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SELF-ORGANIZED CRITICALITY AS A
NEURODYNAMICAL CORRELATE OF
CONSCIOUSNESS:
A neurophysiological approach to measure states of
consciousness based on EEG-complexity features
Dissertation
zur Erlangung des Doktorgrades
der Humanwissenschaften
(Dr. sc. hum.)
der
Fakultät für Medizin
der Universität Regensburg
vorgelegt von
Nike Walter
aus
Braunschweig
im Jahr
2022
SELF-ORGANIZED CRITICALITY AS A
NEURODYNAMICAL CORRELATE OF
CONSCIOUSNESS:
A neurophysiological approach to measure states of
consciousness based on EEG-complexity features
Dissertation
zur Erlangung des Doktorgrades
der Humanwissenschaften
(Dr. sc. hum.)
der
Fakultät für Medizin
der Universität Regensburg
vorgelegt von
Nike Walter
aus
Braunschweig
im Jahr
2022
Dekan: Prof. Dr. Dirk Hellwig
Betreuer: Prof. Dr. Thilo Hinterberger
Tag der mündlichen Prüfung: 26.08.2022
Zusammenfassung
Die Theorie der selbst-organisierten Kritikalität
als neurodynamisches Korrelat des
Bewusstseins: Ein neurophysiologischer Ansatz
zur Messung von Bewusstseinszuständen anhand
EEG-basierter Komplexitätsparameter
Hintergrund und Zielsetzung
Diese Arbeit basiert auf der Hypothese, dass der aus
der Physik stammende theoretische Ansatz der
selbstorganisierten Kritikalität auf die neuronale
Dynamik des menschlichen Gehirns angewendet
werden kann. Aus der Perspektive der
Bewusstseinsforschung ist dies besonders attraktiv,
da die kritische Gehirndynamik eine Nähe zu einem
Phasenübergang impliziert, der mit optimierten
Informationsverarbeitungsfunktionen sowie dem
größten Repertoire an Konfigurationen verbunden
ist, die ein System während seiner zeitlichen
Entwicklung durchläuft. Daher könnte die
selbstorganisierte Kritikalität als neurodynamisches
Korrelat für das Bewusstsein dienen, das die
Möglichkeit bietet, empirisch überprüfbare
neurophysiologische Indizes abzuleiten, die zur
Charakterisierung und Quantifizierung von
Bewusstseinszuständen geeignet sind. Ziel dieser
Arbeit war es, die Anwendbarkeit der
selbstorganisierten Kritikalität als hypothetisches
Korrelationsmaß für das Bewusstsein experimentell
zu untersuchen. Zu diesem Zweck sollten auf der
Grundlage der Analyse von drei 64-Kanal-EEG-
Datensätzen die folgenden Forschungsfragen
beantwortet werden:
(i) Lassen sich auf der Ebene des EEGs Signaturen
selbstorganisierter Kritikalität in Form einer
skalenfreien Verteilung neuronaler Lawinen und des
Vorhandenseins temporaler Autokorrelationen
(LRTC) in der Amplitude neuronaler Oszillationen
finden?
(ii) Sind Kritikalitätsmerkmale geeignet, um
Bewusstseinszustände im Spektrum des Wachseins
zu differenzieren?
(iii) Kann die neuronale Dynamik durch mind-body
Interventionen in Richtung des kritischen Punktes
eines Phasenübergangs verschoben werden, der mit
einer optimierten Informationsverarbeitungsfunktion
verbunden ist?
(iv) Kann eine eindeutige Beziehung zu anderen
nichtlinearen Komplexitätsmerkmalen und
Leistungsspektraldichteparametern identifiziert
werden?
(v) Spiegeln EEG-basierte Kritikalitätsmerkmale
individuelle Persönlichkeitsmerkmale wider?
Material und Methoden
Studie (1): Reanalyse: Dreißig meditationserfahrene
Teilnehmer (Durchschnittsalter 47 Jahre, 11
Frauen/19 Männer, Meditationserfahrung von
mindestens 5 Jahren Praxis oder mehr als 1000
Stunden Gesamtmeditationszeit) wurden mit 64-
Kanal-EEG während einer Sitzung gemessen, die
aus einem aufgabenfreien Ruhezustand, einer
Lesebedingung und drei Meditationsbedingungen
(gedankenlose Leere, Präsenz und fokussierte
Aufmerksamkeit) bestand.
Studie (2): 64-Kanal-EEG wurde von 34 Teilnehmern
(Durchschnittsalter 36,3 ±13,4 Jahre, 24 Frauen/10
Männer) vor, während und nach einer
professionellen Klangschalenmassage
aufgezeichnet. Darüber hinaus wurden
psychometrische Daten erhoben, darunter die
Absorptionskapazität, definiert als die Fähigkeit
Aufmerksamkeitsressourcen für sensorische und
imaginative Erfahrungen einzusetzen, gemessen mit
der Tellegen-Absorptionsskala (TAS-D), subjektive
Veränderungen des Körpergefühls, des emotionalen
Zustands und des mentalen Zustands (CSP-14)
sowie die Phänomenologie des Bewusstseins (PCI-
K).
Studie (3): Elektrophysiologische Daten (64 Kanäle
von EEG, EOG, EKG, Hautleitwert und Atmung)
wurden von 116 Teilnehmern (Durchschnittsalter
40,0 ±13,44 Jahre, 83 Frauen/ 33 Männer) – in
Zusammenarbeit mit dem Institut für Psychologie,
Bundeswehruniversität München -während eines
aufgabenfreien Ruhezustands aufgezeichnet. Das
individuelle Level der sensorischen
Verarbeitungssensibilität wurde mit der High
Sensitive Person Scale (HSPS-G) bewertet.
Die Datensätze wurden mit Analysewerkzeugen aus
der Theorie der selbstorganisierten Kritikalität
(trendbereinigende Fluktuationsanalyse, neuronale
Lawinenanalyse), nichtlinearen
Komplexitätsalgorithmen (Multiskalenentropie,
fraktale Dimension nach Higuchi) und der
Leistungsspektraldichte analysiert. In Studie 1 und 2
wurden die Aufgabenbedingungen kontrastiert und
die Effektstärken mit einem gepaarten zweiseitigen t-
Test verglichen. Die t-Werte wurden anhand der
Falscherkennungsrate für multiples Testen korrigiert.
Zur Berechnung der Korrelationen zwischen den
EEG-Merkmalen wurde die Spearman-
Rangkorrelation verwendet, nachdem mit dem
Shapiro-Wilk-Test festgestellt worden war, dass die
Verteilung nicht für parametrische Tests geeignet
war. Darüber hinaus wurde in Studie 1 eine
Diskriminanzanalyse durchgeführt, um die
Klassifizierungsleistung der EEG-Merkmale zu
bestimmen. Hier wurden eine partielle Kleinste-
Quadrate-Regression (Englisch: Partial Least
Squares Regression) und eine Analyse der
Grenzwertoptimierungskurve (Englisch: receiver
operating charactersitic, ROC) angewandt. Um
festzustellen, ob die EEG-Merkmale individuelle
Charaktereigenschaften widerspiegeln, wurde das
individuelle Level der Absorptionskapazität (Studie
2) und der sensorischen Verarbeitungssensibilität
(Studie 3) mit den EEG-Merkmalen unter
Verwendung der Spearman- Rangkorrelation
korreliert.
Ergebnisse
Signaturen selbstorganisierter Kritikalität in Form
einer skalenfreien Verteilung neuronaler Lawinen
und zeitlichen Autokorrelationen (LRTCs) in der
Amplitude neuronaler Oszillationen wurden in drei
verschiedenen EEG-Datensätzen nachgewiesen.
Sowohl EEG-Kritikalität als auch
Komplexitätsmerkmale waren geeignet,
unterschiedliche Bewusstseinszustände zu
charakterisieren. In Studie 1 zeigten alle drei
meditativen Zustände im Vergleich zum
Ruhezustand signifikant reduzierte
Autokorrelationen mit moderaten Effektgrößen
(Präsenz: d= -0,49, p<.001; gedankenlose Leere: d=
-0,37, p<.001; und fokussierte Aufmerksamkeit: d= -
0,28, p=.003). Der kritische Exponent war geeignet,
um zwischen fokussierte Aufmerksamkeit und
Präsenz zu unterscheiden (d= -0,32, p=.02). In
Studie 2 änderten sich die Kritikalitätsparameter im
Verlauf des Experiments signifikant, wobei die Werte
eine Verschiebung in Richtung des kritischen
Regimes während der Klangbedingung suggerieren.
Beide Analysen des ersten und zweiten Datensatzes
ergaben, dass der kritische Exponent signifikant
negativ mit Werten der Entropie, dem aus der
trendbereinigende Fluktuationsanalyse
resultierenden Skalierungsexponenten, der das
Ausmaß der zeitlichen Autokorrelationen angibt,
sowie der fraktalen Dimension nach Higuchi in jeder
Bedingung korreliert war. Darüber hinaus wurde
festgestellt, dass der kritische Skalierungsexponent
signifikant negativ mit dem Persönlichkeitsmerkmal
der Absorption korreliert (Spearman's ρ= -0,39, p=
.007), während ein Zusammenhang zwischen der
kritischen Dynamik und dem Level der sensorischen
Verarbeitungssensitivität nicht nachgewiesen
werden konnte (Studie 3).
Schlussfolgerung
Die Ergebnisse dieser Arbeit legen nahe, dass die
neuronale Dynamik durch das Phänomen der
selbstorganisierten Kritikalität reguliert wird. EEG-
basierte Kritikalitätsmerkmale erwiesen sich als
sensitiv, um experimentell induzierte Veränderungen
des Bewusstseinszustandes zu erfassen. Darüber
hinaus wurde ein eindeutiger Zusammenhang mit
weiteren nichtlinearen Maßen, die den Grad der
neuronalen Komplexität - in Form von statistischer
Selbstähnlichkeit - bestimmen, festgestellt. Somit
scheint die selbstorganisierte Kritikalität als Korrelate
für das Bewusstsein geeignet zu sein, mit dem
Potential Bewusstseinszuständen zu quantifizieren
und zu charakterisieren. Die Übereinstimmung des
Modells mit den derzeit einflussreichsten Theorien
auf dem Gebiet der Bewusstseinsforschung wird
diskutiert.
