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• W2124698428 abstract "•Spontaneous fluctuations in brain activity reflect functional brain networks.•We review rfMRI for mapping the functional connectome.•We review methods for functional connectomics network analysis.•We describe the WU–Minn Human Connectome Project.•We present exciting new analyses using the latest-released HCP data. Spontaneous fluctuations in activity in different parts of the brain can be used to study functional brain networks. We review the use of resting-state functional MRI (rfMRI) for the purpose of mapping the macroscopic functional connectome. After describing MRI acquisition and image-processing methods commonly used to generate data in a form amenable to connectomics network analysis, we discuss different approaches for estimating network structure from that data. Finally, we describe new possibilities resulting from the high-quality rfMRI data being generated by the Human Connectome Project and highlight some upcoming challenges in functional connectomics. Spontaneous fluctuations in activity in different parts of the brain can be used to study functional brain networks. We review the use of resting-state functional MRI (rfMRI) for the purpose of mapping the macroscopic functional connectome. After describing MRI acquisition and image-processing methods commonly used to generate data in a form amenable to connectomics network analysis, we discuss different approaches for estimating network structure from that data. Finally, we describe new possibilities resulting from the high-quality rfMRI data being generated by the Human Connectome Project and highlight some upcoming challenges in functional connectomics. rfMRI has been used to study spontaneous fluctuations in brain activity since it was first noted that the rfMRI time series from one part of the motor cortex were temporally correlated with other parts of the same functional network, even with the subject at rest [1Biswal B. et al.Functional connectivity in the motor cortex of resting human brain using echo-planar MRI.Magn. Reson. Med. 1995; 34: 537-541Crossref PubMed Scopus (6811) Google Scholar]. Many other large-scale networks of correlated temporal patterns in the ‘resting brain’ have subsequently been identified. These patterns can be distinguished from each other because, although each has a relatively consistent time course across its set of involved regions, the different networks have distinct time courses [2Beckmann C.F. et al.Investigations into resting-state connectivity using independent component analysis.Philos. Trans. R. Soc. Lond. B: Biol. Sci. 2005; 360: 1001-1013Crossref PubMed Scopus (2517) Google Scholar]. These ‘resting-state networks’ (RSNs) persist even during sleep and under anaesthesia [3Picchioni D. et al.Sleep and the functional connectome.Neuroimage. 2013; 80: 387-396Crossref PubMed Scopus (77) Google Scholar] and are consistent across subjects [4Yeo B.T. et al.The organization of the human cerebral cortex estimated by intrinsic functional connectivity.J. Neurophysiol. 2011; 106: 1125-1165Crossref PubMed Scopus (3728) Google Scholar] and, to some extent, across species [5Li L. et al.Mapping putative hubs in human, chimpanzee and rhesus macaque connectomes via diffusion tractography.Neuroimage. 2013; 80: 462-474Crossref PubMed Scopus (76) Google Scholar]. RSNs have also been investigated with other modalities such as magnetoencephalography (MEG) [6Brookes M.J. et al.Investigating the electrophysiological basis of resting state networks using magnetoencephalography.Proc. Natl. Acad. Sci. U.S.A. 2011; 108: 16783-16788Crossref PubMed Scopus (592) Google Scholar, 7de Pasquale F. et al.Temporal dynamics of spontaneous MEG activity in brain networks.Proc. Natl. Acad. Sci. U.S.A. 2010; 107: 6040-6045Crossref PubMed Scopus (497) Google Scholar], but most RSN research to date has used rfMRI. In addition to providing new information about the structure and function of the healthy brain, the study of RSNs has already been shown to have potential clinical value, providing rich and sensitive markers of disease [8Castellanos F.X. et al.Clinical applications of the functional connectome.Neuroimage. 2013; 80: 527-540Crossref PubMed Scopus (209) Google Scholar]. Although there has been concern that some patterns of spatially-extended spontaneous signals may be of non-neural physiological origin, these concerns are increasingly being addressed [9Murphy K. et al.Resting-state fMRI confounds and cleanup.Neuroimage. 2013; 80: 349-359Crossref PubMed Scopus (421) Google Scholar]. It is now generally accepted not only that RSNs do reflect networks of brain function [10Sadaghiani S. Kleinschmidt A. Functional interactions between intrinsic brain activity and behavior.Neuroimage. 2013; 80: 379-386Crossref PubMed Scopus (98) Google Scholar], but also that the extensive set of functional networks identified in the task fMRI literature (e.g., as encoded in the BrainMap meta-analysis database [11Laird A.R. et al.Networks of task co-activations.Neuroimage. 