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Neuroscience of Consciousness, 2021, 7(2), 1–24
DOI: https://doi.org/10.1093/nc/niab023
Review Article
Special Issue: Consciousness science and its theories
Consciousness and complexity: a consilience of evidence
Simone Sarasso1,†, Adenauer Girardi Casali2, Silvia Casarotto1,3, Mario Rosanova1, Corrado Sinigaglia4and Marcello Massimini1,3,*
1Department of Biomedical and Clinical Sciences ‘L. Sacco’, University of Milan, Milan 20157, Italy; 2Instituto de Ciência e Tecnologia, Universidade Federal de São
Paulo, Sao Jose dos Campos, 12247-014, Brazil; 3IRCCS Fondazione Don Carlo Gnocchi ONLUS, Milan 20148, Italy;4Department of Philosophy, University of Milan,
Milan 20122, Italy
†Simone Sarasso, http://orcid.org/0000-0001-9984-4710
*Correspondence address. Department of Biomedical and Clinical Sciences ‘L. Sacco’, University of Milan, Via G.B. Grassi, 74, 20157, Milano, Italy.
Tel: +39.02.503.19885; E-mail: marcello.massimini@unimi.it
Abstract
Over the last years, a surge of empirical studies converged on complexity-related measures as reliable markers of consciousness across
many different conditions, such as sleep, anesthesia, hallucinatory states, coma, and related disorders. Most of these measures were
independently proposed by researchers endorsing disparate frameworks and employing different methods and techniques. Since this
body of evidence has not been systematically reviewed and coherently organized so far, this positive trend has remained somewhat
below the radar. The aim of this paper is to make this consilience of evidence in the science of consciousness explicit. We start with
a systematic assessment of the growing literature on complexity-related measures and identify their common denominator, tracing it
back to core theoretical principles and predictions put forward more than 20 years ago. In doing this, we highlight a consistent trajectory
spanning two decades of consciousness research and provide a provisional taxonomy of the present literature. Finally, we consider all
of the above as a positive ground to approach new questions and devise future experiments that may help consolidate and further
develop a promising eld where empirical research on consciousness appears to have, so far, naturally converged.
Keywords: sleep; coma; anesthesia; information; integration
Introduction
Inferring the presence or the absence of consciousness from phys-
ical brain properties is a major challenge faced by scientists, with
remarkable clinical and ethical implications. Decades of research
on the physical substrate of consciousness did not ensure agree-
ment on the topic, with theoretical proposals still diverging on
fundamental assumptions and interpretations.
The aim of this review is to suggest that, despite this apparent
disagreement, catching a glimpse of recent empirical data reveals
a positive trend of convergence.
In the rst section, we provide a systematic survey of the exist-
ing literature and document an emerging empirical consensus on
a broad spectrum of complexity measures applied to brain sig-
nals as reliable indices of the presence/absence of consciousness
across many different conditions, such as sleep, anesthesia, hallu-
cinatory states, epilepsy, coma, and related disorders. In addition,
we note that this host of studies were independently proposed
by researchers employing different experimental approaches and
endorsing disparate theoretical positions.
In the second section, we revisit early theoretical proposals
linking consciousness to complexity. We show that the original
principles were put forward more than 20 years ago with the
denition of a specic form of complexity, arising from the
coexistence of functional integration and differentiation in the
brain. We then show that this rationale gave rise to novel mea-
sures and to original predictions.
In the third section, we argue that linking early principles
and predictions to current complexity-related metrics can help
interpret and conceptually organize the broad spectrum of cur-
rent proposed methods and measures. Here, we highlight that
they share a common denominator as they all tend to gauge
the coexistence of functional integration and functional dif-
ferentiation in the brain, albeit with different methods and
assumptions. We thus provide a provisional taxonomy to organize
existing complexity metrics and highlight their relationships and
caveats.
In the last section, we use all the above as a solid foothold to
approach new questions and devise future experiments. Among
Received: 19 February 2021; Revised: 19 June 2021; Accepted: 29 July 2021
© The Author(s) 2021. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which
permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
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2Sarasso et al.
others, we consider the problems of understanding the neu-
ronal mechanisms, the spatiotemporal grain, and the localization
of complexity in the brain, as well as the difference between
observational and perturbational approaches to estimating com-
plexity. Finally, we argue that addressing these issues may help
rene methods for assessing consciousness and foster construc-
tive exchange among different theoretical frameworks on solid
empirical grounds.
Current empirical convergence
An outstanding problem in the empirical science of consciousness
is identifying the fundamental physical brain properties that reli-
ably index the presence and the absence of consciousness. Here,
the presence of consciousness is operationalized as the presence
of immediate reports (e.g. those obtained from subjects during
wakefulness) and delayed reports (e.g. those obtained from sub-
jects waking up from unresponsive states such as dreaming and
ketamine anesthesia), as well as minimal but reliable behavioral
signs (such as those provided by patients in a minimally conscious
state). By contrast, the absence of consciousness is operationally
dened as the absence of all of the above.
In this context, consciousness is dened as the capacity for
any kind of experience, a concept that is upstream to further dis-
tinctions, such as those between levels (Laureys 2005;Boly et al.
2013), those between global states of consciousness (Bayne et al.
2016;Mckilliam 2020) (e.g. the distinction between dreaming and
wakeful consciousness), and those between local states of con-
sciousness (Bayne et al. 2016) characterized in terms of specic
conscious contents or phenomenal character.
Such primary distinctions between conscious and unconscious
conditions is the focus of a substantial body of literature, a fun-
damental concern for clinicians, and arguably an important rst
step for understanding the relationship between consciousness
and physical brain properties.
In this section, we unveil the emergence of a new class of
empirical measures that have recently shown a remarkable per-
formance in indexing the presence/absence of consciousness
across a variety of conditions.
Pointing the radar on complexity measures
The existence of a large body of works on complexity measures
has only been recently recognized (Arsiwalla and Verschure 2018)
but has never been systematically reviewed nor taxonomized,
thus remaining somewhat unnoticed. One way to appreciate the
emerging consilience of evidence on such measures is to contrast
them against the background of the disagreements and conict-
ing empirical results characterizing other empirical measures of
consciousness. A rst example is represented by markers of con-
sciousness based on event-related potentials (ERPs). In this case,
several studies (Bekinschtein et al. 2009;Faugeras et al. 2011,2012)
proposed a late, positive, fronto-parietal ERP evoked by visual or
auditory stimuli (called P3b) as a reliable signature of conscious-
ness. More recent studies (Pitts et al. 2014;Silverstein et al. 2015;
Tzovara et al. 2015;Sergent et al. 2021), however, questioned
this interpretation and opened a debate on the precise relation-
ship of P3b to consciousness as opposed to task relevance, report,
and decision processes that are associated with conscious access
mechanisms. Most importantly in the present context, P3b was
found to have a low sensitivity with respect to the presence of
consciousness in clinical conditions (Faugeras et al. 2012;Sitt et al.
2014).
Another example of discrepancy is represented by indices
based on global brain metabolic rates as they can be found
decreased during loss of consciousness in deep sleep and anes-
thesia (Nofzinger et al. 2002;Kaisti et al. 2003), whereas they
increase when consciousness is lost during generalized seizures
(Bai et al. 2010). A similar problem applies to global spectral mea-
sures, such as alpha and delta electroencephalographic (EEG)
power. Indeed, while the presence of a prominent alpha power
typically provides a useful index of preserved brain function also
in brain-injured patients, with the exception of postanoxic alpha-
coma (Westmoreland et al. 1975), alpha is found consistently
decreased in conscious conditions such as dreaming (Esposito
et al. 2004), psychedelic-induced states (Timmermann et al. 2019),
and in locked-in patients (Babiloni et al. 2010). On the other
hand, while EEG delta power is typically found to negatively
correlate with the presence of consciousness, important excep-
tions are found in the literature as EEG can show persistent
large delta waves in conscious participants during the adminis-
tration of the cholinergic antagonist atropine (Ostfeld et al. 1960)
and of the gamma-aminobutyric acid (GABA) reuptake inhibitor
tiagabine (Darmani et al. 2021) and during some instances of
status epilepticus (G¨
okyiˇ
git and Çalis¸kan 1995;Vuilleumier et al.
2000), as well as in rare cases of children with Angelman syn-
drome (Sidorov et al. 2017;den Bakker et al. 2018;Frohlich et al.
2020). Notably, these and other dissociations have been systemat-
ically addressed by a very recent review article (Frohlich et al. 2021)
further questioning the notion that high-amplitude delta oscilla-
tions recorded in humans at the scalp level are a reliable indicator
of unconsciousness.
Against this backdrop, it becomes easier to recognize the emer-
gence of a complementary prole in the relevant literature. Over-
all, a large body of work supports the notion that the presence of
consciousness is invariably associated with high brain complex-
ity, which, vice versa, is found to be consistently decreased during
physiological, pharmacological, or pathological-induced loss of
consciousness.
Four examples of such measures, employing different exper-
imental approaches, including both electrophysiology and
functional brain imaging, and testing various conditions encom-
passing deep sleep, anesthesia, and disorders of consciousness are
shown in Fig. 1. These examples, which are clearly interesting in
their own merit, are especially important for two reasons. First,
because they share a common conceptual denominator in that
they all tend to gauge the joint presence of functional integration
and functional differentiation in the brain. Second, because they
represent the tip of an iceberg of a much broader consilience, as
we demonstrate below.
A systematic literature analysis
In order to substantiate and characterize this emerging con-
vergence, we performed a systematic search on the electronic
database PubMed for original research studies published in
journals and available online using the query: “consciousness”
AND (complexity OR “entropy” OR “fractal” OR (“network” AND
“graph”) OR “information transmission” OR “mutual information”
OR “information ow” OR “information sharing” OR (“information”
AND integration) OR “effective information” OR “effective connec-
tivity” OR “criticality” OR “metastability”). These search criteria
were dened in order to be specic for complexity-related metrics
and to accommodate, at the same time, the variety of empirical
research programmes (i.e. methods to estimate complexity and
experimental approaches; Fig. 1).
