrane voltage. Those formulations naturally emerge from the bidomain model. We determined which formulation is the most relevant to use in an inverse resolution perpective. We developped a 2D finite volume bidomain code, and compared simplified models with the bidomain 21.
• Impact of cardiac motion on ECGi solutions We conducted an investigation into the impact of cardiac motion on both inverse and forward simulations, as well as the localization of sources from ECGI outcomes. This study relied on clinical patient imaging data, generously provided by Simula Research Laboratory, as part of a research visit conducted during the summer of 2023.
• Numerical Investigation of Methods Used In Commercial Clinical Devices for Solving the ECGI Inverse Problem In this work, we assess two ECGI algorithms used in commercial ECGI systems to solve the inverse problem; the Method of Fundamental Solutions (MFS) and the Equivalent Single Layer (ESL). We quantify the performance of these two methods in conjunction with two different activation maps to estimate the activation times and earliest activation sites (ADM et TID). Results for clinical cases, indicate that ESL combined with ADM resulted in better localization accuracy and, in contrast to simulated data, TID and ADM based earliest activation sites can be very different. In fact, TID based activation maps is less robust to noisy and clinical data. This is mainly due to the fact that TID calculates activation times for each cardiac node separately (thepoint of maximum negative slope) without a spatial coherence. Consequently, in noisy data, it frequently provides patchy patterns in the obtained maps. However, activation direction mapping provides better results for clinical data despitethe fact that it tends to over-smooth the spread of activation, which can bemisleading in the excitation origin localization. The post-processing methods and in particular the activation times calculation have a significant impact on the computation of the Activation map and concequently on PVC localization. 24
• Inter-operator segmentation variability induces high premature ventricular contractions localization uncertainty at the heart base Our main purpose is to evaluate the effect of the inter-operator segmentation variability on the PVC localization. Eight different cardiac segmentations from the same single subject CT-scans were performed by researchers within the consortium for Electrocardiographic Imaging. For all generated meshes, eight ventricular stimulation protocols were used; left and right ventricular free walls (LV, RV), apex, left and right ventricular outflow tract (LVOT, RVOT), septum, and two locations at the left and right heart base (LVB, RVB). BSPs were generated using computational models. We designed two test cases: with and without segmentation uncertainty. We found that the high uncertainty is due to the variability of segmentations at the base of the heart. These findings suggest that uncertainty in cardiac segmentation can have a significant impact on ECGI and its interpretability in clinical applications; therefore, careful segmentation is strongly recommended, especially at the base of the heart. 27

8.3 Clinical applications

• Artificial Intelligence for Detection of Ventricular Oversensing Machine Learning Approaches for Noise Detection Within Non-Sustained Ventricular Tachycardia Episodes Remotely Transmitted by Pacemakers and Implantable Cardioverter Defibrillators Pacemakers (PMs) and implantable cardioverter defibrillators (ICDs) increasingly automatically record and remotely transmit non-sustained ventricular tachycardia (NSVT) episodes which may reveal ventricular oversensing. We aimed at developing and validating a machine learning algorithm which accurately classifies NSVT episodes transmitted by PMs and ICDs in order to lighten healthcare workload burden and improve patient safety. PMs or ICDs (Boston Scientific) from four French hospitals with $\ge 1$ transmitted NSVT episode were split into three subgroups: training set, validation set, and test set. Each NSVT episode was labelled as either physiological or non-physiological. Four machine learning algorithms (2DTF-CNN, 2D-DenseNet, 2DTF-VGG, and 1D-AgResNet) were developed using a training and validation dataset. Accuracies of the classifiers were compared with an analysis of the remote monitoring team of the Bordeaux University Hospital using F2 scores (favoring sensitivity over predictive positive value) using an independent test set. We used data collected from 807 devices that transmitted 10.471 NSVT recordings (82% ICD, 18% PM), of which 87 devices (10.8%) transmitted 544 NSVT recordings with non-physiological signals. The classification by the remote monitoring team resulted in an F2 score of 0,932 (sensitivity of 95%, specificity of 99%). The four machine learning algorithms showed high and comparable F2 scores (2DTF-CNN: 0,914, 2D-DenseNet: 0,906, 2DTF-VGG: 0,863, 1D-AgResNet: 0,791) and only 1D-AgResNet had significantly different labeling as compared with the remote monitoring team. Our conclusion is that Machine learning algorithms were accurate in detecting non-physiological signals within EGMs transmitted by pacemaker and ICDs. We think that an artificial intelligence approach may render remote monitoring less resourceful and improve patient safety. 15
• Comparison of two segmentation software tools for deep brain stimulation of the subthalamic and ventro-intermedius nuclei Deep brain stimulation (DBS) relies on precise targeting of key structures such as the subthalamic nucleus (STN) for Parkinson's disease (PD) and the ventro-intermedius nucleus of the thalamus (Vim) for essential tremor (ET). Segmentation software, such as GuideXT© de Boston Scientific and Suretune©, de Medtronic commercially available for atlas-based identification of deep brain structures. However, no study has compared the concordance of the segmentation results between the two software. We retrospectively compared the concordance of segmentation of GuideXT© and Suretune© software by comparing the position of the segmented key structures with clinically predicted targets obtained using the newly developed RebrAIn© software as a reference. We targeted the STN in 44 MRI from PD patients (88 hemispheres) and the Vim in 31 MRI from ET patients (62 hemispheres) who were elected for DBS. In 22 STN targeting (25%), the target positioning was not correlating between GuideXT© and Suretune©. Regarding the Vim, targets were located in the segmented Vim in 37%, the posterior subthalamic area (PSA) in 60%, and the STN in 3% of the cases using GuideXT©; the proportions were 34%, 60%, and 6%, respectively, using Suretune©. The mean distance from the centre of the RebrAIn© targeting to the segmented Vim by Suretune© was closer (0.64 mm) than with GuideXT© (0.96 mm; p = 0.0004). 12

