(Theoretical Neurosciences Group)

The Theoretical Neuroscience Group (TNG) has a long history. It has been founded in 1999 by Dr. Viktor Jirsa, originally based at the Center for Complex Systems and Brain Sciences at Florida Atlantic University, and then relocated to Aix-Marseille University in 2006. The objective of TNG is to gain a deeper understanding of the mechanisms underlying the emergence of brain function and dysfunction from brain network dynamics.  For this purpose, we adopt a “multi-scale” approach using primarily mathematical and computational techniques. Our approach demands to understand the brain by binding in a single framework different resolution levels, and/or different time scales. This also demands to unify different points of view, from mathematical theory of complex systems toward computer-based numerical simulations (looking at the ensemble activity from the graph of elementary components) and behavioral studies. Our major interests are dedicated to understanding brain states including consciousness, behavioral representation in brain dynamics, and brain network disorders, in particular epilepsy, seen as the prototypical “dynamical disorder” (as a disorganization of the normal dynamical system). We seek to discover novel ways to modulate brain networks including stimulation, surgery and pharmaceutical interventions.




Viktor JIRSA

Director of the Institut de Neurosciences des Systèmes

PHONE: +33 4 91 32 42 51


Originally trained in Theoretical Physics and Philosophy in the 1990s, Dr. Jirsa has made contributions to the understanding of how network structure constrains the emergence of functional dynamics using methods from nonlinear dynamic system theory and computational neuroscience. Dr. Jirsa has been awarded several international and national awards for his research including the Francois Erbsmann Prize in 2001, NASPSPA Early Career Distinguished Scholar Award in 2004, and Grand Prix de Recherche de Provence in 2018. He serves on various Editorial Boards and has published more than 150 scientific articles and book chapters, as well as co-edited several books including the Handbook of Brain Connectivity. Dr. Jirsa is one of the Lead Scientists in the Human Brain Project and The Virtual Brain.

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The scientific objective of TNG is to uncover the mechanisms underlying the emergence of brain function from the spatiotemporal organization of large-scale brain networks. Our focus is indeed brain network dynamics. The dynamics of brain networks on the large scale has certain characteristics, typically less relevant in traditional neural network studies. These large-scale features comprise the presence of multiple spatial and temporal scales, time delays via signal transmission, and a highly non-trivial (i.e. inhomogeneous and anisotropic, thus translationally variant) connectivity. Together, these factors impose constraints upon the network dynamics, which is linked to the emergence of behavioral function/dysfunction and can be imaged in the human brain non-invasively (fMRI, EEG, MEG) and invasively (sEEG, iEEG). All of our work in TNG can be understood within this framework and comprises theoretical and computational studies of large-scale network behavior (resting state fluctuations, stimulated brain dynamics, self-organized routing), the development of neuroinformatics tools for studying brain networks (both simulated and empirical) up to the whole-brain scale, and its applications to concrete functions (such as hand writing), dysfunctions (epilepsy, stroke) and aging.

Over the years, TNG has developed a reputation as a long-standing contributor and pioneer in the field of large-scale brain network dynamics, linking generative brain network models to human brain imaging data. Key to the success has been the tight interaction of mathematics, computation and experiment, in which mathematics often needed to abandon “rigor” and experimental data were often looked at “non-biologically” from the system perspective. This unconventional approach contributed to creating a new field, brain connectivity, which shows an uninterrupted series of 15 annual Brain Connectivity workshops and the creation of a new journal with the same name.

Currently ongoing research projects in TNG include

·    The Virtual Brain neuroinformatics project

·    Large-scale brain network theory

·    Brain Dysfunction (Epilepsy)

See below for more details on each of these pillars of research.

The Virtual Brain (TVB) neuroinformatics project

The development of a neuroinformatics platform, The Virtual Brain (TVB), composed of a simulator and computational library for biologically realistic brain network dynamics was a key focus during the current project period. TVB is part of the project Brain Network Recovery Group (Brain NRG, coordinator: AR McIntosh) funded by the James McDonnell Foundation and was identified a cross-cutting research theme of INS at the beginning of the current project period. TNG leads the Virtual Brain project and dedicated most of its efforts during 2010 through 2015 on this project. We have released the Software in October 2012, held an exhibition stand at the Annual Society of Neuroscience Meetings every year since 2011 and offered full-day training workshops worldwide (see section 3). In a nutshell summary: The Virtual Brain is a simplified (i.e. mean-field), data-constrained and dynamic network model of the human adult brain and has been developed and

