To respond to the demands of a constantly changing environment the brain permanently adjusts its architecture, alternating between segregated functioning, as when performing highly automated tasks, and integrated functioning, as when performing tasks that require high cognitive effort (Shine and Poldrack, 2018). This neural adaptation spans multiple time scales, and different regions. In the present work, we employ a metric (FDI), developed in our laboratory (Ruiz de Miras et al., 2019), that captures the dynamics of the complexity of brain activity to try to learn more about the severe mental disorder of schizophrenia.

The fractal dimension (FD; Mandelbrot, 1983) is a quantitative measure of shape complexity used widely for analyzing electroencephalogram (EEG) signals in many neuropsychiatric disorders (Lau et al., 2022). The fractal dimension index (FDI; Ruiz de Miras et al., 2019) is a recent methodology designed for analyzing the complexity of the spatiotemporal dynamics in the brain. FDI is based on computing the 3D fractal dimension (3DFD) and the 4D fractal dimension (4DFD) of cortical activations extracted from the EEG signal. The 3DFD and 4DFD values are computed from the 3D point clouds defined by the cortical activations, induced by a transcranial magnetic stimulation, at each time sample of the epoch being analyzed. FDI is calculated as the product of two different components: the Higuchi fractal dimension (Higuchi, 1988) of the evolution of the 3DFD values in the epoch, noted as HFD (3DFD), and the 4DFD of the 4D representation obtained by putting together all of the 3D point clouds contained in the whole epoch (time is the fourth dimension). The 4DFD component in FDI quantifies the integration of cortical networks, while the HFD (3DFD) component is a measure of the cortical differentiation (Ruiz de Miras et al., 2019).

Schizophrenia is a severe mental disorder whose patients suffer psychotic symptoms and several cognitive and motor dysfunctions (McGrath et al., 2008). The symptoms’ onset is usually at between 14 and 30 years of age, and it is known that the time between the manifestation of symptoms and treatment is one of the best predictors of later prognosis (McGlashan, 1999). Currently, there are no reliable biomarkers for schizophrenia and, therefore, providing tools for an early diagnosis is of great relevance (Nieuwenhuis et al., 2012).

In the last few years, several studies used complexity measures of EEG for analyzing neural activity in schizophrenia (Harmah et al., 2020; Lau et al., 2022). Change complexity was used in Aksentijevic et al. (2021) for analyzing both the spatial and temporal complexity of 16 EEG channels. Kutepov et al. (2020) compared EEG complexity between schizophrenia patients and healthy controls by using three measures of entropy (approximated entropy, sample entropy, and multi-scale entropy). Another entropy measure of EEG, fuzzy entropy, was used in Xiang et al. (2019) for measuring task-related modulation of complexity in schizophrenia. Some other authors studied the complexity of EEG signals in schizophrenia by means of Higuchi’s fractal dimension (HFD; Portnova and Atanov, 2018; Goshvarpour and Goshvarpour, 2020). Fractal analysis of EEG signals was also used for extracting several features, such as HFD and correlation dimension, in recent schizophrenia classifiers based on different machine learning algorithms (Barros et al., 2021; Tian et al., 2022; Ruiz de Miras et al., 2023a). Multifractal and entropy-based features extracted from time series of topological measures (connectivity, clustering, and global efficiency) of functional networks constructed from EEG signals were also successfully used in classifying schizophrenia (Racz et al., 2020).

Increasing evidence suggests that schizophrenia is associated with alterations in the patterns of connectivity observed between different brain regions (Alexander-Bloch et al., 2010; Van Den Heuvel et al., 2010; Van Den Heuvel and Fornito, 2014; Iglesias-Parro et al., 2023). Understanding the complexity of the functional connectivity of neural networks in schizophrenia is crucial not only for understanding the mechanism of schizophrenia, but also for providing potential biomarkers for clinical use. Specifically, several authors have proposed that the pathophysiology of schizophrenia may be associated with changes of integration/segregation patterns in distributed neural networks, such as the default mode network (Wang et al., 2015) and the salience network (Huang et al., 2022). So complexity analyses of the neural activity in those known resting-state networks affected by schizophrenia could also be of great relevance.