Schlüsselwörter
Selbstorganisierte Kritikalität,
Bewusstseinskorrelate, neuronale Dynamik,
Phasenübergang, Komplexität, optimale
Informationsverarbeitung, Meditation,
Hochsensibilität, EEG
Abstract
Self- organized criticality as a neurodynamical
correlate of consciousness:
A neurophysiological approach to measure states of
consciousness based on EEG-complexity features
Background and Objectives
This thesis was based on the hypothesis that the
physics-derived theoretical framework of self-
organized criticality can be applied to the neuronal
dynamics of the human brain. From a consciousness
science perspective, this is especially appealing as
critical brain dynamics imply a vicinity a phase
transition, which is associated with optimized
information processing functions as well as the
largest repertoire of configurations that a system
explores throughout its temporal evolution. Hence,
self-organised criticality could serve as a
neurodynamical correlate for consciousness, which
provides the possibility of deriving empirically
testable neurophysiological indices suitable to
characterise and quantify states of consciousness.
The purpose of this work was to experimentally
examine the feasibility of the self-organized criticality
theory as a correlate for states of consciousness.
Therefore, it was aimed at answering the following
research questions based on the analysis of three 64
channel EEG datasets:
(i) Can signatures of self-organized criticality be
found on the level of the EEG in terms of scale-free
distribution of neuronal avalanches and the presence
of long-range temporal correlations (LRTC) in
neuronal oscillations?
(ii) Are criticality features suitable to differentiate
state of consciousness in the spectrum of
wakefulness?
(iii) Can the neuronal dynamics be shifted towards
the critical point of a phase transition associated with
optimized information processing function by mind-
body interventions?
(iv) Can an explicit relationship to other nonlinear
complexity features and power spectral density
parameter be identified?
(v) Do EEG-based criticality features reflect
individual temperament traits?
Material and Methods
(1): Re-analysis: Thirty participants highly proficient
in meditation (mean age 47 years, 11 females/19
males, meditation experience of at least 5 years
practice or more than 1000 h of total meditation time)
were measured with 64-channel EEG during one
session consisting of a task-free baseline resting, a
reading condition and three meditation conditions,
namely thoughtless emptiness, presence monitoring
and focused attention.
(2): 64-channel EEG was recorded from 34
participants (mean age 36.0 ±13.4 years, 24 females/
10 males) before, during and after a professional
singing bowl massage. Further, psychometric data
was assessed including absorption capacity defined
as the individual’s capacity for engaging attentional
resources in sensory and imaginative experiences
measured by the Tellegen-Absorption Scale (TAS-
D), subjective changes in in body sensation,
emotional state, and mental state (CSP-14) as well
as the phenomenology of consciousness (PCI-K).
(3): Electrophysiological data (64 channels of EEG,
EOG, ECG, skin conductance, and respiration) was
recorded from 116 participants (mean age 40.0 ±13.4
years, 83 females/ 33 males) – in collaboration with
the Institute of Psychology, Bundeswehr University
Munich - during a task-free baseline resting state.
The individual level of sensory processing sensitivity
was assessed using the High Sensitive Person Scale
(HSPS-G).
The datasets were analysed applying analytical tools
from self-organized criticality theory (detrended
fluctuation analysis, neuronal avalanche analysis),
nonlinear complexity algorithms (multiscale entropy,
Higuchi’s fractal dimension) and power spectral
density. In study 1 and 2, task conditions were
contrasted, and effect sizes were compared using a
paired two-tailed t-test calculated across
participants, and features. T-values were corrected
for multiple testing using false discovery rate. To
calculate correlations between the EEG features,
Spearman’s rank correlation was applied after
determining that the distribution was not appropriate
for parametric testing by the Shapiro-Wilk test. In
addition, in study 1, a discrimination analysis was
carried out to determine the classification
performance of the EEG features. Here, partial least
squares regression and receiver operating
characteristics analysis was applied. To determine
whether the EEG features reflect individual
temperament traits, the individual level of absorption
capacity (study 2) and sensory processing sensitivity
(study 3) was correlated with the EEG features using
Spearman’s rank correlation.
Results
Signatures of self-organized criticality in the form of
scale-free distribution of neuronal avalanches and
long-range temporal correlations (LRTCs) in the
amplitude of neural oscillations were observed in
three distinct EEG-datasets. EEG criticality as well as
complexity features were suitable to characterise
distinct states of consciousness. In study 1,
compared to the task-free resting condition, all three
meditative states revealed significantly reduced long-
range temporal correlation with moderate effect sizes
(presence monitoring: d= -0.49, p<.001; thoughtless
emptiness: d= -0.37, p<.001; and focused attention:
d= -0.28, p=.003). The critical exponent was suitable
to differentiate between focused attention and
presence monitoring (d= -0.32, p=.02). Further, in
study 2, the criticality features significantly changed
during the course of the experiment, whereby values
indicated a shift towards the critical regime during the
sound condition. Both analyses of the first and
second dataset revealed that the critical exponent
was significantly negatively correlated with the
sample entropy, the scaling exponent resulting from
the DFA denoting the amount of long-range temporal
correlations as well as Higuchi’s fractal dimension in
each condition, respectively. In addition, the critical
scaling exponent was found to be significantly
negatively correlated with the trait absorption
(Spearman's ρ= -0.39, p= .007), whereas an
association between critical dynamics and the level
of sensory processing sensitivity could not be verified
(study 3).
Conclusion
The findings of this thesis suggest that neuronal
dynamics are governed by the phenomena of self-
organized criticality. EEG-based criticality features
were shown to be sensitive to detect experimentally
induced alterations in the state of consciousness.
Further, an explicit relationship with nonlinear
measures determining the degree of neuronal
complexity was identified. Thus, self-organized
criticality seems feasible as a neurodynamical
correlate for consciousness with the potential to
quantify and characterize states of consciousness.
Its agreement with the current most influencing
theories in the field of consciousness research is
discussed.
Keywords: Self-organised criticality, correlates of
consciousness, neural dynamics, phase transition,
complexity, optimal information processing,
meditation, sensory processing sensitivity, EEG
3
Table of Contents
1. Introduction ......................................................... 7
1.1 Altered States of Consciousness: History, definitions and
measures ........................................................................... 7
1.2 Measuring the brain’s complexity ................................ 24
1.2.1 Dynamical systems and attractors........................ 28
1.2.2 Self-similarity of the EEG ..................................... 33
1.2.3 Higuchi’s fractal dimension .................................. 37
1.2.4 Multiscale entropy ................................................ 44
1.3 Self-organized criticality.............................................. 53
1.3.1 Experimental findings and functional benefits ....... 61
1.3.2 Detrended fluctuation analysis ............................. 68
1.3.3 Neuronal avalanches ........................................... 72
1.3.4 Clinical relevance ................................................ 75
2. Research questions and Aims ........................ 82
3. Material and Methods ....................................... 88
3.1: Mediation states ........................................................ 88
3.1.1 Data acquisition and participants ......................... 88
3.1.2 EEG data processing ........................................... 91
3.1.3 Merging of topographic brain regions ................... 98
4
3.1.4 Comparison between conditions .......................... 99
3.1.5 Statistics .............................................................. 99
3.2 Singing bowl experience ........................................... 102
3.2.1 Data acquisition and participants ....................... 102
3.2.2 EEG data processing ......................................... 105
3.2.3. Comparison between conditions ....................... 106
3.2.4 Statistics ............................................................ 106
3.3 Sensory processing sensitivity .................................. 108
3.3.1 Data acquisition and participants ....................... 108
3.3.2 EEG Data processing ........................................ 109
3.3.3 Statistics ............................................................ 110
4. Results ............................................................. 112
4.1 Meditation states ...................................................... 112
4.1.1 Kruskal-Wallis Test ............................................ 112
4.1.2 Global comparisons of complexity parameter ..... 116
4.1.3 Local comparisons ............................................. 122
4.1.4 Complexity, criticality, and spectral features for each
condition .................................................................... 138
4.1.5 Correlations between complexity, criticality, and
spectral features ......................................................... 144
4.1.6 Discrimination analysis ...................................... 151
5
4.2 Singing bowl experience ........................................... 156
4.2.1 Kruskal-Wallis Test ............................................ 156
4.2.2 Global comparisons ........................................... 157
4.2.3 Local comparisons ............................................. 161
4.2.4 Complexity, criticality, and spectral features for each
condition .................................................................... 167
4.2.5 Correlations between complexity, criticality, and
spectral features ......................................................... 172
4.2.6 Phenomenological data ..................................... 176
4.3 Sensory processing sensitivity .................................. 180
4.3.1 Correlations between sensory processing sensitivity,
complexity, criticality, and spectral features ................ 180
4.3.2 Differences in frequency power spectra, complexity,
and criticality features between highly sensitive and not
sensitive participants .................................................. 182
5. Discussion ....................................................... 187
5.1 The neurophysiology of meditative states ................. 189
5.2 Effects of a singing bowl experience ......................... 201
5.3 Criticality and sensory processing sensitivity............. 207
5.4 Self-organized criticality as a neurodynamical correlate of
consciousness ............................................................... 211
5.4.1 Consciousness as an order parameter ............... 212
6
5.4.2 Oscillatory synchrony ......................................... 215
5.4.3 Coordination dynamics ...................................... 225
5.4.4 The global workspace theory ............................. 228
5.4.5 The integrated information theory ...................... 232
5.5 Limitations ................................................................ 240
6. Summary .......................................................... 249
7.a Appendix I: t-statistics ................................. 255
7.b Appendix II: Questionnaires ....................... 270
8. References ....................................................... 279
9. List of acronyms, figures, and tables .......... 335
7
1. Introduction
“If the doors of perception were cleansed
every thing would appear to man as it is, infinite.
For man has closed himself up,
till he sees all things thro’ narrow chinks of his cavern.”
William Blake, The Marriage of Heaven and Hell
1.1 Altered States of Consciousness: History,
definitions and measures
Understanding and defining consciousness has
challenged thinkers, philosophers, and scientist for
decades. Nowadays, with the development of
greater spatial and temporal resolution of
neuroimaging methods, allowing to investigate
neural correlates of states consciousness more
deeply, consciousness research is reflourishing.
However, as the contemporary philosopher David
Chalmers puts it: “Consciousness poses the most
baffling problems in the science of the mind. There is
nothing that we know more intimately than conscious
experience, but there is nothing harder to explain” [1,
p. 200]. Therefore, no all-encompassing universally
8
agreed definition on consciousness exists and
distinguishing often blurred lines between ordinary
waking consciousness, the tip of the iceberg and
alterations from it, the wide realms beneath, depicts
a challenge. In the literature, consciousness has
often been associated with wakefulness [2] and was
defined by Searle (1993) as “those subjective states
of sentience or awareness that begin when one
awakes in the morning from a dreamless sleep and
continue throughout the day until one goes to sleep
at night or falls into a coma, or dies, or otherwise
becomes, as one would say, ‘unconscious.” [3, p.
