# Projects

## Ongoing Projects:

**Next generation neural mass model: bridging the scales from micro to macroscopic dynamics**

Human Brain Project Core Project Partner: Aix-Marseille Université, Institut de Neuroscience des Systèmes (INS)- UMR INSERM 1106

### Sep 2021 - Mar 2023

**Project Leaders**

**Simona Olmi (ISC- CNR)**

**Viktor Jirsa (INS)**

**Project **** ****aim **** **

The desire to understand large scale brain dynamics, as observed using EEG, MEG and

fMRI has prompted the increasing use of computational models [1] and, among these approaches, we find The Virtual Brain (TVB) project [2] ,which makes use of networks of interconnected neural mass models. However, the inability of a single neural mass model to support event-related desynchronisation/synchronisation [3] or to capture the onset of synchronous oscillations in networks of inhibitory neurons [4], reminds us that these phenomenological models could be improved upon. Of course, building more detailed biophysically realistic models of neurons and their interactions would improve this state of affairs, though at a price: the increase of computational complexity increases together with a decrease of our ability to interpret the behaviour of very high dimensional models in a meaningful way.

Even though recent advances in neuroscience has been impressive both at the microscopic scale of cellular biology of neurons, and the macropic scale of whole-brain functionality, the spatio-temporal gap between these two activity scales is enormous. Here we aim at bridging the gap between highly detailed neuron models and population models that describe the dynamics emergent in large neuronal systems, such as brain connectomes. To address this issue we employ a recently developed exact method [5], which allows to rewrite the dynamics of large networks of spiking neurons in terms of few collective variables representing the firing rate and the mean membrane potential of the neuronal populations [6] or their level of synchronization [7]. These next generation neural mass models we aim to implement, are very much in the original spirit of neural mass modelling, yet importantly they can be interpreted directly in terms of an underlying spiking model. This exact derivation is possible for networks of quadratic integrate-and-fire neurons, representing the normal form of Hodgkin’s class I excitable membranes [8], thanks to the analytic techniques developed for coupled phase oscillators [5].

**Project summary**

The project aims to be a clever blend between classic unifying multiscale frameworks and pyramid-style approaches thanks to the following strengths:

The exact reduction dimension techniques at the basis of the next generation neural mass model have been developed for coupled phase oscillators [5] and allow for an exact (analytical) moving upwards through the scales: while keeping the influence of smaller scales on larger ones they level out their inherent complexity.

Moving downwards through the scales, more detailed modelling parameters can be used, e.g. to test specific hypotheses. Having a 1:1 correspondence between microscopic and mesoscopic level, it will be easier to map the microscopic results to the relative ones in the regional mean field parameters.

The next generation neural mass models (and the relative microscopic models) show multistability and various behaviors at multiple time scales. Therefore it will be no more necessary to resort to oscillator models or single neuron models depending on the phenomena required to model (either neural dynamical features or multistability).

In this framework will be developed a next generation neural mass model encompassing short-term plasticity (STP), which has not yet been implemented in TVB. The resulting plasticity models can then be integrated into single neuron or population models and will serve as a starting point for including more realistic and biologically relevant aspects (e.g. pulsatile interactions or transmission delays). In particular the work plan includes the following steps: a) validation and extension of the next generation neural mass model developed in [9] to take into account finite-size fluctuations of the microscopic synaptic variables [10], synaptic delays [11], electrical coupling via gap junctions [12] and chemical synapses [13]; b) parameter optimization; c) application to Showcase 1 (WP1) in SGA3 to reproduce both resting states and task-related states; d) application to Showcase 2 (WP1) in SGA3 to construct personalized brain models of epileptic patients.

[1] I. Bojak and M. Breakspear, Neuroimaging, neural population models for, In Encyclopedia of Computational Neuroscience, pages 1–29. Springer, 2014.

[2] P. Sanz-Leon, S. A. Knock, A. Spiegler and V. K. Jirsa, NeuroImage 111, 385–430 (2015).

[3] G. Pfurtscheller and F. H. Lopes da Silva, Clin. Neurophysiol. 110, 1842–1857 (1999).

[4] F. Devalle, A. Roxin, and E. Montbrió, PLoS Comp. Bio. 13, e1005881 (2017).

[5] E. Ott and T. M. Antonsen, Chaos, 18, 037113 (2008).

[6] E. Montbrió, D. Pazó, and A. Roxin, Phys. Rev. X 5, 021028 (2015).

[7] D. Pazó and E. Montbrió, Phys. Rev. X 4, 011009 (2014); P. So, T. B. Luke, and E. Barreto, Physica D 267, 16 (2014); C. R. Laing, Phys. Rev. E 90, 010901 (2014).

[8] G. B. Ermentrout, N. Kopell, SIAM J Appl Math 46(2), 233–253 (1986)

[9] H. Taher, A. Torcini and S. Olmi, Exact neural mass model for synaptic-based

working memory, Plos. Comp. Bio. 16(12), e1008533 (2020).

