de Arcangelis, L

Jensen, HJ

Massobrio, P

Pasquale, V

Plenz, D

Frontiers in Systems Neuroscience

English

PubMed

Paolo Massobrio

Lucilla de Arcangelis

Valentina Pasquale

Henrik J. Jensen

Dietmar Plenz

Crossref

Criticality as a signature of healthy neural systems

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EDITORIAL
published: 25 February 2015
doi: 10.3389/fnsys.2015.00022
Criticality as a signature of healthy neural systems
Paolo Massobrio1*, Lucilla de Arcangelis2, Valentina Pasquale3, Henrik J. Jensen4 and Dietmar Plenz5
1 Department Informatics, Bioengineering, Robotics, System Engineering (DIBRIS), University of Genova, Genova, Italy
2 Department Industrial and Information Engineering, Second University of Napoli, Napoli, Italy
3 Fondazione Istituto Italiano di Tecnologia, Genova, Italy
4 Department of Mathematics, Centre for Complexity Science, Imperial College of London, London, UK
5 Section on Critical Brain Dynamics, National Institute of Mental Health (NIH), Bethesda, MD, USA
*Correspondence: paolo.massobrio@unige.it
Edited and reviewed by:
Maria V. Sanchez-Vives, Institució Catalana de Recerca i Estudis Avançats and Institut de Investigacions Biomèdiques August Pi i Sunyer, Spain
Keywords: criticality, neuronal avalanches, critical exponents, power law, network dynamics, healthy neural systems
This Research Topic in “Frontiers in Systems Neuroscience” con-
tains a collection of original contributions and review articles on
the hypothesis that the normal, healthy brain resides in a critical
state. The hypothesis that brain activity, or specifically, neuronal
activity in the cortex, might be critical arose from the premise that
a critical brain can show the fastest and most flexible adaptation
to a rather unpredictable environment (for review see Chialvo,
2010). Over the last decade, numerous signatures of criticality
have been identified in brain activity. Some of the most striking
examples are the probability distributions of size and duration for
intermittent spontaneous activity bursts during ongoing activ-
ity in the cortex (Beggs and Plenz, 2003). These distributions
have been found to follow power laws, which are conserved
across species [rat: (Gireesh and Plenz, 2008); non-human pri-
mate: (Petermann et al., 2009; Yu et al., 2011); MEG: (Poil et al.,
2012; Palva et al., 2013; Shriki et al., 2013); EEG: (Meisel et al.,
2013); fMRI: (Tagliazucchi et al., 2012; Haimovici et al., 2013)]
and experimental preparations, spanning from reduced in vitro
models [i.e., acute and organotypic slices (Beggs and Plenz, 2003)
and dissociated cultures (Pasquale et al., 2008)] to in vivo animal
models (Gireesh and Plenz, 2008; Petermann et al., 2009; Ribeiro
et al., 2010). These scale-free activation patterns, called neuronal
avalanches, provide evidence for criticality in the brain.
The bold claim that the brain is critical has elicited a healthy
dose of skepticism and critique, often on technical grounds. For
example, power laws are ubiquitous in nature, can potentially
emerge from noise, and might not be particular to brain func-
tion (Touboul and Destexhe, 2010). This critique has refocused
the debate on the specific, shallow exponents found for avalanche
power laws, which demonstrate that unique, long-range spatial
correlations are introduced by these dynamics, which require pre-
cisely balanced, weak interactions that differ from noise (Klaus
et al., 2011). Similarly, discussion about the proper power law
model and functional fit (Clauset et al., 2009; Dehghani et al.,
2012) has highlighted the importance of careful identification of
power law cut-offs in avalanche distributions, and their correct
incorporation into appropriate statistical models (e.g., Langlois
et al., 2014; Yu et al., 2014). Importantly, alternative approaches
to avalanche dynamics using temporal scaling (Hardstone et al.,
2012) and spatial scaling of fluctuations in ongoing human brain
activity (Haimovici et al., 2013) have brought further support to
the hypothesis of criticality in the brain.
As evidenced in the contributions to this Special Topic issue,
the exploration and examination of brain activity in the frame-
work of criticality represents a highly active, ongoing field of
research. It has been shown that the distribution of silent
