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Consistency-based thresholding of the human connectome
Abstract
Densely seeded probabilistic tractography yields weighted networks that are nearly fully connected, hence containing many spurious fibers. It is thus necessary to prune spurious connections from probabilistically-derived networks to obtain a more reliable overall estimate of the connectivity. A standard method is to threshold by weight, keeping only the strongest edges. Here, by measuring the consistency of edge weights across subjects, we propose a new thresholding method that aims to reduce the rate of false-positives in group-averaged connectivity matrices. Close inspection of the relationship between consistency, weight, and distance suggests that the most consistent edges are in fact those that are strong for their length, rather than simply strong overall. Hence retaining the most consistent edges preserves more long-distance connections than traditional weight-based thresholding, which penalizes long connections for being weak regardless of anatomy. By comparing our thresholded networks to mouse and macaque tracer data, we also show that consistency-based thresholding exhibits the species-invariant exponential decay of connection weights with distance, while weight-based thresholding does not. We also show that consistency-based thresholding can be used to identify highly consistent and highly inconsistent subnetworks across subjects, enabling more nuanced analyses of group-level connectivity than just the mean connectivity.
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“We note that inter-subject connectome consistency may also be improved using other approaches, e.g., consistency-based thresholding (Baum et al., 2018; Roberts et al., 2017).”
From Quantitative mapping of the brain’s structural connectivity using diffusion MRI tractography: A review (2022) · cites this paper as Roberts et al., 2017
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Self-citationPrinciples and Operation of Virtual Brain Twins
Hashemi, M., Depannemaecker, D., Saggio, M. L., Triebkorn, P., Rabuffo, G., Fousek, J., Ziaeemehr, A., Ší́p, V., Athanasiadis, A., Breyton, M., et al. (2025) · IEEE Reviews in Biomedical Engineering · doi:10.1109/rbme.2025.3562951 · Cited by 54
“[56]furtherhighlightsthisgrowing trendbyderivinggeometriceigenmodes(corticalshape)that accountfortheeffectsoflocalconnectivitythatisexponentially decayingoverthegeodesicdistanceofthecortex,i.e.,the exponentialdistancerule[57],[58],[59],[60].”
Dimitriadis, S. I., Drakesmith, M., Bells, S., Parker, G. D., Linden, D. E. J., & Jones, D. K. (2017) · Frontiers in Neuroscience · doi:10.3389/fnins.2017.00694 · Cited by 43
Madole, J. W., Ritchie, S. J., Cox, S. R., Buchanan, C. R., Hernández, M. V., Maniega, S. M., Wardlaw, J. M., Harris, M. A., Bastin, M. E., Deary, I. J., et al. (2021) · Biological Psychiatry · doi:10.1016/j.biopsych.2020.06.010 · Cited by 45
The large‐scale structural connectome of task‐specific focal dystonia
Hanekamp, S., & Simonyan, K. (2020) · Human Brain Mapping · doi:10.1002/hbm.25012 · Cited by 43
Estimating the impact of structural directionality: How reliable are undirected connectomes?
Kale, P., Zalesky, A., & Gollo, L. L. (2018) · Network Neuroscience · doi:10.1162/netn_a_00040 · Cited by 37
Yang, Y., Zheng, Z., Liu, L., Zheng, H., Zhen, Y., Zheng, Y., Wang, X., & Tang, S. (2023) · Nature Communications · doi:10.1038/s41467-023-42053-4 · Cited by 35
“A group-average structural connectivity matrix was estimated using a consensus approach preserving the density and the edge-length distribution of the individual participant matrices 92 – 94 .”
Román, C., Hernández, C., Figueroa, M. E., Houenou, J., Poupon, C., Mangin, J., & Guevara, P. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.119550 · Cited by 44
Feng, G., Wang, Y., Huang, W., Chen, H., Cheng, J., & Shu, N. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.09.11.557107 · Cited by 4
Connectomes for 40,000 UK Biobank participants: A multi-modal, multi-scale brain network resource
Mansour, L., Biase, M. D. D., Smith, R., Zalesky, A., & Seguin, C. (2023) · bioRxiv · doi:10.1101/2023.03.10.532036 · Cited by 36
Meijer, K., Muhlert, N., Cercignani, M., Sethi, V., Ron, M., Thompson, A., Miller, D. H., Chard, D., Geurts, J., & Ciccarelli, O. (2016) · Multiple Sclerosis · doi:10.1177/1352458515622694 · Cited by 35
“001 Disease duration (years) 20 (8-48) EDSS 6.”
