From Localization to Connectivity and ...
Lei Sheu
1/11/2011

Research interests:
 To study the association of human behaviors and brain
functionality.
 Finding neural biomarkers of disease

What do we know
 Brain functionality depends on both structural and functional
characteristics. Neurons are genetically programmed but regulated and
adjusted accordingly in response to environmental conditions (70% of the
brain neurons are developed after birth).
 Neurons act both as clusters, and networks.
 fMRI measures BOLD signal, an indirect measure of neuronal activity.
 Measurements are subject to errors, which could be contributed by 4M
(machine, man, material, and method)
Level 1
Localization
Level 2
Integration
 Structure Morphology Structure Connectivity
Volumes, Cortical
Thickness, Surface areas,
etc.
(data: MRI structure)
 Functional activation
to stimuli.
Signal changes/
Contrasts: activation,
deactivation
(data: MRI BOLD)
 Morphological Correlations:
Correlation of morphological
descriptors in brain regions of
interest. (data: MRI structure)
 Anatomical Connectivity:
White matter fiber connections
among grey matter regions.
(data: MRI Diffusion)
Functional Connectivity
 Seed Based (functional
connectivity)
 ROIs/Network (effective
connectivity)
(data: MRI BOLD)
Level 3
Complex Networks
(Graph Theoretical
Analysis)
Structure Network
(data: MRI structure and
Diffusion)
Functional Network
(data: MRI BOLDI)
Integrate Structure
and Functional
Networks
Level 1
Localization
 Methods: Data driven
 Within Subject: voxel-
wise general linear Model
(GLM)
 Group : Multiple
regression, ANOVA
 Measures:
 Signal change,
 Activation clusters
Level 2
Integration
Methods: (Data driven/
Hypotheses driven)
Seed Based
Level 3
Complex Networks
 Methods: (Hypotheses
driven)
 Graph theory
 Measures:
 Node degree, degree
distribution and
assortativity
 Clustering coefficient and
ROIs/Networks
motifs
(Hypotheses driven)
 Path length and
SEM, VAR (Granger Causality),
efficiency
SVAR, DCM
 Connection or cost
 Hubs, centrality and
Measures:
robustness
Connectivity strength
 Modularity
Connectivity structural
Functional connectivity:
cross-correlation
PPI: task associated
connectivity
Functional Brain Networks Develop from a “Local to Distributed” Organization
Fair et. al. PLoS 2009
To share the methods we used in fMRI
connectivity analysis

Seed Based Analysis
 Functional Connectivity
 Psycophysiological Interaction (PPI)

Network Base Analysis




(SPM)
(AFNI,R)
Structural Equation Model (SEM)
(R,Matlab
Vector Autoregressive Model (VAR) (Granger Causality)
toolbox)
Structural Vector Autoregressive Model (SVAR)
Dynamic Causal Model (DCM)
(SPM)

Reconstruct BOLD signals (Preprocessing and Level 1 analysis)
 Signal pre-whitening, filtering, and artifact correction
 Physiological noise correction
 Estimate contrast signals (activation/deactivation)

Determine Regions of Interest (ROIs)
 Anatomically defined regions
 Meta analysis results
 Sphere mask over the cluster shown association with the psychophysiological
or psychosocial variables of interest)
 Others

Extract BOLD time series
 Average over ROI
 Median within ROI
 Principle components among voxels within ROI

Remove effects of no interest






Physiological noise
Draft and aliasing (High pass filter)
Series dependency (AR model)
Movement
Tasks of no interest
Covariates (performance)







To examine how the brain regions synchronized with the
activity in the seed regions.
Seed Based
Exploratory
Application: Resting State
Model: GLM
Output: Estimated brain statistical map (i.e., b map)
representing the strength of synchronization with the
seed voxel-wise.
Some setup




High passed filter of 100 second
AR(1) for series dependency correction
Covariate with a time series extracted from white matter area
Covariate with motion parameters




