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High-energy brain dynamics during
anesthesia-induced unconsciousness

James R. Riehl

, Ben J. Palanca

3,4

, and ShiNung Ching

1,2,4

1Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, MO, Etats-Unis
2Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO, Etats-Unis
3Department of Anesthesiology, Washington University School of Medicine, St. Louis, MO, Etats-Unis
4Division of Biology and Biomedical Sciences, Washington University School of Medicine, St. Louis, MO, Etats-Unis

Mots clés: Dynamique du réseau, Functional connectivity, Free energy, Resting-state networks,
General anesthesia, Consciousness

un accès ouvert

journal

ABSTRAIT

Characterizing anesthesia-induced alterations to brain network dynamics provides a
powerful framework to understand the neural mechanisms of unconsciousness. To this
end, increased attention has been directed at how anesthetic drugs alter the functional
connectivity between brain regions as deﬁned through neuroimaging. Cependant, le
effects of anesthesia on temporal dynamics at functional network scales is less well
understood. Ici, we examine such dynamics in view of the free-energy principle, lequel
postulates that brain dynamics tend to promote lower energy (more organized) states.
We speciﬁcally engaged the hypothesis that such low-energy states play an important
role in maintaining conscious awareness. To investigate this hypothesis, we analyzed
resting-state BOLD fMRI data from human volunteers during wakefulness and under
sevoﬂurane general anesthesia. Our approach, which extends an idea previously used
in the characterization of neuron-scale populations, involves thresholding the BOLD time
series and using a normalized Hamiltonian energy function derived from the Ising model.
Our major ﬁnding is that the brain spends signiﬁcantly more time in lower energy states
during eyes-closed wakefulness than during general anesthesia. This effect is especially
pronounced in networks thought to be critical for maintaining awareness, suggesting a
crucial cognitive role for both the structure and the dynamical landscape of these
réseaux.

RÉSUMÉ DE L'AUTEUR

We show that activity in the human brain, as captured by functional magnetic resonance
imaging (IRMf), is more organized during wakefulness than during general anesthesia. Ce
increased organization corresponds to a decrease in a statistical-physics-inspired energy
measure among brain regions of shared functional specialization (resting-state networks)
that have putative roles in conscious awareness and attention. Characterizing the energy
distributions in this way reveals signiﬁcant changes in the dynamics of brain activity in
different states of consciousness, insights that are not observable in the average functional
connectivity data alone. Our results indicate that the ability of brain networks to sustain
stable representations, via their dynamics, may be crucial for consciousness and
cognition.

Citation: Riehl, J.. R., Palanca, B. J., &
Ching, S. (2017). High-energy brain
dynamics during anesthesia-induced
unconsciousness. Réseau
Neurosciences, 1(4), 431–445.
https://doi.org/10.1162/netn_a_00023

EST CE QUE JE:
https://doi.org/10.1162/netn_a_00023

Informations complémentaires:
https://doi.org/10.1162/netn_a_00023

Reçu: 17 May 2017
Accepté: 2 Août 2017

Intérêts concurrents: Les auteurs ont
a déclaré qu'aucun intérêt concurrent
exister.

Auteur correspondant:
James Riehl
jrriehl@wustl.edu

Éditeur de manipulation:
Olaf Sporns

droits d'auteur: © 2017
Massachusetts Institute of Technology
Publié sous Creative Commons
Attribution 4.0 International
(CC PAR 4.0) Licence

La presse du MIT

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High-energy brain dynamics during anesthesia-induced unconsciousness

INTRODUCTION

General anesthesia:
Pharmacologically induced state
of unconsciousness or
unresponsiveness.

Brain network dynamics:
Time-varying changes in connectivity
and patterns of activation among
distinct brain regions.

Wakefulness:
Behavioral regime in which a person
actively responds to external
stimulation of the senses.

Maximum entropy principle:
A model for the activity of a system
should assume as little as possible
beyond prior information and
measured data.

Ising model:
Network model in which nodes take
binary states and energy is computed
based on pairwise interactions,
originally applied to ferromagnetism.

Free-energy principle:
Postulates that as a general rule, le
brain tends to move toward states
having lower energy.

général

anesthesia has

seemingly unambiguous behavioral

While
endpoint—
unconsciousness—the neural mechanisms by which this state is achieved are diverse and
highly enigmatic (Alkire & Miller, 2005; Brun, Lydic, & Schiff, 2010; Brun, Purdon, & Van
Dort, 2011; Mashour & Alkire, 2013). Ainsi, motivated by the premise that consciousness and
cognition rely on a measure of coordination across brain regions and temporal scales, sub-
stantial effort has been directed at examining the effects of anesthetics on networks in the
brain (Hudetz, 2012; Noirhomme et al., 2010; Peltier et al., 2005).
À cet égard, assessing
the ability of brain networks to support and transition between a diversity of stable states is of
paramount interest; such dynamics are thought to be key mediators of robust information pro-
cessing and may be important in understanding ﬂuctuating states in sleep and pathologic disor-
ders of consciousness (Deco & Jirsa, 2012; Golos, Jirsa, & Daucé, 2015; Kinouchi & Copelli,
2006). The primary goal of this paper is to examine the effect of anesthesia on brain network
dynamics through a statistical physics notion of energy and, speciﬁcally, to assess whether the
state of unconsciousness is associated with an altered energy distribution relative to that of
wakefulness.

