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Anintroductiontobrainnetworks
AlexFornito
BrainandMentalHealthLab
MonashInstituteofCognitiveandClinicalNeurosciences
MonashUniversity
e:[email protected]
@AFornito
two fundamental principles of brain organization
segregation
Broca’s Leborgne (akaTan)
integration
1999
1990-1992
development
of
discovery
of BOLD
diffusion
contrast
tractography
Scoville &Milner’sHM
Nature,1993
Huth
etal.Nature,2015
Harlow’sPhineasGage
Polyak, 1957
Ogawaetal.PNAS,1992
Conturo etal.PNAS,1999
Felleman &VanEssen,Cereb Cortex,1991
connectome:
nanoscale
nm
a comprehensivestructuraldescriptionofthe
networkofelementsandconnections
formingthehumanbrain.
Sporns,Tononi,Kötter,PLoS CompBiol,2005
microscale
nmto𝜇m
meso
𝜇m to mm
macroscale
mmtocm
modellingbrainnetworksasgraphs
edge
node
any network can be modelled as a graph of nodes connected by edges
nodes represent fundamental processing units
edges represent the interactions between nodes
a briefhistoryofgraphtheory
LeonhardEuler
(1707-1783)
PaulErdős
(1913-1996)
Alfréd Rényi
(1921-1970)
a briefhistoryofgraphtheory
realnetworkshavehubs
random
realnetworksaresmall-world
scalefree
Barabasi &Albert,Science,1999;
Barabasi &Oltvai,NatRevGenet,2004
WattsandStrogatz,Nature,1999
realnetworksaremodular
Girvan&Newman,PNAS,2004;Clauset,Moore&Newman,Nature,2008
definingnodes
cytoarchitecture
1.
2.
3.
probabilistic
Brainnodesshouldhave:
Intrinsicconsistency
Extrinsicdifferentiation
Spatiallyconstrained
Fornitoetal.NeuroImage,2013
Brodmann,1909
chemoarchitecture
anatomical
Eickhoff etal.NeuroImage,2007
Tzuorio-Mazoyer,etal.NeuroImage,2002
Desikan,etal.NeuroImage,2006
data-driven
Yeoetal.JNeurophysiol,2011
Craddocketal.HumBrainMapp,2012
Poweretal.Neuron,2011
voxel-based
vandenHeuvel etal.NeuroImage,2009
Hayasaka &Laurienti,NeuroImage,2010
Eickhoff etal.NeuroImage,2006
random
Hagmann,etal.PLoS One,2007
Zalesky,etal.NeuroImage,2010
Fornitoetal.FontSysNeurosci,2010
myeloarchitecture
Glasser &VanEssen
JNeurosci 2011
functional
Dosenbach,etal.Science,2010
Fornitoetal.PNAS,2012
multimodal
Glasser etal.
Nature,2016
definingedges
Structuralconnectivity
Thephysical(anatomical)connectionsbetweenbrainregions
Intrinsicallydirected
DirectionalitycannotberesolvedwithMRI
Functionalconnectivity
Astatisticaldependencebetweenspatiallydistinctneurophysiologicalsignals
Estimatedatlevelofmeasuredsignals
Canbedirectedorundirected
Effectiveconnectivity
Theinfluencethatoneneuronalsystemexertsoveranother
Usuallymodel-based
Describescausalinteractionsattheneuronallevel
Friston etal,1994,HumBrainMapping;Fornitoetal,2015,NatRevNeurosci
definingedges
structural
functional
electron
microscopy
tract-tracing
electrophysiology
Bocketal.Nature,2011
Whiteetal.PTRS,1986
Ohetal.Nature,2014
http://connectivity.brain-map.org
Yuetal.Cereb Cortex,2008
geneticlabelling
informatics
Chiangetal.Curr Biol,2011
www.flycircuit.tw
PLI
Axer,etal.NeuroImage,2011
Modha &SinghPNAS,2010
Shanahanetal.Fron CompNeurosci,2013
http://cocomac.org
calciumimaging
ECoG
Bastos etal.Neuron,2015
Brovelli,etal.PNAS,2004
M/EEG
Ahrensetal.NatMethods,2013
fMRI
DWI
Hagmann etal.PLoS One,2007
Engeletal.Neuron,2013
Smithetal.NeuroImage,2011
mappingstructuralconnectivityinhumanswithDWI
Johansen-Berg&Rushworth,AnnRevNeurosci,2014;Mori&Zhang,Neuron,2008;
Tournier etal.Magn ResMed,2011;Isenberg,2011;Thomas,etal.PNAS,2014
measuringconnectionweightswithdiffusionMRI
connectionweightstypicallyestimatedas:
numberofconnectingstreamlines
averagetractFAorotherdiffusivityindex
but:
emergingapproachesinclude:
axondiameter&density(Assaf etal.NeuroImage,2013)
trackdensityimaging(Calamante,etal.NeuroImage,2011)
myelincontent(Deoni etal.Magn ResMed,2008)
