Self-similarity and multifractality in human brain activity: A wavelet-based analysis of scale-free brain dynamics

Analyzing fractal dimension in electroconvulsive therapy: Unraveling complexity in structural and functional neuroimaging

BACKGROUND

Numerous studies show that electroconvulsive therapy (ECT) induces hippocampal neuroplasticity, but findings are inconsistent regarding its clinical relevance. This study aims to investigate ECT-induced plasticity of anterior and posterior hippocampi using mathematical complexity measures in neuroimaging, namely Higuchi's fractal dimension (HFD) for fMRI time series and the fractal dimension of cortical morphology (FD-CM). Furthermore, we explore the potential of these complexity measures to predict ECT treatment response.

METHODS

Twenty patients with a current depressive episode (16 with major depressive disorder and 4 with bipolar disorder) underwent MRI-scans before and after an ECT-series. Twenty healthy controls matched for age and sex were also scanned twice for comparison purposes. Resting-state fMRI data were processed, and HFD was computed for anterior and posterior hippocampi. Group-by-time effects for HFD in anterior and posterior hippocampi were calculated and correlations between HFD changes and improvement in depression severity were examined. For FD-CM analyses, we preprocessed structural MRI with CAT12's surface-based methods. We explored group-by-time effects for FD-CM and the predictive value of baseline HFD and FD-CM for treatment outcome.

RESULTS

Patients exhibited a significant increase in bilateral hippocampal HFD from baseline to follow-up scans. Right anterior hippocampal HFD increase was associated with reductions in depression severity. We found no group differences and group-by-time effects in FD-CM. After applying a whole-brain regression analysis, we found that baseline FD-CM in the left temporal pole predicted reduction of overall depression severity after ECT. Baseline hippocampal HFD did not predict treatment outcome.

CONCLUSION

This study suggests that HFD and FD-CM are promising imaging markers to investigate ECT-induced neuroplasticity associated with treatment response.

Multi-timescale neural dynamics for multisensory integration

Carrying out any everyday task, be it driving in traffic, conversing with friends or playing basketball, requires rapid selection, integration and segregation of stimuli from different sensory modalities. At present, even the most advanced artificial intelligence-based systems are unable to replicate the multisensory processes that the human brain routinely performs, but how neural circuits in the brain carry out these processes is still not well understood. In this Perspective, we discuss recent findings that shed fresh light on the oscillatory neural mechanisms that mediate multisensory integration (MI), including power modulations, phase resetting, phase-amplitude coupling and dynamic functional connectivity. We then consider studies that also suggest multi-timescale dynamics in intrinsic ongoing neural activity and during stimulus-driven bottom-up and cognitive top-down neural network processing in the context of MI. We propose a new concept of MI that emphasizes the critical role of neural dynamics at multiple timescales within and across brain networks, enabling the simultaneous integration, segregation, hierarchical structuring and selection of information in different time windows. To highlight predictions from our multi-timescale concept of MI, real-world scenarios in which multi-timescale processes may coordinate MI in a flexible and adaptive manner are considered.

Quantum multifractality as a probe of phase space in the Dicke model

We study the multifractal behavior of coherent states projected in the energy eigenbasis of the spin-boson Dicke Hamiltonian, a paradigmatic model describing the collective interaction between a single bosonic mode and a set of two-level systems. By examining the linear approximation and parabolic correction to the mass exponents, we find ergodic and multifractal coherent states and show that they reflect details of the structure of the classical phase space, including chaos, regularity, and features of localization. The analysis of multifractality stands as a sensitive tool to detect changes and structures in phase space, complementary to classical tools to investigate it. We also address the difficulties involved in the multifractal analyses of systems with unbounded Hilbert spaces.

A Self-Similarity Logic May Shape the Organization of the Nervous System

From the morphological point of view, the nervous system exhibits a fractal, self-similar geometry at various levels of observations, from single cells up to cell networks. From the functional point of view, it is characterized by a hierarchical organization in which self-similar structures (networks) of different miniaturizations are nested within each other. In particular, neuronal networks, interconnected to form neuronal systems, are formed by neurons, which operate thanks to their molecular networks, mainly having proteins as components that via protein-protein interactions can be assembled in multimeric complexes working as micro-devices. On this basis, the term "self-similarity logic" was introduced to describe a nested organization where, at the various levels, almost the same rules (logic) to perform operations are used. Self-similarity and self-similarity logic both appear to be intimately linked to the biophysical evidence for the nervous system being a pattern-forming system that can flexibly switch from one coherent state to another. Thus, they can represent the key concepts to describe its complexity and its concerted, holistic behavior.

