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CRONOS - 2025

2025​‌Activity reportProject-TeamCRONOS​​

RNSR: 202224368W

Creation of​​​‌ the Project-Team: 2022 December​ 01

Each year, Inria​‌ research teams publish an​​ Activity Report presenting their​​​‌ work and results over​ the reporting period. These​‌ reports follow a common​​ structure, with some optional​​​‌ sections depending on the​ specific team. They typically​‌ begin by outlining the​​ overall objectives and research​​​‌ programme, including the main​ research themes, goals, and​‌ methodological approaches. They also​​ describe the application domains​​​‌ targeted by the team,​ highlighting the scientific or​‌ societal contexts in which​​ their work is situated.​​​‌

The reports then present​ the highlights of the​‌ year, covering major scientific​​ achievements, software developments, or​​​‌ teaching contributions. When relevant,​ they include sections on​‌ software, platforms, and open​​ data, detailing the tools​​​‌ developed and how they​ are shared. A substantial​‌ part is dedicated to​​ new results, where scientific​​​‌ contributions are described in​ detail, often with subsections​‌ specifying participants and associated​​ keywords.

Finally, the Activity​​​‌ Report addresses funding, contracts,​ partnerships, and collaborations at​‌ various levels, from industrial​​ agreements to international cooperations.​​​‌ It also covers dissemination​ and teaching activities, such​‌ as participation in scientific​​ events, outreach, and supervision.​​​‌ The document concludes with​ a presentation of scientific​‌ production, including major publications​​ and those produced during​​​‌ the year.

Keywords

Computer​ Science and Digital Science​‌

  • A5.1.4. Brain-computer interfaces, physiological​​ computing
  • A5.9.2. Estimation, modeling​​​‌
  • A5.9.3. Reconstruction, enhancement
  • A6.1.​ Methods in mathematical modeling​‌
  • A6.2. Scientific computing, Numerical​​ Analysis & Optimization
  • A6.3.​​​‌ Computation-data interaction
  • A6.3.1. Inverse​ problems
  • A6.3.2. Data assimilation​‌
  • A6.3.3. Data processing
  • A6.3.4.​​ Model reduction
  • A6.3.5. Uncertainty​​​‌ Quantification
  • A9.2. Machine learning​
  • A9.3. Signal processing

Other​‌ Research Topics and Application​​ Domains

  • 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
  • B2.2.6. Neurodegenerative​‌ diseases
  • B2.5.1. Sensorimotor disabilities​​
  • B2.6.1. Brain imaging

1​​​‌ Team members, visitors, external​ collaborators

Research Scientists

  • Théodore​‌ Papadopoulo [Team leader​​, INRIA, Senior​​​‌ Researcher, HDR]​
  • Rodrigo Cofre Torres [​‌INRIA, ISFP,​​ from Feb 2025,​​​‌ HDR]
  • Rachid Deriche​ [INRIA, Emeritus​‌, HDR]
  • Samuel​​ Deslauriers-Gauthier [INRIA,​​​‌ ISFP]
  • Olivier Faugeras​ [INRIA, Emeritus​‌, HDR]
  • Romain​​ Veltz [INRIA,​​ HDR]

PhD Students​​​‌

  • Yanis Aeschlimann [UNIV‌ COTE D'AZUR]
  • Laura‌​‌ Gee [INRIA]​​
  • Petru Isan [CHU​​​‌ NICE]
  • Emeline Manka‌ [UNIV COTE D'AZUR‌​‌]

Technical Staff

  • Evgenia​​ Kartsaki [INRIA,​​​‌ Engineer]

Interns and‌ Apprentices

  • Esin Bahar Akcay‌​‌ [UNIV COTE D'AZUR​​, until Feb 2025​​​‌]
  • Julie Feriau [‌INRIA, Intern,‌​‌ from Mar 2025 until​​ Sep 2025]
  • Harshit​​​‌ Harshit [INRIA,‌ Intern, from Apr‌​‌ 2025 until Aug 2025​​]
  • Martyna Nabialczyk [​​​‌UNIV COTE D'AZUR,‌ from Sep 2025]‌​‌
  • Parker Rice [UNIV​​ COTE D'AZUR, from​​​‌ Sep 2025]
  • Madeline‌ Shaw [UNIV COTE‌​‌ D'AZUR, from Mar​​ 2025 until Apr 2025​​​‌]
  • Teodora-Lucia Stei [‌UNIV COTE D'AZUR,‌​‌ until Jan 2025]​​
  • Diego Zuniga Blassio [​​​‌UNIV COTE D'AZUR,‌ Intern, from Mar‌​‌ 2025 until May 2025​​]

Administrative Assistant

  • Claire​​​‌ Senica [INRIA]‌

2 Overall objectives

The‌​‌ objective of Cronos is​​ to develop models, algorithms,​​​‌ and software to estimate,‌ understand, and quantify the‌​‌ whole brain dynamics. We​​ will achieve this objective​​​‌ by modeling the macroscopic‌ architecture and connectivity of‌​‌ the brain at three​​ complexity levels: source, sensor,​​​‌ and group (see Figure‌ 1). These three‌​‌ levels, detailed in Section​​ 3, will be​​​‌ studied through the unifying‌ representation of dynamic networks.‌​‌

Cronos aims at pushing​​ forward the state-of-the-art in​​​‌ computational brain imaging by‌ developing computational tools to‌​‌ integrate the dynamic and​​ partial information provided by​​​‌ each measurement modality (fMRI,‌ dMRI, EEG, MEG, ...)‌​‌1 into a consistent​​ global dynamic network model.​​​‌

Figure 1

A graphic representation of‌ the 3 Cronos axes‌​‌ (sensor, source and group)​​ and their interactions.

Figure​​​‌ 1: Research axes‌ and their interactions

Developing‌​‌ the computational models, algorithms,​​ and software to estimate,​​​‌ understand, and quantify the‌ brain's dynamical networks is‌​‌ a mathematical and computational​​ challenge. Starting from several​​​‌ specific partial models of‌ the brain, the overall‌​‌ goal is to assimilate​​ in a single global​​​‌ numerical model the diversity‌ of observations provided by‌​‌ non-invasive imaging. Indeed, the​​ observations provided by various​​​‌ modalities are based on‌ very different physical and‌​‌ biological principles. They thus​​ reveal very different but​​​‌ complementary aspects of the‌ brain, including its structural‌​‌ organization, electrical activity, and​​ hemodynamic response. In addition,​​​‌ because of the varied‌ nature of the physical‌​‌ principles used for imaging,​​ different modalities also have​​​‌ drastically different spatial and‌ temporal resolutions making their‌​‌ unification challenging. Some examples​​ of sub-objectives we develop​​​‌ are:

  • Go beyond the‌ hypothesis that brain networks‌​‌ are static over a​​ given period of time.​​​‌
  • Study the possibility of‌ estimating brain functional areas‌​‌ simultaneously with the networks.​​
  • Study the impact on​​​‌ the reconstructed networks of‌ various models of activity‌​‌ transfer between brain areas.​​
  • Develop a complete modeling​​​‌ of time delays involved‌ by long range connections.‌​‌
  • Develop network based regularization​​ methods in estimating brain​​​‌ activity.
  • Go from subject‌ specific studies to group‌​‌ level studies and increase​​​‌ the level of abstraction​ implied by the use​‌ of brain networks to​​ open research perspectives in​​​‌ identifying network characteristics and​ invariances.
  • Study the impact​‌ of the model imperfections​​ on the obtained results.​​​‌

Finally, the software implementing​ our models and algorithms​‌ must be accessible to​​ non-technical users. They must​​​‌ therefore provide a level​ of abstraction, ease of​‌ use, and interpretability suitable​​ for neuroscientists, cogniticians, and​​​‌ clinicians.

2.1 Main Research​ hypotheses

To achieve our​‌ goals, we decided to​​ make some hypotheses on​​​‌ the way brain signals​ and networks are modeled.​‌

2.1.1 Brain Signal Modeling​​

To model brain signals,​​​‌ we adopt a signal​ processing perspective, i.e. consider​‌ that at the macroscopic​​ scale we look at​​​‌ signals, general signal modeling​ approaches are sufficient for​‌ the goal of describing​​ brain dynamics. This contrasts​​​‌ with many other teams,​ which often follow a​‌ more constructivist approach, where​​ brain signal models are​​​‌ derived from a computational​ neuroscience perspective, i.e. emerge​‌ from a mathematical modeling​​ of neurons, axons and​​​‌ dendrites or assemblies of​ those (spiking neurons, neural​‌ mass models, ...). Our​​ approach gives more freedom​​​‌ to model signals and​ allows for descriptions with​‌ a very limited number​​ of parameters at the​​​‌ cost of losing some​ connection with the microscopic​‌ reality. Additionally, the reduced​​ number of parameters simplifies​​​‌ the problem of parameter​ identification. Depending on the​‌ type of modeling, we​​ may use rather simple​​​‌ phenomenological descriptions (e.g. a​ region is activated or​‌ not) or more or​​ less complicated signal models​​​‌ (sampled signals with no​ specific temporal models, various​‌ multivariate autoregressive (AR) models,​​ integro-differential equations, ...). Generally​​​‌ speaking, the more we​ will be interested in​‌ dynamic properties of the​​ signals, the more we​​​‌ will need sophisticated signal​ models.

2.1.2 Network Modeling​‌

Classical – deterministic –​​ networks only strictly exist​​​‌ at the microscopic level​ where neurons are connected​‌ together through axons. For​​ usual neural systems, such​​​‌ networks are huge, currently​ unavailable and too complex​‌ for a macroscopic view​​ of the brain. At​​​‌ such a scale, networks​ are of stochastic nature.​‌ Both nodes and edges​​ are only defined probabilistically.​​​‌ We allow ourselves to​ work either directly with​‌ these probablistic networks or​​ with deterministic networks obtained​​​‌ by thresholding the probabilistic​ ones, in which case​‌ it is important to​​ pay attention to the​​​‌ amount of approximation and​ bias introduced by the​‌ thresholding operation. Its is​​ important to note that,​​​‌ while deterministic networks have​ received a lot of​‌ attention, the domain of​​ stochastic networks or its​​​‌ tranfer to computational neurosciences​ is still in its​‌ infancy.

3 Research program​​

As described in Section​​​‌ 2 and Figure 1​, the research program​‌ of Cronos is organized​​ in 3 main axes​​​‌ corresponding to different levels​ of complexity:

  • The Sensor​‌ level aims at extracting​​ information directly from sensor​​​‌ data, without necessarily using​ the underlying brain anatomy.​‌ It can be thought​​ of as a projection​​​‌ of the underlying brain​ networks onto a low​‌ dimensional space thus allowing​​ computationally efficient processing and​​ analysis. This provides a​​​‌ first window for observing‌ and estimating brain dynamics.‌​‌ This sensor space is​​ particularly convenient for the​​​‌ estimation of properties that‌ are projection invariants (e.g.‌​‌ number of sources, state​​ changes, ...). It is​​​‌ also the level that‌ is most suitable for‌​‌ real time applications, such​​ as brain-computer interfaces (BCI).​​​‌
  • The Source level aims‌ at measurement integration into‌​‌ a unified and high​​ dimensional spatio-temporal space, i.e.​​​‌ a computational representation of‌ dynamic brain networks. This‌​‌ is the level that​​ is understood by neuroscientists,​​​‌ cogniticians, and clinicians, and‌ therefore has an essential‌​‌ role to play in​​ the visualization of brain​​​‌ activities.
  • The Group level‌ aims at providing tools‌​‌ to constrain the search​​ space of the two​​​‌ previous levels. This is‌ the natural space to‌​‌ develop statistical models and​​ tests of the functioning​​​‌ of the brain. It‌ is the level that‌​‌ allows the study of​​ inter-subject variability of brain​​​‌ activity and the development‌ of data driven priors.‌​‌ In particular, the topic​​ of making statistics over​​​‌ noisy networks is a‌ challenging task for this‌​‌ level.

These three levels​​ closely interact with each​​​‌ other, as depicted by‌ Fig. 1, towards‌​‌ the ultimate goal of​​ non-invasively and continuously localizing​​​‌ brain activity in the‌ form of brain networks.‌​‌

3.1 Sensor level: the​​ first window on brain​​​‌ dynamics

Sensor level mostly‌ concerns MEG and EEG‌​‌ measurements. These serve 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). As an​​ inexpensive modality, EEG is​​​‌ also widely used for‌ the development of brain-computer‌​‌ interfaces. EEG and MEG​​ are characterized by a​​​‌ high temporal resolution (up‌ to 1000Hz or more),‌​‌ by a poor spatial​​ resolution (measurable events involve​​​‌ several centimers-square portions of‌ the cortex) and by‌​‌ a rather poor signal-to-noise​​ ratio (SNR)2.​​​‌ For both EEG and‌ MEG, the obtained measurements‌​‌ are linear mixtures of​​ the “true” electrical sources​​​‌ that are at a‌ distance of the sensors.‌​‌ MEG and EEG temporal​​ resolution characteristics allow them​​​‌ to reveal changes in‌ the dynamic of the‌​‌ brain activity. This “sensor​​ space” has two main​​​‌ advantages: 1) its relatively‌ small dimension (from a‌​‌ few to several hundreds​​ sensors) compared to that​​​‌ of the “source space”‌ (tens of thousands of‌​‌ degrees of freedom) and​​ 2) its ease-of-use3​​​‌. It is thus‌ opportune to extract as‌​‌ much information as possible​​ from this lower dimensional​​​‌ space, which already contains‌ all the dynamical information‌​‌ of the functioning brain​​ available from these modalities.​​​‌ This involves a better‌ understanding of the invariants‌​‌ between source and sensor​​ levels, which can lead​​​‌ to better BCI classification‌ algorithms. The BCI field‌​‌ not only clearly is​​ an applicative domain that​​​‌ will benefit from this‌ research, but will also‌​‌ help in validation of​​ algorithms and methods. Our​​​‌ ambition is also to‌ study how BCI-like techniques‌​‌ can be used for​​​‌ constraining the reconstruction of​ brain networks, for detecting​‌ some brain events in​​ real time for clinical​​​‌ applications or for creating​ improved cognitive protocols using​‌ real time responses to​​ dynamically adapt stimulations.

This​​​‌ axis relies on three​ major ideas, which are​‌ necessary steps towards the​​ ultimate goal of using​​​‌ MEG or EEG systems​ to non-invasively and continuously​‌ localize brain activity in​​ the form of brain​​​‌ networks (i.e. without averaging​ multiple trials signals).

