Quantifying the informational complexity of consciousness – a review

Quantifying the informational complexity of consciousness – a review

Abstract

The topic of consciousness has puzzled scientists and philosophers for centuries. Current theories of consciousness often propose that for a healthy conscious experience a balance is required between

information integration and neurophysiological differentiation. This brain complexity is expected to decrease during states of unconsciousness or due to severe brain injuries and it is expected to be altered in disorders such as schizophrenia or epilepsy. This theoretical notion has inspired extensive empirical work trying to pinpoint what changes in the brain in different conscious states. One such empirical approach concerns measures of informational complexity which try to quantify variations in states of consciousness. Generally, these can be divided in two types, namely measures of neural signal diversity and graph theoretical measures that relate to functional connectivity and network structure. Various studies have shown that: (a)

informational complexity decreases during states of unconsciousness, (b) these measures are able to distinguish between the severity of various brain injuries, such as patients in vegetative state, minimally conscious patients and locked-in syndrome patients, (c) informational complexity increases in the psychedelic state, (d) various disorders related to more subtle altered fluctuations in consciousness differ in their neurophysiological signature as been determined by informational complexity measures. This line of research can be of incredible significance in clinical settings. It might aid in the identification of biomarkers, assessment of treatment effectivity, early diagnosis and improved surgical precision (e.g. in epilepsy). Promising future directions concern studying more refined fluctuations in everyday healthy consciousness, such as mental fatigue, flow, level of arousal and attention.

Introduction

The phenomenon of consciousness has mystified scientists and philosophers throughout the ages. The question of why and how certain neurophysiological processes lead to conscious experiences has yet to be resolved. Chalmers (1995) argued that for truly understanding consciousness there are two types of problems that must be tackled, the ‘easy’ problems and the ‘hard’ problem. The relatively ‘easy’ problems include questions regarding how information is integrated in the brain, how the brain is able to discriminate between different stimuli and how attention is focused. Solving these types of problems mainly relies on uncovering the underlying mechanisms that explain how certain functions are carried out within the system. The hard problem concerns the relationship between physical processes and phenomenal quality of experience (e.g. the ‘greenness’ of the color green) which is inherently subjective and therefore much more difficult to study scientifically (Chalmers, 1995).

Although there are still many outstanding questions about the nature of consciousness, there is a general consensus that the degree to which one is conscious varies and is related to different brain states. For instance, the transition from wakefulness to sleep is generally perceived as a transition where consciousness slowly fades into unconsciousness (Tononi & Massimini, 2008). An important question in this regard concerns the changes that are taking place in the brain when the level of consciousness increases or decreases. Recently, research has explored spontaneous neural activity during several states of (un)consciousness (e.g. anesthesia, awake). Neural regions and networks that are related to conscious states (i.e. thalamo-cortical networks) undergo functional changes during unconsciousness. That is, in unconscious states (e.g. anesthesia) brain activity patterns become more stereotypical and bear greater resemblance to the underlying

neuroanatomical connections. In contrast, during wakefulness functional activity patterns are more varied and diverse, and less related to structural connectivity (Barttfeld et al., 2015). This indicates that there may be particular neural activity patterns at play that are responsible for producing the representations of consciousness (Pennartz, 2015).

One proposed hypothesis in this regard is that there is a relationship between different levels of consciousness and the dynamics of informational complexity of neural activity (Telesford et al., 2011; Tononi et al., 1994; Edelman, 2003) which has motivated some empirical work. This emerging set of empirical work has led to the development of a variety of complexity measures that try to quantify different levels of consciousness by capturing informational complexity in the brain (Arsiwalla & Verschure, 2018). Findings from various studies that use these complexity measures to study various states of consciousness (e.g. anesthesia, sleep, wakefulness) suggest that informational complexity is decreased in states of unconsciousness (Schartner

et al., 2015; Casali et al., 2013) and the dynamical repertoire and functional connectivity of important networks such as the thalamo-cortical system are often reduced (Luppi et al., 2019; Barttfeld et al., 2015). These findings align with prominent theories of consciousness stating that for an optimal level of

consciousness to arise, information in the brain has to be integrated and differentiated (i.e. diversity of neural repertoire) to a certain degree (Tononi et al., 1994; Telesford et al., 2011; Carhart-Harris et al., 2014). High levels of neural synchrony that coincide with low levels of neural diversity might lead to certain pathological states (e.g. epileptic seizures) (Meeren et al., 2002) while an increased level of neural diversity might lead to altered states of consciousness (e.g. psychedelic state, REM sleep) (Carhart-Harris et al., 2014).

Besides of bearing the promise to enhance our understanding of the workings of consciousness, the development of measures to accurately quantify different states of consciousness could also be highly relevant in clinical settings. For instance, when monitoring anesthetized patients or in the assessment and treatment of patients suffering from disorders of consciousness (DoC) caused by severe brain injuries (e.g. vegetative state, locked-in syndrome). One of the main challenges in the clinical assessment of such patients is to find suitable objective measures that do not rely upon whether these patients have the capacity of interacting with their surroundings (Fingelkurts et al., 2013; Casali et al., 2013). The development of these objective measures of consciousness could help resolve this problem by providing clinicians with the tools to accurately assess the state of consciousness of these types of patients. Furthermore, these measures could also be useful in assessing patients with (neuro)psychiatric disorders that influence conscious experience (e.g. schizophrenia, autism) (Catarino et al., 2011; Liu et al., 2008) or in the study of altered states of consciousness (e.g. psychedelic state) (Schartner et al., 2017).

The purpose of this review is to provide an overview of frequently used techniques that intend to quantify the informational complexity of consciousness and the empirical usefulness of these techniques in distinguishing between different levels of consciousness. The overall focus of this article will be on the use of these techniques in clinical settings. First, some theoretical background will be provided by discussing the relevance of complexity science and complexity-driven methodologies (e.g. network science) and touching upon some prominent theories of consciousness that are relevant in the context of this review. Next, an extensive overview will be given of the most promising complexity measures that are currently used in consciousness research. Then, some clinical applications will be discussed. Finally, some thought will be given to how these measures can be interpreted, certain practical issues that may come up and potential future directions.

Theoretical background

Complexity science and graph theory

Complexity science is an emerging interdisciplinary field of research that studies complex systems. A complex system is a system in which networks of decentralized components interact following elementary rules of operation and hereby produce complex collective behavior. Other key characteristics of such networks are that these operate at a critical point between order and disorder, are capable of advanced information processing and can often adapt through evolution or learning (Thurner et al., 2018). The study of complex systems has been applied to many real-world phenomena such as biological systems (Mazzocchi, 2008), social networks (Hu et al., 2008) and the economy (Arthur, 1999). This line of research is also relevant for the study of consciousness since the human brain is an incredible complex system which is thought to operate at a critical point on the “edge of chaos” (Kelso & Fuchs, 1995; Faure & Korn, 2001). Therefore, complexity science holds great promise for uncovering how higher order cognitive processes such as consciousness emerge from lower level neural interactions (Telesford et al., 2011). Many current theories of consciousness aim to explain how the diversity of conscious experiences can arise from the brain and propose a relationship between the dynamics of informational complexity and different levels of consciousness from which various approaches to measure consciousness have been formalized (Seth & Edelman, 2009).