2013; 80: 505-514Crossref PubMed Scopus (119) Google Scholar]) can be found in rfMRI data [12Smith S.M. et al.Correspondence of the brain's functional architecture during activation and rest.Proc. Natl. Acad. Sci. U.S.A. 2009; 106: 13040-13045Crossref PubMed Scopus (3487) Google Scholar]. The biological significance of such a rich and continuously present set of spontaneous, correlated activities in the resting brain remains poorly understood. Presumably, the brain is continuously engaged in undirected cognitive activities (both conscious thought processes and subconscious activity such as learning/unlearning) and also responds to uncontrolled external stimuli. However, the high level of overall spontaneous activity measured in rfMRI and the correspondingly large energy expenditure [13Raichle M.E. The brain's dark energy.Sci. Am. 2010; 302: 44-49Crossref PubMed Scopus (109) Google Scholar] have been surprising to many. Linking rfMRI investigations of the macroscopic-scale functional connectome to other modalities should further our understanding of resting-state activity and functional connectomics. Other types of connectome-related information include:•macroscopic structural connectomics from diffusion MRI data [14Passingham R.E. What we can and cannot tell about the wiring of the human brain.Neuroimage. 2013; 80: 14-17Crossref PubMed Scopus (10) Google Scholar, 15Sotiropoulos S.N. et al.Advances in diffusion MRI acquisition and processing in the Human Connectome Project.Neuroimage. 2013; 80: 125-143Crossref PubMed Scopus (547) Google Scholar, 16Setsompop K. et al.Pushing the limits of in vivo diffusion MRI for the Human Connectome Project.Neuroimage. 2013; 80: 220-233Crossref PubMed Scopus (329) Google Scholar, 17McNab J.A. et al.The Human Connectome Project and beyond: initial applications of 300 mT/m gradients.Neuroimage. 2013; 80: 234-245Crossref PubMed Scopus (230) Google Scholar, 18O’Donnell L.J. et al.Fiber clustering versus the parcellation-based connectome.Neuroimage. 2013; 80: 283-289Crossref PubMed Scopus (66) Google Scholar, 19Mangin J.F. et al.Toward global tractography.Neuroimage. 2013; 80: 290-296Crossref PubMed Scopus (67) Google Scholar];•the ‘mesoscopic’ connectome of long-distance connections studied at the cellular level [20Kennedy H. et al.Why data coherence and quality is critical for understanding interareal cortical networks.Neuroimage. 2013; 80: 37-45Crossref PubMed Google Scholar, 21da Costa N.M. Martin K.A. Sparse reconstruction of brain circuits: or, how to survive without a microscopic connectome.Neuroimage. 2013; 80: 27-36Crossref PubMed Scopus (25) Google Scholar, 22Stephan K.E. The history of CoCoMac.Neuroimage. 2013; 80: 46-52Crossref PubMed Scopus (27) Google Scholar];•the ‘microscopic’ connectome of all neurons and synapses [23White J.G. et al.The structure of the nervous system of the nematode Caenorhabditis elegans.Philos. Trans. R. Soc. Lond. B: Biol. Sci. 1986; 314: 1-340Crossref PubMed Google Scholar];•electrophysiological measures [24Scholvinck M.L. et al.The contribution of electrophysiology to functional connectivity mapping.Neuroimage. 2013; 80: 297-306Crossref PubMed Scopus (66) Google Scholar, 25David O. et al.Probabilistic functional tractography of the human cortex.Neuroimage. 2013; 80: 307-317Crossref PubMed Scopus (55) Google Scholar, 26Larson-Prior L. et al.Adding dynamics to the Human Connectome Project with MEG.Neuroimage. 2013; 80: 190-201Crossref PubMed Scopus (114) Google Scholar];•ex vivo histological mapping [27Caspers S. et al.Microstructural grey matter parcellation and its relevance for connectome analyses.Neuroimage. 2013; 80: 18-26Crossref PubMed Scopus (30) Google Scholar];•covariance of anatomical measures such as cortical thickness [28Evans A.C. Networks of anatomical covariance.Neuroimage. 2013; 80: 489-504Crossref PubMed Scopus (252) Google Scholar];•task fMRI, behavioural measurements, and genotyping [10Sadaghiani S. Kleinschmidt A. Functional interactions between intrinsic brain activity and behavior.Neuroimage. 2013; 80: 379-386Crossref PubMed Scopus (98) Google Scholar, 11Laird A.R. et al.Networks of task co-activations.Neuroimage. 2013; 80: 505-514Crossref PubMed Scopus (119) Google Scholar, 29Barch D.M. et al.Function in the Human Connectome: task-fMRI and individual differences in behavior.Neuroimage. 2013; 80: 169-189Crossref PubMed Scopus (737) Google Scholar, 30Thompson P.M. et al.Genetics of the connectome.Neuroimage. 2013; 80: 475-488Crossref PubMed Scopus (120) Google Scholar]. Early rfMRI studies typically characterised functional connectivity via a small number of large-scale spatial maps [1Biswal B. et al.Functional connectivity in the motor cortex of resting human brain using echo-planar MRI.Magn. Reson. Med. 1995; 34: 537-541Crossref PubMed Scopus (6811) Google Scholar, 2Beckmann C.F. et al.Investigations into resting-state connectivity using independent component analysis.Philos. Trans. R. Soc. Lond. B: Biol. Sci. 2005; 360: 1001-1013Crossref PubMed Scopus (2517) Google Scholar]. By contrast, the nascent field of ‘connectomics’ [31Sporns O. The human connectome: origins and challenges.Neuroimage. 