3.1.1​‌ Automating the detection of​​ brain state changes from​​​‌ the acquired data

Experimental​ practice in MEG, EEG,​‌ and BCI shows that​​ very valuable information can​​​‌ be obtained directly from​ the “sensor space”. This​‌ encompasses estimating the number​​ 39 or the time​​​‌ courses of sources 35​, 34 or the​‌ detection of changes in​​ the brain dynamical activity.​​​‌ This type of information​ can be an indication​‌ of a “brain state​​ change”. In particular, automating​​​‌ the detection of changes​ in brain states would​‌ allow the splitting of​​ the incoming functional data​​​‌ into segments in which​ the brain network can​‌ be considered as stationary.​​ During such stationary segments​​​‌ of data, the sources​ and their locations remain​‌ fixed, which offers a​​ means to regularize the​​​‌ solution of the inverse​ problem of source reconstruction.​‌ Furthermore, any improvement on​​ EEG signal classification has​​​‌ direct applications for BCI.​ One approach that we​‌ explore is the use​​ of autoregressive spatio-temporal models​​​‌ or lagged correlation measurements​ as a means to​‌ improve classification of MEG/EEG​​ signals. These autoregressive spatio-temporal​​​‌ models constitute a possible​ first step towards using​‌ more sophisticated causality modeling.​​

3.1.2 Better modeling of​​​‌ the spatio-temporal variability of​ brain signals

Hand in​‌ hand with the previous​​ sub-goal is the need​​​‌ to better understand the​ spatio-temporal variability of brain​‌ signals. This variability originates​​ from several factors ranging​​​‌ from the intrinsic variability​ of the brain sources​‌ (even in a same​​ subject) to important differences​​​‌ in the spatial organization​ of the cortex across​‌ subjects or to variations​​ in the way sensors​​​‌ are setup by experimenters.​ Thus, variability occurs not​‌ only across subjects, but​​ also across sessions or​​​‌ even trials for a​ same subject.

The most​‌ common approach developed to​​ cope with the noisy​​​‌ MEG and EEG signals​ is commonly referred to​‌ as evoked potentials: the​​ signal is “clocked” on​​​‌ some stimulus or reaction​ of the subject and​‌ the low amplitude signals​​ – almost completely hidden​​​‌ by background activity –​ are then averaged over​‌ multiple repetitions (trials) of​​ the experiment to improve​​​‌ the SNR. But, because​ of variability, such an​‌ averaging distorts the overall​​ activity and hides specific​​​‌ activities such as high​ frequency components. It is​‌ thus advisable to improve​​ models so that they​​​‌ can “work” in single​ event mode (i.e. without​‌ averaging). Relying on multiple​​ trials to obtain better​​​‌ statistical models of individual​ signals (with techniques such​‌ as dictionary learning, autoregressive​​ models, deep-neural networks, ...)​​​‌ would be an important​ improvement over the current​‌ state-of-the-art as it would​​ provide a more objective​​ and systematic way of​​​‌ characterizing single trial data.‌ Events will be extracted‌​‌ separately for each trial​​ without relying on averaging,​​​‌ but with the knowledge‌ of the “group” model‌​‌ (see Section 3.3).​​ This will allow the​​​‌ study of the variability‌ of brain activity across‌​‌ trials (attention, habituation are​​ e.g. known to change​​​‌ the activity). This is‌ a difficult long term‌​‌ challenge with possible short-middle​​ term advances for some​​​‌ specific cases such as‌ epileptic spikes. This research‌​‌ path is grounded by​​ some of our previous​​​‌ work 2, 6‌. Understanding variability is‌​‌ particularly important for BCI​​ as it is often​​​‌ necessary to “learn” a‌ classifier to detect the‌​‌ subject's brain state with​​ a limited dataset (because​​​‌ of time constraint). At‌ the sensor level, spatial‌​‌ patterns of activity are​​ often described by covariance/correlation​​​‌ matrices. Using Riemannian metric‌ over the space of‌​‌ symmetric definite positive matrices​​ is a powerful technique​​​‌ that has been used‌ these last years by‌​‌ the BCI community 32​​. Extending and improving​​​‌ these techniques as well‌ as finding proper low‌​‌ dimensional spaces that characterize​​ brain activity are other​​​‌ research paths we will‌ follow.

3.1.3 Adapting to‌​‌ new sensor modalities

During​​ the last few years,​​​‌ tremendous improvements have been‌ made on means to‌​‌ acquire functional brain data.​​ Yet, novelty in this​​​‌ domain continues and new‌ sensors are regularly proposed.‌​‌ These sensors can offer​​ more accurate measurements with​​​‌ improved SNR and/or some‌ ease-of-use improvements. For example,‌​‌ the use of room​​ temperature MEG sensors (such​​​‌ as those developed by‌ Mag4Health – see Section‌​‌ 7.2) promise improvements​​ in both aspects. EEG​​​‌ dry electrodes hold the‌ promises to simplify the‌​‌ setup of BCI systems,​​ but are difficult to​​​‌ master. MR machines are‌ also more and more‌​‌ powerful with either higher​​ fields (better signal quality​​​‌ and/or better spatial resolution)‌ or, on the contrary,‌​‌ lower fields (easier to​​ use and better contrasts​​​‌ in some cases). It‌ is important to continually‌​‌ adapt processing methods to​​ exploit the specificities of​​​‌ these new sensors as‌ they become available to‌​‌ the community.

3.2 Source​​ level: the integration space​​​‌

MR images of the‌ brain offer different views‌​‌ of its organization and​​ function via dMRI tractography​​​‌ and fMRI connectivity. When‌ combined with MEG and‌​‌ EEG, we obtain complementary,​​ but highly heterogeneous perspectives​​​‌ on brain networks and‌ their dynamics. The natural‌​‌ space to integrate this​​ complex information is the​​​‌ space of brain sources,‌ allowing a unified model‌​‌ of imaging data. This​​ axis is built over​​​‌ our past research (in‌ the former team Athena‌​‌) in modeling the​​ propagation of the electromagnetic​​​‌ field from brain sources‌ to sensors 7,‌​‌ brain structural connectivity 4​​ or mapping different brain​​​‌ imaging modalities 5.‌ Our plan for fusing‌​‌ the data originating from​​ different modalities into a​​​‌ single network based model‌ can be described in‌​‌ 3 sub-topics.

3.2.1 Source​​ modeling: anatomical, temporal, and​​​‌ numerical constraints

Brain sources‌ refer to regions of‌​‌ interests whose properties link​​​‌ brain activity to the​ observed measurements. For example,​‌ in EEG, brain sources​​ can be modeled as​​​‌ dipoles representing the superposition​ of many synchronous and​‌ parallel neurons. The combination​​ of the electric fields​​​‌ generated by these dipoles​ gives rise to the​‌ potential differences measured at​​ the surface of the​​​‌ scalp in EEG. The​ magnetic fields generated by​‌ these same dipoles give​​ rise to MEG signals.​​​‌ Regardless of the modality,​ the task of recovering​‌ brain sources from imaging​​ data is an inverse​​​‌ problem. This inverse problem​ is ill–posed, either because​‌ of the limited number​​ of sensors (EEG and​​​‌ MEG), because of poor​ signal to noise ratio​‌ (EEG, MEG, fMRI), or​​ because of the limited​​​‌ spatial (dMRI, EEG, MEG)​ or temporal resolution (fMRI,​‌ dMRI). To recover a​​ unique and stable solution,​​​‌ simple mathematical (i.e. not​ fully grounded by biology)​‌ criteria such as minimum​​ norm or sparsity are​​​‌ used to constrain the​ source space. However, these​‌ regularization approaches do not​​ correspond to any specific​​​‌ anatomical or physiological properties​ of the brain and​‌ are therefore quite arbitrary.​​ The challenge we address​​​‌ here is to increase​ the amount of subject​‌ specific anatomical and physiological​​ constraints taken into account​​​‌ for the recovery of​ brain activity from non–invasive​‌ imaging. More specifically, we​​ will investigate how brain​​​‌ networks, and in particular​ their associated delays, can​‌ be used to constrain​​ the inverse problem. Previous​​​‌ work has already shown​ the potential of temporal​‌ regularization based on brain​​ connectivity 4, but​​​‌ the topic remains largely​ open to identifying new​‌ models grounded in physiological​​ data. Another difficulty is​​​‌ the dynamic aspect of​ brain networks: we first​‌ assume that a stationary​​ brain state has been​​​‌ identified (e.g. using methods​ from Section 3.1).​‌ Eventually (as a long​​ term objective), transitions between​​​‌ stationary brain state models​ could be directly modeled​‌ in the networks themselves​​ and estimated from the​​​‌ data. The validation of​ the proposed models is​‌ both challenging and essential​​ and will be explored​​​‌ with our clinical partners​ (see Section 8).​‌ Finally, non-traditional imaging modalities​​ will also be considered.​​​‌ For example, accurate modeling​ of electromyography, in collaboration​‌ with Neurodec, can​​ provide important timing information​​​‌ of sources.

3.2.2 Unified​ network models explaining various​‌ brain measurements

In the​​ previous section, brain activity​​​‌ is estimated from one​ modality using information from​‌ the others as constraints​​ or priors. This obviously​​​‌ favors one modality over​ the others and propagates​‌ errors of processing pipelines​​ via the constraints. This​​​‌ modus operandi, while suboptimal,​ is historically justified: analysis​‌ pipelines have been developed​​ independently for each modality​​​‌ by different communities. Given​ the complementary nature of​‌ the different modalities, it​​ seems relevant to instead​​​‌ construct one global pipeline​ encompassing all brain measurement​‌ modalities into a single​​ unified framework. With brain​​​‌ networks arising as a​ central concept in the​‌ neuroscientific community, we propose​​ to make it the​​​‌ basis of such a​ global model. Doing so​‌ will enable the recovery​​ of brain network dynamics​​ from non–invasive multi–modal data,​​​‌ an important open problem‌ in neuroscience. To achieve‌​‌ this objective, we propose​​ to devise forward models​​​‌ describing the link between‌ brain networks and each‌​‌ of the various imaging​​ modalities. Specifically, effort is​​​‌ needed to evaluate different‌ formalisms describing brain networks‌​‌ that differ in the​​ way nodes and their​​​‌ interactions are defined. For‌ example, we investigate the‌​‌ relationship between electrical (EEG/MEG),​​ architectural (dMRI) and metabolic​​​‌ (fMRI) activities. Separated models‌ – either electric or‌​‌ hemodynamic – have been​​ proposed for some time,​​​‌ but coupling them is‌ an important challenge all‌​‌ the more that the​​ role of some neural​​​‌ constituents (such as glia)‌ is currently not well‌​‌ understood. Such models have​​ already been – at​​​‌ least partly as in‌ 33 – devised. The‌​‌ main challenge is to​​ define one that is​​​‌ sufficiently simple and well‌ spatialized (in particular to‌​‌ incorporate connectivity) in order​​ to be useful for​​​‌ our purpose. We will‌ also consider electromyography in‌​‌ this context, extending brain​​ networks to the peripherial​​​‌ nervous system.

3.2.3 Global‌ inverse problem using all‌​‌ measurements altogether

Models established​​ in the previous section​​​‌ can be used in‌ a global inverse problem‌​‌ involving all the measurements​​ modalities to recover the​​​‌ specific brain network involved‌ in a task. In‌​‌ all cases, we need​​ to solve an inverse​​​‌ problem over a complex‌ network model with a‌​‌ sparse prior as we​​ need to find “simple”​​​‌ networks that can explain‌ our data. Depending on‌​‌ the way networks are​​ modeled, some difficulties may​​​‌ arise. For example, the‌ model defined in 36‌​‌, 37 leads to​​ combinatorial explosion when used​​​‌ for source localization. Finding‌ appropriate models that facilitate‌​‌ the resolution of this​​ inverse problem may require​​​‌ some iterations between this‌ sub-task and the previous‌​‌ one.

3.3 Group level:​​ understanding variability to constrain​​​‌ network properties

Given the‌ high intra- or inter-subject‌​‌ variability of brain activity,​​ it is particularly interesting​​​‌ to be able to‌ characterize the part of‌​‌ the activity that remains​​ invariant (over time for​​​‌ one subject or across‌ different subjects). This will‌​‌ allow a better understanding​​ of brain processes as​​​‌ well as a better‌ understanding of their variability‌​‌ across time or subjects.​​ It also opens the​​​‌ possibility to constrain network‌ models to reduce their‌​‌ complexity and improve their​​ identifiability. The following description​​​‌ mostly refers to group‌ statistics at the source‌​‌ level, but similar techniques​​ are also relevant for​​​‌ the sensor level axis‌ (see Section 3.1).‌​‌ This axis is a​​ long term research effort​​​‌ as it builds upon‌ previous axes.

3.3.1 Matching‌​‌ individual subject models

Reconstructions​​ obtained in Section 3.2​​​‌ will certainly differ even‌ for different measurement sessions‌​‌ obtained with a same​​ subject. An important problem​​​‌ to solve is the‌ matching of instances of‌​‌ such reconstructions (whether they​​ consist in brain networks​​​‌ or spatio-temporal autoregressive models).‌ In general, the relative‌​‌ positions of functional brain​​ areas are fairly well​​​‌ known. However, temporal variations‌ (lag, duration) in these‌​‌ models make the matching​​​‌ problem rather complicated. Finding​ and using some invariants​‌ of the models is​​ one path to find​​​‌ a good compromise that​ would allow for enough​‌ flexibility in the matching​​ process while avoiding the​​​‌ combinatorial complexity that e.g.​ graph matching problems usually​‌ exhibit. Another – long​​ term – possibility would​​​‌ be to directly solve​ “group problems”, but this​‌ would complexify even more​​ the modeling problem and​​​‌ might have the same​ drawbacks as averaging if​‌ not properly done (i.e.​​ hiding some activity or​​​‌ the intrinsic variability of​ the studied phenomenon).

3.3.2​‌ Statistics over brain networks​​

Once the matching of​​​‌ single subject models has​ been solved, statistics will​‌ be necessary to assess​​ the significance of the​​​‌ various model elements (e.g.​ in the case of​‌ dynamic network models, brain​​ areas and their connections).​​​‌ Such statistics can also​ be used as a​‌ basis to derive “group​​ statistical models” describing a​​​‌ family of task-related models​ that can in turn​‌ be used to constrain​​ models used in Section​​​‌ 3.2 and, through a​ forward model to reduce​‌ the dimension of the​​ search space at sensor​​​‌ level (see Section 3.1​). The BCI community​‌ is still divided on​​ the actual benefits in​​​‌ terms of accuracy on​ using the source space​‌ (v.s. the sensor space)​​ for classifying brain signals.​​​‌ The statistical tools developed​ in this sub-axis may​‌ help to address this​​ problem.