312]. Accordingly, from the clinical perspective,
unconsciousness is described as the “absence of
perception of self and environment [4]. However,
importantly, being awake does not necessarily imply
to be conscious [5]. Keeping in mind that any
definition would be tentative at best, for the scope of
this thesis, consciousness will be referred to the first-
person perspective filled with qualia and sensual
experience, the subjective awareness of both
internal and external phenomena [6]. In this context,
9
consciousness corresponds to the capacity of any
kind of experience, “a concept that is upstream to
further distinctions, such as those between levels,
those between global states of consciousness (e.g.
the distinction between dreaming and wakeful
consciousness), and those between local states of
consciousness characterized in terms of specific
conscious contents or phenomenal character” [7].
While the specific modulation of states of
consciousness has already been utilized by ancient
culture since prehistoric times [8], Western
psychology opened up to this field of research in the
beginning of the 20th century, when William James
made the pioneering statement in this lectures on the
varieties of religious experience that “our normal
waking consciousness, rational consciousness as
we call it, is but one special type of consciousness,
whilst all about it, parted from it by the filmiest of
screens, there lie potential forms of consciousness
entirely different. We may go through life without
suspecting their existence; but apply the requisite
stimulus, and at a touch they are there in all their
10
completeness, definite types of mentality which
probably somewhere have their field of application
and adaptation. No account of the universe in its
totality can be final which leaves these other forms of
consciousness quite disregarded“ [9, pp. 378-378].
During that time psychology was mainly influenced
by behaviourism concentrating on operant and
classical condition to modify behaviour based on
work from Ivan Pavlov [10], John B. Watson [11] and
B. F. Skinner [12]. Also, psychoanalysis was driving
the field established by Sigmund Freud [13], who
believed that an individual’s personality had three
components affected by unconscious processes. Out
of Freud’s theories, a number of schools developed
in Europe, such as the ‘individual psychology’ by
Alfred Adler [14], the ‘will therapy’ by Otto Rank [15]
and the theory of the collective unconsciousness and
archetypes by Carl Jung [16]. In the early 1950s a
third force called humanistic psychology arose
highlighting the human potential including higher
functions of the psyche and qualities empathy and
love. This was mainly initiated by Carl Rogers, who
11
revolutionized psychotherapy with his client-centered
approach [17] and Abraham Maslow, who elaborated
on his prominent hierarchy of needs, a model
including the concept of self-actualization, a
development towards personal growth, fulfilment,
appreciation of life and the realization of one’s
abilities [18]. Within the zeitgeist of the late 60s,
shaped by revolutionary cultural movements in the
United States and a growing interest in Eastern
spiritual systems, Maslow replaced the top of his
hierarchy of human needs with the motivational level
of self-transcendence [19]. In the same stance,
Arnold M. Ludwig wrote in 1966: “Beneath man’s thin
veneer of consciousness lies a relatively uncharted
realm of mental activity, in nature and function of
which have neither systematically explored nor
adequately conceptualized”, firstly coining the term
Altered States of Consciousness (ASC), which set a
cornerstone for research into the spectrum in which
experience may be organized. In this work, he
defined ASCs as “any mental state(s), induced by
various physiological, psychological, or
12
pharmacological maneuvers or agents, which can be
recognized subjectively by the individual himself (or
by an objective observer of the individual) as
representing a sufficient deviation in subjective
experience of psychological functioning from certain
general norms for that individual during alert, waking
consciousness” [20, p.225]. A year later, a small
working group of psychologists aimed at “creating a
new psychology that would honour the entire
spectrum of human experience, including various
non-ordinary states of consciousness” [21, p. 3].
Subsequently, the Association of Transpersonal
Psychology was launched in 1967, also founding the
Journal of Transpersonal Psychology [19].
Transpersonal psychology was devoted to higher
order development. Lajoie and Shapiro executed a
review of 40 definitions published during the first two
decades of the beginning of transpersonal
psychology concluding that it "is concerned with the
study of humanity's highest potential, and with the
recognition, understanding, and realization of unitive,
spiritual, and transcendent states of consciousness"
13
[22, p.91]. Proceeding, Charles T. Tart collected
existing work in this domain with the purpose “to
make this a respectable field of investigation” and
emphasized “that one could scientifically approach
altered states of consciousness” for which he
provided the following definition: “An altered state of
consciousness for a given individual is one in which
he clearly feels a qualitative shift in his pattern of
mental functioning, that is, he feels not just a
quantitative shift (more or less alert, more or less
visual imagery, sharper, duller, etc.), but also that
some quality or qualities of his mental processes are
different” [23, pp 1 and 8]. Further, Tart used the term
discrete states of consciousness defined as “a
unique, dynamic pattern or configuration of
psychological structures” [24, p.5]. Tart also pointed
out that Western psychology tends to assume that “a
healthy personality is one which allows the individual
to be well-adjusted in terms of his culture” [25, p.86].
Thus, according to Walsh, the implementation of
Eastern therapy drawn from Buddhist, Hindu and
Taoist knowledge systems in the domain of
14
transpersonal psychology can “change the deeper
beliefs underlying collective pathology that keep us
identified with an erroneous self-sense, trapped at
conventional levels of development, and unaware of
the true nature of our mind and identity” He further
states that “our ordinary state of mind is considerably
more dysfunctional, uncontrolled and
underdeveloped than we usually recognize. This
results in an enormous amount of unnecessary
personal, interpersonal and social suffering…it is
possible to train and develop the mind beyond
conventionally recognized limits and thereby
overcome the usual dysfunction and lack of control.
This can enhance happiness, wellbeing, and
psychological capacities to remarkable degrees “[26,
p.6]. Also, for Stanislav Grof, who focused on what
he calls “technologies of the sacred” such as
psychedelic drugs and specific breathing methods
[27], the term altered states reflects the belief of
mainstream psychiatrists “that only the everyday
state of consciousness is normal and that all
departures from it without exception represent
15
pathological distortions of the correct perception of
reality and have no positive potential“ [21, p.5].
Clarifying that “Transpersonal psychology is
interested in a significant subgroup of these states
that have heuristic, healing, transformative and even
evolutionary potential”, he coined the term
“holotropic” state, literally translated as “oriented
towards wholeness” [21, p.5, 19].
In the early 90s, G. William Farthing characterized
ASC as “a drastic change in the overall patterns of
subjective experience, which is accompanied by
major differences in the cognitive as well as
physiological functions. For typical examples we can
consider here such states as sleeping, hypnagogic
and hypnotic states, a variety of meditative, mystical
and transcendent experiences, and all of the
psychedelic states of consciousness induced by
drugs, etc” [28, pp.202-203]. Additionally, he
structured his explanations in the following points: i)
ASCs are not merely changes in the content of
consciousness; ii) ASCs involve a changed pattern
of subjective experience, not merely a change in one
16
aspect or dimension of consciousness; iii) ASCs are
not necessarily recognized by the individual at the
time that they are happening; they may be inferred
afterwards; iv) ASCs are relatively short-term,
reversible conditions; v) ASCs are identified by
comparison to the individual’s normal waking state of
consciousness; vi) The essence of a state of
consciousness is the individual’s pattern of
subjective experience, not his or her overt behavior
or psychological response. Following the attempts to
categorize ASCs, Fischer mapped a variety of
conscious states on a perception-hallucination-
meditation continuum, differentiating between
ergotropic and trophotropic arousal. While the first
describes aroused, hyperaroused up to ecstatic
states, the latter refers to tranquil and hypoaroused
states [29]. Other authors conceptualized ordinary
and ASC as a function of arousal and absorption [30].
In their work “psychobiology of altered states of
consciousness” Vaitl and colleagues highlighted that
a valid overarching model for ASCs is missing and
remarked domains associate with alterations of
17
consciousness classified by the method of induction.
Here, the categories span from spontaneously
occurring (states of drowsiness, daydreaming,
hypnagogic states, sleep and dreaming, near-death
experiences), physically and physiologically induced
(extreme environmental conditions such as pressure
or temperature, starvation and diet, sexual activity
and orgasm, respiratory manoeuvres),
psychologically induced (sensory deprivation,
homogenization, and overload, rhythm-induced
trance, relaxation, meditation, hypnosis,
biofeedback), to disease induced (psychotic
disorders, coma and vegetative state, epilepsy) and
pharmacologically induced [31]. Also, it has been
argued that ASC share certain features regardless of
their induction method [32]. Whereas the concept of
altered states of consciousness is still under an
ongoing debate [33, 34], much effort has been done
to develop measures to assess the subjective
experience of perceptual alterations. For instance, in
1995 a series of 11 experiments containing different
induction methods was compiled on 1133 probands
18
in six countries to test the hypothesis that ASC have
major dimension in common regardless of their
induction. Here, a phenomenological approach was
used applying the Abnormal Mental States (ABZ)
questionnaire. Psychometric results revealed three
shared dimensions, namely “oceanic
boundlessness”, ‘‘dread of ego dissolution’’ and
‘‘visionary restructuralization’’ [35, 36]. From there
on, the original version from Dittrich and colleagues
was revised and refined [37] and a variety of different
questionnaires were developed such as the
Phenomenology of Consciousness Inventory (PCI)
[38], the Mystical Experience Questionnaire [39] or
the Ego-Dissolution Inventory [40]. For a comparison
between the phenomenological descriptions of
differently induced ASCs, the Altered States
Database has been introduced recently, extracting
data from a specified set of standardized
questionnaires [41]. Whereas the above-mentioned
metrics assess the subjective experience as a
multidimensional phenomenon including domains
such as perception, imagery or working memory,
19
core characteristics of an ASC experiences can be
summarized as an joint alteration in the experience
of space and time [42, 43], a “sense of timelessness
and spacelessness” [44]. Importantly, however, ASC
should not be based on changes in phenomenal
consciousness per se [34] and
neurophenomenological research programs where
launched to bridge the gap between first- and third
person approaches [45, 46]. Hence, to measure
ASC, besides determining individual pattern in
psychometric data, features of electrophysiological
data underlying the induced altered state have to be
characterized (Figure 1). On the search of
electrophysiological markers for consciousness
multiple neurobiological theories were proposed [47–
50]. Especially, the attempt of unrevealing the “neural
correlates of consciousness (NCC) paved the way for
scientific approaches to consciousness as based on
the premise that phenomenal experience is entailed
by neuronal activity in the brain [51]. Thus, the
obstacle of the hard problem, which describes the
obstacle of the qualia of subjective experience, the
20
philosophical question of ‘what it is like” [52] has not
been hindered progress in consciousness research
anymore [53].
