Undirected graphs of frequency-dependent functional connectivity in whole brain networks
Open accessAbstract
We explored properties of whole brain networks based on multivariate spectral analysis of human functional magnetic resonance imaging (fMRI) time-series measured in 90 cortical and subcortical subregions in each of five healthy volunteers studied in the (no-task) resting state. We note that undirected graphs representing conditional independence between multivariate time-series can be more readily approached in the frequency domain than the time domain. Estimators of partial coherency and normalized partial mutual information ϕ , an integrated measure of partial coherence over an arbitrary frequency band, are applied. Using these tools, we replicate the prior observations that bilaterally homologous brain regions tend to be strongly connected and functional connectivity is generally greater at low frequencies [0.0004, 0.1518 Hz]. We also show that long-distance intrahemispheric connections between regions of prefrontal and parietal cortex were more salient at low frequencies than at frequencies greater than 0.3 Hz, whereas many local or short-distance connections, such as those comprising segregated dorsal and ventral paths in posterior cortex, were also represented in the graph of high-frequency connectivity. We conclude that the partial coherency spectrum between a pair of human brain regional fMRI time-series depends on the anatomical distance between regions: long-distance (greater than 7 cm) edges represent conditional dependence between bilaterally symmetric neocortical regions, and between regions of prefrontal and parietal association cortex in the same hemisphere, are predominantly subtended by low-frequency components.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Sparse small-world attributes are robust in that they are reproducible across imaging modalities, disease states, and species.
“Sparse small-world attributes are robust in that they are reproducible across imaging modalities (diffusion MRI, 45,46 resting fMRI, 2,78,102 structural MRI, 48 EEG, 82 MEG, 90 and PET 30,79 ), disease states, and species (such as the cat, macaque, and nematode Caenorhabditis elegans).20”
From Graph theory analysis of complex brain networks: new concepts in brain mapping applied to neurosurgery (2016) · cites this paper as [78]
These modules can be further broken down into submodules in a hierarchical manner.
“These modules can be further broken down into submodules in a hierarchical manner.78”
From Graph theory analysis of complex brain networks: new concepts in brain mapping applied to neurosurgery (2016) · cites this paper as [78]
Translating connectivity patterns to physical space was originally performed in a 2D plane, where lines denoted connections between regions in physical space.
“Translating connectivity patterns to physical space was originally performed in a 2D plane (a), where lines were used to denote connections between regions in physical space.2,78”
From Graph theory analysis of complex brain networks: new concepts in brain mapping applied to neurosurgery (2016) · cites this paper as [78]
Cites
Causality: Models, Reasoning, and Inference
Pearl, J. (2009) · doi:10.1017/cbo9780511803161 · Cited by 11,653 · see citing works
Functional connectivity in the motor cortex of resting human brain using echo‐planar mri
Biswal, B., Zerrin Yetkin, F., Haughton, V. M., & Hyde, J. S. (1995) · Magnetic Resonance in Medicine · doi:10.1002/mrm.1910340409 · Cited by 9,812 · see citing works
Functional connectivity in the resting brain: a network analysis of the default mode hypothesis
Greicius, M. D., Krasnow, B., Reiss, A. L., & Menon, V. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0135058100 · Cited by 6,358 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
<i>Conn</i> : A Functional Connectivity Toolbox for Correlated and Anticorrelated Brain Networks
Whitfield-Gabrieli, S., & Nieto-Castanon, A. (2012) · Brain Connectivity · doi:10.1089/brain.2012.0073 · Cited by 4,885 · see citing works
Exploring the brain network: A review on resting-state fMRI functional connectivity
van den Heuvel, M. P., & Hulshoff Pol, H. E. (2010) · European Neuropsychopharmacology · doi:10.1016/j.euroneuro.2010.03.008 · Cited by 3,326 · see citing works
Efficiency and Cost of Economical Brain Functional Networks
Achard, S., & Bullmore, E. (2007) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0030017 · Cited by 2,553 · see citing works
Self-citationTime–frequency dynamics of resting-state brain connectivity measured with fMRI
Chang, C., & Glover, G. H. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2009.12.011 · Cited by 1,808 · see citing works
Functional brain networks develop from a local to distributed organization
Fair, D. A., Cohen, A. L., Power, J. D., Dosenbach, N. U. F., Church, J. A., Miezin, F. M., Schlaggar, B. L., & Petersen, S. E. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000381 · Cited by 1,530 · see citing works
Default Mode Network Activity and Connectivity in Psychopathology
Whitfield-Gabrieli, S., & Ford, J. M. (2012) · Annual Review of Clinical Psychology · doi:10.1146/annurev-clinpsy-032511-143049 · Cited by 1,465 · see citing works
Whole-brain anatomical networks: does the choice of nodes matter?