Plus généralement, collective organization measures such as energy and entropy have proven
valuable in the analysis of brain activity patterns and in relating of such patterns to cogni-
tive function.
En effet, the two most prevalent principles regarding maximum entropy and
minimum energy are closely related in the context of brain dynamics. The maximum en-
tropy principle states that a set of observations should be described by the distribution having
the highest entropy (Jaynes, 1957). Put simply, a model for observed neural activity should
assume as little as possible beyond what is represented in the data.
It turns out that the
maximum entropy model for a binary state system consisting of only pairwise interactions
is known as the Ising model (Schneidman, Berry, Segev, & Bialek, 2006). This model was orig-
inally proposed to address phase transitions in networks of quantum spin states, but has since
attracted considerable attention in computational neuroscience (Cocco, Leibler, & Monasson,
2009; Roudi, Tyrcha, & Hertz, 2009). Note that in this context, entropy is largely a static con-
cept insofar as it describes a distribution of activation states, and it provides little information
about the dynamics of how those states evolve over time. On the other hand, the free-energy
principle, which postulates that a self-organizing system tends to minimize free or excess en-
ergy (K. Friston, 2010), is primarily a statement about dynamics. The Ising Hamiltonian, lequel
can be thought of as a measure of free energy in a binary state system, is a dynamic quantity
expressing the degree to which neighboring nodes or regions are in alignment over time (Ising,
1925). For a pair of brain regions in which activity is positively correlated, alignment means
that these regions are either both active or both inactive at a particular time, while for anti-
correlated regions, alignment means that they occupy opposite activation states. As the Ising
energy of a network decreases, it moves closer to a state of equilibrium. When invoking the
free-energy principle, we do not claim that the brain ever reaches or even closely approaches
such equilibria. Plutôt, the overall premise of this paper is that by observing the distribu-
tion of these energies over time, it may be possible to broadly characterize different modes
of functionality in the brain. To investigate this issue, we will examine how the energy land-
scapes of brain networks, deﬁned from functional magnetic resonance imaging (IRMf) data,
vary between subjects who are awake and under general anesthesia.

Variations on the Ising model have been used previously to model emergent properties of
brain networks at the neuronal level.
In this setting, individual neurons can be modeled as
being either active or inactive, thus enabling characterization of network statistical properties

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High-energy brain dynamics during anesthesia-induced unconsciousness

Functional connectivity:
Mathematical description of the
relationship between brain regions,
typically in terms of correlations.

Resting-state networks:
Subnetworks in the brain consisting
of regions of shared functional
specialization when the subject is
not engaged in an active task.

within the Ising formalism (Cocco et al., 2009; Hopﬁeld, 1982; Roxin, Riecke, & Solla, 2004;
Schneidman et al., 2006). Cependant, there have been considerably fewer investigations of Ising
energy at the broader spatial level of connectivity between brain regions, which is our interest
herein.

Perhaps the most common analysis of brain network at broad spatial scales involves com-
puting the functional connectivity, wherein the relationship between brain regions is charac-
terized in terms of the covariance of their time-varying signals (K. J.. Friston, 1994; Jiang, Il,
Zang, & Weng, 2004; Mayer, Mannell, Ling, Gasparovic, & Yeo, 2011; Wang et al., 2007). Re-
lated measures, such as the Pearson correlation coefﬁcient, can be projected as edge weights
in a network, taking either positive or negative values depending on whether the corresponding
regions are correlated or anticorrelated. These relationships have been used to deﬁne resting-
state networks (RSNs), parcels of brain regions whose patterns of correlated signal reﬂect shared
functional specialization during task performance (Beckmann, DeLuca, Devlin, & Forgeron, 2005;
Cordes et al., 2000; Smith et al., 2009). By returning to the time series data after computing the
functional connectivity matrices, we take this line of analysis a step further and characterize
the brain’s energy distribution over time.

