Skip to main content

Main menu

  • HOME
  • CONTENT
    • Early Release
    • Featured
    • Current Issue
    • Issue Archive
    • Blog
    • Collections
    • Podcast
  • TOPICS
    • Cognition and Behavior
    • Development
    • Disorders of the Nervous System
    • History, Teaching and Public Awareness
    • Integrative Systems
    • Neuronal Excitability
    • Novel Tools and Methods
    • Sensory and Motor Systems
  • ALERTS
  • FOR AUTHORS
  • ABOUT
    • Overview
    • Editorial Board
    • For the Media
    • Privacy Policy
    • Contact Us
    • Feedback
  • SUBMIT

User menu

Search

  • Advanced search
eNeuro
eNeuro

Advanced Search

 

  • HOME
  • CONTENT
    • Early Release
    • Featured
    • Current Issue
    • Issue Archive
    • Blog
    • Collections
    • Podcast
  • TOPICS
    • Cognition and Behavior
    • Development
    • Disorders of the Nervous System
    • History, Teaching and Public Awareness
    • Integrative Systems
    • Neuronal Excitability
    • Novel Tools and Methods
    • Sensory and Motor Systems
  • ALERTS
  • FOR AUTHORS
  • ABOUT
    • Overview
    • Editorial Board
    • For the Media
    • Privacy Policy
    • Contact Us
    • Feedback
  • SUBMIT
PreviousNext
Research ArticleResearch Article: New Research, Novel Tools and Methods

Neuronal Cascades Shape Whole-Brain Functional Dynamics at Rest

Giovanni Rabuffo, Jan Fousek, Christophe Bernard and Viktor Jirsa
eNeuro 28 September 2021, 8 (5) ENEURO.0283-21.2021; https://doi.org/10.1523/ENEURO.0283-21.2021
Giovanni Rabuffo
Aix Marseille University, INSERM, INS, Institut de Neurosciences des Systèmes, 13005 Marseille, France
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Jan Fousek
Aix Marseille University, INSERM, INS, Institut de Neurosciences des Systèmes, 13005 Marseille, France
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Christophe Bernard
Aix Marseille University, INSERM, INS, Institut de Neurosciences des Systèmes, 13005 Marseille, France
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Viktor Jirsa
Aix Marseille University, INSERM, INS, Institut de Neurosciences des Systèmes, 13005 Marseille, France
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • Article
  • Figures & Data
  • Info & Metrics
  • eLetters
  • PDF
Loading

Article Figures & Data

Figures

  • Tables
  • Extended Data
  • Figure
    • Download figure
    • Open in new tab
    • Download powerpoint
  • Figure 1.
    • Download figure
    • Open in new tab
    • Download powerpoint
    Figure 1.

    Connectome based modeling. A, The mean firing rate r and membrane potential V variables of the NMM are derived as the limit of infinite all-to-all coupled QIF neurons. Applying the Balloon–Windkessel model to V n(t) we obtain the simulated BOLD signal Bn(t) at node n. B, The phase plane of each decoupled node (Iext = 0) has a “down” stable fixed point and an “up” stable focus (full dots). These points are defined at the intersection of the nullclines r˙=0 (orange line) and V˙=0 (green line) where the dynamics freezes. The empty circle marks an unstable fixed point. As the external current Iext is increased, the phase plane of the neural mass changes (see equations in Materials and Methods). In particular, the basin of attraction of the up state gradually becomes larger than that of the down state, while the fixed points move farther apart. C, D, The mouse connectome and structural connectivity Wnm were imported from the tracer experiments of the Allen Institute. The 104 cortical ROIs (corresponding to network nodes) are specified in Table 1. E, When the regions are coupled in a brain network, each node n receives an input current Iext which is the sum of the other nodes’ firing rates, weighted by the structural connectivity. According to panel B, this input provokes a distortion of the local phase plane at node n.

  • Figure 2.
    • Download figure
    • Open in new tab
    • Download powerpoint
    Figure 2.