To examine task-specific connectivity.
Estimate the changes of connectivity
strength from a ‘baseline’ to a task of
interest.
Seed based; exploratory.
Model: GLM with interaction term.
Be aware of the calculation of interaction
term in the GLM.
• GLM Model
y nx 1  X nxp b px 1   nx 1
X  seed  task | seed | task | cov ariates |1
b1: interaction effect on brain activity (
measure of connectivity difference for the
two task conditions)
b2 : mean seed effect on brain activity
(measure of mean connectivity)
b3 : task effect on brain activity (measure of
activation difference for the two
conditions)
Brain Activity at (-16,6,8)


To validate or explore causal relationship
within a ROI network.
GLM: X=AX+e;
A: (aij)nxn
1
aij: path strength ij ;
aij= 0 if no relationship between i and j
ROI1
ROI4
1
A=
ROI3
1
ROI2
ROI5
1
1

0

0
0

0

0
a12
a13
0
0
0
0
a 32
0
a 34
0
0
0
0
0
0
0 

0 
a 35 

0 
0 


Prepare SEM inputs:
 Compute group summary time series for each ROI, e.g.,
eigentimeseries.
 Compute covariance/correlation matrix for the time series in ROIs.
 Compute residual error variance for each ROI
 Calculate effective degree of freedom (adjusted for the
autocorrelation of the time series)

Construct network structure and estimate connection parameters
 Model validation: If the model is determined, then find aij , such that
the covariance error is minimized. Test if each estimated connection
parameter is significant different from 0.
 Model search: Given model constrains to search for model that best fit
the covariance.
•
•
DCM allows you model brain activity at the neuronal level
(which is not directly accessible in fMRI) taking into account
the anatomical architecture of the system and the
interactions within that architecture under different
conditions of stimulus input and context.
The modelled neuronal dynamics (z) are transformed into
area-specific BOLD signals (y) by a hemodynamic forward
model (λ).
3



a
a
a
0
z
z
0c
0






0
b
00



11
1213
1
1
12
12
u




1

 




a
a
0a
z
z
c
00
0000


21
22
24
2
2
21













u

u

3
2
3













a
0
a
a
z
z
0
0
0
0
0
0
b
31
33
34
3 
34
3


u

 
 

3





0
a
a
a
z
z
0
0
0
0
0
0
0


4
4




 424344
 



z3
FG
lef
t
FG
righ
t
z4
z1
LG
lef
t
LG
righ
t
z2
RVF
u2
CONTEXT
LVF
u3
u1
Gianaros et. al, Cerebral Cortex. 2010, Sep
dMPFC vs VS
?
?
?
pACC vs OFC (L/R/M)
?
?
?


Model estimation for each subject
(parameters)
Model selection
- Bayesian Model Selection (BMS)
- Nonparametric method for paired comparison

Group analysis with the selected model
- Random effect analysis
- Comparison of low and high PE groups
- Bayesian average
Distributions of Model Comparison Result from 76 Subjects. Showing below are log of
Bayes Factor (logBF(ij), or the diffence of log model evidences for each pair models i, j
?
?
?
?
?
?
Distributions of Model Comparison Result from 76 Subjects. Showing below are log of
Bayes Factor (logBF(ij), or the diffence of log model evidences for each pair models i, j
?
?
?
?
?
?
Subject’s position,
physiological interfering
State of mind
Experimental
task design
scanner
MRI
Scanning
DICOM
Sources of variation:
•Subject/Material
•Machine
•Man/Operator
•Method
Realignment,
coregistration,
Smoothing,
reslice
Templates
Preprocessing
Smoothe
d images
Design matrix,
Covariates
Threshold
Covariates
Activation
map
Single subject
GLM
Contrast
maps
Group
Analysis
Effect/Corr
elation map
Operator,
environment
Image conversion
Data acquisition
sequence
Machine setup
BP
machine
BP
measurement
Subject’s physiological
reaction
Hemodynamic
Response Function
Signal filtering, high pass
filter, whitening