2013; 80: 53-61Crossref PubMed Scopus (238) Google Scholar] generally attempts to study brain connectivity in a different way, first identifying a number of network nodes (functionally distinct brain regions) and then estimating the functional connections (network edges) between these nodes (Figure 1). To generate nodes, parcellation of the brain is often conducted by clustering together neighbouring voxels (3D pixels) on the basis of similarity of their time series. This typically yields a large number of non-overlapping parcels, with a single contiguous group of voxels in each parcel or node, and is then generally referred to as a ‘hard parcellation’ [32Blumensath T. et al.Spatially constrained hierarchical parcellation of the brain with resting-state FMRI.Neuroimage. 2013; 76: 313-324Crossref PubMed Scopus (164) Google Scholar, 33de Reus M.A. van den Heuvel M.P. The parcellation-based connectome: limitations and extensions.Neuroimage. 2013; 80: 397-404Crossref PubMed Scopus (194) Google Scholar]. Another approach to generating nodes involves high-dimensional independent-component analysis (ICA) [34Beckmann C.F. Modelling with independent components.Neuroimage. 2012; 62: 891-901Crossref PubMed Scopus (156) Google Scholar]. Using ICA, each node is described by a spatial map of varying weights; each map may overlap with other nodes’ maps and may span more than one group of contiguously neighbouring points. Network edges (connections between nodes) are estimated by comparing the fMRI time series associated with the nodes (e.g., the average time series of all voxels in a parcel). In some approaches, the directionality of these connections is estimated in an attempt to infer the direction of information flow through the network (see detailed discussion and references in [35Smith S.M. The future of FMRI connectivity.Neuroimage. 2012; 62: 1257-1266Crossref PubMed Scopus (244) Google Scholar]). As a result, brain connectivity can be represented as a ‘parcellated connectome’, which can be visualized simply as an Nnodes × Nnodes network matrix or a graph (explicitly showing nodes and the strongest edges) or using more sophisticated visualization approaches that embed nodes and edges into spatial representations of the brain [36Margulies D.S. et al.Visualizing the human connectome.Neuroimage. 2013; 80: 445-461Crossref PubMed Scopus (78) Google Scholar]. fMRI data (both task based and resting state) is acquired as a series of volumetric images over time, with each image generally taking 2–3 s to acquire. rfMRI data is typically acquired for 5–15 min, with the subject asked to ‘lie still, think of nothing in particular, and not fall asleep’. The fMRI acquisition is tuned such that the image intensity reflects local blood flow and oxygenation changes resulting from variations in local neural activity [37Ogawa S. et al.Intrinsic signal changes accompanying sensory stimulation: functional brain mapping with magnetic resonance imaging.Proc. Natl. Acad. Sci. U.S.A. 1992; 89: 5951-5955Crossref PubMed Scopus (2802) Google Scholar]. To achieve this sensitivity, and to acquire the fMRI data rapidly, it is common to utilise echo planar imaging (EPI) [38Mansfield P. Multi-planar image formation using NMR spin echoes.J. Phys. C: Solid State Phys. 1977; 10: L55-L58Crossref Scopus (1327) Google Scholar], which acquires the data one 2D slice at a time. Standard acquisitions working at a magnetic field strength of 3 T can achieve a temporal resolution of 2–3 s with a spatial resolution of 3–5 mm. More recently, faster acquisitions have emerged. For example, multiband accelerated EPI acquires multiple slices simultaneously [39Moeller S. et al.Multiband multislice GE–EPI at 7 Tesla, with 16-fold acceleration using partial parallel imaging with application to high spatial and temporal whole-brain fMRI.Magn. Reson. Med. 2010; 63: 1144-1153Crossref PubMed Scopus (907) Google Scholar, 40Setsompop K. et al.Blipped-controlled aliasing in parallel imaging for simultaneous multislice echo planer imaging with reduced g-factor penalty.Magn. Reson. Med. 2012; 67: 1210-1224Crossref PubMed Scopus (818) Google Scholar]. Such approaches enable major improvements in spatial and/or temporal resolution; for example, acquiring data with 2 mm spatial resolution in less than 1 s. Higher temporal resolution of the fMRI data can improve overall statistical sensitivity and also increase the information content of the data (e.g., in terms of reflecting the richness of the neural dynamics) [41Feinberg D.A. et al.Multiplexed echo planar imaging for sub-second whole brain fMRI and fast diffusion imaging.PLoS ONE. 2010; 5: e15710Crossref PubMed Scopus (865) Google Scholar, 42Smith S.M. et al.Temporally-independent functional modes of spontaneous brain activity.Proc. Natl. Acad. Sci. U.S.A. 2012; 109: 3131-3136Crossref PubMed Scopus (545) Google Scholar], although the sluggish response of the brain's haemodynamics (to neural activity) will ultimately place a limit on the usefulness of further improvements in temporal resolution. A four-dimensional rfMRI dataset requires extensive preprocessing before resting-state network analyses can be conducted. The preprocessing reduces the effects of artefacts (such as subject head motion and non-neural physiological signals), spatially aligns the functional data to the subject's high-resolution structural scan, and may subsequently align the data into a ‘standard-space’ reference coordinate system; for example, based on a population-average brain image. A standard sequence of processing steps [43Glasser M.F. et al.The minimal preprocessing pipelines for the Human Connectome Project.Neuroimage. 2013; 80: 105-124Crossref PubMed Scopus (2089) Google Scholar, 44Smith S.M. et al.Resting-state fMRI in the Human Connectome Project.Neuroimage. 2013; 80: 144-168Crossref PubMed Scopus (801) Google Scholar] is as follows.•Realign each time point's image to a reference image, reducing the effects of subject head motion over the duration of the rfMRI acquisition.•Correct the data for MRI spatial distortions.•Remove non-brain parts of the image.•Estimate the alignment transformations between the rfMRI data and the same subject's high-resolution structural image and between the structural image and a population-average brain image.•Optionally, map the cortical data from the 3D voxel matrix (‘volume based’) onto the vertices of a cortical surface representation (‘surface based’), in which a surface mesh follows the intricate convolutions of the cortical sheet. This aids visualization and enables better intersubject alignment (see below).•Optionally, apply spatial smoothing to improve signal-to-noise ratio and ameliorate the effects of functional misalignments across subjects. In the best datasets and when using the most advanced methods for intersubject alignment, smoothing can be minimised. Unless smoothing is constrained to act within the cortical sheet, it will cause undesirable mixing of signal across tissue compartments and across sulcal banks between functionally distinct regions.•Apply filtering to remove the slowest temporal drifts in the data.•Remove other artefacts. This last stage – the removal of other artefacts in the data – includes a diversity of commonly used approaches. Effective artefact removal is particularly important for resting-state analyses, which rely fundamentally on correlations between different voxels’ time series, because these will be corrupted by artefacts that span multiple voxels. (By contrast, task fMRI has the advantage of fitting a prespecified temporal model, which provides greater robustness against artefactual influences.) Artefact clean up [9Murphy K. et al.Resting-state fMRI confounds and cleanup.Neuroimage. 2013; 80: 349-359Crossref PubMed Scopus (421) Google Scholar] can involve one or more of:•regression of confound time series out of the data; for example, those derived from∘average white matter and/or ventricle time series∘head motion parameters (to further remove residual motion-related artefacts)∘separately measured cardiac and breathing signals∘global-average time series (although many researchers consider this to be a blunt tool that makes the interpretation of the final correlations difficult [44Smith S.M. et al.Resting-state fMRI in the Human Connectome Project.Neuroimage. 2013; 80: 144-168Crossref PubMed Scopus (801) Google Scholar]);•removal of corrupted time points [45Power J.D. et al.Spurious but systematic correlations in functional connectivity MRI networks arise from subject motion.Neuroimage. 2011; 59: 2142-2154Crossref PubMed Scopus (4588) Google Scholar];•data-driven structured noise removal, using ICA with automated component classification to remove remaining artefacts [46De Martino F. et al.Classification of fMRI independent components using IC-fingerprints and support vector machine classifiers.Neuroimage. 2007; 34: 177-194Crossref PubMed Scopus (218) Google Scholar];•filtering out the highest temporal frequencies (this is commonly applied when more targeted artefact removal approaches are not available, because the balance between signal and noise is expected to be worst at the highest frequencies; related to this, it is widely presumed that resting-state signals of interest are fundamentally low frequency, but, as discussed below, there is increasing evidence that there is useful signal at relatively high frequencies [47Niazy R.K. et al.Spectral characteristics of resting state networks.Progress Brain Res. 2011; 193: 259-276Crossref PubMed Scopus (138) Google Scholar]). Once preprocessing is complete, the data is ready for some form of connectivity analysis. In early rfMRI studies, connectivity was often summarised by one (or a few) spatial maps spanning the whole brain. For example, in seed-based correlation (Figure 2), a single seed voxel or region of interest is selected, such as a 5-mm