    Two regimes of dFC. A, Given two nodes n and m the edge CA signal Enm(t) (orange box) is defined as the product of the z-scored BOLD signal Bn(t) and Bm(t). Averaging the BOLD-CA matrix over time we obtain the Pearson correlation across each pair of brain regions n and m (in black box, right), defining the static FC. Each column of the BOLD-CA matrix represents an istantaneous realization of the FC (iFC). B, The elements (ti, tj) of the dFCe matrix are defined as the Pearson correlation between iFC(ti) and iFC(tj). Note in panel A the presence of transient bouts of strong BOLD-CA (e.g., in the blue boxes). During these events, the iFC remains relatively correlated for few consecutive time points, which gives rise to diagonal (yellow) blocks in the dFCe matrix. The same CA burst (e.g., at ti) can re-occur in time after long periods of time (e.g., at tj), which gives rise to an off-diagonal dFCe block (e.g., at the crossing of the dashed lines in panel B).

  • Figure 3.
    • Download figure
    • Open in new tab
    • Download powerpoint
    Figure 3.

    Two qualitatively distinct regimes of non-trivial functional dynamics. For every couple of global parameters (G, N) we calculated the dFC in a sliding window approach (dFCw; as in Materials and Methods) and in an edge-centric approach (dFCe; as in Fig. 2A,B). The “switching index” of each dFCw matrix was evaluated as the variance of the respective upper triangular elements. We find two regimes of activity, named monostable and bistable, where qualitatively distinct neuroelectric organizations give rise to large-scale functional dynamics characterized by a non-vanishing switching index. In both regimes, the dFCw and dFCe display off-diagonal blocks, demonstrating a correlation between the functional activity at distinct times. The low global coupling G in the monostable regime (bottom left) does not guarantee a strong communication between the brain network regions, which most of the time populate the low firing rate (“down”) state. A strong noise N pushes the brain regions in the high firing rate (“up”) state for short transients. A higher value of the global coupling in the bistable regime (bottom right) promotes a subgroup of regions in the high firing rate (up) state. Low levels of noise perturb the equilibrium of the system provoking localized switching in both up →down and down →up directions (e.g., at t = 200 ms).

  • Figure 4.
    • Download figure
    • Open in new tab
    • Download powerpoint
    Figure 4.

    Mechanisms of cascade generation in the synthetic model. A, Different regions have a different fate depending on their location in the connectome. We classified the regions in five classes (D, U, J, D*, U*) according to their activity. B, Example exploration of the projected 2D phase space (top) and firing rates activity (bottom) of the “up-U” (light red), “down-D” (light blue), and “jumping-J” (green) regions. C, Distribution of the standardized firing rates in different classes. Class (J) regions have two modes but never cross the ±3 σ threshold (black lines). Class (U*) (dark blue) and class (D*) (dark red) regions dwell most of the time in the up and down states, respectively. Only in important rare occasions the *-regions cross the threshold to jump on the other side, substantially deviating from their baseline activity. The leading role of the *-regions as compared with the other classes is shown using PCA in Extended Data Figure 4-1A,B. D, Example of a cascade: when the (U*) node 63 jumps into the down state, it first drags down the node 62 (with which it shares the strongest structural link in the network). After them, other strongly connected nodes follow the trend.

  • Figure 5.
    • Download figure
    • Open in new tab
    • Download powerpoint
    Figure 5.

    RSN formation. A, top, The standardized firing rate activity in the (U*) and (D*) classes (class-specific average; dark red and dark blue, respectively) is characterized by peaks (the strongest are marked as I, II, III, IV) occurring in correspondence of cascades similar to Figure 4D. A, middle, During a cascade, we also observe a peak of BOLD-CAs, appearing as vertical strips. Many, but not all, edges are recruited. A, bottom, The blocks in the dFCe matrix appear in correspondence of CA events, showing that these bursts generate stable epochs of FC correlated in time. B, In each selected epoch (I, II and III, IV), the large firing rate cascades trigger the jump of other nodes away from baseline activity (circled in black) and promote specific functional hubs at the BOLD level, represented by colored nodes in the network plots. A functional hub is defined by the components of the first leading eigenvector (linear combination of brain regions explaining most of the variance in the data; eigenvalue λ > 0.41) associated to the iFCs at times tI,tII,tIII , and tIV, respectively. The most representative hub regions are depicted in yellow. Gray regions have been excluded as they do not contribute substantially. Only the edges with the highest CAs are displayed. Importantly, CA events generated from neuronal cascades at specific sites support distinct functional networks which are not correlated among themselves (e.g., no off-diagonal dFCe block between I and III).

