Abstract
Electroencephalography (EEG) is among the most widely diffused, inexpensive, and adopted neuroimaging techniques. Nonetheless, EEG requires measurements against a reference site(s), which is typically chosen by the experimenter, and specific pre-processing steps precede analyses. It is therefore valuable to obtain quantities that are minimally affected by reference and pre-processing choices. Here, we show that the topological structure of embedding spaces, constructed either from multi-channel EEG timeseries or from their temporal structure, are subject-specific and robust to re-referencing and pre-processing pipelines. By contrast, the shape of correlation spaces, that is, discrete spaces where each point represents an electrode and the distance between them that is in turn related to the correlation between the respective timeseries, was neither significantly subject-specific nor robust to changes of reference. Our results suggest that the shape of spaces describing the observed configurations of EEG signals holds information about the individual specificity of the underlying individual’s brain dynamics, and that temporal correlations constrain to a large degree the set of possible dynamics. In turn, these encode the differences between subjects’ space of resting state EEG signals. Finally, our results and proposed methodology provide tools to explore the individual topographical landscapes and how they are explored dynamically. We propose therefore to augment conventional topographic analyses with an additional—topological—level of analysis, and to consider them jointly. More generally, these results provide a roadmap for the incorporation of topological analyses within EEG pipelines.
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Data Availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
References
Bari S, Amico E, Vike N, Talavage TM, Goñi J (2019) Uncovering multi-site identifiability based on resting-state functional connectomes. NeuroImage 202:115967
Bassett DS, Sporns O (2017) Network neuroscience. Nat Neurosci 20(3):353–364
Battiston F, Cencetti G, Iacopini I, Latora V, Lucas M, Patania A, Young JG, Petri G (2020) Networks beyond pairwise interactions: structure and dynamics. Phys Rep 874:1–892
Betzel RF, Byrge L, He Y, Goñi J, Zuo XN, Sporns O (2014) Changes in structural and functional connectivity among resting-state networks across the human lifespan. NeuroImage 102:345–357
Biasiucci A, Franceschiello B, Murray MM (2019) Electroencephalography. Curr Biol 29(3):R80–R85. https://doi.org/10.1016/j.cub.2018.11.052
Billings J, Saggar M, Hlinka J, Keilholz S, Petri G (2021) Simplicial and topological descriptions of human brain dynamics. Netw Neurosci. https://doi.org/10.1162/netn_a_00190
Cavanna NJ, Jahanseir M, Sheehy D (2015) A geometric perspective on sparse filtrations. In: Proceedings of the 27th Canadian conference on computational geometry, CCCG 2015, Kingston, Ontario, Canada, August 10–12, 2015, Queen’s University, Ontario, Canada
Chan HL, Kuo PC, Cheng CY, Chen YS (2018) Challenges and future perspectives on electroencephalogram-based biometrics in person recognition. Front Neuroinform 12:66. https://doi.org/10.3389/fninf.2018.00066
Chella F, Pizzella V, Zappasodi F, Marzetti L (2016) Impact of the reference choice on scalp EEG connectivity estimation. J Neural Eng 13(3):36016
Delorme A, Makeig S (2004) EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J Neurosci Methods 134(1):9–21
Deyle ER, Sugihara G (2011) Generalized theorems for nonlinear state space reconstruction. PLoS ONE 6(3):e18295. https://doi.org/10.1371/journal.pone.0018295
Donato I, Gori M, Pettini M, Petri G, De Nigris S, Franzosi R, Vaccarino F (2016) Persistent homology analysis of phase transitions. Phys Rev E 93(5):52138
Edelsbrunner H, Harer J (2008) Persistent homology—a survey. Contemp Math 453:257–282
Fulekar MH (2009) Bioinformatics: applications in life and environmental sciences. Springer Science & Business Media, Boston
Ghrist R (2008) Barcodes: The persistent topology of data. https://doi.org/10.1090/S0273-0979-07-01191-3
Giusti C, Pastalkova E, Curto C, Itskov V (2015) Clique topology reveals intrinsic geometric structure in neural correlations. Proc Natl Acad Sci USA 112(44):13455–13460
