Keywords
 A3.4. Machine learning and statistics
 A6.1. Methods in mathematical modeling
 A6.3. Computationdata interaction
 A9. Artificial intelligence
 A9.2. Machine learning
 A9.3. Signal analysis
 A9.7. AI algorithmics
 B1. Life sciences
 B1.2. Neuroscience and cognitive science
 B1.2.1. Understanding and simulation of the brain and the nervous system
 B1.2.2. Cognitive science
 B1.2.3. Computational neurosciences
 B2.2.2. Nervous system and endocrinology
 B2.2.6. Neurodegenerative diseases
 B2.5.1. Sensorimotor disabilities
 B2.6.1. Brain imaging
1 Team members, visitors, external collaborators
Research Scientists
 Rachid Deriche [Team leader, INRIA, Senior Researcher, HDR]
 Samuel DeslauriersGauthier [INRIA, Researcher]
 Théodore Papadopoulo [INRIA, Senior Researcher, HDR]
PhD Students
 Yanis Aeschlimann [UNIV COTE D'AZUR, from Oct 2022]
 Joan Belo [INRIA]
 Igor Carrara [UNIV COTE D'AZUR]
 Ivana Kojcic [UNIV COTE D'AZUR, until Jul 2022]
 Côme Le Breton [INRIA, until Nov 2022]
 Sara Sedlar [UNIV COTE D'AZUR]
Interns and Apprentices
 Aymene Bouayed [Aix Marseille Université, Intern, from Feb 2022 until Aug 2022]
 Ludovic Corcos [Université de ClermontFerrand, Intern, from May 2022 until Aug 2022]
 Petru Isan [Hopital Pasteur, Nice, Intern]
 Sarah Mouffok [UNIV COTE D'AZUR, Intern, until Aug 2022]
Administrative Assistant
 Claire Senica [INRIA]
External Collaborator
 Maureen Clerc [INRIA, HDR]
2 Overall objectives
2.1 Presentation
The main objective of Athena is to develop rigorous mathematical models and computational tools for analyzing and modeling the complex Central Nervous System structure and function. These models and tools will help to better understand the structure and the functioning of the human brain and address pressing and challenging clinical and neuroscience questions. Exploring new directions to solve these challenging problems will push forward the stateoftheart in Structural and Functional Computational Brain Connectivity Mapping.
The relationship between brain structure and function is fundamental in neuroscience. Developing computational models and techniques that recover the structural and functional connectivities of the brain in vivo is thus of utmost importance: it will definitely improve the understanding of the brain and its mechanisms. On the basis of our expertise and contributions to the field of computational neuroimaging and in order to have an impact on this field, our research focusses mainly on the structural and functional Imaging of the brain with a particular emphasis on signal and image recording from diffusion Magnetic Resonance Imaging (dMRI), MagnetoEncephalography (MEG) and ElectroEncephalography (EEG).
In order to further increase the impact of our research, we also aim to push our contributions towards some applications related to brain diseases with characteristic abnormalities in the microstructure of brain tissues that are not apparent and cannot be revealed reliably by standard imaging techniques. Diffusion MRI, a non invasive imaging modality based on the measurement of the random thermal movement (diffusion) of water molecules within samples can make visible these colateral damages to the fibers of the brain white matter and can also help in the development of new biomarkers related to the progression of certain types of neurodegenerative disease. Diffusion MRI is the imaging modality that we will primarly consider to recover the structural brain connectivity.
Connectivity represents the network infrastructure of the brain. Electric activity corresponds to communications over this network. MEG and EEG (jointly as M/EEG), two noninvasive techniques, reveal part of the cortical electric activity and are instrumental in better understanding the brain functional connectivity and in diagnosing diseases linked to anomalous brain function  that in some cases structural or other functional MR images do not reveal. MEG and EEG are the imaging modalities that we will primarly consider to recover the functional brain connectivity.
In some CNS injuries (medullar injuries, strokes, AMS), the peripheral nervous system may not be able to execute commands that are issued by the brain. Brain Computer Interfaces (BCI) use brain signals such as measured through EEG, and translate in realtime the electrical activity of the brain in commands to control external devices. While BCI is advocated as a means to communicate and help restore mobility or autonomy for very severe cases of disabled patients, it is also a new tool for interactively probing and training the human brain.
These considerations support the need to do research on new models and computational tools to analyse brain signals and imaging data. Our main objective is to push forward the stateoftheart in Structural and Functional Computational Brain Connectivity Mapping to better understand the structure and function of the brain.
In order to tackle these long term and challenging objectives, our strategy is based on the following road map:
 Develop rigorous mathematical and computational tools for the analysis and interpretation of Diffusion MRI and M/EEG data.
 Improve acquisition and processing techniques and push forward the stateoftheart in Computational brain imaging.
 Use our expertise to address with collaborators clinical and neuroscience questions.
This is implemented through:
 Publications in international conferences and journals dedicated to promoting advances in computational methods for Diffusion MRI and M/EEG analysis and/or use of Diffusion MRI and M/EEG in clinical and neuroscience applications.
 A dense network of collaborations with national as well as international neuroimaging laboratories through which we have access equipment and data and with whom we will jointly contribute to solve common crucial problems of interest.
 Software packages developed to be used in a first stage by our national and international collaborators and then made available to other partners.
3 Research program
3.1 Computational diffusion MRI
Diffusion MRI (dMRI) provides a noninvasive way of estimating invivo CNS fiber structures using the average random thermal movement (diffusion) of water molecules as a probe. It's a relatively recent field of research with a history of roughly three decades. It was introduced in the mid 80's by Le Bihan et al 59, Merboldt et al 64 and Taylor et al 78. As of today, it is the unique noninvasive technique capable of describing the neural connectivity in vivo by quantifying the anisotropic diffusion of water molecules in biological tissues.
Diffusion Tensor Imaging & High Angular Resolution Diffusion Imaging
In dMRI, the acquisition and reconstruction of the diffusion signal allows for the reconstruction of the water molecules displacement probability, known as the Ensemble Average Propagator (EAP) 77, 42. Historically, the first model in dMRI is the 2nd order diffusion tensor (DTI) 39, 38 which assumes the EAP to be Gaussian centered at the origin. DTI (Diffusion Tensor Imaging) has now proved to be extremely useful to study the normal and pathological human brain 60, 50. It has led to many applications in clinical diagnosis of neurological diseases and disorder, neurosciences applications in assessing connectivity of different brain regions, and more recently, therapeutic applications, primarily in neurosurgical planning. An important and very successful application of diffusion MRI has been brain ischemia, following the discovery that water diffusion drops immediately after the onset of an ischemic event, when brain cells undergo swelling through cytotoxic edema.
The increasing clinical importance of diffusion imaging has driven our interest to develop new processing tools for Diffusion Tensor MRI. Because of the complexity of the data, this imaging modality raises a large amount of mathematical and computational challenges. We have therefore developed original and efficient algorithms relying on Riemannian geometry, differential geometry, partial differential equations and front propagation techniques to correctly and efficiently estimate, regularize, segment and process Diffusion Tensor MRI (DTMRI) (see 62 and 61).
In DTI, the Gaussian assumption oversimplifies the diffusion of water molecules. While it is adequate for voxels in which there is only a single fiber orientation (or none), it breaks for voxels in which there are more complex internal structures and limitates the ability of the DTI to describe complex, singular and intricate fiber configurations (Ushape, kissing or crossing fibers). To overcome this limitation, socalled Diffusion Spectrum Imaging (DSI) 81 and High Angular Resolution Diffusion Imaging (HARDI) methods such as Qball imaging 79 and other multitensors and compartment models 74, 76, 57, 56, 71 were developed to resolve the orientationnality of more complicated fiber bundle configurations.
QBall imaging (QBI) has been proven very successful in resolving multiple intravoxel fiber orientations in MR images, thanks to its ability to reconstruct the Orientation Distribution Function (ODF, the probability of diffusion in a given direction). These tools play a central role in our work related to the development of a robust and linear spherical harmonic estimation of the HARDI signal and to our development of a regularized, fast and robust analytical QBI solution that outperforms the stateoftheart ODF numerical technique developed by Tuch 79. Those contributions are fundamental and have already started to impact on the Diffusion MRI, HARDI and QBall Imaging community 49. They are at the core of our probabilistic and deterministic tractography algorithms devised to best exploit the full distribution of the fiber ODF (see 46, 4, 47, 5).
Beyond DTI with high order tensors
High Order Tensors (HOT) models to estimate the diffusion function while overcoming the shortcomings of the 2nd order tensor model have also been proposed such as the Generalized Diffusion Tensor Imaging (GDTI) model developed by Ozarslan et al 69, 70 or 4th order Tensor Model 37. For more details, we refer the reader to our articles in 53, 74 where we review HOT models and to our articles in 61, coauthored with some of our close collaborators, where we review recent mathematical models and computational methods for the processing of Diffusion Magnetic Resonance Images, including stateoftheart reconstruction of diffusion models, cerebral white matter connectivity analysis, and segmentation techniques. We also worked on Diffusion Kurtosis Imaging (DKI), of great interest for the company Olea Medical. Indeed, DKI is fastly gaining popularity in the domain for characterizing the diffusion propagator or EAP by its deviation from Gaussianity. Hence it is an important clinical tool for characterizing the whitematter's integrity with biomarkers derived from the 3D 4th order kurtosis tensor (KT) 55.
All these powerful techniques are of utmost importance to acquire a better understanding of the CNS mechanisms and have helped to efficiently tackle and solve a number of important and challenging problems 56, 57. They have also opened up a landscape of extremely exciting research fields for medicine and neuroscience. Hence, due to the complexity of the CNS data and as the magnetic field strength of scanners increases, as the strength and speed of gradients increase and as new acquisition techniques appear 3, these imaging modalities raise a large amount of mathematical and computational challenges at the core of the research we develop at Athena 54, 74.
Improving dMRI acquisitions
One of the most important challenges in diffusion imaging is to improve acquisition schemes and analyse approaches to optimally acquire and accurately represent diffusion profiles in a clinically feasible scanning time. Indeed, a very important and open problem in Diffusion MRI is related to the fact that HARDI scans generally require many times more diffusion gradient than traditional diffusion MRI scan times. This comes at the price of longer scans, which can be problematic for children and people with certain diseases. Patients are usually unable to tolerate long scans and excessive motion of the patient during the acquisition process can force a scan to be aborted or produce useless diffusion MRI images. We have developed novel methods for the acquisition and the processing of diffusion magnetic resonance images, to efficiently provide, with just few measurements, new insights into the structure and anatomy of the brain white matter in vivo.
First, we contributed developing realtime QBall Imaging reconstruction algorithm based on the Kalman filter 45. Then, we started to explore the utility of Compressive Sensing methods to enable faster acquisition of dMRI data by reducing the number of measurements, while maintaining a high quality for the results. Compressed Sensing (CS) is a relatively recent technique which has been proved to accurately reconstruct sparse signals from undersampled measurements acquired below the ShannonNyquist rate 65.
We have also contributed to the reconstruction important features of the diffusion signal as the orientation distribution function and the ensemble average propagator, with a special focus on clinical setting in particular for single and multiple Qshell experiments. Compressive sensing as well as the parametric reconstruction of the diffusion signal in a continuous basis of functions such as the Spherical Polar Fourier basis, have been proved through our contributions to be very useful for deriving simple and analytical closed formulae for many important dMRI features, which can be estimated via a reduced number of measurements 65, 43, 44.
We have also contributed to design optimal acquisition schemes for single and multiple Qshell experiments. In particular, the method proposed in 3 helps generate sampling schemes with optimal angular coverage for multishell acquisitions. The cost function we proposed is an extension of the electrostatic repulsion to multishell and can be used to create acquisition schemes with incremental angular distribution, compatible with prematurely stopped scans. Compared to more commonly used radial sampling, our method improves the angular resolution, as well as fiber crossing discrimination. The optimal sampling schemes, freely available for download, have been selected for use in the HCP (Human Connectome Project).
We think that such kind of contributions open new perspectives for dMRI applications including, for example, tractography where the improved characterization of the fiber orientations is likely to greatly and quickly help tracking through regions with and/or without crossing fibers 52.
dMRI modelling, tissue microstructures features recovery & applications
The dMRI signal is highly complex, hence, the mathematical tools required for processing it have to be commensurate in their complexity. Overall, these last years have seen an explosion of intensive scientific research which has vastly improved and literally changed the face of dMRI. In terms of dMRI models, two trends are clearly visible today: the parametric approaches which attempt to build models of the tissue to explain the signal based on modelparameters such as CHARMED 33, AxCaliber 34 and NODDI 82 to cite but a few, and the nonparametric approaches, which attempt to describe the signal in useful but generic functional bases such as the Spherical Polar Fourier (SPF) basis 36, 35, the Solid Harmonic (SoH) basis 48, the Simple Harmonic Oscillator based Reconstruction and Estimation (SHORE) basis 67 and more recent Mean Apparent Propagator or MAPMRI basis 68.
