ppi, gca, and dcm in resting-state
DESCRIPTION
Physiophysiological interaction (PPI), Granger causality (GCA), and dynamic causal moding (DCM) in resting-state fMRI. These slides are for a pre-conference educational workshop for the biennial conference on resting-state and brain connectivity.TRANSCRIPT
Physiophysiological Interaction (PPI)
Granger Causality Analysis (GCA)and Dynamic Causal Modeling
(DCM) for resting-state fMRI
Xin Di, PhDNew Jersey Institute of Technology
Definition by Friston (1994): “temporal correlations between spatially remote neurophysiological events”
Regular methods:Correlation, coherence, PCA/ICA…
A simple linear model
Connectivity is stable over timeNo causality information
Functional connectivity
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Modulation of connectivity by a third regionPhysiophysiological interaction (PPI) (Friston et al., 1997)
Causal influence (effective causality)Granger causality analysis (GCA) (Goebel et al., 2003)Dynamic causal modeling (DCM) (Friston et al., 2003)
Go beyond simple correlations
Modulatory interaction
X1
Y
X2
+ or x ?
Linear relationship
Model interaction between the two seeds
The relationship between y and x2 is:
Models for modulatory interaction
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2132110 )( xxaaxaay
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21322110 xxaxaxaay
Modulatory interaction
X1
Y
X2
Voxel-wise general linear model (GLM)
• Defining two seeds• Calculating PPI term• Defining individual PPI GLM model for• Group-level GLM analysis
Analysis of modulatory interaction
Defining seeds• Two seeds• Hypothesis-driven• The two seeds should be
somehow connected
Analysis of modulatory interaction
Two mains nodes of each resting-state networks obtained from ICA resultsDi and Biswal, 2013, in PLoS One
Analysis of modulatory interaction
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ROI 1 ROI 2
Deconvolve
Multiply
Convolve
PPI
Deconvolve
Analysis of modulatory interaction
Statistical analysis: Design
parameters
imag
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Sn(1
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PCA
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parameter estimability
(gray not uniquely specified)
Design description...
Basis functions : hrfNumber of sessions : 1
Trials per session : 0 Interscan interval : 2.00 {s}
High pass Filter : Cutoff: 100 {s}Global calculation : mean voxel value
Grand mean scaling : session specificGlobal normalisation : None
An example design matrix
Main effects:time series of two ROIs
Interaction
Covariates:WM/CSFHead motion
Analysis of modulatory interaction
Group analysis: one sample t-test
Modulatory interaction involves three regions Two regions need to be defined as seeds
(combination problem) Reliability of the interaction is lower than the
reliability of the two main effects of time series No causality information
A brief summary of PPI analysis
Based on prediction “whether one time series is useful in forecasting
another”
Granger causality
From wikipedia
Granger Causality model (model 1)
Autoregressive model (model 2)
Equations for Granger Causality
tmtmttt yayayaay ...22110
tmtmttmtmttt xbxbxbyayayaay ...... 221122110
Statistical inference:• F test: var(model 1)/var(model 2)
Whether including history of time series x can significantly explain time series y?
• One sample t-test of each b parameters. Causal effects on specific time points.
Neuronal transmission delay: 50 – 100 ms Typical sampling rate (TR) of fMRI data: 1 – 3 s
Model order can be determined by model comparison (e.g. AIC)
Model order
Implementation of Granger Causality
Regions that are significantly influenced by the right frontal-insular cortex (rFIC) (Zang et al., 2012)
Exploratory - seed-based analysis
Implementation of Granger Causality
Granger causality among nodes of the DMN (Uddin et al., 2008)
ROI-based analysis
Granger causality is based on BOLD delays of 1 – 3 s, while neuronal delays are about 50 – 100 ms
Hemodynamic response is much longer (6s to peak)
Hemodynamic response varied across brain regions
Cerebral blood flow → vascular anatomy
Pitfalls of Granger Causality
HRF for different subjects and different regions (Handwerker et al., 2004)
Granger causality is based on BOLD delays of 1 – 3 s, while neuronal delays are about 50 – 100 ms
Hemodynamic response is much longer (6s to peak)
Hemodynamic response varied across brain regions
Cerebral blood flow → vascular anatomy
Pitfalls of Granger Causality
BOLD Granger Causality reflects vascular anatomy (Webb et al., 2013, in PLoS One)
Granger causality analysis is based on predictability of BOLD signals in 1 – 3 seconds order
Regional variations of hemodynamic responses may mislead Granger causal effects
Granger causality results should be compared with previous neurophysiology studies
A brief summary of Granger causality
DCM was originally developed for fMRI data (Friston et al., 2003)
Generative model Making inference by comparing models Hypothesis-driven
Dynamic causal modeling (DCM)
Differential equation model
Matrix form of the model
Dynamic causal modeling (DCM)
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UCZAZ
Modeling low frequency fluctuations
Fourier series at frequencies:0.01, 0.02, 0.04, and 0.08 Hz
Modeling low frequency fluctuations
Design matrix
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)201.0sin()201.0cos(
sin4
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sin3
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sin2
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sin1
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Di & Biswal, 2013
DCM model
Stochastic DCM (Daunizeau et al., 2009) Deterministic DCM based on crossed spectra but
not time series (Friston et al., 2014) Available in SPM12b
Recent advances on resting-state DCM
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Making inference by comparing models Hypothesis-driven
Defining ROIs (up to 8) Constructing model space Model comparisons Parameter testing
DCM in practice
DCM model definition
All possible models: 46 = 4096Hypothesis constrained models: 3 x 2 x 5 = 30
Model families Critical comments on dynamic causal modelling (Lohmann et al., 2012)
DCM results
Model family Comparison
Model comparison Model parameters results
DCM analysis is highly hypothesis-driven Appropriately defined model space is critical for
DCM analysis
A brief summary of DCM
Higher order models can help to address questions like modulation of connectivity and causality
Each model has pros and cons Hypotheses are important Results should be grounded on anatomical
connections and neurophysiological results
Concluding remarks
Thank you for your attention
Acknowledgement: our lab membersDr. Bharat BiswalSuril GohelRui YuanKeerthana Karunakaran…