Generative network models of altered structural brain connectivity in schizophrenia
Zhang, X., Braun, U., Harneit, A., Zang, Z., Geiger, L. S., Betzel, R. F., Chen, J., Schweiger, J. I., Schwarz, K., Reinwald, J., et al. (2020) · NeuroImage · doi:10.1016/j.neuroimage.2020.117510 · Cited by 42
Mapping the structural connectivity between the periaqueductal gray and the cerebellum in humans
Cacciola, A., Bertino, S., Basile, G. A., Mauro, D. D., Calamuneri, A., Chillemi, G., Duca, A., Bruschetta, D., Flace, P., Favaloro, A., et al. (2019) · Brain Structure and Function · doi:10.1007/s00429-019-01893-x · Cited by 39
Soman, S. M., Vijayakumar, N., Thomson, P., Ball, G., Hyde, C. E., & Silk, T. J. (2023) · Human Brain Mapping · doi:10.1002/hbm.26288 · Cited by 47
Robinson, P. A. (2019) · Physical review. E · doi:10.1103/physreve.99.012421 · Cited by 36
Shen, K., Goulas, A., Grayson, D. S., Eusebio, J., Gati, J. S., Menon, R. S., McIntosh, A. R., & Everling, S. (2019) · NeuroImage · doi:10.1016/j.neuroimage.2019.02.018 · Cited by 36
“…known to be important in determining the brain’s functional organization (Gallos et al., 2012; Goulas et al., 2015) and may be better represented in networks that have been constructed using methods that take the frequency of edge reconstruction across subjects into account (Roberts et al., 2017).”
BackgroundMethodResultInfluentialBuchanan, C. R., Maniega, S. M., Hernández, M. D. C. V., Ballerini, L., Barclay, G., Taylor, A. M., Russ, T. C., Tucker–Drob, E. M., Wardlaw, J. M., Deary, I. J., et al. (2021) · Human Brain Mapping · doi:10.1002/hbm.25473 · Cited by 33
“Our results suggest that multi-scanner network analyses require careful consideration in the treatment of acquisition-specific network sparsities, such as the use of stringent thresholding or other de-noising methods (de Reus & van den Heuvel, 2013; Roberts et al., 2017).”
BackgroundZhang, J., Scholtens, L. H., Wei, Y., van den Heuvel, M. P., Chanes, L., & Barrett, L. F. (2019) · Cerebral Cortex · doi:10.1093/cercor/bhz171 · Cited by 30
“…10 minimum streamlines, 60% prevalence; 5 minimum streamlines, 50% prevalence; 5 minimum streamlines, 70% prevalence; also consistency-thresholded connectome, same density as 5 minimum streamlines, 60% prevalence; Roberts et al. 2017) and found similar results (see Supplementary Texts S1 − S5).”
DDParcel: Deep Learning Anatomical Brain Parcellation From Diffusion MRI
Zhang, F., Cho, K. I. K., Seitz‐Holland, J., Ning, L., Legarreta, J. H., Yogesh Rathi, A., Westin, C., O’Donnell, L. J., & Pasternak, O. (2023) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2023.3331691 · Cited by 29
“The RSD, also known as the coefficient of variation (CV), is defined as the ratio of the standard deviation to the mean, which has been used in previous dMRI studies for the evaluation of brain parcellation consistency [56], [57].”
MethodHierarchical Complexity of the Macro-Scale Neonatal Brain
Blesa, M., Galdi, P., Cox, S. R., Sullivan, G., Stoye, D. Q., Lamb, G. J., Quigley, A. J., Thrippleton, M. J., Escudero, J., Bastin, M. E., et al. (2020) · Cerebral Cortex · doi:10.1093/cercor/bhaa345 · Cited by 28
“This value is compatible with estimates from animal and human studies and was previously adopted for the study of human brain connectomes (Roberts et al. , 2017; Buchanan et al. , 2020) and for similarly generated networks (Roberts et al. , 2016).”
Ball, G., Beare, R. J., & Seal, M. L. (2019) · Human Brain Mapping · doi:10.1002/hbm.24726 · Cited by 27
“, 2012), we also thresholded our matrices based on a measure of edge weight consistency shown to improve estimate of consistent networks across subjects (Roberts et al., 2017).”