4 Application domains​​​‌

4.1 Clinical applications

Cronos​ research has a strong​‌ clinical potential impact for​​ brain diseases like epilepsy,​​​‌ brain cancer surgery, phantom​ pains, traumatic brain injuries,​‌ anoxia and dissorders of​​ consciousness. We closely work​​​‌ with several hospital teams​ and research groups (​‌Pasteur hospital in Nice​​, La Timone hospital​​​‌ in Marseille, CRNL –​ Centre de Recherche en​‌ Neuroscience in Lyon and​​ the Toulouse Neuroimaging center​​​‌) towards exporting our​ research in their medical​‌ contexts. Example of applications​​ are:

  • Better understanding brain​​​‌ stimulation used in awake​ brain surgery and its​‌ relation with brain anatomy​​ and in particular fibers​​​‌ as measured by dMRI.​
  • Real time detection of​‌ epileptic spikes from new​​ generation MEG data and​​​‌ the visualization of their​ associated brain sources in​‌ real time.
  • Use of​​ BCI (see Section 4.2​​​‌) for helping disabled​ people to communicate (e.g.​‌ for patients suffering from​​ Amyotrophic Lateral Sclerosis) or​​​‌ for helping epileptic patients​ to learn how to​‌ control the occurence of​​ seizures.
  • Understand the somatotopy​​​‌ of the thalamus and​ its relation with the​‌ efficiency of the deep​​ brain stimulation therapy.
  • A​​​‌ deeper understanding of the​ neural correlates of disorders​‌ of consciousness, with the​​ goal of identifying objective​​​‌ markers of patients states​ of consciousness.

4.2 Brain​‌ Computer Interfaces (BCI)

BCI​​ is a closely related​​​‌ domain to both the​ “Signal Processing” (Section 2.1.1​‌) and “Network Modeling”​​ (Section 2.1.2) aspects.​​​‌ It typically extracts from​ the signal a “brain​‌ state”' that is a​​ correlate of the “brain​​​‌ network”. While traditional MEG/EEG​ studies have been extensively​‌ exploited by the BCI​​ community, the opposite nourishing​​ of the former field​​​‌ by BCI has been‌ much less explored. There‌​‌ is a continuing dispute​​ in the BCI community​​​‌ on the advantages of‌ going to source space‌​‌ or not (see e.g.​​ 38). By studying​​​‌ the invariants between source‌ and sensor space, we‌​‌ hope not only to​​ provide clues on the​​​‌ above dispute but also‌ to open the opportunity‌​‌ of using BCI-like techniques​​ to ease the more​​​‌ traditional brain signal processing.‌ In some sense, such‌​‌ invariants are the information​​ that BCI exploits in​​​‌ doing classification on sensor‌ data. BCI also has‌​‌ the advantage of providing​​ a more quantitative way​​​‌ (in term of classification‌ quality) to evaluate methods.‌​‌ Controlling the amount of​​ resources (computer power, number​​​‌ and quality of sensors,‌ ...) needed to achieve‌​‌ a given classification accuracy​​ is also a strong​​​‌ BCI concern. This point‌ of view is also‌​‌ complementary to that of​​ more traditional brain signal​​​‌ modeling and can have‌ a significant impact in‌​‌ terms of cost and​​ ease of use in​​​‌ the clinical context.

5‌ Latest software developments, platforms,‌​‌ open data

5.1 Latest​​ software developments

5.1.1 BCI-VIZAPP​​​‌

  • Name:
    Real time EEG‌ applications
  • Keyword:
    EEG
  • Functional‌​‌ Description:
    BCI-VIZAPP is a​​ software suite for designing​​​‌ real-time EEG applications such‌ as BCIs or neurofeedback‌​‌ applications. It has been​​ been developed to build​​​‌ a virtual keyboard for‌ typing text and a‌​‌ photodiode monitoring application for​​ checking timing issues, but​​​‌ can now be also‌ used in other tasks‌​‌ such as EEG monitoring.​​ Originally, it was designed​​​‌ to delegate signal acquisition‌ and processing to OpenViBE‌​‌ but has recently been​​ extended to get some​​​‌ of these capabilities. This‌ allows for more integrated‌​‌ and robust applications but​​ also opens up new​​​‌ algorithmic opportunities, such as‌ real time parameter modification,‌​‌ more controlled interfaces, ...​​
  • News of the Year:​​​‌
    Bci-Vizapp has been enriched‌ with numerous features, notably‌​‌ to read and save​​ certain files created with​​​‌ OpenViBE or with MNE-python,‌ thus allowing an easier‌​‌ communication with them. Bci-Vizapp​​ is also the software​​​‌ base used (or which‌ we aim to use‌​‌ it in the long​​ term) for different current​​​‌ (Demagus and ConnectTC) or‌ past (Techicopa) contracts and‌​‌ has integrated different elements​​ to support them.
  • Contact:​​​‌
    Théodore Papadopoulo
  • Participants:
    Nathanael‌ Foy, Théodore Papadopoulo, Maureen‌​‌ Clerc Gallagher, Come Le​​ Breton, Evgenia Kartsaki, Romain​​​‌ Lacroix, Jean-Luc Szpyrka, Julien‌ Wintz, 5 anonymous participants‌​‌

5.1.2 Tractography.jl

  • Keywords:
    GPGPU,​​ Diffusion MRI
  • Functional Description:​​​‌
    Tractography.jl is a high-performance‌ Julia package for brain‌​‌ tractography that leverages parallel​​ computing and specialized hardware​​​‌ (e.g., GPUs) to reconstruct‌ white matter fiber bundles‌​‌ from diffusion-weighted MRI data.​​ This enables researchers to​​​‌ study the structural connectivity‌ of the brain at‌​‌ unprecedented scales.
  • URL:
  • Contact:
    Romain Veltz
  • Participants:​​​‌
    Romain Veltz, Samuel Deslauriers-Gauthier,‌ Evgenia Kartsaki

5.1.3 tractography‌​‌

  • Name:
    tractography
  • Keywords:
    Tractography,​​ Diffusion MRI
  • Scientific Description:​​​‌

    The tractography package provides‌ a high-performance computational framework‌​‌ for reconstructing the complex​​ 3D trajectories of white​​​‌ matter pathways from diffusion‌ Magnetic Resonance Imaging (dMRI)‌​‌ data.

    This software addresses​​​‌ the computational bottlenecks commonly​ associated with structural connectomics​‌ and neuroimaging research. Specifically,​​ the package implements advanced​​​‌ tractography methods grounded in​ both stochastic differential equations​‌ and partial differential equations​​ reformulations of the tractography​​​‌ problem, enabling a robust​ and precise mapping of​‌ neural topology. To handle​​ the immense computational demands​​​‌ of large-scale, high-resolution dMRI​ datasets, the library is​‌ heavily optimized for parallel​​ execution, seamlessly supporting both​​​‌ multi-core CPU and hardware-accelerated​ GPU architectures.

  • Functional Description:​‌
    `tractography` is a Python​​ package designed for performing​​​‌ tractography, the process of​ reconstructing nerve fiber pathways​‌ from diffusion MRI (dMRI)​​ data. Developed by the​​​‌ Inria CRONOS team, the​ package implements various tractography​‌ algorithms and is optimized​​ for high performance, supporting​​​‌ execution on both CPUs​ and GPUs.
  • URL:
  • Contact:
    Samuel Deslauriers-Gauthier
  • Participants:​​
    Samuel Deslauriers-Gauthier, Romain Veltz,​​​‌ Evgenia Kartsaki

5.1.4 BifurcationKit​

  • Name:
    Automatic computation of​‌ numerical bifurcation diagrams
  • Keywords:​​
    Bifurcation, GPU
  • Functional Description:​​​‌

    This Julia package aims​ at performing automatic bifurcation​‌ analysis of possibly large​​ dimensional equations function of​​​‌ a real parameter by​ taking advantage of iterative​‌ methods, dense / sparse​​ formulation and specific hardware​​​‌ (e.g. GPU).

    It incorporates​ continuation algorithms (PALC, deflated​‌ continuation, ...) based on​​ a Newton-Krylov method to​​​‌ correct the predictor step​ and a Matrix-Free/Dense/Sparse eigensolver​‌ is used to compute​​ stability and bifurcation points.​​​‌

    The package can also​ seek for periodic orbits​‌ of Cauchy problems. It​​ is by now one​​​‌ of the few software​ programs which provide shooting​‌ methods and methods based​​ on finite differences or​​​‌ collocation to compute periodic​ orbits.

    The current package​‌ focuses on large-scale, multi-hardware​​ nonlinear problems and is​​​‌ able to use both​ Matrix and Matrix Free​‌ methods on GPU.

  • News​​ of the Year:
    Development​​​‌ of a Proof of​ Concept (POC) on boundary​‌ value problems (BVP) (with​​ Inria SAM SED). Improved​​​‌ calculation of normal shapes​ of periodic orbits. Correction​‌ of the calculation of​​ normal shapes of equilibrium​​​‌ points.
  • URL:
  • Publication:​
  • Contact:
    Romain Veltz​‌
  • Participant:
    an anonymous participant​​

5.1.5 SynapseElife

  • Keyword:
    Markov​​​‌ model
  • Functional Description:

    This​ is the main library,​‌ written in Julia language,​​ for the simulation of​​​‌ a synapse model. The​ associated publication is 10.7554/eLife.80152.​‌ It implements a model​​ of excitatory synapse in​​​‌ the rat hippocampus.

    This​ code allows to replicate​‌ the results of the​​ paper. It is also​​​‌ used by the Julia​ community to benchmark the​‌ methods for simulating piecewise​​ deterministic Markov processes.

  • URL:​​​‌
  • Publication:
  • Contact:​
    Romain Veltz
  • Participant:
    Romain​‌ Veltz

5.1.6 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 state-of-the art tools​ for modelling bio-electromagnetic propagation​‌ in the quasi-static 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 small updates and‌ bug corrections. Notably, bugs‌​‌ related to the python​​ interface and to Blas/Lapack​​​‌ implementations have been handled.‌
  • URL:
  • Publications:
  • Contact:
    Théodore Papadopoulo
  • Participants:​​​‌
    Eric Larson, Théodore Papadopoulo,‌ 8 anonymous participants

6‌​‌ New results

6.1 Sensor​​ Level: Brain Signal Modeling​​​‌ (see Section 3.1)‌

6.1.1 Electrophysiology and BCI‌​‌

Augmented Covariance Approaches for​​ BCI

Participants: Igor Carrara​​​‌, Théodore Papadopoulo.‌

EEG signals are complex‌​‌ and difficult to characterize,​​ in particular because of​​​‌ their variability. They therefore‌ require the use of‌​‌ specific and adapted signal​​ processing methods. In a​​​‌ recent approach 1,‌ 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 line of work​​ is to explore the​​​‌ possibility of exploiting EEG/MEG‌ autoregressive models to extract‌​‌ as much information as​​ possible without requiring the​​​‌ complex head modeling needed‌ for source reconstruction.

A‌​‌ first result in this​​ line of research is​​​‌ the use of Augmented‌ Covariance Matrices (ACMs) for‌​‌ BCI classification 3.​​ These ACMs appear naturally​​​‌ in the Yule-Walker equations‌ that were derived to‌​‌ recover autoregressive models from​​ data. ACMs being symmetric​​​‌ positive definite matrices, it‌ is natural to apply‌​‌ Riemannian geometry based classification​​ approaches on these objects​​​‌ as they represent the‌ current state-of-the-art. Using these‌​‌ ACMs noticeably improves classification​​ performance on several BCI​​​‌ benchmarks both in the‌ within-session or in the‌​‌ cross-session evaluation protocols4​​. This is due​​​‌ to the fact that‌ ACMs incorporate not only‌​‌ spatial (the classical covariance​​ matrix) but also temporal​​​‌ information. As such, it‌ contains information on the‌​‌ nonlinear components of the​​ signal through the embedding​​​‌ procedure, which allows the‌ leveraging of dynamical systems‌​‌ algorithms. This comes at​​ the cost of introducing​​​‌ two hyper-parameters: the order‌ of the autoregressive model‌​‌ and a delay that​​ controls the time resolution​​​‌ at which the signal‌ is considered, which have‌​‌ to be estimated.

The​​ method also turned out​​​‌ to be useful in‌ the context of learning‌​‌ with a limited amount​​ of training data. This​​​‌ work on limited training‌ data is described in‌​‌ the article 16.​​

Uncertainty Propagation: From EEG​​​‌ Measurements to BCI classification‌

Participants: Julie Feriau,‌​‌ Théodore Papadopoulo.

Affine​​ invariant Log-Euclidean Riemannian metrics​​​‌ have proven over the‌ years to be extremely‌​‌ effective for comparing symmetric​​​‌ positive definite matrices, in​ particular for classifying BCI​‌ data (see previous paragraph).​​ We studied the problem​​​‌ of propagating uncertainty coming​ from measurements in the​‌ computation of these metrics,​​ which has been largely​​​‌ overlooked so far.

Optimizing​ EEG based P300 classifiers​‌

Participants: Martyna Nabialczyk,​​ Evgenia Kartsaki, Théodore​​​‌ Papadopoulo.

The P300​ speller is a virtual​‌ keyboard BCI system that​​ allows paralyzed patients to​​​‌ communicate with the outside​ world. The development of​‌ this system was first​​ carried out in the​​​‌ framework of the former​ Athena team in close​‌ collaboration with doctors at​​ the University Hospital of​​​‌ Nice to ensure that​ the application would ultimately​‌ lead to products that​​ are comfortable, easy to​​​‌ use, and truly beneficial​ to patients and is​‌ still used and developed​​ within Cronos. The​​​‌ system is based on​ the difference in EEG​‌ measurements depending on whether​​ a letter on which​​​‌ a subject is focusing​ its attention is flashed​‌ or not. The obtained​​ signal is quite challenging​​​‌ but exploitable. But this​ system is still based​‌ on a basic linear​​ discriminant analysis classifier. The​​​‌ intent of this work​ is to study how​‌ more modern Riemannian based​​ classifiers can improve the​​​‌ classification performance in various​ situations (within session, cross-session​‌ or cross-subject).

Exploring and​​ exploiting the new capabilities​​​‌ of room temperature MEG​ sensors

Participants: Laura Gee​‌, Théodore Papadopoulo,​​ Christian Bénar [Institut de​​​‌ neurosciences des systèmes, Marseille]​.

Traditionally, MEG sensor​‌ work with SQUIDs (superconducting​​ quantum interference device) that​​​‌ require cryogenic temperatures. Recently,​ new magnetic sensors called​‌ OPMs (Optically Pumped Magnetometers)​​ were developed and do​​​‌ not require such low​ temperatures. In particular, we​‌ are working with the​​ company Mag4Health that develops​​​‌ a MEG machine with​ helium based OPMs that​‌ can work at room​​ temperature. This allows to​​​‌ have sensors closer to​ the head and these​‌ new sensors are also​​ able to measure the​​​‌ 3 components of the​ magnetic field (SQUIDs are​‌ measuring only one such​​ components). But this sensors​​​‌ are also more noisy​ and the 3 measured​‌ components of the magnetic​​ field are not suffering​​​‌ from the same level​ of noise. It is​‌ thus interesting to better​​ study the sensitivity of​​​‌ these new MEG machines​ and to develop methods​‌ that can exploit efficiently​​ the specificities of these​​​‌ sensors. This is the​ subject of the Ph.D​‌ thesis of L. Gee,​​ co-supervized with C. Bénar​​​‌ who work in La​ Timone Hospital, which acquired​‌ recently a 96 (x3​​ channels) Mag4Health device.

