Brain Connectivity Modeler

Purpose

Brain connectivity analysis goes beyond mapping where activation occurs to ask how brain regions interact. This requires choosing among fundamentally different analytical frameworks: functional connectivity (statistical associations), effective connectivity (directed causal influences), and network topology (graph-theoretic properties). Each framework answers different questions and makes different assumptions.

A competent programmer without neuroscience training would not know the critical distinction between functional and effective connectivity, would likely confuse correlation with causation in brain networks, and would not appreciate why motion artifacts are particularly devastating for connectivity analyses. This skill encodes the domain judgment required to select and correctly implement brain connectivity methods.

When to Use This Skill

• Choosing a connectivity method for task-based or resting-state fMRI
• Implementing psychophysiological interaction (PPI) analysis
• Setting up dynamic causal models (DCM)
• Applying graph theory to brain network data
• Evaluating whether Granger causality is appropriate for fMRI
• Reviewing or troubleshooting existing connectivity analyses

Research Planning Protocol

Before executing the domain-specific steps below, you MUST:

1. State the research question — What specific question is this analysis/paradigm addressing?
2. Justify the method choice — Why is this approach appropriate? What alternatives were considered?
3. Declare expected outcomes — What results would support vs. refute the hypothesis?
4. Note assumptions and limitations — What does this method assume? Where could it mislead?
5. Present the plan to the user and WAIT for confirmation before proceeding.

For detailed methodology guidance, see the research-literacy skill.

⚠️ Verification Notice

This skill was generated by AI from academic literature. All parameters, thresholds, and citations require independent verification before use in research. If you find errors, please open an issue.

Functional vs. Effective Connectivity

This is the most fundamental distinction in brain connectivity analysis (Friston, 2011):

Property	Functional Connectivity	Effective Connectivity
Definition	Statistical dependency between time series	Directed causal influence of one region on another
Directionality	Undirected	Directed
Causality	Cannot infer causality	Attempts to infer causal structure
Model requirement	Model-free (correlations)	Model-based (requires explicit neural model)
Hypothesis type	Exploratory or confirmatory	Strictly confirmatory
Primary methods	Correlation, partial correlation, ICA	DCM, PPI, structural equation modeling
Source	Friston, 2011	Friston, 2011; Friston et al., 2003

Domain warning: Functional connectivity (correlation) does not imply direct anatomical or causal connection. Two regions can show high functional connectivity because they share a common input, not because they directly influence each other (Friston, 2011).

Method Selection Decision Tree

What is your connectivity question?
 |
 +-- "Do regions A and B covary in activity?"
 | --> Functional connectivity (correlation, partial correlation)
 |
 +-- "Does the coupling between A and B change with task context?"
 | --> PPI (Friston et al., 1997; O'Reilly et al., 2012)
 |
 +-- "Does region A causally influence region B, and does this
 | change with experimental manipulation?"
 | --> DCM (Friston et al., 2003)
 | Requires: strong prior hypotheses, limited model space
 |
 +-- "What is the network topology (hubs, modules, efficiency)?"
 | --> Graph theory (Bullmore & Sporns, 2009)
 |
 +-- "Does activity in A temporally precede and predict B?"
 --> Granger causality (with STRONG caveats for fMRI;
 see Granger causality section below)

Functional Connectivity Methods

Seed-Based Correlation

1. Extract mean time series from a seed ROI
2. Compute Pearson correlation with all other voxels (or ROIs)
3. Apply Fisher z-transformation: z = 0.5 * ln((1+r)/(1-r)) before group statistics (Fisher, 1921)
4. Enter z-maps into second-level group analysis

Critical preprocessing:

• Apply stringent motion correction: FD threshold < 0.2 mm for scrubbing or censoring (Power et al., 2014)
• Band-pass filter to 0.01-0.1 Hz for resting-state (Biswal et al., 1995; but see Niazy et al., 2011 for caveats)
• Regress out motion parameters (24-parameter model), WM/CSF signals (aCompCor; Behzadi et al., 2007)

Partial Correlation

Partial correlation between regions A and B controls for shared variance with all other regions in the model. This reduces the influence of common inputs but requires careful regularization when the number of regions is large relative to the number of time points (Smith et al., 2011).