BackgroundMethodInfluentialHigh-resolution directed human connectomes and the Consensus Connectome Dynamics
Szalkai, B., Kerepesi, C., Varga, B., & Grolmusz, V. I. (2019) · PLoS ONE · doi:10.1371/journal.pone.0215473 · Cited by 3
Connectomes for 40,000 UK Biobank participants: A multi-modal, multi-scale brain network resource
Sina Mansour, L., Biase, M. A. D., Smith, R. E., Zalesky, A., & Seguin, C. (2023) · NeuroImage · doi:10.1016/j.neuroimage.2023.120407 · Cited by 66
“Group-level FC was computed as the average of functional networks across the 1000 subjects and group-consensus SC was inferred using consistency-based thresholding [94].”
Alloza, C., Blesa, M., Bastin, M. E., Madole, J. W., Buchanan, C. R., Janssen, J., Gibson, J., Deary, I. J., Tucker–Drob, E. M., Whalley, H. C., et al. (2020) · Translational Psychiatry · doi:10.1038/s41398-020-0794-x · Cited by 29
Disrupted brain structural connectivity in Pediatric Bipolar Disorder with psychosis
Fernandes, H. M., Cabral, J., van Hartevelt, T. J., Lord, L.-D., Gleesborg, C., Møller, A., Deco, G., Whybrow, P. C., Petrović, P., James, A. C., et al. (2019) · Scientific Reports · doi:10.1038/s41598-019-50093-4 · Cited by 26
Mareva, S., Akarca, D., The CALM team, & Holmes, J. (2022) · Journal of Child Psychology and Psychiatry · doi:10.1111/jcpp.13685 · Cited by 23
Benchmarking functional connectivity by the structure and geometry of the human brain
Liu, Z.-Q., Betzel, R. F., & Mišić, B. (2021) · bioRxiv · doi:10.1101/2021.10.12.464110 · Cited by 21
“To mitigate concerns about inconsistencies in reconstruction of individual participant connectomes [23, 46], as well as the sensitive dependence of network measures on false positives and false negatives [53], we adopted a group-consensus approach [7, 14, 38].”
BackgroundMethodMillán, A. P., van Straaten, E. C. W., Stam, C. J., Nissen, I. A., Idema, S., Baayen, J. C., Mieghem, P. V., & Hillebrand, A. (2022) · Scientific Reports · doi:10.1038/s41598-022-07730-2 · Cited by 23
Learning in brain-computer interface control evidenced by joint decomposition of brain and behavior
Stiso, J., Corsi, M., Vettel, J. M., Garcia, J. O., Pasqualetti, F., Fallani, F. D. V., Lucas, T. H., & Bassett, D. S. (2020) · Journal of Neural Engineering · doi:10.1088/1741-2552/ab9064 · Cited by 22
“To identify shared spatial features we grouped subgraphs together by their ranked performance loading, and then quantified how consistent edges were across participants [92] (see Methods).”
MethodChen, P., Yang, H., Zheng, X., Jia, H., Hao, J., Xu, X., Li, C., He, X., Chen, R., Okubo, T. S., et al. (2024) · Imaging Neuroscience · doi:10.1162/imag_a_00378 · Cited by 15
“To address potential issues with spurious SC edges arising from probabilistic tractography ( Roberts et al., 2017), we adopted a group-consistency thresholding approach as in previous studies ( Baum et al., 2020; Ge et al., 2023).”
Geometric Scaling Law in Real Neuronal Networks
Zhang, X.-Y., Moore, J. M., Ru, X., & Yan, G. F. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.138401 · Cited by 20
Madole, J. W., Buchanan, C. R., Rhemtulla, M., Ritchie, S. J., Bastin, M. E., Deary, I. J., Cox, S. R., & Tucker–Drob, E. M. (2023) · NeuroImage · doi:10.1016/j.neuroimage.2023.120160 · Cited by 22
Towards deep learning for connectome mapping: A block decomposition framework
Sarwar, T., Seguin, C., Ramamohanarao, K., & Zalesky, A. (2020) · NeuroImage · doi:10.1016/j.neuroimage.2020.116654 · Cited by 22
“Thresholding was performed to eliminate connections comprising the fewest numbers of streamlines, under the assumption that these connections are spurious (van den Heuvel et al., 2017; Roberts et al., 2017).”
