Jody Culham
Brain and Mind Institute
Department of Psychology
Western University
http://www.fmri4newbies.com/
Brain Connectivity
Last Update: March 24, 2013
Last Course: Psychology 9223, W2013, Western University
Networks and Connectivity
• In the analyses we have investigated so far, we
have been considering brain areas in isolation
• More sophisticated statistical techniques have
now become available to investigate networks of
activation
Part I
Structural Connectivity
White Matter
Diffusion Tensor Imaging (DSI)
Diffusion = Brownian Motion
• cumulative random motion of molecules
Robert Brown (1773-1858)
Image from Wikipedia
Longer Time Larger Diffusion
• 2.5 x 2.5 x 2.5 mm cube contains ~ 1020 water molecules
• r2 = 6Dt
– r2 = squared displacement
– D = diffusion coefficient (e.g., 3 x 10-3 mm2/s for water at 37 C)
– t = time
Restricted Diffusion
• diffusion in a particular
direction is affected by cell
membranes, myelin,
microtubules, density of
axons, diameter of fibres,
consistency of fibre
orientation, etc.
Isotropic vs. Anisotropic Diffusion
isotropic
= equal in all
directions
anisotropic
= different in
different directions
Ellipsoids
• eigenvalue =
length of one
axis of ellipsoid
• ranges from 0
to 1
• 1, 2, 3
• fractional
anisotropy (FA)
= nonuniformity
of eigenvalues
• ranges from
0 = sphere to
1 = line
• reflects multiple
factors not just
one (e.g.,
myelination)
Ellipsoids in a Brain
Directions
Left-Right
Anterior-Posterior Superior-Inferior
isotropic
DiffusionWeighted
Intensity
(dark =
high diffusion)
anisotropic
Apparent
Diffusion
Coefficient
(bright =
high diffusion)
Jones, 2008, Cortex
Variety of DTI Maps
Mean
Apparent
Diffusion
Coefficient
(bright =
high diffusion)
Fractional
Anisotropy
(FA)
(bright = anisotropic)
Color-Coded Orientation
Color Coding of Orientation
• red = left-right
• green = anterior-posterior
• blue = superior-inferior
• Note: maps show
orientation NOT direction
– e.g., you can’t discriminate
left right
from
right left
Jones, 2008, Cortex
Deterministic Tractography
• assumes largest
eigenvector reflects
dominant fibre orientation
• can set various tracking
parameters
– e.g., stop tracking if FA < 0.15
– e.g., stop tracking if angle
changes > 50 degrees
• doesn’t allow branching
fibres
Jones, 2008, Cortex
Major Tracts
• based on deterministic tractography
Data from: Catani & Ffytche, 2005
Figure from: Jones, 2008, Cortex
Visual Tracts
Catani et al., 2003, Brain
Limitations of Deterministic Tractography
deterministic
tractography finds
medial but not lateral
fibres from corpus
callosum (red) and
cerebro-spinal tracts
(green)
confidence in
deterministic
tractography?
0<p<1
Jones, 2008, Cortex
Cones of Uncertainty
Jones, 2008, Cortex
Probabilistic Tractography
• propagate a large number of pathways from the
seed point
• pathways sample from the distribution of directions
• output: proportion of pathways from seed point
reach a given voxel
• high probability does not guarantee that the tract
exists
• false positives and false negatives are still a big
problem
• accumulated error problem: the longer the tract, the
more small errors add up
Probabilistic Tractography
LGN seed
optic
radiations
Data from: Geoff Parker
Figure from: Jones, 2008, Cortex
Probabilistic Tractography finds missing fibres
left motor strip seed
3%
7%
Jones, 2008, Cortex
20%
Ambiguity of Overlapping Fibres
Crossing Fibres
Kissing Fibres
Multifibre Models
Jones, 2008, Cortex
One- vs. Multi-Fibre Models
• acoustic radiations (MGN-primary auditory cortex)
Using DTI to Define Areas
• Strictly speaking, “Areas” in the formal anatomical sense are
defined by Function, Architectonics, Connectivity and Topography,
yet imagers typically (and erroneously) only consider Function
functional boundaries
Connectional fingerprints of dorsal premotor (PMd) and ventral premotor (PMV) cortex
define areas with excellent correspondence to functionally determined boundaries
Data from: Tommasini et al., 2007, J Neurosci
Figure from: Johansen-Berg & Behrens, 2009, Ann Rev Neurosci
Stats vs. Tracts
• while pictures of tracts can be very pretty, we’ve seen
many problems gauging their validity
• don’t underestimate the utility of basic stats on mean
ADC, FA, etc.
