# Seed-Based Connectivity

## Seed-Based Connectivity measures

Seed-based connectivity metrics characterize the connectivity patterns with a pre-defined seed or ROI (Region of Interest). These metrics are often used when researchers are interested in one, or a few, individual regions and would like to analyze in detail the connectivity patterns between these areas and the rest of the brain. Perhaps the most common functional connectivity metric is seed-based connectivity maps (SBC), but there are also several variations aimed at studying potential connectivity paths (mSBC), estimating condition-specific connectivity measures (wSBC), or identifying task-related modulations in event-related designs (gPPI)

### Seed-Based Connectivity (SBC) maps

SBC maps represent the level of functional connectivity between a seed/ROI and every voxel or location in the brain. SBC maps are computed as the Fisher-transformed bivariate correlation coefficients between an ROI BOLD timeseries and each individual voxel BOLD timeseries:

where S is the BOLD timeseries at each voxel (for simplicity all timeseries are considered centered to zero mean), R is the average BOLD timeseries within an ROI, r is the spatial map of Pearson correlation coefficients, and Z is the SBC map of Fisher-transformed correlation coefficients for this ROI. The connectivity pattern with an individual seed (see example below for a Medial PreFrontal Cortex seed) often encompasses the same area, indirectly quantifying the level of homogeneity within this region, but also often several other distant areas, directly quantifying inter-regional connectivity strength (e.g. connectivity with other Default Mode Network areas such as PCC and LP in the example below)

### Multivariate Seed-Based Connectivity (mSBC) maps

Multivariate SBC maps are computed as semipartial correlation coefficients between an ROI BOLD timeseries and each individual voxel BOLD timeseries, after controlling for one or several other ROI BOLD timeseries:

where S is the BOLD timeseries at each voxel, R is the average BOLD timeseries within each ROI among a predefined set of ROIs, B is the map of multivariate regression coefficients for each ROI, estimated using an Ordinary Least Squares (OLS) solution to the above linear model, and Z is the mSBC map of Fisher-transformed semipartial correlation coefficients for each ROI

Semipartial or multivariate SBC maps are aimed at investigating potential connectivity paths. They represent the level of effective or direct connectivity between an individual seed/ROI and every voxel or location in the brain after discounting effects that may be mediated or accounted for by other seeds/ROIs (see in example below MPFC effective connectivity while controlling for other 31 network-based ROIs)

### Weighted Seed-Based Connectivity (wSBC) maps

Weighted SBC maps are used to characterize task- or condition- specific functional connectivity strength (i.e. functional connectivity during each task/condition). wSBC maps are computed using a weighted Least Squares (WLS) linear model with user-defined temporal weights identifying each individual experimental task/condition. In block- or event- related task designs, weights are defined as a condition-specific boxcar timeseries convolved with a canonical hemodynamic response function. In pure resting-state analyses, weights are defined to encompass entire runs or sessions (e.g. in a pre- vs. post- intervention design)

where S is the BOLD timeseries at each voxel , R is the average BOLD timeseries within an ROI, w is the temporal weighting function for each condition, computed as the rectified convolution of the task/condition boxcar timeseries h and a canonical hemodynamic response function f, B is the map of bivariate regression coefficients for each condition estimated using a Weighted Least Squares (WLS) solution to the above linear model, and Z is the wSBC map of Fisher-transformed bivariate correlation coefficients for each task/condition

Weighted SBC maps can be interpreted exactly in the same way as standard SBC maps, only restricted to the duration of one specific task or condition (wSBC are defined so that they are exactly equal to SBC maps when using constant weights encompassing the entire timeseries)

### Generalized Psycho-Physiological Interactions (gPPI) maps

gPPI measures represent the level of task-modulated effective connectivity between a seed/ROI and every voxel or location in the brain (i.e. changes in functional association strength covarying with the external or experimental factor). They are mainly aimed at investigating task-related modulation of functional connectivity patterns in the context of event-related designs. gPPI is computed using a separate multiple regression model for each target voxel BOLD timeseres. Each model includes as independent variables: a) all of the selected task effects convolved with a canonical hemodynamic response function (main psychological factor in PPI nomenclature); b) the seed ROI BOLD timeseries (main physiological factor in PPI nomenclature); and c) the interaction term specified as the product of (a) and (b) (PPI term). gPPI output is defined as the map of regression coefficients associated with the interaction term in these models

where S is the BOLD timeseries at each voxel (for simplicity all BOLD timeseries are considered orthogonal to task effects and centered to zero mean), h is the task/condition boxcar timeseries which is convolved with a canonical hemodynamic response function f, and gamma is the gPPI map of regression coefficients for each condition, estimated jointly with alpha and beta parameters using a least squares solution to the above linear model

## How to compute SBC maps in CONN

CONN's SBC measures can be computed using any of the following options:

### Option 1: using CONN's gui

If you have already imported and denoised your data in CONN (either through the GUI or batch commands) go to CONN's Analyses (1st-level) tab, and select 'Seed-to-Voxel' connectivity measures (optionally select 'Create/rename new first-level analysis' if defining multiple sets of first-level analyses). All options here will be set by default to compute SBC maps as described above, so simply click 'Done' and 'Start' to compute SBC maps for each subject, condition, and seed ROI (optionally change the 'local processing' option available in that window to 'distributed processing' if you want to parallelize this pipeline across multiple processors or nodes in an HPC cluster)

### Option 2: using CONN's batch commands

Similarly, if you have already imported and denoised your data in CONN (either through the GUI or batch commands) , you may compute standard SBC maps across all subjects, conditions, and seed ROIs, using Matlab command syntax:

conn_batch( 'Analysis.name', 'SBC', 'Analysis.done', true )

optionally adding to this command any desired alternative field name/value pairs (see doc conn_batch for additional details), for example:

conn_batch( 'filename', '/data/Cambridge/conn_Cambridge.mat', ...

'Analysis.name', 'mSBC', ...

'Analysis.type', 'seed-to-voxel', ...

'Analysis.measure', 'correlation (semipartial)', ...

'Analysis.sources', {'networks.DefaultMode'}, ...

'Analysis.weight', 'none', ...

'Analysis.done', true)