MethodSiless, V., Davidow, J. Y., Nielsen, J. A., Fan, Q., Hedden, T., Hollinshead, M. O., Beam, E., Bustamante, C. M. V., Garrad, M. C., Santillana, R. M., et al. (2020) · NeuroImage · doi:10.1016/j.neuroimage.2020.116703 · Cited by 19
Structure–function coupling in the first month of life: Associations with age and attention
Tooley, U. A., Kenley, J. K., Camacho, M. C., Latham, A. R., Alexopoulos, D., Nielsen, A. N., Smyser, T. A., Warner, B. B., Shimony, J. S., Neil, J. J., et al. (2025) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2412729122 · Cited by 19
Feng, G., Wang, Y., Huang, W., Chen, H., Cheng, J., & Shu, N. (2024) · eLife · doi:10.7554/elife.93325 · Cited by 15
Computational memory capacity predicts aging and cognitive decline
Mijalkov, M., Storm, L., Gerbolés, B. Z., Veréb, D., Xu, Z., Canal-García, A., Sun, J., Chang, Y.-W., Zhao, H., Gómez-Ruiz, E., et al. (2025) · Nature Communications · doi:10.1038/s41467-025-57995-0 · Cited by 14
“The topic and approach of the paper is very timely and the analyses are generally thorough and well described.”
Can hubs of the human connectome be identified consistently with diffusion MRI?
Gajwani, M., Oldham, S., Pang, J. C., Arnatkevic̆iūtė, A., Tiego, J., Bellgrove, M., & Fornito, A. (2023) · bioRxiv · doi:10.1101/2022.12.21.521366 · Cited by 16
“…the strongest or most frequently occurring across individuals (de Reus & van den Heuvel, 2013a), retaining edges that are the least variable across people (Roberts et al., 2017), or retaining edges that preserve a specific proportion of connections in different distance bins (Betzel et al., 2019).”
BackgroundLongitudinal changes of connectomes and graph theory measures in aging
Wang, Y., Rheault, F., Schilling, K. G., Beason‐Held, L. L., Shafer, A. T., Resnick, S. M., & Landman, B. A. (2022) · SPIE Medical Imaging: Image Processing · doi:10.1117/12.2611845 · Cited by 8
“Solutions such as connectome “thresholding” 27 , connectome “cleaning” 28,29 or connectome “normalisation” 30 are proposed in previous studies.”
BackgroundNetwork neuroscience and the connectomics revolution
Betzel, R. F. (2021) · Elsevier eBooks · doi:10.1016/b978-0-12-821861-7.00002-6 · Cited by 18
“[64] James A Roberts, Alistair Perry, Gloria Roberts, Philip B Mitchell, and Michael Breakspear, “Consistency-based thresholding of the human connectome,” Neuroimage 145, 118–129 (2017).”
BackgroundAnat-SFSeg: Anatomically-guided superficial fiber segmentation with point-cloud deep learning
Zhang, D., Zong, F., Zhang, Q., Yue, Y., Zhang, F., Zhao, K., Wang, D., Wang, P., Zhang, X., & Liu, Y. (2024) · Medical Image Analysis · doi:10.1016/j.media.2024.103165 · Cited by 16
Evaluation of tractogram filtering methods using human-like connectome phantoms
Sarwar, T., Ramamohanarao, K., Daducci, A., Schiavi, S., Smith, R. E., & Zalesky, A. (2023) · NeuroImage · doi:10.1016/j.neuroimage.2023.120376 · Cited by 15
“To this end, thresholding is often used to eliminate connections comprising the fewest numbers of streamlines, under the assumption that these connections are spurious (Buchanan et al., 2020; Roberts et al., 2017; Yeh et al., 2021).”
MethodMcColgan, P., Blom, T., Rees, G. E., Seunarine, K. K., Gregory, S., Johnson, E. B., Dürr, A., Roos, R. A. C., Scahill, R. I., Clark, C. A., et al. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/416826 · Cited by 16
“In order to address this issue (Roberts et al., 2016) proposed a novel consistency based thresholding method such that connections are ranked based on their coefficient of variation across a group of participants.”
BackgroundMethodInfluentialCornblath, E. J., Ashourvan, A., Kim, J. Z., Betzel, R. F., Ćirić, R., Baum, G. L., He, X., Ruparel, K., Moore, T. M., Gur, R. C., et al. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/412429 · Cited by 10
“[51] Roberts JA, Perry A, Roberts G, Mitchell PB Breakspear M: Consistency-based thresholding of the human connectome.”
BackgroundGood, T. J., Schirner, M., Shen, K., Ritter, P., Mukherjee, P., Levine, B., & McIntosh, A. R. (2022) · eNeuro · doi:10.1523/eneuro.0075-21.2022 · Cited by 14
“, 2019b), any connections not present in at least 50% of the comparison subjects were set to zero (Roberts et al., 2017).”