Figure 1: Neuroscientific approach to measure altered states of
consciousness. To associate phenomenological changes to
underlying neuronal mechanisms, ASCs can be induced
experimentally. For this, besides substance-based approaches,
a variety of non-pharmacological induction methods such as
breathing techniques, meditation practices or sensory
deprivation can be utilized. By investigating phenomenological
states and electrophysiological patterns simultaneously,
subjective experience can be mapped onto brain functions.
Comparisons across studies capturing a broad range of ASC
experiences may lead to the identification of common structures
shared by differently induced ASCs. Modified from [54].
21
A huge body of literatures exists correlating changes
in oscillatory brain activity with ASC [31]. Several
candidate neurophysiological parameters were
investigated, comprising for instance frequency-
specific synchronization across different brain areas,
local gamma response and event-related potentials
such as the contingent negative variation or the P3b
component. However, most of them have proved
illusory [55]. For example, it has been observed that
gamma synchrony increases during non-rapid eye
movement (NREM) sleep, anaesthesia or seizures
[56, 57] and the P3b was shown to have a low
sensitivity regarding the discrimination of vegetative
and minimally conscious states [58–60]. Thus,
decades of research on the physical substrate of
consciousness did not lead to an agreement on the
topic [7]. Therefore, one of the most compelling
topics in consciousness sciences still remains finding
a reliable biomarker capturing states of
consciousness. In other words, computational
measures that successfully quantify global brain
states from electrophysiological data are required as
22
indices of consciousness [61]. Also, instead of solely
describing correlations, such markers should be
embedded in functional frameworks explaining the
mechanisms underlying changes in the state of
consciousness [31]. In the literature, there is a
consensus that consciousness relates to neural
dynamical complexity, which can be assessed with
quantitative measures [2, 62, 51, 55, 63].
Accordingly, novel indices capturing the degree of
differentiation (the repertoire of different firing
patterns) and integration (neural activity behaving as
a single entity) could be applied and ASC can be
approximated as the results of quantitative changes
in the level of complexity [64, 55]. Investigating
markers suitable to capture how neural signals
combine, dissolve, and reconfigure over time would
be of special interest not only, although especially in
the field of psychotherapy research. Psychological
and psychosomatic interventions aim at modifying a
patient’s mindset, i.e. the emotional and cognitive
disposition or the embodied self-perception.
Therefore, a broad range of techniques enabling a
23
modification of the state of consciousness found their
way in therapeutical practice [65]. For instance, the
concept of mindfulness has been incorporated into a
number of evidenced-based clinical interventions
[66, 67]. It is assumable that changes in neuronal
complexity patterns occur in the course of
therapeutic processes and measures could be useful
for the evaluation of effectiveness [68]. Further, from
a clinical perspective, such analytical tools could be
important for advances in diagnosis paving the way
for determining generalizable fingerprints of
disorders of consciousness [63].
In the following I will outline basic principles
underlying the umbrella term “chaos and complexity”
and introduce methods based on the dynamical
system approach to capture brain state activity on
multiple spatial-temporal scales. In particular, I will
elaborate on the concept of self-organized criticality
(SOC), originally stemming from physics. This model
will be adapted to the brain dynamics and the
usefulness of criticality measures as general gauges
of information processing and potential classifiers for
24
discriminating global states of consciousness will be
investigated.
"The mind as a whole is self-similar
no matter whether it refers to the large or the small."
Anaxagoras, Fragment No. 12 (456 BC)
1.2 Measuring the brain’s complexity
In a special issue of the journal Science for its 125th
anniversary in the year 2005, scientific knowledge
gaps were addressed with 125 questions, which
have not yet been solved. The most fundamental was
“What is the universe made of?”, followed by “What
is the biological basis of consciousness?” [69]. Thus,
answering elementary questions such as “How are
those myriads of elements and interactions
coordinated together in complex living creatures?” or
“How does coherent behaviour emerge out of such a
soup of highly heterogeneous components?” as
already posed in 1944 by Schrödinger [70] is still
contemporary. With the aim of finding general
principles, that could underlie the large-scale
25
organization of biological complexity, approaches
from Statistical Physics have been transferred and
adapted to investigate living organisms [71].
Especially in neuroscience, the understanding of
how the interaction of billions of neurons coordinated
across multiple scales produces emergent
phenomena such as cognition, behaviour and
consciousness has been inspired researchers to
incorporate interdisciplinary perspectives.
A prominent non-invasive electrophysiological
technique to measure electrical activity arising from
the brain is the electroencephalography (EEG). This
method records voltage fluctuations on the scalp
associated with neuronal ionic current representing
the summation of inhibitory and excitatory
postsynaptic potentials. Given its high temporal
resolution in a millisecond range, the EEG is
beneficial in the evaluation of dynamic neuronal
functioning. Historically, the first EEG recording was
performed by Richard Caton, a British physician, in
1875, who recorded electrical activity in rabbits and
monkeys. Half a century later, in 1929, the Germany
26
psychiatrist Hans Berger used EEG in human [72,
73]. Until the 1980s, EEG signals were registered on
paper tape allowing for an interpretation of frequency
of EEG waved by counting pen sways per seconds.
With the introduction of computers enabling
numerical registration of EEG-signals, spectral
analysis methods such as the fast Fourier transform
(FFT) and wavelet transforms were developed,
converting the signal in the frequency domain [74].
Hitherto these linear methods have been the “gold
standard’ in the analysis of electrophysiological data,
characterizing the signal according to the five major
brain rhythms (Table 1). Also, diverse correlations
with cortical functions were observed [75]. However,
for unrevealing the functional role of these rhythms in
major cognitive functions such as attention and multi-
modal coordination, the classification solely based
on the frequency range has been shown to be too
simple [76].
27
Table 1: EEG spectral bands.
Rhythm
Frequency range [Hz]
delta (δ)
1-4
theta (θ)
4-8
alpha (α)
8-12
beta (β)
12-30
gamma (γ)
>30
Nowadays, the dynamical system approach has
become widespread in neuroscience and a fair
amount of research suggests that nonlinear methods
are more appropriate for EEG-analysis [77, 78, 79
80]. Indeed, linear approaches rely on the
assumption of stationary, whereas real biological
time series are nonstationary, meaning that
statistical properties such as its mean value,
standard deviation, or correlation function change
with time. Hence, these may yield faulty results.
Whereas the dynamical system approach found its
way into research and academic training [78], these
methods have not yet been implemented into
everyday clinical practice [81].
28
1.2.1 Dynamical systems and attractors
A dynamical system depicts a model that determines
the evolution in time solely based on the initial state,
hence, implying that the system has memory. A
variety of dynamical systems exist. For instance,
there are linear systems, showing a relation between
causes and effects. There also are nonlinear
systems, in which small causes may have large
effects. If quantities of the systems are preserved
over time, nonlinear systems are termed
conservative, whereas dissipative systems are
thermodynamically open [77]. Mathematically
dynamical systems are described by a coupled set of
first-order ordinary differential equations [82]:
(1)
where the vectors are the dynamical variables of
the system evolving in continuous time. For detailed
mathematical background the reader is referred to
the work by Henry and colleagues (2001) as well as
Kantz and Schreiber (2004) [83, 82]. Accordingly, the
variables describe the state of a system. Each
29
possible state of a dynamical system can be
represented by a point in a so-called phase space,
an abstract multidimensional space. A sequence of
points solving the equations is termed a
trajectory of the dynamical system. In cases of
dissipative systems, the trajectory will converge to a
subset of the phase space with proceeding time. The
subspace is termed attractor as it ‘attracts’
trajectories from all possible initial conditions [77].
Hereby, attractors can vary in their form. For
instance, in linear deterministic dissipative systems
the attractor is a simple point in state space (point
attractor). The repertoire of nonlinear system
dynamics also includes limit cycles, which represent
closed loops corresponding to periodic dynamics,
torus attractors corresponding to quasi-periodic
dynamics as well as strange or chaotic attractors
corresponding to deterministic chaos. A famous
example for the latter is the Lorenz attractor as
depicted in Figure 2 defined by the following
30
equations:
,
and
[84]:
Figure 2: Numerical visualization of the Lorenz attractor as
example of a three-dimensional nonlinear dynamical systems
which shows chaotic behaviour with the parameters =28, =
10, b=
. Modified from [85].
To characterize the dynamics of a nonlinear system
several techniques are used. For instance, the
dimension of the attractor can be captured in degrees
of freedom or the ‘complexity’ of the dynamics. In
cases of point attractors this would be zero and for
limit cycles one, whereas a torus would have an
integer dimension in accordance to the number of
31
superimposed periodic oscillations. A strange or
chaotic attractor would yield a fractal dimension, a
non integer number (e.g. 2.16) [77]. In general,
biological system are dissipative and
thermodynamically open, exchanging entropy with
the environment [86]. This accounts also for the
brain, which has the capacity to form strange
attractor with fractal properties [87].
Further, in dynamical systems such as the brain,
attractors can coexist [88]. In cases of one or more
attractors in the dynamical structure of a system, the
condition is termed bi- or multistability [89]. The
systems’ coordination can be changed by different
mechanisms. The first is called bifurction and
describes a modulation of a control parameter on
which the “attractor landscape” is based on beyond
a critical threshold. In case neural networks these
could include for instance the balance between
excitation and inhibition dependent of certain
concentration of neurotransmitters [90]. Secondly,
perturbation, noise or energy can transiently
destabilize the coordination dynamics and cause a
32
system to lose a pre-existing attractor (Figure 3A)
[89]. Additionally, dynamical system can be
metastable, meaning that there are no attractors In
such regime, however, some traces of fixed points
are still present, which are sometimes called ‘ghost’
attractors [91, 88]. These are successively visited in
the time course, whereby no input or energy
expenditure is required (Figure 3B) [89].
Figure 3: Coordinated system dynamics. (A) Multistable
systems can switch between attractors. As the system is briefly
33
dwelling in each attractor basin, time series are characterized
by long-tailed distributions (here shown on a logarithmic scale).
(B) Metastable systems do not have attractors, rather a
sequence of unstable fixed points and time series are
associated with gamma distributions (here shown in linear
coordinates). Modified from [92].
1.2.2 Self-similarity of the EEG
Generally, fractal geometry is associated with
Euclidian objects, which reflect iterative processes,
i.e. procedural repetitions and recursion,
incorporating the previous state of the system as the
input of a new iteration. Hence, these are dividable
into identical segments, each reduced by a scaling
factor (Figure 4). Such self-similarity cannot only be
defined geometrically, but also statistically. Statistical
self-similarity is also indicated with the term self-
affinity [93]. Moreover, fractal behaviour is not only
evident in space, but also in the time domain [94].