times between consecutive avalanches displays a non-monotonic
behavior (due to the slow alternation between up- and down-
states, Scarpetta and De Candia, 2014), with a power law decay
at short time scales (Lombardi et al., 2014). Further analyses
(Lombardi et al., 2012) demonstrate that avalanche size and inter-
avalanche silent times are correlated, and highlight that avalanche
occurrence exhibits the characteristic periodicity of θ and β/γ
oscillations. This observation is in line with pharmacological
results that connect nested oscillations and neuronal avalanches
in cortex (Gireesh and Plenz, 2008). Experimental observations
of long-term temporal correlations (Botcharova et al., 2014) in
fluctuations of phase synchronization in EEG and MEG signals
suggest that the driving mechanisms behind avalanche activity
are non-local, with all scales contributing to system behavior.
Indeed, an important “keyword” that characterizes such scale-
free systems is the presence of a critical point, indicating the
existence of a critical branching process as underlying structure
that sustains this kind of dynamics. As it emerges in Yu et al.
(2013), the ongoing resting activity in cortical networks organizes
close to an effective thermodynamic critical point, suggesting
the possibility that a critical state may in effect be described
by methodology from thermodynamic equilibrium. As reviewed
in Hesse and Gross (2014), a critical system displays optimal
computational properties, indicating that criticality has been evo-
lutionarily selected as a useful feature for the nervous system. The
progress in the field of criticality and brain dynamics is further
demonstrated by the fact that current discussions, rather than
rejecting criticality altogether, are often focused on the proximity
of brain dynamics to the critical point under different condi-
tions. Based on in vivo recordings of extracellular spiking activity
and modeling work, it has been concluded that the brain does
not reflect a critical state, but its emergent dynamics might self-
organize to a slightly sub-critical regime (Priesemann et al., 2014).
To reside in such a regime can be considered an advantage, since
it might prevent brain activity from becoming epileptic, which
has been associated with supercritical dynamics (Meisel et al.,
2012). Based on modeling (Tomen et al., 2014), it has been sug-
gested that cortical networks, by operating at the sub-critical to
Frontiers in Systems Neuroscience www.frontiersin.org February 2015 | Volume 9 | Article 22 | 1
SYSTEMS NEUROSCIENCE
Massobrio et al. Criticality as a signature of healthy neural systems
critical transition region, could dramatically enhance stimulus
representation.
Thus, if the brain works close to or at a critical point, it is
interesting to investigate the role of criticality on cognition and
long-term temporal correlations observed in behavioral studies
(Papo, 2014). Moreover, little is known about the causes and/or
consequences of a loss of criticality, and its relation with brain
diseases (e.g., epilepsy). The study of how pathogenic mecha-
nisms are related to the critical/non-critical behavior of neuronal
networks would likely provide new insights into the cellular and
synaptic determinants supporting the emergence of critical-like
dynamics and structures in neural systems. At the same time, the
relationship between disrupted criticality and impaired behavior
would help clarify the role of critical dynamics in normal brain
functioning. In this Research Topic, (Tinker and Perez Velazquez,
2014) studied whether power law scaling can be achieved in the
distribution of phase synchronization derived fromMEG record-
ings, acquired from children with or without autism performing
executive function tasks. Interestingly, (Roberts et al., 2014) point
out an issue not well explored in previous works: i.e., that existing
models lack precise physiological descriptions for how the brain
maintains its tuning near a critical point. The authors claim that a
missing fundamental ingredient is a formulation of the reciprocal
coupling between neural activity and metabolic resources. Recent
findings are aligned with the author’s idea, which emerged from
the analysis of disorders involving severe metabolic disturbances
and altered scale-free properties of brain dynamics.
