Connectivity Fingerprints: From Areal Descriptions to Abstract Spaces
Authors: Rogier B. Mars, Richard E. Passingham, Saad Jbabdi
Journal: Trends in Cognitive Sciences (2018)

The concept of the connectivity fingerprint was described 15 years ago to suggest a crucial relationship between the connections (functional integration) and function (functional segregation) of an area. The advent of neuroimaging now allows for this concept to be applied on a much larger scale, describing brain organization in terms of a connectivity space. Describing brain organization in this space is closer to its functional organization and can predict differences in functional activation and behaviour. By abstracting away into connectivity space one can compare brains across individuals and species. Comparing differences in the connectivity fingerprints of areas or subareal units in terms of gradients, one can investigate which dimension of connectivity space is relevant for understanding particular aspects of brain organization. Fifteen years ago, Passingham and colleagues proposed that brain areas can be described in terms of their unique pattern of input and output connections with the rest of the brain, and that these connections are a crucial determinant of their function. We explore how the advent of neuroimaging of connectivity has allowed us to test and extend this proposal. We show that describing the brain in terms of an abstract connectivity space, as opposed to physical locations of areas, provides a natural and powerful framework for thinking about brain function and its variation across the brains of individuals, populations, and species. Fifteen years ago, Passingham and colleagues proposed that brain areas can be described in terms of their unique pattern of input and output connections with the rest of the brain, and that these connections are a crucial determinant of their function. We explore how the advent of neuroimaging of connectivity has allowed us to test and extend this proposal. We show that describing the brain in terms of an abstract connectivity space, as opposed to physical locations of areas, provides a natural and powerful framework for thinking about brain function and its variation across the brains of individuals, populations, and species. Functional brain organization is often described in terms of the principles of segregation and integration [1Friston K.J. et al.Functional connectivity: the principal-component analysis of large (PET) data sets.J. Cereb. Blood Flow Metab. 1993; 13: 5-14Crossref PubMed Google Scholar]. Segregation means a focus on mapping unique brain areas (see Glossary) and ascribing functions to each, while integration describes the interactions and relationships between remote neural populations that are required for complex behavior. Although both principles on their own are valuable, a full understanding of the brain requires both. Fifteen years ago, Passingham et al. suggested that the concept of a connectivity fingerprint could link these two principles [2Passingham R.E. et al.The anatomical basis of functional localization in the cortex.Nat. Rev. Neurosci. 2002; 3: 606-616Crossref PubMed Scopus (0) Google Scholar]. They proposed that the function of each individual area is determined in the main by its unique set of connections with the rest of the brain. Thus, an area is described within the space of connections. The paper used multidimensional scaling to show that each area occupies a unique place within this space. In the original paper it was suggested, but not proven, that the functions of each area depend on the location of that area in this space. The reasoning was that each area performs a transformation from inputs to outputs and that this transformation depended on the information it received and the areas that it could influence. At the time, connectivity was studied almost exclusively using invasive tracer data in non-human species (Box 1). Although the authors suggested that the same conceptual framework could be applied to data acquired through neuroimaging, the paucity of data at the time meant that this extension of the original hypothesis could not be tested.Box 1Historical Overview of Connectivity Research MethodsThe development of the concept of the connectivity fingerprint has been due in no small part to the development of new methods for studying brain organization [81Catani M. et al.Connectomic approaches before the connectome.Neuroimage. 