Analyzing Brain Connectivity for fMRI Data

1. From Localization to Connectivity and ... Lei Sheu 1/11/2011 Analyzing Brain Connectivity for fMRI Data

2. Background • 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)

3. Level 1 Localization Level 2 Integration Level 3 Complex Networks Quantify Brain Activity/Functionarity • (Graph Theoretical Analysis) • Structure Network (data: MRI structure and Diffusion) • Functional Network • (data: MRI BOLDI) • Integrate Structure and Functional Networks • Structure Connectivity • 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) • Structure Morphology Volumes, Cortical Thickness, Surface areas, etc. (data: MRI structure) • Functional activationto stimuli. • Signal changes/ Contrasts: activation, deactivation • (data: MRI BOLD)

4. Level 1 Localization Level 2 Integration Level 3 Complex Networks Methods and Measures (fMRI) • Methods: Data driven • Within Subject: voxel-wise general linear Model (GLM) • Group : Multiple regression, ANOVA • Measures: • Signal change, • Activation clusters • Methods: (Hypotheses driven) • Graph theory • Measures: • Node degree, degree distribution and assortativity • Clustering coefficient and motifs • Path length and efficiency • Connection or cost • Hubs, centrality and robustness • Modularity • Methods:(Data driven/ Hypotheses driven) • Seed Based • Functional connectivity: cross-correlation • PPI: task associated connectivity • ROIs/Networks • (Hypotheses driven) • SEM, VAR (Granger Causality), • SVAR, DCM • Measures: • Connectivity strength • Connectivity structural

5. Brain Network Changes with Age Functional Brain Networks Develop from a “Local to Distributed” Organization Fair et. al. PLoS 2009

6. About this Presentation To share the methods we used in fMRI connectivity analysis • Seed Based Analysis • Functional Connectivity • Psycophysiological Interaction (PPI) • Network Base Analysis • Structural Equation Model (SEM) • Vector Autoregressive Model (VAR) (Granger Causality) • Structural Vector Autoregressive Model (SVAR) • Dynamic Causal Model (DCM) (SPM) (AFNI,R) (R,Matlab toolbox) (SPM)

7. Data Preparation • 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)

8. Functional Connectivity • 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

9. PPI (context-dependent correlation) • 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.

10. PPI • GLM Model 1: interaction effect on brain activity ( measure of connectivity difference for the two task conditions) 2 : mean seed effect on brain activity (measure of mean connectivity) 3 : task effect on brain activity (measure of activation difference for the two conditions)

11. Interaction Effect of Correlation between Brain Activity at (-16,6,-8) and mPFC Seed in Reward Condition Brain Activity at (-16,6,8)

12. Structure Equation Model (SEM) • To validate or explore causal relationship within a ROI network. • GLM: X=AX+e; A: (aij)nxn aij: path strength ij ; aij= 0 if no relationship between i and j e1 e1 ROI1 ROI4 A= ROI3 e1 ROI2 ROI5 e1 e1

13. Run SEM analysis • 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.

14. DCM • DCM allows you model brain activity at theneuronal 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).

15. z4 z3 z1 z2 CONTEXT LVF RVF u2 u3 u1 LG left FG right LG right FG left Neuronal State Equations

16. ? ? ? DCM Models forPE Related Reward Network Systems Gianaros et. al, Cerebral Cortex. 2010, Sep dMPFC vs VS pACC vs OFC (L/R/M) ? ? ?

17. DCM Procedure • 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

18. 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 ? ? ? ? ? ?

19. ? ? ? ? ? ? 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

21. Sources of variation: • Subject/Material • Machine • Man/Operator • Method Subject’s position, physiological interfering State of mind Realignment, coregistration, Smoothing, reslice Design matrix, Covariates Experimental task design Threshold Covariates Templates Activation map scanner Smoothed images Single subject GLM Contrast maps Group Analysis Preprocessing MRI Scanning DICOM Effect/Correlation map Operator, environment Hemodynamic Response Function Machine setup Signal filtering, high pass filter, whitening Image conversion Data acquisition sequence BP measurement BP machine Subject’s physiological reaction