Critical Brain Networks Why do we need a brain at all? Why the brain should be critical?

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Critical Brain Networks

•Why do we need a brain at all?•Why the brain should be critical?

Dante R. Chialvo

Physiology, Northwestern University, Chicago.

[email protected] Reprints: www.chialvo.net

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Reading

– Articles:

» Eguiluz V, Chialvo DR, Cecchi G, Baliki M, AV Apkarian. Scale-free brain functional networks. Phys. Rev. Letters 92, 018102 (2005).

» Chialvo DR. Critical brain networks. Physica A, 340,4,756-765 (2004).

» Beggs J. & Plenz D, Neuronal Avalanches in Neocortical Circuits J. of Neuroscience, 3 23(35):11167 (2003).

– Review:

» Sporns O, Chialvo DR, Kaiser M, and Hilgetag CC. Organization, Development and Function of Complex Brain Networks. Trends in Cognitive Sciences, 8 (9): 387-433 (2004).

– Books :

» How Nature Works. (Per Bak)

» Things that think. (Chialvo, 2006)

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Roadmap

Why do we need a brain at allHow to extract brain networks using fMRI(experimental results)Is anything ever new?(experimental results)Outlook

“Brainome”

Project

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Second: What is special about being critical? Recall Ferromagnetic-paramagnetic Phase-

Transition

T<TC T>TCT~TC

CriticalCriticalSubCriticalSubCritical SuperCriticSuperCriticalal

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Cri

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Snapshots Snapshots of spins of spins states in a states in a model model system system (Ising)(Ising)

1. Complex 2. Critical 3. Networks 4. fMRI nets 5. Ever New? 6. Conclusion

Long Range Correlations Only at the Critical Long Range Correlations Only at the Critical state!state!

Why the brain should be Critical?Why do we need a brain at all?Why do we need a brain at all?

•In a sub-critical world everything would be simple and In a sub-critical world everything would be simple and uniform - there would be nothing to learn. uniform - there would be nothing to learn.

•In a supercritical world, everything would be changing all the In a supercritical world, everything would be changing all the time - it would be impossible to learn. time - it would be impossible to learn.

The brain is necessary to navigate in a complex, critical world .The brain is necessary to navigate in a complex, critical world .

A brain not only have to remember, but also to forget and A brain not only have to remember, but also to forget and adapt.adapt.

•In a sub-critical brain memories would be frozen. In a sub-critical brain memories would be frozen.

•In a supercritical brain, patterns change all the time so no In a supercritical brain, patterns change all the time so no long term memory would be possible.long term memory would be possible.

To be highly To be highly susceptiblesusceptible, the brain itself has to be in the in-, the brain itself has to be in the in-between critical state.between critical state.


What one can observe?

Brain dynamics can be described in similar terms as Brain dynamics can be described in similar terms as thermodynamic systems at the thermodynamic systems at the criticalcritical point point including:including:

At large scaleAt large scale11::• Cortical Long range correlations in space and time Cortical Long range correlations in space and time (scale-free)(scale-free)

At smaller scaleAt smaller scale22::

• “ “Neuronal avalanches” is the normal homeostatic Neuronal avalanches” is the normal homeostatic state of neocortical circuits. ( “cortical-quakes” ).state of neocortical circuits. ( “cortical-quakes” ).


1Eguiluz V, et al Phys. Rev. Letters (2005); Chialvo DR. Physica A, (2004). 2Beggs J. & Plenz D, J. Neuroscience (2003).

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Can we extract functional brain networks with fMRI?


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fMRI

How toHow to extract extract functional brain networks functional brain networks with fMRIwith fMRI

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(I)

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fMRI

My brain’s network (finger tapping)My brain’s network (finger tapping)

Undirected Degree (k)

Nodes spatial locationNodes spatial location

Colors indicate the number of links (or “degree”) of each node. yellow=1, green 2, red=3, blue=4, etc

Indicate Indicate “airports”“airports”


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fMRI

Brain’s degree distribution (i.e., how many links each node Brain’s degree distribution (i.e., how many links each node have)have)

Scale-free

k- with ~ 2

From Eguiluz et al, Phys. Rev. Letters (2005).


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fMRI

Average Degree DistributionAverage Degree Distribution


=2Few but very well connected brain sites

n=22 from 7 subjects


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fMRI

Average Links Length Distribution Average Links Length Distribution


Voxel length“~ Brain radius”

Probability of finding a link between two nodes separated by a distance x <

k()~1/x2


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fMRI

Average Links Length Distribution agrees with recent results (in Average Links Length Distribution agrees with recent results (in resting condition) resting condition)

Functional connectivity vs. Functional connectivity vs. anatomical distance.anatomical distance.

( Symmetric ( Symmetric interhemispheric)interhemispheric)

From Salvador et al, Cerebral From Salvador et al, Cerebral Cortex 2005.Cortex 2005.

PC()~1/x2


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fMRI

Average Links Length Distribution in line with recent proposalsAverage Links Length Distribution in line with recent proposals

Hypothetical connection scheme of cortical interneurons and relationship between coverage and

number of neurons in each class.

Petermann and De los Rios, 2005.

Buzsaki et al, TRENDS in Neurosciences, 2004.


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fMRI

Something that bother us: Degree vs ClusteringSomething that bother us: Degree vs Clustering


Clustering estimates the proportion of nodes forming “triangles”.