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Consciousness and complexity 3
Figure 1. Relevant examples of brain complexity measures as a reliable index of the state of consciousness
Overall, these works support the notion that the presence of consciousness is invariably associated with high brain complexity, which is found to be consistently
decreased during deep sleep [Panel A, modied from (Hahn et al. 2021)], anesthesia [Panel B, modied from (Luppi et al. 2019)], and disorders of consciousness
[Panel B, C, and D, modied from (Luppi et al. 2019), (King et al. 2013), and (Casarotto et al. 2016), respectively]. Notably, these studies employ different
experimental approaches including both neurophysiological measures and functional brain imaging.
Figure 2. Literature on complexity-related measures
Panel A. The histogram represents the number of studies per year of publication (1998–2021) derived from our literature search. No study matched our search
criteria before 2005. The total number of studies identied by our search is 182. Panel B. Number of studies for each of the different neurophysiological and
neuroimaging tools employed. These included scalp and intracranial EEG (either EcoG or SEEG), alone or in combination with direct cortical perturbation (either
TMS or SPES), MEG, as well as fMRI. Panel C. Number of studies for each of the different conditions in which complexity-related measures were applied to index
changes in the state of consciousness. These included sleep, general anesthesia, disorders of consciousness, and other conditions where the state of
consciousness is altered, such as meditation and drug-induced altered states of consciousness, as well as neurological conditions, including epilepsy (grouped
together and labelled “Others” in the Figure).
After excluding from the results of this automatic search stud-
ies that are unrelated to the subject of measuring consciousness
(e.g. clinical studies aimed at testing brain-based measures for
anesthesia monitoring or for the neurophysiological assessment
of partial seizures not involving loss of consciousness), studies
applying complexity measures on other biological signals (e.g.
heart rate variability), and studies exclusively based on modeling
work and animal models, as well as works exclusively employing
proprietary software whose algorithms are not publicly disclosed
(e.g. bispectral index), we identied 182 original studies.
When systematically analyzed, the results of our search high-
light several interesting elements supporting the idea of a strong,
rapidly growing empirical convergence in the literature.
First, the identied studies cover a temporal span of more
than a decade (the rst paper identied dates 2005, Fig. 2A). Sec-
ond, conrming the initial impression drawn from the examples
provided in Fig. 1, this large body of empirical evidence encom-
passes studies employing a wide range of neurophysiological
and neuroimaging tools (Fig. 2B), including scalp and intracra-
nial EEG [either electrocorticography (ECoG) or stereo-EEG (SEEG)]
alone or in combination with direct cortical perturbation [either
transcranial magnetic stimulation (TMS) or single pulse electri-
cal stimulation (SPES)] and magnetoencephalography (MEG), as
well as functional magnetic resonance imaging (fMRI). Third, our
search conrms that complexity-related measures have been suc-
cessfully applied to index changes in the state of consciousness
across a wide range of conditions (Tables 1–4), including sleep
[both rapid eye movement (REM) and nonREM (NREM)], general
anesthesia (employing various anesthetic agents with different
mechanisms of action), meditation, and drug-induced altered
states of consciousness, as well as neurological conditions, includ-
ing epilepsy, coma, and disorders of consciousness (Fig. 2C).
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4Sarasso et al.
Remarkably, across this wide range of conditions and methodolo-
gies, the reliability of complexity-related measures was conrmed
by all studies contrasting the presence versus the absence of con-
sciousness. More specically, consciousness was found invariably
associated with high levels of brain complexity not only during
wakefulness but also during REM sleep (Imperatori et al. 2020)
and even in the extreme case of general anesthesia with ketamine
(Sarasso et al. 2015). Conversely, brain complexity was found
markedly reduced in all cases associated with the loss of con-
sciousness whether during NREM sleep (Hahn et al. 2021), general
anesthesia induced by the use of various compounds (Huang et al.
2016;Hashmi et al. 2017;Lee et al. 2020), or epileptic seizures
(Mateos et al. 2018). Most importantly, in a number of studies
involving the challenging conditions represented by the disorder
of consciousness, the reliability of complexity-related measures
in detecting consciousness was assessed explicitly by testing their
specicity and sensitivity on large cohorts of patients. Notably,
these experiments (Casali et al. 2013;Sitt et al. 2014;Casarotto
et al. 2016;Engemann et al. 2018;Demertzi et al. 2019;Luppi et al.
2019) attained such a high accuracy in discriminating conscious
from unconscious individuals that they were recently highlighted
and formally recommended in a number of international practice
guidelines (Giacino et al. 2018;Kondziella et al. 2020) and expert
reviews (Bai et al. 2020;Comanducci et al. 2020) for the diagnosis
of disorders of consciousness.
Last but not least, it is worth noting that, overall, this large
body of empirical evidence was accumulated by clinicians and
researchers from several independent research groups encom-
passing a wide spectrum of theoretical views.
Consciousness and complexity: rewinding
20 years
Prompted by the consistent results highlighted in the previous
section, we here revisit the original rationale for explicitly linking
consciousness to complexity. In doing so, we identify a set of prin-
ciples and predictions that can help interpret and conceptually
organize the broad spectrum of current methods and measures.
Early theoretical principles
The rst clear landmark linking consciousness to complexity
dates back to more than 20 years ago, when a paper explicitly
titled “Consciousness and complexity” was published in Science
(Giulio Tononi and Edelman 1998). Here, Tononi and Edelman
dened the kind of complexity specically relevant for conscious-
ness as the coexistence of a high degree of functional differen-
tiation and functional integration within a system, conceiving
a testable proposal regarding the neural substrate of conscious
experience called the dynamic core hypothesis (DCH).
Using phenomenology as a springboard, the DCH combined
the two ingredients of integration and differentiation in a novel
framework about the relationships between consciousness and
the brain. As described at the outset of the original paper, a sim-
ple exercise of introspection indicates that each experience is both
integrated (each conscious scene is unied) and highly differenti-
ated (each experience is specic, differing from a huge number
of different conscious states at any given time). Thus, the neu-
ral process underlying conscious experience must be functionally
integrated and, at the same time, highly differentiated. Starting
from this premise, the DCH postulated which basic anatomical
and neurophysiological properties may be specically relevant for
consciousness.
The rst necessary property is a pattern of structural connec-
tivity characterized by the coexistence of functional segregation
and functional integration. Besides the appropriate arrangement
of structural connectivity, the DCH postulated that another nec-
essary property is the presence of effective and rapid reentrant
interactions, granting the formation of a tightly integrated clus-
ter of neurons. Perhaps the most interesting (and dening) claim
of Tononi and Edelman is that none of the above is a sufcient
property for conscious experience and that only if the integrated
cluster is capable of a large repertoire of different states, con-
sciousness is possible.
In a nutshell, the backbone of the DCH consisted in the follow-
ing two principles:
(I) A group of neurons can contribute directly to conscious
experience only if it is part of a distributed functional clus-
ter [i.e. a subset of a neural system with dynamics that
display high statistical dependence internally and relatively
lower dependence with elements outside the subset (Tononi
et al. 1998)] that achieves high integration in hundreds of
milliseconds.
(II) To sustain conscious experience, it is essential that this func-
tional cluster is capable of a large repertoire of different
activity patterns or neural states, as indicated by high values
of complexity.
Early theoretical measures
Even more importantly in the present context, Tononi and Edel-
man proposed a metric, called neural complexity (CN), to quantify
the above-mentioned physiologically observable variables (bal-
anced structural connectivity, integration through fast reentrant
interactions, and the differentiation of neuronal activity) in thala-
mocortical networks. The fundamental insight offered by the DCH
and by the related measure CNis that functional integration and
functional differentiation need to be measured jointly. A basic
concept, with key practical implications, is that measuring the
spatial extent of large-scale synchronous dynamics would not suf-
ce per se. Indeed, one would not take into account whether these
integrated dynamics are differentiated or stereotypical (such as
the ones recorded during unconscious seizures or NREM sleep). On
the other hand, according to the DCH, simply measuring the algo-
rithmic complexity or the entropy of ongoing time series would
not do, which also has practical implications. In this case, in fact,
one would not know whether these differentiated patterns are
generated by one system of interacting elements or by a collection
of independent elements.
Following the intuitions of the DCH and further specifying
the concepts of integration and differentiation, Tononi and col-
leagues later introduced a novel measure called Φ(Tononi 2001;
Tononi and Sporns 2003). A critical difference is that this mea-
sure is based on effective rather than mutual information (the core
measure of CN), thus reecting causal interactions rather than sta-
tistical dependencies. A rst implication is that, through extensive
perturbations of all the subsets of the system, Φcaptures not
only the states the system cycles through within the limited time
of observation but all the potential states the system is capable
of (i.e. its full repertoire of states). Perhaps more importantly,
this perturbational approach bears practical consequences for the
development of empirical metrics. Indeed, the strategy of mea-
suring causal interactions instead of temporal correlations takes
the problem of measuring integration (i.e. the unity of a system)
very seriously, as it avoids confounds due to spurious sources of
integration such as common drivers and correlated inputs.