Characterizing endogenous delta oscillations in human MEG

Rhythmic activity in the delta frequency range (0.5-3 Hz) is a prominent feature of brain dynamics. Here, we examined whether spontaneous delta oscillations, as found in invasive recordings in awake animals, can be observed in non-invasive recordings performed in humans with magnetoencephalography (MEG). In humans, delta activity is commonly reported when processing rhythmic sensory inputs, with direct relationships to behaviour. However, rhythmic brain dynamics observed during rhythmic sensory stimulation cannot be interpreted as an endogenous oscillation. To test for endogenous delta oscillations we analysed human MEG data during rest. For comparison, we additionally analysed two conditions in which participants engaged in spontaneous finger tapping and silent counting, arguing that internally rhythmic behaviours could incite an otherwise silent neural oscillator. A novel set of analysis steps allowed us to show narrow spectral peaks in the delta frequency range in rest, and during overt and covert rhythmic activity. Additional analyses in the time domain revealed that only the resting state condition warranted an interpretation of these peaks as endogenously periodic neural dynamics. In sum, this work shows that using advanced signal processing techniques, it is possible to observe endogenous delta oscillations in non-invasive recordings of human brain dynamics.

Hierarchical overlapping modular structure in the human cerebral cortex improves individual identification

The idea that brain networks have a hierarchical modular organization is pervasive. Increasing evidence suggests that brain modules overlap. However, little is known about the hierarchical overlapping modular structure in the brain. In this study, we developed a framework to uncover brain hierarchical overlapping modular structures based on a nested-spectral partition algorithm and an edge-centric network model. Overlap degree between brain modules is symmetrical across hemispheres, with highest overlap observed in the control and salience/ventral attention networks. Furthermore, brain edges are clustered into two groups: intrasystem and intersystem edges, to form hierarchical overlapping modules. At different levels, modules are self-similar in the degree of overlap. Additionally, the brain's hierarchical structure contains more individual identifiable information than a single-level structure, particularly in the control and salience/ventral attention networks. Our results offer pathways for future studies aimed at relating the organization of hierarchical overlapping modules to brain cognitive behavior and disorders.

The fractal brain: scale-invariance in structure and dynamics

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

Scale-free dynamics of core-periphery topography

The human brain's cerebral cortex exhibits a topographic division into higher-order transmodal core and lower-order unimodal periphery regions. While timescales between the core and periphery region diverge, features of their power spectra, especially scale-free dynamics during resting-state and their mdulation in task states, remain unclear. To answer this question, we investigated the ~1/f-like pink noise manifestation of scale-free dynamics in the core-periphery topography during rest and task states applying infra-slow inter-trial intervals up to 1 min falling inside the BOLD's infra-slow frequency band. The results demonstrate (1) higher resting-state power-law exponent (PLE) in the core compared to the periphery region; (2) significant PLE increases in task across the core and periphery regions; and (3) task-related PLE increases likely followed the task's atypically low event rates, namely the task's periodicity (inter-trial interval = 52-60 s; 0.016-0.019 Hz). A computational model and a replication dataset that used similar infra-slow inter-trial intervals provide further support for our main findings. Altogether, the results show that scale-free dynamics differentiate core and periphery regions in the resting-state and mediate task-related effects.

Turing's cascade instability supports the coordination of the mind, brain, and behavior

Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor-that of the cascade. The time has come to confront Turing's cascading instability, which suggests a geometrical framework driven by power laws and can be studied using multifractal formalism and multiscale probability density function analysis. Here, we review a rapidly growing body of scientific investigations revealing signatures of cascade instability and their consequences for a perceiving, acting, and thinking organism. We review work related to executive functioning (planning to act), postural control (bodily poise for turning plans into action), and effortful perception (action to gather information in a single modality and action to blend multimodal information). We also review findings on neuronal avalanches in the brain, specifically about neural participation in body-wide cascades. Turing's cascade instability blends the mind, brain, and behavior across space and time scales and provides an alternative to the dominant computer metaphor.

Drowsiness detection from polysomnographic data using multivariate selfsimilarity and eigen-wavelet analysis

Because drowsiness is a major cause in vehicle accidents, its automated detection is critical. Scale-free temporal dynamics is known to be typical of physiological and body rhythms. The present work quantifies the benefits of applying a recent and original multivariate selfsimilarity analysis to several modalities of polysomnographic measurements (heart rate, blood pressure, electroencephalogram and respiration), from the MIT-BIH Polysomnographic Database, to better classify drowsiness-related sleep stages. Clinical relevance- This study shows that probing jointly temporal dynamics amongst polysomnographic measurements, with a proposed original multivariate multiscale approach, yields a gain of above 5% in the Area-under-Curve quanti-fying drowsiness-related sleep stage classification performance compared to univariate analysis.