The hypothesis that cortical dynamics resides at a critical
point, at which information processing is optimized, has refo-
cused attempts to explain the tremendous variability in neuronal
activity patterns observed in the brain at all scales. Over the
last several years, this hypothesis has given rise to numerous
conferences and workshops on the brain and criticality (Plenz
and Niebur, 2014). The current Research Topic continues the
endeavor to explore one of the most exciting current concepts on
brain function.
REFERENCES
Beggs, J. M., and Plenz, D. (2003). Neuronal avalanches in neocortical circuits.
J. Neurosci. 23, 11167–11177.
Botcharova, M., Farmer, S., and Berthouze, L. (2014). Markers of criticality in
phase synchronisation. Front. Syst. Neurosci. 8:176. doi: 10.3389/fnsys.2014.
00176
Chialvo, D. R. (2010). Emergent complex neural dynamics. Nat. Phys. 6, 744–750.
doi: 10.1038/nphys1803
Clauset, A., Shalizi, C. R., and Newman, M. E. J. (2009). Power-law distributions in
empirical data. SIAM Rev. 51, 661–703. doi: 10.1137/070710111
Dehghani, N., Hatsopoulos, N. G., Haga, Z. D., Parker, R., Greger, B., Halgren, E.,
et al. (2012). Avalanche analysis from multi-electrode ensemble recordings in
cat, monkey and human cerebral cortex during wakefulness and sleep. Front.
Physiol. 3:302. doi: 10.3389/fphys.2012.00302
Gireesh, E. D., and Plenz, D. (2008). Neuronal avalanches organize as nested theta-
and beta/gamma oscillations during development of cortical layer 2/3. Proc.
Natl. Acad. Sci. U.S.A. 105, 7576–7581. doi: 10.1073/pnas.0800537105
Haimovici, A., Tagliazucchi, E., Balenzuela, P., and Chialvo, D. R. (2013).
Brain organization into resting state networks emerges at criticality on
a model of the human connectome. Phys. Rev. Lett. 110:178101. doi:
10.1103/PhysRevLett.110.178101
Hardstone, R., Poil, S. S., Schiavone, G., Jansen, R., Nikulin, V. V., Mansvelder, H.
D., et al. (2012). Detrended fluctuation analysis: a scale-free view on neuronal
oscillations. Front. Physiol. 3:450. doi: 10.3389/fphys.2012.00450
Hesse, J., and Gross, T. (2014). Self-organized criticality as a fundamental property
of neural systems. Front. Syst. Neurosci. 8:166. doi: 10.3389/fnsys.2014.00166
Klaus, A., Yu, S., and Plenz, D. (2011). Statistical analyses support power law dis-
tributions found in neuronal avalanches. PLoS ONE 6:e19779. doi: 10.1371/
journal.pone.0019779
Langlois, D., Cousineau, D., and Thivierge, J. P. (2014). Maximum likelihood esti-
mators for truncated and censored power-law distributions show how neuronal
avalanches may be misevaluated. Phys. Rev. E Stat. Nonlin. Soft Matter Phys.
89:012709. doi: 10.1103/PhysRevE.89.012709
Lombardi, F., Herrmann, H., Plenz, D., and De Arcangelis, L. (2014). On the tem-
poral organization of neuronal avalanches. Front. Syst. Neurosci. 8:204. doi:
10.3389/fnsys.2014.00204
Lombardi, F., Herrmann, H. J., Perrone-Capano, C., Plenz, D., and De Arcangelis,
L. (2012). Balance between excitation and inhibition controls the tempo-
ral organization of neuronal avalanches. Phys. Rev. Lett. 108:228703. doi:
10.1103/PhysRevLett.108.228703
Meisel, C., Olbrich, E., Shriki, O., and Achermann, P. (2013). Fading signatures of
critical brain dynamics during sustained wakefulness in humans. J. Neurosci. 33,
17363–17372. doi: 10.1523/JNEUROSCI.1516-13.2013
Meisel, C., Storch, A., Hallmeyer-Elgner, S., Bullmore, E., and Gross, T. (2012).
Failure of adaptive self-organized criticality during epileptic seizure attacks.
PLoS Comput. Biol. 8:e1002312. doi: 10.1371/journal.pcbi.1002312
Palva, J. M., Zhigalov, A., Hirvonen, J., Korhonen, O., Linkenkaer-Hansen, K.,
and Palva, S. (2013). Neuronal long-range temporal correlations and avalanche
dynamics are correlated with behavioral scaling laws. Proc. Natl. Acad. Sci.
U.S.A. 110, 3585–3590. doi: 10.1073/pnas.1216855110
Papo, D. (2014). Functional significance of complex fluctuations in brain activity:
from resting state to cognitive neuroscience. Front. Syst. Neurosci. 8:112. doi:
10.3389/fnsys.2014.00112
Pasquale, V., Massobrio, P., Bologna, L. L., Chiappalone, M., and Martinoia,
S. (2008). Self-organization and neuronal avalanches in networks
of dissociated cortical neurons. Neuroscience 153, 1354–1369. doi:
10.1016/j.neuroscience.2008.03.050
Petermann, T., Thiagarajan, T. C., Lebedev, M. A., Nicolelis, M. A., Chialvo, D.
