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Background: The fractal dimension (FD) is a valuable tool for analysing the complexity of neural structures and functions in the human brain. To assess the spatiotemporal complexity of brain activations derived from electroencephalogram (EEG) signals, the fractal dimension index (FDI) was developed. This measure integrates two distinct complexity metrics: 1) integration FD, which calculates the FD of the spatiotemporal coordinates of all significantly active EEG sources (4DFD); and 2) differentiation FD, determined by the complexity of the temporal evolution of the spatial distribution of cortical activations (3DFD), estimated via the Higuchi FD [HFD(3DFD)]. The final FDI value is the product of these two measurements: 4DFD × HFD(3DFD). Although FDI has shown utility in various research on neurological and neurodegenerative disorders, existing literature lacks standardized implementation methods and accessible coding resources, limiting wider adoption within the field., Methods: We introduce an open-source MATLAB software named FDI for measuring FDI values in EEG datasets., Results: By using CUDA for leveraging the GPU massive parallelism to optimize performance, our software facilitates efficient processing of large-scale EEG data while ensuring compatibility with pre-processed data from widely used tools such as Brainstorm and EEGLab. Additionally, we illustrate the applicability of FDI by demonstrating its usage in two neuroimaging studies. Access to the MATLAB source code and a precompiled executable for Windows system is provided freely., Conclusions: With these resources, neuroscientists can readily apply FDI to investigate cortical activity complexity within their own studies., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier Ltd.. All rights reserved.)

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., (© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

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 (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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Ruiz de Miras, Ibáñez-Molina, Soriano and Iglesias-Parro.)

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., (© 2023 The Authors. British Journal of Psychology published by John Wiley & Sons Ltd on behalf of The British Psychological Society.)

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., (© 2023 The Authors. European Journal of Neuroscience published by Federation of European Neuroscience Societies and John Wiley & Sons Ltd.)

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Aguerre, Gómez-Ariza, Ibáñez-Molina and Bajo.)

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2020 Ibáñez-Molina, Soriano and Iglesias-Parro.)

Patients with schizophrenia have often been considered to be "in their own world". However, this casual observation has not been proven by scientific evidence so far. This can be explained because scientific research has usually addressed cognition related to the processing of external stimuli, but only recently have efforts been made to explain thoughts, images and feelings not directly related to the external environment. This internally directed cognition has been called mind wandering. In this paper, we have explored mind wandering in schizophrenia under the hypothesis that a predominance of mind wandering would be a core dysfunction in this disorder. To this end, we collected verbal reports and measured electrophysiological signals from patients with schizophrenia spectrum disorders and matched healthy controls while they were presented with segments of films. The results showed that mind wandering was more frequent in patients than in controls. This higher frequency of mind wandering did not correlate with deficits in attentional, memory or executive functioning. In addition, mind wandering in patients was characterized by a different pattern of Electroencephalography (EEG) complexity in patients than in controls, leading to the suggestion that mind wandering in schizophrenia could be of a different nature. These findings could have relevant implications for the conceptualization of this severe mental disorder.

Background and Objective: Knowing whether a subject is conscious or not is a current challenge with a deep potential clinical impact. Recent theoretical considerations suggest that consciousness is linked to the complexity of distributed interactions within the corticothalamic system. The fractal dimension (FD) is a quantitative parameter that has been extensively used to analyse the complexity of structural and functional patterns of the human brain. In this study we investigate FD to assess whether it can discriminate between consciousness and different states of unconsciousness in healthy individuals., Methods: We study 69 high-density electroencephalogram (hd-EEG) measurements after transcranial magnetic stimulation (TMS) in 18 healthy subjects progressing from wakefulness to non-rapid eye movement (NREM) sleep and sedation induced by different anaesthetic agents (xenon and propofol). We quantify the integration of thalamocortical networks by calculating the FD of a spatiotemporal voxelization obtained from the locations of all sources that are significantly activated by the perturbation (4DFD). Moreover, we study the temporal evolution of the evoked spatial distributions and compute a measure of the differentiation of the response by means of the Higuchi FD (HFD). Finally, a Fractal Dimension Index (FDI) of perturbational complexity is computed as the product of both quantities: integration FD (4DFD) and differentiation FD (HFD)., Results: We found that FDI is significantly lower in sleep and sedation when compared to wakefulness and provides an almost perfect intra-subject discrimination between conscious and unconscious states., Conclusions: These results support the combination of FD measures of cortical integration and cortical differentiation as a novel paradigm of tracking complex spatiotemporal dynamics in the brain that could provide further insights into the link between complexity and the brain's capacity to sustain consciousness., (Copyright © 2019 Elsevier B.V. All rights reserved.)

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.

We explore the idea that cognitive demands of the handwriting would influence the degree of automaticity of the handwriting process, which in turn would affect the geometric parameters of texts. We compared the heterogeneity of handwritten texts in tasks with different cognitive demands; the heterogeneity of texts was analyzed with lacunarity, a measure of geometrical invariance. In Experiment 1, we asked participants to perform two tasks that varied in cognitive demands: transcription and exposition about an autobiographical episode. Lacunarity was significantly lower in transcription. In Experiment 2, we compared a veridical and a fictitious version of a personal event. Lacunarity was lower in veridical texts. We contend that differences in lacunarity of handwritten texts reveal the degree of automaticity in handwriting.

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 (LZC N 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.

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., (Copyright © 2018 Elsevier B.V. All rights reserved.)

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.

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.

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., (Copyright © 2014 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.)

Although there is an extensive literature on the study of the neural correlates of consciousness (NCC) this is a subject that is far from being considered over. In this paper we present a novel experimental paradigm, based on binocular rivalry, to study internally and externally generated conscious experiences. We called this procedure bimodal rivalry. In addition, and assuming the non-linear nature of the EEG signals, we propose the use of fractal dimension to characterize the complexity of the EEG signal associated with each percept. Analysis of the data showed a significant difference in complexity between the internally generated and externally generated percepts. Moreover, EEG complexity was dissimilar for externally generated auditory and visual percepts. These results support fractal dimension analyses as a new tool to characterize conscious perception., (Copyright © 2014 Elsevier Inc. All rights reserved.)