Complexity-scientific methods can provide us with effective tools that may contribute to our understanding of how various brain regions interact and how these dynamics produce emergent phenomena such as consciousness. One such approach is the use of graph theoretical measures (Telesford et al., 2011). Graph theory concerns the study of graphs (i.e. networks) which are mathematical structures composed of nodes which are connected by links (unidirectional or bidirectional). Graph theory is used to model the relationships between the links and nodes in a network (Barabási, 2016). A graph theoretical approach could be useful in neuroscience research since, as stated before, the brain can be viewed as a complex network consisting of various interacting areas that together produce complex behaviors (Van Steen, 2010).

Furthermore, the brain is often believed to have world properties (Bassett & Bullmore, 2006). A small-world network consists of a few long-range connections (integration) and a small average path length (segregation, clustering). This type of network topology is thought to increase the efficiency of information transfer in a network (Watts & Strogatz, 1998).

In neuroscientific research, network analysis can either be based on anatomical connections or functional connectivity. Networks are typically derived from neuroimaging data. First, a connection matrix is produced which indicates the connection strength between the nodes. Next, a threshold (e.g. based on average degree or edge density) is generally applied to make sure low strength connections are removed. The process of thresholding then produces a binary adjacency matrix on which various network analyses can be performed (Telesford et al., 2011). Graph metrics, such as the average path length and the clustering coefficient, are often used to analyze local and global properties of the system (Barabási, 2016). Measures of centrality, like closeness and degree, are suitable for pinpointing the critical components of a network (e.g. hubs) (Borgatti, & Everett, 2006). Examination of community structure in networks (e.g. modularity analyses) is useful to gain insight into the topological organization of a given network (Newman & Girvan, 2004). A

combination of various network measures will provide the best insight into the function and structure of a network. Graph-theoretical measures and functional connectivity analyses have been used extensively in consciousness research (Chennu et al., 2014; Luppi et al., 2019; Barttfeld et al., 2015).

Theories of consciousness – a brief summary

Generally, every conscious scene is experienced as a unified whole. However, conscious scenes are also built up from many different parts which makes the specific experience in question one amongst an extensive repertoire of alternative conscious representations. That is, when having a specific conscious experience, this experience is composed of various modalities (e.g. sensory experiences, thought, emotions) that are integrated into a unified whole, which is more than the sum of its parts and this experience can be distinguished from a range of other potential experiences. This basic idea of how a conscious experience is constructed led to the conception that the average conscious experience is both integrated and differentiated (Seth & Edelman, 2009). Various theories are often sympathetic to the idea that there is an association between consciousness and integrated information or between consciousness and some approximation of differentiation (e.g. signal diversity, entropy) (Tononi et al., 1994; Edelman, 2003; Carhart-Harris et al., 2014). However, these theories might differ in how they define integration and differentiation or use different terms entirely. For the purpose of this review, the current section will briefly discuss some theories of consciousness that are particularly relevant in the context of this review. For a more extensive review of theories of

consciousness see ‘Block (2009)’.

A well-known theory that deals with the viewpoint that neural dynamics, both integrated and differentiated, give rise to conscious experiences is the Dynamic Core Hypothesis (DCH) (Edelman, 2003). The DCH is closely related to the Theory of Neural Group Selection (TNGS), which is a Darwinist interpretation of neural processes originating from immunology and evolutionary biology that proposes neural dynamics and brain development to be inherently selectionist (Seth & Baars, 2005). Both the DCH and TNGS state that neural mechanisms related to conscious processing emerged from evolutionary processes for the function of

multimodal discriminations (Edelman, 2003). According to the DCH, neuronal groups may directly contribute to conscious representations when these are elements of a larger functional cluster (i.e. thalamo-cortical

network) and can attain states of high integration in very short time spans via recurring interactions within this network. Here, the thalamo-cortical system is defined as the dynamic core which consists of neural dynamics that are highly statistically dependent within the system and in contrast, are much less statistically dependent on elements outside this neural system (Tononi & Edelman, 1998). Furthermore, an important assumption of this theory is that the dynamic core is highly differentiated as is indicated by its ability of detailed multimodal discriminability (Seth & Edelman, 2009). This interaction between differentiation and integration in thalamo-cortical networks is thought to be a necessary requirement for conscious states to arise. This brain complexity is assumed to be high in the presence of consciousness such as during normal wakefulness, but low in the absence of consciousness, for instance in deep sleep or under anesthesia (Balduzzi & Tononi, 2008).

Another prominent theory in consciousness research is Integrated Information Theory (IIT) (Tononi, 2008; Tononi et al., 2016; Koch et al., 2016). IIT provides axioms of consciousness using phenomenological experience as a foundation and attempts to relate these axioms to their necessary neural correlates (postulates). According to IIT, a conscious experience needs to be a) real or actual (intrinsic existence), b) structured, in the sense that an experience is composed of various phenomenological components

of information), d) unified, which makes it intrinsically irreducible to independent components (integration) and e) definite, by excluding all potential cause-effect structures that could have accounted for the same state but are not maximally irreducible (exclusion). Here, integrated information Φ (a non-negative number) can be quantified as the amount of information produced by the system as a whole that is maximally irreducible to independent components, while accounting for the causal dynamics of the system (i.e. cause-effect structure) (Tononi, 2008). The complexity of a system is thought to arise from both the integration and differentiation of the information within the system at a certain time point. In the brain, differentiation can be defined as the local functional specialization of different brain areas, whereas integration can be defined as the unification of neural information on a global level (Tononi et al., 2016).

An important theory of consciousness that is more related to neural diversity is the entropic brain hypothesis, developed by Carthart-Harris et al. (2014), and inspired by neuroimaging studies with psychedelic substances. According to the entropic brain hypothesis, the quality and complexity of a conscious experience depends on the degree of entropy (i.e. disorder, uncertainty) within the neural system at a given time point. A distinction is made between two fundamentally different states of consciousness, namely primary

consciousness and secondary consciousness. Primary conscious states, such as the psychedelic state, early psychosis and REM sleep, are characterized by higher entropy, more disorder and increased flexibility. Secondary consciousness is defined as normal waking consciousness, which is more restrained and ordered. The ability to suppress entropy to a certain degree is hypothesized to have developed through evolution and is thought to be necessary for organizing and constraining cognition in everyday conscious functioning.

Furthermore, states with lower entropy and lower disorder, as compared to normal waking consciousness, are expected to be more rigid. Examples of states which are hypothesized to coincide with low levels of brain entropy are anesthesia and deep sleep but also waking states that are viewed as pathological such as depression and OCD. The entropic brain hypothesis proposes that to adopt a state of primary consciousness the brain has to undergo a phase transition beyond a certain critical point. This phase transition is

hypothesized to coincide with increased brain entropy, as indicated by increased variance in critical networks, and with a reduction of the functional connectivity between the default mode network (DMN) and the medial temporal lobe (MTL) (Carthart-Harris et al., 2014).