In the present study, we hypothesized with the capacity of FDI to be adapted for analyzing both long recordings of resting-state EEG signals and localized regions of interest of the brain. To this aim, using the FDI measure, we analyzed the spatio-temporal complexity of brain dynamics for resting-state functional networks in schizophrenia. Our results demonstrated the ability of FDI to be applied on resting-state EEG signals from different regions of interest and revealed a localized decreasing complexity of neural activity of schizophrenia patients, mainly in the salience network.

Fractal dimension index is a measure of complexity which has been used until now for analyzing the brain activations extracted from very short epochs of electroencephalogram (EEG) signals induced by transcranial magnetic stimulation (Ruiz de Miras et al., 2019). In this study we hypothesized with the viability of the FDI methodology for analyzing both long periods of resting state EEG signals and localized regions of interest defined by functional networks. To this end, brain activations at each time sample were defined by a thresholding process (mean plus standard deviation) applied on 15,002 sources extracted from the EEG signal. FDI was then computed on the brain activations corresponding to each resting-state functional network by averaging all the FDI values obtained using a sliding window of 1 s on the epoch. This customized FDI methodology was successfully used for characterizing the brain dynamic changes in schizophrenia, a mental disorder associated with dysfunction in the information flow dynamics in the spontaneous brain networks. Our results demonstrated the ability of FDI to be applied on resting-state EEG signals from different regions of interest and revealed a localized decreasing complexity of neural activity of schizophrenia patients, mainly in the salience network.

We found that FDI was significantly lower in the SCZ group compared to HC for networks AUD, DAN, and SAN (see Figures 4, 5). However, the whole brain and the DMN and VIS networks did not statistically differ in FDI between the SCZ and HC groups. Decreased values of EEG complexity in schizophrenia patients were also reported in some recent studies (Goshvarpour and Goshvarpour, 2020; Kutepov et al., 2020; Aksentijevic et al., 2021). Results in Aksentijevic et al. (2021) showed that schizophrenia patients had lower values of change complexity than healthy subjects. Similar results were obtained by Kutepov et al. (2020) when comparing EEG complexity between schizophrenia patients and healthy controls by using approximated entropy, sample entropy, and multi-scale entropy. In Goshvarpour and Goshvarpour (2020), lower values of HFD were obtained in the patients group compared to normal subjects in all the 19 EEG channels recorded in resting-state. However, some other studies found higher values of complexity in the SCZ group compared to normal controls (Portnova and Atanov, 2018; Xiang et al., 2019). In Xiang et al. (2019), significantly higher values of fuzzy entropy in the frontal and occipital regions were obtained for schizophrenia patients in both conditions, baseline and auditory stimulus. Also, Portnova and Atanov (2018) found significantly higher values of HFD in the schizophrenia group for eight out of 19 EEG channels when the signal was recorded in resting-state. To these contradictory previous results our study adds a new standpoint by analyzing not the complexity of the EEG signal itself, but the 3D and 4D fractal dimensions of the spatiotemporal distribution of the brain activations extracted from the EEG.

According to Yang et al. (2015), from a systemic viewpoint the brain’s adaptability to an ever-changing environment is manifested in its complexity. From this point of view, reduced patterns in complexity could be markers of disease, or in terms of Costa et al. (2005) a generic feature of pathologic dynamics. A higher fractal dimension might indicate increased complexity, self-similarity, and possibly enhanced adaptability of neural networks. Conversely, a lower fractal dimension could imply a reduction in complexity, potentially related to disrupted neural communication changes (Iglesias-Parro et al., 2023). On the other hand, in a healthy brain, fractal dimension may reflect the brain’s ability to efficiently process information, respond to stimuli, and adapt to varying demands. A higher fractal dimension could indicate a balanced interplay between local and global neural processes, enabling cognitive flexibility, robustness, and efficient information processing (Ziukelis et al., 2022). Taken together, our results indicate that individuals diagnosed with schizophrenia compared to the control group presented, in most of the networks, a more rigid temporal resting-state dynamic. These results suggest a more rigid functional connectivity, with less adaptive capacity to segregate information and with a more stereotyped pattern, indicative of a network with less capacity to carry out functional adaptations in the connectivity of its nodes.

