1. Large scale models of the brain Institut des Sciences du Mouvement Viktor Jirsa Theoretical Neuroscience Group Anandamohan Ghosh Rolf Kötter Randy McIntosh Young-Ah Rho Michael Breakspear Stuart Knock Gustavo Deco

3. Honey et al PNAS 2007, Ghosh et al Plos CB 2008, Deco et al PNAS 2009 Izhikevich & Edelman 2008 Henry Markram – Blue Brain Ananthanarayanan et al. IBM 2009 Information processing carried out by large scale neural networks

4. Motivation Mean field models collapse the dynamic characteristics of a voxel into a single neurocomputational unit of neurons with similar statistics Deco et al. PLoS CB2009

5. Globally coupled network of Fitzhugh-Nagumo neurons

6. Network Dynamics

7. Define a continuous field parametrized by the dispersed parameter Rewrite the network equations in terms of q(z,t) Coupled mean fields Assisi, Jirsa, Kelso PRL2005 Stefanescu, Jirsa Plos CB 2009

8. Express the dynamics of the network in z-space in terms of z- spatial modes and the corresponding time dependent amplitudes. Assisi, Jirsa, Kelso PRL2005 Stefanescu, Jirsa Plos CB 2009

9. The mode equations are given by, Mode Equations Assisi, Jirsa, Kelso PRL2005 Stefanescu, Jirsa Plos CB 2009

10. Mode Dynamics

11. Contour lines of equal mean field amplitude in space Network dynamicsMode dynamics Assisi, Jirsa, Kelso PRL2005 Stefanescu, Jirsa Plos CB 2009

12. Jirsa & Stefanescu Bul. Math. Biol (in press) Neural field models Full network Reduced neural field

14. Origin of ultraslow fluctuations: neural activity? Simultaneous EEG and fMRI study finds cross- correlations between BOLD signal and the power fluctuations in each frequency band. Mantini et al. PNAS 2007

15. Generation of the rest state activity? Function? Product of chaotic processes involving the thalamocortical loop (Lopes da Silva et al. 1997; Niedermeyer 1997) Distinct alpha generators (Nunez et al 2001) Large scale connectivity matrix and chaotic neural activity (Honey et al PNAS 2007) Noise driven exploration of the high-dimensional phase space defined by the network with time delays (Ghosh et al Plos CB2008) Stochastic Resonance in the network with time delays (Deco et al PNAS 2009) « Rest state fluctuations reflect unconstrained but consciously directed mental activity » Rest state network fluctuations observed in anaesthesized monkeys (Vincent et al., Nature 2007)

16. Regional map of the primate brain (Kötter & Wanke, 2005) MonkeyHuman

19. Ghosh et al. PLoS CB 2008

20. Ghosh et al Plos CB 2008; Deco et al PNAS 2009 Implementation of large scale model Assisi, Jirsa Kelso PRL 2005 Stefanescu, Jirsa PLoS CB 2009 Jirsa, Stefanescu Bull.Math.Biol (in press)

21. Linear stability analysis linearization Let the solution be characteristic equation in l For N coupled FHN oscillators the characteristic equation is factorizable: Characteristic equation:

22. Ghosh et al. PLoS CB 2008

24. Hemodynamic model: combining Balloon/Windkessel Model with a model of how synaptic activity causes changes in regional flow Nonlinear coupling term: Balloon/Windkessel model Linear coupling term: How evoked changes in blood flow are transformed into a blood oxygenation level dependent(BOLD)

25. Case 1

26. Case 3

27. Compare to Fox et al. PNAS 2005

28. Resting state network in BOLD signals Fox et al. PNAS (2005) Task-negative regions: MPF(medial prefrontal cortex), PCC(posterior cingulate precuneus), LP(Lateral parietal cortex) Task-positive regions: IPS(intraparietal sulcus cortex), FEF(the frontal eye field), MT(middle temporal region)

29. CCPFEFPCIPCIPPFCMVACD CCP++-+-+ FEF++---+ PCI--+++- PCIP+-++-- PFCM--+-+- VACD++---+ Cross correlations between six areas: Ghosh et al PLOS CB 2008 Compare to Fox et al. PNAS 2005

30. 15uV -15uV 0 uV 400fT -400fT 0fT Forward EEG/MEG solution in realistic head models

31. Qf = 1, Qs = 1 Honey et al PNAS 2007; Ghosh et al Plos CB 2008; Jirsa Phil. Trans. Royal Soc. A 2009

32. What is the dynamic mechanism leading to the emergence of these coherent fluctuations? Synchronization?

33. F FitzHugh-Nagumo Neuron Rho, Jirsa & McIntosh (in preparation)

35. BOLD in CCA is correlated with coherence between PCI and CCP, and BOLD time series are shifted with time lag(2.4sec). Rho, Jirsa & McIntosh (in preparation)

37. Other working points, maybe self-sustained oscillations?

38. Deco, Jirsa, McIntosh et al. PNAS (2009) Different working point: What is the role of synchronization? Two clusters of synchronization

39. Synchronization of clusters Red – cluster 1 Black – cluster 2 Blue – difference Power spectrum of ultraslow oscillations with and without time delay Stochastic Resonance Cross correlation as a function of noise level Maximal Power as a function of noise level Deco, Jirsa, McIntosh et al. PNAS (2009)

40. Summary of results Rest state activity is interpreted as the « noise-driven exploration of the equilibrium state of the brain network » The space-time structure is crucial for the emergence of the rest state networks. Intermittent synchronization of subnetworks gives rise to ultra-slow oscillations in BOLD signal. Codebox Research ATIP (CNRS) James S. McDonnell Foundation Thank you