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

Part I

Structural Connectivity

White Matter

Diffusion Tensor Imaging (DSI)

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

Ellipsoids in a Brain

• 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

Visual Tracts

Catani et al., 2003, Brain

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

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 opticradiations

Data from: Geoff ParkerFigure from: Jones, 2008, Cortex

Probabilistic Tractography finds missing fibres

Jones, 2008, Cortex

left motor strip seed

3%

7% 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

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

FA and Age

Scholz et al. (2009)

Can you change white matter?

Van Eimeren et al (2010)

Combining DTI and fMRI

Navas-Sanchez et al. (2014)

Atlas-based Parcellation

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

Hagmann et al., 2006, RadioGraphics

pons, where cerebellar peduncle crossses corticospinal tract

DSI vs. DTI of the optic chiasm

DSI DTI

Wedeen et al., 2008, NeruoImage

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

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.

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

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

A Clear Explanation of PPI

57

Key Idea of PPI

58

• 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

60

Task Regressor

Task Regressor+

ROI Activity

Task Regressorx

ROI Activity=

PPI Regressor

O’Reilly et al., 2012, SCAN

Logic

61

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

62

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!

Graph Theory: Small World Networks

Hubs

Six Degrees of Kevin Bacon

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 millionAverage degrees of separation: 19

Hubs

Graph Theory:Nodes, Edges and Hubs

4

2

4

4

1

2

2

1

2

2

2

2

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

Motifs

verycommon

verycommon

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-basedHubs 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, NeuronFigure from: Huettel et al., 2nd ed.

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