radius sphere centred in the precuneus. The average time course from this seed region is extracted and every other voxel's time series is correlated against it, creating a correlation-strength map spanning all of the brain. Such an approach contains fine spatial detail, but only informs about average correlation with the selected seed. More information is obtained by low-dimensional ICA decomposition, for example, reducing the data to ten to 30 independent spatial maps, each of which is analogous to a distinct seed-based correlation map. This therefore generates a richer description of multiple networks in the brain, but at the expense of no longer dictating in advance the regions with which the connectivity maps are related. In contrast to seed-based correlation and low-dimensional ICA, high-dimensional parcellation into many nodes (potentially hundreds) allows a richer analysis of the network connections; by shifting the emphasis from large-scale maps with fine spatial detail into a network description of nodes and edges, new information can be obtained. For example, whereas two large-scale networks might have some functional interaction (seen as non-zero correlation between their associated time series), a detailed nodes+edges network model may reveal which nodes (subparts of the large-scale networks) are responsible for the correlations seen between the larger-scale networks. Put another way, detailed network modelling facilitates analysis of both functional specialisation (investigating the functional connectivities of each node separately) and functional integration (investigating how nodes interact with each other and form communities of functionally related clusters of nodes). ‘Mapping the functional connectome’ may be regarded as taking a nodes+edges approach to connectivity modelling. To combine or compare connectomes across subjects, it is important to strive for ‘the same’ parcellation in each subject; comparisons between two network models are inherently flawed if they are derived from non-corresponding sets of nodes. One simple approach to this problem is to generate a group-level parcellation and then impose this parcellation onto each subject. If every subject has been transformed into the same space as part of the preprocessing, this is conceptually straightforward. In reality, accurate alignment of functionally corresponding cortical parcels is an exceedingly challenging problem, largely owing to individual variability of cortical folding patterns along with variability of functional parcel locations relative to these folds (see below). Once a parcellation has been applied (e.g., as a set of parcel masks) to a given subject's dataset, each parcel can then be assigned a representative time series based on that subject's rfMRI data, for example, by averaging the time series from all voxels within a parcel. From the resulting Ntimepoints × Nnodes data matrix, one can then compute the subject-specific Nnodes × Nnodes parcellated connectome matrix; for example, by correlating each time series with every other. However, correlation is just one approach (albeit the simplest and most commonly used) for inferring the network edges (elements in the network matrix). The strengths and weaknesses of more sophisticated approaches are considered in the next section. We now discuss in more detail the estimation of network edges, given a set of nodes’ time series. The simplest method, correlation between the time courses of any two brain regions, allows one to infer whether the regions are functionally connected, although many factors other than the direct anatomical node-to-node connection ‘true strength’ can affect correlation coefficients, including variations in signal amplitude and noise level [48Friston K.J. Functional and effective connectivity: a review.Brain Connect. 2011; 1: 13-36Crossref PubMed Scopus (1866) Google Scholar]. Furthermore, correlation cannot reveal anything about causality or even whether connectivity is direct versus indirect [49Marrelec G. et al.Partial correlation for functional brain interactivity investigation in functional MRI.Neuroimage. 2006; 32: 228-237Crossref PubMed Scopus (328) Google Scholar]. A common implicit assumption – that correlation is unambiguously indicative of a direct connection – creates a major problem for network modelling (and graph theory applied to networks estimated from rfMRI) [35Smith S.M. The future of FMRI connectivity.Neuroimage. 