Predictions that are made by the above-discussed theories can often be empirically tested in research using complexity measures to quantify the informational complexity of consciousness and try to capture what happens in the brain when people transition between different levels of consciousness. For instance, IIT predicts that brain injuries will only lead to loss of consciousness if the damage critically disrupts the system’s ability for information integration (Tononi et al., 2016). This prediction can be tested by using measures that can identify the ability for information integration in brain-injured patients and relate this to the severity of their condition. In this case, the brain’s ability for information integration in the relevant thalamo-cortical areas is expected to be more impaired in vegetative state (VS) patients compared to patients that are minimally conscious (MCS) (Casali et al., 2013).

Overview of informational complexity measures

The current section will focus on providing an overview of several important complexity measures and their potential empirical usefulness. The two proposed components of consciousness (i.e. differentiation, integration) could potentially be evaluated with neuroimaging studies and then related to different states of consciousness. Neurophysiological differentiation might be approximated with techniques that compute the diversity of the repertoire of neural states within the system and integration might be approximated with techniques that can specify the functional connectivity between brain areas at different time points (Tononi et al., 2016). As mentioned before, a variety of complexity measures have been developed in the recent years that differ in how they try to capture informational complexity in the brain (Arsiwalla & Verschure, 2018). Some of these measures are claimed to capture neurophysiological differentiation, some measures are claimed to capture integration and some measures purport to capture both. Furthermore, there is great variation in the suitability of these measures for different neurophysiological signals, such as EEG or fMRI. In this way these measures could be used in a complementary way. The following discussion of the various complexity measures is divided into two parts, namely measures of signal diversity, and graph theoretical measures and functional connectivity. In the context of the two proposed dimensions of consciousness, measures of signal diversity can be related to the concept of neurophysiological differentiation and measures relating to graph theory and functional connectivity can be related to the concept of information integration. However, it must be mentioned that this division is not perfect as some measures are related to both signal

diversity and functional connectivity. These measures, such as the Phase-lag entropy (Lee et al., 2017), are discussed in the section that is most suitable.

Measures of signal diversity

A recently developed complexity measure that can be useful in clinical settings is the perturbational complexity index (PCI). A TMS-EEG study of Casali et al. (2013) used the PCI to reliably distinguish between levels of consciousness in healthy participants during wakefulness, various stages of sleep, under sedation and in brain-injured patients displaying a variety of clinical conditions after emerging from a coma. The PCI was acquired in the following way. First, they perturbed the cortex using transcranial magnetic stimulation (TMS) to induce dispersed interactions between various cortical areas and then measured the brain’s response with high density EEG. A binary spatiotemporal matrix of significant sources was extracted from the

electrophysiological signal using nonparametric statistical methods and source modeling. Sources and time samples were assigned 1 in case of significance, 0 in all other cases and were sorted according to their overall activity duration throughout the post stimulus period.Next, the Lempel-Ziv complexity (LZc) index was used to estimate the informational complexity of this binary spatiotemporal matrix (Casali et al., 2013). LZc is a previously-validated method to quantify the compressibility of various biological signals. This measure quantifies complexity by first binarizing the time series data according to a given threshold and then determining the amount of distinct activity patterns. The higher the pattern diversity, the lower the compressibility, and thus the higher the informational complexity present in the signal (Hu et al., 2006).

Casali et al. (2013) operationalized the PCI as “the normalized Lempel-Ziv complexity of the spatiotemporal patterns of cortical activation triggered by a direct TMS perturbation.” A high PCI value can only be achieved when the TMS perturbation spreads to a high number of integrated brain regions that respond in a non-stereotypical way and in this way generate diverse spatiotemporal activity patterns with low compressibility. The results of this study showed that: a) PCI can distinguish between various levels of

(un)consciousness in healthy participants, b) PCI can detect graded transitions between different (un)conscious states. For instance, the PCI values of light sedation lay somewhere in between the values for deep sedation and wakefulness, c) The PCI can be used to distinguish between states of consciousness in brain-injured patients. For instance, the PCI values of locked-in syndrome patients who were awake were similar to those of awake healthy participants, but the values of MCS (minimal conscious state) patients lay in between values for healthy wakefulness and states of sleep or sedation in healthy participants (Casali et al., 2013). This study provides support for the idea that there is a relationship between levels of consciousness and informational complexity. An important advantage of the PCI is that it can be used to assess levels of consciousness in single individuals. This is important for clinical practice since clinicians are more interested in assessing individual patients and less so in differences that can be established at a group level. After its development (Casali et al., 2013), the PCI has been used in multiple studies that have provided additional support for its reliability in discriminating between different levels of consciousness in various clinical conditions (Sarasso et al., 2015; Fecchio et al., 2015; Casarotto et al., 2016; Comolatti et al., 2019).

Schartner et al., (2015) further investigated the effectivity of the Lempel-Ziv algorithm and other complexity measures by examining the complexity of resting state EEG data of healthy participants during wakeful rest, light sedation and deep sedation induced by propofol. For this aim, they compared the Lempel-Ziv algorithm, the amplitude coalition entropy (ACE) which measures the diversity in the configuration of a series (coalition) of active channels using a binarization scheme to define channels as active or inactive (Shanahan, 2010), and the synchrony coalition entropy (SCE) which measures the diversity in the configuration of a series of channel that are synchronous (Schartner et al., 2015). All three measures were able to distinguish between loss of consciousness and the wakeful resting state. LZc, ACE and SCE all recorded a proxy for neurophysiological differentiation in the form of signal diversity and in this way quantified the amount of randomness in the signal where higher randomness correlated with wakeful rest and lower randomness was found during loss of consciousness. In addition, it has been previously found that other measures that quantify the randomness of a neurophysiological signal, such as permutation entropy (Bandt, & Pompe, 2002) and approximate entropy (Pincus, 1995), also decrease with loss of consciousness due to either sleep or anesthesia. These findings might be interpreted as that a certain amount of randomness is required for consciousness to arise. However, it must be mentioned that these measures are a very crude approximation of the neural processes happening in the brain. For instance, calculating the Lempel-Ziv complexity of an EEG signal means taking a huge average of neuronal voltages before binarizing it and then determining the

compressibility of the signal. When taking an average in this way a lot of crucial information might be lost. Therefore, randomness in the signal does not necessarily imply that there is also randomness in the brain.