We propose to investigate the feasibility of using our new models and methods to measure extremely important biological tissue microstructure quantities such as axonal radius and density in white matter. These parameters could indeed provide new insight to better understand the brain's architecture and more importantly could also provide new imaging biomarkers to characterize certain neurodegenerative diseases. This challenging scientific problem, when solved, will lead to direct measurements of important microstructural features that will be integrated in our analysis to provide much greater insight into disease mechanisms, recovery and development. These new microstructural parameters will open the road to go far beyond the limitations of the more simple biomarkers derived from DTI that are clinically used to this date – such as MD (Mean Diffusivity) and FA (Fractional Anisotropy) which are known to be extremely sensitive to confounding factors such as partial volume and axonal dispersion, nonspecific and not able to capture any subtle effects that might be early indicators of diseases 8.
Towards microstructural based tractography
In order to go far beyond traditional fibertracking techniques, we believe that first order information, i.e. fiber orientations, has to be superseeded by second and third order information, such as microstructure details, to improve tractography. However, many of these higher order information methods are relatively new or unexplored and tractography algorithms based on these high order based methods have to be conceived and designed. In this aim, we propose to work with multipleshells to reconstruct the Ensemble Average Propagator (EAP), which represents the whole 3D diffusion process and use the possibility it offers to deduce valuable insights on the microstructural properties of the white matter. Indeed, from a reconstructed EAP one can compute the angular features of the diffusion in an diffusion Orientation Distribution Function (ODF), providing insight in axon orientation, calculate properties of the entire diffusion in a voxel such as the Mean Squared Diffusivity (MSD) and ReturnToOrigin Probability (RTOP), or come forth with biomarkers detailing diffusion along a particular white matter bundle direction such as the ReturntoAxis or ReturntoPlane Probability (RTAP or RTPP). This opens the way to a groundbreaking computational and unified framework for tractography based on EAP and microstructure features 10. Using additional a priori anatomical and/or functional information, we could also constrain the tractography algorithm to start and terminate the streamlines only at valid processing areas of the brain.
This development of a computational and unified framework for tractography, based on EAP, microstructure and a priori anatomical and/or functional features, will open new perspectives in tractography, paving the way to a new generation of realistic and biologically plausible algorithms able to deal with intricate configurations of white matter fibers and to provide an exquisite and intrinsic brain connectivity quantification.
Going beyond the stateoftheart dMRI
Although great improvements in dMRI modelling have been made during the last years, major problems are still unsolved and improvements are still required to better acquire dMRI data, better understand the biophysics of the signal formation, go beyond classical second order tensors invariants and recover high order invariants, recover robust and intrinsic microstructure features, identify biophysically important biomarkers, improve tractography and in fine contribute to reconstruct the complete map of the cerebral connections, the connectome, as well as to better understand brain structure and function.
Therefore, there is still considerable room for improvement when it comes to the concepts and tools able to efficiently acquire, process and analyze the complex structure of dMRI data. Develop groundbreaking dMRI tools and models for brain connectomics is one of the major objective we would like to achieve in order to take dMRI from the benchside to the bedside and lead to a decisive advance and breakthrough in this field.
3.2 MEG and EEG
Electroencephalography (EEG) and Magnetoencephalography (MEG) are two noninvasive techniques for measuring (part of) the electrical activity of the brain. While EEG is an old technique (Hans Berger, a German neuropsychiatrist, measured the first human EEG in 1929), MEG is a rather new one: the first measurements of the magnetic field generated by the electrophysiological activity of the brain were made in 1968 at MIT by D. Cohen. Nowadays, EEG is relatively inexpensive and is routinely used to detect and qualify neural activities (epilepsy detection and characterisation, neural disorder qualification, BCI, ...). MEG is, comparatively, much more expensive as SQUIDS (Superconducting QUantum Interference Device) only operate under very challenging conditions (at liquid helium temperature) and as a specially shielded room must be used to separate the signal of interest from the ambient noise. However, as it reveals a complementary vision to that of EEG and as it is less sensitive to the head structure, it also bears great hopes and an increasing number of MEG machines are being installed throughout the world. Inria and Odyssée/Athena have participated in the acquisition of one such machine installed in the hospital "La Timone" in Marseille.
MEG and EEG can be measured simultaneously (M/EEG) and reveal complementary properties of the electrical fields. The two techniques have temporal resolutions of about the millisecond, which is the typical granularity of the measurable electrical phenomena that arise within the brain. This high temporal resolution makes MEG and EEG attractive for the functional study of the brain. The spatial resolution, on the contrary, is somewhat poor as only a few hundred data points can be acquired simultaneously (about 300400 for MEG and up to 256 for EEG). MEG and EEG are somewhat complementary with fMRI (Functional MRI) and SPECT (SinglePhoton Emission Computed Tomography) in that those provide a very good spatial resolution but a rather poor temporal resolution (of the order of a second for fMRI and a minute for SPECT). Also, contrarily to fMRI, which “only” measures an haemodynamic response linked to the metabolic demand, MEG and EEG measure a direct consequence of the electrical activity of the brain: it is acknowledged that the signals measured by MEG and EEG correspond to the variations of the postsynaptic potentials of the pyramidal cells in the cortex. Pyramidal neurons compose approximately 80% of the neurons of the cortex, and it requires at least about 50,000 active such neurons to generate some measurable signal.
While the few hundred temporal curves obtained using M/EEG have a clear clinical interest, they only provide partial information on the localisation of the sources of the activity (as the measurements are made on or outside of the head). Thus the practical use of M/EEG data raises various problems that are at the core of the Athena research in this topic:
 First, as acquisition is continuous and is run at a rate up to 1kHz, the amount of data generated by each experiment is huge. Data selection and reduction (finding relevant time blocks or frequency bands) and preprocessing (removing artifacts, enhancing the signal to noise ratio, ...) are largely done manually at present. Making a better and more systematic use of the measurements is an important step to optimally exploit the M/EEG data 2.
 With a proper model of the head and of the sources of brain electromagnetic activity, it is possible to simulate the electrical propagation and reconstruct sources that can explain the measured signal. Proposing better models 58, 12 and means to calibrate them 80 so as to have better reconstructions are other important aims of our work.
 Finally, we wish to exploit the temporal resolution of M/EEG and to apply the various methods we have developed to better understand some aspects of the brain functioning, and/or to extract more subtle information out of the measurements. This is of interest not only as a cognitive goal, but it also serves the purpose of validating our algorithms and can lead to the use of such methods in the field of Brain Computer Interfaces. To be able to conduct such kind of experiments, an EEG lab has been set up at Athena.
3.3 Combined M/EEG and dMRI
dMRI provides a global and systematic view of the longrange structural connectivity within the whole brain. In particular, it allows the recovery of the fiber structure of the white matter which can be considered as the wiring connections between distant cortical areas. These white matter based tractograms are analyzed, e.g. to explore the differences in structural connectivity between pathological and normal populations. Moreover, as a byproduct, the tractograms can be processed to reveal the nodes of the brain networks, i.e. by segregating together gray matter that share similar connections to the rest of the white matter. But dMRI does not provide information on:
 the corticocortical pathways (not passing through white matter) and to some extent, on the shortrange connections in the white matter,
 the actual use of connections over time during a given brain activity.
On the opposite, M/EEG measures brain activation over time and provides, after source reconstruction (solving the socalled inverse problem of source reconstruction), time courses of the activity of the cortical areas. Unfortunately, deep brain structures have very little contribution to M/EEG measurements and are thus difficult to analyze. Consequently, M/EEG reveals information about the nodes of the network, but in a more blurry (because of the inverse problem) and fragmented view than dMRI (since it can only reveal brain areas measurable in M/EEG whose activity varies during the experimental protocol). Given its very high temporal resolution, the signal of reconstructed sources can be processed to reveal the functional connectivity between the nodes 75.
While dMRI and M/EEG have been the object of considerable research separately, there have been very few studies on combining the information they provide. Some existing studies deal with the localization of abnormal MEG signals, particularly in the case of epilepsy, and on studying the white matter fibers near the detected abnormal source 63, 66, but to our knowledge there are very few studies merging data coming both from M/EEG and dMRI at the analysis level 72, 51, 40, 73.
Combining the structural and functional information provided by dMRI and M/EEG is a difficult problem as the spatial and temporal resolutions of the two types of measures are extremely different. Still, combining the measurements obtained by these two types of techniques has the great potential of providing a detailed view both in space and time of the functioning brain at a macroscopic level. Consequently, it is a timely and extremely important objective to develop innovative computational tools and models that advance the dMRI and M/EEG stateoftheart and combine these imaging modalities to build a comprehensive dynamical structuralfunctional brain connectivity network to be exploited in brain connectivities diseases.
The CoBCoM ERC project aimed to develop a joint dynamical structuralfunctional brain connectivity network built on advanced and integrated dMRI and M/EEG groundbreaking methods. To this end, CoBCoM develops new generation of computational dMRI and M/EEG models and methods for identifying and characterizing the connectivities on which the joint network is built. The CoBCoM URL summarizes the contributions and publications, some of which given also via Videos Lectures.
The 3IA UCA Chair AIbased Computational Brain Connectomics project aims to reconstruct and analyse the network of neural connections of the brain, called the connectome via a computational brain connectomics framework based on groundbreaking AI algorithms and machine learning tools to gain insight into brain architecture, functioning and neurodegenerative diseases. The avalanche of big data required to reconstruct the connectome and the study of the high complexity of structural and functional interactions within the connectome clearly position brain connectomics as a big data problem where AI & machine learning in particular, represent a very promising trend, as recently demonstrated in computer vision and in some biomedical image datadriven analysis. Partly related to the ERC Advanced Grant CoBCoM, this project aims to construct networks specifically built on new generation of AI algorithms and machine learning tools to reconstruct structural and functional connectomes using advanced and integrated diffusion MRI, Electro and MagnetoEncephalography (EEG & MEG) methods.
Capitalizing on the strengths of dMRI & M/EEG and building on the biophysical and mathematical foundations of our models, CoBCoM and the 3IA UCA Chair AIbased Computational Brain Connectomics contribute to create a joint and solid network which will be exploited to identify and characterize white matter abnormalities in some highimpact brain diseases such as Multiple Sclerosis (MS), Epilepsy and mild Traumatic Brain Injury (mTBI).
4 Application domains
4.1 Applications of diffusion MRI
Clinical domain: Diagnosis of neurological disorder
Various examples of CNS diseases as Alzheimer's and Parkinson's diseases and others like multiple sclerosis, traumatic brain injury and schizophrenia have characteristic abnormalities in the microstructure of brain tissues that are not apparent and cannot be revealed reliably by standard imaging techniques. Diffusion MRI can make visible these colateral damages to the fibers of the CNS white matter that connect different brain regions.
4.2 Applications of M/EEG
Clinical domain: Diagnosis of neurological disorders
The dream of all M/EEG researchers is to alleviate the need for invasive recordings (electrocorticograms or intracerebral electrodes), which are often necessary prior to brain surgery, in order to precisely locate both pathological and vital functional areas. We are involved in this quest, particularly through our collaborations with the La Timone hospital in Marseille.
Subtopics include:
 Diagnosis of neurological disorders such as epilepsy, schizophrenia, tinnitus, ...
 Presurgical planning of brain surgery.
 Collaboration with the Institut de Neurosciences des Systèmes in Marseille on these topics.
Cognitive research
 Aims at better understanding the brain spatiotemporal organisation.
 Collaboration with laboratories of cognitive neuroscience in order to develop methods that suit their needs for sophisticated data analysis.
Brain Computer Interfaces (BCI) aim to allow direct control of external devices using brain signals such as measured through EEG. In our project, BCI can be seen as an application of EEG processing techniques, but also as an object of fundamental and applied research as they open the way for more dynamical and active brain cognitive protocols.
We develop a research collaboration with the eemagine/ANTNeuro company. We collaborate with Nice University Hospital on the usage of BCIbased communication for ALS1 patients.
5 Highlights of the year
The Athena team reached the maximum longevity of an Inria ProjectTeam of 12 years in 2022. Thus, despite a very positive final evaluation, it was ended at December 31st, 2022. It therefore seems appropriate to summarize some of its activity in a few words. Overall, since its inception on July 2010 and up to December 2022, a total of 29 PhD’s students have defended their thesis, 115 journal papers have been published, and 233 conference articles have been presented.
The Cronos projectteam, which members are Théodore Papadopoulo (as team leader), Samuel DeslauriersGauthier, and Rachid Deriche (emeritus) started on December, 1st, 2022, and took over Athena to go further into computational modelling of brain dynamical networks.
6 New software and platforms
6.1 New software
6.1.1 OpenMEEG

