Advances in Understanding Fractals in Affective and Anxiety Disorders.

In this chapter, we review the research that has applied fractal measures to the study of the most common psychological disorders, that is, affective and anxiety disorders. Early studies focused on heart rate, but diverse measures have also been examined, from variations in subjective mood, or hand movements, to electroencephalogram or magnetoencephalogram data. In general, abnormal fractal dynamics in different physiological and behavioural outcomes have been observed in mental disorders. Despite the disparity of variables measured, fractal analysis has shown high sensitivity in discriminating patients from healthy controls. However, and because of this heterogeneity in measures, the results are not straightforward, and more studies are needed in this promising line.

Mutual information of multiple rhythms in schizophrenia.

Interactions between different cortical rhythms, such as slow and fast oscillations, have been hypothesized to underlie many cognitive functions. In patients diagnosed with schizophrenia, there is some evidence indicating that the interplay between slow and fast oscillations might be impaired or disrupted. In this study, we investigated multiple oscillatory interactions in schizophrenia using a novel approach based on information theory. This method allowed us to investigate interactions from a new perspective, where two or more rhythm interactions could be analyzed at the same time. We calculated the mutual information of multiple rhythms (MIMR) for EEG segments registered in resting state. Following previous studies, we focused on rhythm interactions between theta, alpha, and gamma. The results showed that, in general, MIMR was higher in patients than in controls for alpha-gamma and theta-gamma couplings. This finding of an increased coupling between slow and fast rhythms in schizophrenia may indicate complex interactions in the Default Mode Network (DMN) related to hyperactivation of internally guided cognition.

Examining Neural Connectivity in Schizophrenia Using Task-Based EEG: A Graph Theory Approach.

Schizophrenia (SZ) is a complex disorder characterized by a range of symptoms and behaviors that have significant consequences for individuals, families, and society in general. Electroencephalography (EEG) is a valuable tool for understanding the neural dynamics and functional abnormalities associated with schizophrenia. Research studies utilizing EEG have identified specific patterns of brain activity in individuals diagnosed with schizophrenia that may reflect disturbances in neural synchronization and information processing in cortical circuits. Considering the temporal dynamics of functional connectivity provides a more comprehensive understanding of brain networks' organization and how they change during different cognitive states. This temporal perspective would enhance our understanding of the underlying mechanisms of schizophrenia. In the present study, we will use measures based on graph theory to obtain dynamic and static indicators in order to evaluate differences in the functional connectivity of individuals diagnosed with SZ and healthy controls using an ecologically valid task. At the static level, patients showed alterations in their ability to segregate information, particularly in the default mode network (DMN). As for dynamic measures, patients showed reduced values in most metrics (segregation, integration, centrality, and resilience), reflecting a reduced number of dynamic states of brain networks. Our results show the utility of combining static and dynamic indicators of functional connectivity from EEG sensors.

Fractal dimension analysis of resting state functional networks in schizophrenia from EEG signals.

Fractal dimension (FD) has been revealed as a very useful tool in analyzing the changes in brain dynamics present in many neurological disorders. The fractal dimension index (FDI) is a measure of the spatiotemporal complexity of brain activations extracted from EEG signals induced by transcranial magnetic stimulation. In this study, we assess whether the FDI methodology can be also useful for analyzing resting state EEG signals, by characterizing the brain dynamic changes in different functional networks affected by schizophrenia, a mental disorder associated with dysfunction in the information flow dynamics in the spontaneous brain networks. We analyzed 31 resting-state EEG records of 150 s belonging to 20 healthy subjects (HC group) and 11 schizophrenia patients (SCZ group). Brain activations at each time sample were established by a thresholding process applied on the 15,002 sources modeled from the EEG signal. FDI was then computed individually in each resting-state functional network, averaging all the FDI values obtained using a sliding window of 1 s in the epoch. Compared to the HC group, significant lower values of FDI were obtained in the SCZ group for the auditory network (p < 0.05), the dorsal attention network (p < 0.05), and the salience network (p < 0.05). We found strong negative correlations (p < 0.01) between psychopathological scores and FDI in all resting-state networks analyzed, except the visual network. A receiver operating characteristic curve analysis also revealed that the FDI of the salience network performed very well as a potential feature for classifiers of schizophrenia, obtaining an area under curve value of 0.83. These results suggest that FDI is a promising method for assessing the complexity of the brain dynamics in different regions of interest, and from long resting-state EEG signals. Regarding the specific changes associated with schizophrenia in the dynamics of the spontaneous brain networks, FDI distinguished between patients and healthy subjects, and correlated to clinical variables.