2013; 80: 2-13Crossref PubMed Scopus (42) Google Scholar]. Advances in microscopy meant that the brain could be divided up into areas based on differences in cytoarchitecture and myelination, and it later turned out that damage to different parts of the brain led to distinct behavioral impairments. The development of tracers in the early 1960 also meant that the connections between these areas could be studied in detail [82Morecraft R.J. et al.Classic and contemporary neural tract-tracing techniques.Diffusion MRI. Academic Press, 2009: 273-308Crossref Scopus (17) Google Scholar].In the early 1990 the relationship between these two streams of research, areal specialization and exchange of information, was formalized as the principles of segregation and integration in the brain [1Friston K.J. et al.Functional connectivity: the principal-component analysis of large (PET) data sets.J. Cereb. Blood Flow Metab. 1993; 13: 5-14Crossref PubMed Google Scholar, 83Zeki S. A Vision on the Brain. Blackwell Scientific Publications, 1993Google Scholar, 84Tononi G. et al.A measure for brain complexity: relating functional segregation and integration in the nervous system.Proc. Natl. Acad. Sci. U. S. A. 1994; 91: 5033-5037Crossref PubMed Scopus (733) Google Scholar]. With the increasing availability of data from tracer studies, it could be appreciated that different areas had unique characteristics [85Felleman D.J. Van Essen D.C. Distributed hierarchical processing in the primate cerebral cortex.Cereb. Cortex. 1991; 1: 1-47Crossref PubMed Google Scholar]. A further step was taken when it was appreciated that there was topography in the areal connections [86Young M.P. Objective analysis of the topological organization of the primate cortical visual system.Nature. 1992; 358: 152-155Crossref PubMed Scopus (299) Google Scholar]. Large-scale collations of tracer data, such as the CoCoMac database for macaque tracer data [87Stephan K.E. et al.Advanced database methodology for the Collation of Connectivity data on the Macaque brain (CoCoMac).Philos. Trans. R. Soc. Lond. B Biol. Sci. 2001; 356: 1159-1186Crossref PubMed Scopus (215) Google Scholar, 88Bakker R. et al.CoCoMac 2.0 and the future of tract-tracing databases.Front. Neuroinformatics. 2012; 6: 30Crossref PubMed Scopus (0) Google Scholar], meant that these relationships between the connectivity profiles of areas could be analyzed statistically [89Kötter R. et al.Connectional characteristics of areas in Walker's map of primate prefrontal cortex.Neurocomputing. 2001; 38–40: 741-746Crossref Scopus (0) Google Scholar]. This prompted Passingham et al. [2Passingham R.E. et al.The anatomical basis of functional localization in the cortex.Nat. Rev. Neurosci. 2002; 3: 606-616Crossref PubMed Scopus (0) Google Scholar] to argue that each area had a unique pattern of connections and to argue that neuroimaging might be used to characterize the functional profiles of the different areas.The 2002 paper provided one of the inspirations for the current movement of mapping the human connectome [90Sporns O. et al.The human connectome: a structural description of the human brain.PLoS Comput. Biol. 2005; 1: e42Crossref PubMed Scopus (1270) Google Scholar]. Large datasets are easily obtained from neuroimaging and this has inspired the application of many techniques from network science to the description of the brain [91Bullmore E. Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems.Nat. Rev. Neurosci. 2009; 10: 186-198Crossref PubMed Scopus (4228) Google Scholar]. In turn, these techniques have made connectivity research suitable for many applications, opening the door for the connectivity fingerprint as a tool in fundamental and clinical neuroscience [43Mars R.B. et al.Comparing brains by matching connectivity profiles.Neurosci. Biobehav. Rev. 2016; 60: 90-97Crossref PubMed Scopus (13) Google Scholar, 92Buckholtz J.W. Meyer-Lindenberg A. Psychopathology and the human connectome: toward a transdiagnostic model of risk for mental illness.Neuron. 2012; 74: 990-1004Abstract Full Text Full Text PDF PubMed Scopus (148) Google Scholar]. The development of the concept of the connectivity fingerprint has been due in no small part to the development of new methods for studying brain organization [81Catani M. et al.Connectomic approaches before the connectome.Neuroimage. 2013; 80: 2-13Crossref PubMed Scopus (42) Google Scholar]. Advances in microscopy meant that the brain could be divided up into areas based on differences in cytoarchitecture and myelination, and it later turned out that damage to different parts of the brain led to distinct behavioral impairments. The development of tracers in the early 1960 also meant that the connections between these areas could be studied in detail [82Morecraft R.J. et al.Classic and contemporary neural tract-tracing techniques.Diffusion MRI. Academic Press, 2009: 273-308Crossref Scopus (17) Google Scholar]. In the early 1990 the relationship between these two streams of research, areal specialization and exchange of information, was formalized as the principles of segregation and integration in the brain [1Friston K.J. et al.Functional connectivity: the principal-component analysis of large (PET) data sets.J. Cereb. Blood Flow Metab. 