In 2017, Schartner et al. conducted a MEG study to examine the LZc, ACE and SCE during the psychedelic state induced by ketamine, LSD or psilocybin. Interestingly, they found an increase in the neurophysiological signal diversity for all three psychedelic substances compared to the signal diversity found at resting state wakefulness. This increase was seen for all the complexity measures used in the study and the changes in signal diversity were located at the same place for all three substances (i.e. parietal and occipital cortex) even though these substances differ in their underlying pharmacological mechanism. Furthermore, the increase in signal diversity appeared to be related to the intensity of the psychedelic experience as measured by subjective reporting, where higher diversity coincided with a more vivid experience. These findings provide support for the entropic brain hypothesis of Carhart-Harris et al. (2014) according to which there is a

relationship between the degree of general randomness (signal diversity, entropy) of the neural dynamical interactions and the vividness of a conscious experience. In this way, psychedelic states would yield high entropy values, states of unconsciousness such as coma would yield low entropy values and the entropy values of normal wakefulness would lie somewhere in between. However, it must be mentioned that all the above-mentioned measures are only capturing a proxy for differentiation and not integration. Furthermore, LZc and ACE are calculated by binarizing the EEG data according to a given threshold which simplifies the continuous EEG signal and may cause some crucial information to be lost during this calculation (Schartner et al., 2015). Graph-theoretical measures and functional connectivity

As mentioned before, graph-theoretical measures and functional connectivity analyses have been used extensively in consciousness research. For instance, a resting state functional MRI study of Luppi et al. (2019) combined graph theoretical measures with measures of dynamic connectivity in participants during various stages of consciousness (i.e. awake, anesthesia) and DoC patients. They aimed to relate spatio-temporal interactions between brain integration and entropy to different levels of consciousness. The findings of this study show cortical networks to be particularly affected by stage transitions into unconsciousness during states of high integration as was reflected by a reduction in the diversity of functional activity patterns and informational complexity. On the other hand, functional disruptions between thalamo-cortical areas were more associated with states of high segregation. From their findings the authors conclude that consciousness depends on the spatio-temporal interplay between integration and diversity of functional connectivity patterns. The disintegration of this interaction may be one of the neural correlates of loss of consciousness.

A study of Barttfeld et al. (2015) investigated small-world properties and functional connectivity patterns of spontaneous brain activity in monkeys during various states of consciousness (awake vs.

anesthesia). Under low and high levels of anesthesia, interactions between brain regions were dominated by a very limited set of stereotypical connectivity patterns that were closely related to underlying anatomical connectivity. The awake state showed a greater variety of functional connectivity patterns that exhibited increased diversity and were not as much related to structural connectivity. The Small World index was computed to further examine the changes in connectivity patterns. Under anesthesia, the Small World index decreased monotonically with loss of consciousness. Fewer long-range connections were observed and the coupling strength between long-distance brain areas was reduced as compared to wakefulness. Barttfeld et al. (2015) concluded from their findings that sedation leads to a reduction in the brain’s ability to integrate different areas into an efficient coherent network. This might provide support for the theoretical notion that both global integration and the presence of heterogeneous activity patterns are requirements for

consciousness to arise. For clinical purposes, the possibility of residual consciousness in non-communicative brain-injured patients may be examined by observing dynamical changes in resting state activity.

Lee et al. (2017) further examined the idea that the conscious brain generates a diverse range of functional connectivity patterns while less diverse and stereotypical activity patterns are observed under anesthesia. They introduced the Phase-lag entropy (PLE) which quantifies “the diversity of functional

connectivity patterns in the phase relationship between two MEG/EEG signals.” After propofol-induced loss of consciousness, frontal channel dynamics showed a reduction in diversity and became more stereotypical as reflected by lower PLE values. Phase-lag entropy has proven superior to previously developed measures that examine phase synchronization between two time-series signals, such as the Phase Coherence (PC) (Mormann et al., 2000) and the Phase Lag Index (PLI) (Stam et al., 2007) which reflect the strength of connectivity and not so much diversity. PC and PLI are computed under the assumption of stationarity. Phase synchronization values of PC and PLI are acquired by averaging phase differences over a period of multiple seconds.

transfer in the brain is intrinsically non-stationary with the emergence and disappearance of synchrony in millisecond time windows (Friston, 2001). The main advantage of Phase-lag entropy is that it accounts for non-stationarity in the signal by extracting the temporal pattern of the phase relationship over a time period in the tens of millisecond range.

Another approach that could reflect brain network integration is by analyzing functional connectivity and network structure in certain frequency bands (e.g. alpha, theta) and determine how these are affected by different levels of consciousness. Chennu et al. (2014) examined the efficiency of functional network

connectivity in the Alpha frequency range (8-12 Hz) using graph-theoretical measures (e.g. clustering

coefficient, characteristic path length) comparing resting state EEG data of DoC patients and healthy controls. A reduction in local and global efficiency of DoC patient alpha networks was found compared to controls. Furthermore, the patients appeared to lack structured long-distance interactions and fewer hubs in the alpha frequency range were observed. Interestingly, this effect seemed to be reversed for the delta and theta frequency bands.

Another measure of complexity that might be related to integration is the Weighted Symbolic mutual information (wSMI). This measure uses EEG to try to capture global information sharing between neural regions by evaluating the degree to which two EEG signals present nonrandom joint fluctuations, and hereby indicating the degree of information sharing between these two sources (King et al., 2013). First, the continuous EEG signal is transformed into discrete symbols by obtaining the signal’s sub-vectors which all consist of k measures. A unique symbol is then allocated to each sub-vector and the parameter k fixes the amount of possible symbols (k!). For instance, when k = 4, there are 4! = 24 possible symbols. These symbols are then weighted to reduce the possibility of common source artifacts which is the artificial increase in the similarity between two EEG channels due to common EEG artifacts such as eye blinks or muscle contractions. Next, the joint probabilities of each pair of symbols are computed to determine the absence or presence of coupling between the two channels by generating joint probability matrices for each pair of channels. In case of the presence of a coupling between two channels the coupling strength is also computed. King et al., (2013) computed wSMI for awake patients who were either in a vegetative state, minimally conscious or fully conscious and healthy controls. The results showed that the values of wSMI increased significantly with consciousness and wSMI was able to accurately distinguish between levels of consciousness in patients with disorders of consciousness and healthy controls. This held true for each etiology and it did not matter whether it was a recent injury or a chronic condition. wSMI was also compared to other measures of signal correlation, such as Phase Locking Value (PLV) (Aydore et al., 2013) and proved superior in distinguishing between various states of consciousness (King et al., 2013). An important advantage of the wSMI is that it transforms the continuous EEG signal into various symbols and that these symbols are weighted. Compared to previously mentioned measures such as Lempel-Ziv complexity and amplitude coalition entropy which binarize the data according to a given threshold, the approach of wSMI of weighting the various symbols extracted from the signal may enhance the discriminative power of this particular measure.