[10] V. Schmutz, W. Gerstner, T. Schwalger, J. Math. Neurosci. 10(1), 1–32 (2020).

[11] F. Devalle, E. Montbrió, D. Pazó, Phys. Rev. E 98(4), 042214 (2018)

[12] E. Montbrió, D. Pazó, Exact mean-field theory explains the dual role of electricalsynapses in collective synchronization, Phys. Rev. Lett. 125(24), 248101 (2020).

[12] S. Coombes, A. Byrne, In: F. Corinto, A. Torcini, editors. Nonlinear Dynamics inComputational Neuroscience. Springer; 1–16 (2019).

**Next generation neural mass model**

Grant INRIA Sophia Antipolis (for a PhD position)

### Nov 2018 - Feb 2022

The PhD course was led by **Simona Olmi **from ISC, CNR and consisted in the recruitment and supervision of the PhD student Halgurd Taher. The grant amounts to 105.000 euros.

A major goal of neuroscience, statistical physics and nonlinear dynamics is to understand how brain functions arise from the collective dynamics of cortical circuits. Often reported collective phenomena include oscillations, synchronous dynamics or more general rhythms, characteristic of various neural circuits [1]. Oscillations of neural activity are ubiquitous in the brain in many frequency bands and it has been argued that they play a functional role in cortical processing [2]. In particular, the mechanisms underlying the coupling between neural oscillations at different timescales have recently received much attention from experimentalists and theoreticians [3]. The most studied example of this phenomenon, usually termed cross-frequency coupling (CFC), concerns the coupling between θ and γ oscillatory activity in the rodent hippocampus [4]. Furthermore, CFC appears to be implicated in cognitive operations: multi-item representation, long-distance communication, and stimulus parsing [3].

It has been recently suggested that simple neural architectures involving few excitatory and inhibitory populations are able to reproduce the mechanisms underlying CFC [5]. These and other evidences suggest that information is encoded in the population response and hence can be captured via macroscopic measures of the network activity [6]. The collective behavior is particularly relevant given that current brain measurement techniques, such as EEG or fMRI, provide data averaged over the activity of a large number of neurons. So far the analysis of spiking neural circuits has been mainly addressed through numerical simulations, with limitations in the maximal affordable number of neurons due to the available numerical resources. Alternatively, researchers have formulated effective mean-field representation of the neural dynamics at the level of populations, in terms of neural mass models [7]. However an extremely powerful exact method recently developed, is the Ott-Antonsen (OA) Ansatz [8], which allows to rewrite the dynamics of fully-coupled networks of phase oscillators in terms of few collective variables in the thermodynamic limit. Only recently a few studies, published in statistical physics journals, revealed the possibility, by applying and extending the OA Ansatz, to

derive exact neural field models starting from microscopic spiking neural circuits [9,10]. This novel exact reduction methodology (ERM) allows to reproduce the collective evolution of a population of spiking Θ-neurons [11] with a few collective variables representing the firing rate and the mean membrane potential of the neuronal populations [10] or their level of synchronization [9].

These results are particularly relevant for the neuroscience community, since the Θ-neuron is a paradigmatic model employed, for example, for the study of working memory and for the reproduction of θ-γ coupled rhythms emerging in the auditory cortex [12]. However, these theoretical results have not been yet applied to address relevant issues in neuroscience.

References:

[1] G. Buzsaki, Rhythms of the Brain (Oxford University Press, USA, 2006), 1st ed., ISBN 0195301064.

[2] T. Womelsdorf et al., Science 316, 1609 (2007); X.-J. Wang, Physiological reviews 90, 1195 (2010).

[3] A. Hyafil, A.-L. Giraud, L. Fontolan, and B. Gutkin, Trends in Neurosciences 38, 725 (2015).

[4] J. E. Lisman and O. Jensen, Neuron 77, 1002 (2013).

[5] L. Fontolan, M. Krupa, A. Hyafil, and B. Gutkin, The Journal of Mathematical Neuroscience 3, 1 (2013).

[6] B. B. Averbeck, P. E. Latham, and A. Pouget, Nature Reviews Neuroscience 7, 358 (2006).

[7] G. Deco, V. K. Jirsa, P. A. Robinson, M. Breakspear, and K. Friston, PLoS Comput Biol 4, e1000092 (2008); J. Touboul, F. Wendling, P. Chauvel, O. Faugeras, Neural computation, 23(12), 3232-86 (2011).

[8] E. Ott and T. M. Antonsen, Chaos, 18, 037113 (2008).

[9] D. Pazó and E. Montbrió, Phys. Rev. X 4, 011009 (2014); P. So, T. B. Luke, and E. Barreto, Physica D 267, 16 (2014); C. R. Laing, Phys. Rev. E 90, 010901 (2014).

[10] E. Montbrió, D. Pazó, and A. Roxin, Phys. Rev. X 5, 021028 (2015).

[11] G. Ermentrout and N. Kopell, SIAM Journal on Applied Mathematics 46, 233 (1986).