Energy-based analysis can further illuminate properties of the underlying brain network
dynamics, even at the coarser spatial resolutions of fMRI. Par exemple, energy distributions
on networks built from resting-state fMRI data have been modeled using a stochastic gradient
descent algorithm to ﬁnd local energy minima (regarded as equilibria of the underlying network
dynamics) and estimate their corresponding basins of attraction (Gu et al., 2016). En effet, ce
energy characterization revealed positive correlations between observed and predicted rates of
regional activation. Our objective is to examine how alterations in the energy landscape may
relate to a systematic alteration in cognitive state (namely, a state of general anesthesia). Dans ce
regard, it has been predicted from simulations that the awake resting (c'est à dire., unanesthetized) state
corresponds to network states that are closer to equilibrium (Hudetz, Humphries, & Binder,
2014).

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The main contribution of our work is that, for the ﬁrst time, we provide empirical evidence
that wakeful consciousness correlates to the brain spending more time in lower energy states
than under general anesthesia. To do so, we introduce a correlation-normalized Hamiltonian,
in order to assay the energy landscapes in a manner that is invariant to the overall strength of
functional connectivity. We observe the effect across a majority of RSNs, and notably in the
default mode and somatomotor networks. In contrast, the energy landscapes of the vision and
language RSNs were mostly robust to general anesthesia.

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RÉSULTATS

Global Reduction in Functional Connectivity During General Anesthesia

Our analyses focus on within-RSN functional connectivity and energy dynamics. Chiffre 1
shows the functional connectivity matrices for each of the seven deﬁned RSNs, averaged over
all subjects (see Materials and Methods). The top row corresponds to the awake resting state,
while the second row corresponds to general anesthesia. While most correlations are pos-
itive, there exist scattered weak anticorrelations between regions, which can be seen in the
histograms on the bottom row of Figure 1. We may surmise from these matrices that the overall
connectivity patterns are similar between the two conditions. If we perform a linear regression
relating the mean correlation coefﬁcients during wakefulness and under general anesthesia,
shown in Figure 2, we see that the mean functional connectivity during wakefulness is

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High-energy brain dynamics during anesthesia-induced unconsciousness

DAN

VAN

SMN

VIS

FPC

LAN

DMN

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100

10-1

10-2

10-3

10-4

-0.2

wakefulness
anesthesia

0.5

-0.5

-1

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mean correlation ( r)

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-0.2

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mean correlation ( r)

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-0.2

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0.4
mean correlation ( r)

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-0.2

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0.4
mean correlation ( r)

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-0.2

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0.4
mean correlation ( r)

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-0.2

0.2

0.4
mean correlation ( r)

0.6

0.8

-0.2

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mean correlation ( r)

0.6

0.8

Chiffre 1. Correlation matrices (matrices of Pearson correlation coefﬁcient ρ) averaged over all subjects in states of wakefulness (top) et
general anesthesia (middle) for each RSN. Note that the number of regions varies across RSNs. Although the majority of correlations are
positive, there are indeed scattered weak anticorrelations between regions, as shown in the histograms on the bottom row.

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Chiffre 2. Linear regression through the origin reveals that the mean correlation coefﬁcients during
wakefulness are higher than those during general anesthesia in relatively consistent proportions
across RSNs.

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High-energy brain dynamics during anesthesia-induced unconsciousness

Sevoﬂurane:
Sedative drug used to administer
general anesthesia by inhalation.

environ 1.26 times stronger than that during general anesthesia. Although there is some
small variation across the RSNs, particularly in the somatomotor network, the overall effect
is relatively consistent across brain regions, a known phenomenon associated with general
anesthesia (Boveroux et al., 2010; Palanca et al., 2015). In what follows, by characterizing the
energies of the BOLD time series data in the context of these functional connectivity networks,
we provide additional insight into the how the dynamics of the brain are affected by general
anesthesia and how these effects vary across RSNs.

An Anesthesia-Induced Shift to High-Energy Dynamics

Since sevoﬂurane anesthesia appears to globally weaken intracortical functional connectivity,
we proceeded to compute the Ising energies according to a normalized Hamiltonian function
(that is invariant to a uniform scaling in correlation; see Methods). Figure 3A–G shows the
resulting energy distributions on a normalized abscissa for each of the seven different RSNs.
The plots depict a trend in which the energy landscape under general anesthesia has less den-
sity in the lower range of normalized energies versus that of wakefulness (as is the convention,

