Fractal Analysis in MATLAB: A Tutorial for Neuroscientists.

MATLAB is one of the software platforms most widely used for scientific computation. MATLAB includes a large set of functions, packages, and toolboxes that make it simple and fast to obtain complex mathematical and statistical computations for many applications. In this chapter, we review some tools available in MATLAB for performing fractal analyses on typical neuroscientific data in a practical way. We provide detailed examples of how to calculate the fractal dimension of 1D, 2D, and 3D data in MATLAB. Furthermore, we review other software packages for fractal analysis.

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.

Spatio-Temporal Fractal Dimension Analysis from Resting State EEG Signals in Parkinson's Disease.

Complexity analysis of electroencephalogram (EEG) signals has emerged as a valuable tool for characterizing Parkinson's disease (PD). Fractal dimension (FD) is a widely employed method for measuring the complexity of shapes with many applications in neurodegenerative disorders. Nevertheless, very little is known on the fractal characteristics of EEG in PD measured by FD. In this study we performed a spatio-temporal analysis of EEG in PD using FD in four dimensions (4DFD). We analyzed 42 resting-state EEG recordings comprising two groups: 27 PD patients without dementia and 15 healthy control subjects (HC). From the original resting-state EEG we derived the cortical activations defined by a source reconstruction at each time sample, generating point clouds in three dimensions. Then, a sliding window of one second (the fourth dimension) was used to compute the value of 4DFD by means of the box-counting algorithm. Our results showed a significantly higher value of 4DFD in the PD group (p < 0.001). Moreover, as a diagnostic classifier of PD, 4DFD obtained an area under curve value of 0.97 for a receiver operating characteristic curve analysis. These results suggest that 4DFD could be a promising method for characterizing the specific changes in the brain dynamics associated with PD.

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.

A cross-sectional and longitudinal study on the protective effect of bilingualism against dementia using brain atrophy and cognitive measures.

BACKGROUND: Evidence from previous studies suggests that bilingualism contributes to cognitive reserve because bilinguals manifest the first symptoms of Alzheimer's disease (AD) up to 5 years later than monolinguals. Other cross-sectional studies demonstrate that bilinguals show greater amounts of brain atrophy and hypometabolism than monolinguals, despite sharing the same diagnosis and suffering from the same symptoms. However, these studies may be biased by possible pre-existing between-group differences. METHODS: In this study, we used global parenchymal measures of atrophy and cognitive tests to investigate the protective effect of bilingualism against dementia cross-sectionally and prospectively, using a sample of bilinguals and monolinguals in the same clinical stage and matched on sociodemographic variables. RESULTS: Our results suggest that the two groups did not differ in their cognitive status at baseline, but bilinguals had less parenchymal volume than monolinguals, especially in areas related to brain atrophy in dementia. In addition, a longitudinal prospective analysis revealed that monolinguals lost more parenchyma and had more cognitive decline than bilinguals in a mean follow-up period of 7 months. CONCLUSION: These results provide the first prospective evidence that bilingualism may act as a neuroprotective factor against dementia and could be considered a factor in cognitive reserve.

Complexity analysis of cortical surface detects changes in future Alzheimer's disease converters.

Alzheimer's disease (AD) is a neurological disorder that creates neurodegenerative changes at several structural and functional levels in human brain tissue. The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of the human brain. In this study, we investigate spherical harmonic-based FD (SHFD), thickness, and local gyrification index (LGI) to assess whether they identify cortical surface abnormalities toward the conversion to AD. We study 33 AD patients, 122 mild cognitive impairment (MCI) patients (50 MCI converters and 29 MCI nonconverters), and 32 healthy controls (HC). SHFD, thickness, and LGI methodology allowed us to perform not only global level but also local level assessments in each cortical surface vertex. First, we found that global SHFD decreased in AD and future MCI converters compared to HC, and in MCI converters compared to MCI nonconverters. Second, we found that local white matter SHFD was reduced in AD compared to HC and MCI mainly in medial temporal lobe. Third, local white-matter SHFD was significantly reduced in MCI converters compared to MCI nonconverters in distributed areas, including the medial frontal lobe. Thickness and LGI metrics presented a reduction in AD compared to HC. Thickness was significantly reduced in MCI converters compared to healthy controls in entorhinal cortex and lateral temporal. In summary, SHFD was the only surface measure showing differences between MCI individuals that will convert or remain stable in the next 4 years. We suggest that SHFD may be an optimal complement to thickness loss analysis in monitoring longitudinal changes in preclinical and clinical stages of AD. Hum Brain Mapp 38:5905-5918, 2017. © 2017 Wiley Periodicals, Inc.