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Consciousness and complexity 5
Table 1. Papers assessing changes in the state of consciousness during general anesthesia
First author (year) Journal abbreviation DOI Data type
Jordan (2008) Anesthesiology 10.1097/ALN.0b013e31818d6c55 EEG
Lee (2009) Conscious Cogn 10.1016/j.concog.2008.10.005 EEG
Ferrarelli (2010) Proc Natl Acad Sci USA 10.1073/pnas.0913008107 TMS-EEG
Lee (2010) Anesthesiology 10.1097/ALN.0b013e3181f229b5 EEG
Li (2010) J Neural Eng 10.1088/1741-2560/7/4/046010 EEG
Kaskinoro (2011) Br J Anaesth 10.1093/bja/aer196 EEG
Ku (2011) PloS One 10.1371/journal.pone.0025155 EEG
Lee (2011) Anesthesiology 10.1097/ALN.0b013e31821102c9 EEG
Schrouff (2011) NeuroImage 10.1016/j.neuroimage.2011.04.020 fMRI
Barrett (2012) PloS One 10.1371/journal.pone.0029072 EEG
Nicolaou (2012) PloS One 10.1371/journal.pone.0033869 EEG
Schr¨
oter (2012) J Neurosci 10.1523/JNEUROSCI.6046-11.2012 EEGfMRI
Casali (2013) Sci Transl Med 10.1126/scitranslmed.3006294 TMS-EEG
Gili (2013) J Neurosci 10.1523/JNEUROSCI.3480-12.2013 fMRI
Guldenmund (2013) Brain Connect 10.1089/brain.2012.0117 fMRI
Jordan (2013) Anesthesiology 10.1097/ALN.0b013e3182a7ca92 EEGfMRI
Kuhlmann (2013) PloS One 10.1371/journal.pone.0056434 EEG
Lee (2013b) Anesthesiology 10.1097/ALN.0b013e3182a8ec8c EEG
Lee (2013c) Anesthesiology 10.1097/ALN.0b013e31829103f5 EEG
Monti (2013) PloS Comput Biol 10.1371/journal.pcbi.1003271 fMRI
Shin (2013) PloS One 10.1371/journal.pone.0070899 EEG
Alonso (2014) Front Neural Circuits 10.3389/fncir.2014.00020 SEEG
Liu (2014) PloS One 10.1371/journal.pone.0092182 fMRI
Maksimow (2014) PloS One 10.1371/journal.pone.0113616 EEG
Untergehrer (2014) PloS One 10.1371/journal.pone.0087498 EEG
Liang (2015a) Hum Brain Mapp fMRI
Liang (2015b) Clin Neurophysiol 10.1016/j.clinph.2014.05.012 EEG
Moon (2015) PloS Comput Biol 10.1371/journal.pcbi.1004225 EEG
Sarasso (2015) Curr Biol 10.1016/j.cub.2015.10.014 TMS-EEG
Schartner (2015) PloS One 10.1371/journal.pone.0133532 EEG
Casarotto (2016) Ann Neurol 10.1002/ana.24779 TMS-EEG
Huang (2016) Neuroimage 10.1016/j.neuroimage.2015.08.062 fMRI
Liang (2016) J Clin Monit Comput 10.1007/s10877-015-9738-z EEG
Blain-Moraes (2017) Front Hum Neurosci 10.3389/fnhum.2017.00328 EEG
Crone (2017) Cereb Cortex 10.1093/cercor/bhw112 fMRI
Hashmi (2017) Anesthesiology 10.1097/ALN.0000000000001509 fMRI
Lee (2017a) Hum Brain Mapp 10.1002/hbm.23708 EEG
Lee (2017b) Sci Rep 10.1038/s41598-017-15082-5 EEG
Wang (2017) Neurosci Lett 10.1016/j.neulet.2017.05.045 EEG
Eagleman (2018) Front Neurosci 10.3389/fnins.2018.00645 EEG
Huang (2018) Br J Anaesth 10.1016/j.bja.2018.04.031 SEEG
Kim (2018a) Front Hum Neurosci 10.3389/fnhum.2018.00042 EEG
Kim (2018b) PloS Comput Biol 10.1371/journal.pcbi.1006424 EEG
Lee (2018) Entropy 10.3390/e20070518 fMRI
Li (2018) PloS One 10.1371/journal.pone.0192358 fMRI
Afshani (2019) Cogn Neurodyn 10.1007/s11571-019-09553w EEG
Colombo (2019) Neuroimage 10.1016/j.neuroimage.2019.01.024 EEGTMS-EEG
Comolatti (2019) Brain Stimul 10.1016/j.brs.2019.05.013 TMS-EEGSPES-SEEG
Demertzi (2019) Sci Adv 10.1126/sciadv.aat7603 fMRI
Eagleman (2019) PloS One 10.1371/journal.pone.0223921 EEG
Golkowski (2019) Anesthesiology 10.1097/ALN.0000000000002704 fMRI
Kim (2019) Entropy 10.3390/e21100981 EEG
Lange (2019) Sci Rep 10.1038/s41598-019-52949-1 EcoG
Lee (2019) NeuroImage 10.1016/j.neuroimage.2018.12.011 EEG
Li (2019) NeuroImage 10.1016/j.neuroimage.2019.03.076 EEG
Lioi (2019) Anaesthesia EEG
Liu (2019) Brain Imaging Behav 10.1007/s11682-018-9886-0 fMRI
Luppi (2019) Nat Commun 10.1038/s41467-019-12658-9 fMRI
Pappas (2019b) Anesthesiology 10.1097/ALN.0000000000002977 EEG
Pappas (2019a) NeuroImage 10.1016/j.neuroimage.2018.10.078 fMRI
Ruiz de Miras (2019) Comput Methods Programs Biomed 10.1016/j.cmpb.2019.04.017 TMS-EEG
Wenzel (2019) Cell Syst 10.1016/j.cels.2019.03.007 SEEG
Farnes (2020) PloS One 10.1371/journal.pone.0242056 EEGTMS-EEG
(continued)
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6Sarasso et al.
Table 1. (Continued)
First author (year) Journal abbreviation DOI Data type
Lee (2020) Sci Rep 10.1038/s41598-020-59264-0 EEG
Liang (2020a) Anesthesiology 10.1097/ALN.0000000000003015 EcoG
Pullon (2020) Anesthesiology 10.1097/ALN.0000000000003398 EEG
Varley (2020c) Sci Rep 10.1038/s41598-020-57695-3 fMRI
Wang (2020a) NeuroImage Clin 10.1016/j.nicl.2020.102188 fMRI
Yan (2020) Clin EEG Neurosci 10.1177/1550059420976303 EEG
Table 2. Papers assessing changes in the state of consciousness following severe brain injury
First author (year) Journal abbreviation DOI Data type
Cauda (2009) J Neurol Neurosurg Psychiatry 10.1136/jnnp.2007.142349 fMRI
Pollonini (2010) Brain Topogr 10.1007/s10548-010-0139-9 EEG
Sarà (2010) Nonlinear Dynamics Psychol Life Sci PMID: 20021774 EEG
Gosseries (2011) Funct Neurol PMID: 21693085 EEG
Sarà (2011) Neurorehab Neural Rep 10.1177/1545968310378508 EEG
Wu (2011) Clin Neurophysiol 10.1016/j.clinph.2010.05.036 EEG
Zhou (2011) Conscious Cogn 10.1016/j.concog.2010.08.003 fMRI
Achard (2012) Proc Natl Acad Sci U S A 10.1073/pnas.1208933109 fMRI
Fingelkurts (2012) Open Neuroimag J 10.2174/1874440001206010055 EEG
Rosanova (2012) Brain 10.1093/brain/awr340 TMS-EEG
Casali (2013) Sci Transl Med 10.1126/scitranslmed.3006294 TMS-EEG
Fingelkurts (2013) Clin EEG Neurosci 10.1177/1550059412474929 EEG
King (2013) Curr Biol 10.1016/j.cub.2013.07.075 EEG
M¨
aki-Marttunen (2013) Front Neuroinform 10.3389/fninf.2013.00024 fMRI
Ragazzoni (2013) PloS One 10.1371/journal.pone.0057069 TMS-EEG
Chennu (2014) PloS Comput Biol 10.1371/journal.pcbi.1003887 EEG
Crone (2014) Neuroimage Clin 10.1016/j.nicl.2013.12.005 fMRI
Liu (2014) PloS One 10.1371/journal.pone.0092182 fMRI
Marinazzo (2014) Clin EEG Neurosci 10.1177/1550059413510703 EEG
Sitt (2014) Brain 10.1093/brain/awu141 EEG
Varotto (2014) Clin Neurophysiol 10.1016/j.clinph.2013.06.016 EEG
Crone (2015) NeuroImage 10.1016/j.neuroimage.2015.01.037 fMRI
Bai (2016) Front Neurosci 10.3389/fnins.2016.00473 TMS-EEG
Casarotto (2016) Ann Neurol 10.1002/ana.24779 TMS-EEG
Claassen (2016) Ann Neurol 10.1002/ana.24752 EEG
Fingelkurts (2016) Open Neuroimag J 10.2174/1874440001610010041 EEG
Huang (2016) Neuroimage 10.1016/j.neuroimage.2015.08.062 fMRI
Kuceyeski (2016) Neuroimage Clin 10.1016/j.nicl.2016.04.006 fMRI
Naro (2016) Brain Topogr 10.1007/s10548-016-0489-z EEG
Piarulli (2016) J Neurol 10.1007/s00415-016-8196-y EEG
Tagliazucchi (2016) J R Soc Interface 10.1098/rsif.2015.1027 fMRI
Amico (2017) NeuroImage 10.1016/j.neuroimage.2017.01.020 fMRI
Bodart (2017) Neuroimage Clin 10.1016/j.nicl.2017.02.002 TMS-EEG
Chennu (2017) Brain 10.1093/brain/awx163 EEG
Fingelkurts (2017) Clin EEG Neurosci 10.1177/1550059417696180 EEG
Naro (2017) Neuroscience 10.1016/j.neuroscience.2017.02.053 EEG
Wislowska (2017) Sci Rep 10.1038/s41598-017-00323-4 EEG
Bodart (2018a) Brain Stimul 10.1016/j.brs.2017.11.006 TMS-EEG
Cavaliere (2018) Front Neurol 10.3389/fneur.2018.00861 fMRI
Dell’Italia (2018) Front Neurol 10.3389/fneur.2018.00439 fMRI
Di Perri (2018) Hum Brain Mapp 10.1002/hbm.23826 fMRI
Engemann (2018) Brain 10.1093/brain/awy251 EEG
Rosanova (2018) Nat Commun 10.1038/s41467-018-06871-1 TMS-EEG
Sinitsyn (2018) Hum Brain Mapp 10.1002/hbm.24050 fMRI
Stefan (2018) Brain Topogr 10.1007/s10548-018-0643-x EEG