R., and Plenz, D. (2009). Spontaneous cortical activity in awake monkeys com-
posed of neuronal avalanches. Proc. Natl. Acad. Sci. U.S.A. 106, 15921–15926.
doi: 10.1073/pnas.0904089106
Plenz, D., and Niebur, E. (2014). Criticality in Neural Systems. Weinheim: Wiley.
Poil, S.-S., Hardstone, R., Mansvelder, H. D., and Linkenkaer-Hansen, K. (2012).
Critical-state dynamics of avalanches and oscillations jointly emerge from bal-
anced excitation/inhibition in neuronal networks. J. Neurosci. 32, 9817–9823.
doi: 10.1523/jneurosci.5990-11.2012
Priesemann, V., Wibral, M., Valderrama, M., Pröpper, R., Le Van Quyen, M., Geisel,
T., et al. (2014). Spike avalanches in vivo suggest a driven, slightly subcritical
brain state. Front. Syst. Neurosci. 8:108. doi: 10.3389/fnsys.2014.00108
Ribeiro, T. L., Copelli, M., Caixeta, F., Belchior, H., Chialvo, D. R., Nicolelis, M.,
et al. (2010). Spike avalanches exhibit universal dynamics across the sleep-wake
cycle. PLoS ONE 5:e14129. doi: 10.1371/journal.pone.0014129
Roberts, J. A., Iyer, K. K., Vanhatalo, S., and Breakspear, M. (2014). Critical role
for resource constraints in neural models. Front. Syst. Neurosci. 8:154. doi:
10.3389/fnsys.2014.00154
Scarpetta, S., and De Candia, A. (2014). Alternation of up and down states at a
dynamical phase-transition of a neural network with spatiotemporal attractors.
Front. Syst. Neurosci. 8:88. doi: 10.3389/fnsys.2014.00088
Shriki, O., Alstott, J., Carver, F., Holroyd, T., Henson, R. N. A., Smith, M. L., et al.
(2013). Neuronal avalanches in the restingMEG of the human brain. J. Neurosci.
33, 7079–7090. doi: 10.1523/JNEUROSCI.4286-12.2013
Tagliazucchi, E., Balenzuela, P., Fraiman, D., and Chialvo, D. R. (2012). Criticality
in large-scale brain FMRI dynamics unveiled by a novel point process analysis.
Front. Physiol. 3:15. doi: 10.3389/fphys.2012.00015
Tinker, J., and Perez Velazquez, J. L. (2014). Power law scaling in synchroniza-
tion of brain signals depends on cognitive load. Front. Syst. Neurosci. 8:73. doi:
10.3389/fnsys.2014.00073
Tomen, N., Rotermund, D., and Ernst, U. (2014). Marginally subcritical dynam-
ics explain enhanced stimulus discriminability under attention. Front. Syst.
Neurosci. 8:151. doi: 10.3389/fnsys.2014.00151
Touboul, J., and Destexhe, A. (2010). Can power-law scaling and neu-
ronal avalanches arise from stochastic dynamics? PLoS ONE 5:e8982. doi:
10.1371/journal.pone.0008982
Frontiers in Systems Neuroscience www.frontiersin.org February 2015 | Volume 9 | Article 22 | 2
Massobrio et al. Criticality as a signature of healthy neural systems
Yu, S., Klaus, A., Yang, H., and Plenz, D. (2014). Scale-invariant neuronal avalanche
dynamics and the cut-off in size distributions. PLoS ONE 9:e99761. doi:
10.1371/journal.pone.0099761
Yu, S., Yang, H., Nakahara, H., Santos, G. S., Nikolic, D., and Plenz, D. (2011).
Higher-order interactions characterized in cortical activity. J. Neurosci. 31,
17514–17526. doi: 10.1523/JNEUROSCI.3127-11.2011
Yu, S., Yang, H., Shriki, O., and Plenz, D. (2013). Universal organization of resting
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doi: 10.3389/fnsys.2013.00042
Conflict of Interest Statement: The authors declare that the research was con-
ducted in the absence of any commercial or financial relationships that could be
construed as a potential conflict of interest.
Received: 03 December 2014; accepted: 10 February 2015; published online: 25
February 2015.
Citation: Massobrio P, de Arcangelis L, Pasquale V, Jensen HJ and Plenz D (2015)
Criticality as a signature of healthy neural systems. Front. Syst. Neurosci. 9:22. doi:
10.3389/fnsys.2015.00022
This article was submitted to the journal Frontiers in Systems Neuroscience.
Copyright © 2015 Massobrio, de Arcangelis, Pasquale, Jensen and Plenz. This is an
open-access article distributed under the terms of the Creative Commons Attribution
License (CC BY). The use, distribution or reproduction in other forums is permit-
ted, provided the original author(s) or licensor are credited and that the original
publication in this journal is cited, in accordance with accepted academic practice.
No use, distribution or reproduction is permitted which does not comply with these
terms.
Frontiers in Systems Neuroscience www.frontiersin.org February 2015 | Volume 9 | Article 22 | 3