Giusti C, Ghrist R, Bassett DS (2016) Twos company, three (or more) is a simplex. J Comput Neurosci 41(1):1–14
Grave de Peralta Menendez R, Gonzalez Andino S, Morand S, Michel C, Landis T (2000) Imaging the electrical activity of the brain: ELECTRA. Hum Brain Mapp 9(1):1–12
Haufe S, Ewald A (2019) A simulation framework for benchmarking EEG-based brain connectivity estimation methodologies. Brain Topogr 32(4):625–642
Hu S, Yao D, Bringas-Vega ML, Qin Y, Valdes-Sosa PA (2019) The statistics of eeg unipolar references: derivations and properties. Brain Topogr 32(4):696–703
Hutchison RM, Womelsdorf T, Allen EA, Bandettini PA, Calhoun VD, Corbetta M, Della Penna S, Duyn JH, Glover GH, Gonzalez-Castillo J et al (2013) Dynamic functional connectivity: promise, issues, and interpretations. NeuroImage 80:360–378
Iacopini I, Petri G, Barrat A, Latora V (2019) Simplicial models of social contagion. Nat Commun 10(1):1–9
Ibáñez-Marcelo E, Campioni L, Manzoni D, Santarcangelo EL, Petri G (2019a) Spectral and topological analyses of the cortical representation of the head position: does hypnotizability matter? Brain Behav 9(6):e01277
Ibáñez-Marcelo E, Campioni L, Phinyomark A, Petri G, Santarcangelo EL (2019b) Topology highlights mesoscopic functional equivalence between imagery and perception: the case of hypnotizability. NeuroImage 200:437–449
Kelley K, Preacher KJ (2012) On effect size. Psychol Methods 17(2):137
Lee S, Kang H, Chung MK, Kim BN, Lee DS (2012) Persistent brain network homology from the perspective of dendrogram. IEEE Trans Med Imaging 31(12):2267–2277
Lehmann D (1987) Principles of spatial analysis. In: Gevins A, Rémond A (eds) Handbook of electroencephalography and clinical neurophysiology: methods of analysis of brain electrical and magnetic signals, vol 1. Elsevier, Amsterdam, pp 309–354
Lehmann D, Michel CM (2011) EEG-defined functional microstates as basic building blocks of mental processes. Clin Neurophysiol 122(6):1073–1074. https://doi.org/10.1016/j.clinph.2010.11.003
Leon PS, Knock SA, Woodman MM, Domide L, Mersmann J, McIntosh AR, Jirsa V, Marinazzo D, Plesser HE (2013) The virtual brain: a simulator of primate brain network dynamics. Front Neuroinform. https://doi.org/10.3389/fninf.2013.00010
Lepage KQ, Kramer MA, Chu CJ (2014) A statistically robust EEG re-referencing procedure to mitigate reference effect. J Neurosci Methods 235:101–116. https://doi.org/10.1016/j.jneumeth.2014.05.008
Luck SJ (2014) An introduction to the event-related potential technique. A Bradford book. MIT Press. https://books.google.com/books?id=SzavAwAAQBAJ
Marcel S, Millan JDR (2007) Person authentication using brainwaves (EEG) and maximum a posteriori model adaptation. IEEE Trans Pattern Anal Mach Intell 29(4):743–752
Marinazzo D, Riera JJ, Marzetti L et al (2019) Controversies in EEG source imaging and connectivity: modeling, validation, benchmarking. Brain Topogr 32:527–529. https://doi.org/10.1007/s10548-019-00709-9
Michel CM, Murray MM (2012) Towards the utilization of EEG as a brain imaging tool. NeuroImage 61(2):371–385. https://doi.org/10.1016/j.neuroimage.2011.12.039
Michel CM, Thut G, Morand S, Khateb A, Pegna AJ, Grave de Peralta R, Gonzalez S, Seeck M, Landis T (2001) Electric source imaging of human brain functions. Brain Res Rev 36(2):108–118. https://doi.org/10.1016/S0165-0173(01)00086-8
Michel CM, Murray MM, Lantz G, Gonzalez S, Spinelli L, Grave de Peralta R (2004) EEG source imaging. Clin Neurophysiol 115(10):2195–2222. https://doi.org/10.1016/j.clinph.2004.06.001
Michel CM, Koenig T, Brandeis D, Gianotti LR, Wackermann J (2009) Electrical neuroimaging. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511596889
Murray MM, Brunet D, Michel CM (2008) Topographic ERP analyses: a step-by-step tutorial review. Brain Topogr 20(4):249–264. https://doi.org/10.1007/s10548-008-0054-5
Myers A, Munch E, Khasawneh FA (2019) Persistent homology of complex networks for dynamic state detection. Phys Rev E 100(2):22314
Noakes L (1991) The Takens embedding theorem. Int J Bifurcat Chaos 1(04):867–872
Perrin F, Pernier J, Bertrand O, Echallier JF (1989) Spherical splines for scalp potential and current density mapping. Electroencephalogr Clin Neurophysiol 72(2):184–187
