Capturing the non-stationarity of whole-brain dynamics underlying human brain states

Brain dynamics depicts an extremely complex energy landscape that changes over time, and its characterisation is a central unsolved problem in neuroscience. We approximate the non-stationary landscape sustained by the human brain through a novel mathematical formalism that allows us characterise the attractor structure, i.e. the stationary points and their connections. Due to its time-varying nature, the structure of the global attractor and the corresponding number of energy levels changes over time. We apply this formalism to distinguish quantitatively between the different human brain states of wakefulness and different stages of sleep, as a step towards future clinical applications.J.A.G., I.G. and J.A.L have been partially supported by Spanish Ministerio de Economía y Competitividad and FEDER, projects MTM2015-63723-P, PGC2018-096540-B-I00, Proyecto US-1254251 del Fondo Europeo de Desarrollo Regional (FEDER) y la Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía, dentro del Programa Operativo FEDER 2014-2020 and Proyecto PAIDI 2020 P20_00592. S.S.P. is supported by the Research Project PGC2018-096641-B-I00 (Ministerio de Ciencia, Innovación y Universidades / Agencia Estatal de Investigación /FEDER, UE). G.D. is supported by the Spanish Research Project PSI2016-75688-P (Agencia Estatal de Investigacíon/Fondo Europeo de Desarrollo Regional, European Union); by the European Union’s Horizon 2020 Research and Innovation Programme under Grant Agreements 720270 (Human Brain Project [HBP] SGA1) and 785907 (HBP SGA2); and by the Catalan Agency for Management of University and Research Grants Programme 2017 SGR 1545. M.L.K. is supported by the European Research Council Consolidator Grant: CAREGIVING (615539) and Center for Music in the Brain, funded by the Danish National Research Foundation (DNRF117). H.L. and data acquisition were supported by the Bundesministerium für Bildung und Forschung (grant no. 01 EV 0703); H.L. and E.T. by the LOEWE Neuronale Koordination Forschungsschwerpunkt Frankfurt (NeFF); H.L. also by Christian-Albrechts-University Kiel and the CRC1261 (Deutsche Fors-chungsge-meinschaft). We thank Astrid Morzelewski for sleep scoring of the EEGs