Connectivity in resting-state fMRI can be evaluated through a variety of different methods. These include methods for static functional connectivity, such as seed-correlation, spatial independent component analysis, and graph theoretical approaches. In addition, dynamic functional connectivity can be assessed using methods such as sliding window correlation, time-frequency analysis, co-activation patterns and temporal independence component analysis.
Seed-based Correlation
In seed-based correlation, connectivity is defined from a reference waveform derived from the time-series data in some “seed” region. Once this reference is defined, a voxel-wise correlation between the reference and the time-course for every voxel in the image is performed, to get correlation maps, which are subsequently thresholded at some significance value. Voxels surviving the thresholding define the connectivity map for that seed.
Seeds can be derived from single voxels (1), or regions of interest (ROI)(2), where in the latter case the reference waveform is typically the average time-course across the ROI. The location of these seeds are often chosen a priori based on structural (2) or functional information (3), or are defined from task-based fMRI experiments (1). To get connectivity information about more than one system, multiple distinct seeds need to be used in the correlation analysis.
Generally speaking, seed-based correlation is equivalent to a general linear model (GLM) analysis on task-based fMRI data (4), where a seed-derived time-course takes the place of the GLM model regressor, and the correlation coefficient corresponds to the GLM regression coefficient.
Spatial ICA
Spatial independent component analysis (s-ICA) is quite distinct from seed-based correlation, in that s-ICA tries to solve the blind source separation problem (5) by decomposing the space-time data into a linear mixture of spatial “sources” (6,7), each with an associated time-course. Here, the spatial sources can be represented as coefficient or statistical parametric maps, and are analogous to the correlation maps derived from seed-correlation.
While the data model in s-ICA is linear, just like the seed-correlation or GLM models, in this case both the spatial maps and the connectivity time-courses are unknown, and the solution to both sets of unknowns is defined by choosing the decomposition that maximizes the statistical independence between the different spatial sources. Two of the most popular choices in fMRI are the mutual information-based infomax principle (8), or maximizing non-Gaussianity via negentropy (9). Interestingly, it has been suggested that these s-ICA algorithms used in fMRI are actually more selective for spatial sparsity, rather than statistical independence (10).
Unlike seed-correlation, s-ICA estimates the connectivity maps from multiple systems simultaneously. However, one input that is required is the dimensionality, or number of sources, and while this is at most the number of time-points in the data, it is typically much less. The dimensionality can be chosen a priori (6), or by maximizing Bayesian model evidence or using the Bayesian information criterion (7).
Graph Theory
Broadly speaking, if seed-correlation and s-ICA are considered voxel-based linear models, graph theoretical approaches are based on more explicit network models that describe the data as a collection of spatial nodes, and edges that reflect the connectivity between nodes (11). Typically, the nodes are defined through a parcellation, which is essentially a binning of the brain’s voxels into different parcels (nodes). Edges are formed by taking the representative time-course from each node and evaluating its connectivity with every other node in the network. Connectivity (edge strength) can be defined using full correlation (12), partial correlation (13), or one of many other connectivity metrics such as mutual information (14). Typically, the network is summarized using a symmetric network or association matrix, where each row/column corresponds to a node, and the entries in the matrix represent the edge strengths.
A number of different analysis procedures can be performed on the network matrices to identify various network features. This includes computing node degree (how many connections a node has), small-worldness (15), community detection through modularity maximization (16), the InfoMap algorithm (17), or hierarchical clustering (18).
The results of a network analysis can depend on an appropriate parcellation of the brain (19). Parcellations can be derived from prior information or structural boundaries, but are more commonly defined through data-driven approaches such as k-means (20) or spectral clustering (21). Network nodes can also be defined through ICA (22), although in this case the nodes are often not single, contiguous parcels.
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