  • Figure 6.
    • Download figure
    • Open in new tab
    • Download powerpoint
    Figure 6.

    Neuronal cascades and neuronal avalanches. A, Standardized EEG activity extracted from a resting-state human EEG/fMRI dataset (top). The activity is binarized assigning a unitary/null value every time the activity in a region is above/below a certain threshold (e.g., ±3 σ; black lines). The obtained binary raster plot (bottom) is characterized by intermittent epochs of deviations from baseline activity. Neuronal avalanches are defined as consecutive deviations from baseline activity (e.g., red box). B, We extract the global magnitude of the deviations from baseline (top, gray signal) by summing the binary EEG raster plot over the ROIs. This signal is convoluted with a Gaussian kernel [width = 1 BOLD TR] and downsampled to obtain the same resolution of the BOLD activity, which defines the neuronal cascades signal (blue). Neuronal cascades can be thought of as clustering of high magnitude avalanches, whose occurrence in time is not homogeneous (bottom).

  • Figure 7.
    • Download figure
    • Open in new tab
    • Download powerpoint
    Figure 7.

    Neuronal cascades drive the functional dynamics. A, Example of neuronal cascades in the monostable and bistable synthetic regime and for a representative subject of the empiric EEG/fMRI human dataset. B, The BOLD-CA in simulated and empiric mouse and human datasets (middle panels) are characterized by sudden collective events involving large network parts (vertical stripes). The root sum square of BOLD-CA across all edges (RSS, green lines, top panels) defines the global CA amplitude signal for each dataset. Concurrently, the dFCe matrices (bottom panels) display both diagonal and off-diagonal blocks, remarking the non-trivial re-occurrence of the same stable functional network at distinct times (see Fig. 2B). At a visual inspection, the BOLD-CA events happen in coincidence with dFCe blocks and, most notably, the neuronal cascades and RSS signals (blue and green lines in panels B, C, respectively) co-fluctuate in most instances.

  • Figure 8.
    • Download figure
    • Open in new tab
    • Download powerpoint
    Figure 8.

    A, The largest BOLD-CAs events (CA, above the 98th percentile of the RSS; Fig. 4C, green line) are distinguished from non-events (nCA, below threshold). We report the synthetic and empiric correlations between iFCs at times within CA events (left in every panel), between CA events and non-events nCA (center of panels), within non-events nCA (right of panels). These correlations are by definition the off-diagonal values of the dFCe matrix (see Fig. 2A,B). The distribution of the correlations within events is wider and explains the greatest off-diagonal correlation values of the dFCe across all the synthetic and empiric datasets. This principle is explicitly shown in panel B, where the original dFCe extracted from an empiric human trial (top) was sorted according to increasing RSS (bottom), leading to the clustering of high correlations toward high CA times. This shows that most of the non-trivial temporal correlations involve CA times falling in the last quartile of the RSS (above the 75th percentile, central green line). Thus, the strongest CA events drive the dynamics of FC.

  • Figure 9.
    • Download figure
    • Open in new tab
    • Download powerpoint
    Figure 9.

    A, top, Correlation between the cascade magnitude and the BOLD-CA amplitude (Fig. 4B,C, blue and green lines) for different time lags in several EEG/fMRI trials extracted from a Human cohort of resting subjects. Negative lag is associated with a shift backward of the BOLD signal. A, bottom, The cross-correlation averaged across trials shows a clear trend (blue line). The peak of correlation at lag –2 sampling points (1 pt = 1.94 s), as well as the rapid fall for positive lags, confirms that the EEG precedes the BOLD activity by few seconds. The same profile is evaluated by comparing the largest cascades with the BOLD-CA signals extracted from 1000 time-shuffled (example in green), 1000 phase-randomized (cross-spectrum preserved, example in orange), and 1000 phase-randomized (cross-spectrum not preserved, example in red) BOLD surrogates for every subject (see Extended Data Fig. 9-1A,B for surrogate properties). B, The distribution of the mean, maximum, and variance of the cross-correlations for each surrogate model is displayed and compared with the empiric values. In particular, the variance plot shows a clear significance of the results (single subject results in Extended Data Fig. 9-1C).