Inverse​​​‌ Problems in Electromyography

Participants:​ Madeline Shaw, Emeline​‌ Manka, Samuel Deslauriers-Gauthier​​.

Although surface Electromyography​​​‌ (EMG) and Electroencephalography (EEG)​ share identical underlying physics​‌ governed by Maxwell’s equations—both​​ aiming to recover physiological​​​‌ sources from non-invasive recordings—their​ methodological approaches have historically​‌ remained distinct. This project​​ aims to bridge that​​​‌ gap by adapting advanced​ forward modeling and inverse​‌ problem techniques originally developed​​ for EEG to the​​​‌ domain of EMG. Our​ primary objective is the​‌ estimation of motor unit​​ spike trains using subject-specific​​ volume conductors, necessitating the​​​‌ adaptation of established tools‌ to handle anatomical extraction‌​‌ from MRI, tissue conductivity​​ estimation, and complex volume​​​‌ deformations during movement. Concurrently,‌ we are applying EEG-inspired‌​‌ algorithms, including Minimum Norm​​ Estimates and Maximum Entropy​​​‌ on the Mean, to‌ solve the inverse problem‌​‌ in EMG. The performance​​ of these novel approaches​​​‌ is quantified using real‌ forearm data validated against‌​‌ ground-truth intramuscular recordings, with​​ ultimate applications in motor​​​‌ control analysis, neurorehabilitation, and‌ muscle-computer interfaces.

6.1.2 Diffusion‌​‌ MRI

Mathematical Analysis of​​ Tractography Algorithms

Participants: Samuel​​​‌ Deslauriers-Gauthier, Evgenia Kartsaki‌, Romain Veltz.‌​‌

Current dMRI fiber tractography​​ algorithms function as numerical​​​‌ approximations to an often‌ ill-defined problem. Historically, the‌​‌ field has prioritized the​​ empirical capacity to trace​​​‌ white matter trajectories over‌ mathematical formulation or numerical‌​‌ precision. Data-driven approaches, for​​ example jointly using diffusion​​​‌ and functional MRI data‌ 20, have been‌​‌ prioritized to validate and​​ advance tractography. In this​​​‌ work, we revisited these‌ algorithms through a rigorous‌​‌ mathematical lens, reformulating them​​ as classical stochastic differential​​​‌ equations and partial differential‌ equations. This framework allowed‌​‌ us to derive new​​ algorithms with well-characterized parameter​​​‌ behaviors 19, 30‌ and to investigate direct‌​‌ solutions to the associated​​ Fokker-Planck equations 29.​​​‌ Motivated by this theoretical‌ foundation, we developed high-performance‌​‌ GPU-accelerated software (see 5.1.2​​, 5.1.3). These​​​‌ tools enabled the generation‌ of connectivity matrices based‌​‌ on a record-breaking five​​ hundred billion streamlines 18​​​‌, providing exceptionally tight‌ bounds on connectivity uncertainty.‌​‌ These results were presented​​ at JuliaCon Paris 2025​​​‌ and the inaugural International‌ Society for Tractography Conference‌​‌ 18, 19.​​ A manuscript is being​​​‌ written for submission to‌ a journal.

6.2 Source‌​‌ Level: Brain Dynamic Network​​ Modeling (see Section 3.2​​​‌)

6.2.1 Understanding Brain‌ Functional Connectivity

Modeling Direct‌​‌ Electrostimulation for Functional Brain​​ Mapping

Participants: Emeline Manka​​​‌, Samuel Deslauriers-Gauthier,‌ Théodore Papadopoulo, Evgenia‌​‌ Kartsaki, Petru Isan​​, Fabien Almairac [CHU​​​‌ Nice, Université Côte d'Azur]‌.

Optimizing the balance‌​‌ between maximum lesion removal​​ and the preservation of​​​‌ functional tissue remains the‌ primary challenge in glioma‌​‌ surgery. While direct electrostimulation​​ during awake surgery is​​​‌ the current gold standard‌ for functional mapping, it‌​‌ is not viable for​​ all patients. In this​​​‌ work, we addressed this‌ limitation by developing a‌​‌ patient-specific conductivity model of​​ the head to simulate​​​‌ electrophysiological signals.

We validated‌ this physical approach using‌​‌ data recorded during awake​​ surgeries on two patients​​​‌ at Nice University Hospital.‌ Using anatomical MRI (pre-‌​‌ and post-operative) and electrocorticography​​ recordings, we constructed tetrahedral​​​‌ meshes and simulated the‌ propagation of stimulation artifacts‌​‌ using a Finite Element​​ Method. Our results demonstrate​​​‌ a strong correlation between‌ simulated and observed artifact‌​‌ amplitude distributions, effectively validating​​ the physical conductivity model.​​​‌ Notably, we found that‌ the presence of the‌​‌ resection cavity did not​​ significantly alter the simulation​​​‌ fit. Furthermore, we proposed‌ a one-source model for‌​‌ brain evoked potentials. While​​ preliminary results are promising​​​‌ for certain cortical sites,‌ the complexity of other‌​‌ observed patterns suggests that​​​‌ future iterations must incorporate​ heterogeneous conductivities (differentiating white​‌ and grey matter) and​​ explicit propagation pathways via​​​‌ white matter tracts.

This​ work was presented at​‌ the annual conference of​​ the Organization for Human​​​‌ Brain Mapping 31.​

Log-Euclidean Frameworks for Smooth​‌ Brain Connectivity Trajectories

Participants:​​ Olivier Bisson [EPIONE, Inria]​​​‌, Yanis Aeschlimann,​ Samuel Deslauriers-Gauthier, Xavier​‌ Pennec [EPIONE, Inria].​​

The brain is often​​​‌ studied from a network​ perspective, where functional activity​‌ is assessed using functional​​ magnetic resonance imaging to​​​‌ estimate connectivity between predefined​ neuronal regions. Functional connectivity​‌ can be represented by​​ correlation matrices computed over​​​‌ time, where each matrix​ captures the Pearson correlation​‌ between the mean fMRI​​ signals of different regions​​​‌ within a sliding window.​ We introduce several Log-Euclidean​‌ Riemannian framework for constructing​​ smooth approximations of functional​​​‌ brain connectivity trajectories. Representing​ dynamic functional connectivity as​‌ time series of full-rank​​ correlation matrices, we leverage​​​‌ recent theoretical Log-Euclidean diffeomorphisms​ to map these trajectories​‌ in practice into Euclidean​​ spaces where polynomial regression​​​‌ becomes feasible. Pulling back​ the regressed curve ensures​‌ that each estimated point​​ remains a valid correlation​​​‌ matrix, enabling a smooth,​ interpretable, and geometrically consistent​‌ approximation of the original​​ brain connectivity dynamics. Experiments​​​‌ on fMRI-derived connectivity trajectories​ demonstrate the geometric consistency​‌ and computational efficiency of​​ our approach.

This work​​​‌ was published in 17​.

Characterizing Dynamic Functional​‌ Connectivity Subnetwork Contributions in​​ Narrative Classification with Shapley​​​‌ Values

Participants: Aurora Rossi​ [COATI, Inria], Yanis​‌ Aeschlimann, Emanuele Natale​​ [COATI, Inria], Samuel​​​‌ Deslauriers-Gauthier, Peter Ford​ Dominey [MR1093-CAPS, INSERM].​‌

Functional connectivity derived from​​ functional magnetic resonance imaging​​​‌ data has been increasingly​ used to study brain​‌ activity. In this study,​​ we model brain dynamic​​​‌ functional connectivity during narrative​ tasks as a temporal​‌ brain network and employ​​ a machine learning model​​​‌ to classify in a​ supervised setting the modality​‌ (audio, movie), the content​​ (airport, restaurant situations) of​​​‌ narratives, and both combined.​ Leveraging Shapley values, we​‌ analyze subnetwork contributions within​​ Yeo parcellations (7- and​​​‌ 17- subnetworks) to explore​ their involvement in narrative​‌ modality and comprehension. This​​ work represents the first​​​‌ application of this approach​ to functional aspects of​‌ the brain, validated by​​ existing literature, and provides​​​‌ novel insights at the​ whole-brain level. Our findings​‌ suggest that schematic representations​​ in narratives may not​​​‌ depend solely on pre-existing​ knowledge of the top-down​‌ process to guide perception​​ and understanding, but may​​​‌ also emerge from a​ bottom-up process driven by​‌ the temporal parietal subnetwork.​​

This work has been​​​‌ published in 15.​

6.2.2 Dynamical models towards​‌ Whole Brain Models

Whole​​ brains models are models​​​‌ of the whole brain​ modeled using a graph​‌ where each node is​​ used to describe a​​​‌ cortical area and where​ the edges represent the​‌ connections between the cortical​​ areas. Whole brains models​​​‌ are very attractive from​ a modeling point of​‌ view because we can​​ use data such as​​​‌ structural connectivity from diffusion​ MRI in place of​‌ the graph edges. One​​ needs to assign a​​ dynamics to each node​​​‌ in order to study‌ the structure-function mapping and‌​‌ thus study the link​​ between fMRI and MRI.​​​‌ Traditionally, heuristically derived models‌ of the dynamics of‌​‌ populations of neurons are​​ used for the dynamics​​​‌ of the nodes. However,‌ the model of neural‌​‌ populations can be rigorously​​ derived from the dynamics​​​‌ of large networks of‌ interconnected neurons making the‌​‌ link direct between microscopic​​ elements and mesoscopic components.​​​‌

The Impact of Homeostatic‌ Inhibitory Plasticity in a‌​‌ Generative Biophysical Model

Participants:​​ Iván Mindlin [Sorbonne Université,​​​‌ Institut du Cerveau -‌ Paris Brain Institute -‌​‌ ICM, Inserm, CNRS, 75013,​​ Paris, France], Carlos​​​‌ Coronel-Oliveros [rinity College Dublin,‌ The University of Dublin,‌​‌ Dublin, Ireland.], Jacobo​​ D. Sitt [Sorbonne Université,​​​‌ Institut du Cerveau -‌ Paris Brain Institute -‌​‌ ICM, Inserm, CNRS, 75013,​​ Paris, France], Rodrigo​​​‌ Cofre, Andrea Luppi‌ [Department of Psychiatry, University‌​‌ of Oxford, Oxford, UK]​​, Thomas Andrillon [Sorbonne​​​‌ Université, Institut du Cerveau‌ - Paris Brain Institute‌​‌ - ICM, Inserm, CNRS,​​ 75013, Paris, France],​​​‌ Yonatan Sanz-Perl [Center for‌ Brain and Cognition, Computational‌​‌ Neuroscience Group, Universitat Pompeu​​ Fabra, Spain], Rubén​​​‌ Herzog [Instituto de Física‌ Interdisciplinar y Sistemas Complejos‌​‌ (IFISC, UIB-CSIC), Campus UIB,​​ Palma de Mallorca, Spain]​​​‌.

A main characteristic‌ of biological systems is‌​‌ their capacity to dynamically​​ adapt to environmental changes.​​​‌ In the brain, synaptic‌ plasticity enables the strengthening‌​‌ or weakening of connections​​ between neurons, allowing neural​​​‌ circuits to adapt based‌ on experience, learning, and‌​‌ environmental changes. Yet, it​​ is homeostatically regulated such​​​‌ that it avoids excessive‌ proliferation of synaptic contacts.‌​‌ These mechanisms can be​​ studied with large-scale models​​​‌ of brain activity. Here,‌ we embed a biologically‌​‌ grounded inhibitory-homeostatic plasticity rule​​ into the Dynamic Mean​​​‌ Field (DMF) model, creating‌ a Homeostatic Dynamic Mean‌​‌ Field (HDMF) model that​​ dynamically tunes local excitation–inhibition​​​‌ balance. Convergence of excitatory‌ firing rates is reached‌​‌ by mapping a large​​ range of coupling strength​​​‌ to parameters of inhibitory‌ synapses. The HDMF reproduces‌​‌ statistical observables of brain​​ activity as well as​​​‌ the original DMF, and‌ can sustain neuromodulatory perturbations‌​‌ without overhead computations. The​​ HDMF can generate unprecedented​​​‌ sleep-like slow-wave activity, which‌ can also coexist with‌​‌ wake-like asynchronous dynamics, permitting​​ to model dissociated states​​​‌ of consciousness such as‌ parasomnias. Together, these results‌​‌ show that a single​​ homeostatic rule broadens the​​​‌ stability and expressiveness of‌ the DMF, providing a‌​‌ unified platform for studying​​ how local adaptive processes​​​‌ shape the diverse global‌ dynamics of the human‌​‌ brain.

This work is​​ available as a preprint​​​‌ 27.

Simulated 5-HT2A‌ Receptor Activation Accounts for‌​‌ the High Complexity of​​ Brain Activity during Psychedelic​​​‌ States

Participants: Hugo M‌ Martin [CNRS, NeuroPsi Institute‌​‌ Paris, France], Rodrigo​​ Cofre, Alain Destexhe​​​‌ [CNRS, NeuroPsi Institute Paris,‌ France].

Serotonergic psychedelics,‌​‌ such as lysergic acid​​ diethylamide (LSD), psilocybin, and​​​‌ Dimethyltryptamine (DMT), have strong‌ effects on human brain‌​‌ activity, yet their mechanisms​​ of action at the​​​‌ whole-brain level are only‌ partially understood. Here, we‌​‌ present a biophysically-based meanfield​​​‌ model that integrates cellular​ and network-level details to​‌ simulate the effects of​​ these compounds at different​​​‌ spatial scales. By incorporating​ the brain-wide distribution of​‌ 5-HT 2A receptors, our​​ model mechanistically links receptor​​​‌ activation to a reduction​ in leak membrane potassium​‌ conductance, consistent with electrophysiological​​ data. Our simulations reveal​​​‌ that this microscopic perturbation​ leads to the emergence​‌ of a brain state​​ characterized by asynchronous and​​​‌ irregular dynamics with increased​ firing rates, as well​‌ as significant alterations in​​ spectral power. Specifically, we​​​‌ find a robust decrease​ in power within the​‌ delta, theta, and alpha​​ frequency bands, a result​​​‌ consistent with empirical findings.​ This change in dynamics​‌ is accompanied by an​​ increase in spontaneous complexity,​​​‌ as quantified by the​ Lempel-Ziv complexity index, as​‌ observed experimentally. Furthermore, our​​ model accurately replicates experimental​​​‌ findings regarding the Perturbational​ Complexity Index, demonstrating that​‌ it does not increase​​ significantly by psychedelic drug​​​‌ administration. This crucial dissociation,​ where spontaneous complexity and​‌ spectral power are increased​​ while perturbational complexity is​​​‌ preserved, highlights the distinct​ neurophysiological substrates underlying different​‌ metrics in psychedelic states.​​ Our multiscale model provides​​​‌ a robust, mechanistic framework​ for understanding how serotoninergic​‌ psychedelics modulate global brain​​ activity.

This work is​​​‌ available as a preprint​ 26.