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Chiffre 3. The difference in energy distribution during wakefulness and general anesthesia for each
RSN (A–G). Summarized in the bar plot H, wakefulness correlates to the brain spending signiﬁcantly
more time in lower energies than during general anesthesia. In paired-sample t tests, * indicates that
p < 0.1 while ** indicates that p < 0.01. Note that by convention the Ising Hamiltonian becomes more negative with decreasing energy. The strengths of these effects are quantiﬁed in the slopes of plot I, listed in the legend. The networks with the strongest effects are DMN and SMN, whereas the landscapes of LAN and VIS are more invariant to anesthesia. Network Neuroscience 435 High-energy brain dynamics during anesthesia-induced unconsciousness the Ising Hamiltonian becomes more negative with decreasing energy). Speciﬁcally, when computing the relative densities in the lesser (< 0.5) versus greater half (> 0.5) of the normal-
ized energy distributions, as summarized in Figure 3H–I, we observe a robust effect wherein
the human brain spends more time in lesser-half energy states during wakefulness than during
anesthesia. This result holds across most RSNs, with the exception of the language, vision, et
dorsal attention networks, in which the effect is not statistically signiﬁcant, c'est, the p values
resulting from paired-sample t tests were greater that 0.1. The magnitude of the difference is
largest in the somatomotor and default mode networks, indicating that the dynamics of these
networks may be more susceptible to sevoﬂurane or generally may play an important role in
maintaining conscious awareness (see Discussion).

Comparing the slopes in Figure 3I to those in Figure 2, we see that the relative change in
functional connectivity is generally smaller than the change in energy distribution and is also
not necessarily a good predictor of this change. Ainsi, the energy characterization indeed
provides information that cannot be determined directly from the correlation matrices.

Low-Energy States Are Relatively More Frequent Within RSNs Than at the Global Level

We also computed the energy landscapes of the aggregated network consisting of all seven
identiﬁed RSNs averaged over the nine subjects under each condition. Chiffre 4 shows a his-
togram of the results comparing wakefulness to general anesthesia. We observe in the bar
plot, comparing to SMN from Figure 3H, that the amount of time spent in lesser-half versus
greater-half energy states is much larger at the RSN level than globally. Cependant, the relative
proportion of time spent in lesser-half energy states during wakefulness versus general anes-
thesia is consistent between both scales. This suggests that within-RSN brain activity is more
likely to hold patterns closer to equilibrium when compared with global brain activity, mais ça
general anesthesia correlates to similar relative energy changes at both scales.

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Chiffre 4. Energy distributions of the aggregated seven-RSN network during wakefulness and gen-
eral anesthesia, averaged over all subjects. A linear scale is used here for the y-axis since zero
values cause portions of the data to be undeﬁned on the log scale. We see in the bar plot that the
fraction of time spent in lesser-half energies is much smaller for the aggregate network than at the
RSN level (SMN shown for comparison), although the ratio of these quantities between wakefulness
and anesthesia is comparable across scales.

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High-energy brain dynamics during anesthesia-induced unconsciousness

DISCUSSION

Our results represent the ﬁrst demonstration that general anesthesia alters the energy landscape
of neural dynamics. We speciﬁcally showed that key resting-state networks in humans exhibit
a pronounced shift to higher energy dynamics during unconsciousness. There are diverse the-
ories regarding the mechanisms of anesthesia-induced unconsciousness, though many coa-
lesce around notions of hierarchy, synchrony, and integration within and between cortical and
subcortical brain networks (Brown et al., 2011; Lewis et al., 2012; Mashour & Alkire, 2013;
Tononi & Edelman, 1998). We have shown here that at broad spatial scales and at second-to-
second timescales accessible through fMRI, anesthetic-induced unconsciousness is associated
with patterns of cortical activity that are further from equilibrium. This suggests that the un-
derlying dynamics are less capable of supporting stable conﬁgurations. Such dynamics are
thought to be instrumental for efﬁcient information processing and mentation (Hudetz et al.,
2014; Hudson, Calderon, Pfaff, & Proekt, 2014; Kitzbichler, Forgeron, Christensen, & Bullmore,
2009), and thus the alterations to energy that we show here—reﬂective of a transition toward
instability—are readily reconcilable with the state of unconsciousness.

Énergie, Entropy, and Complexity

We note that our analyses are based on the physics framework of energy/order rather than
on the intensity of metabolic activity (c'est à dire., physiological energy) as assayed, par exemple, via
positron emission tomography. During general anesthesia, reductions in cerebral metabolic
rate and oxygen consumption are reproducible phenomena (Hirsch & Taylor, 2016).

Since there is signiﬁcant literature on entropic properties of brain activity in the context
of general anesthesia, especially over faster timescales (par exemple., Liang et al., 2015), it is worth
discussing how these results differ from an entropy-based analysis. One practical reason for
using energies rather than entropies in this context is that the entropies can be numerically
problematic to compute. An early step in computing the entropy is to ﬁt the data to a probability
distribution such as a multivariate Gaussian. Dans ce cas, given a covariance matrix Σ for the
1
2 ln(|2πeΣ|). Cependant, since the empirical
Gaussian ﬁt, the resulting entropy is given by
covariance matrices are poorly conditioned (≈ 1018
), these determinants and corresponding
entropies are generally very small and of questionable value. Computing the energies as we
have done by means of transformation to a binary state system enables a tractable analysis.
En outre, these measures are interpretable in terms of the free-energy principle for dynamic
activity in the brain.