2012; 62: 1257-1266Crossref PubMed Scopus (244) Google Scholar]. The distinction between simple correlation and trying to estimate the underlying, direct, causal connections (sometimes referred to as the distinction between functional and effective connectivity [50Friston K.J. functional and effective connectivity in neuroimaging: a synthesis.Hum. Brain Mapp. 1994; 2: 56-78Crossref Scopus (1670) Google Scholar]) is important for deciphering the underlying biological networks. For example, in a three-node network A→B→C, all three nodes’ time series will be correlated, so correlation will incorrectly estimate a fully-connected network (including an A–C connection). However, another simple estimation method, partial correlation, aims to more accurately estimate the direct connections (though not their directionalities). In the three-node network example, this works by taking each pair of time series in turn and regressing out the third from each of the two time series in question before estimating the correlation between the two. (For more than three nodes, all of the other Nnodes – 2 nodes are regressed out of the two under consideration.) In this case, regression of B out of A and C removes the correlation between A and C and hence the spurious third edge (A–C). A wide range of different network modelling approaches can be placed along a spectrum (Figure 3). This starts with neural-level brain simulations at one end [51Nakagawa T.T. et al.Bottom up modeling of the connectome: linking structure and function in the resting brain and their changes in aging.Neuroimage. 2013; 80: 318-329Crossref PubMed Scopus (56) Google Scholar], includes network modelling methods in the middle that can be applied to real rfMRI data (with full and partial correlation sitting at the simple extreme), and ends with abstract graph-theoretical network analyses that require the network to have already been estimated. Of the methods for connectivity modelling that have been applied to rfMRI data, at one extreme are complex models of effective connectivity with many parameters, each representing a biological or physical measure such as average neuronal activity and (separately) the haemodynamic response to neural activity; this model is ideally fit to data using probabilistic (e.g., Bayesian) methods. One such approach is dynamic causal modelling (DCM) [52Woolrich M.W. Stephan K.E. Biophysical network models and the human connectome.Neuroimage. 2013; 80: 330-338Crossref PubMed Scopus (54) Google Scholar]. Not only is the model complex, but so is the Bayesian inference method, which is computationally more sophisticated than simple ‘point estimate’ model fitting. Estimating quantitative, biologically meaningful parameters is clearly of great value if we want to find and interpret changes in functional networks, for example, as a result of disease. Moving towards the simpler end of the modelling spectrum, with methods such as structural equation modelling [53McIntosh A.R. Gonzales-Lima F. Structural equation modeling and its application to network analysis in functional brain imaging.Hum. Brain Mapp. 1994; 2: 2-22Crossref Scopus (692) Google Scholar], model parameters refer to statistical relationships between data variables (e.g., causations or correlations between node time series) as opposed to underlying biological or physical quantities. At the simplest extreme are mathematically straightforward methods such as correlation. The simpler methods are in general more robust (with respect to fitting the model to the data) and faster to compute. Related to this, and the fact that they have many fewer parameters to estimate, the simpler methods can handle a much larger number of network nodes than the more complex methods; they do not require the scope of possible network models to be preconstrained, making them computationally feasible for attempting network discovery. However, simpler methods provide descriptions of the data rather than being directly tied to underlying, more biologically interpretable network parameters. These considerations motivate a desire to work at the more complex, biophysically interpretable level, but they also restrict the practicality of the analyses that are feasible. For example, although DCM was originally developed for task data, it has recently been extended [54Friston K.J. et al.Network discovery with DCM.Neuroimage. 2011; 56: 1202-1221Crossref PubMed Scopus (204) Google Scholar] to allow modelling of resting-state data and to search across a wide range of possible network matrix models (rather than requiring the prespecification of just a few). However, this is currently practical (in terms of both computational expense and mathematical robustness) only for networks with a small number of nodes (<10). A major challenge for functional connectomics will be to enable application of biologically interpretable models using large numbers of nodes in a robust and practical way. Currently, if one wishes to conduct connectomics network modelling using a reasonably large number of nodes (50–500), one pragmatic compromise is to use partial correlation. The estimation of partial correlation effectively involves inverting the full correlation matrix, a process that is often quite unstable depending on the quality of the data and the number of original time points. Hence, improved estimation can often be achieved by ‘regularisi" @default.
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• W2124698428 title "Functional connectomics from resting-state fMRI" @default.
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