FA histograms in
patients with
traumatic brain injury
FA histograms in
controls
Benson et al., 2007, J Neurotrauma
correlation between
mean FA and posttraumatic amnesia
Diffusion Spectrum Imaging (DSI)
DSI vs. DTI
• Diffusion Tensor Imaging
– find main direction and FA within each voxel
– cannot image crossing fibers
• Diffusion Spectrum Imaging
– find distribution of fiber orientations within each voxel
– can image crossing fibers
– other techniques (HARDI, Q-BALL) are similar in spirit
Fiber Distributions Within A Voxel
Seunarine & Alexander, 2009, In Johanssen-Berg & Behrens (Eds.), Diffusion MRI
FA vs. Distributions
fODF = fiber orientation distribution function
Seunarine & Alexander, 2009, In Johanssen-Berg & Behrens (Eds.), Diffusion MRI
Example
pons, where
cerebellar peduncle
crossses
corticospinal tract
Hagmann et al., 2006, RadioGraphics
DSI vs. DTI of the optic chiasm
DSI
Wedeen et al., 2008, NeruoImage
DTI
DSI vs. DTI of Callosal Fibres
So why isn’t everyone using DSI vs. DTI?
• Despite the clear advantages of DSI, most
diffusion-based tractography still relies on DTI
• DSI scans are very long (min ~40 min)
• Rapid improvements are being made in
scanning technology and postprocessing that
should make DSI easier to do
Part II
Functional and Effective
Connectivity
Resting State Scan
• a scan in which the subject relaxes without
falling asleep and is told not to think about
anything in particular while activation is
measured throughout the brain
I don’t feel
good
The only true resting state?
Functional Connectivity
• Areas show correlations in activation
• Those areas may or may not be directly interconnected
Step 1: Extract time course from area of interest = “seed”. Filter out high
frequencies, leaving low frequencies < ~0.1 Hz (~1 cycle/10 s).
MT+ motion complex
resting state scan (10 mins)
Step 2: Look for other areas that are show correlated activity in the same scan
V6 (another motion selective area
correlation with MT+: r > .8
Default Mode Network
Fox & Raichle, 2007, Nat Rev Neurosci
Fox and Raichle, 2007, Nat. Rev. Neurosci.
• During resting state scans, there are two
networks in which areas are correlated with
each other and anticorrelated with areas in
the other network
Default Mode in Anesthetized Monkeys
saccade
task
Monkey default mode network
posterior cingulate seed
Human default mode network
Data from: Vincent et al., 2007, Nature
Figure from: Fox & Raichle, 2007, Nat Rev Neurosci
LIP
tracer
• suggests that
the default mode
network does not
just reflect
uncontrolled
cognition
ICA and Resting State Connectivity
• ICA can be used to examine resting state
connectivity
ICA Identifies RS Subnetworks
Data from: Beckman et al., 2005, J Neurosci
Figure from: Huettel et al., 2nd ed.
Correlation ≠Causation
Figure from: Huettel et al., 2nd ed.
Partial Least Squares (PLS)
• data-driven approach developed by Randy McIntosh &
co.