8.4 High performance computing and Microscopic models

• A population based study of the effect of ion concentrations on the ECG We have used a population of models to investigate a problem faced by researchers who are trying to infer blood metabolyte concentrations from the ECG. There is in most subjects a clear relation between ECG features and concentrations of sodium and potassium, but these relations differ strongly between subjects. We have shown that inter-subject differences in the heterogeneity of intrinsic cardiac cell properties are a possible explanation for these differences 11.
• Computational methods for the microscopic EMI model The MICROCARD project has developed numerical methods to simulate cardiac electrical activity on cell-by-cell (EMI) models: 1) efficient higher-order time stepping achieved by combining low-overhead spatial adaptivity on the algebraic level with progressive spectral deferred correction methods, and 2) substructuring domain decomposition preconditioners tailored to address the complexities of our heterogeneous problem structures. These methods have been tested using artificial 3D tissue geometries of upto a few hundreds of cells that we generated 16, 19.
• Mesh of a 1 cubic millimeter of cardiac tissue In addition, thanks to improvements in the Mmg code and in mesh generation software we were able to build such meshes of cardiac tissue structure up to 1 cubic millimeter (7 thousand cells, 270 million tetrahedra), a larger volume than can be simulated yet, without resorting to mesh replication. An HPC-capable version of the simulation code is being developed which should be able to handle much larger cases.
• Mesh partitions that respect the geometry of cardiac cells We have also started to work on partitioning these meshes, which requires not only to balance the partitions in accordance with the target machine, but also to keep the cardiac cells intact within each partition. A first prototype was written using the Metis library, and aims at being transferred to the OpenCARP software platoform.
• Finite volume methods for the microscopic EMI model We pursued our work 17 within the MICROCARD European project. The Two-point flux approximation (TPFA) finite volume (FV) scheme was generalized naturally to the extracellular-membrane-intracellular (EMI) model on an admissibile orhtogonal mesh. Under strong regularity assumptions, an error estimates was derrived on the electrical potentials and the transmembrne voltages as well in the case of single myocyte. We believe that extending the proof to the case of many cardiac cells is straightforwad, and the convergence analysis might be easily deduced from the existence proof in 33, even with minimal regularity of the data. In fact, the ODEs from the non-standard transimission conditions on the cell membrane, are coupled with large sets of nonlinear equations that require time-integration specific to the EMI. Indeed, The FV method simplifies the implementation of this coupling by introducing the a Dirichlet to Neuman operator to rewrite the problem as an evolution one on the membrane only. We plan to implement the scheme and compare it to finite elements and a boundary elements discretizations on simple 2D test cases. Afterwards, we aim to generalize the scheme to a FV-like method that is more robust with respect to the more general meshes.

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 Fondation EDF to fund a research project about Electrical Impedance Tomography.

10.1 International initiatives

10.2 International research visitors

10.3 European initiatives

10.4 National initiatives

10.5 Regional 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, 195-240HALback 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 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
• 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 2016HALDOIback to textback to text
• 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/S0021999111005122DOIback to text

12.2 Publications of the year

12.3 Cited publications

• 31 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, 62HALDOIback to text
• 32 bookAssessing the credibility of computational modeling through verification and validation: Application to medical devices.2018back to text
• 33 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 textback to text
• 34 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 2016HALback to text
• 35 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
• 36 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 2018HALback to text
• 37 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
• 38 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, 425-428HALback to text
• 39 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, 1115-1140HALback to textback to text
• 40 articleJ.Josselin Duchateau, M.Mark Potse and R.Remi Dubois. Spatially Coherent Activation Maps for Electrocardiographic Imaging.IEEE Transactions on Biomedical Engineering64May 2017, 1149-1156HALDOIback to text
• 41 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 textback to textback to text
• 42 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
• 43 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
• 44 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
• 45 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
• 46 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 2018HALback to text
• 47 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 2022HALback to text
• 48 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
• 49 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
• 50 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
• 51 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 2016HALback to text
• 52 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 2020HALDOIback to text
• 53 articleM.Mark Potse. Scalable and Accurate ECG Simulation for Reaction-Diffusion Models of the Human Heart.Frontiers in Physiology9April 2018, 370HALDOIback to text
• 54 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 textback to text