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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Inter-subject connectome consistency may also be improved using other approaches such as consistency-based thresholding.
“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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“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).”
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DDParcel: Deep Learning Anatomical Brain Parcellation From Diffusion MRI
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“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).”
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“, 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 · see citing works
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 63 · see citing works
“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 · see citing works
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 · see citing works
Mareva, S., Akarca, D., The CALM team, & Holmes, J. (2022) · Journal of Child Psychology and Psychiatry · doi:10.1111/jcpp.13685 · Cited by 20 · see citing works
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 22 · see citing works
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 · see citing works
“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 · see citing works
“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 · see citing works
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 16 · see citing works
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 21 · see citing works
“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 · see citing works
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 13 · see citing works
Feng, G., Wang, Y., Huang, W., Chen, H., Cheng, J., & Shu, N. (2024) · eLife · doi:10.7554/elife.93325 · Cited by 15 · see citing works
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 13 · see citing works
“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., & Landman, B. (2022) · Medical Imaging · doi:10.1117/12.2611845 · Cited by 16
“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 · see citing works
“[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 · see citing works
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 13 · see citing works
“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 · see citing works
“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 8 · see citing works
“[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 · see citing works
“, 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
Gursoy, F., & Badur, B. (2020) · J. Complex Networks · doi:10.1093/comnet/cnab019 · Cited by 14
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 · see citing works
“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 15 · see citing works
“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 · see citing works
“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 · see citing works
“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 16 · see citing works
“…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 9 · see citing works
“Using a consistency-based thresholding method rather than a weight-based one can produce reliable connectomes of 30% density (Roberts et al. 2017).”
- 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 · 2016: 1
- 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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