[12] M. Dipoppa and B. S. Gutkin, PNAS 110, 12828 (2013); M. Krupa, S. Gielen, and B. Gutkin, J. Comput. Neurosci. 37, 357 (2014)

## Past Projects:

**Control of multi-scale neural networks: bridging the scales from micro to macroscopic dynamics**

Grant PROCOPE 2019 (Partenariat Hubert Curien)

### Jan 2019 - Dec 2020

The aim of the project is to investigate the dynamics of neural networks at different scales ranging from micro to macro: multi-scale networks in fact are composed of dynamical units arranged in locally connected sub-networks, which can interact also over long distances with elements of other sub-networks. A combination of mathematical analysis and computational modelling can serve as an indispensable complement to experimental verification in furthering our understanding of multi-scale dynamical evolution. This in order to address the problem of developing innovative dynamical control schemes to re-engineer the architecture of the networks and to improve the robustness of the network against critical perturbations. The development of an efficient dynamical control scheme is a key feature to achieve desired collective evolutions and it can find application in neural prosthetic or can be useful to avoid pathological synchronisation in neural circuits. Using various models of coupled neural elements, we particularly aim to understand the interplay of multi-scale dynamics, stochasticity and time delay for the control of neural networks. Additionally, we aim at applying this framework to investigate on one side biologically realistic large-scale brain activity and on the other side real-world networks, e.g. the mechanisms underlying the coupling between neural oscillations at different timescales in neural architectures composed of inhibitory and/or excitatory populations.

The German group will provide theoretical control methods based on noise and time delay and the French group will implement them for the multi-scale neural networks. Second, the German group will explore conditions for occurrence of stochastic phenomena such as coherence resonance and stochastic resonance and their control in networks, and the French group will extend these ideas to multi-scale neural networks.

Third, the German group will work on numerical simulations on noisy and time-delayed dynamics and the French group will perform analytical investigations of multi-scale neural networks. The theoretical understanding of the emergent mesoscopic and macroscopic behaviour in multi-scale networks will be achieved by employing refined indicators developed in the context of nonlinear dynamics to characterise the dynamics at various levels of resolution.

The French node was led by **Simona Olmi **from ISC, CNR and included the PhD student Halgurd Taher and the postdoc Emre Baspinar for two years.

The grant amounts to 12.000 euros used to reimburse travel expenses in order to enhance and guarantee a collaboration between the partners.

**Complex Oscillatory Systems: Modeling and Analysis**

Marie Curie European Joint Doctorate (MC-EJD)

### Jan 2015 - Aug 2019

Many natural and artificial systems are often composed of oscillatory elements which, besides evolving according to their own non-trivial internal dynamics, mutually interact. As a result, many temporal and spatial scales are typically present, often accompanied by the spontaneous emergence of collective properties. Altogether, such features make the task of understanding the resulting evolution a challenging interdisciplinary problem. Zero-knowledge methods do generally require too large amount of data to allow drawing meaningful conclusions. In order to overcome this limitation, it is necessary to add skilful hypotheses about the structure of the underlying model and, thereby, on the relevant variables. This task is often tackled in an ad hoc way and the approach is based rather on personal preferences than on objective elements. The goal of this project is to fill the gap, by developing a general and coherent set of tools for the system identification and control, as well as to improve our ability to make predictions.

Complex Oscillatory Systems: Modeling and Analysis (COSMOS) was a Europe-wide consortium of 8 universities who together hosted 15 PhD students over 4 years. COSMOS has been made possible by a €3.9 M grant by the European Commission through its Marie Curie Initial Training Network scheme (Program H2020-EU.1.3.1, Grant agreement ID: 642563).

The Florence node of COSMOS was led by the three PIs Roberto Livi, Duccio Fanelli from the Department of Physics and Astronomy of the University of Florence (Network Theory) and **Thomas Kreuz** from ISC, CNR (Data Analysis) and included the two Early Stage Researchers (PhD students) Clement Zankoc and **Eero Satuvuri** for two years as well as for one year Pau Clusella, Maxime Lucas, and **Irene Malvestio**.

**Neural Engineering Transformtive Technologies**

Marie Curie Initial Training Network (MC-ITN)

### Sept 2012 - Aug 2016

Neural Engineering is an inherently new discipline that brings together

engineering, biophysics and mathematics to design and develop brain-computer interface systems, cognitive computers and neural prosthetics.

Neural Engineering Transformative Technologies (NETT) was a Europe-wide consortium of 18 universities, research institutes and private companies who together hosted 17 PhD students and 3 postdoctoral researchers over 4 years. NETT has been made possible by a €5.3M grant by the European Commission through its Marie Curie Initial Training Network scheme (Program FP7-People-2011-ITN, Grant agreement ID: 289146).

The Florence node of NETT was led by the two PIs **Alessandro Torcini** (Network Theory) and **Thomas Kreuz** (Data Analysis) and included the Experienced Researcher (Postdoc) **Mario Mulansky** and the two Early Stage Researchers (PhD students) **David Angulo Garcia** and **Nebojsa Bozanic**.