Finally, recent advances in theoretical neuroscience propose that changes in directed functional connectivity could be related to integrated information (Seth et al., 2011). An important measure for causal interactions within a system is Granger Causality (GC). This is a statistical method to determine the degree to which the past state of one time-series signal can predict the future state of another time-series signal, in addition to the extent that the past state of the latter signal already predict its own future. In this way, causal interactions between two signals can be quantified (Granger, 1969). In neuroscientific research, the use of GC is sometimes criticized because it is computed with the assumption of stationarity, while brain activity is intrinsically non-stationary (Friston, 2001; Seth et al., 2015). A study of Barrett et al (2012) used GC to analyze the EEG data of anesthetized participants (propofol) focusing on signals localized to the anterior and posterior cingulate cortices. This accounted for the challenge of non-stationarity by dividing the time-series data into short time-segments. The findings showed bidirectional GC to be significantly increased during loss of consciousness with the highest increase observed for beta and gamma frequencies. These changes were mainly observed between the anterior (ACC) and posterior cingulate cortices (PCC). These results could be interpreted as contradicting the theoretical notion that loss of consciousness under anesthesia is related to a reduction of functional connectivity. However, the authors state that there are two scenarios in which high values of synchrony could be in agreement with a general reduction of information integration. First, high values of synchrony could reflect a pathological increase of brain integration at the cost of differentiation, which might lead to loss of consciousness (e.g. epilepsy). Second, the analyses were limited to the assessment of functional connectivity in only two brain regions (i.e. ACC and PCC). An increase in functional connectivity between these two areas may coincide with a broader disintegration of functional connectivity, which could be assessed by taking a wider range of brain areas into account (Barrett et al., 2012).

In addition to EEG, GC is also used as a measure in fMRI studies. For instance, a study of Liao et al. (2011) analyzed resting state fMRI with GC analysis and graph theoretical measures to attempt to map out the topological architecture of causal directionality in the human brain network. The results of these analyses suggest the possibility of small-world properties within the directed influence network of the human brain. However, it must be mentioned that the use of GC for fMRI has been criticized and multiple important factors have been identified that may curtail the validity of GC in fMRI research. For instance, an important limitation is the hemodynamic variability and delay across different neural areas which can complicate the interpretation of GC analyses (Deshpande et al., 2010). Other important limitations are measurement noise (Nalatore & Rangarajan, 2007) and low sampling rates (Witt & Meyerand, 2009).

Clinical applications

As mentioned before, the development of measures to accurately quantify levels of consciousness could be highly relevant in clinical settings. This line of research could offer an overall insight into the underlying mechanisms of various types of pathologies that are known to affect consciousness and hereby could potentially lead to the identification of certain neural signatures and biomarkers of these pathologies. This in turn could aid in the development of new and more effective treatments and more accurate assessment of risk factors. Furthermore, these measures could be helpful when monitoring anesthetized patients (Shin et al., 2020), determining levels of consciousness in unresponsive patients (Casali et al., 2013) and the treatment of patients with neuropsychiatric disorders (e.g. epilepsy, schizophrenia) (Haneef & Chiang, 2014; Micheloyannis et al., 2006). In the previous section, a lot of attention has been devoted to discussing empirical studies that concerned either patients with severe brain injuries or anesthetized or asleep subjects, and comparing the level of consciousness of these types of subjects with awake subjects. These studies have shown that complexity measures such as the PCI (Casali et al., 2013), Lempel-Ziv complexity (Schartner et al., 2015), wMSI (King et al., 2013) and Phase-lag entropy (Lee et al.,2017) can be useful in (a) distinguishing between levels of consciousness in patients with severe brain injuries (Chennu et al., 2014; Casali et al., 2013; King et al., 2013), (b) assessing anesthetic depth (Schartner et al., 2015; Shin et al., 2020), (c) distinguishing between various stages of sleep (Casali et al., 2013) and (d) studying the psychedelic state (Schartner et al., 2017; Carthart-Harris et al., 2014). However, there has also been some empirical work done with different types of clinical populations, concerning often more refined fluctuations in consciousness. It has been hypothesized that disorders such as epilepsy, schizophrenia and autism are related to more subtle alterations in consciousness (Bor, 2012). The focus of the current section will be on research that has been carried out to assess informational complexity in these types of (neuro)psychiatric patients groups.

Epilepsy

A disorder of consciousness that has been extensively studied using complexity measures and graph theory is epilepsy. Epilepsy is a disorder that is characterized by recurring and unexpected pathological changes in neural activity, also known as ‘seizures’. During seizures, neural activity is typically

hyper-synchronous and unrestrained and often leads to loss of consciousness. In case of focal epileptic seizures, the abnormal activity starts in a small area of the brain and then spreads out to a wider area of the brain (Abásolo et al., 2007). For clinical purposes, it is important to improve seizure detection and prediction, as this might lead to improvements of quality of life for patients who cannot be treated successfully with anti-seizure medication, as is often the case with Temporal Lobe Epilepsy (TLE) (Artan, 2016). Traditional and linear methods of analyzing the EEG signal of epileptic patients have not led to sufficient detection of neural changes that happen prior to, during and after occurrence of seizures (Abásolo et al., 2007). As neural activity in the brain is inherently linear on multiple scales (Korn & Faure, 2003), seizure detection methods that use non-linear analyses might be more promising (Abásolo et al., 2007). One suitable candidate method is Lempel-Ziv complexity. Lempel-Ziv and other complexity measures have already been successfully used in prediction of life-threatening cardiac arrhythmias (Zhang et al., 1999; Marwan et al., 2002), and therefore may also be useful in detection and prediction of epileptic seizures.

Abásolo et al. (2007) analyzed the inter-cranial EEG recordings of several patients, using Lempel-Ziv complexity and approximate entropy. The latter is a method to determine the degree of (ir)regularity in a time series signal (Pincus, 1995). The EEGs were recorded during pre-surgical monitoring. The findings of this analysis indicate that informational complexity and irregularity increase during seizures. Interestingly, the peak of complexity and irregularity in the signal was measured in different focal electrodes at different time points, showing the spreading activation pattern that is so characteristic for seizure activity. Another study that

examined neural activity during seizures, analyzed EEG recordings of epilepsy patients of both ictal (seizure) and non-ictal (non-seizure) periods, using Lempel-Ziv Complexity and Multiscale Lempel-Ziv Complexity (Artan, 2016). In contrast to Lempel-Ziv, the Multiscale Lempel-Ziv Complexity is able to distinguish between signals consisting of components that vary in their amplitudes but are similar in randomness (Sarlabous et al., 2009). Compared to Lempel-Ziv, Multiscale Lempel-Ziv Complexity turned out to be more sensitive in distinguishing ictal period from non-ictal periods (Artan, 2016). The results from the two above-mentioned studies indicate that measuring informational complexity during seizures can be quite promising in uncovering the underlying neurological processes in more detail. For clinical purposes, it has yet to be determined which measure gives the most refined results while also be low enough in computational costs. Furthermore, it must be mentioned that in the previously-discussed studies, the sample size was quite low, which is a clear limitation of

generalizability to the larger patient population.

