Network (voxel-level) measures
Network measures attempt to summarize properties of the entire voxel-to-voxel connectome (all functionals connections between every pair of voxels in the brain) into a series of reduced and interpretable measures at each individual voxel. These include measures that address properties specified a priori, and estimate how those properties are expressed in each individual subject, such as Intrinsic Connectivity (IC), Global Correlation (GCOR), and Local Correlation (LCOR), as well as data-driven measures that are first informed by group-level properties and then attempt to determine how those observed properties are expressed in each individual subject, such as Independent Component Analyses (group-ICA), Principal Component Analyses (group-PCA), and Multivariate Pattern Analyses (group-MVPA).
Intrinsic Connectivity (IC)
IC maps represent a measure of node centrality at each voxel, characterized by the strength of connectivity between a given voxel and the rest of the brain. IC is defined as the root mean square of correlation coefficients between each individual voxel and all of the voxels in the brain (Intrinsic Connectivity Contrast, Martuzzi et al. 2011)
where r is the map of voxel-to-voxel correlations between every pair of voxels, M is a pre-defined mask (by default covering the entire brain), and IC is the Intrinsic Connectivity map
Global Correlation (GCOR)
GCOR maps represents a measure of node centrality at each voxel, characterized by the strength and sign of connectivity between a given voxel and the rest of the brain. GCOR is defined as the average of correlation coefficients between each individual voxel and all of the voxels in the brain:
where r is the map of voxel-to-voxel correlations between every pair of voxels, M is a pre-defined mask (by default covering the entire brain), and GCOR is the Global Correlation map. The spatial average of a GCOR map represents the GCOR quality control measure (Saad et al. 2013) which can be used as a subject-level covariate characterizing brain-wide correlation properties
Local Correlation (LCOR)
LCOR maps represent a measure of local coherence at each voxel, characterized by the strength and sign of connectivity between a given voxel and the neighboring areas in the brain. LCOR is defined as the average of correlation coefficients between each individual voxel and a region of neighboring voxels (Integrated Local Correlation, Deshpande et al. 2009) :
where r is the map of voxel-to-voxel correlations between every pair of voxels, w is an isotropic Gaussian weighting function with size sigma characterizing the size of the local neighborhoods, and LCOR is the Local Correlation map
Multivariate Correlation (MCOR) (group-MVPA)
MCOR maps represent for each voxel the m most salient spatial features of the SBC maps seeded at this same voxel. MCOR maps are defined from a Singular Value Decomposition (SVD, Strang 2007), separately for each seed-voxel, of the patterns of seed-based correlations across all subjects:
where r is the map of voxel-to-voxel correlations between every pair of voxels for each subject n, Q is an orthogonal spatial basis characterizing the m most salient SBC spatial patterns over a pre-defined mask area M (by default covering the entire brain) for each seed voxel x, and MCOR are the m-th dimensional Multivariate Connectivity maps for each subject . MCOR maps can be used to perform Multivariate Pattern Analyses (Norman et al. 2006) evaluating differences between subjects in the entire patterns of seed-to-voxel connectivity
Independent Component Analyses (group-ICA)
ICA maps represent a measure of different networks expression and connectivity at each voxel. CONN's ICA implementation follows Calhoun's group-ICA methodology (Calhoun et al. 2001), with optional subject-level dimensionality reduction, concatenation across subjects, group-level Singular Value Decomposition for dimensionality reduction, a fastICA algorithm for group-level independent component definition (Hyvarinen 1999, with G1/tanh, G2/gauss, or G3/pow3 non-linear contrast function), and GICA1 or GICA3 for subject-level back-projection (see Calhoun et al. 2001 for method details)
Principal Component Analyses (group-PCA)
CONN's PCA implementation is identical to the above Calhoun's group-ICA methodology but without the ICA rotation/weighting step, so the spatial maps represent the group-level maximal-variance components instead
Notes on dimensionality reduction
All of the above properties are either directly or indirectly defined from r, the maps of voxel-to-voxel correlations between every pair of voxels for each subject and condition. It is often useful to represent these symmetric voxel-to-voxel correlation maps in terms of their orthogonal Singular Value Decomposition (SVD) components:
where r is the map of voxel-to-voxel correlations between every pair of voxels for one individual subject and condition, Q is an orthogonal spatial basis characterizing each of the m maximal-variance spatial components or eigenvectors of r, and sigma are the eigenvalues of r characterizing the variance associated with each of these components.