1993; 13: 5-14Crossref PubMed Google Scholar, 83Zeki S. A Vision on the Brain. Blackwell Scientific Publications, 1993Google Scholar, 84Tononi G. et al.A measure for brain complexity: relating functional segregation and integration in the nervous system.Proc. Natl. Acad. Sci. U. S. A. 1994; 91: 5033-5037Crossref PubMed Scopus (733) Google Scholar]. With the increasing availability of data from tracer studies, it could be appreciated that different areas had unique characteristics [85Felleman D.J. Van Essen D.C. Distributed hierarchical processing in the primate cerebral cortex.Cereb. Cortex. 1991; 1: 1-47Crossref PubMed Google Scholar]. A further step was taken when it was appreciated that there was topography in the areal connections [86Young M.P. Objective analysis of the topological organization of the primate cortical visual system.Nature. 1992; 358: 152-155Crossref PubMed Scopus (299) Google Scholar]. Large-scale collations of tracer data, such as the CoCoMac database for macaque tracer data [87Stephan K.E. et al.Advanced database methodology for the Collation of Connectivity data on the Macaque brain (CoCoMac).Philos. Trans. R. Soc. Lond. B Biol. Sci. 2001; 356: 1159-1186Crossref PubMed Scopus (215) Google Scholar, 88Bakker R. et al.CoCoMac 2.0 and the future of tract-tracing databases.Front. Neuroinformatics. 2012; 6: 30Crossref PubMed Scopus (0) Google Scholar], meant that these relationships between the connectivity profiles of areas could be analyzed statistically [89Kötter R. et al.Connectional characteristics of areas in Walker's map of primate prefrontal cortex.Neurocomputing. 2001; 38–40: 741-746Crossref Scopus (0) Google Scholar]. This prompted Passingham et al. [2Passingham R.E. et al.The anatomical basis of functional localization in the cortex.Nat. Rev. Neurosci. 2002; 3: 606-616Crossref PubMed Scopus (0) Google Scholar] to argue that each area had a unique pattern of connections and to argue that neuroimaging might be used to characterize the functional profiles of the different areas. The 2002 paper provided one of the inspirations for the current movement of mapping the human connectome [90Sporns O. et al.The human connectome: a structural description of the human brain.PLoS Comput. Biol. 2005; 1: e42Crossref PubMed Scopus (1270) Google Scholar]. Large datasets are easily obtained from neuroimaging and this has inspired the application of many techniques from network science to the description of the brain [91Bullmore E. Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems.Nat. Rev. Neurosci. 2009; 10: 186-198Crossref PubMed Scopus (4228) Google Scholar]. In turn, these techniques have made connectivity research suitable for many applications, opening the door for the connectivity fingerprint as a tool in fundamental and clinical neuroscience [43Mars R.B. et al.Comparing brains by matching connectivity profiles.Neurosci. Biobehav. Rev. 2016; 60: 90-97Crossref PubMed Scopus (13) Google Scholar, 92Buckholtz J.W. Meyer-Lindenberg A. Psychopathology and the human connectome: toward a transdiagnostic model of risk for mental illness.Neuron. 2012; 74: 990-1004Abstract Full Text Full Text PDF PubMed Scopus (148) Google Scholar]. Since the original paper, the field of connectivity research has taken off in an unprecedented manner [3Behrens T.E.J. Sporns O. Human connectomics.Curr. Opin. Neurobiol. 2012; 22: 144-153Crossref PubMed Scopus (137) Google Scholar, 4Van Essen D.C. Cartography and connectomes.Neuron. 2013; 80: 775-790Abstract Full Text Full Text PDF PubMed Scopus (0) Google Scholar]. Techniques such as diffusion magnetic resonance imaging (MRI) tractography and resting state functional MRI (fMRI) covariance allow mapping of the connectivity of an individual's brain in minutes. Connectivity fingerprints can now be defined easily and related to a wide array of variables given the development of tools for fast data acquisition and advanced connectivity analyses [5Craddock R.C. et al.Imaging human connectomes at the macroscale.Nat. Methods. 2013; 10: 524-539Crossref PubMed Scopus (171) Google Scholar, 6Rubinov M. Sporns O. 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Here, we show that the connectivity fingerprint and its relation to function has become a valuable window into understanding the anatomical and functional organization of the brain. It is now routine to use neuroimaging to describe connectivity fingerprints at the level of the voxel, and to do so across areas, networks, individuals, and species. The original paper took the term fingerprint from the unique receptor profiles of areas that were established by Karl Zilles and colleagues [11Geyer S. et al.Receptor autoradiographic mapping of the mesial motor and premotor cortex of the macaque monkey.J. Comp. Neurol. 