Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data Yoshio Takane McGill...
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![Page 1: Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data Yoshio Takane McGill University and University of Victoria September 19, 2013.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649e425503460f94b35580/html5/thumbnails/1.jpg)
Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data
Yoshio Takane McGill University and University of Victoria
September 19, 2013This talk is dedicated to Professor Haruo Yanai
of St. Luke College of Nursing
![Page 2: Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data Yoshio Takane McGill University and University of Victoria September 19, 2013.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649e425503460f94b35580/html5/thumbnails/2.jpg)
Structural Equation Models (SEMs)
• Methods for investigating if hypothesized relationships among observed variables are consistent with data
path analysis (sociology) simultaneous equation models (econometrics)• Latent variables to simplify the relationships
among observed variables (psychometrics)
![Page 3: Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data Yoshio Takane McGill University and University of Victoria September 19, 2013.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649e425503460f94b35580/html5/thumbnails/3.jpg)
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Chi-square = 46.917DF = 8
P-value = .000AIC =72.917
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![Page 4: Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data Yoshio Takane McGill University and University of Victoria September 19, 2013.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649e425503460f94b35580/html5/thumbnails/4.jpg)
Effective Connectivity
SPC
V5
V1
V1 = Primary Visual CortexV5 = Middle Temporal AreaSPC = Superior Parietal Cortex
Attention to Visual Motion Study (Friston et al, 2003)
![Page 5: Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data Yoshio Takane McGill University and University of Victoria September 19, 2013.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649e425503460f94b35580/html5/thumbnails/5.jpg)
Time Series of Three ROIs• Five BOLD signals for each ROI
ROIs Constructs or latent variables BOLD signals Observed variables
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The Attention to Visual Motion Data
Source: Friston et al. (2003)
u1 = Photicu2 = Motionu3 = Attention
![Page 7: Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data Yoshio Takane McGill University and University of Victoria September 19, 2013.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649e425503460f94b35580/html5/thumbnails/7.jpg)
Model Equations
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![Page 8: Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data Yoshio Takane McGill University and University of Victoria September 19, 2013.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649e425503460f94b35580/html5/thumbnails/8.jpg)
Shift Matrices
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0 0 0 0 0
0 0 0 1 0
S
is a matrix of shift ( 0,1, , )
is the number of lagslS T T l l q
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Experimental Stimuli
1 2[ , , , ] kU u u u
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Time Series of Experimental Stimuli
u1 = Photicu2 = Motionu3 = Attention
![Page 11: Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data Yoshio Takane McGill University and University of Victoria September 19, 2013.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649e425503460f94b35580/html5/thumbnails/11.jpg)
Model Features
(1) Features in Conventional SEM– Contemporaneous Effects of ROIs on other ROIs
(2) New Features– Time Lagged Effects– Stimulus Effects a) Direct effects b) Modulating effects
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Model Fitting
Estimate model parameters in such a way as to minimize the sum of squared residuals under some side conditions
size sample theis where3), 2, ,1( '
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![Page 13: Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data Yoshio Takane McGill University and University of Victoria September 19, 2013.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649e425503460f94b35580/html5/thumbnails/13.jpg)
• Assessment of reliability – Bootstrap method
• Data are correlated• A modified moving block bootstrap method
A Special Bootstrap Method
(Zhang and Browne, 2010; Buhlman, 2002)
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Result 1 : Attention to Visual Motion Data• Estimates, SE, p-values
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Result 1: Attention to Visual Motion Data
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Result 2: Memory Task Data
PCUN
MOG
MTG
HIP
INS
THA
DCG
Source: Wang et al. (2010)
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Result 2: Memory Task Data
PCUN
MOG
MTG
HIP
INS
THA
DCG
![Page 18: Statistical Models for the Analysis of Brain Connectivity Based on fMRI Data Yoshio Takane McGill University and University of Victoria September 19, 2013.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649e425503460f94b35580/html5/thumbnails/18.jpg)
A Summary so far
• Dynamic GSCA can accommodate more complex and elaborate models
• Single optimization criterion/ Simple and reliable algorithm
• Modified moving block bootstrap method to handle correlated observations
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Extensions of Dynamic GSCA
1. Dynamic GSCA with latent interactions
2. Simultaneous analysis of multi-subject data
• Multi-sample (multi-group) comparison• Multilevel analysis
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Latent Interaction
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Multiple Subjects
A recent article posted at a blog site called NEUROSKEPTIC is questioning the validity of some procedure in SPM (Does it mean “Spurious Positive Mapping” rather than “Statistical Parametric Mapping?”) based on Eklund et al. (2012), who examined nearly 1500 individual resting-state fMRI data sets by SPM, and found significant task unrelated activations in a majority of cases.