Nevertheless, our analysis here can be viewed as a type of complexity characterization since
lower Ising energies may be interpreted as more organized (ou, less “complex”) activity over
temps. From this perspective, one might infer from our results that sevoﬂurane anesthesia in-
duces more randomness and thus more complexity of brain dynamics, which stands in contrast
to previous ﬁndings and hypotheses that associate unconsciousness (including states of gen-
eral anesthesia) with a decrease in complexity (Tononi, 2004; Tononi & Edelman, 1998). Pour
example, the entropic brain hypothesis (Carhart-Harris et al., 2014) suggests that complexity
constrains the level of consciousness, with higher complexity enabling more primitive con-
scious experience, while lower complexity is presumably associated with conditions such as
anesthesia and deep sleep. It should be noted that some of these ﬁndings, such as Solovey et al.
(2015), are based on electrophysiological recordings sampled at much higher rates than the
second-to-second timescales we consider herein. Cependant, there is also fMRI-based evi-
dence of increased stability during unconsciousness (Tagliazucchi et al., 2016). Also in the
fMRI domain, Hudetz, Liu, and Pillay (2015) and Hudetz, Liu, Pillay, Boly, and Tononi (2016)

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High-energy brain dynamics during anesthesia-induced unconsciousness

associated wakeful consciousness with a larger repertoire of brain states and thus higher en-
tropy when compared with propofol anesthesia. What seems at ﬁrst glance to be a conﬂict
between these prior descriptions and our current results reveals upon closer inspection some
subtle but important distinctions between the concepts of energy, entropy, complexity, et
stability in the context of brain dynamics. These descriptors, while conceptually related, do
have distinct technical meanings. It is important to emphasize that the Ising energy spectrum
holistically describes the fraction of time spent in states that are (mis)aligned with the average
functional connectivity. This concept of energy is thus not a direct measure of entropy or sta-
bility and should not be interpreted as a surrogate for these other notions. En fait, it is quite
possible that sevoﬂurane anesthesia correlates to both an increase in average Ising energy and
a contraction in the repertoire of reachable states. Dans ce cas, the activity may be “simpler” in
the sense of diversity of patterns manifest, but more apt to display temporal ﬂuctuations. Ce
would be consistent with the simulation results of Hudetz et al. (2014), in which increased ac-
tivity in wakeful consciousness leads to a greater number of local state changes, which tends
to both decrease the energy of the system while also expanding the range of states that can
be explored. Our ﬁndings may be an empirical substantiation of this phenomenon. Ainsi, notre
characterization of normalized energy ultimately provides a description of brain dynamics that
is complementary to existing theories of unconsciousness.

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Resting-State Networks and General Anesthesia

Our results indicate that the largest marker of sevoﬂurane-induced unconsciousness in energy
distributions lies in the somatomotor and default mode networks. The former is thought to
be involved in motor and somatosensory processing, though it has rarely been implicated in
mechanisms of anesthetic unconsciousness. This ﬁnding is not surprising, cependant, as our
surrogate for loss of consciousness is lack of motor responses to noxious stimulation. Disrup-
tion of dynamic cortical activity in somatomotor regions is a plausible correlate or mechanism
for unresponsiveness. The latter ﬁnding regarding the default mode network is supported by
several previous ﬁndings that the DMN is closely linked to conscious awareness. For exam-
ple, Horovitz et al. (2009) found that sleep-induced reduction of consciousness correlates to
signiﬁcant changes in functional connectivity between DMN components, particularly with
respect to the frontal cortex (Horovitz et al., 2009). En outre, Greicius et al. (2008) reported
that low levels of conscious sedation are commensurate with weaker correlations between the
posterior cingulate cortex and other regions of the DMN (Greicius et al., 2008). In a neurolog-
ical study on patients with various degrees of conscious impairment, Vanhaudenhuyse et al.
(2010) found negative correlations of clinical consciousness to connectivity in multiple areas
of the DMN (Vanhaudenhuyse et al., 2010).

Strong effects on the energy landscape were also observed in the ventral attention network
and frontoparietal control network, both of which are thought to be involved in initiating and
modifying transient changes in attention and information processing (Dosenbach et al., 2007),
the disruption of which is consistent with the state of unconsciousness. Our prior functional
connectivity analyses also highlighted disruptions in the VAN (Palanca et al., 2015).

As previously mentioned, many prior studies have characterized widespread weakening in
functional connectivity within and between resting-state networks during general anesthesia
(par exemple., Boveroux et al., 2010; Liu et al., 2012), though none have characterized network dynam-
ics in terms of energy landscapes. It is of note that in these prior works, “low-level” sensory
networks such as the visual network appear most robust to the effects of anesthesia, similar
to what we observe in the energy landscapes of these networks. Since our results suggest that

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sevoﬂurane-induced unconsciousness results in an even greater change to the energy distribu-
tions than to functional connectivty at the RSN level (as evidenced in the slopes of Figures 3I
et 2), an energy-based analysis is potentially an even more sensitive marker of clinical
unconsciousness than direct functional connectivity measures.