Keywords:
Health, Neuroimaging, Medical imaging

Scientific Description:
OpenMEEG provides a symmetric boundary element method (BEM) implementation for solving the forward problem of electromagnetic propagation over heterogeneous media made of several domains of homogeneous and isotropic conductivities. OpenMEEG works for the quasistatic regime (frequencies < 100Hz and medium diameter < 1m).

Functional Description:
OpenMEEG provides stateofthe art tools for modelling bioelectromagnetic propagation in the quasistatic regime. It is based on the symmetric BEM for the EEG/MEG forward problem, with a distributed source model. OpenMEEG has also been used to model the forward problem of ECoG, for modelling nerves or the cochlea. OpenMEEG is a free, open software written in C++ with python bindings. OpenMEEG is used through a command line interface, but is also interfaced in graphical interfaces such as BrainStorm, FieldTrip or SPM.

Release Contributions:
OpenMEEG has had a large update including notably the parallelisation of some operators and bug corrections. The new version allows in addition the use of nonnested domains.

News of the Year:
The python interface of OpenMEEG has been improved and now allows to pass python data structures (meshes, conductivities) to characterize the gain matrices to be calculated without going through files. This is done to ease a future integration of OpenMEEG in MNEpython. A code factorization also took place to allow in the long term to facilitate the integration in OpenMEEG of the work of K. Maksymenko on the efficient calculation of gain matrices for several conductivity values. This work has not yet been released.
 URL:
 Publications:

Contact:
Théodore Papadopoulo

Participants:
Alexandre Gramfort, Emmanuel Olivi, Geoffray Adde, Jan Kybic, Kai Dang, Maureen Clerc Gallagher, Perrine Landreau, Renaud Keriven, Théodore Papadopoulo
6.1.2 BCIVIZAPP

Name:
BCI visual applications

Keywords:
Health, BrainComputer Interface, GUI (Graphical User Interface)

Scientific Description:
BciVizapp is a library that allows (in interaction with OpenViBE) to build BCI (Brain Computer Interfaces) applications based on the P300 speller principle. BciVizapp provides a library that allows you to create the BCI's stimulation part as part of the Qt toolkit. Being able to use a standard toolkit to make BCI applications is a strong BciVizapp originality. Indeed, in general the use of such toolkits is prohibited by the need for a very precise control of the display timings, which generally eliminates highlevel graphic toolkits such as Qt.

Functional Description:
BCIVIZAPP includes a virtual keyboard for typing text, a photodiode monitoring application for checking timing issues. It communicates with the OpenViBE acquisition server for signal acquisition and with the OpenViBE designer for signal processing. The configuration is performed through a wizard.
This software is a new version following the CoAdapt P300 stimulator software.

News of the Year:
BciVizapp is undergoing a deep transmutation following, among other things, the impulse of the SED of Inria Sophia Antipolis Méditerranée in the ADT BciBrowser. Signal processing which was once based only on OpenViBE can now be done internally by the software. This has led to the development of different substitutable "backends" which can do this processing. In 2022, this software has finalized the change to a new database format that logs all parameters to ease the reproducibility of results. It also gained a possibility to replay old P300 datasets to reproduce results and evaluate performance changes in various conditions (software changes, electrode selection, ...). Tools to deal with dry electrodes EEG caps were also added and will be used in a forthcoming P300 speller acquisition campaign. This software basis has also received improvements from Côme Le Breton to implement a neurofeedback protocol aiming at doing a study on epileptic patient with Hospital La Timone in Marseille.

Contact:
Théodore Papadopoulo

Participants:
Nathanaël Foy, Romain Lacroix, Maureen Clerc Gallagher, Théodore Papadopoulo, Yang Ji, Come Le Breton
6.1.3 A4D fMRI

Name:
Anisotropic 4D filtering of functional MRI

Keywords:
FMRI, Denoising, Anisotropic

Scientific Description:
Based on the idea that large image variations should be preserved as they occur during brain activations, whereas small variations considered as noise should be removed, the A4DfMRI applies an anisotropic regularization, thus recovering the location and the duration of brain activations.

Functional Description:
A4DfMRI provides a simple command line that takes as input an fMRI image in Nifti format and denoises it. The output is saved in a new Nifti file.

Release Contributions:
This is the first version of the software which implements the A4DfMRI algorighm. It allows the denoising of arbitrary fMRI acquisition with only a few parameters to set. Two implementations are provided, one relying only on numpy and one on tensorflow.

News of the Year:
This is the first version of the software which implements the A4DfMRI algorighm. It allows the denoising of arbitrary fMRI acquisition with only a few parameters to set. Two implementations are provided, one relying only on numpy and one on tensorflow.
 Publication:

Authors:
Isa Costantini, Samuel DeslauriersGauthier

Contact:
Samuel DeslauriersGauthier
7 New results
7.1 Computational Diffusion MRI
A Riemannian revisiting of structure–function mapping based on eigenmodes
Participants: Samuel DeslauriersGauthier, Mauro Zucchelli, Hiba Laghrissi, Rachid Deriche.
Understanding the link between brain structure and function may not only improve our knowledge of brain organization, but also lead to better quantification of pathology. To quantify this link, recent studies have attempted to predict the brain's functional connectivity from its structural connectivity. However, functional connectivity matrices live in the Riemannian manifold of the symmetric positive definite space and a specific attention must be paid to operate on this appropriate space. In this work we investigated the implications of using a distance based on an affine invariant Riemannian metric in the context of structure–function mapping. Specifically, we revisit previously proposed structure–function mappings based on eigendecomposition and test them on 100 healthy subjects from the Human Connectome Project using this adapted notion of distance. First, we show that using this Riemannian distance significantly alters the notion of similarity between subjects from a functional point of view. We also show that using this distance improves the correlation between the structural and functional similarity of different subjects. Finally, by using a distance appropriate to this manifold, we demonstrate the importance of mapping function from structure under the Riemannian manifold and show in particular that it is possible to outperform the group average and the so–called glass ceiling on the performance of mappings based on eigenmodes.
This work has been published in 15.
CNN and diffusion MRI’s 4th degree rotational invariants for Alzheimer’s disease identification
Participants: Aymene Mohammed Bouayed, Samuel DeslauriersGauthier, Mauro Zucchelli, Rachid Deriche.
Recently, a general analytical formula to extract all the Rotation Invariant Features (RIFs) of the diffusion Magnetic Resonance Imaging (dMRI) signal was proposed. The features extracted using this formula represent a generalisation of the usual second degree RIFs such as the mean diffusivity. In this work, we study the usefulness of all the 12 algebraically independent RIFs extracted from 4th degree spherical harmonics that model the dMRI signal per voxel in the context of Alzheimer Disease (AD) identification. To do so, and since we are working with imbalanced data sets, we first introduce a nonlinear metric to evaluate the performance of the models, the (Bscore). This proposed metric allows high score only when both classes are distinguished correctly. We use the proposed metric in conjunction with a deep Convolutional Neural Network that operates on subject slices to identify if a subject has AD or not. We find that microstructure information communicated by RIFs is indeed useful to AD identification and that not all RIFs are equivalently useful. We also identify the two best RIF combinations for the ADNISIEMENS and the ADNIGE medical data sets respectively. The combination of these RIFs achieves a classification Bscore of 73.62% and 72.31% on the previous data sets respectively. We note the importance of combining high degree RIFs with low degree ones to improve the classification performance.
This work has been published in 20.
DORIS: A diffusion MRIbased 10 tissue class deep learning segmentation algorithm tailored to improve anatomicallyconstrained tractography
Participants: Guillaume Theaud [Université de Sherbrooke], Manon Edde [Université de Sherbrooke], Mathieu Dumont [Imeka Solutions, Sherbrooke], Clement Zotti [Imeka Solutions, Sherbrooke], Mauro Zucchelli, Samuel DeslauriersGauthier, PierreMarc Jodoin [Université de Sherbrooke], Maxime Descoteaux [Université de Sherbrooke], Rachid Deriche.
Modern tractography algorithms such as anatomicallyconstrained tractography (ACT) are based on segmentation maps of white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF). These maps are generally estimated from a T1weighted (T1w) image and then registered in diffusion weighted images (DWI) space. Registration of T1w to diffusion space and partial volume estimation are challenging and rarely voxelperfect. Diffusionbased segmentation would, thus, potentially allow not to have higher quality anatomical priors injected in the tractography process. On the other hand, even if FAbased tractography is possible without T1 registration, the literature shows that this technique suffers from multiple issues such as holes in the tracking mask and a high proportion of generated broken and anatomically implausible streamlines. Therefore, there is an important need for a tissue segmentation algorithm that works directly in the native diffusion space. We propose DORIS, a DWIbased deep learning segmentation algorithm. DORIS outputs 10 different tissue classes including WM, GM, CSF, ventricles, and 6 other subcortical structures (putamen, pallidum, hippocampus, caudate, amygdala, and thalamus). DORIS was trained and validated on a wide range of subjects, including 1,000 individuals from 22 to 90 years old from clinical and research DWI acquisitions, from 5 public databases. In the absence of a “true” ground truth in diffusion space, DORIS used a silver standard strategy from Freesurfer output registered onto the DWI. This strategy is extensively evaluated and discussed in the current study. Segmentation maps provided by DORIS are quantitatively compared to Freesurfer and FSLfast and the impacts on tractography are evaluated. Overall, we show that DORIS is fast, accurate, and reproducible and that DORISbased tractograms produce bundles with a longer mean length and fewer anatomically implausible streamlines.
This work has been published in 18.
Localization of brain microstructure changes associated with Alzheimer’s disease using class activation maps
Participants: Aymene Mohammed Bouayed, Samuel DeslauriersGauthier, Rachid Deriche.
Recently, we have proposed a general analytical formula to extract all of the 4th order Rotation Invariant Features (RIFs) from diffusion Magnetic Resonance Imaging (dMRI) data. These invariants have been shown to be linked to the underling brain microstructure and were recently used to identify Alzheimer Disease (AD) patients. While these features indeed contain information that is useful to the identification of AD, the classification is based on the analysis of the whole brain volume and does not pinpoint local changes associated with AD. In this work, we propose to use explainable AI tools, namely Class Activation Maps (CAMs), to localize brain microstructure changes associated with AD.
This work has been published in 27.
Hyperbolic model captures temporal small worldness of brain dynamics
Participants: Aurora Rossi [COATI, Inria], Pierluigi Crescenzi [COATI, Inria], Samuel DeslaurierGauthier, Emanuele Natale [COATI, Inria].
Brain activity can be represented as a complex network This work is about looking for the best model that simulates the functional connectivity of the brain and can be used as a null model. We show that the Hyperbolic model not only is close to real data but it has the same behaviour.
This work has been published in 31
Rotation invariant features for Alzheimer’s disease identification using convolutional neural networks
Participants: Aymene Mohammed Bouayed, Samuel DeslauriersGauthier, Rachid Deriche.
Rotation Invariant Features (RIFs) extracted from dMRI scans represent a generalisation of the usually used 2nd order invariants such as Fractional Anisotropy (FA) and Mean Diffusivity (MD). This work studies the usefulness all of the 12 algebraically independent RIFs extracted from 4th order Spherical Harmonics in the context of Alzheimer Disease (AD) identification. To do so, we introduce a fair metric (Bscore) that we use to evaluate the proposed deep Convolutional Neural Network (Subject CNN) which operates on subject slices to classify the whole subject while avoiding overfitting. On the ADNISIEMENS1 data set that contains 46 AD and 352 Normal Connectivity (NC) subjects respectively, we observe that the 12 algebraically independent 4th order RIFs are not equivalently useful to the classification task. A particular combination of a low degree RIF with a high degree one achieves the best performance of 82.67% Bscore and 84.88% accuracy on this data set. Also, the generated 3D Class Activation Maps (CAMs) show that to classify a subject as AD or NC the model focuses on the value of the RIFs in the white matter around the ventricul
This work has been published in 28.
Graph alignment exploiting the spatial organisation improves the similarity of brain networks
Participants: Anna Calissano [Epione inria], Samuel DeslauriersGauthier, Xavier Pennec [Epione, Inria], Theo Papadopoulo.
Every brain is unique, having its structural and functional organisation shaped by both genetic and environmental factors over the course of its development. Brain image studies tend to produce results by averaging across a group of subjects, under a common assumption that it is possible to subdivide the cortex into homogeneous areas while maintaining a correspondence across subjects. This paper questions such assumption: can the structural and functional properties of a specific region of an atlas be assumed to be the same across subjects? This question is addressed by looking at the network representation of the brain, with nodes corresponding to brain regions and edges to their structural relationships. We perform graph matching on a set of control patients and on parcellations of different granularity to understand which is the connectivity misalignment between regions. The graph matching is unsupervised and reveals interesting insight on local misalignment of brain regions across subjects
This work has been published in 25.
A revisiting of structurefunction mapping using graph convolutional networks
Participants: Sarah Mouffok, Samuel DeslauriersGauthier, Rachid Deriche.
Being able to infer the function of a brain given the knowledge of its structure is valuable in order to understand the impact of structural alterations caused by injuries and/or diseases on the function of the brain. Indeed, devising a mapping from brain structural connectivity (SC) to brain functional connectivity (FC) is motivated by the thought that structure is the physical support on which function operates. Consequently, using supervised learning, we attempt to predict a subject’s FC matrix from their SC matrix. This work has been performed within the framework of Mouffok's internship’s and extends our previous work in which an autoencoder architecture is used to perform the aforementioned task. We have extended our previous work and altered the GCN architecture in multiple ways. First, using separate weight sets for the secondorder Chebyshev polynomial leads to small improvements in performances as quantified by the MSE, and a nonnegligible increase in Pearson correlation. Second, this separation of weight sets enabled the usage of higher Chebyshev polynomial orders. Increasing the order of the Chebyshev polynomial does not increase performances. However, through the observation of the first order Chebyshev Polynomial that makes no use of SC information and still yields good results, we found out that the estimations of the network were in fact very close to the FC matrix estimated by the reference estimator, both in MSE and Pearson Correlation, leading to the conclusion that the network is converging towards the mean. Moreover, using the Affine Invariant Riemannian Metric on Symmetric Positive Definite matrices does not lead to an estimation of the Frechet Mean, but it does output estimations that are correlated to the real functional connectivity almost as much as the mean’s correlation to real functional connectivity. The current architecture does not seem to be appropriate for this loss, as the loss seems to reach a local minimal value early on in the learning.
This work has been published in 26.
7.2 Unveiling brain activity using M/EEG and its applications to Brain Computer Interfaces
Embedding neurophysiological signals
Participants: Pierre Guetschel [University of Freiburg], Théodore Papadopoulo, Michael Tangermann [University of Freiburg].
Neurophysiological timeseries recordings of brain activity like the electroencephalogram (EEG) or local field potentials can be decoded by machine learning models in order to either control an application, e.g., for communication or rehabilitation after stroke, or to passively monitor the ongoing brain state of the subject, e.g., in a demanding work environment. A typical decoding challenge faced by a braincomputer interface (BCI) is the small dataset size compared to other domains of machine learning like computer vision or natural language processing. The possibilities to tackle classification or regression problems in BCI are to either train a regular model on the available small training data sets or through transfer learning, which utilizes data from other sessions, subjects, or even datasets to train a model. Transfer learning is nontrivial because of the nonstationary of EEG signals between subjects but also within subjects. This variability calls for explicit calibration phases at the start of every session, before BCI applications can be used online. In this study, we present arguments to BCI researchers to encourage the use of embeddings for EEG decoding. In particular, we introduce a simple domain adaptation technique involving both deep learning (when learning the embeddings from the source data) and classical machine learning (for fast calibration on the target data). This technique allows us to learn embeddings across subjects, which deliver a generalized data representation. These can then be fed into subjectspecific classifiers in order to minimize their need for calibration data. We conducted offline experiments on the 14 subjects of the High Gamma EEGBCI Dataset [1]. Embedding functions were obtained by training EEGNet [2] using a leaveonesubjectout (LOSO) protocol, and the embedding vectors were classified by the logistic regression algorithm. Our pipeline was compared to two baseline approaches: EEGNet without subjectspecific calibration and the standard FBCSP pipeline in a withinsubject training. We observed that the representations learned by the embedding functions were indeed nonstationary across subjects, justifying the need for an additional subjectspecific calibration. We also observed that the subjectspecific calibration indeed improved the score. Finally, our data suggest, that building upon embeddings requires fewer individual calibration data than the FBCSP baseline to reach satisfactory scores.
