As to describe different mental content is also

As described above, univariate analyses carry some limitations that multivariate analysis is able to overcome. One of the most important MPVA findings is that representations are not restricted to specific areas and they are characterized by idiosyncratic patterns related to distinct tasks (or stimuli). However, in order to distinguish and to describe different mental content is also important to consider when and how neurons interact with each other (Vaadia et al., 1995). Neural activity, and by extension neural codes, are constrained by connectivity. Nowadays, it is clear that brain regions do not work in isolation, and information processing depends on continuous local and long-range interactions. The most common approach to investigate how specific neurons communicate with each other over time is functional connectivity (FC). Generally, this term refers to the temporal covariance between distinct brain regions activity, which is assumed to be driven by their interaction. Traditional application of functional connectivity involves first the selection of “seed” regions of interest, based on their activity in specific tasks or coarse anatomical parcellation of the brain, and then the analysis of correlations between these regions and other voxels. This approach has provided many insights into the neural architecture, and identified several neural networks at rest or enabled during specific task. Still, it has some limitations. First, seeds are often defined on the basis of different averaged activation, and this procedure has the same disadvantages of univariate analysis, that is to assume that regions with greater activation (or activation differences) are most interactive or that their interactions are most informative. But, voxels activation may differ between stimuli (or from baseline) in the absence of differences in the averaged time-locked amplitude. Some MVPA studies tried to address this issue by classifying patterns of correlations among multiple regions. Anyway, regardless of which method is used to analyze data (univariate or multivariate), seed-based functional connectivity is affected by the small number of regions selected (“seeds”) with respect to the total number of voxels, resulting in loss of information. Doing so, only a small subset of possible interactions is considered. One might wonder why this method is used and why pairwise voxels analysis are not the most common way to compute temporal covariance. Despite its limitations, seed-based analysis is widely used because it allows to avoid statistical challenges related to big data and to test specific models with greater power. Comparing every voxel with one another is computationally demanding (50.000 voxels mean 1.249.975.000 unique voxel pairs to be tested). Notwithstanding, recent advances in computer engineering opened up new possibilities. One innovative method that takes into account the full set of voxels is the Full Correlation Matrix Analysis (FCMA) (Wang et al., 2015). To surmount the seed-based limitations, FCMA performs unbiased multivariate analysis of the whole-brain. It uses matrices made out of temporal correlations in BOLD activity of every voxel with every other voxel, separated for epochs of interest. These matrices represent the input of classifier.  Instead of working with activity patterns, the processing units are correlation patterns. Thus, the classifier can now determine which correlations predict conditions. Therefore, it allows to detect regions with differential interaction patterns as a function of experimental task. Obviously, the main problem is the huge amount of data to analyze. FCMA exploits flexible parallelization and provided algorithm optimization that speed up the computational processing. Thanks to this method is possible to obtain new findings in brain connectivity. For example, in the same paper where they present FCMA, Wang et al. (2015) used it with a face/scene dataset. Results revealed the involvement of mPFC and precuneus in object category perception, and suggested the role of mPFC in modulating face processing (but not scene) apparent in local and long-range correlations. 
Another issue of functional connectivity analysis is related to the fact that temporal covariance between brain regions, locked to the processing of external stimuli, is caused by different sources of variation. The BOLD signal can be divided in stimulus-induced signal, intrinsic neural signal (fluctuations not related to the processing of external stimuli) and non-neuronal artifacts (such as heartbeat or breathing). To some extent, standard analysis can differentiate between these sources. As long as physiological changes are uncorrelated with the design, they can be controlled by comparing two or more experimental conditions. Also, stimulus-induced signal can be regressed out providing a measure of intrinsic neural signal (“background connectivity”; Norman-Haignere et al.,2012). Problems arise with stimulus-induced response. For example, Simony et al. (2015) found that stimulus induced covariance detected with standard FC analysis are biased by intrinsic signals. Along with that they proposed a new statistical approach to better address connectivity patterns elicited during task, named inter-subject functional connectivity (ISFC). In ISFC, regional covariance is calculated across participants (region A/participant 1 with region B/participant 2). As a result, intrinsic neural responses and non-neuronal artifacts are ruled out since they vary across participants randomly and never align. The resulting covariance values are low and not statistically significant. At the same time, neural activity covariance locked to stimuli is shared across participants and it can be isolated. They tested this model to probe how the Default Mode Network changes when subjects listen to an auditory narrative and different scrambled versions of the same. Results show that with FC analysis there is no difference in the DMN configuration with respect to the narrative version. Whereas, ISFC detected distinct network configurations changing together with conditions. 

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