34
Figure 4: Examples of geometrically self-similar fractals. (A)
The Mandelbrot set. (A) the curve and (B) the snowflake
described by Niels F.H. von Koch. (C) shows the Sierpinski
triangle. Modofied from [93].
For instance, the time evolution of a dynamical
system is represented by the time series .
Specified over a time interval , the mean signal
is governed by:
(2)
Further, the time series can be described in the
frequency domain , represented by the amplitude
, which is given by the Fourier transform of
:
(3)
35
The power spectral density is given by:
(4)
In case of a fractal time series, the power spectrum
obeys a power law:
(5)
where f the frequency and β the spectral exponent
[95]. Historically, the case of β= 0 was called white
noise, according to the fact that its power spectral
density is the same at all frequencies within a fixed
bandwidth. Statistically, white noise depicts an
uncorrelated process. The case β= 1 is referred to as
pink noise and β= 2 is termed Brownian noise, also
known as red noise, which is a highly correlated
process (Figure 5). Importantly, in contrast to
periodic phenomena, which would generate
characteristic peaks in the power spectrum, a time
series with 1/f power spectrum has no characteristic
time scale. Therefore, fluctuations of a 1/f process
would appear similar under temporal magnification
such as fractal shapes remain identical in the spatial
36
domain. As a power-law function is indicative of
scale-invariance, the arrhythmic brain activity
contributing to this 1/f slope has been termed “scale-
free brain activity” [96, 97].
Figure 5: Examples of noise processes. (A) white noise, (B) pink
noise, (C) Brownian noise. Adapted from [98].
Several algorithms exist to extract complexity
features from electrophysiological data [7, 99]. In this
thesis, I will focus on two algorithms, namely
Higuchi’s fractal dimension and the multiscale
37
entropy analysis, which are described in the
following.
1.2.3 Higuchi’s fractal dimension
As mentioned above dynamical systems such as the
brain can exhibit attractors with fractal properties.
Most approaches characterizing attractors of
nonlinear systems rely on the reconstruction of the
systems dynamics in state space by a procedure
called embedding [100], such as, for example, the
calculation of the correlation dimension D2 [101] or
the Lyapunov exponents [102]. However, the
reconstruction of the phase space from a given
observation in time is accompanied by time
consumption as surrogate data testing is essential to
justify conclusions and involves pitfalls such as
biases by autocorrelation effects in the time series
[77]. Therefore, algorithms were developed to
calculate the fractal dimension directly in the time
domain allowing to examine systems dynamic
without reconstructing the attractor. Among existing
algorithms such as Katz’s [103] or Petrosian’s
38
method [104], Higuchi’s fractal dimension (HFD)
depicts the most accurate one [105, 106]. Originally
introduced in 1988 as a nonlinear approach
originating from chaos theory to capture natural
phenomena such as the earth’s changing magnetic
field [105], the measure has been implemented over
time in biological and medical research. Nowadays,
HFD is widely applied in basic and clinical
neurophysiological research to measure the
complexity of neuronal activity in different
neurophysiological conditions [107]. The algorithm
constructs new time series for from a
starting time series of samples: :
(6)
where indicates the initial time sample, denotes
the time interval and int(r) is integer part of a real
number r.
39
As an illustration, for and , the
algorithm produces 4 times series [108]:
(7)
Then, the average length of each of the time
series is computed as follows:
(8)
where indicates the total length of the original data
series.
is a normalization factor. The
calculation is repeated for ranging from 1 to .,
resulting in a sum of average lengths :
40
A fractal curve follows the relationship
(10)
Hence, when plotting against
,
can be estimated as the slope using a least squares
linear best fitting procedure:
(11)
Where
and depicts the number of values
for which the linear regression is calculated (
.
Numerical values of HFD have the lower and upper
limits of 1 and 2, respectively. Considering a curve
that represents the amplitude of a given time series
signal as a function of time on a 2D plane, a simple
(9)
41
curve has a dimension equal 1 and a plane has a
dimension equal 2. HFD can be imaged as a
measure of the “degree of filling out” the plane by the
curve and hence, its complexity [80]. Accordingly,
HFD close to one would represent a smooth curve
with low complexity, whereas HFD=2 would
correspond to complex curve, such as white noise
practically filling 100% of the plane. Hereby, the
fractal dimension of a time series is related to the
spectral exponent β:
(12)
It has been shown that if , then
with the established limits if then
and if then [105, 95]. Important to
note, HFD gives no information of the systems nature
generating the signal, e.g., it is not determinable
whether the system behaves deterministic, chaotic or
stochastic. Instead, HFD depicts a tool to
demonstrate relative changes in the signals’
complexity, for instance, before and after an
intervention [80; 74].
42
The choice of this algorithm is motivated by several
studies, showing that the HFD is promising for the
discrimination of states of consciousness. For
instance, it has been used to measure the depth of
sedation in intensive care unit [109], showing that
HFD values decrease with the depth of anaesthesia
[110]. In the context of anaesthesia it has been found
that HFD is accurate in estimating the bispectral
index (BIS), a method which quantifies the degree of
phase coupling between EEG components [111]. It
has been concluded that HFD depicts an even more
promising method for the assessment of anaesthesia
depth [112], especially in combination with other
measures such as the burst suppression ratio [113].
Further, it has been effectively used for the
discrimination between sleep stages [114], even
using a single EEG channel [115], as well as
between sleep and propofol induced EEG spindles
[116]. In the context of diseases, already over a
decade ago, HFD has been applied in
neurophysiology for the detection of epileptic
seizure, providing better temporal resolution than
43
spectral analysis [117]. Especially in combination
with other nonlinear features, HFD is suitable for
epileptiform EEG analysis [118] and has been
implemented in the development of diagnostic tools
such as an automated classifier [119]. Further, it has
been shown that HFD values are suitable serving as
a biomarker for early detection of Alzheimer’s
disease (AD) as the EEG signal of AD patients
reveals significantly reduced HFD values in the
parietal areas [120], as well as in temporal-occipital
regions [121]. Staudinger and Polikar achieved a
diagnostic accuracy of 78 % for AD, training a
support vector machine with HFD combined with
features of several nonlinear signal complexity
measures [122]. Additionally, it is suggested that
HFD is suitable to discriminate between normal and
hypnotic states, as well as between relaxation and
imagination tasks [123]. It was showed that HFD
revealed differences between internal vs. external
percepts and discriminates external visual from
auditory percepts [124]. Also, HFD provided better
results than linear measures as part of a system for
44
classification of subject’s hypnotic susceptibility [125]
and a real-time fractal dimension based algorithm
has been proposed for the recognition of emotions
inducted via sound stimuli [126].
1.2.4 Multiscale entropy
Another approach to calculate the complexity of a
time series are entropy measures. Generally, the
entropy of a single discrete random variable is a
measure of its average uncertainty. Multiple
mathematical methods exist such as Shannon’s
entropy [127] or the Kolmogorov-Sinai entropy [128,
129]. However, the latter is limited in use of
estimating the entropy of time series of finite length
[130]. In 1991, Pincus introduced a parameter
termed approximate entropy , which applies for the
analysis of “real-world” time series [131]. This has
further been modified and termed sample entropy ,
which allows an estimation less depending on the
time series length describing the complexity more
accurate with better consistency [132, 133]. The
parameter has been defined by Richman and
45
Moorman, starting from the definition of the
entropy, a lower bound of the Kolmogorov-Sinai
entropy, suggested by Grassberger and Procaccia
[129, 132]:
,
(13)
estimated by the statistic:
(14)
where = data points of the time series
, and= length of the vector sequences
.
depicts the tolerated distance level, a percentage
of the standard deviation serving as a similarity
criterion. defines the probability that other
vectors are similar to vector matching for
points, i.e., the number of vectors satisfying
, where is the Euclidean
distance and thus, that any two vectors are within
of each other:
(15)
46
To illustrate the function of the algorithm, a simulated
time series is shown in Figure 6. Here,
a two-component template sequence () and
a three-component template sequence
() are considered. The number of
sequences matching these template sequences are
calculated. In this example, the number would yield
2 for the two-component template sequence
( and ) and one for the three-
component template sequence ().
This procedure is then repeated for the next template
sequences ( and ),
respectively. The number of matching sequences are
summed up and added to the previous value. The
calculations are repeated for all possible sequences
().
Finally, is determined as the natural logarithm of
the ratio between the total number of two-component
template matches and the number of three-
component- template matches. Hence the parameter
reflects the probability that sequences that match
47
each other for the first data point will also match for
the next point [130].
Figure 6: Simulated time series to illustrate the procedure of
calculation the sample entropy for the case and a given
positive real value [130].
This algorithm, however, was shown to assign a
higher value of entropy to pathologic time series that
are assumed to represent less complexity compared
to time series derived from healthy participants [134,
135]. Costa and colleagues suggested that such
misleading results might be explainable by the fact,
that these measures are based on a single scale
[135] and advanced the algorithm further termining
the introduced methods multiscale entropy. Given a
one-dimensional discrete time series
of length , the multiscale entropy
48
algorithm is based on the construction of a
consecutive coarse-grained time series ,
determined by the scale factor [130]. Here, the
original times series is divided into windows of the
length and data points are averaged for each
window according to:
(16)
Then, the entropy measure is calculated for each
course-grained time series (Figure 7) and plotted
[130]. For , the time series is the original
time series. The length of each coarse-grained time
series is equal to the original time series divided by
the scale factor [130].
49
Figure 7: Schematic illustration of the coarse-gaining
procedure. Adapted from [130].
As values are based on a lower probability of
repeated sequences in the data, higher values
represent more complexity. For instance, higher
scale one entropy values are representative of white
noise series compared to 1/f time series (Figure 8).
50
Figure 8: MSE analysis of simulated white and 1/f noise time
series. The value of the sample entropy is plotted against the
scale factor, which specifies the number of data points
averaged to obtain each element of the coarse-grained time
series [130].