Robustness to Connection Density

In our primary analysis, rather than thresholding the correlations between BOLD signals to
eliminate weakly correlated edges in the functional connectivity networks, we assumed a com-
pletely connected network in which both strong and weak correlations may exist. Since our
normalized energy measure weights the contribution of each edge by the correlation coefﬁ-
cient, weak correlations contribute relatively little to the total energy. Cependant, there remains
a risk that in aggregate, these correlations could induce a bias in the results. We therefore
veriﬁed the robustness of our ﬁndings to this assumption by performing the analysis on a se-
ries of thresholded networks with varying edge densities, following methods similar to those
used in Tagliazucchi et al. (2016). Chiffre 5 shows that the qualitative results are quite robust
to the deletion of weakly correlated edges, as we continue to see signiﬁcant differences be-
tween the energy distributions corresponding to wakefulness and anesthesia in the same RSNs
as the complete network case. Although the magnitudes of the differences (indicated by the
slopes in the ﬁgures on the bottom row) decrease as the networks become more sparse, ce
is to be expected since including only the most highly correlated edges will trivially reduce
the frequency that connected pairs deviate from expected correlation across all RSNs in both
wakeful and anesthetized states. Par exemple, in the limit as the edge density decreases to
include only a few almost perfectly correlated region pairs, which are indeed observed, le
normalized energy distributions for both cases would converge to a peak around negative one
and the corresponding difference in energies would therefore decrease to zero. The detailed
energy distributions for each RSN in the thresholded cases are provided in the Supplementary
Information (Riehl, Palanca, & Ching,, 2017).

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Chiffre 5. Thresholding the functional connectivity matrices to eliminate edges between weakly correlated regions does not qualitatively
alter the results.

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High-energy brain dynamics during anesthesia-induced unconsciousness

The primary reason for using the normalized Ising Hamiltonian rather than the standard
unnormalized one was to remove a potential source of bias due to alterations in functional
connectivity between conditions of wakefulness and anesthesia. Since the correlations are
lower across all RSNs during anesthesia, this would most likely have a direct effect on the
energies, if not removed via normalization. Nevertheless, it may still be informative to see the
difference in raw energies between the two conditions. Although difﬁcult to compare with
the normalized case, we observed qualitatively an even greater difference in energy distribu-
tions between the two conditions for most RSNs, with the exception of VIS and LAN (see the
Supplementary Information for detailed ﬁgures; Riehl et al., 2017).

Mechanisms of Energy Alteration

The mechanisms behind the dynamics driving the brain toward lower energy states remain un-
certain. Cependant, we do know some theoretical principles that govern any potential dynamics
within this framework. D'abord, the balance between correlated and anticorrelated brain regions
plays a critical role in the resulting equilibria and convergence properties, and is closely related
to excitatory and inhibitory connections. Par exemple, networks consisting of entirely corre-
lated or entirely anticorrelated activity tend to converge toward an equilibrium, but a mixture
of both may remain in ﬂuctuation even in the fully deterministic case (Ramazi, Riehl, & Cao,
2016). In the case of Hudetz et al. (2014), it appears that only positive correlation values were
used, and the result was that widespread alignment was observed for the cases when switching
was less random and more deterministic.

It is also worth mentioning that mutual excitation, mutual inhibition, and anticorrelation
may all play signiﬁcant roles in the functionality and thus energy landscapes of brain networks
(Uddin, Clare Kelly, Biswal, Xavier Castellanos, & Milham, 2009). Although correlation (concernant-
spectively anticorrelation) between regions does not necessarily imply excitatory (respectivement
inhibitory) activity in the underlying physiology, in order to include these effects, un modèle
should be able to capture all three types of interactions listed above. While our framework in-
deed accounts for all three, some previous analyses compute energies based only on coactive
régions, which may not be sufﬁcient to capture the various types of interactions. Par exemple,
by choosing the activation state in {0, 1} plutôt que {−1, +1} while computing the energy
using a Hamiltonian similar to Equation 3 (Gu et al., 2016), there is a risk of neglecting the
signiﬁcance of correlated brain regions being simultaneously inactive or inhibited.

Limitations

While neuroimaging has been used extensively for characterizations of (stationary) functional
connectivité, its use as a modality for examining brain dynamics remains limited because of
the relatively coarse nature of the BOLD signal and low sampling rate. Par conséquent, we must
be careful in limiting the interpretation of our results to only the spatial scale of RSNs and
dynamics over relatively long temporal epochs. The role of networks at ﬁner spatiotemporal
scales is beyond the explanatory power of our current data. We utilized global signal regression
to minimize signal artifacts related to micromovements of the head, but this may have the
additional effect of shifting the distribution of correlation coefﬁcients toward negative values.
We are also unable to evaluate the possibility that the apparent integrity of the language and
visual RSNs reﬂect ongoing neural phenomena, such as dreaming.