Integration-segregation dynamics in functional networks of individuals diagnosed with schizophrenia.

Schizophrenia has been associated with dysfunction in information integration/segregation dynamics. One of the neural networks whose role has been most investigated in schizophrenia is the default mode network (DMN). In this study, we have explored the possible alteration of integration and segregation dynamics in individuals diagnosed with schizophrenia with respect to healthy controls, based on the study of the topological properties of the graphs derived from the functional connectivity between the nodes of the DMN in the resting state. Our results indicate that the patients show a diminution of the modularity of the DMN and a higher global efficiency, in sparse graphs. Our data emphasise the interest in studying temporal changes in network measures and are compatible with the hypothesis of randomization of functional networks in schizophrenia.

Electrophysiological correlates of dispositional mindfulness: A quantitative and complexity EEG study.

While growing evidence supports that dispositional mindfulness relates to psychological health and cognitive enhancement, to date there have been only a few attempts to characterize its neural underpinnings. In the present study, we aimed at exploring the electrophysiological (EEG) signature of dispositional mindfulness using quantitative and complexity measures of EEG during resting state and while performing a learning task. Hundred twenty participants were assessed with the Five Facet Mindfulness Questionnaire and underwent 5 min eyes-closed resting state and 5 min at task EEG recording. We hypothesized that high mindfulness individuals would show patterns of brain activity related to (a) lower involvement of the default mode network (DMN) at rest (reduced frontal gamma power) and (b) a state of 'task readiness' reflected in a more similar pattern from rest to task (reduced overall q-EEG power at rest but not at task), as compared to their low mindfulness counterparts. Dispositional mindfulness was significantly linked to reduced frontal gamma power at rest and lower overall power during rest but not at task. In addition, we found a trend towards higher entropy during task performance in mindful individuals, which has recently been reported during mindfulness meditation. Altogether, our results add to those from expert meditators to show that high (dispositional) mindfulness seems to have a specific electrophysiological pattern characteristic of less involvement of the DMN and mind-wandering processes.

Alpha and gamma EEG coherence during on-task and mind wandering states in schizophrenia.

OBJECTIVE: Electroencephalographic (EEG) coherence is one of the most relevant physiological measures used to detect abnormalities in patients with schizophrenia. The present study applies a task-related EEG coherence approach to understand cognitive processing in patients with schizophrenia and healthy controls. METHODS: EEG coherence for alpha and gamma frequency bands was analyzed in a group of patients with schizophrenia and a group of healthy controls during the performance of an ecological task of sustained attention. We compared EEG coherence when participants presented externally directed cognitive states (On-Task) and when they presented cognitive distraction episodes (Mind-Wandering). RESULTS: Results reflect cortical differences between groups (higher coherence for schizophrenia in the frontocentral and fronto-temporal regions, and higher coherence for healthy-controls in the postero-central regions), especially in the On-Task condition for the alpha band, compared to Mind-Wandering episodes. Few individual differences in gamma coherence were found. CONCLUSIONS: The current study provides evidence of neurophysiological differences underlying different cognitive states in schizophrenia and healthy controls. SIGNIFICANCE: Differences between groups may reflect inhibitory processes necessary for the successful processing of information, especially in the alpha band, given its role in cortical inhibition processes. Patients may activate compensatory inhibitory mechanisms when performing the task, reflected in increased coherence in fronto-temporal regions.

Electrophysiological Prints of Grit.