When using this representation, it is also possible to remove from consideration those components explaining minimal residual variance in the BOLD signal after all standard preprocessing and denoising steps, simply by using a value of m lower than the rank of the matrix r. This is often useful for computational simplicity, but also as an additional subject-level denoising strategy, as well as to minimize potential differences in effective degrees of freedom of the residual BOLD signal across subjects. This procedure is referred to as "subject-level dimensionality reduction", and in CONN it can be optionally applied to any of the above network measures. The default recommended value in CONN keeps the first 64 components to characterize the voxel-to-voxel correlation matrix separately for each individual subject and experimental condition (see Whitfield-Gabrieli and Nieto-Castanon 2012 for method details; see Calhoun et al. 2001 for subject-level dimensionality reduction in the context of group-level ICA)
Calhoun, V. D., Adali, T., Pearlson, G. D., & Pekar, J. J. (2001). A method for making group inferences from functional MRI data using independent component analysis. Human brain mapping, 14(3), 140-151
Deshpande, G., LaConte, S., Peltier, S., & Hu, X. (2009). Integrated local correlation: a new measure of local coherence in fMRI data. Human brain mapping, 30(1), 13-23
Hyvarinen, A. (1999). Fast and robust fixed-point algorithms for independent component analysis. IEEE transactions on Neural Networks, 10(3), 626-634
Martuzzi, R., Ramani, R., Qiu, M., Shen, X., Papademetris, X., & Constable, R. T. (2011). A whole-brain voxel based measure of intrinsic connectivity contrast reveals local changes in tissue connectivity with anesthetic without a priori assumptions on thresholds or regions of interest. Neuroimage, 58(4), 1044-1050
Norman, K. A., Polyn, S. M., Detre, G. J., & Haxby, J. V. (2006). Beyond mind-reading: multi-voxel pattern analysis of fMRI data. Trends in cognitive sciences, 10(9), 424-430
Saad, Z. S., Reynolds, R. C., Jo, H. J., Gotts, S. J., Chen, G., Martin, A., & Cox, R. W. (2013). Correcting brain-wide correlation differences in resting-state FMRI. Brain connectivity, 3(4), 339-352
Strang, G. (1993). Introduction to linear algebra (Vol. 3). Wellesley, MA: Wellesley-Cambridge Press
Whitfield-Gabrieli, S., & Nieto-Castanon, A. (2012). Conn: a functional connectivity toolbox for correlated and anticorrelated brain networks. Brain connectivity, 2(3), 125-141
How to compute network (voxel-level) measures in CONN
All CONN's network (voxel-level) 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 'Voxel-to-Voxel' connectivity measures. Select 'Create new first-level analysis' and give this analysis a name (e.g. LCOR), then in the 'Analysis type' field select the type of network measure you would like to compute (e.g. LocalCorrelation). All options there will be set by default to standard values appropriate to the chosen measure. Modify these options if needed and simply click 'Done' and 'Start' to compute the corresponding maps for each subject and condition (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 any network maps across all subjects and conditions using Matlab command syntax:
conn_batch( 'vvAnalysis.name', 'LCOR', 'vvAnalysis.measures', 'LocalCorrelation', 'vvAnalysis.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', ...
'vvAnalysis.name', 'LCOR', ...
'vvAnalysis.measures.names', 'LocalCorrelation', ...
'vvAnalysis.measures.kernelsupport', 25, ...