Tables

  • Figures
  • Extended Data
    • View popup
    Table 1

    List of brain ROIs of the Allen Mouse Atlas considered in the simulations

    ROI ID:ROI name:ROI ID:ROI name:
    0Right primary motor area52Left primary motor area
    1Right secondary motor area53Left secondary motor area
    2Right primary somatosensory area, nose54Left primary somatosensory area, nose
    3Right primary somatosensory area, barrel field55Left primary somatosensory area, barrel field
    4Right primary somatosensory area, lower limb56Left primary somatosensory area, lower limb
    5Right primary somatosensory area, mouth57Left primary somatosensory area, mouth
    6Right primary somatosensory area, upper limb58Left primary somatosensory area, upper limb
    7Right supplemental somatosensory area59Left supplemental somatosensory area
    8Right gustatory areas60Left gustatory areas
    9Right visceral area61Left Visceral area
    10Right dorsal auditory area62Left dorsal auditory area
    11Right primary auditory area63Left primary auditory area
    12Right ventral auditory area64Left ventral auditory area
    13Right primary visual area65Left primary visual area
    14Right anterior cingulate area, dorsal part66Left anterior cingulate area, dorsal part
    15Right anterior cingulate area, ventral part67Left anterior cingulate area, ventral part
    16Right agranular insular area, dorsal part68Left agranular insular area, dorsal part
    17Right retrosplenial area, dorsal part69Left retrosplenial area, dorsal part
    18Right retrosplenial area, ventral part70Left retrosplenial area, ventral part
    19Right temporal association areas71Left temporal association areas
    20Right perirhinal area72Left perirhinal area
    21Right ectorhinal area73Left ectorhinal area
    22Right main olfactory bulb74Left main olfactory bulb
    23Right anterior olfactory nucleus75Left anterior olfactory nucleus
    24Right piriform area76Left piriform area
    25Right cortical amygdalar area, posterior part77Left cortical amygdalar area, posterior part
    26Right field CA178Left field CA1
    27Right field CA379Left field CA3
    28Right dentate gyrus80Left dentate gyrus
    29Right entorhinal area, lateral part81Left entorhinal area, lateral part
    30Right entorhinal area, medial part, dorsal zone82Left entorhinal area, medial part, dorsal zone
    31Right subiculum83Left subiculum
    32Right caudoputamen84Left caudoputamen
    33Right nucleus accumbens85Left nucleus accumbens
    34Right olfactory tubercle86Left olfactory tubercle
    35Right substantia innominata87Left substantia innominata
    36Right lateral hypothalamic area88Left lateral hypothalamic area
    37Right superior colliculus, sensory related89Left superior colliculus, sensory related
    38Right inferior colliculus90Left inferior colliculus
    39Right midbrain reticular nucleus91Left midbrain reticular nucleus
    40Right superior colliculus, motor related92Left superior colliculus, motor related
    41Right periaqueductal gray93Left periaqueductal gray
    42Right pontine reticular nucleus, caudal part94Left pontine reticular nucleus, caudal part
    43Right pontine reticular nucleus95Left pontine reticular nucleus
    44Right intermediate reticular nucleus96Left intermediate reticular nucleus
    45Right central lobule97Left central lobule
    46Right culmen98Left culmen
    47Right simple lobule99Left simple lobule
    48Right ansiform lobule100Left ansiform lobule
    49Right paramedian lobule101Left paramedian lobule
    50Right copula pyramidis102Left copula pyramidis
    51Right paraflocculus103Left paraflocculus

Extended Data

  • Figures
  • Tables
  • Extended Data Figure 4-1

    A, The first three principal components extracted from 1200 s of simulated firing rate activity in the bistable regime reveal a dominant contribution of the jumping regions (green ROIs corresponding to class J in Fig. 4A). B, The analysis of the first principal component of the simulated firing rate extracted from nonoverlapping 2-s time windows (corresponding to 2000 firing rate time points) reveals the intermittent contribution of the regions from classes U* and D* (dark red and dark blue ROIs, respectively), which become active carriers of the system variance during times associated to the neuronal cascades (e.g., around t = 600 s corresponding to Epoch III in Fig. 5A). Download Figure 4-1, EPS file.