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A commentary of the article said “It is quite common to find such spontaneous activations in individual data. However, those activations are not synchronized across individuals, so they tend to disappear when multiple-subject data are simultaneously analyzed.”
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Second Model• Measurement model: -- Extracts the most representative variations of ROIs across subjects within groups -- Multiple-set canonical correlation analysis (instead of PCA-like model as before) -- Homogeneity across subjects, but not across ROIs• Structural model remains essentially the same
as before (but includes latent interactions)
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The Bootstrap Method
• Sample from subjects • Equivalent to sampling blocks of length equal
to T
• Calculate mean, sd, and p-values for estimated parameterst and fit indices
• We may also bootstrap any contrasts between parameters (e.g., directionality of influence).
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An Example Data Set• 210 matrices denoted by Zk(g)j (as opposed to ) • 15 subjects (indexed by k) in each of two groups
indexed by g (1: normal, 2: schizophrenic)• 7 ROIs indexed by j• Each Zk(g)j is a 214 (time points) by the number
of voxels matrix for each ROI.• The total number of voxels in the 7 ROIs is 777,
giving rise to nearly 5 million data points.
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Equality Constraints
• We may constrain (ROI j’s activations) across groups
• We may also constrain other structural parameters equal across groups
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Analyses
• No stimulus effects; 7 ROIs are bidirectionally connected; Time-lagged effects of order 1
• Analysis I: All parameters are assumed equal across groups.
• Analysis II: No parameters are assumed equal. (Equivalent to two separate analyses.)
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Time Series of ROIs: Assumed Equal Across Groups
IPL-L
PreCG-L
CL-L
CL-R
IPL-R
PreCG-R
SMA
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Time Series of ROIs: Separate Groups
Normals Schizophrenics
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The Second Order PCA of SeparateTime Series for ROIs
Normal 49.2%. 35.7% 1 0.8740 0.3319 IPL-L 2 0.9515 0.0541 PreCG-L 3 0.9431 -0.0444 CL-L 4 0.9360 0.1513 CL-R 5 0.9621 -0.0422 IPL-R 6 0.9547 0.1525 PreCG-R 7 0.8805 0.3406 SMAschizophrenic 1 -0.1473 0.8472 IPL-L 2 0.1945 0.9284 PreCG-L 3 -0.0357 0.9442 CL-L 4 0.7038 -0.1592 CL-R 5 -0.0068 0.9564 IPL-R 6 0.2163 0.9042 PreCG-R 7 0.4833 0.6976 SMA
I II
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Time Series for ROIs: ROI 4 Equated Across Groups
Normals Schizophrenics
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Future Prospects
• User friendly program• More flexible constraints• Groups created by repeated measurements• Time varying regression coefficients in
structural models• Nonlinear models(?); Differential equations
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Contributions by
• Kwanghee Jung (McGill Univ. of Texas at Houston)
• Lixing Zhou (McGill)• Heungsun Hwang (McGill)• Todd Woodward (University of British
Columbia)
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Thank you
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Historical 1
• Unified SEM (Kim et al., 2007) – autoregressive effects
• Extended unified SEM (Gates et al., 2010) – stimulus effects
• GSCA (Hwang & Takane, 2004) – PCA-SEM• Dynamic GSCA (Jung et al., 2012)
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Historical 2
• Regularized GCANO (Takane et al., 2008)• Functional GCANO (Hwang et al., 2012)• GCANO –PCA (Hwang et al., 2013)• Dynamic GCANO – GCANO-SEM