consistently refined since 2010. The fusion of an individual’s brain structure with computational neuroscience modelling allows creating one model per subject or patient, systematically assessing the modelled parameters that relate to individual functional differences (personalized modelling). The functions of the brain model are governed by realistic neuroelectric and neurovascular processes and are constrained by subject-specific anatomical information derived from non-invasive brain Imaging (anatomical MRI, diffusion tensor imaging (DTI)). The Virtual Brain comprises a ready-to-execute dynamic neuroelectric simulation; refined geometry in 3D physical space; detailed personalized brain connectivity (large library of empirical Connectomes); large repertoire of mathematical brain region models; and a complete set of forward solutions mimicking imaging modalities commonly used in brain mapping including functional Magnetic Resonance Imaging (fMRI), Magnetoencephalography (MEG), Electro-encephalography (EEG) and StereoElectroEncephalography (SEEG). Backed by a powerful, scalable and modular neuroinformatics platform and simulator, TVB can be used to construct individualized virtual brain models from neuroimaging data to study brain disorders and explore intervention and treatment options. Model attributes are fully customizable, including their geometry, connectivity, regional neurotransmitter distributions and signal transmission properties. The insertion of medical devices such as SEEG or stimulation electrodes can be virtually emulated to study their influence on brain function, to validate their efficacy, and to predict their reliability under a range of operating conditions. One patent application for TVB was submitted.


Large-scale brain network theory

The core metier of TNG is the research of mechanisms relevant to the spatiotemporal organization of brain network dynamics. Scientific accomplishments in this domain during the current contract period include the “reverse engineering” of key dynamical mechanisms underlying resting state (rs) brain dynamics. We have first focused on how to reproduce within computational models the Functional Connectivity (FC) patterns characteristically observed during rs, assuming that they reflect the collective dynamics of brain structural circuits. We have demonstrated that brain network models operating near criticality reproduce best empirical resting state correlations and naturally give rise to a rich repertoire of available dynamical states (Ghosh et al 2008; Deco et al 2011, 2012). Other mechanisms were proposed (Hlinka & Coombes PRL 2010; Deco et al 2009), but did not hold up against further empirical testing, whereas our proposal of near criticality produced novel biomarkers and paradigms (e.g. for the analysis of aging) as described in the following. Moving beyond time-averaged FC, we have also studied dynamic FC. Near criticality, the noise-driven exploration of the repertoire of dynamical states, should manifest itself as a structured variability across time of FC networks. We have confirmed this prediction, developing new methods to detect switching Functional Connectivity Dynamics (FCD) patterns in human resting state fMRI and other data. We have furthermore provided the first ever whole-brain mean-field model able to reproduce them (Hansen et al., 2015) and characterized realistic itinerant dynamics between attractors in a connectome-based spin-glass model of large-scale brain activity (Golos et al 2015). Near criticality predicts also certain transient behaviors following stimulation (Spiegler et al 2016), which have been tested in TMS studies in collaboration with Mireille Bonnard (DCP) in perturbation paradigms able to alter the resting state FCD (Bonnard et al 2016).

We have performed rigorous theoretical investigations of the link between structural and functional connectivity, mediated by collective network dynamics. We have provided theoretical frameworks, which allow treating the space-time structure of network couplings as a whole with regard to its effects upon network synchronization and, consequently, exchange of information between different coupled units. By decomposing the spatial distribution of time delays into spatial patterns within the couplings’ space-time structure, we could analytically compute the synchronization characteristics of the network. We demonstrated that it is not just the connectivity that matters in oscillatory large-scale networks, as the brain, but time delays are of equal importance (Petkoski et al, 2016). We could also provide analytical expressions for the amount of information exchanged between any two oscillating units (or modules) within a (hierarchical) network of arbitrarily complex topology, showing that alternative information routing patterns can be selected by switching between alternative dynamical states of fixed structural circuit (Battaglia et al., 2012; Kirst et al., 2016). Our tools of investigation can also be applied to the modelling of specific brain systems. We have demonstrated that functional hubs organize in cliques controlling the dynamics of a developing neural circuit in the hippocampus (Luccioli et al, 2014). By employing a very simple model of the striatum we have reproduced experimental results “in vitro” obtained Carrillo-Reidl et al. (2008), revealing that medium spiny neurons organize in assemblies with correlated and anti-correlated dynamics, establishing a characteristic FC encoding the sensori stimuli (Angulo-Garcia et al., 2016).