• identifies components (latent variables) whose amplitude
is affected by the experimental manipulation (unlike ICA)
• output = set of weights applied to experimental
conditions and set of voxels where activation was
influenced by those weights
• components can be evaluated statistically through
permutation tests
– resample original data to determine probability of a given effect
size
Psychophysiological Interactions (PPI)
• identify the effect of an experimental manipulation
on the functional connectivity between two regions
• Subjects watched a
moving pattern passively
or paid attention to its
speed
• With attention, there was
a steeper slope in the
relationship between the
primary visual cortex and
motion-selective area
MT+/V5
Friston et al., 1997, NeuroImage
46
Key Idea of PPI
•
If two areas are interacting, their activity will go up and
down in synch
•
This effect may be task dependent
•
It should be more than can be explained by the shared
main effect of task
47
Based on O’Reilly et al., 2012, SCAN
PPI Example
• Task: Participants actively navigate through VR maze
• Control: Participants passively travel through VR maze
• Standard fMRI analysis
– Task – Control
• Activation in prefrontal cortex (PFC) and hippocampus (HC)
• Hypotheses:
1. PFC and HC are independently activated during active navigation
2. PFC and HC work together interactively during active navigation
• Prediction
– If PFC and HC interact, their activity should be more correlated during
active navigation than passive control
48
Based on O’Reilly et al., 2012, SCAN
Regressors
Task Regressor
Task Regressor
+
ROI Activity
Task Regressor
x
ROI Activity
=
PPI Regressor
O’Reilly et al., 2012, SCAN
49
Logic
Baseline: Red and Task: Red and blue
blue are antiare positively
correlated
correlated
Task Regressor
x
ROI Activity
=
PPI Regressor
• Regions that are correlated because of inherent
connectivity (as one would see in resting state) don’t
show up because correlation during task and
anticorrelation during baseline cancel each other out
• Regions that interact more during task than baseline
show up because correlation outweighs anticorrelation
50
Based on O’Reilly et al., 2012, SCAN
Regressors
Task Regressor
x
ROI Activity
=
PPI Regressor
• Even though we are only interested in the PPI regressor, we must
include the Task Regressor and ROI Activity as covariates of no
interest
• This ensures we are only looking at interactions over and above the
task activation (which may have been the basis for selecting the
region) and the inherent correlation
• Because the PPI Regressor is highly correlated with the other two
regressors, PPI has relatively low statistical power
• As in any analysis, it is beneficial to include other regressors of no
interest to soak up known sources of noise (e.g., error trials, head
motion)
51
Based on O’Reilly et al., 2012, SCAN
Structural Equation Modelling (SEM)
• statistical approach for inferring causal
relationships amongst variables
• derived from econometrics and applied to fMRI
Structural Equation Modelling Example
PFC high
PFC low
Büchel & Friston, 1997, Cerebral Cortex
55
Dynamic Causal Modelling (DCM)
• create model of
connections (perhaps
based on known
structural connections)
• examine how
experimental
manipulations affect
connectivity
Grol et al., 2007, J Neurosci
Granger Causality Modelling (GCM)
• identifies how the past history in one voxel affects the
activation in other voxels
• doesn’t require a priori models of networks
• need to demonstrate that it’s not an artifact of different
HRF latencies
– show that effect occurs in some but not all conditions
Does A:red improve prediction
of B:blue relative to prediction
from other info alone (e.g.,
B:green and Z:purple)
Graph Theory: Small World Networks
Hubs
10 most connected
actors in Hollywood
Sex Degrees of Copulation
Matthew Perry
HIV/AIDS hub
• “Patient Zero”: Gaetan Dugas
• Canadian flight attendant
• 250 partners/year
• 40 of 248 people diagnosed
with AIDS in 1982 had had sex
with him or someone who had
9-11 Terrorist Links
Internet nodes in 1998: 800 million
Average degrees of separation: 19
Hubs
Graph Theory:
Nodes, Edges and Hubs
The whole diagram is called a “graph”
Global
hub
Node
Edge
2
4
2
1234
2
2
4
1
Degree
2
2
4
Cluster
2
1
Provincial
hub
Provincial
hub
Undirected vs. Directed Edges
Undirected
Directed
Thresholding of Edges
threshold
Length and Clustering
highly clustered
long paths
highly clustered
short paths
weakly clustered
short paths
L = path length
C = clustering
coefficient
Scale-Free Networks
Sporns, Networks of the Brain
Motifs
very
common
very
common
Example: Monkey Anatomical Connections
The Brain: It’s a Small World After All
Bullmore & Sporns, 2009, Nat Rev Neurosci
Brain Hubs
Area 46 (DLPFC) = global hub
Example 2: Human Anatomical and
Functional Connections
Bullmore & Sporns, 2009, Nat Rev Neurosci
DSI-based Hubs in Humans
Hagmann et al., 2008, PLoS Biology
Resting State Connectivity-based
Hubs in Humans
van den Heuvel et al., 2008, NeuroImage
Example 3: It’s a Small Worm After All
C. elegans
~1 mm
302 neurons
Combinations of Connectivity Measures
Data from: Andrews-Hanna et al., 2007, Neuron
Figure from: Huettel et al., 2nd ed.
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