• Use regularized partial correlation (e.g., L1-penalized precision matrix) when the number of ROIs exceeds ~20% of the number of time points (Varoquaux et al., 2010)

Independent Component Analysis (ICA)

ICA decomposes the whole-brain fMRI signal into spatially independent components, each representing a network (Beckmann & Smith, 2004).

• Model order (number of components): 20-25 for major networks; 70-100 for fine-grained parcellation (Smith et al., 2009)
• Group ICA: Use temporal concatenation or dual regression (Beckmann et al., 2009; Nickerson et al., 2017)
• Artifact identification: Classify components as signal or noise based on spatial pattern, power spectrum, and temporal properties (Griffanti et al., 2017)

Psychophysiological Interactions (PPI)

PPI tests whether the functional coupling between a seed region and other brain areas changes as a function of psychological context (e.g., task condition; Friston et al., 1997).

PPI Model Specification

The PPI GLM includes three regressors:

1. Physiological regressor: Deconvolved time series from the seed region (the neural signal estimate)
2. Psychological regressor: The task regressor (e.g., condition A vs. condition B)
3. Interaction term: Element-wise product of the physiological and psychological regressors, reconvolved with the HRF

The interaction term is the regressor of interest. A significant PPI effect means that functional coupling with the seed region differs between task conditions (O'Reilly et al., 2012).

Generalized PPI (gPPI)

Standard PPI tests one psychological contrast at a time. Generalized PPI (gPPI) includes all task conditions simultaneously (McLaren et al., 2012):

• Create separate PPI terms for each condition
• Include all main-effect task regressors and the seed time series
• More sensitive than standard PPI because it properly accounts for all conditions
• Recommended over standard PPI for designs with more than two conditions (McLaren et al., 2012)

PPI Practical Considerations

Parameter	Recommendation	Source
Seed ROI definition	Functional (from activation map) or anatomical atlas; 6-10 mm sphere typical	O'Reilly et al., 2012
Deconvolution	Required for interaction term (SPM default); extract neural signal before computing interaction	Gitelman et al., 2003
Minimum events per condition	20+ per condition for stable PPI estimates	O'Reilly et al., 2012
Multiple seed regions	Run separate PPI analyses per seed, then correct for multiple comparisons	O'Reilly et al., 2012

Dynamic Causal Modeling (DCM)

DCM models the causal architecture of brain regions using a biophysical generative model of neural dynamics and hemodynamic coupling (Friston et al., 2003).

DCM Model Specification

A DCM is defined by three matrices:

Matrix	Function	Interpretation
A (intrinsic)	Fixed connections between regions (always on)	Baseline coupling strength
B (modulatory)	Condition-dependent modulation of connections	How task context changes coupling (the key experimental question)
C (driving input)	Which regions receive direct task input	Where external stimuli enter the network

DCM Requirements and Constraints

Requirement	Guideline	Source
Number of regions	3-8 regions maximum	Stephan et al., 2010
Prior hypotheses	Strong prior hypotheses about network architecture required	Stephan et al., 2010
Model space size	Keep total models < 20-30 for reliable BMS	Stephan et al., 2009
Task design	Event-related or block designs with clear experimental manipulation	Friston et al., 2003
Time series extraction	From first eigenvariate of activated voxels within ROI	Stephan et al., 2010
Data quality	Strong task activation in all modeled regions	Stephan et al., 2010

Bayesian Model Selection (BMS)

After estimating all candidate models, use BMS to identify the winning model (Stephan et al., 2009):

• Fixed-effects BMS (FFX): Assumes all subjects have the same model. Use when sample is homogeneous
• Random-effects BMS (RFX): Allows different subjects to have different optimal models. Use for heterogeneous populations (Stephan et al., 2009)
• Family-level inference: Group models into families sharing a feature (e.g., all models with a particular connection), then compare families. More robust than individual model comparison (Penny et al., 2010)
• Report exceedance probability (probability that a model/family is more likely than all others) and protected exceedance probability (corrected for chance; Rigoux et al., 2014)

DCM Pitfalls

• Too many models: Exhaustive model comparison with > 30 models leads to unreliable BMS (Stephan et al., 2010)
• No activation in modeled regions: DCM requires that included regions show significant task-related activation. Including silent regions produces unreliable estimates
• Confusing DCM with Granger causality: DCM models neural dynamics, not temporal precedence in BOLD signals

Granger Causality

Granger causality tests whether past values of time series X improve prediction of time series Y beyond Y's own past (Granger, 1969).