While scientific interest in understanding the grit trait has grown exponentially in recent years, one important gap in the grit literature relates to its biological and neural substrate. In the present study, we adopted a hypotheses-driven approach in a large sample of young adults (N = 120) with diverse educational backgrounds and work experiences in order to investigate the electrophysiological correlates of grit both during rest and while performing a learning task. Additionally, we selected a measure of impulsiveness to better understand the neural similarities and differences between grit and related self-control constructs. Based on previous work that implicated the prefrontal cortex in grit, we hypothesized that high grit participants would have lower frontal theta/beta ratio (a broadly used index that reflects prefrontally-mediated top-down processes, which might indicate better control over subcortical information). Furthermore, we expected the perseverance of effort facet of grit to be linked to higher complexity during task engagement because previous research has shown complexity indexes (entropy and fractal dimension) to be linked to effort while performing cognitive tasks. Our results revealed that although there were no differences at rest as a function of grit, the participants with high grit and high consistency of interest scores exhibited lower frontal theta/beta ratios during the learning task. This pattern suggests that individual differences in grit might be more evident when top-down control processes are at work. Furthermore, there was a positive association between perseverance of effort and entropy at task, which might indicate more effort and engagement in the task. Finally, no association was found between the neural indexes (frontal theta/beta ratio, entropy, or fractal dimension) and impulsiveness, neither impulsiveness mediated between grit and brain measures. Finally, when controlling for impulsiveness and demographic variables (gender, age, education, and work experience) the effects at the facet level remained statistically significant. While there is still a long way to fully understand the neural mechanisms of grit, the present work constitutes a step toward unveiling the electrophysiological prints of grit.

Local Oscillatory Brain Dynamics of Mind Wandering in Schizophrenia.

A number of studies have focused on brain dynamics underlying mind wandering (MW) states in healthy people. However, there is limited understanding of how the oscillatory dynamics accompanying MW states and task-focused states are characterized in clinical populations. In this study, we explored EEG local synchrony of MW associated with schizophrenia, under the premise that changes in attention that arise during MW are associated with a different pattern of brain activity. To this end, we measured the power of EEG oscillations in different frequency bands, recorded while participants watched short video clips. In the group of participants diagnosed with schizophrenia, the power in MW states was significantly lower than during task-focused states, mainly in the frontal and posterior regions. However, in the group of healthy controls, the differences in power between the task-focused and MW states occurred exclusively in the posterior region. Furthermore, the power of the frequency bands during MW and during episodes of task-focused attention correlated with cognitive variables such as processing speed and working memory. These findings on dynamic changes of local synchronization in different frequency bands and areas of the cortex can improve our understanding of mental disorders, such as schizophrenia.

Mutual Information of Multiple Rhythms for EEG Signals.

Electroencephalograms (EEG) are one of the most commonly used measures to study brain functioning at a macroscopic level. The structure of the EEG time series is composed of many neural rhythms interacting at different spatiotemporal scales. This interaction is often named as cross frequency coupling, and consists of transient couplings between various parameters of different rhythms. This coupling has been hypothesized to be a basic mechanism involved in cognitive functions. There are several methods to measure cross frequency coupling between two rhythms but no single method has been selected as the gold standard. Current methods only serve to explore two rhythms at a time, are computationally demanding, and impose assumptions about the nature of the signal. Here we present a new approach based on Information Theory in which we can characterize the interaction of more than two rhythms in a given EEG time series. It estimates the mutual information of multiple rhythms (MIMR) extracted from the original signal. We tested this measure using simulated and real empirical data. We simulated signals composed of three frequencies and background noise. When the coupling between each frequency component was manipulated, we found a significant variation in the MIMR. In addition, we found that MIMR was sensitive to real EEG time series collected with open vs. closed eyes, and intra-cortical recordings from epileptic and non-epileptic signals registered at different regions of the brain. MIMR is presented as a tool to explore multiple rhythms, easy to compute and without a priori assumptions.

Differential Effects of Simulated Cortical Network Lesions on Synchrony and EEG Complexity.