Zalesky, A., Fornito, A., Harding, I. H., Cocchi, L., Yücel, M., Pantelis, C., & Bullmore, E. T. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2009.12.027 · Cited by 1,169 · see citing works
Self-citationImaging structural co-variance between human brain regions
Alexander-Bloch, A., Giedd, J. N., & Bullmore, E. (2013) · Nature Reviews Neuroscience · doi:10.1038/nrn3465 · Cited by 1,064 · see citing works
Self-citationvan den Heuvel, M. P., Mandl, R. C. W., Kahn, R. S., & Hulshoff Pol, H. E. (2009) · Human Brain Mapping · doi:10.1002/hbm.20737 · Cited by 987 · see citing works
Defining functional areas in individual human brains using resting functional connectivity MRI
Cohen, A. L., Fair, D. A., Dosenbach, N. U. F., Miezin, F. M., Dierker, D., Van Essen, D. C., Schlaggar, B. L., & Petersen, S. E. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2008.01.066 · Cited by 582 · see citing works
Networks of anatomical covariance
Evans, A. C. (2013) · NeuroImage · doi:10.1016/j.neuroimage.2013.05.054 · Cited by 429 · see citing works
Wang, J.-H., Zuo, X.-N., Gohel, S., Milham, M. P., Biswal, B. B., & He, Y. (2011) · PLoS ONE · doi:10.1371/journal.pone.0021976 · Cited by 416 · see citing works
Exploring the network dynamics underlying brain activity during rest
Cabral, J., Kringelbach, M. L., & Deco, G. (2014) · Progress in Neurobiology · doi:10.1016/j.pneurobio.2013.12.005 · Cited by 351 · see citing works
Small worlds inside big brains
Sporns, O., & Honey, C. J. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0609523103 · Cited by 307 · see citing works
Development of a large-scale functional brain network during human non-rapid eye movement sleep
Spoormaker, V. I., Schröter, M. S., Gleiser, P. M., Andrade, K. C., Dresler, M., Wehrle, R., Sämann, P. G., & Czisch, M. (2010) · The Journal of Neuroscience · doi:10.1523/jneurosci.2015-10.2010 · Cited by 273 · see citing works
Church, J. A., Fair, D. A., Dosenbach, N. U. F., Cohen, A. L., Miezin, F. M., Petersen, S. E., & Schlaggar, B. L. (2009) · Brain · doi:10.1093/brain/awn223 · Cited by 278 · see citing works
Brain anatomical networks in early human brain development
Fan, Y., Shi, F., Smith, J. K., Lin, W., Gilmore, J. H., & Shen, D. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2010.07.025 · Cited by 225 · see citing works
Striatum-Based Circuitry of Adolescent Depression and Anhedonia
Gabbay, V., Ely, B. A., Li, Q., Bangaru, S. D., Panzer, A. M., Alonso, C. M., Castellanos, F. X., & Milham, M. P. (2013) · Journal of the American Academy of Child & Adolescent Psychiatry · doi:10.1016/j.jaac.2013.04.003 · Cited by 222 · see citing works
A simple view of the brain through a frequency-specific functional connectivity measure
Salvador, R., Martínez, A., Pomarol-Clotet, E., Gomar, J., Vila, F., Sarró, S., Capdevila, A., & Bullmore, E. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2007.08.018 · Cited by 225 · see citing works
Self-citationDisrupted Small-World Brain Networks in Moderate Alzheimer's Disease: A Resting-State fMRI Study
Zhao, X., Liu, Y., Wang, X., Liu, B., Xi, Q., Guo, Q., Jiang, H., Jiang, T., & Wang, P. (2012) · PLoS ONE · doi:10.1371/journal.pone.0033540 · Cited by 215 · see citing works
Atypically diffuse functional connectivity between caudate nuclei and cerebral cortex in autism
Turner, K. C., Frost, L., Linsenbardt, D., McIlroy, J. R., & Müller, R.-A. (2006) · Behavioral and Brain Functions · doi:10.1186/1744-9081-2-34 · Cited by 207 · see citing works
Versace, A., Thompson, W. K., Zhou, D., Almeida, J. R. C., Hassel, S., Klein, C. R., Kupfer, D. J., & Phillips, M. L. (2010) · Biological Psychiatry · doi:10.1016/j.biopsych.2009.11.025 · Cited by 194 · see citing works
Optimal trajectories of brain state transitions
Gu, S., Betzel, R. F., Mattar, M. G., Cieslak, M., Delio, P. R., Grafton, S. T., Pasqualetti, F., & Bassett, D. S. (2017) · NeuroImage · doi:10.1016/j.neuroimage.2017.01.003 · Cited by 183 · see citing works
