Connectivity measures may be used to test the alteration of brain connectivity in pathological occurrences. Resting state data in functional MRI (rsfMRI), as well as task-related designs, can be analysed with fcMRI. Different software for connectivity measures are freely available; however, the usual protocol to perform connectivity analyses comprises the following steps:
a) Functional data acquisition
Using the typical EPI MRI sequences, it is possible to collect data from experiments both with the resting-state conditions and with a task design.
b) Structural data acquisition.
To plot the functional results on the real brain anatomy of patient, anatomical MRI acquisition is performed for each subject. Also, this allows for the definition of the Grey Matter, White Matter and Cerebrospinal Fluid areas for the segmentation operation to perform noise corrections in the functional images.
c) ROI definition:
ROIs may be defined in different ways to achieve the best connections analysis model suitable for the aims of the study. It is possible to use text files with a list of the Montreal Neurological Institute (MNI) positions or a list of Talairach locations; also, on the web, there are several freely available tools for the conversion in these two References Systems (http://sprout022.sprout.yale.edu/mni2tal/mni2tal.html).
Voxels position is related to functional areas using a complete list of Brodmann areas. This fact allows for voxel-to-voxel analysis as well as “seed areas” to voxel, and ROI-to-ROI analysis of connectivity properties at the single subject level and the group level.
In all our research projects, functional connectivity toolbox Conn (www.nitrc.org/projects/conn) [19] was employed; CONN has implemented the CompCor algorithm for physiological and other noise sources reduction strategies. CONN allows for removal of movement, temporal covariates accounting, and a temporal filtering of BOLD signal oscillations. Further, Conn noise reduction strategy allows for the physiological interpretation of anticorrelations, for it does not rely on global signal regression.
In CONN software the usual fMRI preprocessing is performed: spatial preprocessing procedures include slice-timing correction, realignment, coregistration, normalisation, and spatial smoothing. In addition to these steps, the CONN software employs segmentation of Grey Matter, White Matter, and CSF areas to use during removal of temporal confounding factors. Conn spatial preprocessing is implemented by SPM software (Wellcome Department of Imaging Neuroscience, London, UK; www.fil.ion.ucl.ac.uk/spm). Both SPM and Conn run in the Matlab calculation environment (The MathWorks, Natick, Massachusetts). Regarding statistical parametric mapping, this was performed in the framework of General Linear Model (GLM) (Friston et al. 1995) as implemented by FSL (FMRIB Software Library v5.0) by the Analysis Group (FMRIB, Oxford, UK). Usual random effects procedures, as developed by Holmes and Friston [20], to describe multi-subject functional neuroimaging data for valid population inference.
To avoid confounders and limit the noise for the evaluation of the neural activity and connectivity as possible, a robust statistical analysis must address the study of noise sources in fMRI. The first step of this procedure is the denoising of the BOLD signal, aimed to define, explore, and remove possible confounders such as patient movement induced alterations. Nevertheless, it is also possible to assess the spectral contribution of all the frequencies fluctuations of the BOLD signal in both resting state, and task-driven experiments: data filtering by separating bands components allows for the contributions exploration of low or fast components of the signals.
Usually, in fcMRI, two levels of the analysis may be identified: the first level for within-subject analysis, and the second level for between-subjects analysis. Notably, the former level defines and explores functional connectivity of different kinds of sources for each subject. Successively, a second-level analysis is performed to study between-subjects contrasts of interest, hence to define population phenotypes. These two processes highlight some variables that may be defined as covariates and included in the GLM model.
As previously reported, BOLD signals from voxels and ROIs of interest can be processed in CONN software using several indices of connectivity. Connectivity measure is performed at the voxel-to-voxel level and, to discuss connectivity properties in connection with spatially segregated brain functions, a seed to voxel, and ROI to ROI analysis can be performed. Usually, brain areas of interest were spatially labelled as in Broadmann areas atlas (BA) to characterise the source regions for the extraction of the time series of interest. These areas are subsequently used as labels for targets in ROI-to-ROI analysis, and seed to voxel analysis. All Ddata presented in this paper focuses on the zero-lagged bivariate-correlation and linear measure of functional connectivity between two sources, x and y, defined as [19]:
Equation 1 Bivariate correlation
$$ r={\left({x}^t\cdot x\right)}^{\frac{1}{2}}\cdot b\cdot {\left({y}^t\cdot y\right)}^{-\frac{1}{2}} $$
where.
Equation 2 Bivariate regression
$$ b=\frac{x^t\cdot y}{x^t\cdot x} $$
This is the Voxel-Level Functional Connectivity MRI measurement derived from the Voxel-to-Voxel Connectivity Matrix r(x,y); in this project, the strength of the global connectivity pattern between each voxel and the rest of the brain with the Intrinsic connectivity contrast (ICC) [21] was characterised.
Equation 3 Intrinsic connectivity contrast index
$$ {C}_n(G)=\frac{1}{\left|G\right|-1}\cdot \left|{G}_n\right| $$
Successively, it is possible to use the “cost function” as a measure, at ROI and network level, of the links properties. In particular, for ROI-level tests:
Equation 4 Cost function of the n node graph G
$$ C(G)=\frac{1}{\left|G\right|}\cdot \sum \limits_{n\in G}{C}_n(G) $$
while, for network-level measures, we can define:
Equation 5 Cost at network level
$$ ICC=\frac{1}{\left|\varOmega \right|}\sum \limits_{y\in \varOmega }{\left|r\left(x,y\right)\right|}^2 $$
where Cn(G) represents the cost in graph G, and |G| represents the number of nodes in graph G [19, 22].
The word “cost” is used to define the weight property of the link, a way to determine the intensity of the link between nodes and all over the network (or net path). The weight of a path in a graph can be defined as the sum of the weights of the traversed edges.
Indices like the Betweenness Centrality, an indicator of the number of “shortest paths” for a specific node, can be used to describe some “community” properties of the nodes. A node with high betweenness centrality has a great importance in the network.
All these parameters can give us the numeric evaluation of the topological properties of the network realised by the ROIs of the brain connected by the function execution task [23].
A display of fcMRI can be achieved through several representations employing CONN toolbox for Matlab. It is possible to show the performed graph-theory analysis of the ROIs networks, characterising the topological properties of the brain networks related to the disease; the characterisation is obtained through graphics and pictures, as reported in the figures of the next paragraph.
This fact allows the researchers for several considerations about the areas involved and the functions performed by these regions. The definition of the network’s organisation is related to the “self-organisation” property of the brain.
Self-organization is one of the emerging properties of the brain networks that can be related to the mechanism activated by the brain trying to solve the inefficiency associated with the action of the diseases in the brain.
This is a significant contribution arising from the application of the complex networks theory to the brain behaviour, and it refers to the so-called Networks Medicine.