Large scale models of the brain

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

3. Information processing carried out by large scale neural networks 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

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

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

10. Mode Dynamics

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

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

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 chaoticprocessesinvolving the thalamocorticalloop (Lopes da Silva et al. 1997; Niedermeyer 1997) • Distinct alpha generators (Nunez et al 2001) • Large scaleconnectivitymatrix and chaotic neural activity (Honey et al PNAS 2007) • Noise driven exploration of the high-dimensional phase spacedefined by the network with time delays (Ghosh et al Plos CB2008) • StochasticResonance in the network with time delays (Deco et al PNAS 2009) • « Rest state fluctuations reflectunconstrained but consciouslydirected mental activity » • Rest state network fluctuations observed in anaesthesizedmonkeys (Vincent et al., Nature 2007)

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

19. Ghosh et al. PLoS CB 2008

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

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

23. 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 • Task-negative regions: MPF(medial prefrontal cortex), PCC(posterior cingulate precuneus), LP(Lateral parietal cortex) • Task-positive regions: IPS(intraparietalsulcus cortex), FEF(the frontal eye field), MT(middle temporal region) Fox et al. PNAS (2005)

29. Cross correlations between six areas: Ghosh et al PLOS CB 2008 Compare to Fox et al. PNAS 2005

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

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

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)

34. 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)

36. Rho, Jirsa & McIntosh (in preparation)

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

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

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. Thank you Codebox Research ATIP (CNRS) James S. McDonnell Foundation