Wielek (2018) PloS One 10.1371/journal.pone.0190458 EEG
Cacciola (2019) J Clin Med 10.3390/jcm8030306 EEG
Comolatti (2019) Brain Stimul 10.1016/j.brs.2019.05.013 TMS-EEGSPES-SEEG
Demertzi (2019) Sci Adv 10.1126/sciadv.aat7603 fMRI
Lee (2019a) NeuroImage 10.1016/j.neuroimage.2018.12.011 EEG
Luppi (2019) Nat Commun 10.1038/s41467-019-12658-9 fMRI
Malagurski (2019) NeuroImage 10.1016/j.neuroimage.2019.03.012 fMRI
(continued)
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Consciousness and complexity 7
Table 2. (Continued)
First author (year) Journal abbreviation DOI Data type
Rizkallah (2019) NeuroImage Clin 10.1016/j.nicl.2019.101841 EEG
Xia (2019) Neuroreport 10.1097/WNR.0000000000001362 TMS-EEG
Abeyasinghe (2020) J Clin Med 10.3390/jcm9051342 fMRI
Cai (2020b) J Neural Eng 10.1088/1741-2552/ab79f5 EEG
Cai (2020a) J Neural Eng 10.1088/1741-2552/ab8b2c EEG
Carrière (2020) Brain Sci 10.3390/brainsci10070469 EEG
Huang (2020) Neurocrit Care 10.1007/s12028-020-01051w EEG
Liang (2020b) IEEE Trans Neural Syst Rehabil Eng 10.1109/TNSRE.2020.2964819 EEG
Lutkenhoff (2020) Brain Stimul 10.1016/j.brs.2020.07.012 TMS-EEG
Martens (2020) Neuroimage Clin 10.1016/j.nicl.2020.102426 EEG
Nadin (2020) Neurosci Conscious 10.1093/nc/niaa017 EEG
Rudas (2020) Brain Connect 10.1089/brain.2019.0716 fMRI
Sangare (2020) Brain Sci 10.3390/brainsci10110845 EEG
Sinitsyn (2020) Brain Sci 10.3390/brainsci10120917 TMS-EEG
Varley (2020b) PloS One 10.1371/journal.pone.0223812 fMRI
Wang (2020b) Int J Neurosci 10.1080/00207454.2019.1702543 EEG
Wu (2020) Entropy 10.3390/e22121411 EcoG
Zhang (2020) Front Hum Neurosci 10.3389/fnhum.2020.560586 EEG
Naro (2021) Int J Neural Syst 10.1142/S0129065720500525 EEG
Table 3. Papers assessing changes in the state of consciousness during sleep
First author (year) Journal abbreviation DOI Data type
Burioka (2005) Clin EEG Neurosci 10.1177/155005940503600106 EEG
Massimini (2005) Science 10.1126/science.1117256 TMS-EEG
Massimini (2010) Cogn Neurosci 10.1080/17588921003731578 TMS-EEG
Spoormaker (2010) J Neurosci 10.1523/JNEUROSCI.2015-10.2010 fMRI
Boly (2012) Proc Natl Acad Sci U S A 10.1073/pnas.1111133109 fMRI
Chu (2012) J Neurosci 10.1523/JNEUROSCI.5669-11.2012 EEG
Casali (2013) Sci Transl Med 10.1126/scitranslmed.3006294 TMS-EEG
Lee (2013a) Front Neuroinform 10.3389/fninf.2013.00033 EEG
Tagliazucchi (2013) Proc Natl Acad Sci U S A 10.1073/pnas.1312848110 fMRI
Zorick (2013) PloS One 10.1371/journal.pone.0068360 EEG
Uehara (2014) Cereb Cortex 10.1093/cercor/bht004 EEG fMRI
Allegrini (2015) Phys Rev E 10.1103/PhysRevE.92.032808 EEG
Pigorini (2015) NeuroImage 10.1016/j.neuroimage.2015.02.056 SPES-SEEG
Usami (2015) Hum Brain Mapp 10.1002/hbm.22948 SPES-EcoG
Andrillon (2016) J Neurosci 10.1523/JNEUROSCI.0902-16.2016 EEG
Casarotto (2016) Ann Neurol 10.1002/ana.24779 TMS-EEG
Guevara Erra (2016) Phys Rev E 10.1103/PhysRevE.94.052402 EEGSEEGMEG
Tagliazucchi (2016) Brain Struct Funct 10.1007/s00429-015-1162-0 fMRI
Lioi (2017) Physiol Meas 10.1088/1361-6579/aa81b5 EEG
Schartner (2017b) Neurosci Conscious 10.1093/nc/niw022 SEEG
Wislowska (2017) Sci Rep 10.1038/s41598-017-00323-4 EEG
Isler (2018) PloS One 10.1371/journal.pone.0206237 EEG
Li (2018) PloS One 10.1371/journal.pone.0192358 fMRI
Mateos (2018) Cogn Neurodyn 10.1007/s11571-017-9459-8 EEGSEEGMEG
Rosanova (2018) Nat Commun 10.1038/s41467-018-06871-1 TMS-EEG
Wielek (2018) PloS One 10.1371/journal.pone.0190458 EEG
Bocaccio (2019) J R Soc Interface 10.1098/rsif.2019.0262 fMRI
Comolatti (2019) Brain Stimul 10.1016/j.brs.2019.05.013 TMS-EEGSPES-SEEG
Imperatori (2019) Sci Rep 10.1038/s41598-019-45289-7 EEG
Kung (2019) Hum Brain Mapp 10.1002/hbm.24590 EEG fMRI
Lee (2019b) Sci Rep 10.1038/s41598-019-41274-2 TMS-EEG
Miskovic (2019) Hum Brain Mapp 10.1002/hbm.24393 EEG
Ruiz de Miras (2019) Comput Methods Programs Biomed 10.1016/j.cmpb.2019.04.017 TMS-EEG
Usami (2019) Sleep 10.1093/sleep/zsz050 SPES-EcoG
Frohlich (2020) Neurosci Conscious 10.1093/nc/niaa005 EEG
Hou (2020) Sleep 10.1093/sleep/zsaa226 EEG
Imperatori (2020) Sleep 10.1093/sleep/zsaa247 EEG
Wang (2020) Neuroimage Clin 10.1016/j.nicl.2020.102188 fMRI
Hahn (2021) NeuroImage 10.1016/j.neuroimage.2020.117470 fMRI
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8Sarasso et al.
Table 4. Papers assessing changes in the state of consciousness during epileptic seizures and other conditions (e.g. psychedelics,
meditation)
First author (year) Journal abbreviation DOI Data type
Epilepsy
Vaudano (2009) PloS One 10.1371/journal.pone.0006475 EEG fMRI
Song (2011) PloS One 10.1371/journal.pone.0017294 fMRI
Li (2015) J Neurol Sci 10.1016/j.jns.2015.04.054 fMRI
Guevara Erra (2016) Phys Rev E 10.1103/PhysRevE.94.052402 EEGSEEGMEG
Mateos (2017) Phys Rev E 10.1103/PhysRevE.96.062410 EEGSEEG MEG
Mateos (2018) Cogn Neurodyn 10.1007/s11571-017-9459-8 EEG SEEG MEG
Dheer (2020) Heliyon 10.1016/j.heliyon.2020.e05769 SEEG
Psychedelics
Tagliazucchi (2014) Hum Brain Mapp 10.1002/hbm.22562 fMRI
Lebedev (2015) Hum Brain Mapp 10.1002/hbm.22833 fMRI
Palhano-Fontes (2015) PloS One 10.1371/journal.pone.0118143 fMRI
Schartner (2017a) Sci Rep 10.1038/srep46421 MEG
Viol (2017) Sci Rep 10.1038/s41598-017-06854-0 fMRI
Preller (2019) Proc Natl Acad Sci U S A 10.1073/pnas.1815129116 fMRI
Viol (2019) Entropy 10.3390/e21020128 fMRI
Barnett (2020) NeuroImage 10.1016/j.neuroimage.2019.116462 MEG
Varley (2020a) NeuroImage 10.1016/j.neuroimage.2020.117049 fMRI
Luppi (2021) NeuroImage 10.1016/j.neuroimage.2020.117653 fMRI
Meditation
Panda (2016) Front Hum Neurosci 10.3389/fnhum.2016.00372 EEG fMRI
Escrichs (2019) Front Syst Neurosci 10.3389/fnsys.2019.00027 fMRI
D¨
urschmid (2020) PLoS One 10.1371/journal.pone.0233589 MEG
Fetal and neonatal
Moser (2019) Front Syst Neurosci 10.3389/fnsys.2019.00023 MEG
Mechanical stimulation of the olfactory system
Piarulli (2018) Sci Rep 10.1038/s41598-018-24924-9 EEG
Given the obvious computational burden of both CNand Φ,
parallel attempts were made in order to develop more applica-
ble measures. In this context, causal density (cd) was proposed
by Seth and colleagues (Seth 2005) as a viable method to mea-
sure the coexistence of differentiation and integration, which they
called the “relevant complexity” (Seth et al. 2006). By leverag-
ing the econometric concept of Granger causality, a measure of
causal inuence based on time-series inference, cd measures the
overall causal interactivity sustained by a system. Specically, cd
captures the dynamical heterogeneity among network elements
(differentiation) as well as their global dynamical integration.
Given that the number of parameters to be estimated is lower with
respect to both CNand Φ, cd is, in principle, more tractable. Poten-
tial drawbacks of cd are that it estimates causal interaction only
from an observational perspective and that its reliability can be
signicantly affected by time-series nonstationarity.
In the following years, these measures were further rened
based on both theoretical and practical considerations (Barrett
and Seth 2011;Toker and Sommer 2019). Yet, the original
formulation of CN,Φ, and cd represents the rst attempt at mea-
suring a new kind of complexity and a valid reference for our
analysis of the empirical metrics that were subsequently applied.