Clustering relatively independent of connectivity

Assortative


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fMRI

Group statistics Group statistics


rc N C L <k> Crand Lrand

0.6 31503 0.14 11.4 13.41

2.0 4.3x10-

4

3.9

0.7 17174 0.13 12.9 6.29 2.1 3.7x10-

4

5.3

0.8 4891 0.15 6. 4.12 2.2 8.9x10-

4

6.0

“Small-world”

C >> Crand

L ~

Lrand Network N C L <k> . Crand Lrand

C. Elegans1

282 0.28 2.65 7.68 . 0.025 2.1

Macaque VC2

32 0.55 1.77 9.85 . 0.318 1.5

Cat Cortex2

65 0.54 1.87 17.48

. 0.273 1.4

fMRI-results

Previous related results

Brain Brain networks are networks are small-word small-word and scale-freeand scale-free


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L ~ 5 predicted LONG AGO by Szentagothai


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fMRI

Finger tapping vs. Finger tapping vs. MusicMusic


•Different tasksDifferent tasks•Different networksDifferent networks•Similar scalingSimilar scaling


Networks are scale free across tasks!Networks are scale free across tasks!

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Is anything

ever new?


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Warren McCulloch Gerhardt von Bonin

Percival Bailey

J. Neurophysiology, 1941. J. G. Dusser de Barenne, Garol and McCulloch FUNCTIONAL ORGANIZATION OF SENSORY AND ADJACENT CORTEX OF THE MONKEY.

Ever new? 1940 McCulloch Chemical Neuronography...

Illinois Neuropsychiatric Institute (Chicago).

Recording cortical activity after local Strychninization


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Adjacency matrix of cortico-cortical “functional” connectivity, after

McCulloch (1940)


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Network analysis of 1940 Chemical Neuronography

Chimpanzee’ Degree and Link Length distribution(calculated from McCullock ,1940 data)

• Non-homogeneous degree• Similar scaling


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We have seen:“In vivo” brain activity lacks a characteristic scale (“scale-free” networks). Theory, consequences… Assortative features …? theory?. Similar analysis for MEG?

The fMRI method allows, in principle, to study the brain “in a dance” rather than “in a pose” and to address dynamical states as emotion, pain, pleasure, uncooperative patients, coma etc). Realizing Brodman’s dream: towards the “Brainome” Integrating the cognitive picture by looking at a list of the 100 most relevant behavior as the “phenotype” and to the 100 or so cortical areas a the “genotype”. ( I.E., equating “activated cortical areas” with “gene expression” and “behavior” with “functional genomics”.)

Blah-Blah-logy


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Brain are critical

Brookhaven N. Lab. 1991

“Per, the brain for me is critical”…

“Yes, for me too Dante!”

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Open Parenthesis

261. Introduction 2. Complex Networks 3. Catalogue 4. fMRI nets 5. Ever New? 6. Cortical Cultures 7. Conclusion

It takes little to listen...

Functional Magnetic Resonance Imaging of Female and Functional Magnetic Resonance Imaging of Female and Males listening the same story (Mean of 6 Brains, each)Males listening the same story (Mean of 6 Brains, each)

Male

Female

# of SD away from mean


It takes more to talk...

““PET Studies of Memory: Novel versus Practiced Free Recall of PET Studies of Memory: Novel versus Practiced Free Recall of Word Lists” NeuroImage (1995)Word Lists” NeuroImage (1995) Andreasen et al. Andreasen et al.


It takes a whole network for other things ...

““Areas of brain activation in males and females during viewing of Areas of brain activation in males and females during viewing of erotic film excerpts” Human Brain Mapping (2002) Karama et erotic film excerpts” Human Brain Mapping (2002) Karama et al.al.

Females

(Left and Right )•Medial prefrontal cortex•Orbitofrontal •Cingulate gyrus•Thalamus•Insula•Ventral striatum•Amygdala•Occipitotemporal cortex

Males:

•All of the above plus•Hypothalamus

MalesFemales

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Brains are networks producing behavior ...

“Behavior” (usually bursty, complex, intermittent)

Large scale Small scale

at various scales…

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Brains are networks producing behavior ...

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Current technology already allows, in principle, to get data towards constructingthe “Brainome”… it will looks like this:

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A few conflictive demands ...

As a collective As a collective the brain the brain have a few conflictive demandshave a few conflictive demands::

» “ “Integrated” but “segregated”. (Sporns, Integrated” but “segregated”. (Sporns, Edelman,TononiEdelman,Tononi11; Pietronero; Pietronero22) )

Q: how different is this from being posed at a phase Q: how different is this from being posed at a phase transition? transition?

» “ “Robust” (structurally stable attractors) but “flexible” Robust” (structurally stable attractors) but “flexible” (today’s good behavior is not tomorrow anymore)(today’s good behavior is not tomorrow anymore)

Q: Which structure and dynamics we know of could satisfy Q: Which structure and dynamics we know of could satisfy that? (Per Bakthat? (Per Bak33 ) )

» Brain are Complex but obviously Self-organized, Darwin Brain are Complex but obviously Self-organized, Darwin Darwin Darwin...Darwin Darwin...

Q: how is it done? (Per Bak, D. PlenzQ: how is it done? (Per Bak, D. Plenz44, others), others)1) O. Sporns, et al, Cerebral Cortex, (2000); 10(2): 127 2) M. De Lucia et al, Physical Review E 71, 016114 (2005)

3) Per Bak, How Nature Works, Oxford Univ. Press, 1997 4) Beggs J. & Plenz D. J. of Neuroscience, 3 23(35):11167 (2003).


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Close Parenthesis

Critical Brain Networks Why do we need a brain at all? Why the brain should be critical?

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