Several caveats must be acknowledged regarding our use of sevoﬂurane, one of many
drugs known to induce altered states of consciousness. As we have discussed in a previ-
ous study, precisely correlating loss of responsiveness with sevoﬂurane dose and concurrent

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High-energy brain dynamics during anesthesia-induced unconsciousness

BOLD fMRI:
Neuroimaging method in which
brain activity is estimated by
measuring variations in blood
oxygen content via nuclear magnetic
resonance.

BOLD fMRI is difﬁcult in part because of movement artifacts incurred during sedation (sevoﬂu-
rane %vol concentration 0.6–1.0%) (Palanca et al., 2015). As with other reports in this area,
we are unable to control for the possibility that observations reﬂect anesthetic effects on the
BOLD signal rather than loss of consciousness. At sedative doses, sevoﬂurane alters cerebral
blood ﬂow and BOLD signal amplitude in a heterogeneous manner across the cerebral cortex
(Qiu, Ramani, Swetye, Rajeevan, & Constable, 2008). Similar studies have not been reported
for sevoﬂurane concentrations used in this study. The possibility also remains that participants
held at 1.2% sevoﬂurane may have retained elements of consciousness during portions of the
fMRI data acquisition. While we operationalized the loss of consciousness endpoint by assess-
ing the lack of withdrawal following noxious ﬁngernail bed stimulation, we concede that mul-
tiple factors could lead to an inaccurate inference (Sanders, Tononi, Laureys, & Sleigh, 2012).
Responsiveness may have been ablated in the context of an intact consciousness through alter-
ation of pain threshold or sensory processing, reduced motivation to respond, or perturbation
in attention. Recent investigations suggest that even at doses of inhalational anesthetics com-
parable to what is used for surgical anesthesia, patients (Sanders et al., 2017) and volunteers
can still exhibit responses to verbal command (Pavone et al., 2017). Ainsi, while loss of
responsiveness was ascertained prior to scanning, whether this state persisted is unknown
and remains a topic of ongoing investigation. Enfin, it remains to be seen how well our
results generalize to other states induced by anesthetics with different molecular mechanisms
of action.

CONCLUSION

En résumé, we have provided empirical evidence that at the macroscopic scale the human
brain spends signiﬁcantly more time in lower energy, more organized states during wakefulness
than during general anesthesia. This ﬁnding is consistent with the free-energy principle and
the notion of low-energy states being important for neural information processing. De plus,
standard functional connectivity measures are not sufﬁcient to arrive at these conclusions,
indicating that energy-based analysis may be a valuable tool for characterizing macroscale
brain dynamics in other cognitive states.

MATERIALS AND METHODS

Our results build on a prior investigation of the BOLD functional connectivity changes asso-
ciated with sevoﬂurane general anesthesia (Palanca et al., 2015) and use the same dataset.

Ethics Statement

All data were collected with approval from the Human Research Protection Ofﬁce at the
Washington University School of Medicine. Written informed consent was obtained from all
participants.

Participants and Data

Brieﬂy, resting-state blood-oxygen-level dependent (AUDACIEUX) functional magnetic resonance
imaging (IRMf) data were acquired from nine healthy subjects during quiet wakefulness and
from nine subjects rendered unresponsive by the anesthetic drug sevoﬂurane (1.2 vol%). Six
of the subjects were imaged in both wakeful and unconscious states, meaning that data used
for this study were collected from a total of 12 sujets. To ensure that no bias resulted from
the inclusion of unpaired data from six volunteers, we also performed the analysis on only
the six subjects with paired data. Ces résultats, included in the Supplementary Information

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High-energy brain dynamics during anesthesia-induced unconsciousness

(Riehl et al., 2017), turned out very similar to our main results, in some cases resulting in
even greater contrast between wakeful and anesthetized conditions, indicating that any bias
incurred from this choice was negligible. The volunteers breathed spontaneously through a
mask during anesthesia. Unconsciousness was assessed by unresponsiveness to noxious nail
bed pressure. Imaging was commenced after at least 15 min of equilibration to the sevoﬂurane.
A Siemens 3T Trio MRI scan was used to acquire echoplanar BOLD images (4 mm isotropic
voxels, TR 2200 ms, TE 27 ms, FOV 256 mm, FA 90 degrees, 36 slices/volume, 200 volumes
per run).

A total of 3,715 frames (136 min) were collected from awake subjects and 3,131 frames
(114 min) from unconscious subjects. A complete exposition regarding the neuroimaging
equipment and scan procedures can be found in Palanca et al. (2015).

