The DOI matches its Crossref record; 241 of the 241 references it cites were found in a registry or an index.
Mathematical framework for large-scale brain network modeling in The Virtual Brain
Open accessAbstract
In this article, we describe the mathematical framework of the computational model at the core of the tool The Virtual Brain (TVB), designed to simulate collective whole brain dynamics by virtualizing brain structure and function, allowing simultaneous outputs of a number of experimental modalities such as electro- and magnetoencephalography (EEG, MEG) and functional Magnetic Resonance Imaging (fMRI). The implementation allows for a systematic exploration and manipulation of every underlying component of a large-scale brain network model (BNM), such as the neural mass model governing the local dynamics or the structural connectivity constraining the space time structure of the network couplings. Here, a consistent notation for the generalized BNM is given, so that in this form the equations represent a direct link between the mathematical description of BNMs and the components of the numerical implementation in TVB. Finally, we made a summary of the forward models implemented for mapping simulated neural activity (EEG, MEG, sterotactic electroencephalogram (sEEG), fMRI), identifying their advantages and limitations.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
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?
In the citing paper
“Models can involve highly parameterized simulations of regional activity (Hansen et al., 2015; Messe et al., 2014; Sanz-Leon et al., 2015), or sparser analytic predictions of FC using graph metrics of mutual communication (Goni et al., 2014; Grayson et al., 2016) (although, both approaches appear to be comparably effective; see Figure 1D).”
From Development of large-scale functional networks from birth to adulthood: A guide to the neuroimaging literature (2017) · cites this paper as Sanz-Leon et al., 2015
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., & Joliot, M. (2002) · NeuroImage · doi:10.1006/nimg.2001.0978 · Cited by 16,319
Desikan, R. S., Ségonne, F., Fischl, B., Quinn, B. T., Dickerson, B. C., Blacker, D., Buckner, R. L., Dale, A. M., Maguire, R. P., Hyman, B. T., et al. (2006) · NeuroImage · doi:10.1016/j.neuroimage.2006.01.021 · Cited by 13,324
Cortical Surface-Based Analysis
Dale, A. M., Fischl, B., & Sereno, M. I. (1999) · NeuroImage · doi:10.1006/nimg.1998.0395 · Cited by 10,910
Oostenveld, R., Fries, P., Maris, E., & Schoffelen, J.-M. (2011) · Computational Intelligence and Neuroscience · doi:10.1155/2011/156869 · Cited by 10,323
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
Statistical parametric maps in functional imaging: A general linear approach
Friston, K. J., Holmes, A. P., Worsley, K. J., Poline, J. ‐., Frith, C. D., & Frackowiak, R. S. J. (1994) · Human Brain Mapping · doi:10.1002/hbm.460020402 · Cited by 9,688
The organization of the human cerebral cortex estimated by intrinsic functional connectivity
Thomas Yeo, B. T., Krienen, F. M., Sepulcre, J., Sabuncu, M. R., Lashkari, D., Hollinshead, M., Roffman, J. L., Smoller, J. W., Zöllei, L., Polimeni, J. R., et al. (2011) · Journal of Neurophysiology · doi:10.1152/jn.00338.2011 · Cited by 9,182
The organization of the human cerebellum estimated by intrinsic functional connectivity
Buckner, R. L., Krienen, F. M., Castellanos, A., Diaz, J. C., & Yeo, B. T. T. (2011) · Journal of Neurophysiology · doi:10.1152/jn.00339.2011 · Cited by 7,304
Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging
Fox, M. D., & Raichle, M. E. (2007) · Nature Reviews Neuroscience · doi:10.1038/nrn2201 · Cited by 6,700
Brain magnetic resonance imaging with contrast dependent on blood oxygenation.