This work has been published in 19.
Current distribution of distributed allpolar cochlear implant stimulation mode measured insitu
Participants: Pierre Stahl [Oticon Medical], Kai Dang, Clair Vandersteen [Nice University Hospital], Nicolas Guevara [Nice University Hospital], Maureen Clerc.
Oticon Medical cochlear implants use a stimulation mode called Distributed AllPolar (DAP) that connects all nonstimulating available intracochlear electrodes and an extracochlear reference electrode. It results in a complex distribution of current that is yet undescribed. The present study aims at providing a first characterization of this current distribution. A Neuro Zti was modified to allow the measurement of current returning to each electrode during a DAP stimulation and was implanted in an exvivo human head. Maps of distributed current were then created for different stimulation conditions with different charge levels. Results show that, on average, about 20% of current returns to the extracochlear reference electrode, while the remaining 80% is distributed between intracochlear electrodes. The position of the stimulating electrode changed this ratio, and about 10% more current to the extracochlear return in case of the first 3 basal electrodes than for apical and mid position electrodes was observed. Increasing the charge level led to small but significant change in the ratio, and about 4% more current to the extracochlear return was measured when increasing the charge level from 11.7 to 70 nC. Further research is needed to show if DAP yields better speech understanding than other stimulation modes.
This work has been published in 17.
Auditory attention analysis during music listening: Making the link between machine learning, electrophysiology and cognition
Participants: Joan Belo, Maureen Clerc, Daniele Schon [CNRS, INS, AixMarseille Université].
This part describes the work performed within the framework of Joan Belo's PhD defended on Dec. 5th, 2022.
The ability to focus attention on a particular sound in a noisy environment is crucial for daytoday life. But this ability is undermined in people with cochlear implants. One solution to this problem would be to create a new type of device that could selectively amplify the source of interest. This could be achieved by using a recent method called Auditory Attention Detection, which allows to detect which source within a set of multiple concurrent sources an individual is attending to, based solely on brain activity. However, the performance of this technique varies greatly from one individual to another, partly because of physiological factors but possibly also because of cognitive and behavioral ones. The aim of this PhD work is therefore to investigate how specific cognitive and behavioral factors may influence the performance of auditory attention detection and more specifically in a natural music listening context.
This work has been published in 21.
Usability of phase synchrony neuromarkers in neurofeedback protocols for epileptic seizures reduction
Participants: Côme Le Breton, Théodore Papadopoulo, Maureen Clerc.
This part describes the work performed within the framework of Côme Lebreton's PhD defended on Oct. 18th, 2022. A video of the PhD defense is available via the following YouTube link
The brain is an organ that oversees many vital functions. Despite its fascinating complexity associated to its incredible consistency, failures can occur and have severe consequences such as in epilepsy disorders. Major functions in the brain are enabled through the oscillatory activity of neuronal assemblies. These oscillations occur at different rhythms, over different regions, depending on the mental task. They can be described by two quantities: their amplitude and their phase. In particular, the phase characterizes over time the oscillatory pattern of a neuronal assembly. Phase synchrony measures the similarity between two oscillations by capturing the stability of a phase relationship between neuronal assembly activities and informs on a functional relationship between these assemblies. While synchronization between the oscillatory activities of brain regions is presented as a necessary coordinator between brain areas, its excess, such as in epilepsy, causes dramatic outcomes, indicating that a balance is necessary. For these reasons and others detailed in this manuscript, this work focuses on the realtime modulation of phase synchrony between distinct brain areas by means of electroencephalography (EEG) to offer new treatment opportunities for certain epileptic disorders.
In a first contribution, focusing on the retrieval of the phase from EEG signals, the Morlet wavelet transforms of sinusoids, weighted sums of sinusoids, oscillating bursts and overlapping oscillating bursts are formally derived. Simplifications are proposed to allow for compact expressions of the phase.Their properties and parameters are discussed.These derivations notably show that for close frequency components with similar energy the phase is not trustworthy.They also show that for too close bursts, the phase cannot be reliably recovered. Nonetheless, in reasonable and practical conditions, the recovery based on the Morlet Wavelet transform of the properties of alpha bursts (amplitude and phase) is attempted and provides satisfactory preliminary results on selected real data. The second contribution is an attempt to reproduce a study showing the potential of phase synchrony in differentiating between epileptic and healthy brains with statistical improvements to handle highly correlated data, inherent to EEG and phase synchrony measures. Original strategies to correct for the biases are proposed and detailed. Contrarily to what was published, the mean phase coherence is shown to be generally higher in temporal lobe epilepsy patients than in controls. While adapting the statistical analysis moderated the results, it did not overturn the conclusions. In a third contribution, an EEG dataset of resting states and simple tasks was acquired on healthy subjects to search for trainable phase synchrony neuromarkers. The study of bare phase differences along the anteroposterior axis showed that there exists predominant phase differences in the alpha frequency band, notably during eyes closed resting state. These phase differences, which are different from one subject to the other, are stable across recordings over long periods. A simple model of two sources is proposed to account for this finding and lead to reconsider some properties of phase synchrony measures. Ultimately, while the realtime modulation of a phase synchrony marker was not achieved, especially because the identi
cation of such a marker was demonstrated nontrivial, the various contributions lay more foundations to the search for phasebased neural markers. Primarily through the development of theoretical but also software contributions. These software contributions are part of an ongoing research protocol with hospital La Timone in Marseille.
This work has been published in 23.
7.3 Combined fMRI, M/EEG and dMRI and its applications
An anisotropic 4D filtering approach to recover brain activation from paradigmfree functional MRI data
Participants: Isa Costantini, Samuel DeslauriersGauthier, Rachid Deriche.
Context: Functional Magnetic Resonance Imaging (fMRI) is a noninvasive imaging technique that provides an indirect view into brain activity via the blood oxygen level dependent (BOLD) response. In particular, restingstate fMRI poses challenges to the recovery of brain activity without prior knowledge on the experimental paradigm, as it is the case for task fMRI. Conventional methods to infer brain activity from the fMRI signals, for example, the general linear model (GLM), require the knowledge of the experimental paradigm to define regressors and estimate the contribution of each voxel's time course to the task. To overcome this limitation, approaches to deconvolve the BOLD response and recover the underlying neural activations without a priori information on the task have been proposed. Stateoftheart techniques, and in particular the total activation (TA), formulate the deconvolution as an optimization problem with decoupled spatial and temporal regularization and an optimization strategy that alternates between the constraints.
Approach: In this work, we propose a paradigmfree regularization algorithm named Anisotropic 4DfMRI (A4DfMRI) that is applied on the 4D fMRI image, acting simultaneously in the 3D space and 1D time dimensions. Based on the idea that large image variations should be preserved as they occur during brain activations, whereas small variations considered as noise should be removed, the A4DfMRI applies an anisotropic regularization, thus recovering the location and the duration of brain activations.
Results: Using the experimental paradigm as ground truth, the A4DfMRI is validated on synthetic and real taskfMRI data from 51 subjects, and its performance is compared to the TA. Results show higher correlations of the recovered time courses with the ground truth compared to the TA and lower computational times. In addition, we show that the A4DfMRI recovers activity that agrees with the GLM, without requiring or using any knowledge of the experimental paradigm.
This work has been published in 14.
Reconstruction of cortical activity from MEG data using brain networks and transmission delays estimated from dMRI
Participants: Ivana Kojčić, Théodore Papadopoulo, Rachid Deriche, Samuel DeslauriersGauthier.
This part describes the work performed within the framework of Ivana Kojčić's PhD defended on Nov. 18th, 2022.
White matter fibers transfer information between brain regions with delays that are observable with magnetoencephalography and electroencephalography (M/EEG) due to their millisecond temporal resolution. We can represent the brain as a graph where nodes are the cortical sources or areas and edges are the physical connections between them: either local (between adjacent vertices on the cortical mesh) or nonlocal (longrange white matter fibers). Longrange anatomical connections can be obtained with diffusion MRI (dMRI) tractography which yields a set of streamlines representing white matter fiber bundles. Given the streamlines’ lengths and the information conduction speed, transmission delays can be estimated for each connection. dMRI can thus give an insight into interaction delays of the macroscopic brain network. Localizing and recovering electrical activity of the brain from M/EEG measurements is known as the M/EEG inverse problem. Generally, there are more unknowns (brain sources) than the number of sensors, so the solution is nonunique and the problem illposed. To obtain a unique solution, prior constraints on the characteristics of source distributions are needed. Traditional linear inverse methods deploy different constraints which can favour solutions with minimum norm, impose smoothness constraints in space and/or time along the cortical surface, etc. Yet, structural connectivity is rarely considered and transmission delays almost always neglected.
The first contribution of this thesis consists of a multimodal preprocessing pipeline used to integrate structural MRI, dMRI and MEG data into a same framework, and of a simulation procedure of sourcelevel brain activity that was used as a synthetic dataset to validate the proposed reconstruction approaches. In the second contribution, we proposed a new framework to solve the M/EEG inverse problem called ConnectivityInformed M/EEG Inverse Problem (CIMIP), where prior transmission delays supported by dMRI were included to enforce temporal smoothness between time courses of connected sources. This was done by incorporating a Laplacian operator into the regularization, that operates on a timedependent connectivity graph. Nonetheless, some limitations of the CIMIP approach arised, mainly due to the nature of the Laplacian, which acts on the whole graph, favours smooth solutions across all connections, for all delays, and it is agnostic to directionality.
In this thesis, we aimed to investigate patterns of brain activity during visuomotor tasks, during which only a few regions typically get significantly activated, as shown by previous studies. This led us to our third contribution, an extension of the CIMIP approach that addresses the aforementioned limitations, named CIMIP_OML (Optimal Masked Laplacian). We restricted the full source space network (the whole cortical mesh) to a network of regions of interest and tried to find how the information is transferred between its nodes. To describe the interactions between nodes in a directed graph, we used the concept of network motifs. We proposed an algorithm that (1) searches for an optimal network motif – an optimal pattern of interaction between different regions and (2) reconstructs source activity given the found motif.
Promising results are shown for both simulated and real MEG data for a visuomotor task and compared with 3 different stateoftheart reconstruction methods. To conclude, we tackled a difficult problem of exploiting delays supported by dMRI for the reconstruction of brain activity, while also considering the directionality in the information transfer, and provided new insights into the complex patterns of brain activity.
This work has been published in 22.
Domain specific convolutional neural networks for dMRI and M/EEG signal analysis
Participants: Sara Sedlar, Théodore Papadopoulo, Samuel DeslauriersGauthier, Rachid Deriche.
This part describes the work performed within the framework of Sara Sedlar's PhD defended on Dec. 22nd, 2022.