Early theoretical predictions
Besides delineating a novel trajectory from phenomenology to
a new class of measures, as described above, the DCH frame-
work also laid specic predictions on the relationship between
consciousness and brain complexity. Specically:
- The structural architecture (high density of connections,
strong local connectivity, patchiness in the connectivity
among neuronal groups, and large numbers of short reentrant
circuits) of certain brain regions will be much more effective
in generating high complexity than that of other regions. It
follows that at least some regions of the thalamocortical sys-
tem are endowed with the specic anatomical requirements
supporting conscious experience, while others, such as the
cerebellum or the basal ganglia, are not.
- Altering these anatomical requirements, as in the case of brain
lesions involving thalamocortical networks leading to disor-
ders of consciousness, will result in a decrease in complexity.
- Anatomical requirements being equal, changes in functional
neuronal properties that affect reentry, integration, and dif-
ferentiation will result in the loss of complexity and, in turn,
of consciousness in conditions such as NREM sleep, general
anesthesia, and generalized seizures.
- High complexity and conscious experience can be supported
by intrinsic brain interactions even in the absence of sensory
inputs and motor outputs. As such, complexity will be high
during REM sleep (a state of sleep in which subjects almost
always dream) and in other disconnected states.
The empirical test of this set of predictions was initially ham-
pered by limitations inherent to human recording/imaging tech-
niques and by a lower computational power at the time. However,
as soon as the appropriate equipment and analysis tools became
available, the accumulation of relevant empirical data accelerated
and complexity measures were endorsed by an increasing number
of scholars (Alkire et al. 2008;Sitt et al. 2013;Rufni 2017;Aru et al.
2020) in conjunction with an obvious increase of original works
in the last decade (Fig. 2). Due to a considerable gap between the
time of the original predictions and the moment a critical amount
of relevant data became available (almost 20years, as shown in
Fig. 2A), it is understandable that the two events are not always
connected explicitly. This gap, however, represents an interesting
opportunity, in at least two respects. On the one hand, recent
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Consciousness and complexity 9
experiments can be almost considered as an independent set of
validation tests for early predictions. On the other, the original
core concept of integration and differentiation can be employed
as an objective principle to analyze current empirical approaches
to measuring brain complexity.
Consciousness and complexity: a
provisional taxonomy
In the previous section, we reappraised the original rationale for
linking consciousness to complexity. According to this proposal,
the complexity that is relevant for consciousness seems to be a
matter of balance, a balance between diversity and unity, or, more
technically, the amount/repertoire of differentiated states (diver-
sity) that can be generated by a set of interacting elements (unity).
At least in principle, in order to quantify complexity, one should
know the exact structure of the interactions within a system. This
becomes obviously impossible when it comes to real brains, and
empirical approximations are warranted. Our survey of the liter-
ature reveals that current empirical complexity-related measures
have addressed this problem according to different strategies.
Recognizing that other schemes of classications might be
possible, we here provide a provisional taxonomy of this large
body of literature along two main dimensions that we think are
conceptually and practically useful.
The rst dimension relates to the problem of estimating the
repertoire of differentiated states available to a system. Here, we
identify two main approaches adopted by different studies, which
mainly differ in the way they treat brain activity time series. We
then report their relevant empirical intuitions, dene their ratio-
nale, and highlight their operational aspects. Finally, we identify
a number of works proposing interesting mixed approaches.
The second dimension addresses the problem of constraining
the repertoire of states only to those generated by interactions
within the system, i.e. the problem of properly assessing the
integration or the unity of the system by evaluating its internal
interactions from a causal perspective.
Estimating the repertoire of states. A rst
strategy: topological differentiation
Let us start with the rst dimension of the problem, i.e. the esti-
mation of the repertoire of states. A rst strategy adopted for
estimating this repertoire makes use of time series in order to
extract the topological properties of the underlying network, the
complexity of which is then captured by measures of segregation
and integration. We identify the core ingredients (see below) of
this strategy in 102 publications included in our literature search
(Supplementary Table S1).
The underlying rationale is that the ability of a system to
generate a large repertoire of states should correspond to topolog-
ical features characterized by functionally segregated and densely
connected modules that are at the same time integrated through
longer-range, sparse connections.
Operationally, this rst strategy entails a two-step procedure:
(i) the extraction of a network of interacting elements from empiri-
cal data and (ii) the estimation of the balance between segregation
and integration within this network (Fig. 3).
1) Network extraction: network elements or nodes are dened
at different temporal resolutions (from milliseconds to
seconds) and at different spatial scales (from groups of neu-
rons to macroareas and functional subnetworks) depend-
ing on the adopted investigational techniques (from inva-
sive to noninvasive M/EEG techniques and fMRI). Network
edges (i.e. the relationships between interacting nodes) are
identied by employing different metrics, such as temporal
correlations, coherence, phase synchronization, and mea-
sures of information ow (Barnett et al. 2020;Nadin et al.
2020).
2) Complexity estimation: the majority of studies estimate the
balance between segregation and integration by employing
metrics of graph theory, such as measures of network mod-
ularity, density, node centrality, clustering coefcient, local
and global efciency, and small-worldness (Chennu et al.
2017;Luppi et al. 2021). Others use functional connectivity
techniques that allow for the quantication of connections
both within and between different functional subnetworks
(Schrouff et al. 2011). Finally, the spatial complexity of
connections between elements, as measured by entropic,
algorithmic, and fractal indices, can also be employed
to gauge the balance of local segregation and global
integration within the reconstructed network (Viol et al.
2019).
Notably, some studies only perform the rst step and
characterize the connectivity between distributed neuronal
groups without explicitly accounting for the balance between the
segregation and integration of the underlying network (Liang et al.
2016;Huang et al. 2018). Although valuable from a descriptive
point of view, these approaches are less explicitly related to brain
complexity.
Figure 3. Schematic representation of the rst strategy for estimating the repertoire of brain states (topological differentiation)
A network of interacting elements is extracted from empirical data (M/EEG or fMRI time series) using different methods (e.g. temporal correlations, coherence,
phase synchronization or measures of information ow). Complexity is then estimated on the extracted network by applying different metrics of segregation and
integration, such as measures of network modularity, density, node centrality, clustering coefcient, local and global efciency, and small-worldness, or by
applying functional connectivity, entropic, algorithmic or fractal indices.
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10 Sarasso et al.
Figure 4. Schematic representation of the second strategy for estimating the repertoire of brain states (temporal differentiation)
Patterns or states of brain activation are extracted directly from brain activity time series or by applying a variety of methods such as signal binarization or
symbolization, signal transformations (e.g. principal components and surface Laplacian), embedding or cluster analysis. Complexity is then estimated on the
extracted temporal patterns by means of entropy measures, fractal measures, indexes of algorithmic complexity, number and distribution of microstates,
methods based on recurrence quantication analysis, and empirical approximations of integrated information (Φ) or by applying measures of information
sharing, such as mutual information or transfer entropy.
Figure 5. Schematic representation of the mixed strategy for estimating the repertoire of brain states
This strategy adopts a combination of the other two in that it extracts topological properties from empirical data (as in the rst strategy) and then quanties their
differentiation over time (as in the second strategy).
Estimating the repertoire of states. A second
strategy: temporal differentiation
An alternative strategy (adopted by 86 publications derived from
our literature search; Supplementary Table S1) is to directly esti-
mate complexity based on the amount of information (or differ-
entiation) encoded in the temporal dynamics of brain activations.
The underlying rationale is that the size of the repertoire of
available states is a function of the number of nonredundant
patterns generated during the temporal evolution of the system.
Operationally, this second strategy entails a two-step proce-
dure: (i) the extraction of temporal patterns of activity that result
from the interactions among neuronal groups and (ii) the estima-
tion of the complexity or information content of the resulting time
series (Fig. 4).
Pattern extraction: different studies dene patterns or states of
brain activation in a variety of ways and at multiple spatiotempo-
ral scales depending on the employed techniques. Patterns can
be identied as absolute signal uctuations (Tagliazucchi et al.
2013) or by applying methods such as signal binarization or sym-
bolization, signal transformations (e.g. principal components and
surface Laplacian), embedding, or cluster analysis (Demertzi et al.
2019;Wenzel et al. 2019).
Complexity estimation: once activation patterns have been
identied, a variety of metrics can be used to quantify tempo-
ral complexity, such as entropies, fractal measures, indexes of
algorithmic complexity, number and distribution of microstates,
methods based on recurrence quantication analysis, and empir-
ical approximations of integrated information (Φ). Examples of
such applications can be found in Andrillon et al. (2016),Mateos
et al. (2018), and Liu et al. (2019). Measures of information shar-
ing, such as mutual information or transfer entropy (which are
more typically used to construct the edges between nodes in a
graph, as in the rst strategy), can also be employed as indexes of
the amount of information exchanged by interacting brain regions
(King et al. 2013).
It is worth noting that, also in this case, a small subset of
studies (see, e.g. Massimini et al. 2005;Usami et al. 2015) only
performed the rst step explicitly, thus quantifying the differenti-
ation only in a qualitative manner (i.e. without formally applying
quantitative measures to estimate complexity).
Estimating the repertoire of states. A mixed
strategy and its relationships to metastability
and criticality
A small number of studies (23 in our literature search) adopted a
combination of the above-mentioned strategies in that they make
use of time series in order to construct the topological proper-
ties of the underlying network (as in the rst strategy) and then
quantify their differentiation over time (as in the second strategy).
Operationally, this approach generally works by employing rela-
tively short temporal sliding windows in order to construct a time
series of quasi-stable network congurations, which is then used
to estimate the repertoire of states available to the system (Fig. 5).
Examples of such mixed strategy can be found in Golkowski et al.
(2019) and Cai et al. (2020a).