Ogawa, S., Lee, T. M., Kay, A. R., & Tank, D. W. (1990) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.87.24.9868 · Cited by 6,483
Flagged first, then by citations
Research works printed but not linked: 1
- Spiegler, 2015, The critical brain: dissipation and restin-state networks, PNAS
Cited by
Sorted by citations
Items 301–355 of 355
Spatiotemporal brain complexity quantifies consciousness outside of perturbation paradigmsPreprint
Breyton, M., Fousek, J., Rabuffo, G., Sorrentino, P., Kusch, L., Massimini, M., Petkoski, S., & Jirsa, V. (2025) · eLife · doi:10.7554/elife.98920.2 · Cited by 2
Self-citationCollocation Methods for Solving Two-Dimensional Neural Field Models on Complex Triangulated Domains
Martin, R., Chappell, D. J., Chuzhanova, N. A., et al. (2017) · Springer eBooks · doi:10.1007/978-3-319-59387-6_17
Biophysical modeling of the neural origin of EEG and MEG signalsPreprint
Næss, S., Halnes, G., Hagen, E., Hagler, D. J., Dale, A. M., Einevoll, G. T., & Ness, T. V. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.07.01.181875
“The Virtual Brain (TVB) is an excellent example of a software for whole-brain network simulations [Sanz-Leon et al., 2013, 2015; Ritter et al., 2013], where detailed and potentially personalized head models can be combined with tractography-based methods identifying the connectivity between brain…”
MethodOn higher order computations, rewiring the connectome, and non-von Neumann computer architecturePreprint
Ambroszkiewicz, S. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1603.02238
Sasaki, K., Yamamoto, T., Watanabe, I., et al. (2021) · American Journal of Sports Science · doi:10.11648/j.ajss.20210901.12
“Sociological predictive models are widely used in the field of information technology [10] and cerebral functions in biology [8, 11, 12].”
MethodSakthivadivel, D. A. R. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.04.19.440551
“The precise mathematical formulation of this brain network model is found in [28].”
BackgroundMitjans, A. G., Paz-Linares, D., Areces-González, A., Li, M., Wang, Y., Bringas-Vega, M., & Valdes-Sosa, P. A. (2020) · arXiv (Cornell University)
Data-driven computational modeling predicts “superhubs” play key role in epileptic dynamics
Muldoon, S. F. (2021) · Neuron · doi:10.1016/j.neuron.2021.07.024
MEG and Multimodal Integration
Ahlfors, S. P. (2019) · Springer eBooks · doi:10.1007/978-3-319-62657-4_7-1
KÜRKCÜ, S. (2022) · Ankara Üniversitesi Dil ve Tarih-Coğrafya Fakültesi Dergisi · doi:10.33171/dtcfjournal.2022.62.1.31
Multiscale cosimulation design template for neuroscience applicationsPreprint
Kusch, L., Diaz-Pier, S., Klijn, W., et al. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.07.13.499940
Self-citationThe effect of exogenously induced magnetic fields on neurotransmitter dynamicsPreprint
Rivas, M., & Martínez-Garcia, M. (2022) · Research Square · doi:10.21203/rs.3.rs-2028408/v1
Ellison, R., Matar, M., Gökoğlu, S. A., & Prabhu, R. K. (2022) · Research Square · doi:10.21203/rs.3.rs-2142272/v1
Image Guidance for Intracranial Surgery with Supervisory-Control Robots
Cardinale, F., Revay, M., d’Orio, P., Raspante, S., Bianchi, L. M. G., Al-Orabi, K., Berta, L., & Russo, G. L. (2022) · Springer eBooks · doi:10.1007/978-3-031-08380-8_4
Zhao, X., Chen, K., Wang, H., Gao, Y., Ji, X., & Li, Y. (2023) · Cognitive Neurodynamics · doi:10.1007/s11571-023-09941-3
“…including data-driven (Messe et al. 2014; Misic et al. 2016), model-based such as biophysical (Breakspear 2017; Deco et al. 2009; Honey et al. 2007; Sanz-Leon et al. 2015), and communication models (Crofts and Higham 2009; Goni et al. 2013; Graham and Rockmore 2011; Misic et al. 2015).”
A 2D Cortical Flat Map Space for Computationally Efficient Mammalian Brain Simulation
Woodward, A., Gong, R., Nakae, K., et al. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-45382-3_27
Feng, G., Wang, Y., Huang, W., Chen, H., Cheng, J., & Shu, N. (2024) · eLife · doi:10.7554/elife.93325.1
Stenroos, P., Guillemain, I., Tesler, F., Montigon, O., Collomb, N., Stupar, V., Alain Destexhe, A., Coizet, V., Olivier David, A., & Barbier, E. (2024) · eLife · doi:10.7554/elife.90318.2
Ellison, R., Matar, M., Gökoğlu, S. A., et al. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.05.13.593972
“…depends on module conceptualization and characteristics of the connectivity data (Sporns and Betzel, 2016), and the 76 brain regions in the primate connectome (Leon et al., 2013; Leon et al., 2015) is markedly less than that needed to identify meaningful modules (Fortunato and Barthélemy, 2007).”