Another approach to studying the brain dynamics of loss of consciousness during epileptic seizures with the use of graph theoretical measures. Graph theoretical analyses are expected to aid in the

improvement of localization of epileptic seizures, especially in temporal lobe epilepsy, and hereby can lead to increased surgical precision so that healthy cortical tissues can be spared in the procedure (Bernhardt et al., 2015). Graph theoretical measures have been successfully used in the analysis of data acquired from resting-state fMRI, surface EEG and inter-cranial EEG recordings (Haneef & Chiang, 2014). For instance, a study of Quraan et al. (2013) analyzed the surface EEG of temporal lobe epilepsy patients to examine functional network structure in various frequency bands. Their findings show decreased small-worldness and low clustering coefficient in alpha networks, while the opposite was found for the theta frequency band. Interestingly, the same pattern was found in the previously-discussed study of Chennu et al. (2014) for patients with other types of DoC, such as patients in a vegetative state and patients who were minimally conscious. As mentioned before, the brain healthy network has been shown to exhibit small-world properties (Bassett & Bullmore, 2006). In epilepsy patients, a more regular network structure has been observed. This has, for instance, been shown by a structural MRI network study of Bernhardt et al. (2011) that showed epilepsy patients to have increased path length between brain areas but higher local clustering compared to controls. This altered type of network organization, consisting of increased clustering in local areas combined with decreased connectivity on a global level has suggested to be a contributing factor to the

hyper-synchronous neural activity during seizures and might therefore be associated with seizure-related loss of consciousness (Bernhardt et al., 2015). Furthermore, structural and functional brain imaging research has found a connection between decreased small-world properties and the cognitive decline that is often present in epilepsy (Vlooswijk et al., 2011; Vaessen et al., 2012).

Schizophrenia and psychosis

Schizophrenia is illness that is characterized by recurring psychotic episodes. In states of psychosis, conscious experience is altered as is indicated by extreme disorganized thinking, lack of reality testing abilities and the occurrence of hallucinations and delusions (Bor, 2012; Kapur, 2003). Therefore, schizophrenia may be of interest in the context of analyzing informational complexity to examine the underlying neural mechanisms of the altered state of consciousness in psychosis. A study of Fernández et al. (2011) used Lempel-Ziv

complexity to analyze resting state MEG recordings of schizophrenic patients and healthy controls. The results showed schizophrenia patients to have a higher neural complexity in resting state compared to healthy controls as indicated by higher LZc values, and this high neural complexity was especially prominent in central cortical regions. Interestingly, they also found the LZc values to be strongly reliant on age, where complexity values strongly declined with age which is similar to patterns found in neurodegenerative diseases (Fernández et al., 2011). This is the opposite pattern as is exhibited in healthy people, since there is a general tendency for complexity scores to increase throughout adulthood until early senescence (Anokhin et al., 1996). In

schizophrenia, there is also a tendency for positive symptoms (e.g. hallucinations, delusions) to decrease with age, while negative symptoms (e.g. cognitive impairment, flattened affect) generally persist (Schultz et al., 1997). It could be that the observed age-related complexity pattern changes in schizophrenic patients are a reflection of this tendency.

In addition to Lempel-Ziv complexity, there have also been some empirical studies that examined functional connectivity patterns and network organization in schizophrenia. A study of Micheloyannis et al. (2006) aimed to assess whether disruptions in functional connectivity patterns can be found in schizophrenia.

They used graph theoretical measures to examine small-world properties in the EEG signal of schizophrenic patients and healthy controls. The findings showed the healthy subjects to have small-world properties in the alpha, beta and gamma frequency bands whereas the small-world pattern was significantly diminished in schizophrenic patients. Interestingly, as mentioned-before, reduced small-world properties in the alpha frequency band have also been found in order disorders of consciousness such as epilepsy (Quraan et al., 2013) and states of coma (Chennu et al., 2014). In these types of disorders the pattern was reversed in the theta and delta frequency bands. It would therefore be interesting to investigate whether this is also the case in schizophrenia. Liu et al. (2008) further investigated small-world network properties in schizophrenia with a resting-state fMRI study. They compared functional connectivity patterns of schizophrenic patients with healthy controls and found small-world network topology in schizophrenic patients to be significantly altered throughout the brain as was indicated by an overall lower degree and strength of connectivity, longer absolute path lengths and a decreased overall clustering coefficient. These results provide support for the idea that the pathological altered conscious experience in schizophrenia may be characterized by a dysfunction in overall functional brain integration (Friston, 2005). Interestingly, the disruption of small-world network efficiency was correlated with the duration of the illness, where a longer duration was associated with more disruption of small-world network efficiency (Liu et al., 2008).

An interesting viewpoint about psychosis came from Kapur (2003). He argues that the psychotic state can be viewed as a “disorder of aberrant salience”, where the excessive experience of salience of surrounding factors is hypothesized to be caused by the dysregulation of the dopaminergic system (Kapur, 2003). This conception as psychosis as a “disorder of aberrant salience” reminds one of Carthart-Harris’s et al. (2014) analysis of the psychedelic state, which is among other things related to a higher sensitivity to perturbational influences of environmental factors. As Carthart-Harris et al. (2014) argued, the psychedelic state may in some ways be akin to states of early psychosis, as these states are both hypothesized to be related to a primary mode of consciousness which may be characterized by higher brain entropy compared to everyday wakeful consciousness. In early states of psychosis, patients often report a sense of an enhanced state of

consciousness, increased vividness and salience (Kapur, 2003), similarly to what is reported by people in a psychedelic state (Schartner et al., 2017). During psychedelic experiences people are generally aware that they are under influence of a psychedelic substance and in early psychosis there is still some intact reality testing left. When patients move into a state of full-blown psychosis, their thoughts, experiences and behavior become increasingly disorganized which leads the patient to ‘lose touch with reality’ and unable to function in daily life (Kapur, 2003). An intriguing question to further investigate could be whether there is a tipping point at the onset of psychosis where neural diversity becomes so excessive that it comes at the expense of integration, and in this way integration of conscious scenes into a coherent whole is no longer possible.

Finally, a distinction must be made between schizophrenia and psychosis. While schizophrenia is characterized by recurring psychotic episodes, there are also many other types of psychotic disorders (Jongsma et al., 2019) which may have different mechanisms that lead to the expression of psychosis. This possible different underlying mechanisms may lead to subtle differences in the altered conscious experience of different types of psychosis. An interesting future direction may be to research various types of psychosis with complexity measures and graph theory and try to determine whether a difference can be found in the neural signature of informational complexity and network structures of these different types of patients.

Other conditions

In addition to epilepsy and schizophrenia, there are also some empirical studies available concerning other disorders, such as autism, or specific mental states, such as mental fatigue. Here, some of this empirical work will be discussed.