definingedges
structural
functional
electron
microscopy
tract-tracing
electrophysiology
Bocketal.Nature,2011
Whiteetal.PTRS,1986
Ohetal.Nature,2014
http://connectivity.brain-map.org
Yuetal.Cereb Cortex,2008
geneticlabelling
collated
Chiangetal.Curr Biol,2011
www.flycircuit.tw
PLI
Axer,etal.NeuroImage,2011
Modha &SinghPNAS,2010
Shanahanetal.Fron CompNeurosci,2013
http://cocomac.org
calciumimaging
ECoG
Bastos etal.Neuron,2015
Brovelli,etal.PNAS,2004
M/EEG
Ahrensetal.NatMethods,2013
fMRI
DWI
Hagmann etal.PLoS One,2007
Engeletal.Neuron,2013
Fornitoetal.NeuroImage,2013
Smithetal.NeuroImage,2011
mappingfunctionalconnectivitywithfMRI
statisticaldependence
correlation
partialcorrelation
mutualinformation
…
etc
rest
Fox&Raichle,NatRevNeurosci,2002
Achard etal.JNeurosci,2005
Smithetal.NeuroImage,2011
task
dynamics
Zalesky etal.PNAS,2014
Hutchison,etal.NeuroImage,2013
Fornitoetal.PNAS,2012
Fornitoetal.Biol Psychiatry,2012
Coleetal.NatNeurosci,2013
topologicalbiasesofcommonfunctionalconnectivitymeasures
Fornito, Zalesky & Bullmore, 2016, Fundamentals of Brain Network Analysis
Zalesky, Fornito, Bullmore, NeuroImage, 2012
fromdatatograph
definenodes&edges
functional
connectivity
buildgraph
structural
connectivity
adjacency
matrix
braingraph
Fornito, Zalesky, & Breakspear. 2015, Nat Rev Neurosci
matricesandgraphsareformallyequivalent
Fornito, Zalesky & Bullmore, 2016, Fundamentals of Brain Network Analysis
whichgraphbestrepresentsthebrain?
binary
weighted
heterogeneousnodes
directed
heterogeneousedges
hybrid
whichgraphbestrepresentsthebrain?
Fornito, Zalesky, & Breakspear. 2013, NeuroImage; Fornito, Zalesky, Bullmore, 2016, Fundamentals of Brain Network Analysis
fromdatatograph
definenodes&edges
functional
connectivity
buildgraph
structural
connectivity
adjacency
matrix
braingraph
Fornito, Zalesky, & Breakspear. 2015, Nat Rev Neurosci
networkanalysis
connectivity
topology
fromdatatograph
definenodes&edges
functional
connectivity
buildgraph
structural
connectivity
networkanalysis
adjacency
matrix
connectivity
Networkthresholding&statistics
AndrewZalesky
Paths,diffusion&communication
Bratislav Misic
Modularity(static&dynamic)
braingraph
SarahMuldoon
Centrality&hubs
Martijn vandenHeuvel
Null&generativemodels
PetraVertes
Fornito, Zalesky, & Breakspear. 2015, Nat Rev Neurosci
topology
summary
Graphs provide useful models of brain networks
A unified framework for representing multiscale organization
There are different methods for defining brain nodes and edges
Each has pros and cons; constrains interpretation of findings
Brain networks can be directed/undirected and weighted/unweighted
Node/edge heterogeneity and dynamics can also be accomodated
Brain networks can be analysed at the level of connectivity or topology
Effects can be mapped at individual edges, nodes, or globally
resources
graphtheory/networkscience
Newman(2010)Networks:Anintroduction.
Newman(2003)SIAMRev.
Albert&Barabasi (2002)RevModernPhysics
graphtheoryandthebrain
Sporns (2011)Networksofthebrain.
Amazon
http://amzn.to/1MLgMhU
Elsevier
http://bit.ly/1Hp29OZ
Sporns (2012)Discoveringthehumanconnectome.
Bullmore &Sporns (2009)NatRevNeurosci.
Bullmore &Bassett(2011)Annu RevClin Psychol.
Fornito,Zalesky &Breakspear (2013)NeuroImage.
software
Brainconnectivitytoolbox:
https://sites.google.com/site/bctnet/
Graphanalysistoolbox:
https://www.nitrc.org/projects/gat/
Network-basedstatistic:
http://www.nitrc.org/projects/nbs/
Task-relatedfunctionalconnectivity(cPPI):
http://www.nitrc.org/projects/cppi_toolbox/
Anopen-accessjournalfornetwork
neuroscienceatalllevels,
frommoleculartomacroscales
Networkvisualization
http://immersive.erc.monash.edu.au/neuromarvl/
http://www.mitpressjournals.org/netn