Data preprocessing was handled exactly as in Palanca et al. (2015) and detailed also in
Kafashan, Ching, and Palanca (2016). Cortical gray matter was parcellated into 6 mm
régions.
We selected 1,076 regions on the basis of a winner-take-all algorithm for exclusive mem-
bership (Hacker et al., 2013) in the following resting-state networks: dorsal attention (DAN,
94 régions), ventral attention (VAN, 118 régions), somatomotor (SMN, 313 régions), visuel
(VIS, 105 régions), frontoparietal (FPC, 86 régions), langue (LAN, 100 régions), default mode
(DMN, 260 régions). All BOLD signals underwent denoising for motion artifact, through re-
gression of whole-brain global signal and censoring of corrupted frames.

Functional Connectivity Analysis

To estimate functional connectivity between brain regions, we calculated Pearson correla-
tions between each pair of regions, generating a (symmetric) connection weighting matrix J,
in which each entry Jij is the correlation coefﬁcient between regions i and j. Rather than
thresholding the matrix to preserve only the strongest correlations, we assume a completely
connected network in which both strong and weak correlations may exist. To ensure that no
signiﬁcant bias resulted from this assumption, we veriﬁed the robustness of our ﬁndings to
network density by performing identical analyses on thresholded networks with varying edge
densities (see Discussion: Robustness to Connection Density).

Ising Energy Calculation and Normalization

(t) denote the BOLD fMRI contrast at a given region i and time t, and let ¯xi denote the
(t) ∈ {+1, −1}

Let ˜xi
mean of ˜xi over the recorded time. We deﬁne a quantized activation state xi
as follows:

(t) = sign( ˜xi

(t) − ¯xi

(1)

As shown in Schneidman et al. (2006), the maximum entropy model for a two-state system
dominated by pairwise interactions is the Ising model. The dynamic energy is computed
according to the Hamiltonian for the Ising model, which is given by

H(X(t)) = − ∑
je,j

Jijxi

(t)xj

(t),

(2)

where Jij denoted the Pearson correlation coefﬁcient between regions i and j. At each time t,
this energy is minimized for a given region pair {je, j} when the sign of xi
(t) is the same
as the sign of correlation coefﬁcient Jij. Namely, when regions i and j have positive corre-
lation, then energy is minimized when these regions are either both active or both inactive.

(t)xj

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Chiffre 6. Diagram of the energy computation process. Average correlations between pairs of BOLD signal data populate the functional
connectivity matrices. Binarized BOLD signals (red) are generated from BOLD time series (blue). The average correlations are in turn used to
compute the energies of the binarized BOLD signal data, which are collected in histograms for each RSN.

Inversement, when regions i and j are anticorrelated, energy is minimized when these regions
are in opposite activation states.

Since we are primarily interested in comparing energy levels across RSNs and under dif-
ferent states of arousal, we prefer an energy measure that is independent of network size and
total functional connectivity level. Donc, we deﬁne the following normalized energy:

ˆ
H(X(t)) = −

∑je,j Jijxi
∑je,j

(t)xj
|
|Jij

(t)

(3)

Note that the resulting measure is invariant to arbitrary scaling of the J matrix. Par conséquent,
the lower levels of functional connectivity observed during anesthesia when compared with
wakefulness will not bias a comparison of energy distributions. For further discussion and a
comparison of normalized versus unnormalized energy, see the Supplementary Information
(Riehl et al., 2017). Chiffre 6 shows a schematic of the process described in this section, comment
we compute normalized energy distributions from BOLD signals.

CONTRIBUTIONS DES AUTEURS

James R. Riehl: Conceptualisation; Analyse formelle; Enquête; Méthodologie; Validation;
Visualisation; Rédaction – ébauche originale; Rédaction – révision & édition. Ben J. Palanca: Data cu-
ration; Acquisition de financement; Enquête; Validation; Rédaction – révision & édition. ShiNung
Ching: Conceptualisation; Acquisition de financement; Enquête; Méthodologie; Project admin-
istration; Surveillance; Validation; Visualisation; Rédaction – ébauche originale; Rédaction – révision &
édition.

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INFORMATIONS SUR LE FINANCEMENT

This work was partially supported by the U.S. Air Force Ofﬁce of Scientiﬁc Research: 15RT0189
(SC); the National Science Foundation: ECCS-1509342 (SC), CMMI-1537015 (SC); the Na-
tional Institutes of Health: 1R21NS096590-01A1 (SC), UL1 TR000448 (BP), KL2TR000450
(BP), R21AG052821 (BP); and the Foundation for Anesthesia Education and Research: FAER
MRTG-CT-02/15/2010 (BP). ShiNung Ching holds a Career Award at the Scientiﬁc Interface
from the Burroughs-Wellcome Fund.

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