BackgroundMethodInfluentialStenroos, P., Guillemain, I., Tesler, F., Montigon, O., Collomb, N., Stupar, V., Alain Destexhe, A., Coizet, V., Olivier David, A., & Barbier, E. (2024) · eLife · doi:10.7554/elife.90318.3
Jin, H., Abdelnour, F., Verma, P., Sipes, B. S., Nagarajan, S. S., & Raj, A. (2024) · Imaging Neuroscience · doi:10.1162/imag_a_00307
“…non-linear model solutions can be vastly different depending on the parameter regime, certain model parameters are hand-tuned to be near a bifurcation point and only the remaining parameters are optimized for by fitting to the empirical data, typically using a grid search optimization [85, 60].”
BackgroundAnaïs, V., Blanco, S., Chevallier, C., Eustache, F., Jacques Gautrais, A., Grandpeix, J., Joly, J., Segobin, S. H., & Gagnepain, P. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.03.26.645487
Transition in “Digital Brain” Researches, and Surrogate-based Generative Model
Okuno, T., Tsukada, H., & Hata, J. (2025) · The Brain & Neural Networks · doi:10.3902/jnns.32.12
Monteverdi, A., Ramusino, M. C., Conca, F., et al. (2025) · Research Square · doi:10.21203/rs.3.rs-6550081/v1
Hater, T., Courson, J., Lu, H., Diaz-Pier, S., & Manos, T. (2025) · PubMed · doi:10.48550/arxiv.2505.16861 · Cited by 1
Effective workflow from multimodal MRI data to model-based prediction
Jung, K., Wischnewski, K. J., Eickhoff, S. B., & Popovych, O. V. (2025) · Scientific Reports · doi:10.1038/s41598-025-04511-5
Siu, P. H., Karoly, P. J., Sina Mansour, L., Soto-Breceda, A., Kuhlmann, L., Cook, M. J., & Grayden, D. B. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.07.27.667083
“The most common implementation of the Epileptor model, as implemented in the Virtual Brain Project (TVB) [51], characterises the dynamical behaviour of epileptic seizures using five state variables ( x 1 , y 1 , x 2 , y 2 , z ) plus a dummy variable ( u ) within region i [49].”
Steeghs-Turchina, M., Srinivasan, R., Nunez, P. L., & Nunez, M. D. (2025) · NeuroImage · doi:10.1016/j.neuroimage.2025.121418
Ziaeemehr, A., Woodman, M., Domide, L., Petkoski, S., Jirsa, V., & Hashemi, M. (2025) · eLife · doi:10.7554/elife.106194.3 · Cited by 2
Self-citationGaglioti, G., Cardinale, A., Lupo, C., Nieus, T. R., Marmoreo, F., Focacci, E., Gutzen, R., Denker, M., Pigorini, A., Massimini, M., et al. (2026) · Neurocomputing · doi:10.1016/j.neucom.2026.132735
Hong, X., Lin, Y.-S., & Wu, Z. (2025) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2025.3646479
“Brain regions communicate via neural networks, and signal transmission requires finite time, resulting in measurable interregional delays [35], [36].”
From Ions to Chaos: exploring a whole-brain modelling framework in the mousePreprint
Lagunas, S. A. M., An, J., Stefanovski, L., & Ritter, P. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2025.12.04.691835
Pelz, M., Janušonis, S., & Handy, G. (2026) · SIAM Journal on Life Sciences · doi:10.1137/25m1827852
“It is important to note that a number of advanced software platforms simulate neural dynamics at multiple scales, including NEURON [37], tools from the Open Brain Institute [41], and The Virtual Brain [87].”
Digital twins support cross-modal and cross-centric classification of mild cognitive impairment
Amato, L. G., Minino, R., Lassi, M., et al. (2026) · Communications Medicine · doi:10.1038/s43856-025-01281-z
Vallet, A., Blanco, S., Chevallier, C., Eustache, F., Jacques Gautrais, A., Grandpeix, J., Joly, J., Segobin, S. H., & Gagnepain, P. (2026) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1014035
Monteverdi, A., Ramusino, M. C., Conca, F., Augello, A., Totaro, C., Grasso, P. A., Castelnovo, A., Lorenzi, R. M., Terzaghi, M., Farina, L. M., et al. (2026) · Research Square · doi:10.21203/rs.3.rs-9181475/v1
Development of a computational and neuroinformatics framework for large-scale brain modelling
Sanz‐Leon, P. (2014) · theses.fr (ABES) · doi:10.70675/95aa5361zb69ez4251z8f52zdb68cf9af526
Self-citationEpidynamics : seizures in the unfolding of a high codimension singularity
Saggio, M. L. (2018) · theses.fr (ABES) · doi:10.70675/9c5e2f9az0a05z4e15zbfa9zd3c1c14c0106
Resting-state dynamics in epilepsy : mechanistic insights from large-scale brain network modeling
Courtiol, J. (2020) · theses.fr (ABES) · doi:10.70675/0e102279zeb19z4f46zbf0ezbf7bdf9dd296
Modeling and analysis of spatiotemporal dynamics of patients with Alzheimer’s disease
Arbabyazd, L. (2021) · theses.fr (ABES) · doi:10.70675/b101b126z96c0z43d7z9500z89e423a07a72
Bouté, J. (2023) · theses.fr (ABES) · doi:10.70675/966a40d5za9f3z4912zb2e7z569a1ee3f16d
Fabbrizzi, M., Amato, L. G., Martinelli, L., Carpaneto, J., Bartolini, E., Calderoni, S., Retico, A., Vergani, A. A., & Mazzoni, A. (2026) · PLOS Digital Health · doi:10.1371/journal.pdig.0001445
“In order to reduce computational time, the cortical mesh was downsampled from FreeSurfer’s original fsaverage with 327680 triangles to the fsaverage5, which has 20,484 vertices and 40,960 triangles (for comparison, the TVB default cortical mesh [35] uses 16,384 vertices and 32,760 triangles).”