Analysis of​‌ Large Size Networks of​​ Hopfield Neurons

Participants: Olivier​​​‌ Faugeras, Etienne Tanré​ [INRIA / LJAD, Nice,​‌ France].

We revisit​​ the problem of characterizing​​​‌ the thermodynamic limit of​ a fully connected network​‌ of Hopfield-like neurons. Our​​ contributions are: a) a​​​‌ complete description of the​ mean-field equations as a​‌ set of stochastic differential​​ equations depending on a​​​‌ mean and covariance functions,​ b) a provably convergent​‌ method for estimating these​​ functions, and c) numerical​​​‌ results of this estimation​ as well as examples​‌ of the resulting dynamics.​​ The mathematical tools are​​​‌ the theory of Large​ Deviations, Itô stochastic calculus,​‌ and the theory of​​ Volterra equations.

This work​​​‌ has been published in​ 12.

Pros and​‌ Cons of Mean Field​​ Representations of Large Size​​​‌ Networks of Spiking Neurons​

Participants: Olivier Faugeras,​‌ Romain Veltz.

We​​ have laid out a​​​‌ roadmap for classifying the​ behaviors of large ensembles​‌ of networks of spiking​​ neurons through the analysis​​​‌ of the corresponding nonlinear​ Fokker-Planck equation. Rather than​‌ using this equation to​​ simulate the network equations,​​​‌ we apply advanced methods​ for analyzing the bifurcations​‌ of its solutions. This​​ analysis can then be​​​‌ used to predict the​ behaviors of the original​‌ network. We have used​​ the example of a​​​‌ fully connected network of​ N Fitzhugh-Nagumo neurons with​‌ electrical and chemical synapses​​ to convey the interest​​​‌ of our approach.

A​ manuscript is being written​‌ for submission to a​​ journal.

Analysis of a​​​‌ Mean–field Limit of Interacting​ Two-dimensional Nonlinear Integrate-and-fire Neurons​‌

Participants: Romain Veltz.​​

We study in this​​​‌ work 28 the solutions​ of a McKean-Vlasov stochastic​‌ differential equation (SDE) driven​​ by a Poisson process.​​​‌ In neuroscience, this SDE​ models the mean field​‌ limit of a system​​ of N interacting excitatory​​ neurons, with N large.​​​‌ Each neuron spikes randomly‌ with a rate depending‌​‌ on its membrane potential.​​ At each spiking time,​​​‌ the neuron potential is‌ reset to the value‌​‌ v¯, its​​ adaptation variable is incremented​​​‌ by w¯ and‌ all other neurons receive‌​‌ an additional amount J​​/N of potential​​​‌ after some delay where‌ J is the connection‌​‌ strength. Between jumps, the​​ neurons drift according to​​​‌ some two-dimensional ordinary differential‌ equation with explosive behavior.‌​‌ We prove the existence​​ and uniqueness of solutions​​​‌ of a heuristically derived‌ mean-field limit of the‌​‌ system when N→​​. We then​​​‌ study the existence of‌ stationary distributions and provide‌​‌ several properties (regularity, tail​​ decay, etc.) based on​​​‌ a Doeblin estimate using‌ a Lyapunov function. Numerical‌​‌ simulations are provided to​​ assess the hypotheses underlying​​​‌ the results.

These results‌ set the basis for‌​‌ the rigorous study of​​ mean-field models of stochastic​​​‌ networks of neurons, each‌ described with an adaptive‌​‌ exponential integrate-and-fire model, whose​​ use is widespread in​​​‌ whole brain models.

Mean-field‌ Analysis of a Neural‌​‌ Network with Stochastic STDP​​

Participants: Pascal Helson [Université​​​‌ de Bordeaux], Etienne‌ Tanré, Romain Veltz‌​‌.

In this work​​ 25, we study​​​‌ neural networks with stochastic‌ synaptic plasticity.

Analyzing biological‌​‌ spiking neural network models​​ with synaptic plasticity has​​​‌ proven to be challenging‌ both theoretically and numerically.‌​‌ In a network with​​ N all-to-all connected neurons,​​​‌ the number of synaptic‌ connections is on the‌​‌ order of N2​​, making these models​​​‌ computationally demanding. Furthermore, the‌ intricate coupling between neuron‌​‌ and synapse dynamics, along​​ with the heterogeneity generated​​​‌ by plasticity, hinder the‌ use of classic theoretical‌​‌ tools such as mean-field​​ or slow-fast analyses to​​​‌ study the dynamics of‌ the plastic network. To‌​‌ address these challenges, we​​ study a stochastic spike-timing-dependent​​​‌ plasticity (STDP) model of‌ connection in a probabilistic‌​‌ Wilson-Cowan spiking neural network​​ model, which features binary​​​‌ neural activity. Taking the‌ large N limit, we‌​‌ obtain a simplified yet​​ accurate representation of the​​​‌ original spiking network. Our‌ approach not only reduces‌​‌ computational complexity but also​​ provides insights into the​​​‌ dynamics of this spiking‌ neural network with plasticity.‌​‌ The model obtained is​​ mathematically exact and capable​​​‌ of tracking transient changes.‌ This analysis marks the‌​‌ first exploration of the​​ dynamics, of McKean-Vlasov type,​​​‌ in a network of‌ spiking neurons interacting with‌​‌ STDP.

6.2.3 Clinical applications​​

Optimization of Brain Models​​​‌ to Simulate the Effects‌ of Anesthesia

Participants: Parker‌​‌ Rice, Evgenia Kartsaki​​, Samuel Deslauriers-Gauthier,​​​‌ Rodrigo Cofre.

Various‌ whole-brain computational models have‌​‌ recently been developed to​​ explore brain mechanisms. This​​​‌ project focuses on optimizing‌ the parameters of a‌​‌ model designed to simulate​​ the effects of anesthesia​​​‌ on brain networks. Building‌ on an existing approach‌​‌ based on biophysical mean-field​​ models that incorporate membrane​​​‌ conductances and synaptic receptors,‌ the goal is to‌​‌ adjust the model parameters​​ to best match experimental​​​‌ data.

Transcranial Direct Current‌ Stimulation Modulates Primate Brain‌​‌ Dynamics Across States of​​​‌ Consciousness

Participants: Guylaine Hoffner​ [Cognitive Neuroimaging Unit, CEA,​‌ INSERM, Université Paris-Saclay, NeuroSpin​​ Center, Gif-sur-Yvette, France],​​​‌ Pablo Castro [Institute of​ Neuroscience (NeuroPSI), Paris-Saclay University,​‌ CNRS, Gif-sur-Yvette, France],​​ Lynn Uhrig [Department of​​​‌ Anesthesiology and Critical Care,​ Necker Hospital, AP-HP, Université​‌ Paris Cité, Paris, France]​​, Camilo Miguel Signorelli​​​‌ [Department of Computer Science,​ University of Oxford, Oxford,​‌ United Kingdom], Morgan​​ Dupont [Cognitive Neuroimaging Unit,​​​‌ CEA, INSERM, Université Paris-Saclay,​ NeuroSpin Center, Gif-sur-Yvette, France]​‌, Jordy Tasserie [Center​​ for Brain Circuit Therapeutics,​​​‌ Department of Neurology, Brigham​ & Women’s Hospital, Harvard​‌ Medical School, Boston, USA]​​, Alain Destexhe [Institute​​​‌ of Neuroscience (NeuroPSI), Paris-Saclay​ University, CNRS, Gif-sur-Yvette, France]​‌, Rodrigo Cofre,​​ Jacobo Sitt [Sorbonne Université,​​​‌ Institut du Cerveau –​ Paris Brain Institute (ICM),​‌ Inserm, CNRS, Paris, France]​​, Béchir Jarraya [Cognitive​​​‌ Neuroimaging Unit, CEA, INSERM,​ Université Paris-Saclay, NeuroSpin Center,​‌ Gif-sur-Yvette, France].

The​​ resting primate brain is​​​‌ traversed by spontaneous functional​ connectivity patterns that show​‌ striking differences between conscious​​ and unconscious states. Transcranial​​​‌ direct current stimulation (tDCS),​ a non-invasive neuromodulatory technique,​‌ can improve signs of​​ consciousness in disorders of​​​‌ consciousness (DOCs); however, can​ it influence both conscious​‌ and unconscious dynamic functional​​ connectivity? We investigated the​​​‌ modulatory effect of prefrontal​ cortex (PFC) tDCS on​‌ brain dynamics in awake​​ and anesthetized non-human primates​​​‌ using functional MRI. In​ awake macaques receiving either​‌ anodal or cathodal tDCS,​​ we found that cathodal​​​‌ stimulation robustly disrupted the​ repertoire of functional connectivity​‌ patterns, increased structure–function correlation​​ (SFC), decreased Shannon entropy,​​​‌ and favored transitions toward​ anatomically based patterns. Under​‌ deep sedation, anodal tDCS​​ significantly altered brain pattern​​​‌ distribution and reduced SFC.​ The prefrontal stimulation also​‌ modified dynamic connectivity arrangements​​ typically associated with consciousness​​​‌ and unconsciousness. Our findings​ offer compelling evidence that​‌ PFC tDCS induces striking​​ modifications in the fMRI-based​​​‌ dynamic organization of the​ brain across different states​‌ of consciousness. This study​​ contributes to an enhanced​​​‌ understanding of tDCS neuromodulation​ mechanisms and has important​‌ clinical implications for DOCs.​​

This work has been​​​‌ published in 13.​

A Mesoscale Framework for​‌ Psychedelic Drug Action in​​ the Human Brain

Participants:​​​‌ Rui Dai [Michigan Psychedelic​ Center, University of Michigan​‌ Medical School, Ann Arbor,​​ MI, USA], Rodrigo​​​‌ Cofre, Christopher Timmermann​ [UCL Centre for Consciousness​‌ Research, Department of Experimental​​ Psychology, University College London,​​​‌ London, United Kingdom],​ Robin L Carhart-Harris [Departments​‌ of Neurology and Psychiatry,​​ University of California, San​​​‌ Francisco, San Francisco, CA,​ USA], Anthony G​‌ Hudetz [Department of Anesthesiology,​​ University of Michigan Medical​​​‌ School, Ann Arbor, MI,​ USA], Zirui Huang​‌ [Center for Consciousness Science,​​ University of Michigan Medical​​​‌ School, Ann Arbor, MI,​ USA], George A​‌ Mashour [Department of Anesthesiology,​​ University of Michigan Medical​​​‌ School, Ann Arbor, MI,​ USA].

The mechanism​‌ of psychedelic drug action​​ is a dynamic area​​​‌ of neuroscience, with two​ major lines of investigation:​‌ (1) laboratory studies at​​ the molecular and cellular​​​‌ level, and (2) human​ neuroimaging studies of functional​‌ brain networks. Despite considerable​​ progress, there remains insufficient​​ understanding of the link​​​‌ between molecular/cellular substrates of‌ psychedelics and the whole-brain‌​‌ network effects that result.​​ In this work, we​​​‌ report a study of‌ psychedelic action that focuses‌​‌ on the intermediate spatial​​ scale of local brain​​​‌ regions (<1 cm3‌ ). We analyzed the‌​‌ effects of classical psychedelics​​ (dimethyltryptamine [DMT], lysergic acid​​​‌ diethylamide [LSD], psilocybin) and‌ non-classical psychedelics (nitrous oxide,‌​‌ ketamine) in humans using​​ functional magnetic resonance imaging.​​​‌ We found that all‌ five drugs reduced regional‌​‌ homogeneity, that is, they​​ disrupted local synchrony, in​​​‌ small-scale brain regions; this‌ disruption occurred extensively in‌​‌ cortical regions and sparsely​​ in subcortical regions. Dynamic​​​‌ analysis of both regional‌ homogeneity and global functional‌​‌ connectivity showed an inverse​​ pattern, with large-scale functional​​​‌ connectivity being enhanced as‌ local synchrony declined. We‌​‌ then conducted dominance analysis​​ to assess the contribution​​​‌ of various neurotransmitter receptors‌ to changes in regional‌​‌ homogeneity. DMT, LSD, and​​ psilocybin showed the 5-HT​​​‌ receptors as the most‌ dominant association; by contrast,‌​‌ regional homogeneity changes attributable​​ to both nitrous oxide​​​‌ and ketamine were most‌ strongly associated with the‌​‌ NMDA receptor. Both neuronal​​ (including interneurons) and non-neuronal​​​‌ cell types were linked‌ to psychedelic-induced changes in‌​‌ synchrony at the level​​ of local brain regions.​​​‌ These data, across five‌ drugs from two drug‌​‌ classes, provide evidence that​​ a diverse set of​​​‌ molecular and cellular events‌ lead to a common‌​‌ outcome of disrupted synchrony​​ in local brain regions,​​​‌ which in turn mediate‌ drug-specific changes in global‌​‌ functional connectivity effects.

This​​ work is available as​​​‌ a preprint 24.‌

6.3 Group Level (see‌​‌ Section 3.3)

Alignment​​ of Brain Networks

Participants:​​​‌ Yanis Aeschlimann, Samuel‌ Deslauriers-Gauthier, Théodore Papadopoulo‌​‌, Anna Calissano [University​​ College of London].​​​‌

Every brain is unique,‌ having its structural and‌​‌ functional organization 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 project​​ questions such an assumption:​​​‌ can the structural and‌ functional properties of a‌​‌ specific region of an​​ atlas be assumed to​​​‌ be the same across‌ subjects? In this work,‌​‌ 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. Structural connectivity is‌ one view of brain‌​‌ networks provided by dMRI,​​ but these networks can​​​‌ also be observed from‌ a functional point of‌​‌ view via fMRI. We​​ thus propose to simultaneously​​​‌ exploit structural and functional‌ information in the alignment‌​‌ process. This allows us​​ to explore multiple perspective​​​‌ of brain networks. Our‌ results show that the‌​‌ permutations induced by one​​ type of connectivity (structural,​​​‌ functional) are not always‌ supported by the other‌​‌ connectivity network, but when​​ considering a combined alignment,​​​‌ it is possible to‌ find permutations of regions‌​‌ which are supported by​​​‌ both connectome modalities, leading​ to an increased similarity​‌ of functional and structural​​ connectivity across subjects.

This​​​‌ work has been published​ in 9, 22​‌ and in the thesis​​ of Yanis Aeschlimann 21​​​‌.

6.4 Other Results​

We report here results​‌ either obtained in the​​ framework of the team​​​‌ that preceeded Cronos and​ that are only published​‌ now, or works that​​ do not fit well​​​‌ with the main team​ objectives.