Brain function has been proposed to arise as a result of the coordinated activity between distributed brain areas. An important issue in the study of brain activity is the characterization of the synchrony among these areas and the resulting complexity of the system. However, the variety of ways to define and, hence, measure brain synchrony and complexity has sometimes led to inconsistent results. Here, we study the relationship between synchrony and commonly used complexity estimators of electroencephalogram (EEG) activity and we explore how simulated lesions in anatomically based cortical networks would affect key functional measures of activity. We explored this question using different types of neural network lesions while the brain dynamics was modeled with a time-delayed set of 66 Kuramoto oscillators. Each oscillator modeled a region of the cortex (node), and the connectivity and spatial location between different areas informed the creation of a network structure (edges). Each type of lesion consisted on successive lesions of nodes or edges during the simulation of the neural dynamics. For each type of lesion, we measured the synchrony among oscillators and three complexity estimators (Higuchi's Fractal Dimension, Sample Entropy and Lempel-Ziv Complexity) of the simulated EEGs. We found a general negative correlation between EEG complexity metrics and synchrony but Sample Entropy and Lempel-Ziv showed a positive correlation with synchrony when the edges of the network were deleted. This suggests an intricate relationship between synchrony of the system and its estimated complexity. Hence, complexity seems to depend on the multiple states of interaction between the oscillators of the system. Our results can contribute to the interpretation of the functional meaning of EEG complexity.

EEG Multiscale Complexity in Schizophrenia During Picture Naming.

Introduction: Patients with schizophrenia show cognitive deficits that are evident both behaviourally and with EEG recordings. Recent studies have suggested that non-linear analyses of EEG might more adequately reflect the complex, irregular, non-stationary behavior of neural processes than more traditional ERP measures. Non-linear analyses have been mainly applied to EEGs from patients at rest, whereas differences in complexity might be more evident during task performance. Objective: We aimed to investigate changes in non-linear brain dynamics of patients with schizophrenia during cognitive processing. Method: 18 patients and 17 matched healthy controls were asked to name pictures. EEG data were collected at rest and while they were performing a naming task. EEGs were analyzed with the classical Lempel-Ziv Complexity (LZC) and with the Multiscale LZC. Electrodes were grouped in seven regions of interest (ROI). Results: As expected, controls had fewer naming errors than patients. Regarding EEG complexity, the interaction between Group, Task and ROI indicated that patients showed higher complexity values in right frontal regions only at rest, where no differences in complexity between patients and controls were found during the naming task. EEG complexity increased from rest to task in controls in left temporal-parietal regions, while no changes from rest to task were observed in patients. Finally, differences in complexity between patients and controls depended on the frequency bands: higher values of complexity in patients at rest were only observed in fast bands, indicating greater heterogeneity in patients in local dynamics of neuronal assemblies. Conclusion: Consistent with previous studies, schizophrenic patients showed higher complexity than controls in frontal regions at rest. Interestingly, we found different modulations of brain complexity during a simple cognitive task between patients and controls. These data can be interpreted as indicating schizophrenia-related failures to adapt brain functioning to the task, which is reflected in poorer behavioral performance. HIGHLIGHTS:     - We measured classical and multiscale Lempel-Ziv Complexity (LZCN and MLZC) of the EEG signal of patients with schizophrenia and controls at rest and while performing a cognitive task.    - We found that patients and controls showed a different pattern of brain complexity depending on their cognitive state (at rest or under cognitive challenge).    - Our results illustrate the value of the MLZC in the characterization of the pattern of brain complexity in schizophrenia on function of frequency bands.    - Nonlinear methodologies of EEG analysis can help to characterize brain dysfunction in schizophrenia.

Fractal dimension of EEG signals and heart dynamics in discrete emotional states.

In this study, we explored the fractal dimension (FD; a measure of signal complexity) of 28 EEG channels with positive and negative emotional states. The EEG of participants and their ECG were registered while watching short video clips that induced fear, disgust, humour, or neutral emotions. In order to better understand the nature of these emotions, the Higuchi FD of EEG segments and the heart rate variability (HRV) of the ECG associated with each emotion were obtained. Our results exhibited similar patterns of results with both measures. Humour elicited the highest FD scores in most EEG channels and the highest HRV, while fear, among all emotions, produced the lowest scores in both measures. These results may contribute to the understanding of the relationship between cortical and heart dynamics and their role on emotion perception.

Autism: Hard to Switch from Details to the Whole.