Another disorder that has been hypothesized to be related to subtle alterations in consciousness is autism (Bor, 2012). Autism spectrum conditions (ASC) concern various neurodevelopmental conditions that are characterized by a reduction of behavioral adaptability, disturbances in social interactions, repetitive behaviors and altered sensory processing patterns, particularly in the visual domain (Catarino et al., 2011). There has been an increasing interest in studying altered neural activity and connectivity patterns in ASC, as identifying specific atypical neural patterns can lead to the development of more reliable biomarkers that can aid early diagnosis. For instance, Bosl et al. (2011) examined the complexity of resting state EEG recordings of infants at high risk of developing ASC, using multi-scale entropy (MSE). MSE performs a multi-time scale analysis to measure the entropy within the system at different time points which indicates the complexity of the signal (Costa et al., 2005). They found an overall reduction of EEG complexity in the high-risk infants

compared to controls, which suggests that EEG complexity analyses might be useful for identifying a biomarker for the risk of developing ASC. Catarino et al. (2011) investigated neural complexity of adults with ASC

compared to controls. The participants performed two tasks, a social task (recognition of facial expressions) and a purely visual task (recognition of objects). The adults with ASC showed lower EEG complexity in both tasks as compared to controls, which was most apparent in parietal and occipital cortical areas. However, both groups showed higher EEG complexity for the social task compared to the purely visual task. This observation was interpreted as that the ASC social and behavioral symptoms may reflect a more general alteration in neural functioning. Since functions concerning language, emotions and social abilities are neurally more demanding, these functions may be specifically at risk to be affected by disturbances in integrative ability at the neural level that might be characteristic of patients with ASC (Catarino et al., 2011).

Complexity measures may also be useful when assessing the effect of a treatment as is shown by a study of Cerquera et al. (2012). This study examined the effect of neurofeedback treatment in patients with Attention Deficit/Hyperactivity Disorder (ADHD), using nonlinear dynamics measures to compare resting-state EEG complexity prior to and right after a neurofeedback treatment session. ADHD is inherently a disorder of attention (Cerquera et al., 2012). Since attention and consciousness are closely related concepts (Posner, 1994), the altered experience in ADHD may be related to underlying disruptions in consciousness and informational complexity. The study of Cerquera et al. (2012) used several measures such as the Largest Lyapunov Exponent (LLE), which is a way of approximating the degree of chaos in a given system by

quantifying exponential separation of trajectories that are initially close but start to diverge increasingly over time (Faure & Korn, 2001). They further used Lempel-Ziv complexity, multiscale entropy and the Hurst exponent, of which a high value in the latter signifies a long-term positive autocorrelation in a time series signal (Mielniczuk & Wojdyłło, 2007). After the neurofeedback session, higher values of LLE were observed and lower values of Lempel-Ziv complexity and the Hurst exponent were observed. No significant changes were found for multiscale entropy. The authors interpreted these results as that the degree of randomness may have been reduced after neurofeedback treatment. They further stated that deterministic behavior to some degree, as signified by the EEG signal, may be reduced in ADHD conditions and can be increased with help of neurofeedback therapy (Cerquera et al., 2012). However, as mentioned before, measures such as Lempel-Ziv complexity are a very crude approximation of the neural processes happening in the brain and a lot of crucial information might be lost in the computation. Therefore, a reduction of randomness in the signal does not necessarily imply a relation between this randomness reduction and the degree of randomness in the brain, if there is any. Nonetheless, the findings of this study are interesting since these suggest that brain complexity in conscious processing may be influenced over relatively short time scales. More research and more refined methods of computing brain complexity may therefore be incredibly promising of assessing effect of treatments in different types of cognitive, neurological and psychiatric disorders.

An EEG study of Sun et al. (2014) investigated changes in functional connectivity patterns in the Alpha frequency band during mental fatigue, using graph theoretical measures. Subtle fluctuations in healthy consciousness may be related to fluctuations in levels of arousal and attention, as the latter two concepts are closely related to consciousness (Posner, 1994; Laureys et al., 2009). Therefore, concepts such as mental fatigue may be suitable to study with informational complexity measures to uncover the subtle changes in consciousness that might be happening as individuals become increasingly mentally fatigued. Mental fatigue is related to high demands on cognitive systems for long time periods and is a well-known form of

neurocognitive strain. Mental fatigue often leads to a decrease in cognitive performance (e.g. slower reaction times, more errors), also known as time-on-task (TOT) effects. This is particularly relevant in industries where workers are expected to work long hours without rest, since TOT-effects can lead to more errors, decreased productivity and an increased risk for accidents (Sun et al., 2014). In the experiment, the participants carried out a cognitively demanding sustained attention task, namely the psychomotor vigilance task (Dinges et al., 1997), while their EEG was recorded. Sun et al. (2014) compared the first and last five minutes of the task, looking at both the behavioral measures and functional connectivity. Behavioral results indicated clear TOT-effects, as was shown by increased reaction times. From the graph theoretical analyses, it was shown that functional small-world topologies were altered during a state of mental fatigue. This was indicated by longer characteristic path lengths which correlated with the degree to which performance worsened during fatigued states. Furthermore, there was a disruption of inter-hemispheric connectivity during mental fatigue, which might have been a contributing factor to the observed longer characteristic path lengths. These reduced small-world properties during fatigued states suggest a reduction in efficient information integration ability. Interestingly, a subset of participants did not show a decline in performance, which is in accordance with the idea that there are individual differences in how sensitive people are to TOT-effects (Parasuraman & Jiang, 2012). These results could indicate that there are individual differences in the robustness of small-world

properties, which may lead some individuals to be able to tolerate higher levels of neurocognitive strain without any performance decline.

Conclusion

From empirical studies using informational complexity measures to study different levels of consciousness (e.g. anesthesia, sleep) or altered conscious processing in certain neuro-pathologies (e.g. epilepsy, schizophrenia), it becomes clear that these measures can be utilized for studying consciousness-related processes. It seems that for a healthy level of consciousness, a certain pattern of information transfer is required. As has been shown from an extensive body of empirical work, the healthy brain operates through a small-world network organization, both structurally and functionally (Bassett & Bullmore, 2006; Telesford et al., 2011). As mentioned before, small-world networks are believed to be optimal in the sense that this organization allows information flow to be efficiently transferred both on a local and global level (Watts & Strogatz, 1998). As shown from empirical studies on various disorders, a disruption in the small-world organization often leads to problems. For example, in epilepsy a higher local clustering in combination with decreased global integration due to longer path lengths is observed which is believed to contribute to the abnormal neural activity during seizures (Bernhardt et al., 2015). In schizophrenia, the small-world

organization is shown to be disrupted in a different way, namely by a decrease in local clustering combined with less effective global integration. Furthermore, the extent to which the small-world organization is disrupted in schizophrenia relates to illness duration (Liu et al., 2008). In disorders of consciousness due to brain injuries, small-world properties in the alpha frequency band are shown to be decreased, while the opposite is true for network organization in the theta and delta frequency bands (Chennu et al., 2014). Thus, it might be that dynamical electro-physiological networks contribute differently to consciousness and

information processing in different frequency bands. Further research of small-world organization therefore holds great promise to uncover the various neural signatures related to disruption of small-world organization that often coincide with different disorders.