Investigating the Cognitive​‌ Drivers of Auditory Attention​​ Detection

Participants: Joan Belo​​​‌, Maureen Clerc,​ Daniele Schön [Institut de​‌ Neurosciences des Systèmes].​​

While M/EEG-based Auditory Attention​​​‌ Detection (AAD) can identify​ which audio stream a​‌ user is focusing on,​​ performance varies significantly between​​​‌ individuals. This work investigated​ the hypothesis that executive​‌ functions—specifically sustained attention, working​​ memory, and attentional inhibition—underlie​​​‌ this variability. We designed​ a challenging paradigm using​‌ dichotic polyphonic piano excerpts​​ presented to 41 participants​​​‌ with varying musical expertise.​

Our results demonstrate that​‌ attentional inhibition is a​​ significant predictor of AAD​​​‌ performance, explaining 6% of​ reconstruction accuracy and 8%​‌ of classification accuracy. Surprisingly,​​ neither musical expertise nor​​​‌ other executive functions showed​ a significant impact. These​‌ findings indicate that cognitive​​ control mechanisms directly affect​​​‌ the robustness of neural​ auditory representations, providing crucial​‌ insights for the development​​ of next-generation, neuro-steered hearing​​​‌ aids.

This work was​ published in 10.​‌

Improving Generative Fairness in​​ VAEs on Imbalanced Data​​​‌

Participants: Aymene Mohammed Bouayed​ [Be-Ys Research], Samuel​‌ Deslauriers-Gauthier, Adrian Iaccovelli​​ [Be-Ys Research], David​​​‌ Naccache [DIENS, ENS, CNRS,​ PSL University].

Variational​‌ Autoencoders (VAE) utilizing global​​ priors typically mirror the​​​‌ class frequencies of the​ training set within the​‌ latent space. This characteristic​​ leads to the underrepresentation​​​‌ of tail classes and​ reduced generative fairness when​‌ applied to imbalanced datasets.​​ While existing methods improve​​​‌ robustness via heavy-tailed Student's​ t-distribution priors, they continue​‌ to allocate latent volume​​ proportionally to class frequency.​​​‌

In this work, we​ address this limitation by​‌ explicitly enforcing equitable latent​​ space allocation. We propose​​​‌ Conditional-VAE, a method that​ defines a per-class Student's​‌ t joint prior over​​ latent and output variables​​​‌ to prevent dominance by​ majority classes. The model​‌ is optimized using a​​ closed-form objective derived from​​​‌ the β-power divergence. Furthermore,​ to ensure class-balanced generation,​‌ we derive an equal-weight​​ latent mixture of Student's​​​‌ t-distributions. Experimental results on​ standard databases (SVHN-LT, CIFAR100-LT,​‌ and CelebA) demonstrate that​​ Conditional-VAE consistently achieves lower​​​‌ Fréchet inception distance scores​ than both VAE and​‌ Gaussian-based VAE baselines, particularly​​ under severe class imbalance.​​​‌ In per-class F1 evaluations,​ the proposed approach substantially​‌ improves generative fairness and​​ diversity compared to conditional​​​‌ Gaussian VAEs in highly​ imbalanced regimes.

This work​‌ is available as a​​ preprint 23.

CNN​​​‌ Explainability with Multivector Tucker​ Saliency Maps for Self-Supervised​‌ Models

Participants: Aymene Mohammed​​ Bouayed [Be-Ys Research],​​​‌ Samuel Deslauriers-Gauthier, Adrian​ Iaccovelli [Be-Ys Research, France]​‌, David Naccache [DIENS,​​ ENS, CNRS, PSL University]​​​‌.

Interpreting the decisions​ of Convolutional Neural Networks​‌ (CNN) is essential for​​ understanding their behavior, yet​​ it remains a significant​​​‌ challenge, particularly for self-supervised‌ models. Most existing methods‌​‌ for generating saliency maps​​ rely on reference labels,​​​‌ restricting their use to‌ supervised tasks. The EigenCAM‌​‌ approach is the only​​ notable label-independent alternative, leveraging​​​‌ singular value decomposition to‌ generate saliency maps applicable‌​‌ across CNN models, but​​ it does not fully​​​‌ exploit the tensorial structure‌ of feature maps. In‌​‌ this work, we introduce​​ the Tucker Saliency Map​​​‌ (TSM) method, which applies‌ Tucker tensor decomposition to‌​‌ better capture the inherent​​ structure of feature maps,​​​‌ producing more accurate singular‌ vectors and values. These‌​‌ are used to generate​​ high-fidelity saliency maps, effectively​​​‌ highlighting objects of interest‌ in the input. We‌​‌ further extend EigenCAM and​​ TSM into multivector variants—Multivec-EigenCAM​​​‌ and Multivector Tucker Saliency‌ Maps (MTSM)—which utilize all‌​‌ singular vectors and values,​​ further improving saliency map​​​‌ quality. Quantitative evaluations on‌ supervised classification models demonstrate‌​‌ that TSM, Multivec-EigenCAM, and​​ MTSM achieve competitive performance​​​‌ with label-dependent methods. Moreover,‌ TSM enhances interpretability by‌​‌ approximately 50% over EigenCAM​​ for both supervised and​​​‌ self-supervised models. Multivec-EigenCAM and‌ MTSM further advance state-of-the-art‌​‌ interpretability performance on self-supervised​​ models, with MTSM achieving​​​‌ the best results.

This‌ work has been published‌​‌ in 11.

7​​ Bilateral contracts and grants​​​‌ with industry

7.1 Bilateral‌ contracts with industry

FinalSpark:‌​‌ collaborative research agreement -​​ 2024-2028

Participants: Patricia Reynaud-Bouret​​​‌ [DR CNRS, LJAD],‌ Paula Pousinha [MCF, IPMC]‌​‌, Ingrid Bethus [PR,​​ IPMC], Evgenia Kartsaki​​​‌, Gilles Scarella [IG,‌ CNRS, LJAD], Gregorio‌​‌ Rebecchi [PhD student, LJAD]​​, Romain Veltz.​​​‌

This is a collaborative‌ research agreement on the‌​‌ study of the “deformation​​ of the neuronal network​​​‌ by synaptic plasticity”. G.‌ Rebecchi is a Ph.D.‌​‌ student, since October 1st,​​ 2024 under the supervision​​​‌ of P. Reynaud-Bouret and‌ I. Bethus on the‌​‌ topic described above. This​​ PhD is funded by​​​‌ CNRS and by FinalSpark.‌

  1. Description of the transfer.‌​‌Knowledge transfer. This is​​ a collaborative research agreement​​​‌ between FinalSpark, Université‌ Côte d'Azur, Inria and‌​‌ CNRS. The Parties wishes​​ to collaborate in order​​​‌ to understand more precisely‌ the synaptic connectivity of‌​‌ the neurospheres and how​​ it can be manipulated.​​​‌
  2. Transfer modalities. It is‌ based on a contract.‌​‌ The study is on-going.​​
  3. Contribution. R. Veltz is​​​‌ one of the parties‌ on the contract as‌​‌ an expert in dynamical​​ systems and synapses models.​​​‌

7.2 Bilateral Grants with‌ Industry

Demagus: BPI Grant‌​‌ April 2022–September 2025

Participants:​​ Laura Gee, Éléonore​​​‌ Haupaix-Birgy, Noémie Gonnier‌, Côme Le Breton‌​‌, Théodore Papadopoulo,​​ Julien Wintz.

This​​​‌ grant has been obtained‌ with the startup Mag4Health,‌​‌ CNRS and INSERM (see​​ Section 3.1.3). This​​​‌ company develops a new‌ MEG machine working with‌​‌ optically pumped magnetometers (magnetic​​ sensors), which potentially means​​​‌ lower costs and better‌ measurements. Cronos is in‌​‌ charge of developing a​​ real time interface for​​​‌ signal visualization, source reconstruction‌ and epileptic spikes detection.‌​‌ The initial funding was​​ for 2 years, but​​​‌ three extensions of 6‌ months have been obtained.‌​‌ This work is related​​​‌ to the research goals​ described in Section 3.1.3​‌.

8 Partnerships and​​ cooperations

8.1 International initiatives​​​‌

SynPlasTool

Participants: Romain Veltz​, Hélène Marie [IPMC]​‌.

  • Title:
    Development of​​ the Synapse Plasticity Tool​​​‌ for prediction of synapse​ plasticity outcome in silico.​‌
  • Coordinator Name :
    Hélène​​ Marie
  • Partner Institution:
    IPMC​​​‌
  • Date/Duration:
    2024-2026

SynPlasTool is​ funded by FC3R, obtained​‌ in collaboration with H.​​ Marie (IPMC), 37500 euros.​​​‌ The main goal is​ to make easily accessible​‌ (web platform, ...) to​​ experimentalists the model that​​​‌ we developed 10.7554/eLife.80152.​ It is mainly a​‌ programming project that relies​​ on the software described​​​‌ in 5.1.5.

8.1.1​ Associate Teams in the​‌ framework of an Inria​​ International Lab or in​​​‌ the framework of an​ Inria International Program

MUSCULAR​‌ (Inria London Programme)

Participants:​​ Samuel Deslauriers-Gauthier.

  • Coordinator​​​‌ Name :
    Samuel Deslauriers-Gauthier​
  • Partner Institution:
    Imperial College​‌ London
  • Date/Duration:
    2023-2025
  • Web​​ site

During its third​​​‌ year, the associated team​ MUSCULAR (Inria London Programme)​‌ continued its effort on​​ developing novel algorithms to​​​‌ estimate motor unit spike​ trains from surface electromyography​‌ (EMG). Two different approaches​​ are pursued in parallel:​​​‌ electrode location optimization and​ physics-informed inverse problems.

Electrode​‌ optimization: The first approach​​ is based on the​​​‌ idea that the electrode​ configuration is not optimized​‌ and leads to variations​​ in sensitivity across populations.​​​‌ For example, the number​ of identified motor neurons​‌ is typically larger in​​ males than females. We​​​‌ also observe variations in​ sensitivity across target muscle​‌ groups within a single​​ individual. Using the forward​​​‌ models developed during the​ first year, we generated​‌ highly realistic EMG signals,​​ using our previously developed​​​‌ myoelectric digital twin 8​, representing a large​‌ population of individuals with​​ varying anatomical features. The​​​‌ large amount of data​ generated allowed us to​‌ globally optimize electrode design​​ for specific populations (females/males)​​​‌ or for specific muscle​ architectures (e.g. pennate v.s.​‌ fusiform). The strength of​​ this approach is to​​​‌ leverage highly realistic simulations​ to optimize over a​‌ large population whose EMG​​ signals would be unfeasible​​​‌ to acquire in vivo​ (potentially thousands of individuals).​‌

Physics informed inverse problems:​​ The second approach leverages​​​‌ volume conductor knowledge to​ enhance the estimation of​‌ motor unit spike trains.​​ Using anatomical MRI data​​​‌ of the forearm —​ acquired in various positions​‌ during the first year​​ with optimized sequences —​​​‌ the team has constructed​ physically realistic forward models​‌ for EMG in two​​ subjects. We are now​​​‌ investigating the theoretical aspects​ of the problem, building​‌ on our expertise in​​ electroencephalography (EEG). One of​​​‌ the challenges we have​ investigated is the inclusion​‌ of the known temporal​​ components of EMG, which​​​‌ are typically unknown in​ EEG.

The members of​‌ MUSCULAR also submitted an​​ EIC Pathfinder proposal which​​​‌ was rated excellent (4.75​ / 5.00), but unfortunately​‌ not funded. Given this​​ excellent feedback, we have​​​‌ started improving the proposal​ for resubmittion in early​‌ 2026.

While this is​​ the last year of​​​‌ the associated team, we​ have secured funding for​‌ a student exchange which​​ ensure the teams will​​ continue collaborating into 2026.​​​‌

8.2 International research visitors‌

8.2.1 Visits of international‌​‌ scientists

  • In September, L.​​ Florack and L. Smolders​​​‌ from Eindhoven Technological University‌ visited the team to‌​‌ discuss their work on​​ geodesic tractography and brain​​​‌ structure–function mapping.
  • P. Ford-Dominey‌ visited the team on‌​‌ several occations to discuss​​ input-driven functional connectivity. These​​​‌ discussion led to an‌ ANR proposal currently in‌​‌ review.

8.3 National initiatives​​

ANR ChaMaNe, Mathematical Challenges​​​‌ in Neurosciences

Participants: Romain‌ Veltz.

  • Coordinator Name‌​‌ :
    Delphine Salort (Sorbonne​​ Université)
  • Partner Institutions:
    • Partner​​​‌ 1: Biologie Computationnelle et‌ Quantitative (CQB), France
    • Partner‌​‌ 2: LJAD, Université Nice,​​ France
  • Date/Duration:
    2020-2025
  • Web​​​‌ site

This project aimed‌ at a mathematical study,‌​‌ on the one hand,​​ of the intrinsic dynamics​​​‌ of a neuron and‌ their consequences, and on‌​‌ the other hand, of​​ the qualitative dynamics of​​​‌ large neural networks with‌ respect to the intrinsic‌​‌ behavior of the individual​​ neurons, the interactions between​​​‌ them, memory effects, spatial‌ structure, etc.

FHU InnovPain‌​‌ 2

Participants: Petru Isan​​, Théodore Papadopoulo,​​​‌ Romain Veltz.

  • Coordinator‌ Name :
    Denys Fontaine‌​‌ (Pasteur Hospital)
  • Date/Duration:
    2023–2027​​
  • Web site

The FHU​​​‌ INOVPAIN is a Hospital-University‌ Federation focused on chronic‌​‌ refractory pain and innovative​​ therapeutic solutions. It involves​​​‌ 6 hospital facilities, 13‌ academic research teams and‌​‌ 12 platforms and core​​ facilities.

Inria-Inserm fellowship

Participants:​​​‌ Laura Gee, Théodore‌ Papadopoulo, Christian Bénar‌​‌.

  • Date/Duration:
    2024–2027

The​​ Ph.D. of L. Gee​​​‌ is funded by an‌ Inria-Inserm fellowship (see section‌​‌ 6 for a description​​ of the work).

ANR​​​‌ NeuroMotor

Participants: Samuel Deslauriers-Gauthier‌.

  • Coordinator Name :‌​‌
    François Hug (LAMHESS, Université​​ Côte d'Azur)
  • Date/Duration:
    2024–2027​​​‌

There are many physical‌ disabilities with a neurological‌​‌ origin, such as stroke​​ and spinal cord injuries,​​​‌ that significantly impact a‌ person’s mobility, physical capacity,‌​‌ stamina, or dexterity. In​​ the era of personalized​​​‌ medicine, optimizing the treatment‌ of these physical disabilities‌​‌ requires: i) accessing direct​​ information on the neural​​​‌ commands that are sent‌ to the muscles, and‌​‌ ii) integrating this knowledge​​ into the development and​​​‌ assessment of rehabilitation and‌ neurotechnology aimed at restoring‌​‌ movement. The breakthrough of​​ our approach lies in​​​‌ changing the level at‌ which we observe the‌​‌ control of movement, i.e.,​​ shifting focus from the​​​‌ level of whole muscles‌ to the spinal (alpha)‌​‌ motor neurons. To achieve​​ this, we will combine​​​‌ the use of dense‌ grids of surface EMG‌​‌ electrodes with algorithms that​​ decode the firing activity​​​‌ of spinal motor neurons.‌ By unraveling the “neural‌​‌ code” for movement generation,​​ we will address critical​​​‌ gaps in our understanding‌ of the control of‌​‌ movement in health and​​ disease. In this project,​​​‌ we will decode the‌ activity of large populations‌​‌ of motor neurons from​​ different muscles. We will​​​‌ identify motor neuron synergies,‌ defined as functional groups‌​‌ of motor neurons that​​ share inputs from various​​​‌ supraspinal, spinal and sensory‌ sources. In this translational‌​‌ project, we will examine​​ the structure and plasticity​​​‌ of these synergies in‌ both healthy controls and‌​‌ patients with neurological impairments​​​‌ (stroke, spinal cord injury).​ We will also enhance​‌ the electrode design to​​ facilitate the transfer of​​​‌ these methods into clinical​ settings.