Petri G, Scolamiero M, Donato I, Vaccarino F (2013) Topological strata of weighted complex networks. PLoS ONE 8(6):e66506
Petri G, Expert P, Turkheimer F, Carhart-Harris R, Nutt D, Hellyer PJ, Vaccarino F (2014) Homological scaffolds of brain functional networks. J R Soc Interface 11(101):20140873
Poulos M, Rangoussi M, Alexandris N (1999) Neural network based person identification using EEG features. In: Proceedings—1999 IEEE international conference on acoustics, speech, and signal processing, vol 2. ICASSP99 (Cat. No. 99CH36258), IEEE, pp 1117–1120
Rajapandian M, Amico E, Abbas K, Ventresca M, Goñi J (2020) Uncovering differential identifiability in network properties of human brain functional connectomes. Netw Neurosci 4(3):698–713
Reininghaus J, Huber S, Bauer U, Kwitt R (2015) A stable multi-scale kernel for topological machine learning. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 4741–4748
Sakkalis V (2011) Review of advanced techniques for the estimation of brain connectivity measured with EEG/MEG. Comput Biol Med 41(12):1110–1117
Sawilowsky SS (2009) New effect size rules of thumb. J Mod Appl Stat Methods 8(2):26
Schirner M, Domide L, Perdikis D, Triebkorn P, Stefanovski L, Pai R, Popa P, Valean B, Palmer J, Langford C, Blickensdörfer A, van der Vlag M, Diaz-Pier S, Peyser A, Klijn W, Pleiter D, Nahm A, Schmid O, Woodman M, Zehl L, Fousek J, Petkoski S, Kusch L, Hashemi M, Marinazzo D, Mangin JF, Flöel A, Akintoye S, Stahl BC, Cepic M, Johnson E, Deco G, McIntosh AR, Hilgetag CC, Morgan M, Schuller B, Upton A, McMurtrie C, Dickscheid T, Bjaalie JG, Amunts K, Mersmann J, Jirsa V, Ritter P (2021) Brain modelling as a service: the virtual brain on EBRAINS. arXiv preprint. http://arxiv.org/abs/2102.05888
Sporns O (2013) Network attributes for segregation and integration in the human brain. Curr Opin Neurobiol 23(2):162–171
Tenke CE, Kayser J (2005) Reference-free quantification of EEG spectra: combining current source density (CSD) and frequency principal components analysis (fPCA). Clin Neurophysiol 116(12):2826–2846
Tivadar RI, Retsa C, Turoman N, Matusz PJ, Murray MM (2018) Sounds enhance visual completion processes. NeuroImage 179:480–488
Tivadar RI, Murray MM, Tivadar RI, Murray MM (2019) A primer on electroencephalography and event-related potentials for organizational neuroscience. Organ Res Methods 22(1):69–94. https://doi.org/10.1177/1094428118804657
Varley TF, Denny V, Sporns O, Patania A (2020) Topological analysis of differential effects of ketamine and propofol anesthesia on brain dynamics. bioRxiv
Vaughan HG (1982) The neural origins of human event-related potentials. Ann N Y Acad Sci 388(1):125–138
Wong PKH (2012) Introduction to brain topography. Springer Science & Business Media, Boston
Yao D, Qin Y, Hu S, Dong L, Vega M, Sosa PAV (2019) Which reference should we use for EEG and ERP practice? Brain Topogr 32(4):530–549. https://doi.org/10.1007/s10548-019-00707-x
Zomorodian A, Carlsson G (2005) Computing persistent homology. Discrete Comput Geom 33(2):249–274
Funding
B.F. and M.M.M. are supported by the Fondation Asile des aveugles (Grant Number 232933 to M.M.M.). M.M.M. is also supported by The Swiss National Science Foundation (Grant Number 169206). R.T. is supported by the Swiss National Science Foundation (#320030_188737). G.P. and J.B. acknowledge support during the preparation of this work from Intesa Sanpaolo Innovation Center. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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MMM, BF and GP conceived the study. RT gathered and pre-processed the data. JB structured and carried out the topological data analysis over the three embedding types. BF, GP, JB and RT interpreted together the results. RT and JB wrote the first draft of the manuscript. BF supervised the neuroscientific contents and GP the topological ones. All authors contributed to the final draft and review.
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Billings, J., Tivadar, R., Murray, M.M. et al. Topological Features of Electroencephalography are Robust to Re-referencing and Preprocessing. Brain Topogr 35, 79–95 (2022). https://doi.org/10.1007/s10548-021-00882-w
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DOI: https://doi.org/10.1007/s10548-021-00882-w