It is interesting to note that the high variability of such quasi-
stable congurations or quasi-stationary states is also considered
a mark of metastable regimes, where the system is out of equilib-
rium and is driven to visit different states by intrinsic or extrinsic
events (Tognoli and Kelso 2014;Deco et al. 2017;Cavanna et al.
2018). Some of the studies in our literature search make explicit
use of such concepts and estimate complexity by the level of
integration of different neuronal assemblies during events such
as rapid transition periods (Fingelkurts et al. 2013) or intrinsic
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Consciousness and complexity 11
ignitions across brain areas (Deco et al. 2017;Escrichs et al. 2019;
Hahn et al. 2021). Metastability is, in turn, related to the phe-
nomena of criticality and phase transition in dynamical systems:
the variability of states or network congurations is generally
maximized at critical values of specic parameters controlling
the dynamics of the system. In subcritical regimes, interactions
among the elements become dominant and the system tends
toward complete order. At the other extreme, in supercritical
regimes, external sources and local uctuations dominate the
dynamics and the system fragments into a multitude of inde-
pendent clusters. The balance between order (integration) and
disorder (segregation) can thus also be estimated by markers of
criticality, such as measures of scale-free behaviors (Allegrini et al.
2015;Bocaccio et al. 2019;Colombo et al. 2019;D¨
urschmid et al.
2020), hysteresis (Kim et al. 2018a), and dynamical instability
(Alonso et al. 2014).
Estimating integration: observation vs
perturbation
Irrespective of the strategy adopted to estimate the repertoire
of states, one key aspect relates to the methods adopted to
assess integration, i.e. to constrain such repertoire to those
states that are generated by genuine interactions among neuronal
groups.
This is important as it tackles the problem of distinguishing
between a unitary system made of tightly interacting elements
and an aggregate of largely independent generators of activ-
ity. Adopting a causal perspective is a viable way to approach
this issue and best approximate the structure of the interactions
within a system, which, as discussed above, represents a key pre-
requisite to quantify the relevant complexity. In practical terms,
measuring causal relationships as opposed to statistical depen-
dencies contrasts the inuence of spurious sources of integration,
such as common drivers and correlated inputs, and minimizes
the inuence of noise, which can articially affect complexity
estimations (e.g. in the presence of random patterns).
The ideal way to do so is to perturb the system in a con-
trolled manner in order to reliably establish causes and effects
(Paus 2005;Pearl 2009;Pearl and Mackenzie 2018). However, the
vast majority of studies (159 in our literature search; see Sup-
plementary Table S1) adopted an observational strategy, often
assisted by specic methods to mitigate the risk of confusing cor-
relation with causation (Friston 2011). Some of these are aimed
at diminishing activities and patterns originating from sources
other than interacting neuronal elements. Examples of such appli-
cations are methods of signal decomposition, surface Laplacian,
and source reconstruction to reduce spurious, non-neural corre-
lations (Schartner et al. 2017b); symbolic and multiscale strategies
to reduce the impact of noise and random uctuations (Lee et al.
2018); and the use of measures such as weighted symbolic mutual
information, which is based on disregarding co-occurrences of
identical or opposite-sign patterns in order to reduce the effects of
common drivers (King et al. 2013). Statistical measures of directed
connectivity, such as transfer entropy and Granger causality, both
in time and frequency domain, are frequently used as proba-
bilistic accounts of actual causation (Barrett et al. 2012). Corre-
lating temporal complexity with structural connectivity or with
the activity of known integrated functional networks is another
way to substantiate the causal origin of the observed informa-
tion (Tagliazucchi et al. 2013;Tagliazucchi 2016). Finally, dynamic
causal modeling was also applied to the problem of consciousness,
although this approach is more commonly used to character-
ize the type and strength of interactions across a small number
of brain areas rather than estimating complexity (Vaudano et al.
2009;Preller et al. 2019).
On the other hand, only a small number of studies (23 in
our literature search, see Supplementary Table S1) assessed the
causal structure of a system by analyzing its responses to direct
cortical perturbations, which enable extracting only the pat-
terns of activity that are generated through effective interactions.
Operationally, these studies employed a “perturb and measure”
approach based on the use of noninvasive techniques, such
as navigated TMS and high-density electroencephalography (hd-
EEG), as well as invasive intracranial electrical stimulations and
recordings (Massimini et al. 2005;Ragazzoni et al. 2013;Pigorini
et al. 2015;Usami et al. 2019;Sinitsyn et al. 2020). In particular,
a subset of these studies, explicitly inspired by theoretical prin-
ciples (Tononi 2004), combined this perturbational approach with
strategies such as nonparametric statistical analysis and algorith-
mic complexity at the sources level (Casali et al. 2013) or principal
component decomposition and recurrence quantication analy-
sis at the sensors level (Comolatti et al. 2019), yielding indices of
“perturbational complexity” (or PCI—Perturbational Complexity
index; Fig. 6).
Far from being denitive, this taxonomic attempt illustrates
the wide range of approaches that have been adopted to estimat-
ing brain complexity, highlights their relationship, and identies
some of their caveats. In this latter respect, our analysis identi-
ed instances in which measures of differentiation were applied to
Figure 6. A perturbational approach to brain complexity
The causal structure of a system is assessed by applying local direct cortical perturbations, and complexity is estimated by retaining only the patterns of activity
that are generated through effective interactions engendered by the perturbation.
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12 Sarasso et al.
signals obtained from single brain regions or recording channels.
These metrics, albeit practically useful, necessarily rely on the
strong assumption that the degree of differentiation they quan-
tify reects properties of the system as a whole (i.e. they take
integration for granted). Clearly, in these cases, the estimation
of the relevant complexity can be confounded by patterns pro-
duced by independent neural generators or noise. On the other
hand of the spectrum, we found measures that were solely based
on global spatiotemporal correlations. These measures, which do
not explicitly account for differentiation, can provide high val-
ues for patterns that are highly correlated but stereotypical and
not complex. In between these two extremes, the vast major-
ity of the identied works (133 out of 182) employed methods to
estimate both integration and differentiation. This recent trend
provides strong evidence for a shared commitment to develop
practical indices of consciousness that gauge the balance between
diversity and unity in the brain in noticeable agreement with early
theoretical proposals.
Consciousness and complexity: the next
20 years
In the previous sections, we have highlighted an interesting tra-
jectory traversing the science of consciousness over the last two
decades. The emerging consilience is that measures of complex-
ity, all designed to capture the joint presence of integration and
differentiation in the brain, represent reliable indices of the state
of consciousness. Starting from this common empirical back-
ground, we now consider open issues of both practical and the-
oretical relevance that should be addressed in the years to come
in order to further advance this promising front.
Complexity and the capacity for consciousness
Assessing sensitivity and specicity across different conditions is
the ultimate practical guide to judge how a given marker approx-
imates neuronal processes that are relevant to the presence or
absence of consciousness. While some studies assessed the per-
formance of complexity-related metrics only at the group level
and others provided a precise quantication of their accuracy
in a clinical setting, they all concurred on the same conclu-
sion: complexity is higher in conditions in which consciousness
is present and lower in conditions where this is lost. Such a
high degree of consistency across different conditions, including
challenging cases, such as disconnected consciousness in dream-
ing and ketamine anesthesia, hallucinatory states, and patients
with severe brain injuries, is remarkable when compared to the
discrepancies characterizing other classes of measures.
For example, when directly compared, complexity measures
largely outperform ERPs, such as the P3b, in the detection of
minimally conscious patients, the latter being characterized by
lower sensitivity (Sitt et al. 2014). Also, complexity remains high
in conscious subjects during REM sleep or ketamine hallucina-
tions (Casarotto et al. 2016;Farnes et al. 2020), whereas ERPs
to global deviant stimuli typically disappear (Strauss et al. 2015;
Bravermanov´
aet al. 2018). Likewise, complexity measures con-
sistently show high values and dissociate from EEG alpha power,
which is known to decrease in conditions of disconnected con-
sciousness, such as during dreaming, hallucinations, and in the
locked-in syndrome (Esposito et al. 2004;Babiloni et al. 2010;
Timmermann et al. 2019). Measuring brain complexity also over-
comes some of the limitations of indices quantifying scalp EEG
delta power; indeed, wakefulness-like complexity values can be
detected even when high-amplitude slow waves dominate the
spontaneous scalp EEG in some minimally conscious patients
(Casarotto et al. 2016) as well as in conscious children with Angel-
man syndrome (Frohlich et al. 2020) and in healthy conscious
subjects administered with the GABA reuptake inhibitor tiagabine
(Darmani et al. 2021). On the other hand, gamma band synchrony
[an early proposed neural correlate of consciousness (Crick and
Koch 1990)] and brain metabolism can persist or even increase
during epileptic seizures (Pockett and Holmes 2009;Bai et al. 2010),
whereas complexity is found invariably reduced (see, e.g. Song
et al. 2011;Mateos et al. 2018), consistent with the loss of con-
sciousness characterizing this condition. Overall, it seems that
complexity is more reliable than other metrics, arguably offering
not only better diagnostic accuracy but also a potential guide to
identify, among the many facets of brain activity, core properties
that are more relevant to consciousness.
Clearly, discrepancies will be found also in the case of
complexity-related measures. As we will discuss later, this is to
be expected if only one considers the number of different methods
and spatiotemporal scales at which complexity is estimated. The
taxonomy described in the previous section is meant to provide
a framework to help interpret potentially emerging conicting
results and to select the most promising set of measurement
strategies. Toward this aim, it will be critical for future studies
to precisely identify how they dene and quantify complexity and
to explicitly report each measure’s performance in terms of sensi-
tivity and specicity whenever a ground-truth about the state of
consciousness of individual subjects is available (Demertzi et al.
2017).