Wei, D., Yang, J., Li, W., Wang, K., Zhang, Q., & Qiu, J. (2014) · Cortex · doi:10.1016/j.cortex.2013.09.004 · Cited by 164 · see citing works
Drakesmith, M., Caeyenberghs, K., Dutt, A., Lewis, G., David, A. S., & Jones, D. K. (2015) · NeuroImage · doi:10.1016/j.neuroimage.2015.05.011 · Cited by 157 · see citing works
Detecting hierarchical genome folding with network modularity
Norton, H. K., Emerson, D. J., Huang, H., Kim, J., Titus, K. R., Gu, S., Bassett, D. S., & Phillips-Cremins, J. E. (2018) · Nature Methods · doi:10.1038/nmeth.4560 · Cited by 146 · see citing works
Functional connectivity and network analysis of midbrain and brainstem nuclei
Bär, K.-J., de la Cruz, F., Schumann, A., Koehler, S., Sauer, H., Critchley, H., & Wagner, G. (2016) · NeuroImage · doi:10.1016/j.neuroimage.2016.03.071 · Cited by 134 · see citing works
Intrinsic Functional Brain Architecture Derived from Graph Theoretical Analysis in the Human Fetus
Thomason, M. E., Brown, J. A., Dassanayake, M. T., Shastri, R., Marusak, H. A., Hernandez-Andrade, E., Yeo, L., Mody, S., Berman, S., Hassan, S. S., et al. (2014) · PLoS ONE · doi:10.1371/journal.pone.0094423 · Cited by 130 · see citing works
Caeyenberghs, K., Leemans, A., Heitger, M. H., Leunissen, I., Dhollander, T., Sunaert, S., Dupont, P., & Swinnen, S. P. (2012) · Brain · doi:10.1093/brain/aws048 · Cited by 129 · see citing works
Evolution of brain network dynamics in neurodevelopment
Chai, L. R., Khambhati, A. N., Ciric, R., Moore, T. M., Gur, R. C., Gur, R. E., Satterthwaite, T. D., & Bassett, D. S. (2017) · Network Neuroscience · doi:10.1162/netn_a_00001 · Cited by 100 · see citing works
Castellanos, F. X., Kelly, C., & Milham, M. P. (2009) · The Canadian Journal of Psychiatry · doi:10.1177/070674370905401003 · Cited by 88 · see citing works
Common and distinct brain networks underlying panic and social anxiety disorders
Kim, Y.-K., & Yoon, H.-K. (2018) · Progress in Neuro-Psychopharmacology and Biological Psychiatry · doi:10.1016/j.pnpbp.2017.06.017 · Cited by 78 · see citing works
Hart, M. G., Ypma, R. J. F., Romero-Garcia, R., Price, S. J., & Suckling, J. (2016) · Journal of Neurosurgery · doi:10.3171/2015.4.jns142683 · Cited by 74 · see citing works
Self-citation
- Authors
- Salvador, R., Suckling, J., Schwarzbauer, C., & Bullmore, E.
- Affiliations
- University of Cambridge (GB)
- Brain Mapping Unit and Wolfson Brain Imaging Centre, Departments of Psychiatry and Clinical Neurosciences, Addenbrooke's Hospital, University of CambridgeCambridge CB2 2QQ, UK
- MRC Cognition and Brain Sciences Unit (GB)
- ORCID
- Salvador, Raymond
- Venue
- Philosophical Transactions of the Royal Society B: Biological Sciences
- Publisher
- The Royal Society
- Published
- 2005-05-29
- Volume
- 360
- Issue
- 1457
- Pages
- 937-946
- ISSN
- 0962-8436 (ISSN-L)
- 1471-2970
- PMC
- PMC1854928
- OpenAlex
- W2155525875
- Cited by
- 437
- References
- 3
- Citations by year
- 2026: 3 · 2025: 6 · 2024: 8 · 2023: 11 · 2022: 12 · 2021: 22 · 2020: 19 · 2019: 18 · 2018: 32 · 2017: 26 · 2016: 32 · 2015: 28 · 2014: 21 · 2013: 32 · 2012: 33
- FWCI
- 8.11
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Philosophical Transactions of the Royal Society B Biological Sciences (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Medical Research Council
- National Institute of Mental Health
- National Institute of Biomedical Imaging and Bioengineering
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
- Keywords
- functional connectivity, whole-brain networks, undirected graphs, partial coherence, resting-state fMRI, anatomical distance, long-distance connections, prefrontal cortex, parietal cortex, spectral analysis
- MeSH terms
- Brain, Brain Mapping, Humans, Image Processing, Computer-Assisted, Magnetic Resonance Imaging, Models, Neurological, Neural Pathways, Time Factors, Multivariate Analysis
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