Virant, R., & Linne, M. (2026) · Communications in computer and information science · doi:10.1007/978-3-032-28819-6_20
The structural grammar of integration and competition in the human connectome
Kelemen, S. F., Goñi, J., Pequito, S., & Ashourvan, A. (2026) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2026.1810942 · Cited by 1
Schmitt, O., Morawska, P., Prathapan, V., & Eipert, P. (2026) · The Cerebellum · doi:10.1007/s12311-026-02042-x
Brain Network Excitability Predicts Clinical Severity in Multiple SclerosisPreprint
Amato, L. G., Angiolelli, M., Demuru, M., Lopez, E. T., Quarantelli, M., Granata, C., Depannemaecker, D., Jirsa, V., Bonavita, S., Mazzoni, A., et al. (2026) · medRxiv · doi:10.64898/2026.07.10.26357763
Self-citationIn silico methodologies in computational medicine: From complex disease modeling to virtual clinics
Italia, M., Otero, J. G., Azzimonti, L., García‐Aznar, J. M., Dercole, F., & Belmonte-Beitia, J. (2026) · Biophysics Reviews · doi:10.1063/5.0285118
Seizure recruitment properties are dependent upon dynamotype: A modeling study
Karosas, D. M., Saggio, M. L., & Stacey, W. C. (2026) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1013975
“Neural mass models other than the Epileptor can be implemented in the virtual brain framework [30].”
Biophysically inspired mean-field model of neuronal populations driven by ion-exchange mechanisms
Rabuffo, G., Bandyopadhyay, A., Calabrese, C., Gudibanda, K., Depannemaecker, D., Takarabe, L. M., Chatterjee, S., Saggio, M. L., Desroches, M., Ivanov, A., et al. (2026) · eLife · doi:10.7554/elife.104249.3
Self-citationMechanistic versus descriptive interpretation of brain activity pattern reconstruction
Jung, K., Eickhoff, S. B., & Patil, K. R. (2026) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2609630123
Metadata
- Authors
- Sanz-Leon, P., Knock, S. A., Spiegler, A., & Jirsa, V. K.
- Affiliations
- QIMR Berghofer Medical Research Institute (AU)
- Inserm (FR)
- Corresponding author
- Jirsa, Viktor K.
- Venue
- NeuroImage
- Publisher
- Elsevier BV
- Published
- 2015-05
- Volume
- 111
- Pages
- 385-430
- ISSN
- 1053-8119 (ISSN-L)
- OpenAlex
- W2074725578
- Semantic Scholar
- 23be65f2b2fee15432e3086c0d98a6610709848f
- Cited by
- 356
- References
- 240
- Citations by year
- 2026: 27 · 2025: 53 · 2024: 41 · 2023: 34 · 2022: 37 · 2021: 36 · 2020: 29 · 2019: 23 · 2018: 25 · 2017: 21 · 2016: 15 · 2015: 13
- FWCI
- 14.82
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- NeuroImage (publishedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- Funders
- James S. McDonnell Foundation (FP7-ICT BrainScales - 2009-6)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
- Keywords
- The Virtual Brain, whole-brain dynamics, neural mass model, structural connectivity, forward model, EEG, MEG, functional MRI, stereoelectroencephalography, mathematical notation, computational neuroscience simulation
- MeSH terms
- Brain, Humans, Models, Neurological, Nerve Net, Functional Neuroimaging
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