Paolo eMassobrio

Lucilla ede Arcangelis

Valentina ePasquale

Henrik Jeldtoft Jensen

Dietmar ePlenz

Directory of Open Access Journals

MASSOBRIO, PAOLO

de Arcangelis, Lucilla

PASQUALE, VALENTINA

Jensen, Henrik J.

Plenz, Dietmar

Archivio istituzionale della ricerca - Università di Genova

Massobrio, Paolo

DE ARCANGELIS, Lucilla

Pasquale, Valentina

Archivio Istituzionale della Ricerca - Università degli Studi della Campania "Luigi Vanvitelli"

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EDITORIALpublished: 25 February 2015doi: 10.3389/fnsys.2015.00022Criticality as a signature of healthy neural systemsPaolo Massobrio1*, Lucilla de Arcangelis2, Valentina Pasquale3, Henrik J. Jensen4 and Dietmar Plenz51 Department Informatics, Bioengineering, Robotics, System Engineering (DIBRIS), University of Genova, Genova, Italy2 Department Industrial and Information Engineering, Second University of Napoli, Napoli, Italy3 Fondazione Istituto Italiano di Tecnologia, Genova, Italy4 Department of Mathematics, Centre for Complexity Science, Imperial College of London, London, UK5 Section on Critical Brain Dynamics, National Institute of Mental Health (NIH), Bethesda, MD, USA*Correspondence: paolo.massobrio@unige.itEdited and reviewed by:Maria V. Sanchez-Vives, Institució Catalana de Recerca i Estudis Avançats and Institut de Investigacions Biomèdiques August Pi i Sunyer, SpainKeywords: criticality, neuronal avalanches, critical exponents, power law, network dynamics, healthy neural systemsThis Research Topic in “Frontiers in Systems Neuroscience” con-tains a collection of original contributions and review articles onthe hypothesis that the normal, healthy brain resides in a criticalstate. The hypothesis that brain activity, or specifically, neuronalactivity in the cortex, might be critical arose from the premise thata critical brain can show the fastest and most flexible adaptationto a rather unpredictable environment (for review see Chialvo,2010). Over the last decade, numerous signatures of criticalityhave been identified in brain activity. Some of the most strikingexamples are the probability distributions of size and duration forintermittent spontaneous activity bursts during ongoing activ-ity in the cortex (Beggs and Plenz, 2003). These distributionshave been found to follow power laws, which are conservedacross species [rat: (Gireesh and Plenz, 2008); non-human pri-mate: (Petermann et al., 2009; Yu et al., 2011); MEG: (Poil et al.,2012; Palva et al., 2013; Shriki et al., 2013); EEG: (Meisel et al.,2013); fMRI: (Tagliazucchi et al., 2012; Haimovici et al., 2013)]and experimental preparations, spanning from reduced in vitromodels [i.e., acute and organotypic slices (Beggs and Plenz, 2003)and dissociated cultures (Pasquale et al., 2008)] to in vivo animalmodels (Gireesh and Plenz, 2008; Petermann et al., 2009; Ribeiroet al., 2010). These scale-free activation patterns, called neuronalavalanches, provide evidence for criticality in the brain.The bold claim that the brain is critical has elicited a healthydose of skepticism and critique, often on technical grounds. Forexample, power laws are ubiquitous in nature, can potentiallyemerge from noise, and might not be particular to brain func-tion (Touboul and Destexhe, 2010). This critique has refocusedthe debate on the specific, shallow exponents found for avalanchepower laws, which demonstrate that unique, long-range spatialcorrelations are introduced by these dynamics, which require pre-cisely balanced, weak interactions that differ from noise (Klauset al., 2011). Similarly, discussion about the proper power lawmodel and functional fit (Clauset et al., 2009; Dehghani et al.,2012) has highlighted the importance of careful identification ofpower law cut-offs in avalanche distributions, and their correctincorporation into appropriate statistical models (e.g., Langloiset al., 2014; Yu et al., 2014). Importantly, alternative approachesto avalanche dynamics using temporal scaling (Hardstone et al.,2012) and spatial scaling of fluctuations in ongoing human brainactivity (Haimovici et al., 2013) have brought further support tothe hypothesis of criticality in the brain.As evidenced in the contributions to this Special Topic issue,the exploration and examination