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Brain Connectivity
http://www.fmri4newbies.com/
Last Update: December 1, 2014Last Course: Psychology 9223, F2014, Western University
Jody CulhamBrain and Mind Institute
Department of PsychologyWestern 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
Diffusion = Brownian Motion
Robert Brown (1773-1858)Image from Wikipedia
• cumulative random motion of molecules
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
Slide from Anna Matejko
Measure diffusion in at least 6 directions(more directions is better)
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
• eigenvalue = length of one axis of ellipsoid• ranges from 0 to 1 1, 2, 3
• Calculated for each voxel
• MD= measures overall water diffusion in a voxel
• Insensitive to the orientation of fibers
• Often used clinically
• High MD often indicates poorer white matter integrity
MD= (λ1 + λ2+ λ3)/3
Mean Diffusivity (MD)
Slide modified from Anna Matejko
high MD = whitelow MD = black
• an + iso + tropy = not + equal + turn
• non-uniformity of eigenvalues• measure of how elongated an
ellipsoid is• varies from 0 (sphere) to 1 (line)• indicates high white matter integrity
Fractional Anisotropy
high FA = whitelow FA = black
DirectionsLeft-Right Anterior-Posterior Superior-Inferior
Diffusion-WeightedIntensity(dark =
high diffusion)
ApparentDiffusion
Coefficient(bright =
high diffusion)
isotropic
anisotropic
Jones, 2008, Cortex
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 fromright left
Jones, 2008, Cortex
Variety of DTI Maps
MeanApparentDiffusion
Coefficient(bright =
high diffusion)
FractionalAnisotropy
(FA)(bright = anisotropic)
Color-Coded Orientation
• Many microscopic and macroscopic factors can contribute to anisotropy
• myelination• ~20%
• axon diameter• axon density
Tournier et al (2011)
Sources of FA
http://www.diffusion-imaging.com/2012/10/voxel-based-versus-track-based.html
Longitudinal vs. Radial Diffusivity
LowFA
HighFA
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, 2005Figure from: Jones, 2008, Cortex
Limitations of Deterministic Tractography
Jones, 2008, Cortex
deterministic tractography finds medial but not lateral fibres from corpus callosum (red) and cerebro-spinal tracts (green)
confidence in deterministic tractography?
0 < p < 1
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 opticradiations
Data from: Geoff ParkerFigure from: Jones, 2008, Cortex
Probabilistic Tractography finds missing fibres
Jones, 2008, Cortex
left motor strip seed
3%
7% 20%
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
Connectional fingerprints of dorsal premotor (PMd) and ventral premotor (PMV) cortexdefine areas with excellent correspondence to functionally determined boundaries
functional boundaries
Data from: Tommasini et al., 2007, J NeurosciFigure 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
correlation between mean FA and post-traumatic amnesia
Benson et al., 2007, J Neurotrauma
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
Hagmann et al., 2006, RadioGraphics
pons, where cerebellar peduncle crossses corticospinal tract
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
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
http://xkcd.com/1453/
Critique of fMRI Critique of Resting State?
OUR RESTING STATE CONNECTIVITY STUDY IDENTIFIED THE BRAIN NETWORKS IMPLICATED IN DROWSINESS, BACK PAIN, AND HAVING TO PEE REALLY BADLY
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).
Step 2: Look for other areas that are show correlated activity in the same scan
MT+ motion complexresting state scan (10 mins)
V6 (another motion selective areacorrelation with MT+: r > .8
Default Mode Network
• During resting state scans, there are two networks in which areas are correlated with each other and anticorrelated with areas in the other network
Fox and Raichle, 2007, Nat. Rev. Neurosci.Fox & Raichle, 2007, Nat Rev Neurosci
Default Mode in Anesthetized Monkeys
Data from: Vincent et al., 2007, NatureFigure from: Fox & Raichle, 2007, Nat Rev Neurosci
saccadetask
LIPtracer
Monkey default mode network
Human default mode network
posterior cingulate seed
• 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 NeurosciFigure 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
Friston et al., 1997, NeuroImage
• 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
Key Idea of PPI
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• 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
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:H1: PFC and HC are independently activated during active navigation
H2: 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 control59
Based on O’Reilly et al., 2012, SCAN
Regressors
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Task Regressor
Task Regressor+
ROI Activity
Task Regressorx
ROI Activity=
PPI Regressor
O’Reilly et al., 2012, SCAN
Logic
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Task Regressorx
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
Task: Red and blue are positively
correlated
Baseline: Red and blue are anti-
correlated
Based on O’Reilly et al., 2012, SCAN
Regressors
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Task Regressorx
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)
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
• Participants viewed moving stimuli• Connectivity between V5 and PPC was
modulated by activation in PFC
66
PFC high
PFC low
Büchel & Friston, 1997, Cerebral Cortex
Activity in V5 (= MT+ = motion-selective area)
Act
ivity
in P
PC
(po
ster
ior
parie
tal c
orte
x)
PFC = prefrontal cortex
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)
Warning: Many reviewers are highly skeptical of GCM applied to fMRI data. Use at your own risk!
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
Graph Theory:Nodes, Edges and Hubs
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2
4
4
1
2
2
1
2
2
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Provincialhub
Provincialhub
Globalhub
Node
Edge
Cluster
1234 Degree
The whole diagram is called a “graph”
Directed
Undirected
Undirected vs. Directed Edges
Thresholding of Edges
threshold
Length and Clustering
L = path length
C = clustering coefficient
highly clusteredlong paths
highly clusteredshort paths
weakly clusteredshort paths
The Brain: It’s a Small World After All
Bullmore & Sporns, 2009, Nat Rev Neurosci
Example 2: Human Anatomical and Functional Connections
Bullmore & Sporns, 2009, Nat Rev Neurosci
Resting State Connectivity-basedHubs in Humans
van den Heuvel et al., 2008, NeuroImage
Combinations of Connectivity Measures
Data from: Andrews-Hanna et al., 2007, NeuronFigure from: Huettel et al., 2nd ed.