1998; 397: 231-250Crossref PubMed Scopus (60) Google Scholar]. Although neuroimaging has investigated the connectivity of areas as defined by cytoarchitecture [12Caspers S. et al.Microstructural grey matter parcellation and its relevance for connectome analyses.Neuroimage. 2013; 80: 18-26Crossref PubMed Scopus (0) Google Scholar], it has become common to identify regions based on changes in connectivity at the voxel level. Connectivity-based mapping of areas has become a major part of cortical cartography (Box 2; [13Sporns O. Cerebral cartography and connectomics.Philos. Trans. R. Soc. B Biol. Sci. 2015; 370 (20140173–20140173)Crossref PubMed Scopus (25) Google Scholar]).Box 2Cortical Cartography Using Connectivity-Based ParcellationsEach area has a unique connectivity fingerprint that is critical in determining its function. Passingham et al. [2Passingham R.E. et al.The anatomical basis of functional localization in the cortex.Nat. Rev. Neurosci. 2002; 3: 606-616Crossref PubMed Scopus (0) Google Scholar] illustrated their point using meta-analyses of tracer data obtained in the macaque, showing that no regions in prefrontal or premotor cortex showed a similar pattern of connections to the rest of frontal cortex. However, postulating the idea of an areal connectivity fingerprint suggests that the border of a cortical area can be demonstrated by a change in the connectivity profile.Early approaches [93Cohen A.L. et al.Defining functional areas in individual human brains using resting functional connectivity MRI.Neuroimage. 2008; 41: 45-57Crossref PubMed Scopus (330) Google Scholar] tested whether functional connectivity can be used to detect areal borders. They compared the whole-brain connectivity fingerprint of an area in inferior parietal cortex with that of increasingly distant areas. They showed a sharp transition in connectivity patterns, rather than a consistent decline with distance from the seed, and argued that this demonstrates borders between areas. Mapping of boundaries in this way can be used to parcellate the entire cortical sheet [94Gordon E.M. et al.Generation and evaluation of a cortical area parcellation from resting-state correlations.Cereb. Cortex. 2016; 26: 288-303Crossref PubMed Google Scholar].An alternative parcellation approach exploits the unique profile of areas by grouping voxels based on their similarity in connectivity. Employing the at the time newly established technique of diffusion MRI tractography, this approach was originally used to identify two medial frontal areas overlapping with the supplementary and presupplementary motor areas [95Johansen-Berg H. et al.Changes in connectivity profiles define functionally distinct regions in human medial frontal cortex.Proc. Natl. Acad. Sci. U. S. A. 2004; 101: 13335-13340Crossref PubMed Scopus (448) Google Scholar]. This approach has since become well established, with high test–retest reliability [96Klein J.C. et al.Connectivity-based parcellation of human cortex using diffusion MRI: establishing reproducibility, validity and observer independence in BA 44/45 and SMA/pre-SMA.Neuroimage. 2007; 34: 204-211Crossref PubMed Scopus (135) Google Scholar] and consistency across groups [97Anwander A. et al.Connectivity-based parcellation of Broca's area.Cereb. Cortex. 2006; 17: 816-825Crossref PubMed Scopus (370) Google Scholar, 98Fan L. et al.Connectivity-based parcellation of the human temporal pole using diffusion tensor imaging.Cereb. Cortex. 2014; 24: 3365-3378Crossref PubMed Scopus (0) Google Scholar]. Where results could be compared to existing cytoarchitectonic maps, the overlap was high [99Henssen A. et al.Cytoarchitecture and probability maps of the human medial orbitofrontal cortex.Cortex. 2016; 75: 87-112Crossref PubMed Scopus (16) Google Scholar, 100Mars R.B. et al.Diffusion-weighted imaging tractography-based parcellation of the human parietal cortex and comparison with human and macaque resting-state functional connectivity.J. Neurosci. 2011; 31: 4087-4100Crossref PubMed Scopus (265) Google Scholar], affording the confidence to parcellate regions of the brain for which no prior anatomical investigation was attempted [101Liu H. et al.Connectivity-based parcellation of the human frontal pole with diffusion tensor imaging.J. Neurosci. 2013; 33: 6782-6790Crossref PubMed Scopus (59) Google Scholar, 102Mars R.B. et al.Connectivity-based subdivisions of the human right "temporoparietal junction area": evidence for different areas participating in different cortical networks.Cereb. Cortex. 2012; 22: 1894-1903Crossref PubMed Scopus (243) Google Scholar], often showing high correspondence with functional regions [103Schurz M. et al.Specifying the brain anatomy underlying temporo-parietal junction activations for theory of mind: a review using probabilistic atlases from different imaging modalities.Hum. Brain Mapp. 2017; 38: 4788-4805Crossref PubMed Scopus (9) Google Scholar, 104Krall S.C. et al.The role of the right temporoparietal junction in attention and social interaction as revealed by ALE meta-analysis.Brain Struct. Funct. 