The MSE analysis was chosen as several studies
demonstrated that the MSE is useful for quantifying
neural complexity in the context of states of
consciousness [136]. For instance, Miskovic and
colleagues showed significant MSE changes across
the human sleep cycle in the EEG [137]. Also, in one
study MSE values were used as input data to train an
artificial neural network for monitoring the depth of
anaesthesia during surgery. The effectiveness of this
51
proposed new index was analysed by correlation
analysis with the bispectral index (BIS), indicating an
accurate and robust measurement of the depth of
anaesthesia [138]. Regarding the potential of MSE
values as biomarkers in the context of disease,
Takahashi et al. recorded resting state EEG data of
drug-naïve schizophrenia patients pre- and post-
treatment with antipsychotics. In comparison to
healthy controls, patients showed higher complexity
in fronto-centro-temporal brain regions. After
antipsychotic treatment the signal complexity
decreased to healthy control subject levels
selectively in fronto-central regions, highlighting the
usefulness of MSE to identify abnormal temporal
dynamics [139]. Further, MSE was used to
distinguish EEG data derived from Alzheimer’s
disease patients and age- and sex-matched healthy
controls. Here, significant negative correlations
between the sample entropy averaged over all scales
factors and cognitive decline as assessed with the
Mini-Mental State Examination were reported [140].
A link between MSE values and memory
52
consolidation was also proposed by other studies
[141]. As an example, significant MSE differences
were reported in a visual memory task, which
involved making the executive decision of
remembering or forgetting the visual stimuli. Hereby,
greater complexity in the prefrontal and frontal lobe
was observed, when participants intentionally
memorized a visual scene [142].
However, to understand the complexity of brain
activity and its function, a comprehensive theoretical
framework is required describing the multitude of
interaction of billions of neurons. In the following I will
elaborate on the concept of self-organized criticality,
which has originally been introduced as an
explanation of ubiquitous 1/f noise [143]. In recent
years, the hypothesis arose that self-organized
criticality is a fundamental property of neural systems
[144]. As described in the following, the theory states
that the brain state space dynamics self-organize
towards a phase transition, an attractor termed the
critical state. This premise is especially compelling,
as the critical state has been associated with optimal
53
information processing functions [145] and has been
handled as promising for quantifying consciousness
[146].
“Who could ever calculate the path of a molecule?
How do we know that the creations of worlds
are not determined by falling grains of sand?”
Victor Hugo, les Misérables
1.3 Self-organized criticality
Self-organized criticality, in the sense of statistical
physics, is defined as a specific type of behavior,
seen when a system undergoes a phase transition.
During a phase transition, macroscopic properties of
the system, termed the order parameters, change as
a function of a so-called control parameter. For
example, when water gets boiled, a phase transition
from liquid to a vaporous phase occurs. Here, the
order parameter would reflect the phase’s entropy
(such as water or vapor), whereas the control
parameter is the temperature. Modifying the control
parameter gradually changes the order parameter
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until a specific point, at which the values of the order
parameter vary abruptly. Graphically, phase
transitions are either marked by a discontinuity of the
phase diagram (a jump of the order parameter) or by
a point of non-differentiability reflected as a sharp
corner. The latter is termed a continuous second
order phase transition, which allows the system to be
poised exactly between two phases. In that case the
system is in the critical state, residing between two
qualitative distinct types of behavior such as ordered
and disorder. A system at criticality is therefore
sometimes referred to as on the “edge of chaos”. If
the control parameter is below the critical value, the
state is called subcritical, whereas values above the
critical state results in a supercritical state [147, 144,
148]. Systems in a critical state show complex
behavior with inherent characteristics such as scale-
invariance meaning that no scale in time or space
dominates the behavioral pattern. This mode is
reflected by spatial and temporal correlations scaling
of a power law over several orders of magnitude.
Hence, these give rise to self-similar fractal-like
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structure over many scales [149]. Power laws refer
to a probability density function expressed by
, for and denoting the scaling
exponent. The scale invariance is shown when
power laws are plotted logarithmically, indicated as a
straight line: .
Multiplying the plotted coordinate units of such a
graph with a common factor is not resulting in any
change of the slope . A zooming in or zooming out
produces a similar slope with a constant scaling
exponent. For an illustration of the phenomenon, the
two-dimensional Ising model, a classic example of
the ferromagnetic-paramagnetic second-order phase
transition is considered (Figure 9).
The Ising model consists of a lattice in a piece of iron,
whereby each site of the lattice corresponds to a
dipole moment. Below the so-called Curie point
(Tc=1043 K), iron is magnetized even in the absent
of an external field. Here, nearest neighbour
interactions dominate and almost all spins of the
electrons are aligned in the same direction yielding
an ordered state, which creates a net magnetization.
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However, with increasing temperature, the thermal
fluctuations dominate the tendency to align. Spins
are pointed in different directions resulting in a more
disordered state. At T> Tc permanent magnetic
characteristics get lost, and iron becomes
paramagnetic. During the critical phase at Tc where
order and disorder is balanced, the correlation
length, reflecting statistical correlations between any
pair of elements in the systems, is maximized.
Further, the averaged correlation length follows a
power law:, with the critical exponent
. Also, the order parameter of the system at
criticality can be described with power laws. For
instance, the magnetization is governed
by:, with . [147, 150, 148].
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Figure 9: (A) Diagram of the spins in the Ising model in an
ordered state at low temperature, a complex state at critical
temperature and a disordered state at high temperature,
adapted from [150]. (B) Simulation of a 2D Ising model with
length = 256 in subcritical, critical and supercritical states as
temperatures increases from left to right panels. Black areas
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reflect a spin pointed up and white square represent spins
down, adapted from [148]. (C) modified from [151].
Alan Turing was probably the first one speculating
that the brain could be in a critical regime in his
seminal paper on the topic of artificial intelligence
written in 1950 [152]. This was around the same time
when Donald Hebb (1949) formulated his theory on
cell assembly formation as a principle of cortical
functions, often summarized as “Cells that fire
together wire together ”[153]. A decade later
advances in explaining the principles of self-
organization and nonequilibrium phase transitions
such as Herman Haken’s pioneering work on
synergetics and Stuart Kauffmann’s investigations
paved the way for the understanding the brain in
terms of a complex system [154–156]. Back then, the
potential equivalence between neuronal networks
and systems exhibiting a phase transition such as
cellular automata, binary lattices evolving iteratively,
was highlighted [157]. The field further progressed,
when Christopher Langton, one of the founders of the
field of artificial life, published an approach to
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parametrize the space of cellular automata. In his
work, Langton (1990) showed the occurrence of a
phase transition between highly ordered,
deterministic and highly disorder, chaotic dynamics.
Further, he outlined that the vicinity of the transition
point supported optimal processing, transmission
and storage of information [158] (Figure 10).
Figure 10: A binary cellular automaton represents an n-
dimensional array of binary cells. The states are update
synchronously in discrete time steps, whereby each state t+1
depends on the state of the cells at time t. Langton (1990)
identified different classes corresponding to different dynamical
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regimes characterized by the ratio of transitions to an arbitrary
state selected as the “quiescent state” (parameter λ). Class IV
depicts a transitional state analogous to complex behavior
arising in the critical regime. Taken from Heiney et al (2021),
adapted from Langton (1990) [149, 158].
This so-called “computation at the edge of chaos”
[159, 160], was in accordance with theories from Per
Bak, who pioneered the science of self-organised
criticality, promoting critical phase transitions as an
ubiquitous mechanisms to generate complexity,
ubiquitous 1/f noise and the preponderance of fractal
structures in nature. In his book “How nature works”
he uses the canonical example of a sand pile [143].
The sandpile model, which is analogous to a cellular
automata, randomly placing chips on a finite grid,
describes the process of a random positioning of
sand grains on a pile. This results in a slope, which
builds up until it reaches a specific, critical threshold
value, the transition point. At this point the system is
out of balance and from here on, the dropping of
more sand grains leads to an avalanche. During an
avalanche the site collapses transferring sand into
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the adjacent site, extending their slope. This dynamic
was found to be governed by power laws [161].
Importantly, the concept of criticality as proposed by
Bak, Tang and Wiesenfeld fundamentally differs from
the critical point at phase transitions in equilibriums
statistical mechanics as no tuning of a parameter, for
instance temperature, is required. Hence, the critical
point is an attractor, to which the system self-
organized, whereby the scaling properties are
insensitive to the parameters of the model [161].]
However, after a rapid increase of publications in this
field in the 1990s, interest slowly receded [144].
Hence, the conjecture of critical brain dynamics has
come a long way before it was only recently put to
experimental testing ground and revived [162].
1.3.1 Experimental findings and functional benefits
In vitro cultures exhibit spontaneous dynamical
activity, brief bursts of activity followed by longer
intervals of quiescence [163]. In 2003, Beggs and
Plenz hypothesized that the propagation of activity in
networks of cortical neurons is describable by
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equations that govern cascades indicative of a state
of self-organized criticality. In their study, they
recorded spontaneous negative local field potentials
(LFP) of mature organotypical cultures and acute
slices of rat cortex using a multielectrode array [164].
Indeed, the propagation of synchronized LFP
followed a power law with a scaling exponent of -3/2
as it would be predicted from a network of globally
coupled nonlinear threshold elements [165]. The
authors termed this new mode of network activity
“neuronal avalanches” [164, 166]. Subsequently,
avalanches were investigated in superficial layers of
rat prefrontal cortex [167] and during development of
cortical layer 2/3 [168]. Authors showed that nested
beta/gamma oscillations organized as neuronal
avalanches during up-states, which required an
activation of the dopamine D1 receptor [168].
Homeostatic regulation of avalanche dynamic and
the role of the excitation/inhibition (E/I) balance was
then studied in a series of experiments, selectively
blocking excitatory and inhibitory synaptic
transmission by pharmacological means [169].
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Further, in vivo experiments confirmed power law
statistic and spontaneous activity in form of neuronal
avalanches in cats under anaesthesia [170, 171], in
awake monkeys [170, 172] and in rats traversing the
wake-sleep cycle [173]. First signatures of criticality
in the human brain were reported by Linkenkaer-
Hansen and colleagues, who focused on the
temporal fluctuations employing a method called
detrended fluctuation analysis (DFA) and reported
scale-free temporal statistics in EEG data [174]. One
more step towards evidencing criticality was
achieved when Shriki and colleagues analysed
resting-state brain activity from 124 participants
using magnetoencephalography (MEG). Here, large
deflections at single MEG sensors were identified
and analysed as cascades. The authors reported that
cascade size distribution obeyed power laws with an
exponent of -3/2 at timescales where the branching
parameter was close to 1. A scaling and coarse
graining of the sensor array did not change this
relationship [175]. Using intracranial depth
recordings in humans it was further shown that
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avalanche distributions follow a power law, whereby
these differed between states of vigilance with larger
and longer avalanches during rapid eye movement
(REM) sleep [176]. Interestingly, Priesemann and
colleagues analysed highly parallel spike recordings
from animals and LFP from human, suggesting that
the dynamic is self-organized towards a slightly
subcritical brain state [177]. The authors suggest that
potential advantages may be a safety margin from
supercriticality and developed methods to precisely
quantify the distance to the critical point [178, 179].