Beyond neural circuits and linking our efforts to cognitive/functional architectures, we have applied concepts from nonlinear dynamical systems theory to the analysis of how structured motor behaviour can emerge from network dynamics. We have in particular developed a general dynamical framework, based on the theory of Structured Flows on Manifolds (SFMs) for the analysis and the interpretation of movement patterns, allowing to compare different possible dynamical architectures compatible with the observed behaviours and assess their relative efficiency and likelihood. Using the example of a composite movement we have illustrated how different architectures can be characterized by their degree of time scale separation between the internal elements of the architecture (i.e. the functional modes) and external interventions. We revealed a trade-off of the interactions between internal and external influences (Perdikis et al 2011a), which offers a theoretical justification for the efficient composition of complex processes out of non-trivial elementary processes or functional modes. In a companion study (Perdikis et al 2011b) we applied these concepts to the concrete example of handwriting and developed a functional architecture capable of writing complete words, where all the encoding is performed in the synaptic weights of the network (Huys et al, 2014).

Finally, the theory and modelling of neural network dynamics have also inspired performing algorithms for network topology inference (Stetter et al., 2012; Orlandi et al., 2014), benchmark for a worldwide crowdsourcing challenge (Orlandi et al., 2015) and for applications to Brain

Three key publications (2012-2016) for “large-scale brain network theory”:

Deco G, Jirsa VK, Mcintosh AR. Resting brains never rest: computational insights into potential cognitive architectures. Trends Neurosci. 2013;36: 268–274.

Hansen ECA, Battaglia D, Spiegler A, Deco G, Jirsa VK. Functional connectivity dynamics: modeling the switching behavior of the resting state. NeuroImage. 2015;105: 525–535.

Kirst C, Timme M, Battaglia D. Dynamic information routing in complex networks. Nat Comms. 2016;7: 11061.

Brain Dysfunction

We are interested in brain network disorders. So far we think about neurodegenerative disorders including Alzheimer, Multiple Sclerosis and Stroke. Our workhorse of brain network disorders has been Epilepsy, being often considered the prototypical dynamic network instability. Scientific accomplishments include the establishment of a novel mathematical framework for the study of the Phenomenological dynamics of Epilepsy and the classification of seizure-like events (SLEs). Based on first mathematical principles in nonlinear dynamics, in particular fast-slow systems, we have developed a mathematical model, the Epileptor, predicting details of seizure discharge properties, which we tested electrophysiologically initially in the rat, then in other species including humans, rodents, and zebrafish. The model describes fast spiking, spike wave events, and the dynamics of seizure onset, time course, and offset. Conceptual key is the postulate of the existence of a slow (multi-factorial) variable, which may be manifested for instance by extracellular potassium. Evoking these laws and applying them to experimental data allows us to identify bifurcations from experimental data and the formulation of a canonical model. The concentration on the ensemble of elements of seizure evolution results in simplification of each element, but predicts novel more complex behaviors based and can inspire yet unexplored paradigms for therapeutical intervention. This work has been performed in collaboration with the PhysioNet team of Christophe Bernard and has resulted in a highly cited article in Brain (Jirsa et al. 2014) and a number of subsequent mathematical treatments (El Houssaini et al (2015), Proix et al (2014), Saggio et al (2017)).

A second achievement is the proof-of-concept of the possibility of building personalized brain network models of epileptic patients, essentially integrating all INS teams. In our works (Proix et al 2014; Jirsa et al., 2016) we argue that large-scale brain network models using our Virtual Brain approach may make the link between non-stationary network dynamics (such as seizure propagation) and person-specific structural indicators including connectivity. We take advantage of two recent developments in system neuroscience: first, adding Connectomics to Genomics in personalized medicine; and, second, using patient-specific connectomes in large-scale brain networks as generative models of neuroimaging signals. Our approach to build the Virtual Epileptic Personalized (VEP) brain model comprises structural and functional network modelling linked with clinical hypothesis formulation. Novel methodological pipelines were developed to satisfy the TVB constraints (Proix et al 2016). The VEP model is evaluated via simulation, data fitting and mathematical analysis. The result of this evaluation predicts the most likely propagation patterns through the patient’s brain and allows the exploration of brain intervention strategies. These steps lead to the virtualization of individual patient brains with a significant predictive value. Two patent applications were submitted using these techniques, one optimizing the SEEG electrode placement, another to control the seizure propagation patterns. Various grant applications to this end are in preparation to run clinical trials based on Virtual Brain modelling of Epileptic Patients.

Three key publications (2012-2016) for “Epilepsy”:

Jirsa VK, Stacey WC, Quilichini PP, Ivanov AI, Bernard C. On the nature of seizure dynamics. Brain. 2014;137: 2210–2230.

Proix T, Bartolomei F, Chauvel P, Bernard C, Jirsa VK. Permittivity coupling across brain regions determines seizure recruitment in partial epilepsy. J Neurosci. Society for Neuroscience; 2014;34: 15009–15021.

Jirsa VK, Proix T, Perdikis D, Woodman MM, Wang H, et al. The Virtual Epileptic Patient: Individualized whole-brain models of epilepsy spread. Neuroimage. 2016 Jul 28.