BackgroundExtracting the signed backbone of intrinsically dense weighted networks
Gürsoy, F., & Badur, B. (2021) · Journal of Complex Networks · doi:10.1093/comnet/cnab019 · Cited by 16
Trade-offs among cost, integration, and segregation in the human connectome
Ma, J., Chen, X., Gu, Y., Li, L., Cam-CAN, Lin, Y. L., & Dai, Z. (2022) · Network Neuroscience · doi:10.1162/netn_a_00291 · Cited by 11
“retaining edges that existed in more than 50% of the participants’ structural brain networks (Fukushima et al., 2018; Roberts et al., 2017; Zalesky et al., 2016).”
BackgroundMethodBrainnetome atlas of preadolescent children based on anatomical connectivity profiles
Li, W., Fan, L., Shi, W., Lu, Y., Li, J., Luo, N., Wang, H., Chu, C., Ma, L., Song, M., et al. (2022) · Cerebral Cortex · doi:10.1093/cercor/bhac415 · Cited by 17
“After removing the false positive connections (Roberts et al. 2017), the connection matrix was obtained.”
MethodBasile, G. A., Quartu, M., Bertino, S., Serra, M. P., Trucas, M., Boi, M., Demontis, R., Bramanti, A., Anastasi, G. P., Milardi, D., et al. (2022) · Brain Structure and Function · doi:10.1007/s00429-022-02561-3 · Cited by 12
“While most of the spurious fiber tracts are also characterized by low between-subject consistency (Roberts et al. 2017) and are subsequently filtered out after group aggregation of individual tractograms (especially after z-thresholding of the resulting maximum probability maps), it is worth noting that even at the gr…”
BackgroundEigenmodes of the brain: revisiting connectomics and geometryPreprint
Sina Mansour, L., Behjat, H., Ville, D. V. D., Smith, R. E., Yeo, B. T. T., & Zalesky, A. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.04.16.589843 · Cited by 11
“Notably, due to the exponential decay in the prevalence of connections as a function of streamline length 12,14 , a stringent threshold (low density) is likely to disproportionately eliminate long-range connections 26,27 .”
BackgroundWang, M., Hou, Y., Magrou, L., Autio, J. A., Misery, P., Coalson, T., Reid, E., Xu, Y., Lamy, C., Falchier, A., et al. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.04.27.489651 · Cited by 18
“…models of the cerebral cortex and its spatially embedded nature (Bassett and Sporns, 2017; Beul et al., 2017; Burt et al., 2018; Chaudhuri et al., 2015; Ercsey-Ravasz et al., 2013; Froudist-Walsh et al., 2021; Goulas et al., 2019; Markov et al., 2013; Roberts et al., 2017; Theodoni et al., 2021).”
BackgroundChen, Y., Zhang, Z.-K., Yong He, A., & Zhou, C. (2020) · Cerebral Cortex · doi:10.1093/cercor/bhaa060 · Cited by 11
“Using a consistency-based thresholding method rather than a weight-based one can produce reliable connectomes of 30% density (Roberts et al. 2017).”
Metadata
- Authors
- Roberts, J. A., Perry, A., Roberts, G., Mitchell, P. B., & Breakspear, M.
- Affiliations
- QIMR Berghofer Medical Research Institute (AU)
- Black Dog Institute (AU)
- Corresponding author
- Roberts, James A.
- Venue
- NeuroImage
- Publisher
- Elsevier BV
- Published
- 2017-01
- Volume
- 145
- Issue
- Pt A
- Pages
- 118-129
- ISSN
- 1053-8119 (ISSN-L)
- OpenAlex
- W2523692751
- Cited by
- 189
- References
- 50
- Citations by year
- 2026: 18 · 2025: 19 · 2024: 19 · 2023: 23 · 2022: 25 · 2021: 20 · 2020: 19 · 2019: 17 · 2018: 20 · 2017: 8
- FWCI
- 13.30
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- NeuroImage (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Health and Medical Research Council (1037196)
- Australian Research Council (CE140100007)
- Topics
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Keywords
- human connectome, probabilistic tractography, long-distance connections, false positives, white matter connectivity
- MeSH terms
- Adolescent, Adult, Animals, Female, Humans, Image Processing, Computer-Assisted, Male, Nerve Net, Neural Pathways, Young Adult, Diffusion Tensor Imaging, Connectome, White Matter
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