of brain activity in the frame-work of criticality represents a highly active, ongoing field ofresearch. It has been shown that the distribution of silenttimes between consecutive avalanches displays a non-monotonicbehavior (due to the slow alternation between up- and down-states, Scarpetta and De Candia, 2014), with a power law decayat short time scales (Lombardi et al., 2014). Further analyses(Lombardi et al., 2012) demonstrate that avalanche size and inter-avalanche silent times are correlated, and highlight that avalancheoccurrence exhibits the characteristic periodicity of θ and β/γoscillations. This observation is in line with pharmacologicalresults that connect nested oscillations and neuronal avalanchesin cortex (Gireesh and Plenz, 2008). Experimental observationsof long-term temporal correlations (Botcharova et al., 2014) influctuations of phase synchronization in EEG and MEG signalssuggest that the driving mechanisms behind avalanche activityare non-local, with all scales contributing to system behavior.Indeed, an important “keyword” that characterizes such scale-free systems is the presence of a critical point, indicating theexistence of a critical branching process as underlying structurethat sustains this kind of dynamics. As it emerges in Yu et al.(2013), the ongoing resting activity in cortical networks organizesclose to an effective thermodynamic critical point, suggestingthe possibility that a critical state may in effect be describedby methodology from thermodynamic equilibrium. As reviewedin Hesse and Gross (2014), a critical system displays optimalcomputational properties, indicating that criticality has been evo-lutionarily selected as a useful feature for the nervous system. Theprogress in the field of criticality and brain dynamics is furtherdemonstrated by the fact that current discussions, rather thanrejecting criticality altogether, are often focused on the proximityof brain dynamics to the critical point under different condi-tions. Based on in vivo recordings of extracellular spiking activityand modeling work, it has been concluded that the brain doesnot reflect a critical state, but its emergent dynamics might self-organize to a slightly sub-critical regime (Priesemann et al., 2014).To reside in such a regime can be considered an advantage, sinceit might prevent brain activity from becoming epileptic, whichhas been associated with supercritical dynamics (Meisel et al.,2012). Based on modeling (Tomen et al., 2014), it has been sug-gested that cortical networks, by operating at the sub-critical toFrontiers in Systems Neuroscience www.frontiersin.org February 2015 | Volume 9 | Article 22 | 1SYSTEMS NEUROSCIENCEMassobrio et al. Criticality as a signature of healthy neural systemscritical transition region, could dramatically enhance stimulusrepresentation.Thus, if the brain works close to or at a critical point, it isinteresting to investigate the role of criticality on cognition andlong-term temporal correlations observed in behavioral studies(Papo, 2014). Moreover, little is known about the causes and/orconsequences of a loss of criticality, and its relation with braindiseases (e.g., epilepsy). The study of how pathogenic mecha-nisms are related to the critical/non-critical behavior of neuronalnetworks would likely provide new insights into the cellular andsynaptic determinants supporting the emergence of critical-likedynamics and structures in neural systems. At the same time, therelationship between disrupted criticality and impaired behaviorwould help clarify the role of critical dynamics in normal brainfunctioning. In this Research Topic, (Tinker and Perez Velazquez,2014) studied whether power law scaling can be achieved in thedistribution of phase synchronization derived from MEG record-ings, acquired from children with or without autism performingexecutive function tasks. Interestingly, (Roberts et al., 2014) pointout an issue not well explored in previous works: i.e., that existingmodels lack precise physiological descriptions for how the brainmaintains its tuning near a critical point. The authors claim that amissing fundamental ingredient is a formulation of the reciprocalcoupling between neural activity and metabolic resources. Recentfindings are aligned with