2015; 220: 587-604Crossref PubMed Scopus (73) Google Scholar]. Most recently and most dramatically, functional connectivity in combination with MRI sequences sensitive to structural markers and task activations has been used to produce a new map of the human cerebral cortex [76Glasser M.F. et al.A multi-modal parcellation of human cerebral cortex.Nature. 2016; 536: 171-178Crossref PubMed Google Scholar]. Each area has a unique connectivity fingerprint that is critical in determining its function. Passingham et al. [2Passingham R.E. et al.The anatomical basis of functional localization in the cortex.Nat. Rev. Neurosci. 2002; 3: 606-616Crossref PubMed Scopus (0) Google Scholar] illustrated their point using meta-analyses of tracer data obtained in the macaque, showing that no regions in prefrontal or premotor cortex showed a similar pattern of connections to the rest of frontal cortex. However, postulating the idea of an areal connectivity fingerprint suggests that the border of a cortical area can be demonstrated by a change in the connectivity profile. Early approaches [93Cohen A.L. et al.Defining functional areas in individual human brains using resting functional connectivity MRI.Neuroimage. 2008; 41: 45-57Crossref PubMed Scopus (330) Google Scholar] tested whether functional connectivity can be used to detect areal borders. They compared the whole-brain connectivity fingerprint of an area in inferior parietal cortex with that of increasingly distant areas. They showed a sharp transition in connectivity patterns, rather than a consistent decline with distance from the seed, and argued that this demonstrates borders between areas. Mapping of boundaries in this way can be used to parcellate the entire cortical sheet [94Gordon E.M. et al.Generation and evaluation of a cortical area parcellation from resting-state correlations.Cereb. Cortex. 2016; 26: 288-303Crossref PubMed Google Scholar]. An alternative parcellation approach exploits the unique profile of areas by grouping voxels based on their similarity in connectivity. Employing the at the time newly established technique of diffusion MRI tractography, this approach was originally used to identify two medial frontal areas overlapping with the supplementary and presupplementary motor areas [95Johansen-Berg H. et al.Changes in connectivity profiles define functionally distinct regions in human medial frontal cortex.Proc. Natl. Acad. Sci. U. S. A. 2004; 101: 13335-13340Crossref PubMed Scopus (448) Google Scholar]. This approach has since become well established, with high test–retest reliability [96Klein J.C. et al.Connectivity-based parcellation of human cortex using diffusion MRI: establishing reproducibility, validity and observer independence in BA 44/45 and SMA/pre-SMA.Neuroimage. 2007; 34: 204-211Crossref PubMed Scopus (135) Google Scholar] and consistency across groups [97Anwander A. et al.Connectivity-based parcellation of Broca's area.Cereb. Cortex. 2006; 17: 816-825Crossref PubMed Scopus (370) Google Scholar, 98Fan L. et al.Connectivity-based parcellation of the human temporal pole using diffusion tensor imaging.Cereb. Cortex. 2014; 24: 3365-3378Crossref PubMed Scopus (0) Google Scholar]. Where results could be compared to existing cytoarchitectonic maps, the overlap was high [99Henssen A. et al.Cytoarchitecture and probability maps of the human medial orbitofrontal cortex.Cortex. 2016; 75: 87-112Crossref PubMed Scopus (16) Google Scholar, 100Mars R.B. et al.Diffusion-weighted imaging tractography-based parcellation of the human parietal cortex and comparison with human and macaque resting-state functional connectivity.J. Neurosci. 2011; 31: 4087-4100Crossref PubMed Scopus (265) Google Scholar], affording the confidence to parcellate regions of the brain for which no prior anatomical investigation was attempted [101Liu H. et al.Connectivity-based parcellation of the human frontal pole with diffusion tensor imaging.J. Neurosci. 2013; 33: 6782-6790Crossref PubMed Scopus (59) Google Scholar, 102Mars R.B. et al.Connectivity-based subdivisions of the human right "temporoparietal junction area": evidence for different areas participating in different cortical networks.Cereb. Cortex. 2012; 22: 1894-1903Crossref PubMed Scopus (243) Google Scholar], often showing high correspondence with functional regions [103Schurz M. et al.Specifying the brain anatomy underlying temporo-parietal junction activations for theory of mind: a review using probabilistic atlases from different imaging modalities.Hum. Brain Mapp. 2017; 38: 4788-4805Crossref PubMed Scopus (9) Google Scholar, 104Krall S.C. et al.The role of the right temporoparietal junction in attention and social interaction as revealed by ALE meta-analysis.Brain Struct. Funct. 