We also found strong negative correlations in the SCZ group between PANSS-P and the FDI of the whole brain and networks AUD, DAN, DMN, and SAN, and between PANSS-G and the FDI of networks AUD and SAN (see Figure 6 and Table 2). This result, which relates a decrease in FDI to an increase in the severity of the disease, is of great relevance because it indicates that FDI is a potential indicator in evaluating the clinical symptoms of schizophrenia. In clinical practice, schizophrenia is usually diagnosed by observing positive symptoms (delusions, hallucinations, speech disorders, and thought disorder) and negative symptoms (avolition, alogia, anhedonia, asociality, and blunted affect). However, positive and negative symptoms may have contrary effects on brain functional organizations (Zhou et al., 2007; Bernard et al., 2017), and it has been proposed that the possible reason for these inconsistent observations may be that positive and negative symptoms have separate mechanisms (Wang et al., 2023). Thus, our results are consistent with this differentiation, in that reduced network complexity was significantly correlated with the severity of positive psychotic symptoms but not with that of negative ones, inversely associated with cognitive measures. It would be possible that positive symptoms are physiologically characterized by neural networks with more rigid dynamics and a tendency to change in a more stereotypical way.

Since many recent studies have used EEG complexity measures as features in machine learning classifiers of schizophrenia (Racz et al., 2020; Barros et al., 2021; Tian et al., 2022; Ruiz de Miras et al., 2023a), we also assessed the performance of FDI as a potential feature for classifying schizophrenia patients by means of an ROC curve analysis (see Figure 7). Our results showed that FDI could be a promising feature to be used in classifiers based on EEG measures, especially when computed for the SAN network (AUC = 0.83). These results reinforce the hypothesis that cognitive networks—but not visual networks—would be differentially active in schizophrenia (Keane et al., 2022). Moreover, FDI as a feature could add a broader perspective when analyzing complexity in current machine learning classifiers which are based on linear and non-linear measures computed directly on the EEG signal, because the input EEG signal is used in FDI to extract the brain activations over time, which allows for analyzing 3D and 4D complexity through fractal dimension.

Fractal dimension index relies on repeatedly computing the fractal dimension of 3D and 4D point clouds, which is not trivial and could be computationally intensive. Nevertheless, we have already developed very efficient implementations of the computation of 3DFD and 4DFD through parallel execution on GPU. This software was already described and made publicly available in Ruiz de Miras et al. (2023b).

In conclusion, in this study we have presented a novel methodology, based on the FDI measure, for performing the complexity analysis of resting-state EEG signals. FDI performs a spatiotemporal analysis of brain dynamics by combining two components: 4DFD as a quantification of cortical integration, and HFD (3DFD) as a measure of cortical differentiation. Our complexity analysis based on the FDI of resting-state EEGs applied differentially on resting-state functional networks obtained very good results in differentiating schizophrenia patients from healthy subjects. Moreover, FDI was strongly correlated with clinical scores of schizophrenia. All these results suggest that FDI can be used for analyzing the complexity of brain dynamics from resting-state EEG signals, being a promising tool for obtaining a deeper understanding of the neurodegeneration present in neurological disorders such as schizophrenia.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving humans were approved by Universidad de Jaén (Spain)—Hospital San Agustín de Linares (Spain). The studies were conducted in accordance with the local legislation and institutional requirements. The participants provided their written informed consent to participate in this study.

JR: conceptualization, methodology, software, formal analysis, investigation, data curation, writing original draft, and funding acquisition. AI-M and MS: methodology, investigation, resources, data curation, review, and editing original draft. SI-P: methodology, formal analysis, investigation, resources, data curation, writing original draft, and funding acquisition. All authors contributed to the article and approved the submitted version.

This work is part of the research project PID2019-105145RB-I00 supported by the Spanish Government (MCIN/AEI/10.13039/501100011033).

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.

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