The analysis of neuroimaging data is essential for the interpretation of the functional or structural characteristics of the human brain. New machine learning algorithms usually require a high amount of data often infeasible to acquire in clinical and practical conditions. This requirement is a consequence of significant data variability arising from numerous factors (various recording procedures, subjects and sessions, presence of high levels of noise). To address this problem, in this thesis, we have investigated and proposed convolutional machine learning models adapted to the properties and well grounded assumptions about the acquired data. Therefore, the models are endowed with valuable knowledge and consequently more efficiently learn to perform certain inferences. In particular, we have studied models for the analysis of noninvasive and invivo structural and functional neuroimaging data, namely diffusion Magnetic Resonance Imaging (dMRI) and magneto and electroencephalography (M/EEG) signals.
Diffusion MRI is a nuclear imaging modality which captures microstructural properties of the examined tissue. As qspace sampling has been the most widely used high angular resolution diffusion imaging protocol (HARDI) over the last decade, we have studied spherical rotation equivariant convolutional neural networks (CNNs) for dMRI local modeling. As a first contribution, we have proposed a spherical Unet for the estimation of fiber orientation distribution functions (fODFs) with convolutions and nonlinearities realized in the spectral and signal domains, respectively. To avoid aliasing, our second contribution proposes a Fourier domain CNN for microstructure parameter estimation, where nonlinearities are defined in the spectral domain.
M/EEG are functional imaging techniques which measure magnetic field strength and electric field potential caused by neural electric activities in the cerebral cortex. Measured signals can be explained by Maxwell’s equations with quasistatic approximations. Consequently, we can assume that cortical brain activities spread instantaneously and linearly over the measuring sensors, thus a multivariate M/EEG signal can be represented as a sum of rank1 multivariate signals corresponding to individual sources in the cortex and noise. Considering this assumption, the second part of the thesis firstly investigates an M/EEG spatial and temporal dictionary learning approach with an L0 constraint. A second contribution is a CNN classifier with rank1 spatiotemporal kernels regularized in the spectral domain, where the spatial components of the kernels are represented in terms of spherical harmonics basis, while the temporal components are represented in terms of discrete cosine basis
Forward modelling of M/EEG: Towards a new automatic head and brain tissue segmentation system
Participants: Ludovic Corcos, Samuel DeslauriersGauthier, Theo Papadopoulo.
Magnetoencephalography and electroencephalography (together M/EEG) are imaging modalities that allow the noninvasive measurement of the magnetic field and the electric potential generated by cortical activity. Inferring which brain areas generated the observed M/EEG measurements is not a trivial task and is referred to as the inverse problem. A common way to solve the problem is to assume than brain sources act like current dipoles in a volume conductor, in this case the head whose geometry can be obtained from magnetic resonance imaging (MRI). The relationship between brain sources and M/EEG measurements can therefore be modeled, a process called the solving forward problem. This process can be seen as injecting anatomical priors into the inverse problem. However, extracting the anatomical information from MRI needed to solve the forward problem is lengthy and tedious with existing tools. In this work, we present the first step in the creation of an automated pipeline to generate a volume conductor model from T1 and T2 images.
This work has been published in 30.
Autoregressive models for M/EEG signal analysis
Participants: Agathe Senellart, Igor Carrara, Côme Le Breton, Théodore Papadopoulo.
Electroencephalotherapy (EEG) is a widely used and inexpensive modality that serves as a support not only for experiments aimed at understanding the functioning of the brain when it performs certain tasks, but also for the characterization of certain pathologies (such as epilepsy) or the development of braincomputer interfaces. But EEG signals are complex and difficult to characterize, in particular because of their variability, whether in the same subject through the repetition of the same experiment or a fortiori when one wants to carry out multisubject analyses. They therefore require the use of specific and adapted signal processing methods. In a recent approach 41, sources were modeled as an autoregressive model which explains a portion of a signal. This approach works at the level of the source space (i.e. the cortex), which requires modeling of the head and makes it quite expensive. However, EEG measurements can be considered as a linear mixture of sources and therefore it is possible to estimate an autoregressive model directly at the measurement level. The objectives of this work is to explore the possibility of exploiting EEG/MEG autoregressive models to extract as much information as possible without requiring the complex head modelling required for source reconstruction.
This work has been presented in 29. Two journal papers are in preparation.
A shallow convolutional neural network with rank1 Fourier domain weights for brain signal classification
Participants: Sara Sedlar, Samuel DeslauriersGauthier, Rachid Deriche, Théodore Papadopoulo.
Electro and magnetoencephalography (MEG) signals are measured by sensors placed on the scalp (EEG) or slightly above it (MEG). Such measurements can be represented as linear combinations of source signals occurring in different cortical regions and are characterized by a high temporal, but low spatial resolution. Depending on the performed task, the signals exhibit different temporal and spatial patterns. These signals are affected by a significant amount of noise coming from measuring devices or from the subject itself and suffer from high intra and intersubject variability which make their analysis quite challenging. Deep learning approaches have been successfully used in different domains of medical signal analysis. However, they often require large amounts of data, otherwise they either suffer from overfitting or exhibit poor generalization power. In this work, we propose a rank1 convolutional neural network (CNN) with Fourier domain kernels for MEEG signal classification. Since the spread of the source signals across sensors is instantaneous and linear, we have used rank1 trainable kernels in our model, where both spatial and temporal components are represented in Fourier domain, which acts as a regularization space. Assuming that the head can be modeled by a sphere, spatial kernels are represented in the basis of spherical harmonics. This representation is less sensitive to the spatial distribution of sensors which varies between subjects and sessions. In order to constrain temporal kernels to focus on feature extraction from certain frequency range, they are represented as linear combinations of discrete cosine coefficients. The model is compared with the stateoftheart CNN models on the passive brain computer interface problem of mental workload classification from EEG signals and motortask MEG signal classification. We have shown that our model can achieve stateofthe art performance with significantly lower number of parameters and achieve improvement when the number of available training subjects is smaller. Given this and its speed both during train and test phase, it is well suited for portable devices in brain computer interfaces.
This work has been published in 32.
Identifying subcortical connectivity during brain tumor surgery: A multimodal study
Participants: Fabien Almairac, Petru Isan, Marie Onno, Théodore Papadopoulo, Lydiane Mondot, Stéphane Chanalet, Charlotte Fernandez, Maureen Clerc, Rachid Deriche, Denys Fontaine, Patryk Filipiak.
Bipolar direct electrical stimulation (DES) of an awake patient is the reference technique for identifying brain structures to achieve maximal safe tumor resection. Unfortunately, DES cannot be performed in all cases. Alternative surgical tools are therefore needed to aid identification of subcortical connectivity during brain tumor removal. Moreover, although functional responses to DES are well documented, its electrophysiological effect on brain networks is poorly known. In this study, we sought to (i) evaluate the combined use of electrocorticography (ECoG) and tractography for identification of white matter (WM) tracts under the functional control of DES, and (ii) provide clues to the electrophysiological effects of bipolar stimulation on neural pathways. We included 12 brain tumor patients with a mean age of 38 years [2059] (five women, six lesions on the left side) who had had a functional brain mapping under awake craniotomy. After tumor resection, 14 ECoG electrodes (one strip of six, and two strips of four electrodes) were positioned along the cortical terminations of the associative tracts of interest previously reconstructed with probabilistic tractography. Electrophysiological recordings of subcortical evoked potentials (SCEPs) were acquired during bipolar stimulation of functional sites of the WM identified during the awake phase of a surgery. Correlations between the obtained structural and electrophysiological data were measured subject to verification with the functional neurocognitive responses induced by DES. SCEPs were observed in 11 out of 12 patients in response to the stimulation of functional sites of the white matter. In one patient, subcortical stimulation elicited neither functional nor electrophysiological response. On average, 4.26 cortical electrodes [19] recorded SCEPs, usually located close to the subcortical stimulation site (mean Euclidean distance = 32.22 ±9.65 mm). The median length of the stimulated fibers from the subcortical site to the “activated” electrodes was 43.24 ±19.55 mm, belonging to tracts of median lengths of 89.84 ±24.65 mm. The electrophysiological (delay, amplitude, and speed of propagation) and structural (number and lengths of streamlines, and mean fractional anisotropy) measures were significantly correlated. SCEPs were elicited with bipolar stimulation on various associative WM tracts. In our experimental settings, their propagation was essentially limited to a subpart of the bundles, suggesting a selectivity of action of the DES on the brain networks. Correlations between functional, structural, and electrophysiological biomarkers portend the combined use of evoked potentials and tractography as a potential intraoperative tool to achieve maximum safe resection in brain tumor surgery.
This work has been submitted to the journal Brain and is currently under evaluation.
8 Bilateral contracts and grants with industry
8.1 Bilateral Grants with Industry
Participants: Théodore Papadopoulo.
A BPI grant proposal has been obtained in 2022 with the startup Mag4Health (other partners are CNRS and INSERM). This company develops a new MEG machine working with optically pumped magnetometers (magnetic sensors), which potentially means lower costs and better measurements. ATHENA is in charge of developing a real time interface for signal visualization, source reconstruction and epileptic spikes detection. The initial funding is for 2 years, but an extension is already expected.
9 Partnerships and cooperations
9.1 International initiatives
9.1.1 Associate Teams in the framework of an Inria International Lab or in the framework of an Inria International Program
An associate team proposal was submitted by S. DeslauriersGauthier within the framework of Inria London Programme in collaboration with Dario Farina of Imperial College London. The nature and objective of this proposal is to increase the bandwidth between the EEG and EMG communities and promote a mutually beneficial exchange of methodology and knowledge. The Athena team has a longstanding history in forward modelling and inverse problem in electroencephalography and magnetoencephalography. The Imperial College London team has extensive expertise in the processing and analysis of EMG signals for neurorehabilitation and the control of movements. By collaborating via the associated team, the two research labs will rapidly move forward both the EMG and the EEG communities.
9.2 National initiatives
3IA UCA Chair : AIBased Computational Brain Connectomics
Participants: Rachid Deriche (P.I), Samuel DeslauriersGauthier, Théodore Papadopoulo, Sara Sedlar, Mauro Zucchelli.
Start date: October, 2019 Duration: 48 months.This project aims to reconstruct and analyse the network of neural connections of the brain, called the connectome via a computational brain connectomics framework based on groundbreaking AI algorithms and machine learning tools to gain insight into brain architecture, functioning and neurodegenerative diseases.
The avalanche of big data required to reconstruct the connectome and the study of the high complexity of structural and functional interactions within the connectome clearly position brain connectomics as a big data problem where AI & machine learning in particular, represent a very promising trend, as recently demonstrated in computer vision and in some biomedical image datadriven analysis. Partly related to the ERC AdG CoBCoM, the computational brain connectomics framework we develop in this project will construct networks specifically built on new generation of AI algorithms and machine learning tools to reconstruct a structural and functional connectome using advanced and integrated dMRI, EEG & MEG methods. This project completes CoBCoM by specifically investigating the AI added value in brain mapping, opens also exciting prospects and paves the way to translate the large amounts of high dimensional heterogeneous and complex brain data into knowledge for better contribute to neurodegenerative diseases detection and diagnosis.
EPIFEED
Participants: Angela Marchi, Côme Le Breton, Fabrice Bartolomei, Théodore Papadopoulo, Christian Bénar, JeanMichel Badier, Julien Wintz.
Start date: February 2023 Duration:24 months.Electroencephalography (EEG) Neurofeedback (NFB) is a potential treatment for drug resistant epileptic patients (DREP). NFB training helps to selfregulate specific activities of the brain. This technique is interesting for different neuropathologies, and it is known to reduce the frequency of epileptic seizures by modulating the amplitude of slow cortical rhythms in DREP. An increase in cerebral synchrony during the interictal and ictal period in DREP is well known, so we propose here an innovative NFB method based on the realtime acquisition of synchrony, with as objective measures of treatment success the frequency (and severity) and psychiatric comorbidities. This works aims at leveraging the work done in the Ph.D. thesis of C. Le Breton for a study of the utility of NFB for epileptic patients.