Subsequently, spatial critical dynamics were also
described in whole brain functional neuroimaging
(fMRI) data [180].
Such studies provided proof-of-principle that SOC
could be a unifying framework to understand
complex patterns of activity in the brain and, by
extension, cognition, behaviour and consciousness
[92]. Work on criticality in physical systems suggest
that systems in a critical state exhibit optimal
computational properties [92] and it has been shown
that critical dynamics in the brain would be
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equivalently accompanied by functional benefits
[145]. SOC implies a balanced signal propagation,
which can have important implications for the
dynamics of neural networks. Such balance is based
on the likelihood that one spike causes each other
neuron to fire and can be captured by the branching
parameter σ, which is defined as the ratio of
descendants, the number of events in a temporal
interval t and the ancestors, the number of events in
the following interval t+1 (Figure 11) [181, 145, 182].
Accordingly, experimental evidence suggest that
critical dynamics emerge when excitation and
inhibition is balanced [183–185]. Importantly, the
balance between independence and
interdependence among neurons is fundamental for
the transmission and processing of information [186].
Computational advantages of criticality have been
demonstrated in neural network models and
empirical recordings. For instance, it has been shown
that that the dynamic range of a neural network is
maximized at a critical point [187, 188], which has
also been suggested by an in vitro experiments
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manipulating cultures pharmacologically close to
criticality [189] as well in vivo recordings from rats
[190]. Further, optimal information transmission,
storage and capacity has been reported in neuronal
models at criticality [191–193], in vivo [194] and in
animal studies [195]. Importantly, the observed
scale-free patterns close to a critical point of a phase
transition imply the largest variability and thus, the
largest number of configurations and repertoire of
possible brain states [151].
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Figure 11: Schematic illustration of the branching ratio. Adapted
from [149] and [181]. Blue nodes represent active ones and
gray nodes are inactive. The middle regime of σ= 1 corresponds
to the critical state, in which activity is self-sustained. The case
of σ< 1 corresponds to a subcritical state in which activity will
die out over time. A supercritical state is indicated by a σ> 1, in
which activity will increase with time.
To summarise, key experimental observations in
support of the criticality hypothesis are (i) neuronal
avalanches with power law distribution and (ii) long-
range temporal correlations in the amplitude of
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neural oscillations [196]. These can be determined
by analytical metrics as described in the following.
1.3.2 Detrended fluctuation analysis
The detrended fluctuation analysis (DFA) depicts a
prominent method to quantify the scale-free nature of
physiological time series by estimating long-range
temporal correlations (LRTC), the scale-free decay
of temporal (auto)correlations. The algorithm
captures fluctuations of the signal at different time
scales determining the statistical self-affinity of a
signal [197–199]:
(17)
where and are values of a 1-dimensional
process at time windows of length and t,
respectively. L depicts the Window length factor and
H denotes the Hurst parameter, a dimensionless
estimator of self-affinity. The algorithm consists of
two steps (Figure 12). First, the data series is
shifted by the mean of the time series and
cumulatively summed:
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(18)
Then, the signal profile is divided into a set of non-
overlapping separate time “boxes” of various sizes
Δ. Subsequently, in each segmentation the data is
locally fit to a polynomial . The local
polynomial trends fit within each box are subtracted
and the root-mean-square of the residuals
(“fluctuations”) is calculated:
(19)
Subsequently, the mean fluctuation per window size
is plotted against the window size on a logarithmic
scale. The scaling exponent α is estimated as the
slope of the least-squares fit line. The resulting DFA
exponent α can be interpreted as an estimation of the
Hurst parameter. If 0< α< 0.5, the process is of a
stationary nature, exhibits anti-correlations and has a
memory. In the case of 0.5< α< 1, the process is
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stationary, exhibits positive correlations and has a
memory. A random process with no memory is
governed by α = 0.5, whereas when 1< α< 2, then
the process is non-stationary, meaning that the
signal’s statistical characteristics change with time
[199]. Stationary processes can be modelled as
fractional Gaussian noise with H= α and non-
stationary processes can be modelled as fractional
Brownian motion with H= α -1 [200].
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Figure 12: Stepwise explanation of the detrended fluctuation
analysis. (A) shows an original time series taken from a 1/f
signal sampled at 5 Hz with a duration of 100 s. (B) The
cumulative sum of the time series. (C) Removal of the linear
trend from the signal for each time window. (D) Plot of the mean
fluctuation per window size against window size on a
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logarithmic scale. In this example the scaling exponent is α=1,
estimated as the slope of the best fit line. Adapted from [199].
1.3.3 Neuronal avalanches
For the neuronal avalanche analysis, the time series
is first z-scored. Then, a certain threshold is applied
and negative and positive excursions beyond the
threshold are identified as concrete event (Figure
13A,B) [201]. Subsequently, the time series is
discretized with time bins of the duration Δt. Neuronal
avalanches are defined as a contiguous sequence of
time bins of activity preceded, ending with at least
one time bin of quiescence [175].
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.
Figure 13: (A) Schematic illustration of the event identification
process. Adapted from [175]. (B) Avalanche definition.
Neuronal avalanches are defined as a contiguous sequence of
time bins of activity preceded, ending with at least one time bin
of quiescence. Modified from [202]. (C) Probability distribution
of the relationship between size and likelihood of avalanches
shown in double logarithmic coordinates. At criticality a scale-
free process yields a power law relationship with a critical
exponent of -3/2. Adapted from [92].
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A hallmark that a neural network operates near a
critical point is given by a power law scaling of
avalanche size distribution ()) (Figure 13B),
duration distribution ()) and average size
conditioned on given duration data (). The
resulting critical scaling exponents and show
a relationship according to [203, 204]:
(20)
(21)
(22)
(23)
Another method for establishing criticality involves
investigating the averaged, scale-invariant profiles of
cortical fluctuations. Typically, avalanche shapes are
inverted parabolas, depicting fractal copies of each
other when different avalanche sizes are examined.
Hence, in a critical state mean temporal profiles of
avalanches should be identical across scales, e.g.
long duration avalanches are supposed to have the
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same scaled mean shape as short avalanches (
Figure 14) [203].
Figure 14: Shape collapse procedure [149]. First, raw
avalanche shapes are determined by averaging the profile of all
avalanches with a given duration. Then, the avalanches are
scaled to a uniform length and finally, the scaling parameter is
estimated by using a quadratic polynomial. Adapted from [201].
1.3.4 Clinical relevance
The concept of combining consciousness and
criticality is promising for a wide range of clinical
applications (Figure 15) [148]. For instance, findings
suggest that criticality-based markers could
potentially be used to assess the depth of
anaesthesia [205]. An analysis of long-range
temporal correlations (LRTC) combined with spectral
data successfully differentiated between
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wakefulness from induced unconsciousness. The
authors suggesting that the loss of consciousness
may be accompanied with an increase in regularity
and a decrease in network repertoire limiting
cognitive processing [206]. Further, signatures of
criticality were applied to predict, localize, and
characterize epileptic seizures. Whereas some
studies identified power-law distribution during
seizure intervals [207–209], others report a deviation
from critical dynamics [210, 211]. Additionally, a few
studies investigated criticality in neurodegenerative
diseases such as Alzheimer’s disease (AD). Findings
suggest that criticality inspired markers such as the
level of autocorrelations and synchronization as well
as differences in the power-law exponent in the
frontal and pre-frontal lobes may be beneficial for
disease monitoring and the diagnostic evaluation of
early-onset [212]. Whereas in AD patients a scale-
free distribution of spontaneous fluctuations was
maintained, Parkinson disease has been suggested
to represent a situation of departure from a critical
state, whereby motor symptom severity was found to
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be positively correlated with the scaling exponent of
an adaption of the detrended fluctuation analyses
(DFA) [213]. As criticality implies optimal information
capacity and transmission in models [193], the role
of criticality in aspects of attention, cognition and
learning has also been a topic of investigation. As an
example, it has been shown that power law scaling
decreases with increased cognitive load in a MEG
study of children with high-functional autism, who
underwent executive function tasks [214]. Further
studies suggested that focused cognitive tasks
induce subcritical dynamics [215]. In contrast, an
EEG study of 210 neurotypical adults undergoing an
object recognition tasks demonstrated that variation
in 1/f noise robustly predicted cognitive processing
speed [216]. Suggesting that critical state dynamics
are important for language acquisition, Dimitriadis et
al. carried out a MEG study of children with reading
difficulties. Here, temporal correlations decreased in
the left temporoparietal region at rest compared to a
age and IQ matched control group [217]. In line with
these findings, increased LRTC positively correlated
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with language score was demonstrated in a high-
density EEG study of neurotypical children [218].
Also, high intelligence has been associated with
near-criticality dynamics in a resting-state as shown
in a recent functional magnetic resonance imaging
(fMRI) study of neurotypical adults with varying IQ
scores [219]. Furthermore, criticality-based markers
were used to improve the understanding of
psychiatric conditions. For instance, in one study
MEG was recorded from patient with major
depressive disorder (MDD) and healthy controls
during an eyes-closed resting state. The magnitude
of temporal correlations over the left- temporo-
central region was suitable to predict severity of
depression assessed with the Hamilton Depression
Rating Scale. In comparison to controls, patients with
MDD exhibit absent LRTC in the theta frequency
band, which was interpreted as a possible underlying
defect in limbic-cortical networks [220]. The latter
could not be confirmed in an EEG study of patients
with MDD, whereas increased LRTC scaling
exponents were correlated positively with depression
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severity. Here, the authors concluded that rumination
and psychomotor retardation may be the reason for
the persistence of LRTC [221]. Also, higher LRTC
scaling exponents were shown in patients with MDD
at baseline compared to healthy controls in EEG
data. The strength of LRTC decreased after an
intervention consisting of stress reduction training or
mindfulness training in both cohorts [222]. Other
studies examined whether alterations in LRTC during
sleep could be a signature of depression reporting no
statistical significant differences through the sleep
stages [223, 224]. Regarding schizophrenia and
schizoaffective disorders, an attenuation of LRTC
scaling exponents was found in alpha and beta
frequency bands compared to healthy controls in an
EEG study indicating decreased temporal correlation
and precision [225]. These results have been
confirmed in other studies [226] and have been
associated with the ‘disconnection hypothesis’,
considering that the core symptoms of schizophrenia
are related to aberrant connectivity between distinct
brain regions [227, 228]. Interestingly, first studies
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with healthy participants provided evidence that
neurofeedback can restore critical brain dynamics. It
has been speculated that neurofeedback alters
excitation associated with increases in temporal
improvement and hence, could balance psychiatric
conditions, which have been characterized by
decreased LRTC [229, 230]. In summary, the
concept of criticality has several domains of clinical
application. While criticality-based markers are not
yet part of clinical routine and despite some
controversies, these could prove beneficial in
diagnosis, prognosis or treatment of a variety of
diseases and may pave an important avenue of
future research for understanding brain-related
disorders and the relationship between neural and
cognitive flexibility [148].