Practically, to the extent that they have been extensively vali-
dated in benchmark conditions, indices of brain complexity can
be effectively employed analogously to other scalar measures
that are normally employed in medicine. Just like measuring
the ejection fraction provides a rough but useful index of the
heart’s capacity to sustain hemodynamic functions, measuring
complexity may provide a rough but useful index to infer the
brain’s ability to sustain consciousness. For example, detecting
wakefulness-like complexity levels in the brain of a patient who
is behaviorally unresponsive and inaccessible through ERPs indi-
cates that this patient is disconnected on the output and/or input
side rather than unconscious (Casarotto et al. 2016;Rohaut et al.
2017;Bayne et al. 2020a). Whether more subtle, monotonically
varying changes in brain complexity are meaningful with respect
to graded changes in conscious states is an open question (Cecconi
et al. 2020;Bayne et al. 2020b). Answering this question would
require not only performing measurements at the optimal spa-
tiotemporal scale (see more about this below) but also a shared
notion of levels of consciousness (Bayne et al. 2016;Mckilliam
2020). In this concern, early proposals have provisionally dened
empirical measures of the coexistence of integration and differen-
tiation as indices of the “capacity for” rather than of the “level of”
consciousness (Massimini et al. 2009). As already noted above, this
notion entails the general capacity for any kind of experience that
is not necessarily associated with the cognitive operations typi-
cal of wakefulness. Indeed, high brain complexity can be detected
in conscious conditions where the functional requirements of
wakefulness are relaxed or absent, such as during dreaming and
ketamine anesthesia (Sarasso et al. 2015;Casarotto et al. 2016).
Mechanisms of loss and recovery of complexity
As loss and recovery of consciousness can be reliably tracked
by shifts in brain complexity in humans, it is crucial to explore
the mechanisms of these changes at the neuronal level. For
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Consciousness and complexity 13
example, one may ask why, as multiple studies have demon-
strated, complexity collapses when consciousness fades during
sleep and anesthesia, structural connections remaining equal.
Interestingly, recent studies have drawn connections between
specic changes in postsynaptic properties of single neurons and
the brain capacity for engaging in complex patterns of interac-
tions. A rst candidate mechanism, called neuronal bistability, is
the tendency of cortical neurons to plunge into a silent, hyper-
polarized state (OFF-period) upon receiving an input (Steriade
et al. 1993). This tendency is due to adaptation mechanisms,
which become prominent when activity-dependent potassium
currents are stronger (Sanchez-Vives and McCormick 2000) or
when the excitation/inhibition balance is shifted toward the lat-
ter (Funk et al. 2017). A wealth of animal studies has shown the
occurrence of neuronal OFF-periods during sleep and anesthesia,
where they are associated with the appearance of EEG slow waves
(Steriade et al. 1993;Sanchez-Vives et al. 2017). Crucially, converg-
ing noninvasive and intracranial works in humans, rodents, and
cortical slices (D’Andola et al. 2018;Comolatti et al. 2019;Dasilva
et al. 2021) have recently demonstrated that neuronal OFF-periods
determine a dramatic collapse of brain complexity (loss of both
integration and differentiation), as measured by PCI, during NREM
sleep and anesthesia. Perhaps even more relevant in the present
context, a direct link between bistability and loss of complexity
has also been demonstrated in brain-injured humans (Rosanova
et al. 2018); not only the buildup of causal interactions and com-
plexity is blocked by OFF-periods in unconscious patients but also
both global brain complexity and consciousness recover when
OFF-periods disappear.
In light of the above, it is not surprising that conditions char-
acterized by low brain complexity tend to be associated with the
presence of slow waves, as both are linked to neuronal bistability.
However, interesting dissociations are also possible. For exam-
ple, EEG macroscale recordings can be at once characterized by
a predominant delta spectral power and preserved complexity
(Frohlich et al. 2020;Darmani et al. 2021). This apparent para-
dox might be explained by a mixed pattern at the mesoscale level
where focal but powerful cortical sources of slow waves emerge
in a brain that is otherwise in a state of wake-like complexity
(Frohlich et al. 2021). On the other hand, low brain complexity
can be found in the absence of slow waves in the ongoing brain
activity even when measured at a ner spatial scale. For example,
pharmacologically increasing excitation without blocking bista-
bility results in wake-like spectral features associated with low
perturbational complexity assessed by means of electrical stim-
ulation in cortical slices (D’Andola et al. 2018). This nding can
be understood if one considers that bistability, due to its intrinsic
activity-dependent nature, is a latent neuronal property that pre-
vents the emergence of large-scale cause-effect chains supporting
brain complexity even when slow waves are not present in the
ongoing prestimulus activity.
Another candidate postsynaptic mechanism that may account
for the disruption of brain complexity is the decoupling between
the apical and basal dendritic compartment of Layer 5 pyramidal
neurons (Takahashi et al. 2016;Aru et al. 2020). Experiments in
rodents have shown that this gating occurs under different anes-
thetics and that it may be controlled by higher-order thalamic
nuclei (Suzuki and Larkum 2020;Takahashi et al. 2020). Crucially,
the apical compartment receives feedbacks from corticocorti-
cal and thalamocortical loops, whereas the basal compartment
mainly receives the feedforward stream from specic areas lower
in the processing hierarchy. This dendritic decoupling is, at least
in principle, in a key position to break down recurrent interactions
across distributed areas, thus impairing functional integration in
the brain. To the extent that this effect can be demonstrated at the
whole-brain level and generalized to other conditions (e.g. sleep
and coma), it may point to a fundamental neuronal determinant
of the changes in complexity that are observed upon loss and
recovery of consciousness. It will be important for future studies
to explore whether and how neuronal decoupling and bistability,
which are nonmutually exclusive, interact during physiological,
pharmacological, and pathological loss of consciousness.
The examples discussed above suggest that we may soon
develop a multiscale understanding, from single neurons to global
brain measures, of the mechanisms of loss and recovery of brain
complexity during different states of consciousness. Such opti-
mistic predictions are justied for at least two reasons. The rst
reason is the availability of animal models in which clinically
relevant complexity indices, such as PCI (Arena et al. 2021;Dasilva
et al. 2021;Barbero-Castillo et al. 2021) or the repertoire of fMRI
dynamics (Barttfeld et al. 2015), can already be measured and
manipulated. Lesioning and optogenetic interventions in these
models may e.g. reveal whether there are specic groups of neu-
rons that are more important than others in sustaining complexity
and whether we can directly act upon these nodes. Importantly,
animal models grant direct access to subcortical structures that
may play a key role, such as the thalamus (Redinbaugh et al.
2020). The second reason for optimism is the parallel develop-
ment of whole-brain, data-driven computer simulations in which
changes in complexity across different brain states are explic-
itly modeled at multiple scales (Deco et al. 2015;Zamora-L´
opez
et al. 2016;Goldman et al. 2019). This computational neuroscience
approach aims at offering a mechanistic framework for character-
izing brain states in terms of the underlying causal mechanisms
and the resulting complexity. Although discussing the role of com-
puter simulations is clearly beyond the scope of the present paper,
it is perhaps important to highlight that this kind of modeling
effort, specically pursued within the Human Brain Project, also
aims at predicting the effects of pharmacological and electro-
magnetic perturbations needed to force transitions between brain
states (Zamora-L´
opez et al. 2016;Kringelbach and Deco 2020).
In a long-term perspective, employing this multiscale approach
encompassing animal and in silico models holds the promise that
we might learn, one day, how to act on cellular targets in order to
restore complexity and possibly consciousness in injured human
brains.
Spatiotemporal scales of complexity
In humans, animal models, and computer simulations, complex-
ity can be assessed at different spatiotemporal scales. As we have
seen in the taxonomy section, neuroimaging studies of functional
or effective connectivity in the brain examine interactions at the
spatial level of voxels and at the temporal level of blood-oxygen
uctuations on the order of seconds. On the other hand, EEG-
based measures of complexity explore a coarser spatial scale,
but with much ner temporal sampling, on the order of millisec-
onds. These differences are expected to dramatically affect the
estimation of brain complexity. For example, considering corti-
cal areas at the time scale of seconds would necessarily minimize
the estimates of differentiation by reducing the repertoire of pos-
sible states. At the other end of the spectrum, recordings of single
neurons on a time window of a few milliseconds are likely to
underestimate causal interactions, and thus integration, due to
synaptic failures (Galarreta and Hestrin 1998), noise, and conduc-
tion delays (hundreds of milliseconds) characterizing large-scale
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14 Sarasso et al.
communication. Where is the tradeoff? What is the optimal spa-
tiotemporal grain at which measurements should be performed?
Although recent advances in the mathematical analysis of multi-
scale systems have made progress in addressing the problem (Hoel
et al. 2013,2016;Rosas et al. 2020), determining in a principled
way what counts as the “most appropriate” grain is of course very
challenging.
Following the same logic that led to the identication of com-
plexity as a relevant physical brain property, phenomenology
may also guide the search for the optimal spatiotemporal scale.
In this perspective, the appropriate grain at which complexity
should be measured is the same spatiotemporal grain that is
relevant for experience. For example, regarding time, there is
a general agreement that an “instant” of experience is on the
order of tens to hundreds of milliseconds rather than a few mil-
liseconds or tens of seconds (Libet et al. 1991;Bachmann 2000;
Holcombe 2009). Regarding space, experiments employing direct
cortical stimulation in humans suggest that the minimal activated
volume required to elicit phosphenes of different colors roughly
corresponds to the size of a cortical minicolumn (Schmidt et al.
1996), whereas such color discrimination is lost when the acti-
vated volume is increased to the size of an hypercolumn (Tehovnik
and Slocum 2007). Whether single neuron stimulation further
increases perceptual differentiation or rather results in no percep-
tual effects at all is an important open question to be addressed
in order to dene the spatial grain at which neuronal interac-
tions become relevant for consciousness. For the moment, taking
into account minicolumns on a time window of hundreds of mil-
liseconds may represent a reasonable starting point for measuring
integration and differentiation in the brain. If we could work at
such a scale, absolute complexity values would certainly sky-
rocket with respect to current readouts, making some justice to
the actual complexity of the brain and allowing for more mean-
ingful comparisons across experimental models, perhaps even
between human and animal experiments.
