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
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
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
Globally coupled network of Fitzhugh

Nagumo neurons
Network Dynamics
•
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
•
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
The mode equations are given by,
Mode Equations
Assisi,
Jirsa
, Kelso
PRL2005
Stefanescu
,
Jirsa
Plos
CB 2009
Mode Dynamics
Contour lines of equal mean field amplitude in
space
Network dynamics
Mode dynamics
Assisi,
Jirsa
, Kelso
PRL2005
Stefanescu
,
Jirsa
Plos
CB 2009
Jirsa
&
Stefanescu
Bul. Math.
Biol
(in press)
Neural field models
Full network
Reduced neural field
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
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)
Regional map of the
primate
brain (
Kötter
&
Wanke
, 2005)
Monkey
Human
Ghosh et al. PLoS CB 2008
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)
Linear stability analysis
linearization
Let the solution be
characteristic equation
in
For
N
coupled FHN oscillators the characteristic equation is factorizable:
Characteristic equation:
Ghosh
et al.
PLoS
CB 2008
Ghosh
et al.
PLoS
CB 2008
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)
Case 1
Case 3
Compare to Fox et al. PNAS 2005
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)
CCP
FEF
PCI
PCIP
PFCM
VACD
CCP
+
+

+

+
FEF
+
+



+
PCI


+
+
+

PCIP
+

+
+


PFCM


+

+

VACD
+
+



+
Cross correlations between six
areas:
Ghosh
et al PLOS CB 2008
Compare to Fox et al. PNAS 2005
15uV

15uV
0 uV
400fT

400fT
0fT
Forward EEG/MEG solution in realistic
head models
Qf = 1, Qs = 1
Honey et al PNAS 2007;
Ghosh
et al
Plos
CB 2008;
Jirsa
Phil. Trans. Royal Soc. A 2009
What is the dynamic mechanism leading to the
emergence of these coherent fluctuations?
Synchronization?
F
FitzHugh

Nagumo
Neuron
Rho,
Jirsa
& McIntosh (in preparation)
Rho,
Jirsa
& McIntosh (in preparation)
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)
Rho,
Jirsa
& McIntosh (in preparation)
Other working points, maybe self

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