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Figure 15: Illustration of long-range temporal correlations
(LRTC) as a function of criticality in different conditions.
Adapted from [231] and [148]. The grey area represents the
physiological range of brain dynamics. Black arrays show the
deviations towards a subcritical regime (left) or a supercritical
regime (right) according to findings in the literature [148].
Double arrays imply contradictory evidence for both increases
and decreases in LRTC.
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2. Research questions and Aims
I. Can signatures of self-organized criticality be
found on the level of the EEG?
For this purpose, electrophysiological data
(64-channel EEG) will be analyzed in respect
to the key experimental observations in
support of the criticality hypothesis: (1)
neuronal avalanches with power law
distribution, (2) long-range temporal
correlations (LRTCs) in the amplitude of
neural oscillations. To note, in this thesis I will
not aim at answering whether the brain is
critical, rather than outline possible
interpretations of experimental results. Many
studies have been conducted and
controversies emerged. To date, there is no
study enabling to confirm or disprove the
criticality hypothesis in neuronal networks.
However, with this research, I aim to
contribute to the expanding field suggesting
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features of criticality to quantify
consciousness.
II. Are criticality features suitable to differentiate
states in the spectrum of wakeful
consciousness and to characterize
electrophysiological correlates of altered
states of consciousness?
The framework of self-organized criticality
seems promising for developing physiological
markers of consciousness alterations.
However, to identify their potential utility in
monitoring neurophysiological changes in
response to interventions as well as
diagnostics, it has to be shown that EEG-
based criticality parameters are suitable to
sufficiently differentiate mental states in the
spectrum of wakelfulness. First, this will be
tested on an EEG dataset of professional
meditators performing three distinct
meditative tasks. Second, it will be
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investigated whether the measures are
suitable to reflect state changes in the
temporal course of a relaxation process.
III. Can critical dynamics be induced by
psychophysical (mind-body) interventions?
Critical dynamics are associated with brain
activity tuned towards optimized information
processing functions, such as input
susceptibility, maximized dynamic range,
storage capacity and computational power. In
other words, the optimal brain state. Here,
criticality measures are proposed as general
gauges of information processing. At the
same time, findings suggest that
psychological self-regulation techniques such
as mindful focused attention during meditation
enhance allocation of attentional resources
and thereby, information processing
capacities. However, how critical dynamics
relate to cognitive function is poorly
understood. Therefore, I aim at testing
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whether altered states of consciousness, here
specifically induced by distinct meditation
tasks and a vibroacoustic relaxation process
represent neuronal activity exhibiting
dynamics closer the critical point of a phase
transition compared to a baseline task-free
condition.
IV. Can an explicit relationship to other nonlinear
complexity features power spectral density
parameter be identified?
This thesis is based on the contemporary
proposal that consciousness represents a
dynamic process of self-sustained
coordinated brain-scale activity of
simultaneous integration and differentiation
and thus, might be quantifiable by the degree
of neural complexity. Whereas self-organized
criticality can be seen as a theoretical
framework for the emergence of complex
patterns of activity in the brain, to date, the
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relationship between complexity and criticality
in neural systems has not been determined
experimentally. Therefore, besides applying
analytical tools from criticality theory to EEG
data recorded during meditative tasks and a
relaxation process as well as sampled from a
cohort with different levels of sensory
processing sensitivity, also nonlinear methods
to quantify neural complexity, namely fractal
dimension analysis, and multiscale entropy
analysis will be used. In addition, the standard
methods using spectral decomposition will be
applied to the datasets. The resulting EEG-
based features will then be evaluated with
respect to their comparability in the
discrimination of brain states. In this stance,
correlations between criticality and complexity
measures as well as spectral data will be
analysed.
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V. Do EEG-based complexity and criticality
features reflect individual temperament traits?
For this purpose, it will be determined whether
EEG complexity and criticality features
correlate with the temperament traits
absorption defined as the individual’s capacity
for engaging attentional resources in sensory
and imaginative experiences (study 2) as well
as the individual level of sensory processing
sensitivity (study 3).
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3. Material and Methods
3.1: Mediation states
3.1.1 Data acquisition and participants
An EEG data set, which has been recorded and
previously analysed by T. Hinterberger in the spectral
domain was used for reanalysis [232]. Data were
recorded from 30 participants (mean age 47 years,
11 females/19 males) with a meditation experience
of at least 5 years practice or more than 1000 h of
total meditation time. On average, participants had
meditated for 20 years and 6498 hours. Participants
were associated with different kinds of spiritual
traditions. For instance, six participants were Zen
Buddhist monks in Japan. Based on these
backgrounds, the subjects developed an individual
‘idiosyncratic’ meditation style.
Data were recorded using a 72-channels QuickAmp
amplifier system (BrainProducts GmbH, Munich,
Germany). EEG was measured with a 64-channel
ANT Waveguard electrode cap (ANT B.V.,
Enschede, The Netherlands) with active shielding
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and Ag/AgCl electrodes, which were arranged
according to the international 10/10 system with
grounding at the participant’s shoulder. To note, the
data was provided by Prof. Dr. Hinterberger for a re-
analysis.
The experimental procedure started with an initial 15
min baseline resting, including 5min with eyes open,
5 min with eyes closed and 5 min silently reading a
neutral text from a book or a computer screen. Then,
after a short break, participants were asked to
meditate in their own preferred style (idiosyncratic
meditation) for 20- 30 min. Next, three specific
meditative tasks were instruction lasting 2 min each
(Figure 16). These were in accordance to
classification categories established by Travis and
Shear [233].
i) presence monitoring (instruction: “Try to
be in a state of high presence at the place
you are in this room at each moment of
time.”)
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ii) thoughtless emptiness (instruction: “Try to
maintain the state of emptiness from all
thought as well as possible.”)
iii) focused attention (instruction: “Direct your
attention on a sport in the middle of the
forehead above your eyes.”)
Instructions were spoken by the same experimenter.
Participants kept their eyes closed during the
meditation tasks. Afterwards, all meditators reported
that they were able to reach and maintain the
instructed mental states [234, 232].
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Figure 16: Experimental procedure. Modified from [232].
3.1.2 EEG data processing
Matlab (MathWorks, Natrick, USA) was used for data
processing. Data was sampled at 250 samples/sec
in a range from DC to 70 Hz with a notch filter at 50
Hz. After detrending the 64 EEG channels, a
correction for eye movement was done using a linear
correction algorithm, which detects eye blinks as well
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as movement events and uses those periods for
determining a correction factor for each channel.
Then, the EOG was multiplied with this factor and
subtracted from the EEG. The efficiency of the
algorithm was previously demonstrated [235].
Subsequently, the following analysis tools were
applied to the data as described in the following.
Power spectral density (PSD): A power spectrum
time series was calculated using the Fast Fourier
Transform (FFT) for the following frequency bands:
• Delta: 1-3.5 Hz
• Theta: 4-7.5
• Alpha1: 8-10
• Alpha2: 10.5-12 Hz
• Beta1: 12.5–15 Hz
• Beta2: 15.5–25 Hz
• Gamma1: 25.5–45 Hz
• Global: 1–45 Hz
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To obtain a measure of the power spectral density
(PSD) FFT values were squared and all FFT bins
within a frequency band range were averaged. EEG
PSD was calculated for each participant, task,
electrode, and frequency band.
Neuronal avalanches: For the neuronal avalanche
analysis the NCC toolbox was used [201]. First, the
signal from each electrode was z-scored. A threshold
of ±3 SD was applied [175]. Negative and positive
excursions beyond the threshold were identified as
concrete events. The time series obtained from each
electrode was discretized with time bins of the
duration Δt=5s. Neuronal avalanches are defined as
a contiguous sequence of time bins of activity
preceded, ending with at least one time bin of
quiescence. Avalanche properties were determined
using the function avprops.m, which calculates the
duration (number of active time bins), the size
(total number of events) as well as the shape
(number of events at each time at each time bin). The
average size given duration distribution () was
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calculated using the build in function
sizegivdurwls.m, which computes the scaling
parameter and standard deviation using the
weighted least squares method (see equations (20 to
(23) [203, 204]. Mean temporal profiles of avalanche
shapes were calculated using the function
avgshapes.m and an avalanche shape collapse has
been performed (avshapecollapse.m), determining
the shape collapse scaling parameter [201].
Subsequently, differences between the value of the
obtained critical exponent and the shape
collapse scaling parameter were calculated, as these
should be identical for brain dynamics operating in a
critical regime [204]. The resulting variable was
termed .
Detrended fluctuation analysis: To estimate long-
range temporal correlations (LRTC), detrended
fluctuation analysis (DFA) was used, an algorithm
which, captures fluctuations of the signal at different
time scales determining the statistical self-affinity of
a signal [199]. Here, an algorithm described by
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Colombo and colleagues (2016) was used [231].
First, the cumulative sum of the time series was
calculated. Then, the signal profile was divided into a
set of non-overlapping separate time “boxes” of
length . Subsequently, local polynomial trends fit
within each box were subtracted and the root-mean-
square of the residuals was calculated. Here, the
detrend order, specifying the degree of polynomials
was set to 2. The local detrending was repeated for
50 automatically determined box sizes and the
power-law relationship between root-mean-square
fluctuations and box sizes was determined by means
of regression. The resulting exponent was termed α
(see equations (18(19).
Fractal dimension: As a measure of signal complexity
in the time domain the algorithm proposed by Higuchi
was applied to calculate the fractal dimension (see
equations (6, and 8 to (11) [105]. The value of ,
the maximum number of sub-series composed from
the original, can be determined by examining the
data and plotting the fractal dimension over a range
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of k. For k greater than the fractal dimension
plateaus, reaching a saturation point [107]. In this
work that was the case for = 5.
Multiscale entropy: The multiscale entropy was
calculated using an algorithm described by Costa
and colleagues (2005), which is based on the
construction of a coarse-grained time series by
averaging the