ANR spinPAIN-PATH

Participants:​‌ Romain Veltz.

  • Coordinator​​ Name :
    Emmanuel Deval​​​‌ (IPMC, Université Côte d'Azur)​
  • Date/Duration:
    2025–2029

The main​‌ objective of this project​​ is to better understand​​​‌ spinal pain processes, which​ still remain to be​‌ fully deciphered. It will​​ focus on the role​​​‌ of particular ion channels,​ Acid-Sensing Ion Channels (ASICs),​‌ highly expressed in the​​ spinal pain neuronal network​​​‌ but where their functions​ have yet to be​‌ fully elucidated. Indeed, if​​ their role in pain​​​‌ has been largely documented​ in peripheral sensory neurons,​‌ far less is known​​ in the central nervous​​​‌ system (CNS), particularly at​ the spinal cord level.​‌ This project is based​​ on preliminary data, demonstrating​​​‌ (i) a large expression​ of particular ASIC subunits​‌ in spinal neurons both​​ in mouse and human,​​​‌ and (ii) a potent​ analgesic effect of specific​‌ ASIC blockers injected intrathecally​​ in mice. Importantly, the​​​‌ in vivo analgesic effect​ observed in mice with​‌ the ASIC1a inhibitor, mambalgin-1,​​ can be as strong​​​‌ as that of morphine​ and partially independent of​‌ the endogenous opioid system,​​ opening new potential therapeutic​​​‌ perspectives in a context​ of world opioid crisis.​‌ In line with the​​ preliminary data, the specific​​​‌ aims are 1) to​ localize the different ASIC​‌ subunits in the different​​ neuronal populations and characterize​​​‌ their association in the​ spinal dorsal horn (SDH)​‌ of both mice and​​ humans, 2) to assess​​​‌ their overall contribution to​ the SDH network activity​‌ by combining in vitro​​ primary culture model with​​​‌ computational modeling and, 3)​ to explore the in​‌ vivo and ex vivo​​ contribution of spinal ASICs​​​‌ to long-term sensitization processes,​ with a particular focus​‌ on inhibitory interneurons, in​​ neuropathic pain condition, which​​​‌ needs new therapeutic perspectives​ and where spinal ASICs​‌ have been already involved.​​

8.4 Regional initiatives

NeuroMod​​​‌

Participants: Rodrigo Cofre Torres​, Samuel Deslauriers-Gauthier,​‌ Olivier Faugeras, Evgenia​​ Kartsaki, Théodore Papadopoulo​​​‌, Romain Veltz.​

The NeuroMod Institute​​​‌ for Modeling in Neuroscience​ and Cognition aims at​‌ promoting modeling as an​​ approach for integrating brain​​​‌ mechanisms and cognitive functions.​ To meet this central​‌ challenge of integration in​​ cognitive science, the institute​​​‌ relies on the interdisciplinary​ resources available within the​‌ Université Côte d’Azur: more​​ than 250 researchers and​​​‌ 16 laboratories.

Université Côte​ d'Azur encourages interaction between​‌ human sciences (psychology, behavioral​​ economics, language sciences), modeling​​​‌ (computer science, mathematics, physics,​ etc.) and neuroscience (biology,​‌ neurophysiology, cognitive neuroscience, medicine,​​ etc.). NeuroMod is unique​​​‌ because of the variety​ of approaches used to​‌ integrate different models at​​ multiple levels, from neurons​​​‌ and their molecular mechanisms,​ to cognitive processes and​‌ behaviors, through neural network​​ dynamics.

NeuroMod also provides​​​‌ interdisciplinary training for Master​ students, PhD students and​‌ future faculty members. We​​ opened an international elite​​​‌ degree in Modeling for​ Neuronal and Cognitive Systems​‌ (Master of Science Mod4NeuCog)​​ and a national Master's​​ degree in Cognitive Science.​​​‌

Cronos is deeply involved‌ in this regional initiative‌​‌ through its researchers, but​​ also through its engineer​​​‌ E. Kartsaki, who devotes‌ part of its time‌​‌ to software projects of​​ the institute.

PSI ion​​​‌ channels

Participants: Théodore Papadopoulo‌, Romain Veltz.‌​‌

  • Coordinator Name :
    M.​​ Mantegazza, E. Lingueglia (IPMC,​​​‌ Université Côte d'Azur)
  • Date/Duration:‌
    2025–2031

The Programme Stratégique‌​‌ IdEx (PSI) Ion Channels​​ capitalizes on Université Côte​​​‌ d’Azur’s teams already present‌ in former LABEX ICST‌​‌ 1.0 and 2.0 projects​​ (F. Lesage, M. Mantegazza,​​​‌ E. Lingueglia & E.‌ Deval, and E. Honoré‌​‌ from IPMC, G. Sandoz​​ from iBV and L.​​​‌ Counillon from LP2M) to‌ include new teams (from‌​‌ IPMC (H. Marie/J. Barik,​​ M. Chami/A. DaCosta, P.​​​‌ Blancou/T. Simon) and iBV‌ (O. Soriani), strengthening basic‌​‌ and translational research in​​ biology, but also from​​​‌ Inria (T. Papadopoulo) and‌ the J. A. Dieudonné‌​‌ laboratory (P. Reynaud-Bouret) for​​ mathematical modeling, and UR2CA​​​‌ (D. Fontaine/M. Lanteri-Minet) for‌ clinics) in order to‌​‌ fully exploit the University’s​​ strengths and extend its​​​‌ scope to build a‌ multidisciplinary approach targeting the‌​‌ pathophysiology of ion channels​​ and excitability5.​​​‌

The PSI has several‌ objectives:

  • Train PhD students‌​‌ offering competitive PhD fellowships.​​
  • Boost Université Côte d’Azur’s​​​‌ International development and visibility.‌
  • Develop technological innovations.
  • Strengthen‌​‌ interaction with industry and​​ the University Hospital.
  • Help​​​‌ the evolution of Université‌ Côte d’Azur’s teams.

The‌​‌ landscape of the PSI​​ Ion Channels will cover​​​‌ from basic science to‌ translation and innovation through‌​‌ cutting edge techniques (ex​​ vivo & in vivo​​​‌ electrophysiology, neurostimulation, optopharmacology, transcriptomics,‌ high-speed imaging), integrative science‌​‌ (neuroinflammation, mouse and zebrafish​​ models, computational modeling and​​​‌ AI), pathophysiology (pain, migraine,‌ cancer, heart disease, autism,‌​‌ intellectual disabilities, Alzheimer's disease,​​ mental disorders, epilepsy) and​​​‌ therapy (neurostimulation, pharmacology, precision‌ medicine).

9 Dissemination

Participants:‌​‌ Rodrigo Cofre, Rachid​​ Deriche, Samuel Deslauriers-Gauthier​​​‌, Olivier Faugeras,‌ Théodore Papadopoulo, Romain‌​‌ Veltz.

9.1 Promoting​​ scientific activities

9.1.1 Scientific​​​‌ events: organisation

Chair of‌ conference program committees
  • Théodore‌​‌ Papadopoulo was in the​​ scientific committee of NeuroMod​​​‌ days 2025.
Reviewer
  • Théodore‌ Papadopoulo served for the‌​‌ conferences ICIP, ISBI and​​ CORTICO and for the​​​‌ NeurIPS workshop entitled “Foundation‌ Models for the Brain‌​‌ and Body”6.​​
  • Samuel Deslauriers-Gauthier served for​​​‌ the International Conference on‌ Geometric Science of Information‌​‌ (GSI), for the MICCAI​​ workshop CDMRI, and for​​​‌ ISBI.

9.1.2 Journal

Member‌ of the editorial boards‌​‌
  • Olivier Faugeras is the​​ Editor-in-Chief of “Mathematical Neuroscience​​​‌ and Applications” (MNA), published‌ by Episciences.
  • Théodore Papadopoulo‌​‌ serves as Associate Editor​​ in “Frontiers: Brain Imaging​​​‌ Methods” and as Review‌ Editor for “Frontiers: Artificial‌​‌ Intelligence in Radiology”.
  • Romain​​ Veltz is an Editor​​​‌ for “Mathematical Neuroscience and‌ Applications” (MNA).
Reviewer -‌​‌ reviewing activities
  • Théodore Papadopoulo​​ served several international journals​​​‌ (IEEE Transactions on Biomedical‌ Engineering, IEEE Transactions on‌​‌ Neural Systems and Rehabilitation​​ Engineering, Computers in Biology​​​‌ and Medicine, IEEE Transactions‌ on Medical Imaging, IEEE‌​‌ Transactions on Automation Science​​ and Engineering).
  • Samuel Deslauriers-Gauthier​​​‌ reviewed for Medical Imaging‌ Analysis (MedIA).
  • Rodrigo Cofre‌​‌ reviewed for Cell Reports​​​‌ and Nature Communications.
  • Romain​ Veltz reviewed for the​‌ journals SIAM, Stochastic Processes​​ and Applications, PLOS Computational​​​‌ Biology, Journal of Mathematical​ Imaging and Vision, Mathematical​‌ Neurosciences and Applications.

9.1.3​​ Invited talks

  • Romain Veltz​​​‌ , “Theoretical / numerical​ study of modulated traveling​‌ pulses in inhibition stabilized​​ networks”, ANR ChaMaNe, February​​​‌ 2025
  • Théodore Papadopoulo “Brain​ Computer Interfaces… a field​‌ with many challenges and​​ opportunities”, MOMI workshop, Sophia​​​‌ Antipolis, May 26th, 2025.​
  • Romain Veltz , “Pros​‌ / cons of mean​​ field representations of large​​​‌ size networks of spiking​ neurons”, CAMDAM workshop, Montreal,​‌ Canada, June 4th, 2025.​​
  • Théodore Papadopoulo “Estimating and​​​‌ Exploiting Brain Dynamics”, BMW​ workshop, Frejus, June 17th,​‌ 2025.
  • Romain Veltz ,​​ “SYNPLASTOOL : development of​​​‌ a GUI tool for​ the prediction of synapse​‌ plasticity outcome in silico”,​​ Replacement in Neuroscience, November​​​‌ 2025 (online, 700 persons).​
  • Rodrigo Cofre , “Computational​‌ and Neurobiological Modeling of​​ Structure-Function Coupling in Different​​​‌ Consciousness States”, presented at​ the NeuroMod Meeting 2025,​‌ Antibes, July 8th, 2025.​​
  • Samuel Deslauriers-Gauthier presented at​​​‌ the Neuromod Institute Open​ Day.

9.1.4 Leadership within​‌ the scientific community

  • Olivier​​ Faugeras is a member​​​‌ of the French Academy​ of Sciences.
  • Rachid Deriche​‌ is a member of​​ Academia Europaea.

9.1.5 Scientific​​​‌ expertise

  • Théodore Papadopoulo was​ member of a panel​‌ in the ANR-NSF CNS​​ grant selection.
  • Théodore Papadopoulo​​​‌ was selected to be​ a member of a​‌ EIC Pathfinder grant selection​​ panel. Due to a​​​‌ conflict of interest, he​ had to resign.
  • Théodore​‌ Papadopoulo reviewed project proposals​​ for Université de Toulouse​​​‌ and Université Côte d'Azur.​
  • Théodore Papadopoulo is the​‌ scientific referent of Yuxiu​​ Shao, recently hired at​​​‌ Université Côte d'Azur on​ a NeuroMod-LJAD CPJ (Chaire​‌ de Professeur Junior) position.​​
  • Samuel Deslauriers-Gauthier reviewed project​​​‌ proposals for the Institut​ des Neurosciences cliniques de​‌ Rennes.

9.1.6 Research administration​​

  • Théodore Papadopoulo is the​​​‌ director of the NeuroMod​ Institute.
  • Théodore Papadopoulo​‌ is a member of​​ the Neuromod scientific council​​​‌ and represents Neuromod in​ the EUR Healthy (EUR:​‌ Universitary Research School) and​​ in the Maison de​​​‌ la Simulation of Université​ Côte d'Azur.
  • Théodore Papadopoulo​‌ is a member of​​ the steering committee of​​​‌ the IHU RespiERA.​
  • Théodore Papadopoulo is the​‌ alternate Inria representative at​​ the CRBSP (Comité de​​​‌ la recherche en matière​ biomédicale et de santé​‌ publique) of the University​​ Hospital of Nice.

9.2​​​‌ Teaching - Supervision -​ Juries - Educational and​‌ pedagogical outreach

9.2.1 Teaching​​

  • Master: Théodore PapadopouloInverse​​​‌ problems for brain functional​ imaging, 3h ETD,​‌ M2, Mathématiques, Vision et​​ Apprentissage, ENS Cachan, France.​​​‌
  • Master: Théodore Papadopoulo and​ Samuel Deslauriers-Gauthier , Functional​‌ Brain Imaging, each​​ 15h ETD, M1,M2 in​​​‌ the MSc Mod4NeuCog of​ Université Côte d'Azur.
  • Master:​‌ Théodore Papadopoulo and Samuel​​ Deslauriers-Gauthier , Application of​​​‌ machine learning to MRI,​ electophysiology & brain computer​‌ interfaces, each 10h​​ ETD, M1, M2 in​​​‌ the MSc Data Science​ and Artificial Intelligence of​‌ Université Côte d'Azur.
  • Master:​​ Samuel Deslauriers-Gauthier and Romain​​​‌ Veltz , Introduction to​ Python programming and simulation​‌, each 15h ETD,​​ M1, MSc Mod4NeuCog of​​ Université Côte d'Azur.
  • Master:​​​‌ Romain Veltz , Mathematical‌ methods for neuroscience,‌​‌ 24h ETD, M2, Mathématiques,​​ Vision et Apprentissage, ENS​​​‌ Cachan, France.
  • Master: Rodrigo‌ Cofre , Scientific Communication‌​‌, 24h ETD, M2,​​ MSc Mod4NeuCog of Université​​​‌ Côte d'Azur, France.
  • Master:‌ Rodrigo Cofre , Introduction‌​‌ to modeling in neuroscience​​ and cognition, 8h​​​‌ ETD, M1, MSc Mod4NeuCog‌ of Université Côte d'Azur,‌​‌ France.
  • Master: Rodrigo Cofre​​ , Digital expertise I​​​‌, 8h ETD, M1,‌ MSc SmartEdTech of Université‌​‌ Côte d'Azur, France.
  • Master:​​ Rodrigo Cofre , Digital​​​‌ expertise II, 8h‌ ETD, M2, MSc SmartEdTech‌​‌ of Université Côte d'Azur,​​ France.