Another important feature of healthy consciousness is related to the neural diversity of the signal, as is measured with techniques such as Lempel-Ziv complexity and multiscale entropy. Compared to healthy individuals, disordered states and states of unconsciousness are often associated with abnormalities in the neural signal. In epilepsy and schizophrenia the neural diversity of the signal is often increased (Fernández et al., 2011; Abásolo et al., 2007)) while in states of unconsciousness (Casali et al., 2013) but also disorders such as autism (Catarino et al., 2011) the neural signal diversity is decreased. An outstanding question regards what we are exactly measuring when using signal diversity techniques. Complexity measures such as Lempel-Ziv complexity are calculated using binarized matrices of signal activity, or synchronies such as synchrony coalition entropy. The measures are used to quantify the degree of randomness in these matrices. Are these measures an accurate reflection of complexity, as defined by a combination of coinciding integration and differentiation? Concerning integration, it must be said that measures such as Lempel-Ziv are not necessarily related to causal interactions. As mentioned by Schartner et al. (2015), synchronous or active EEG channels that show dynamic variations can also be related to isolated processes, where every channel displays its own chaotic patterns.

Furthermore, increases in signal diversity often coincide with decreases in integrative dynamics in certain disorders as indicated by reduced small-world properties (Fernández et al., 2011; Quraan et al., 2013) and in the psychedelic state increased signal diversity coincides with reduced functional connectivity between the default mode network and the medial temporal lobes (Carthart-Harris et al., 2014). In other cases, reduced signal diversity coincides with reduced connectivity (Casali et al., 2013). Whether there is a causal relation between decreases/increases of neural diversity and integration has yet to be discovered. It might be that there is a delicate balancing act between neural diversity and integration in the brain, where too much or too little of either one might lead to pathologically altered states of consciousness (Bor, 2012) or to

unconsciousness (Chennu et al., 2014). Finally, as previously-mentioned, measures such as Lempel-Ziv are an incredibly crude approximation of neural processes that happen in the brain. It could be that these measures are an estimation of the amount of different (cognitive) processes going on per 4 second epoch, which are very likely to increase with consciousness or with the altered levels of consciousness occurring in the psychedelic state. If measures such as Lempel-Ziv indeed capture the amount of different cognitive processes as they unfold dynamically over time, this may be interpreted as an estimation of neurophysiological differentiation.

It is important to resist the temptation to reduce the characteristics of the brain network and conscious processing to a single value. As the brain is a complex system, it can be of great value to combine several measures as these techniques could be capturing a variety of informational complexity features

(Telesford et al., 2011). As Schartner et al. (2015) showed by comparing Lempel-Ziv complexity, amplitude coalition entropy and synchrony coalition entropy during various levels of anesthetic depth and in addition, using a modelling approach, these measures show different behaviors. For instance, synchrony coalition entropy showed the strongest peak at an in-between level of general synchrony, while simultaneously the other two measures showed a small dip in the signal. As applied to the EEG signal during anesthesia, these two “distinct flavors of complexity” were shown to be reduced. Furthermore, Lempel-Ziv complexity can be measured in a localized way (Schartner et al., 2017), which might allow a comparison of various

neuroanatomical regions in levels of informational complexity. Moreover, it could be very useful to combine EEG/MEG measures with fMRI measures, since the former has satisfactory temporal resolution and the latter has sufficient spatial resolution. In this way, measures derived from these two types of neuroimaging can be used in a complementary way, thus providing a more complete picture of the dynamical brain processes related to information transfer and conscious states. Therefore, it would be very promising to combine extensive graph theoretical analysis with measures of neural signal diversity such as Lempel-Ziv or multi-scale entropy.

Since consciousness research with informational complexity measures may be highly relevant in clinical settings, the issue of computational cost must be addressed. For any new technique, the marketability in clinical settings is related to efficiency and expenses, and must be an improvement on these two factors compared to currently available techniques. Time of acquisition is of fundamental importance in clinical practice, and new techniques are required to integrate successfully in the time demanding clinical workflow (Petrella, 2011). For instance, measures such as Lempel-Ziv complexity and the Hurst exponent are quite low in computational cost compared to other complexity measures such as multi-scale entropy (Abásolo, 2007) or the Largest Lyapunov Exponent (Cerquera et al., 2012) and could therefore be more suitable. Furthermore, a study of Whitlow et al. (2011) has shown that resting-state fMRI scans acquired during short time periods of around 2 minutes are sufficient to do extensive graph theoretical analyses, such as small-world network analyses, which makes this method cost-effective and feasible. Another advantage is that patients do not need to actively engage in a behavioral task during the resting-state fMRI scan procedure. Both the fact that it is a time efficient method and that no active engagement is needed may make this technique particularly more suitable for more challenging patient populations, such as infants or patients who are very ill (Petrella, 2011).

Finally, some promising future directions must be mentioned. Most of the measures discussed in this article are a quite crude estimation of what is happening in the brain and have been used to distinguish between very distinct levels of consciousness, such as anesthesia versus wakefulness. An emerging line of research concerns the study of more refined fluctuations in healthy awake consciousness. One of these studies, which was previously-mentioned, concerned mental fatigue. This study showed marked changes in the small-world properties of participants after performing a mentally taxing task for 20 minutes and this effect correlated with performance decline. Interestingly, some participants seemed to be less susceptible to the effects of mental fatigue as was indicated by their performance on the task and less reduced small-world properties (Sun et al., 2014). As mental fatigue may be a risk factor for accidents in industries where people are expected to work very long hours without any break, it is important to gain more insight into the mechanism of mental fatigue and why some individuals seem to be more susceptible to its effects on performance than others. The findings of studies like these are intriguing since these suggest that brain complexity may be influenced over relatively short time spans. More research and more refined methods of computing brain complexity may therefore be incredibly promising for assessing more refined fluctuations of healthy consciousness such as mental fatigue, flow, level of arousal and attention.

For instance, as opposed to states of low arousal or mental fatigue, the flow state is often regarded as an enhanced state of consciousness as compared to normal waking consciousness (Csikszentmihalyi & Csikszentmihalyi, 1992). This is indicated by better and more efficient performance, increased motivation, enhanced creativity and a great sense of enjoyment (Csikszentmihalyi & LeFevre, 1989). It would be interesting to study this state in more detail in the context of informational complexity. As is shown in the mental fatigue study, functional network organization can change over relatively short time periods. Maybe in the case of flow, something changes in the functional network as well which might enhance efficiency of information transfer as compared to normal wakeful consciousness leading to this enhanced conscious experience. Furthermore, a clear distinction must be made between conscious level and conscious content. Conscious level refers to different states ranging from coma to vivid wakefulness while conscious content relates to the phenomenological factors of conscious experience (e.g. the smell of a rose), also called ‘qualia’. Conscious level and conscious content are related to a certain extent since the number of potential contents tend to increase with conscious level. The measures discussed in the current work are mainly related to conscious level.

Although it might not be possible to measure conscious content directly, more refined measures might be able to capture certain aspects of the phenomenological quality of experience in more detail.

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