ConnectTC
Participants: Fabien Almairac, Petru Isan, Théodore Papadopoulo.
Start date: July 2019 Duration: 60 monthsThis grant was obtained from Nice Pasteur hospital to do a multimodal study of the connectome of patients suffering from a brain glioma during awake brain surgery. It aims at better understanding the effects of bipolar direct electrical stimulation (DES) that is used during surgery to delineate the resection region. This study combines ECoG measurements (measured during DES) and white matter fiber tracts obtained with diffusion MRI to better understand how DES operates in the patient brain (which areas are stimulated and how the local stimulation is propagated to other brain areas). The goal is to acquire data on at least 30 participants. It has been extended to at least summer 2024 due to difficulties which arose in obtaining this number of subjects (Covid, ...).
Auditory attention analysis during music listening
Participants: Maureen Clerc, Joan Belo, Oticon Medical.
The Ph.D, of Joan Belo is funded by this joint grant from Oticon Medical and Region Provence Alpes Côtes d'Azur. The goal of the project is to better understand the link between the decoding of auditory attention during naturalistic music listening using recent EEG methods known as Auditory Attention Detection and several cognitive functions and behavioral indicators that are important for listening in complex auditory situation, such as working memory or mind wandering. This is done with the aim of improving the efficiency of next generation cochlear implants by taking into account the individual cognitive aspects.10 Dissemination
10.1 Promoting scientific activities
Participants: Rachid Deriche, Théodore Papadopoulo, Samuel DeslauriersGauthier.
10.1.1 Scientific events: selection
Reviewer
 R. Deriche served several international conferences (ISBI, MICCAI, ISMRM, ...) and international workshops (CDMRI MICCAI, MFCA).
 S. DeslauriersGauthier served several international conferences (ISBI, MICCAI) and international workshops (CDMRI MICCAI).
 T. Papadopoulo served several international conferences (ISBI, ICIP).
Member of the conference program committees
 T. Papadopoulo was in the scientific committee of GRETSI 2022.
10.1.2 Journal
Member of the editorial boards
 R. Deriche is member of the Editorial Board of the Journal of Neural Engineering, editorial board member at Springer for the book series entitled Computational Imaging and Vision and member of the Editorial Board of the Medical Image Analysis Journal
 S. DeslauriersGauthier served as Guest Editor for the special issue on Advances in Brain Functional and Structural Networks Modeling via Graph Theory of the journal Frontiers in Neuroscience.
 T. Papadopoulo serves as Associate Editor in Frontiers: Brain Imaging Methods and as Review Editor for Frontiers: Artificial Intelligence in Radiology.
Reviewer  reviewing activities
 R. Deriche serves several international journals (NeuroImage, IEEE Transactions on Medical Imaging, Magnetic Resonance in Medicine, Medical Image Analysis Journal,Journal of Neural Engineering ...).
 S. DeslauriersGauthier serves several international journals (NeuroImage, IEEE Transactions on Biomedical Engineering, Journal of Neural Engineering, Medical Image Analysis, Science Advances).
 T. Papadopoulo served several international journals (Computers and Mathematics with Applications, Frontiers in Neurosciences, Frontiers in Neural Circuits, IEEE Transactions on Biomedical Engineering, NeuroImage, NeuroImage Reports, Physics & Medicine in Biology, Scientific Reports).
10.1.3 Invited talks
 R. Deriche gave a keynote speech at AbuDhabi AI Connect  1213 Dec. 2022 AbuDhabi (EAU).
10.1.4 Scientific expertise
 R. Deriche served several national and international institutions in reviewing applications : 3IA UCA Chairs, ERC AdG and StG Grants, Swiss National Science Foundation, EPFL, the Netherlands Organisation for Scientific Research (NWO).
 S. DeslauriersGauthier reviewed funding applications for the Fonds de recherche Nature et technologie du Québec.
 S. DeslauriersGauthier reviewed funding applications for the ANR Jeunes Chercheuses et Jeunes Chercheurs.
 T. Papadopoulo served in reviewing applications for the Neuromod institute of Université Côte d'Azur.
 T. Papadopoulo served in reviewing for several internal programs of Université Côte d'Azur (see membership in academic council below).
 T. Papadopoulo was member of the INSERM committee responsible for the selection of INSERM program of collaborative research in health (MESSIDORE).
 T. Papadopoulo served as a reviewer for the European call FETOPEN.
10.1.5 Research administration
 T. Papadopoulo is elected member in the academic council of Côte d'Azur University.
 T. Papadopoulo is the head of the Technological Development Committee of Inria Sophia Antipolis Méditerranée.
 T. Papadopoulo is a member of the Neuromod scientific council and represents Neuromod in the EUR Healthy (EUR: Universitary Research School).
10.2 Teaching  Supervision  Juries
10.2.1 Teaching
 Master: T. Papadopoulo, Inverse problems for brain functional imaging, 24 ETD, M2, Mathématiques, Vision et Apprentissage, ENS Cachan, France.
 Master: T. Papadopoulo, Functional Brain Imaging, 10 ETD, M1,M2 in the MSc Mod4NeuCog of Université Côte d'Azur.
 Master: S. DeslauriersGauthier, Functional Brain Imaging, 10 ETD, M1,M2 in the MSc Mod4NeuCog of Université Côte d'Azur.
10.2.2 Supervision
 PhD defended on Dec. 22nd, 2022: Sara Sedlar, "Domain specific convolutional neural networks for dMRI and M/EEG signal analysis", Université Côte d'Azur, started October 2018. Supervisors: Théodore Papadopoulo and Samuel DeslauriersGauthier
 PhD defended on Nov. 18th, 2022: Ivana Kojcic, "Reconstruction of cortical activity from MEG data using brain networks and transmission delays estimated from dMRI", Université Côte d'Azur, started October 2018. Supervisors: Théodore Papadopoulo and Samuel DeslauriersGauthier.
 PhD defended on Oct. 18th, 2022: Côme Le Breton, "Non invasive analysis of epileptogenetic networks and their response to neurofeedback", started June 2019. Supervisors: Maureen Clerc and Théodore Papadopoulo.
 PhD defended on Dec. 5th, 2022: Joan Belo, "Auditory attention analysis during music listening  Making the link between machine learning, electrophysiology and cognition", started June 2019. Supervisors: Maureen Clerc and Daniele Schön.
 PhD in progress: I. Carrara, "Autoregressive models for MEG/EEG processing", started in Oct. 2021. Supervisor: Théodore Papadopoulo.
 PhD in progress: Y. Aeschlimann, started in Oct. 2022. Supervisors: Samuel DeslauriersGauthier, Théodore Papadopoulo.
10.2.3 Juries
 T. Papadopoulo participated in the jury of C. Le Breton at Université Côte d'Azur on Oct. 18th, 2022.
 R. Deriche, S. DeslaurierGauthier and T. Papadopoulo participated in the PhD Jury of I. Kojcic at Université Côte d'Azur on Nov. 18th, 2022.
 R. Deriche, S. DeslaurierGauthier and T. Papadopoulo participated in the PhD Jury of S. Sedlar at Université Côte d'Azur on Dec. 22nd, 2022.
10.3 Popularization
 T. Papadopoulo and C. Le Breton presented the P300 Speller at the inauguration of TerraNumerica in June 2022.
11 Scientific production
11.1 Major publications
 1 articleStructural connectivity to reconstruct brain activation and effective connectivity between brain regions.Journal of Neural Engineering173June 2020, 035006
 2 articleConsensus Matching Pursuit for MultiTrial EEG Signals.Journal of Neuroscience Methods1802009, 161170
 3 articleDesign of multishell sampling schemes with uniform coverage in diffusion MRI.Magnetic Resonance in Medicine696June 2013, 15341540
 4 articleRegularized, Fast, and Robust Analytical QBall Imaging.Magnetic Resonance in Medicine5832007, 497510URL: ftp://ftpsop.inria.fr/odyssee/Publications/2007/descoteauxangelinoetal:07.pdf
 5 articleDeterministic and Probabilistic Tractography Based on Complex Fibre Orientation Distributions.IEEE Transactions in Medical Imaging282February 2009, 269286URL: ftp://ftpsop.inria.fr/odyssee/Publications/2009/descoteauxdericheetal:09.pdf
 6 articleWhite Matter Information Flow Mapping from Diffusion MRI and EEG.NeuroImageJuly 2019
 7 articleA Unified Framework for Multimodal Structurefunction Mapping Based on Eigenmodes.Medical Image AnalysisAugust 2020, 22
 8 articleMAPL: Tissue Microstructure Estimation Using LaplacianRegularized MAPMRI and its Application to HCP Data.NeuroImage134July 2016, 365–385
 9 articleNetwork alignment and similarity reveal atlasbased topological differences in structural connectomes.Network NeuroscienceMay 2021
 10 articleAxTract: Toward microstructure informed tractography.Human Brain Mapping3811November 2017, 54855500URL: http://onlinelibrary.wiley.com/doi/10.1002/hbm.23741/abstract
 11 articleAdaptive Waveform Learning: A Framework for Modeling Variability in Neurophysiological Signals.IEEE Transactions on Signal Processing65August 2017, 4324  4338
 12 articleA Trilinear Immersed Finite Element Method for Solving the Electroencephalography Forward Problem.SIAM Journal on Scientific Computing3242010, 23792394
 13 articleA Computational Framework For Generating Rotation Invariant Features And Its Application In Diffusion MRI.Medical Image AnalysisFebruary 2020
11.2 Publications of the year
International journals
 14 articleAn Anisotropic 4D Filtering Approach to Recover Brain Activation From ParadigmFree Functional MRI Data.Frontiers in Neuroimaging12022, 815423
 15 articleA Riemannian Revisiting of Structure–Function Mapping Based on Eigenmodes.Frontiers in Neuroimaging1May 2022
 16 articleTranscriptomic and cellular decoding of functional brain connectivity changes reveal regional brain vulnerability to pro and antiinflammatory therapies.Brain, Behavior, and Immunity1022022, 312323
 17 articleCurrent distribution of distributed allpolar cochlear implant stimulation mode measured insitu.PLoS ONE1710October 2022, e0275961
 18 articleDORIS: a diffusion MRIbased 10 tissue class deep learning segmentation algorithm tailored to improve anatomicallyconstrained tractography.Frontiers in NeuroimagingJune 2022
International peerreviewed conferences
 19 inproceedingsEmbedding neurophysiological signals.Proceedings of the IEEE MetroXRAINE conferenceRoma, ItalyOctober 2022
Conferences without proceedings
 20 inproceedingsCNN and diffusion MRI's 4th degree rotational invariants for Alzheimer's disease identification.International Workshop on Learning with Imbalanced Domains: Theory and ApplicationsGrenoble, FranceSeptember 2022
Doctoral dissertations and habilitation theses
 21 thesisAuditory attention analysis during music listening  Making the link between machine learning, electrophysiology and cognition.Université Côte D'AzurDecember 2022
 22 thesisReconstruction of cortical activity from MEG data using brain networks and transmission delays estimated from dMRI.Université Côte d'AzurNovember 2022
 23 thesisUsability of phase synchrony neuromarkers in neurofeedback protocols for epileptic seizures reduction.Université Côte d'AzurOctober 2022
 24 thesisDomain specific convolutional neural networks for dMRI and M/EEG signal analysis.Universite Cote d'AzurDecember 2022
Reports & preprints
 25 miscGraph Alignment Exploiting the Spatial Organisation Improves the Similarity of Brain Networks.December 2022
 26 miscA revisiting of structurefunction mapping using Graph Convolutional Networks.September 2022
Other scientific publications
 27 inproceedingsLocalization of Brain Microstructure Changes Associated with Alzheimer's Disease using Class Activation Maps.Soph.I.A Summit 2022 : fifth edition of the international AI conferenceSophia Antipolis, FranceNovember 2022
 28 inproceedingsRotation invariant features for Alzheimer's disease identification using convolutional neural networks.NeuroMod Meeting 2022Antibes, FranceJune 2022, 11
 29 inproceedingsOn the use of the "Augmented" autocovariance matrix for the classification of BCIEEG.Proceedings of Cortico DaysAutrans, FranceMarch 2022
 30 inproceedingsForward modelling of M/EEG: Towards a new automatic head and brain tissue segmentation system.SophI.A 2022 : fifth international AI conferenceProceedings of SophIA 2022Sophia Antipolis, FranceNovember 2022
 31 inproceedingsHyperbolic Model Captures Temporal Small Worldness of Brain Dynamics.NeuroMod meeting 2022Antibes, FranceJune 2022
 32 inproceedingsShallow convolutional neural network with rank1 Fourier domain weights for brain signal classification.Proceedings of SophIA 2022Sophia Antipolis, FranceNovember 2022
11.3 Cited publications
 33 articleComposite hindered and restricted model of diffusion (CHARMED) MR imaging of the human brain.Neuroimage271August 2005, 4858
 34 articleAxCaliber: a method for measuring axon diameter distribution from diffusion MRI.Magnetic Resonance in Medicine5962008, 134754URL: http://www.ncbi.nlm.nih.gov/pubmed/18506799
 35 incollectionApparent Intravoxel Fibre Population Dispersion (FPD) Using Spherical Harmonics.Medical Image Computing and ComputerAssisted Intervention  MICCAI 20116892Lecture Notes in Computer ScienceSpringer Berlin / Heidelberg2011, 157165URL: http://dx.doi.org/10.1007/9783642236297_20
 36 articleEfficient and robust computation of PDF features from diffusion MR signal.Medical Image Analysis1352009, 715729
 37 articleRegularized PositiveDefinite FourthOrder Tensor Field Estimation from DWMRI.NeuroImage451March 2009, S153162.URL: http://www.sciencedirect.com/science/journal/10538119
 38 articleEstimation of the effective selfdiffusion tensor from the NMR spin echo.Journal of Magnetic ResonanceB1031994, 247254
 39 articleMR Diffusion Tensor Spectroscopy and imaging.Biophysical Journal6611994, 259267
 40 conferenceUsing diffusion MRI information in the Maximum Entropy on Mean framework to solve MEG/EEG inverse problem.BIOMAGHalifax, CanadaAugust 2014
 41 articleStructural connectivity to reconstruct brain activation and effective connectivity between brain regions.Journal of Neural Engineering173June 2020, 035006
 42 bookPrinciples of nuclear magnetic resonance microscopy.OxfordOxford University Press1991