the author’s idea, which emerged fromthe analysis of disorders involving severe metabolic disturbancesand altered scale-free properties of brain dynamics.The hypothesis that cortical dynamics resides at a criticalpoint, at which information processing is optimized, has refo-cused attempts to explain the tremendous variability in neuronalactivity patterns observed in the brain at all scales. Over thelast several years, this hypothesis has given rise to numerousconferences and workshops on the brain and criticality (Plenzand Niebur, 2014). The current Research Topic continues theendeavor to explore one of the most exciting current concepts onbrain function.REFERENCESBeggs, J. M., and Plenz, D. (2003). Neuronal avalanches in neocortical circuits.J. Neurosci. 23, 11167–11177.Botcharova, M., Farmer, S., and Berthouze, L. (2014). Markers of criticality inphase synchronisation. Front. Syst. Neurosci. 8:176. doi: 10.3389/fnsys.2014.00176Chialvo, D. R. (2010). Emergent complex neural dynamics. Nat. Phys. 6, 744–750.doi: 10.1038/nphys1803Clauset, A., Shalizi, C. R., and Newman, M. E. J. (2009). Power-law distributions inempirical data. SIAM Rev. 51, 661–703. doi: 10.1137/070710111Dehghani, N., Hatsopoulos, N. G., Haga, Z. D., Parker, R., Greger, B., Halgren, E.,et al. (2012). Avalanche analysis from multi-electrode ensemble recordings incat, monkey and human cerebral cortex during wakefulness and sleep. Front.Physiol. 3:302. doi: 10.3389/fphys.2012.00302Gireesh, E. D., and Plenz, D. (2008). Neuronal avalanches organize as nested theta-and beta/gamma oscillations during development of cortical layer 2/3. Proc.Natl. Acad. Sci. U.S.A. 105, 7576–7581. doi: 10.1073/pnas.0800537105Haimovici, A., Tagliazucchi, E., Balenzuela, P., and Chialvo, D. R. (2013).Brain organization into resting state networks emerges at criticality ona model of the human connectome. Phys. Rev. Lett. 110:178101. doi:10.1103/PhysRevLett.110.178101Hardstone, R., Poil, S. S., Schiavone, G., Jansen, R., Nikulin, V. V., Mansvelder, H.D., et al. (2012). Detrended fluctuation analysis: a scale-free view on neuronaloscillations. Front. Physiol. 3:450. doi: 10.3389/fphys.2012.00450Hesse, J., and Gross, T. (2014). Self-organized criticality as a fundamental propertyof neural systems. Front. Syst. Neurosci. 8:166. doi: 10.3389/fnsys.2014.00166Klaus, A., Yu, S., and Plenz, D. (2011). Statistical analyses support power law dis-tributions found in neuronal avalanches. PLoS ONE 6:e19779. doi: 10.1371/journal.pone.0019779Langlois, D., Cousineau, D., and Thivierge, J. P. (2014). Maximum likelihood esti-mators for truncated and censored power-law distributions show how neuronalavalanches may be misevaluated. Phys. Rev. E Stat. Nonlin. Soft Matter Phys.89:012709. doi: 10.1103/PhysRevE.89.012709Lombardi, F., Herrmann, H., Plenz, D., and De Arcangelis, L. (2014). On the tem-poral organization of neuronal avalanches. Front. Syst. 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Neurosci. 7:42.doi: 10.3389/fnsys.2013.00042Conflict of Interest Statement: The authors declare that the research was con-ducted in the absence of any commercial or financial relationships that could beconstrued as a potential conflict of interest.Received: 03 December 2014; accepted: 10 February 2015; published online: 25February 2015.Citation: Massobrio P, de Arcangelis L, Pasquale V, Jensen HJ and Plenz D (2015)Criticality as a signature of healthy neural systems. Front. Syst. Neurosci. 9:22. doi:10.3389/fnsys.2015.00022This article was submitted to the journal Frontiers in Systems Neuroscience.Copyright © 2015 Massobrio, de Arcangelis, Pasquale, Jensen and Plenz. This is anopen-access article distributed under the terms of the Creative Commons AttributionLicense (CC BY). The use, distribution or reproduction in other forums is permit-ted, provided the original author(s) or licensor are credited and that the originalpublication in this journal is cited, in accordance with accepted academic practice.No use, distribution or reproduction is permitted which does not comply with theseterms.Frontiers in Systems Neuroscience www.frontiersin.org February 2015 | Volume 9 | Article 22 | 3

Criticality as a signature of healthy neural systems

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