2015; 220: 587-604Crossref PubMed Scopus (73) Google Scholar]. Most recently and most dramatically, functional connectivity in combination with MRI sequences sensitive to structural markers and task activations has been used to produce a new map of the human cerebral cortex [76Glasser M.F. et al.A multi-modal parcellation of human cerebral cortex.Nature. 2016; 536: 171-178Crossref PubMed Google Scholar]. However, the main innovation of the concept of the connectivity fingerprint as used in neuroimaging has been to classify areas not in terms of their physical location but in terms of their connectivity. The point can be illustrated with reference to the extrastriate body area (EBA). This area was originally identified as a cortical region that responded to images of the human body as compared to control stimuli [14Downing P.E. et al.A cortical area selective for visual processing of the human body.Science. 2001; 293: 2470-2473Crossref PubMed Scopus (1137) Google Scholar]. It was viewed as a purely perceptual area [15Downing P.E. Peelen M.V. The role of occipitotemporal body-selective regions in person perception.Cogn. Neurosci. 2011; 2: 186-203Crossref PubMed Scopus (0) Google Scholar]. It was taken on the basis of its location to be one of the areas in the ventral perceptual visual stream that projects into the inferior temporal lobe, rather than one of the areas in the dorsal action stream that projects to the posterior parietal cortex [16Goodale M.A. Milner A.D. Separate visual pathways to perception and action.Trends Neurosci. 1992; 15: 6Abstract Full Text PDF Scopus (3225) Google Scholar]. However, more recent evidence from functional imaging shows that the EBA is active when subjects need to incorporate information on the posture of their own body into an action plan, even in the absence of any visual stimuli related to the body [17Zimmermann M. et al.Motor planning is facilitated by adopting an action's goal posture: an fMRI study.Cereb. Cortex. 2012; 22: 122-131Crossref PubMed Scopus (0) Google Scholar]. This prompted the hypothesis that the connectivity of the EBA is reminiscent of a dorsal stream area, rather than a ventral stream area [18Zimmermann M. et al.Is the extrastriate body area part of the dorsal visuomotor stream?.Brain Struct. Funct. 2018; 223: 31-46Crossref PubMed Scopus (3) Google Scholar]. As expected, compared to the fusiform body area, the EBA shows greater functional connectivity with the dorsal stream. Moreover, a classifier trained to dissociate dorsal and ventral stream areas based on their connectivity assigned the left EBA as being closer to the dorsal stream than areas in its physical proximity. This result illustrates the point that quantifying an area in terms of its connectivity is critical when trying to understand its function. The point can be generalized beyond specific patterns such as the distinction between dorsal and ventral stream connectivity. One approach consists of finding generic dimensions of connectivity [19Margulies D.S. et al.Situating the default-mode network along a principal gradient of macroscale cortical organization.Proc. Natl. Acad. Sci. U. S. A. 2016; 113: 12574-12579Crossref PubMed Scopus (0) Google Scholar]. In such a space, physical distances represent brain connections, in the sense that brain locations that are near each other in connectivity space are more connected to each other, that is they have resting state time series that correlate more closely. Such a space can be defined using results from spectral graph theory [20Higham D.J. et al.Spectral clustering and its use in bioinformatics.J. Comput. Appl. Math. 2007; 204: 25-37Crossref Scopus (0) Google Scholar]. The dimensions of connectivity are defined as the eigenvectors of the connectivity graph Laplacian [21Belkin M. Niyogi P. Laplacian Eigenmaps and spectral techniques for embedding and clustering.Advances in Neural Information Processing Systems. MIT Press, 2007: 585-591Google Scholar, 22Cerliani L. et al.Probabilistic tractography recovers a rostrocaudal trajectory of connectivity variability in the human insular cortex.Hum. Brain Mapp. 2012; 33: 2005-2034Crossref PubMed Scopus (0) Google Scholar]. We used these methods in Figure 1. This compares brain activity as represented in physical space and brain activity as represented in connectivity space. Comparing local peaks of activity for two different task contrasts, the peaks appear to be scattered around various parts of association cortex with no obvious organization in physical space, but they form clear and distinct clusters in connectivity space. This suggests that the connectivity dimensions form an abstract space that is more closely related to differences in function. The results in Figure 1 demonst