43
phdthesisQSpace diffusion MRI: Acquisition and signal processing.The overall goal of this thesis is to develop novel methods for the acquisition and the processing of diffusion magnetic resonance images (MRI), to provide new insights into the structure and anatomy of the brain white matter in vivo. Diffusion MRI is a noninvasive technique that measures locally the diffusion of water molecules. The latter are hindered by tissue structure, and therefore the characterization of water molecules displacement gives information on the nature, orientation, microstructure of the underlying tissue. Because of the strong anisotropy observed in white matter fiber tracts, this tool is most popular for the analysis of brain connectivity. One of the modality of acquisition and reconstruction, called diffusion tensor imaging, is now an established tool in research and clinical applications, for the detection of neural diseases and for preoperative planning. Being modelbased, the diffusion tensor cannot describe complex intravoxel configurations, with multiple populations of fibers crossing. Since then, for a finer description of water molecules displacement, modelfree approaches have recently been proposed, aiming at overcome the limitations of the diffusion tensor. Most of these techniques are still extremely demanding in acquisition time, and involve challenging reconstruction problems. The first part of this thesis proceeds from a description of the tissue microstructure, and a physical explanation of the origin of acquired diffusion signal. We give a review of the reconstruction methods and corresponding acquisition techniques in diffusion MRI. Several reconstruction methods are presented, and are categorized into modelbased and modelfree techniques. The first contribution of this thesis is related to the parametric reconstruction of the diffusion signal in a continuous basis of functions. We develop on a previous proposed method called Spherical Polar Fourier basis, and propose a continuous basis with a significant reduction of the dimension for the same power of description. We also derive the expression of the Laplace regularization operator in this basis, for a better robustness to noise. The second contribution is also related to the reconstruction of the diffusion signal, and the orientation distribution function, with a special focus on clinical setting. We propose a realtime reconstruction algorithm based on the Kalman filter to reconstruct the ODF in constant solid angle. We develop on top of the Kalman filter a motion detection algorithm, based on a monitoring and statistical analysis of the Kalman filter residuals. We are able to give a precise and sensitive motion detection, at no additional cost on the online acquisition system, as compared to systems based on camera and computer vision. The two last contributions are related to the acquisition methods in diffusion MRI, in particular for single and multiple
$q$ shell experiments. We first describe a geometric approach to generate angular uniform schemes, that offer optimal angular coverage per shell and as a whole. Then we investigate on the link between the choice of a parametric basis of functions, and the design of sampling protocols. We give explicit methods to generate sampling schemes with minimal condition number, for the reconstruction in spherical harmonics (in Qball imaging) and the reconstruction in the modified spherical polar Fourier basis, proposed in this thesis. The conclusion of this approach is that the sampling method should be driven by the physical constraints of the scanner, and at the same time by the choice of a specific basis to represent the diffusion signal, and with an overall uniform coverage of the space of sampling directions, for a good rotational invariance. The new sampling schemes generated with this technique are available for download from my web page.University of Nice Sophia AntipolisJuly 2012  44 phdthesisEstimation and Processing of Ensemble Average Propagator and Its Features in Diffusion MRI.University of Nice Sophia AntipolisMay 2012
 45 articleOptimal RealTime QBall Imaging Using Regularized Kalman Filtering with Incremental Orientation Sets.Medical Image Analysis134August 2009, 564579URL: http://dx.doi.org/10.1016/j.media.2009.05.008
 46 articleApparent Diffusion Coefficients from High Angular Resolution Diffusion Imaging: Estimation and Applications.Magnetic Resonance in Medicine562006, 395410URL: ftp://ftpsop.inria.fr/odyssee/Publications/2006/descoteauxangelinoetal:06c.pdf
 47 articleHigh Angular Resolution Diffusion MRI Segmentation Using RegionBased Statistical Surface Evolution.Journal of Mathematical Imaging and Vision332In this article we develop a new method to segment high angular resolution diffusion imaging (HARDI) data. We first estimate the orientation distribution function (ODF) using a fast and robust spherical harmonic (SH) method. Then, we use a regionbased statistical surface evolution on this image of ODFs to efficiently find coherent white matter fiber bundles. We show that our method is appropriate to propagate through regions of fiber crossings and we show that our results outperform stateoftheart diffusion tensor (DT) imaging segmentation methods, inherently limited by the DT model. Results obtained on synthetic data, on a biological phantom, on real datasets and on all 13 subjects of a public NMR database show that our method is reproducible, automatic and brings a strong added value to diffusion MRI segmentation.February 2009, 239252URL: ftp://ftpsop.inria.fr/odyssee/Publications/2009/descoteauxderiche:09.pdf
 48 articleMultiple qshell diffusion propagator imaging.Medical Image Analysis1542011, 603621
 49 phdthesisHigh Angular Resolution Diffusion MRI: From Local Estimation to Segmentation and Tractography.University of Nice Sophia AntipolisFebruary 2008, URL: ftp://ftpsop.inria.fr/odyssee/Publications/PhDs/descoteaux_thesis.pdf
 50 articleClinical Applications of Diffusion Tensor Imaging.Journal of Magnetic Resonance Imaging192004, 618
 51 conferenceGlial tumor localization and characterization using DTI augmented MEG modelling.Proceedings of BiomagBiomagHalifax, Canada2014
 52 incollectionFrom Diffusion MRI to Brain Connectomics.Modeling in Computational Biology and Medicine: A Multidisciplinary EndeavorSpringer2013, 6193231
 53 incollectionFrom Second to Higher Order Tensors in DiffusionMRI.Tensors in Image Processing and Computer VisionAdvances in Pattern RecognitionSpringer LondonMay 2009, 9315URL: http://www.springer.com/computer/computer+imaging/book/9781848822986
 54 phdthesisHigh Order Models in Diffusion MRI and Applications.Diffusion MRI (dMRI) is a powerful tool for inferring the architecture of the cerebral white matter invivo and noninvasively. Based on model assumptions, reconstructed diffusion functions can provide subvoxel resolution microstructural information of the white matter superior to the resolution of the raw diffusion images. In the com monly used Diffusion Tensor Imaging (DTI) the diffusion function is modelled by a second order tensor. However, since it is limited in regions with fiber inhomogeneity, recent research has produced numerous reconstruction techniques that infer the fiber layout in the underlying white matter with greater accuracy. These techniques rep resent the diffusion function by complex shaped spherical functions. In this thesis we address two problems  first we examine one such reconstruction technique closely, and second we propose a generic way of extracting geometric features from a wide class of reconstructed diffusion spherical functions to characterize the white matter. In this thesis we make a number of contributions. First we examine, Generalized DTI, which uses Cartesian tensors of order higher than two to model the diffusion profile (the diffusion coefficient along multiple spatial directions) in regions with fiber inhomogeneity. We propose two independent methods for estimating fourth order dif fusion tensors with a positive diffusion profile, which is an important consideration since negative diffusion is nonphysical. Then we propose an analytical approxima tion for estimating the diffusion propagator (the probability density function describ ing the diffusion process) from tensors of order higher than two, which allows us to measure both a modified diffusion profile and the propagator, which contain comple mentary information, from regions with fiber inhomogeneity. The analytical formu lation allows us to efficiently estimate the propagator which is needed to infer the underlying fiber layout. Finally we propose a generic method for extracting the max ima from a wide class of diffusion spherical functions (functions on a sphere), since these indicate the fiber layout in the white matter. We also extract other geomet ric features from these complex shaped spherical diffusion functions to propose new biomarkers for characterizing the white matter. To illustrate the maximaextraction, we also propose extensions to well known deterministic tractography methods where we apply maxima extraction to complex shaped orientation distribution functions (ODFs) to trace fibers through regions with fiber crossings.University of Nice Sophia AntipolisApril 2011, URL: ftp://ftpsop.inria.fr/athena/Publications/PhDs/ghosh:11.pdf
 55 articleConstrained Diffusion Kurtosis Imaging Using Ternary Quartics & MLE.Magnetic Resonance in MedicineArticle first published online: 2 JUL 2013  Volume 71, Issue 4, April 2014, Pages: 15811591July 2013
 56 bookH.Heidi JohansenBergT. E.Timothy E. J. BehrensDiffusion MRI : From Quantitative Measurement to In vivo Neuroanatomy.Elevier  Academic Press2009
 57 bookD. K.Derek K. JonesDiffusion MRI: Theory, Methods, and Applications.Oxford University Press2011
 58 articleA Common Formalism for the Integral Formulations of the Forward EEG Problem.IEEE Transactions on Medical Imaging24January 2005, 1228URL: ftp://ftpsop.inria.fr/odyssee/Publications/2005/kybicclercetal:05.pdf
 59 articleImagerie de Diffusion in vivo par Résonnance Magnétique Nucléaire.CR Académie des Sciences3011985, 11091112
 60 articleDiffusion tensor imaging: concepts and applications.J Magn Reson Imaging.1342001, 53446URL: http://www.ncbi.nlm.nih.gov/pubmed/11276097
 61 articleMathematical Methods for Diffusion MRI Processing.NeuroImage451March 2009, S111S122URL: ftp://ftpsop.inria.fr/odyssee/Publications/2009/lengletcampbelletal:09.pdf
 62 articleDTI Segmentation by Statistical Surface Evolution.IEEE Transactions on Medical Imaging,2506June 2006, 685700URL: ftp://ftpsop.inria.fr/odyssee/Publications/2006/lengletroussonetal:06c.pdf
 63 inproceedingsWhite Matter Abnormalities in Children with Temporal Lobe Epilepsy: A DTI and MEG Study.17th International Conference on Biomagnetism Advances in BiomagnetismBiomag2010Springer2010, 397400
 64 articleSelfdiffusion NMR Imaging Using Stimulated Echoes.J. Magn. Reson.641985, 479486
 65 phdthesisDiffusion MRI & Compressive Sensing.Nice Sophia Antipolis UniversitySeptember 2013
 66 articleMagnetoencephalography and diffusion tensor imaging in gelastic seizures secondary to a cingulate gyrus lesion.Clinical neurology and neurosurgery10922007, 182187
 67 inproceedingsSimple harmonic oscillator based reconstruction and estimation for threedimensional qspace MRI.ISMRM 17th Annual Meeting and Exhibition, Honolulu,2009, 1396.URL: http://stbb.nichd.nih.gov/abstracts.html
 68 articleMean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure.Neuroimage78September 2013, 1632URL: https://www.sciencedirect.com/science/article/pii/S1053811913003431
 69 articleGeneralized Diffusion Tensor Imaging and Analytical Relationships Between Diffusion Tensor Imaging and High Angular Resolution Imaging.Magnetic Resonance in Medicine502003, 955965
 70 articleGeneralized Scalar Measures for Diffusion MRI Using Trace, Variance and Entropy.Magnetic Resonance in Medicine5342005, 866876
 71 articleCompartment models of the diffusion MR signal in brain white matter: A taxonomy and comparison.NeuroImage592012, 22412254URL: https://doi.org/10.1016/j.neuroimage.2011.09.081
 72 inproceedingsA nested cortex parcellation combining analysis of MEG forward problem and diffusion MRI tractography.IEEE International Symposium on Biomedical Imaging (ISBI)IEEEBarcelonaMay 2012, 518521
 73 conferencePropagation of epileptic spikes revealed by diffusionbased constrained MEG source reconstruction.19th International Conference on Biomagnetism (BIOMAG 2014)Halifax, CanadaAugust 2014, URL: http://www.biomag2014.org
 74 incollectionHigherOrder Tensors in Diffusion Imaging.Visualization and Processing of Tensors and Higher Order Descriptors for MultiValued DataDagstuhl ReportsDiffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higherorder tensors provide a powerful mathemat ical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion Imaging (HARDI) or Diffusional Kurtosis Imaging. This survey gives a careful introduction to the foundations of higherorder tensor algebra, and explains how some concepts from linear algebra generalize to the higherorder case. From the application side, it re views a variety of distinct higherorder tensor models that arise in the context of diffusion imaging, such as higherorder diffusion tensors, qball or fiber Orientation Distribution Functions (ODFs), and fourthorder covariance and kurtosis tensors. By bridging the gap between mathematical foundations and application, it provides an introduction that is suitable for practitioners and applied mathematicians alike, and propels the field by stimulating further exchange between the two.Springer2013
 75 conferenceDetection of largescale networks in EEG and comparison with fMRI.Proceedings of BiomagBIOMAGParis, FranceAugust 2012
 76 articleBall and Rackets: Inferring Fibre Fanning from Diffusionweighted MRI.NeuroImage60January 2012, 14121425URL: http://dx.doi.org/10.1016/j.neuroimage.2012.01.056
 77 articleSpin diffusion measurements: spin echoes in the presence of a timedependent field gradient.Journal of Chemical Physics421965, 288292
 78 articleThe spatial mapping of translational diffusion coefficients by the NMR imaging technique.Phys. Med. Biol.301985, 345349URL: https://iopscience.iop.org/article/10.1088/00319155/30/4/009
 79 articleQBall Imaging.Magnetic Resonance in Medicine5262004, 13581372
 80 inproceedingsIn vivo conductivity estimation using somatosensory evoked potentials and cortical constraint on the source.Proceedings of ISBIApril 2007, 10361039URL: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4193466
 81 articleMapping complex tissue architecture with diffusion spectrum magnetic resonance imaging.Magnetic Resonance in Medicine5462005, 13771386
 82 articleNODDI: Practical in vivo neurite orientation dispersion and density imaging of the human brain.NeuroImage61March 2012, 10001016URL: http://dx.doi.org/10.1016/j.neuroimage.2012.03.072