Severe Limitations for fMRI

Limitation	Explanation	Source
Hemodynamic confound	The HRF varies across brain regions by 1-2 seconds. A region with a faster HRF will appear to "Granger-cause" a region with a slower HRF, regardless of true neural timing	David et al., 2008; Seth et al., 2013
Low temporal resolution	fMRI TR (0.5-3 seconds) is far slower than neural dynamics (milliseconds), aliasing true causal structure	Seth et al., 2013
Downsampling artifacts	Subsampling a continuous process can reverse the apparent causal direction	Seth et al., 2013

Domain warning: Granger causality applied to fMRI BOLD signals is widely considered unreliable for inferring neural causal direction due to hemodynamic variability (David et al., 2008; Seth et al., 2013). If causal inference is needed, use DCM (which explicitly models the hemodynamic delay) or consider EEG/MEG (which has millisecond temporal resolution).

Graph Theory for Brain Networks

Graph theory characterizes the topological organization of brain networks (Bullmore & Sporns, 2009).

Node Definition

Method	Description	Example Atlases	Source
Anatomical parcellation	Predefined atlas regions	AAL (116 regions), Harvard-Oxford	Tzourio-Mazoyer et al., 2002
Functional parcellation	Data-driven boundaries	Schaefer (100-1000 parcels), Gordon (333 parcels)	Schaefer et al., 2018; Gordon et al., 2016
Voxel-level	Each voxel is a node	~100,000 nodes	Computationally expensive; rarely used for full graph metrics

Recommendation: Use functional parcellation (Schaefer or Gordon atlases) for most analyses. Functional parcels better respect the true boundaries of functional regions than anatomical atlases (Schaefer et al., 2018).

Edge Definition

Method	Description	Threshold Approach	Source
Correlation	Pearson r between time series	Proportional (top 10-20% of connections) or absolute (r > 0.2-0.3)	Bullmore & Sporns, 2009
Partial correlation	Controls for indirect connections	Same thresholding options	Varoquaux et al., 2010
Coherence	Frequency-domain coupling	Magnitude squared coherence > threshold	Sun et al., 2004

Domain warning: Thresholding strategy dramatically affects graph metrics. Always report results across a range of thresholds or use proportional thresholding to control for differences in overall connectivity strength across subjects (van den Heuvel et al., 2017).

Key Graph Metrics

Metric	Meaning	Normalization	Source
Clustering coefficient	Proportion of a node's neighbors that are also connected to each other	Normalize against random networks (C/C_random)	Watts & Strogatz, 1998
Characteristic path length	Average shortest path between all node pairs	Normalize against random networks (L/L_random)	Watts & Strogatz, 1998
Small-worldness	sigma = (C/C_random) / (L/L_random); sigma > 1 indicates small-world	N/A (already normalized)	Watts & Strogatz, 1998; Humphries & Gurney, 2008
Modularity (Q)	Strength of community structure; Q > 0.3 typically indicates strong modular organization	Compare against null distribution	Newman, 2006
Hub measures	Degree centrality, betweenness centrality, participation coefficient	Z-score within network	Bullmore & Sporns, 2009
Global efficiency	Inverse of mean shortest path length	Normalize against random networks	Latora & Marchiori, 2001

Normalization requirement: Raw graph metrics are meaningless without comparison to null models. Always normalize against random networks (preserving degree distribution) or lattice networks (Watts & Strogatz, 1998; Rubinov & Sporns, 2010). Generate at least 1,000 random networks for stable null distributions.