Localization of complexity
Another key question is whether the relevant complexity is gener-
ated in specic parts of the brain. It is indeed very likely that while
some structural and functional arrangements are well suited for
optimizing the coexistence of integration and differentiation, oth-
ers may not. An extreme example is offered by the cerebellum. In
this structure, myriads of microzones process inputs and produce
outputs that are only feedforward (with no excitatory reverber-
ant activity) and largely independent. In spite of the richness of
the inputs (vestibular, visual, somatosensory, auditory, motor
etc.) that various modules receive and process at an extraordi-
nary pace, the strictly modular structure of the cerebellum is
inherently incompatible with integration and high levels of com-
plexity. In essence, considering its internal architecture, it is very
likely that the cerebellum is not a single entity capable of high
complexity but just an aggregate of small independent modules
each traversed by a different data stream. This may explain why
lesions of the cerebellum, which has four times more neurons
than the cerebral cortex (Herculano-Houzel 2012), do not seem
to affect consciousness (Lemon and Edgley 2010). Future imag-
ing and electrophysiological studies are warranted to empirically
conrm the difference between cerebellar and neocortical circuits
with respect to their capacity to generate the relevant complexity.
Whether signicant differences in the capacity for complexity
can also be found within the cerebral cortex is an open question.
Indeed, the cytoarchitectonics and the intrinsic arrangement of
connections varies largely also across cortical areas. Especially
in the posterior cortex, connections within each area are orga-
nized in a grid-like manner and across areas in a pyramid-like,
convergent-divergent manner (Salin and Bullier 1995). This kind
of architecture leads to a high level of systematic overlap in the
connections among neurons, giving rise to a core network that
“hangs together” tightly—in other words, it is functionally highly
integrated (Haun and Tononi 2019;Deco et al. 2021). By con-
trast, cortical areas in which neurons are organized into more
segregated modules (akin to the cerebellum), or in which the con-
nections are organized more randomly, with less overlap, may be
much less integrated. Available empirical evidence from macro-
scopic EEG and fMRI recordings in humans and monkeys suggest
that posterior cortical areas are more relevant than others. Over-
all, these studies performed in sleep, propofol anesthesia (Luppi
et al. 2019;Hahn et al. 2021) and post-comatose patients (King
et al. 2013;Sitt et al. 2014;Luppi et al. 2019) converge in showing
that loss and recovery of consciousness corresponds to changes in
complexity located in posterior cortical regions.
The question of whether these regions are privileged by virtue
of their particular grid-like structure (characterized by high den-
sity of connections, strong local connectivity, patchiness in the
connectivity, and large numbers of short reentrant circuits) has
also theoretical relevance. This in view of the recent debate high-
lighting the apparent paradox that grid-like structures, such as
articial expander graphs, that are easy to build due to their
low algorithmic structural complexity, can give rise to high levels
of integrated information (Aaronson 2014). The fact that similar
structures can be found within the human brain and that they are
more represented in some regions than in others, offers a unique
opportunity to tackle this problem empirically. Arguably, starting
from us humans, in whom phenomenology and physics can be
compared directly, represents a rst, mandatory step to under-
stand the relationship between circuit architecture, the relevant
complexity, and consciousness. For example, testing experimen-
tally in humans whether neural circuits connected in a grid-like
manner are hot spots for complexity and whether they are funda-
mental for sustaining the presence of consciousness and account
for phenomenal properties, such as the experience of extended
space (Haun and Tononi 2019), would provide valuable data to
inform theoretical debates.
Given the likelihood that complexity is generated in some part
of the brain but not in others, an additional problem will be den-
ing the borders of the relevant subset of elements and whether
these boundaries can shift in physiological or pathological states
of consciousness. The relevance of this problem was already clear
in the original formulation of the DCH, which dened a strat-
egy to identify, based on statistical dependence (see above), the
functional cluster (Tononi et al. 1998) generating the relevant com-
plexity. This has been further qualied by a causal perspective
in the latest formulation of Integrated Information Theory (IIT)
(Oizumi et al. 2014). In a nutshell, the problem boils down to
nding the borders that include the subset of elements that gen-
erate more complexity than any other, smaller or larger, subset.
Although we can safely assume that some structures such as the
retina and the cerebellum with their intrinsic lack of integration
would rest outside of these borders, in practice, it will be very
difcult to identify sharp edges within the brain. In fact, the pos-
sibility that these may even cut across cortical layers or neuronal
populations makes an exhaustive search a daunting proposition.
Dynamic and causal complexity
As already noted above, the example of the cerebellum is note-
worthy as it suggests that some brain structures that are well
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Consciousness and complexity 15
suited for supporting important functions, and from which we
can decode neural activity relevant to behavior (Jiang et al. 2015a;
Friston and Herreros 2016), may not be necessary for conscious-
ness because they do not have the appropriate internal causal
structure. Although, to an external observer, the dynamics of
cerebellar activity may seem complex, a causal approach by
perturbing single microzones and by recording from the rest of
the cerebellum is expected to reveal minimal interactions across
modules and minimal complexity. In general, the possibility of
a dissociation between complexity measures derived from the
observation of ongoing brain dynamics and those based on the
assessment of the underlying causal structure has interesting
implications. Indeed, besides the intuitable case of the cerebel-
lum, one can also conceive and test cases in which the opposite
dissociation might occur, i.e. low dynamical complexity in ongo-
ing activity with a concomitant high complexity of the underlying
causal structure. For example, while measures of ongoing com-
plexity tend to decrease when conscious subjects close their eyes
and alpha rhythm becomes dominant (Stam et al. 1993), the per-
turbational complexity index does not change and remains high
whether eyes are opened or closed (Casali et al. 2013). Perhaps
more interestingly, one could even consider experiments investi-
gating states of “pure consciousness” (Sullivan 1995), also known
as “naked awareness” or “pure presence.” These conditions, whose
phenomenology is well described by the century-old tradition
of meditation practices, are characterized by a vividly present
awareness yet devoid of any perceptual object and occur without
monitoring the environment or self or attending to any particu-
lar content, as well as in the absence of reasoning and behaviors.
How would these states, in which consciousness is vividly present
while little function is performed and little information is being
processed look like in terms of complexity measures? The limited
literature currently available during meditation provide evidence
of a reduction of complexity in the stream of observable ongoing
brain dynamics (Aftanas and Golocheikine 2002;Irrmischer et al.
2018;Escrichs et al. 2019), whereas perturbation measures with
TMS-EEG suggest the presence of a preserved underlying causal
structure (Bodart et al. 2018a). Future studies, systematically per-
forming these kinds of comparisons within the same individual
will be very important to further dene the practical implica-
tions inherent to the different approaches (e.g. observational vs
perturbational) highlighted in the taxonomy section.
Conclusion
To conclude, we would like to suggest how the body of convergent
results highlighted by the present review may easily coalesce in a
front where the eld has a tangible opportunity to advance. For
example, rening methods for measuring complexity, comparing
their accuracy, and identifying their neuronal determinants at the
appropriate spatiotemporal scale are practical steps within reach.
These will be key to improve the way we assess consciousness and
to gain the mechanistic insight needed to promote its recovery in
pathological conditions.
Besides practical implications, connecting the dots of an
interesting trajectory spanning a few decades of conscious-
ness research bears conceptual relevance. In this respect, the
early principles linking consciousness to complexity (Tononi and
Edelman 1998) not only did provide a useful reference to pro-
visionally taxonomize current empirical metrics but may also
represent an interesting basis for future exchanges among differ-
ent theoretical frameworks. For example, besides the Integrated
Information Theory (Tononi 2004), which represents the direct
evolution of the DCH, other frameworks, such as the Global
Neuronal Workspace, the Kolmogorov Complexity Theory of Con-
sciousness, and the Free Energy Principle, have more recently
embraced, albeit starting from different premises, an explicit
complexity-related framework (Dehaene et al. 2014;Rufni 2017;
Friston et al. 2020). Hence, while the focus on functional inte-
gration and differentiation seems to now constitute a common
ground, other elements discussed in the present review may offer
a concrete opportunity to explore interesting differences.
In this vein, one may ask a few specic questions. How do the
different frameworks operationally dene the boundaries of the
subset of neurons generating the relevant complexity? The local-
ization and extent of the physical substrate of consciousness is
likely to differ depending on the way one answers this question.
Also, why do some theories focus on the complexity of ongoing
observable neuronal dynamics, whereas others emphasize the
complexity of the underlying causal structure? It will be key to
clarify this aspect, as it entails a substantially different under-
standing of the kind of information that matters for conscious-
ness, extrinsic in the rst case, intrinsic in the latter (Searle 2013;
Koch and Tononi 2013). Finally, how do current theories consider
the possibility that phenomenology-inspired principles related to
complexity may be useful also in the search for content-specic
neural correlates of consciousness? Asking this may sound pre-
mature now, but attempts have been made in this direction (Haun
and Tononi 2019), and major initiatives, such as the Templeton
Foundation’s Structured Adversarial Collaboration project, are in
place to judge their merit.
Altogether, by considering the past positive trend highlighted
in this review, we should all feel encouraged to face these kinds
of questions head-on and to put forward specic principles and
predictions, even if perceived as counterintuitive and hard to test
at present. To the extent that these are both precise and daring,
there are reasons to believe that they will likely be useful in 20
years from now.
Supplementary data
Supplementary data is available at NCONSC Journal online.
Data availability
There is no data associated with this manuscript.
Funding
This work was supported by the European Union’s Horizon 2020
Framework Program for Research and Innovation under Specic
Grant Agreement No. 945539 (Human Brain Project SGA3), by
Fondazione Regionale per la Ricerca Biomedica (Regione Lombar-
dia), Project ERAPERMED2019-101, GA779282, by the Tiny Blue
Dot Foundation, by the Canadian Institute for Advanced Research
(CIFAR) and by the São Paulo Research Foundation (FAPESP) grant
2016/08263-9.
Conict of interest statement
None declared.
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