9.2.2 Supervision

  • PhD​​​‌ defended in December: Yanis‌ Aeschlimann , "Brain networks‌​‌ from simultaneous modelling of​​ functional MRI and diffusion​​​‌ MRI", started in Oct.‌ 2022. Supervisors: Samuel Deslauriers-Gauthier‌​‌ , Théodore Papadopoulo  21​​.
  • PhD in progress:​​​‌ Petru Isan , "Cerebral‌ eletrophysiological exploitation of in‌​‌ vivo evoked potentials to​​ guide the resection of​​​‌ adult brain tumors", started‌ in Oct. 2023. Supervisor:‌​‌ F. Almairac. Co-Supervisors: Théodore​​ Papadopoulo , Samuel Deslauriers-Gauthier​​​‌ .
  • PhD in progress:‌ Émeline Manka , "Modeling‌​‌ of evoked potentials by​​ direct current stimulation and​​​‌ their links to electromyography",‌ started in Oct. 2024.‌​‌ Supervisors: Samuel Deslauriers-Gauthier ,​​ Théodore Papadopoulo .
  • PhD​​​‌ in progress: Laura Gee‌ , "Exploring and exploiting‌​‌ the new capabilities of​​ room temperature MEG sensors",​​​‌ started in Dec. 2024.‌ Supervisors: Théodore Papadopoulo ,‌​‌ C.Bénar (INSERM, Marseille).
  • PhD​​ in progress: A. Bouayed,​​​‌ "Fast, interpretable and fair‌ image generation on imbalanced‌​‌ data", to be defended​​ in March 2026. Supervisors:​​​‌ D. Naccache, A. Iaccovelli,‌ Samuel Deslauriers-Gauthier .
  • PhD‌​‌ in progress: P. Castro,​​ "New approaches in modeling​​​‌ and fMRI data analysis‌ of the brain in‌​‌ different states of consciousness",​​ to be defended in​​​‌ September 2027. Supervisors: B.‌ Jarraya (NeuroSpin, Paris), A.‌​‌ Destexhe (NeuroPsi, Paris), Rodrigo​​ Cofre .
  • Romain Veltz​​​‌ supervised the M2 student‌ A. Ackay on "Bifurcation‌​‌ Theory in Whole-Brain Models:​​ Exploring Cortical Dynamics for​​​‌ Wake and Sleep State‌ Transitions", November 2024 to‌​‌ February 2025.
  • Samuel Deslauriers-Gauthier​​ and Romain Veltz supervised​​​‌ the M2 internship (InterMaths‌ Network) of H. Harshit‌​‌ on "A Finite Volume​​ Framework for Probabilistic Tractography",​​​‌ April 2025 to August‌ 2025.
  • Samuel Deslauriers-Gauthier and‌​‌ Rodrigo Cofre supervised the​​ M2 internship (MSc Mod4NeuCog​​​‌ of Université Côte d'Azur)‌ of P. Rice on‌​‌ "Optimization of whole brain​​ models to simulate the​​​‌ effect of anesthesia".
  • Samuel‌ Deslauriers-Gauthier supervised the M2‌​‌ internship (MSc Mod4NeuCog of​​ Université Côte d'Azur) of​​​‌ T. Stei on "Predicting‌ task-related functional connectivity from‌​‌ structural connectivity".
  • Théodore Papadopoulo​​ supervised the M2 student​​​‌ J. Feriau on "Uncertainty‌ propagation: From electroencephalogram measurements‌​‌ to BCI classification".
  • Rodrigo​​ Cofre supervised the M1​​​‌ student D. Zuniga on‌ "Dynamical Structure-Function Correlations of‌​‌ fMRI Human Brain Signals​​ under LSD".
  • Samuel Deslauriers-Gauthier​​​‌ supervised the M1 internship‌ (MSc Mod4NeuCog of Université‌​‌ Côte d'Azur) of M.​​ Shaw on "Inverse problems​​​‌ in electromyography (EMG)".

9.2.3‌ Juries

  • Olivier Faugeras was‌​‌ a member of several​​ committees awarding prizes from​​​‌ the French Academy of‌ Sciences.
  • Théodore Papadopoulo participated‌​‌ as a reviewer in​​​‌ the PhD jury of​ I. Siviero at Université​‌ of Verona on June​​ 19th, 2025.
  • Théodore Papadopoulo​​​‌ participated as a reviewer​ in the PhD jury​‌ of S. Reynaud at​​ IMT Atlantique in Brest​​​‌ on September 29th, 2025.​
  • Théodore Papadopoulo participated as​‌ a reviewer in the​​ PhD jury of H.​​​‌ Agouram at University of​ Aix-Marseille on December 9th,​‌ 2025.
  • Théodore Papadopoulo and​​ Samuel Deslauriers-Gauthier participated in​​​‌ the PhD jury of​ Y. Aeschlimann at Université​‌ Côte d'Azur on December​​ 15th, 2025.
  • Romain Veltz​​​‌ participated in the PhD​ jury of A. Rossi​‌ at Université Côte d'Azur​​ on September 25th, 2025.​​​‌
  • Samuel Deslauriers-Gauthier participated in​ the PhD jury of​‌ L. Smolders at Eindhoven​​ University of Technology on​​​‌ January 12th, 2025.
  • Samuel​ Deslauriers-Gauthier was part of​‌ the M2 jury for​​ the MSc Mod4NeuCog of​​​‌ Université Côte d'Azur.
  • Rodrigo​ Cofre participated in the​‌ Comité de suivi de​​ thèse (CST) of I.​​​‌ Mindlin: PhD student at​ the Sorbonne University (ED3C​‌ Cerveau - Cognition -​​ Comportement), PhD under the​​​‌ direction of J. Sitt,​ ICM Paris.
  • Rodrigo Cofre​‌ participated in the CST​​ of C. Picard: PhD​​​‌ student at the Paris-Saclay​ University (Ècole doctorale Biosigne),​‌ under the direction of​​ V. Ego-Stern, NeusoPsi Saclay.​​​‌
  • Rodrigo Cofre participated in​ the CST of L.​‌ Martineau: PhD student at​​ IRMA Strasbourg University (Ècole​​​‌ doctorale Mathèmatiques, Sciences de​ l'information et de l'ingenieur),​‌ under the direction of​​ S. Geffray et C.​​​‌ Pouzat.
  • Rodrigo Cofre participated​ in the CST of​‌ T. Hardy: PhD student​​ at Université Paris-Cité (INCC​​​‌ UMR 8002, CNRS, 75006​ Paris), under the direction​‌ of C. Sergent.
  • Théodore​​ Papadopoulo participated in the​​​‌ CST of L. Abdalah:​ PhD student at Université​‌ Côte d'Azur, under the​​ direction of V. Zarzoso​​​‌ and W. Da Cruz​ Freitas.
  • Romain Veltz participated​‌ in the CST of​​ A. Bavoil: PhD student​​​‌ at Université Côte d'Azur,​ under the direction of​‌ J.B. Caillay and A.​​ Nême.
  • Romain Veltz participated​​​‌ in the CST of​ P. Izan: PhD student​‌ at Université Côte d'Azur,​​ under the direction of​​​‌ F. Almairac and Samuel​ Deslauriers-Gauthier .
  • Romain Veltz​‌ participated in the CST​​ of G. Rebecchi: PhD​​​‌ student at Université Côte​ d'Azur, under the direction​‌ of P. Reynaud-Bouret and​​ I. Bethus.

9.3 Popularization​​​‌

9.3.1 Specific official responsibilities​ in science outreach structures​‌

  • Romain Veltz is Science​​ Outreach Officer at the​​​‌ Inria Centre at Université​ Côte d'Azur since 2025.​‌ He was responsible for​​ the Chiche program,​​​‌ organized the Café'In, coordinated​ Intro, and ran the​‌ one-week MATHC2+ internship for​​ 10th-grade students.

9.3.2 Participation​​​‌ in Live events

  • Romain​ Veltz has given a​‌ one hour conference to​​ the Fête de la​​​‌ Science at Juan-les-Pins in​ front of a general​‌ audience on October 11th,​​ 2025.
  • Rodrigo Cofre has​​​‌ given a one hour​ talk at Cafe'In INRIA​‌ "Explorer la conscience avec​​ des drogues : De​​​‌ l’anesthésie générale aux psychédéliques​ en thérapie? " on​‌ April 24th, 2025.
  • Rodrigo​​ Cofre has given a​​​‌ one hour conference to​ the Fête de la​‌ Science at Juan-les-Pins in​​ front of a general​​ audience on October 10th,​​​‌ 2025.
  • Romain Veltz gave‌ 8 chiches (one hour‌​‌ each) to 10th-grade students.​​
  • Théodore Papadopoulo and I.​​​‌ Bethus gave an interview‌ at BFM TV Côte‌​‌ d'Azur in the contexts​​ Brain's week and NeuroMod.​​​‌

10 Scientific production

10.1‌ Major publications

10.2 Publications of the‌​‌ year

International journals

International​‌ peer-reviewed conferences

Conferences​​​‌ without proceedings

Scientific book chapters

  • 20‌​‌ inbookE.Etienne St-Onge​​, G.Gabriel Girard​​​‌, K.Kurt Schilling‌, A.Alessandro Daducci‌​‌, S.Samuel Deslauriers-Gauthier​​, L.Laurent Petit​​​‌ and M.Maxime Descoteaux‌. Improving tractography using‌​‌ anatomical priors &amp; multimodal​​ integration.Handbook of​​​‌ Diffusion MR TractographyElsevier‌2025, 347-362HAL‌​‌DOIback to text​​

Doctoral dissertations and habilitation​​​‌ theses

Reports‌ & preprints

Other​​ scientific publications

Scientific popularization

10.3 Cited​‌ publications

  • 32 articleA.​​Alexandre Barachant, S.​​​‌Stéphane Bonnet, M.​Marco Congedo and C.​‌Christian Jutten. Classification​​ of covariance matrices using​​​‌ a Riemannian-based kernel for​ BCI applications.Neurocomputing​‌112July 2013,​​ 172-178HALDOIback​​​‌ to text
  • 33 article​S.Solenna Blanchard,​‌ T.Théodore Papadopoulo,​​ C.Christian Bénar,​​​‌ N.Nicole Voges,​ M.Maureen Clerc,​‌ H.Habib Benali,​​ J.Jan Warnking,​​​‌ O.Olivier David and​ F.Fabrice Wendling.​‌ Relationship Between Flow and​​ Metabolism in BOLD Signals:​​​‌ Insights from Biophysical Models​.Brain Topography24​‌12011, 40--53​​URL: http://dx.doi.org/10.1007/s10548-010-0166-6DOIback​​​‌ to text
  • 34 inproceedings​T.Tom Dupré la​‌ Tour, T.Thomas​​ Moreau, M.Mainak​​​‌ Jas and A.Alexandre​ Gramfort. Multivariate Convolutional​‌ Sparse Coding for Electromagnetic​​ Brain Signals.Advances​​​‌ in Neural Information Processing​ Systems31Curran Associates,​‌ Inc.2018, URL:​​ https://proceedings.neurips.cc/paper/2018/file/64f1f27bf1b4ec22924fd0acb550c235-Paper.pdfback to text​​​‌
  • 35 articleS.S.​ Hitziger, M.M.​‌ Clerc, S.S.​​ Saillet, C.C.​​​‌ Bénar and T.T.​ Papadopoulo. Adaptive Waveform​‌ Learning: A Framework for​​ Modeling Variability in Neurophysiological​​​‌ Signals.IEEE Transactions​ on Signal Processing65​‌16April 2017,​​ 4324--4338HALDOIback​​​‌ to text
  • 36 inproceedings​I.Ivana Kojċić,​‌ T.Théodore Papadopoulo,​​ R.Rachid Deriche and​​​‌ S.Samuel Deslauriers-Gauthier.​ Connectivity-informed M/EEG inverse problem​‌.GRAIL 2020 -​​ MICCAI Workshop on GRaphs​​​‌ in biomedicAl Image anaLysis​Lima, PeruOctober 2020​‌HALback to text​​
  • 37 inproceedingsI.Ivana​​​‌ Kojċić, T.Théodore​ Papadopoulo, R.Rachid​‌ Deriche and S.Samuel​​ Deslauriers-Gauthier. Incorporating transmission​​​‌ delays supported by diffusion​ MRI in MEG source​‌ reconstruction.ISBI 2021​​ - IEEE International Symposium​​​‌ on Biomedical ImagingNice,​ FranceApril 2021HAL​‌back to text
  • 38​​ articleJ. T.Jussi​​​‌ T. Lindgren. As​ above, so below? Towards​‌ understanding inverse models in​​ BCI.Journal of​​​‌ Neural Engineering151​December 2017back to​‌ text
  • 39 articleJ.​​ C.J. C. Mosher​​​‌ and R. M.R.​ M. Leahy. Source​‌ localization using recursively applied​​ and projected (RAP) MUSIC​​​‌.IEEE Transactions on​ Signal Processing472​‌February 1988, 332​​ -- 340DOIback​​​‌ to text
  1. 1MR:​ magnetic resonance, fMRI: functional​‌ magnetic resonance imaging, dMRI:​​ diffusion magnetic resonance imaging,​​​‌ EEG: electroencephalography, MEG: magnetoencephalography.​
  2. 2The SNR further​‌ depends on several factors​​ such as the technology​​ used in the sensor​​​‌ (dry/wet, active/passive electrodes, ...),‌ on the quality of‌​‌ the amplifier, on the​​ quality of the setup,​​​‌ ...
  3. 3Going to‌ source space requires to‌​‌ create a head model​​ which, for better efficiency,​​​‌ requires to be adapted‌ to the subject. In‌​‌ turn, this means acquiring​​ MR data and apply​​​‌ complex processes to it.‌
  4. 4We refer to‌​‌ a within-session evaluation when​​ the training data is​​​‌ acquired in the same‌ session as the testing‌​‌ data. When this is​​ not the case, we​​​‌ have a cross-session evaluation.‌
  5. 5IPMC: Institut de‌​‌ Pharmacologie Moléculaire et Cellulaire​​, iBV: Institut de​​​‌ Biologie Valrose, LP2M:‌ Laboratoire de Physiomédecine Moléculaire‌​‌, UR2CA: Unité de​​ Recherche Clinique Côte d’Azur​​​‌.
  6. 6

    ICIP: International‌ Conference on Image Processing,‌​‌ ISBI: International Symposium on​​ Biomedical Imaging, CORTICO: COllectif​​​‌ pour la Recherche Transdisciplinaire‌ sur les Interfaces Cerveau-Ordinateur,‌​‌ CVPR: Conference on Computer​​ Vision and Pattern Recognition,​​​‌ NeurIPS: Neural Information Processing‌ Systems.