Common Pitfalls

1. Confusing functional connectivity with effective connectivity: Correlation between two regions does not imply direct or causal connection. Two regions may correlate because they receive common input from a third region (Friston, 2011)
2. Motion artifacts in connectivity: Head motion creates spurious short-distance positive correlations and spurious long-distance negative correlations, mimicking real connectivity patterns (Power et al., 2012). Use stringent motion thresholds (FD < 0.2 mm; Power et al., 2014) and aggressive confound regression
3. Not Fisher z-transforming correlations: Pearson r values are bounded and non-normally distributed. Always apply Fisher z-transformation before parametric group statistics (Fisher, 1921)
4. Arbitrary graph thresholds: Reporting graph metrics at a single threshold without sensitivity analysis across thresholds can produce unreliable or threshold-dependent conclusions (van den Heuvel et al., 2017)
5. Too many DCM models: Exhaustive model comparison across > 30 models leads to unreliable Bayesian model selection. Constrain the model space based on prior hypotheses (Stephan et al., 2010)
6. Using Granger causality with fMRI: Regional HRF variability can reverse apparent causal direction in BOLD signals (David et al., 2008; Seth et al., 2013)
7. Confounding connectivity with coactivation: Two regions that are both activated by a task may show correlation due to shared task-driven variance, not intrinsic neural coupling. Regress out task effects before computing resting-state-style connectivity on task data (Cole et al., 2019)
8. Ignoring global signal effects: Global signal regression introduces artifactual anticorrelations. If using it, acknowledge this limitation (Murphy & Fox, 2017)

Minimum Reporting Checklist

• Connectivity type (functional, effective, or graph-theoretic) and justification
• ROI/node definition method, atlas used, number of regions
• Time series extraction method (mean, first eigenvariate, PCA)
• Preprocessing for connectivity (band-pass filter frequencies, confound model, motion threshold)
• Edge definition (correlation type, thresholding method and values)
• For PPI: seed region definition, deconvolution method, conditions in PPI model
• For DCM: model space (A, B, C matrices for all models), BMS method (FFX/RFX), model evidence
• For graph theory: normalization method, number of null networks, range of thresholds tested
• Fisher z-transformation applied (yes/no)
• Motion exclusion criteria and mean FD of included subjects
• Software package and version