  • Extended Data Figure 9-1

    A, Example of the edge CA time series in the original human dataset, compared to the respective phase-randomized and time-shuffled surrogates. Notice that the large CA events are preserved only in the first two surrogate models, but they are shifted in time. B, Distribution of the BOLD-CA amplitudes (the RSS of the edge CAs) in the time-shuffled (same distribution as in the original dataset) and in the phase randomized surrogates where the cross-spectrum is preserved (orange) or not (purple). C, Single-trial analysis of variance distribution (similar to Fig. 9B). The legend reports the p-values of the real observed variance versus the three surrogate distributions. Download Figure 9-1, EPS file.

Back to top

In this issue

eneuro: 8 (5)
eNeuro
Vol. 8, Issue 5
September/October 2021
  • Table of Contents
  • Index by author
  • Ed Board (PDF)
Email

Thank you for sharing this eNeuro article.

NOTE: We request your email address only to inform the recipient that it was you who recommended this article, and that it is not junk mail. We do not retain these email addresses.

Enter multiple addresses on separate lines or separate them with commas.
Neuronal Cascades Shape Whole-Brain Functional Dynamics at Rest
(Your Name) has forwarded a page to you from eNeuro
(Your Name) thought you would be interested in this article in eNeuro.
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Print
View Full Page PDF
Citation Tools
Neuronal Cascades Shape Whole-Brain Functional Dynamics at Rest
Giovanni Rabuffo, Jan Fousek, Christophe Bernard, Viktor Jirsa
eNeuro 28 September 2021, 8 (5) ENEURO.0283-21.2021; DOI: 10.1523/ENEURO.0283-21.2021

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
Respond to this article
Share
Neuronal Cascades Shape Whole-Brain Functional Dynamics at Rest
Giovanni Rabuffo, Jan Fousek, Christophe Bernard, Viktor Jirsa
eNeuro 28 September 2021, 8 (5) ENEURO.0283-21.2021; DOI: 10.1523/ENEURO.0283-21.2021
Twitter logo Facebook logo Mendeley logo
  • Tweet Widget
  • Facebook Like
  • Google Plus One

Jump to section

  • Article
    • Visual Abstract
    • Abstract
    • Significance Statement
    • Introduction
    • Materials and Methods
    • Results
    • Discussion
    • Footnotes
    • References
    • Synthesis
    • Author Response
  • Figures & Data
  • Info & Metrics
  • eLetters
  • PDF

Keywords

  • EEG/fMRI
  • network modeling
  • neuronal cascades
  • resting state

Responses to this article

Respond to this article

Jump to comment:

No eLetters have been published for this article.

Related Articles

Cited By...

More in this TOC Section

Research Article: New Research

  • Release of extracellular matrix components after human traumatic brain injury
  • Action intentions reactivate representations of task-relevant cognitive cues
  • Interference underlies attenuation upon relearning in sensorimotor adaptation
Show more Research Article: New Research

Novel Tools and Methods

  • Adapt-A-Maze: An Open Source Adaptable and Automated Rodent Behavior Maze System
  • Generation of iPSC lines with tagged α-synuclein for visualization of endogenous protein in human cellular models of neurodegenerative disorders
  • Chronic Intraventricular Cannulation for the Study of Glymphatic Transport
Show more Novel Tools and Methods

Subjects

  • Novel Tools and Methods
  • Home
  • Alerts
  • Follow SFN on BlueSky
  • Visit Society for Neuroscience on Facebook
  • Follow Society for Neuroscience on Twitter
  • Follow Society for Neuroscience on LinkedIn
  • Visit Society for Neuroscience on Youtube
  • Follow our RSS feeds

Content

  • Early Release
  • Current Issue
  • Latest Articles
  • Issue Archive
  • Blog
  • Browse by Topic

Information

  • For Authors
  • For the Media

About

  • About the Journal
  • Editorial Board
  • Privacy Notice
  • Contact
  • Feedback
(eNeuro logo)
(SfN logo)

Copyright © 2025 by the Society for Neuroscience.
eNeuro eISSN: 2373-2822

The ideas and opinions expressed in eNeuro do not necessarily reflect those of SfN or the eNeuro Editorial Board. Publication of an advertisement or other product mention in eNeuro should not be construed as an endorsement of the manufacturer’s claims. SfN does not assume any responsibility for any injury and/or damage to persons or property arising from or related to any use of any material contained in eNeuro.