It has long been proposed that individuals with autism exhibit a superior processing of details at the expense of an impaired global processing. This theory has received some empirical support, but results are mixed. In this research we have studied local and global processing in ASD and Typically Developing children, with an adaptation of the Navon task, designed to measure congruency effects between local and global stimuli and switching cost between local and global tasks. ASD children showed preserved global processing; however, compared to Typically Developing children, they exhibited more facilitation from congruent local stimuli when they performed the global task. In addition, children with ASD had more switching cost than Typically Developing children only when they switched from the local to the global task, reflecting a specific difficulty to disengage from local stimuli. Together, results suggest that ASD is characterized by a tendency to process local details, they benefit from the processing of local stimuli at the expense of increasing cost to disengage from local stimuli when global processing is needed. Thus, this work demonstrates experimentally the advantages and disadvantages of the increased local processing in children with ASD.

Neurocomputational Model of EEG Complexity during Mind Wandering.

Mind wandering (MW) can be understood as a transient state in which attention drifts from an external task to internal self-generated thoughts. MW has been associated with the activation of the Default Mode Network (DMN). In addition, it has been shown that the activity of the DMN is anti-correlated with activation in brain networks related to the processing of external events (e.g., Salience network, SN). In this study, we present a mean field model based on weakly coupled Kuramoto oscillators. We simulated the oscillatory activity of the entire brain and explored the role of the interaction between the nodes from the DMN and SN in MW states. External stimulation was added to the network model in two opposite conditions. Stimuli could be presented when oscillators in the SN showed more internal coherence (synchrony) than in the DMN, or, on the contrary, when the coherence in the SN was lower than in the DMN. The resulting phases of the oscillators were analyzed and used to simulate EEG signals. Our results showed that the structural complexity from both simulated and real data was higher when the model was stimulated during periods in which DMN was more coherent than the SN. Overall, our results provided a plausible mechanistic explanation to MW as a state in which high coherence in the DMN partially suppresses the capacity of the system to process external stimuli.

Effect of the average delay and mean connectivity of the Kuramoto model on the complexity of the output electroencephalograms.

Cognitive functions result from the interplay of distributed brain areas operating in large-scale networks. These networks can be modelled with a number of parameters that represent their underlying dynamics. One particularly fruitful model to simulate key aspects of the large-scale brain networks is the Kuramoto model, which simulates the phase evolution of several weakly coupled oscillators that represent the mean oscillatory behavior of different cortical regions. Here, we inspected the dependency of two widespread nonlinear complexity markers, Sample Entropy (SampEn) and Lempel-Ziv Complexity (LZC), on EEG activity generated with a Kuramoto phase model where the time delay and connectivity strength among oscillators varied. We also added different levels of noise to the electroencephalogram (EEG) signals. Our results indicated that both complexity metrics reflected the changes in the delays and global synchrony levels, but we found that SampEn was slightly more sensitive to the state transition and its results were less affected by the presence of noise. These results help in the effort to understand the dynamics of EEG recordings and their relationship to large-scale networks.

Multiscale Lempel-Ziv complexity for EEG measures.

OBJECTIVE: To demonstrate that the classical calculation of Lempel-Ziv complexity (LZC) has an important limitation when applied to EEGs with rapid rhythms, and to propose a multiscale approach that overcomes this limitation. METHODS: We have evaluated, both with simulated and real EEGs, whether LZC calculation neglects functional characteristics of rapid EEG rhythms. In addition, we have proposed a procedure to obtain multiple binarization sequences that yield a spectrum of LZC, and we have explored whether complexity would be better captured using this computation. RESULTS: In our simulated signals, classical LZC did not capture modulations of a rapid component when a slower component of more amplitude was included in the signal. In real EEGs from healthy participants with eyes closed and eyes open, classical LZC calculation failed to show any difference between these two conditions. However, a multiscale LZC showed that complexity was lower for eyes closed than for eyes open conditions. CONCLUSIONS: As hypothesized, our new approximation captures the complexity of series with fast components masked by slower rhythms. SIGNIFICANCE: The method we introduce significantly improves LZC calculation, and it allows a better characterization of complexity of EEG signals.