References

• Beckmann, C. F., & Smith, S. M. (2004). Probabilistic independent component analysis for functional magnetic resonance imaging. IEEE Transactions on Medical Imaging, 23(2), 137-152.
• Beckmann, C. F., Mackay, C. E., Filippini, N., & Smith, S. M. (2009). Group comparison of resting-state fMRI data using multi-subject ICA and dual regression. NeuroImage, 47(S1), S148.
• Behzadi, Y., Restom, K., Liau, J., & Liu, T. T. (2007). A component based noise correction method (CompCor) for BOLD and perfusion based fMRI. NeuroImage, 37(1), 90-101.
• Biswal, B., Yetkin, F. Z., Haughton, V. M., & Hyde, J. S. (1995). Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magnetic Resonance in Medicine, 34(4), 537-541.
• Bullmore, E., & Sporns, O. (2009). Complex brain networks: Graph theoretical analysis of structural and functional systems. Nature Reviews Neuroscience, 10(3), 186-198.
• Cole, M. W., Ito, T., Bassett, D. S., & Schultz, D. H. (2019). Activity flow over resting-state networks shapes cognitive task activations. Nature Neuroscience, 19, 1718-1726.
• David, O., Guillemain, I., Saillet, S., et al. (2008). Identifying neural drivers with functional MRI: An electrophysiological validation. PLoS Biology, 6(12), e315.
• Fisher, R. A. (1921). On the "probable error" of a coefficient of correlation deduced from a small sample. Metron, 1, 3-32.
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• Friston, K. J., Buechel, C., Fink, G. R., et al. (1997). Psychophysiological and modulatory interactions in neuroimaging. NeuroImage, 6(3), 218-229.
• Friston, K. J., Harrison, L., & Penny, W. (2003). Dynamic causal modelling. NeuroImage, 19(4), 1273-1302.
• Gitelman, D. R., Penny, W. D., Ashburner, J., & Friston, K. J. (2003). Modeling regional and psychophysiologic interactions in fMRI: The importance of hemodynamic deconvolution. NeuroImage, 19(1), 200-207.
• Gordon, E. M., Laumann, T. O., Adeyemo, B., et al. (2016). Generation and evaluation of a cortical area parcellation from resting-state correlations. Cerebral Cortex, 26(1), 288-303.
• Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438.
• Griffanti, L., Douaud, G., Bijsterbosch, J., et al. (2017). Hand classification of fMRI ICA noise components. NeuroImage, 154, 188-205.
• Humphries, M. D., & Gurney, K. (2008). Network "small-world-ness": A quantitative method for determining canonical network equivalence. PLoS ONE, 3(4), e0002051.
• Latora, V., & Marchiori, M. (2001). Efficient behavior of small-world networks. Physical Review Letters, 87(19), 198701.
• McLaren, D. G., Ries, M. L., Xu, G., & Johnson, S. C. (2012). A generalized form of context-dependent psychophysiological interactions (gPPI). NeuroImage, 61(4), 1277-1286.
• Murphy, K., & Fox, M. D. (2017). Towards a consensus regarding global signal regression for resting state functional connectivity MRI. NeuroImage, 154, 169-173.
• Newman, M. E. J. (2006). Modularity and community structure in networks. PNAS, 103(23), 8577-8582.
• Nickerson, L. D., Smith, S. M., Ongur, D., & Beckmann, C. F. (2017). Using dual regression to investigate network shape and amplitude in functional connectivity analyses. Frontiers in Neuroscience, 11, 115.
• Niazy, R. K., Xie, J., Miller, K., Beckmann, C. F., & Smith, S. M. (2011). Spectral characteristics of resting state networks. Progress in Brain Research, 193, 259-276.
• O'Reilly, J. X., Woolrich, M. W., Behrens, T. E. J., et al. (2012). Tools of the trade: Psychophysiological interactions and functional connectivity. Social Cognitive and Affective Neuroscience, 7(5), 604-609.
• Penny, W. D., Stephan, K. E., Daunizeau, J., et al. (2010). Comparing families of dynamic causal models. PLoS Computational Biology, 6(3), e1000709.
• Power, J. D., Barnes, K. A., Snyder, A. Z., et al. (2012). Spurious but systematic correlations in functional connectivity MRI networks arise from subject motion. NeuroImage, 59(3), 2142-2154.
• Power, J. D., Mitra, A., Laumann, T. O., et al. (2014). Methods to detect, characterize, and remove motion artifact in resting state fMRI. NeuroImage, 84, 320-341.
• Rigoux, L., Stephan, K. E., Friston, K. J., & Daunizeau, J. (2014). Bayesian model selection for group studies revisited. NeuroImage, 84, 971-985.
• Rubinov, M., & Sporns, O. (2010). Complex network measures of brain connectivity: Uses and interpretations. NeuroImage, 52(3), 1059-1069.
• Schaefer, A., Kong, R., Gordon, E. M., et al. (2018). Local-global parcellation of the human cerebral cortex from intrinsic functional connectivity MRI. Cerebral Cortex, 28(9), 3095-3114.
• Seth, A. K., Barrett, A. B., & Barnett, L. (2015). Granger causality analysis in neuroscience and neuroimaging. Journal of Neuroscience, 35(8), 3293-3297.
• Smith, S. M., Fox, P. T., Miller, K. L., et al. (2009). Correspondence of the brain's functional architecture during activation and rest. PNAS, 106(31), 13040-13045.
• Smith, S. M., Miller, K. L., Salimi-Khorshidi, G., et al. (2011). Network modelling methods for FMRI. NeuroImage, 54(2), 875-891.
• Stephan, K. E., Penny, W. D., Daunizeau, J., et al. (2009). Bayesian model selection for group studies. NeuroImage, 46(4), 1004-1017.
• Stephan, K. E., Penny, W. D., Moran, R. J., et al. (2010). Ten simple rules for dynamic causal modelling. NeuroImage, 49(4), 3099-3109.
• Sun, F. T., Miller, L. M., & D'Esposito, M. (2004). Measuring interregional functional connectivity using coherence and partial coherence analyses of fMRI data. NeuroImage, 21(2), 647-658.
• Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., et al. (2002). Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage, 15(1), 273-289.
• van den Heuvel, M. P., de Lange, S. C., Zalesky, A., et al. (2017). Proportional thresholding in resting-state fMRI functional connectivity networks and consequences for patient-control connectome studies. NeuroImage, 159, 437-449.
• Varoquaux, G., Gramfort, A., Poline, J. B., & Thirion, B. (2010). Brain covariance selection: Better individual functional connectivity models using population prior. NIPS, 2334-2342.
• Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of "small-world" networks. Nature, 393(6684), 440-442.

See references/ for detailed method implementation guides and parameter lookup tables.