Functional brain-heart interplay extends to the multifractal domain

The study of functional brain-heart interplay has provided meaningful insights in cardiology and neuroscience. Regarding biosignal processing, this interplay involves predominantly neural and heartbeat linear dynamics expressed via time and frequency domain-related features. However, the dynamics of central and autonomous nervous systems show nonlinear and multifractal behaviours, and the extent to which this behaviour influences brain-heart interactions is currently unknown. Here, we report a novel signal processing framework aimed at quantifying nonlinear functional brain-heart interplay in the non-Gaussian and multifractal domains that combines electroencephalography (EEG) and heart rate variability series. This framework relies on a maximal information coefficient analysis between nonlinear multiscale features derived from EEG spectra and from an inhomogeneous point-process model for heartbeat dynamics. Experimental results were gathered from 24 healthy volunteers during a resting state and a cold pressor test, revealing that synchronous changes between brain and heartbeat multifractal spectra occur at higher EEG frequency bands and through nonlinear/complex cardiovascular control. We conclude that significant bodily, sympathovagal changes such as those elicited by cold-pressure stimuli affect the functional brain-heart interplay beyond second-order statistics, thus extending it to multifractal dynamics. These results provide a platform to define novel nervous-system-targeted biomarkers. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Modified wavelet analysis of ECoG-pattern as promising tool for detection of the blood-brain barrier leakage

A new approach for detection oscillatory patterns and estimation of their dynamics based by a modified CWT skeleton method is presented. The method opens up additional perspectives for the analysis of subtle changes in the oscillatory activity of complex nonstationary signals. The method was applied to analyze unique experimental signals obtained in usual conditions and after the non-invasive increase in the blood–brain barrier (BBB) permeability in 10 male Wistar rats. The results of the wavelet-analysis of electrocorticography (ECoG) recorded in a normal physiological state and after an increase in the BBB permeability of animals demonstrate significant changes between these states during wakefulness of animals and an essential smoothing of these differences during sleep. Sleep is closely related to the processes of observed changes in the BBB permeability.

Spectral Independent Component Analysis with noise modeling for M/EEG source separation

BACKGROUND

Independent Component Analysis (ICA) is a widespread tool for exploration and denoising of electroencephalography (EEG) or magnetoencephalography (MEG) signals. In its most common formulation, ICA assumes that the signal matrix is a noiseless linear mixture of independent sources that are assumed non-Gaussian. A limitation is that it enforces to estimate as many sources as sensors or to rely on a detrimental PCA step.

METHODS

We present the Spectral Matching ICA (SMICA) model. Signals are modelled as a linear mixing of independent sources corrupted by additive noise, where sources and the noise are stationary Gaussian time series. Thanks to the Gaussian assumption, the negative log-likelihood has a simple expression as a sum of 'divergences' between the empirical spectral covariance matrices of the signals and those predicted by the model. The model parameters can then be estimated by the expectation-maximization (EM) algorithm.

RESULTS

On phantom MEG datasets with low amplitude dipole sources (20 nAm), SMICA makes a median dipole localization error of 1.5 mm while competing methods make an error ≥7 mm. Experiments on EEG datasets show that SMICA identifies a source subspace which contains sources that have less pairwise mutual information, and are better explained by the projection of a single dipole on the scalp. With 10 sources, the number of strongly dipolar sources (dipolarity >90%) is more than 80% for SMICA while competing methods do not exceed 65%.

COMPARISON WITH EXISTING METHODS

With the noisy model of SMICA, the number of sources to be recovered is controlled by choosing the size of the mixing matrix to be fitted rather than by a preprocessing step of dimension reduction which is required in traditional noise-free ICA methods.

CONCLUSIONS

SMICA is a promising alternative to other noiseless ICA models based on non-Gaussian assumptions.

Revisiting Functional Connectivity for Infraslow Scale-Free Brain Dynamics Using Complex Wavelets

The analysis of human brain functional networks is achieved by computing functional connectivity indices reflecting phase coupling and interactions between remote brain regions. In magneto- and electroencephalography, the most frequently used functional connectivity indices are constructed based on Fourier-based cross-spectral estimation applied to specific fast and band-limited oscillatory regimes. Recently, infraslow arrhythmic fluctuations (below the 1 Hz) were recognized as playing a leading role in spontaneous brain activity. The present work aims to propose to assess functional connectivity from fractal dynamics, thus extending the assessment of functional connectivity to the infraslow arrhythmic or scale-free temporal dynamics of M/EEG-quantified brain activity. Instead of being based on Fourier analysis, new Imaginary Coherence and weighted Phase Lag indices are constructed from complex-wavelet representations. Their performances are first assessed on synthetic data by means of Monte-Carlo simulations, and they are then compared favorably against the classical Fourier-based indices. These new assessments of functional connectivity indices are also applied to MEG data collected on 36 individuals both at rest and during the learning of a visual motion discrimination task. They demonstrate a higher statistical sensitivity, compared to their Fourier counterparts, in capturing significant and relevant functional interactions in the infraslow regime and modulations from rest to task. Notably, the consistent overall increase in functional connectivity assessed from fractal dynamics from rest to task correlated with a change in temporal dynamics as well as with improved performance in task completion, which suggests that the complex-wavelet weighted Phase Lag index is the sole index is able to capture brain plasticity in the infraslow scale-free regime.

Patient, interrupted: MEG oscillation dynamics reveal temporal dysconnectivity in schizophrenia

Current theories of schizophrenia emphasize the role of altered information integration as the core dysfunction of this illness. While ample neuroimaging evidence for such accounts comes from investigations of spatial connectivity, understanding temporal disruptions is important to fully capture the essence of dysconnectivity in schizophrenia. Recent electrophysiology studies suggest that long-range temporal correlation (LRTC) in the amplitude dynamics of neural oscillations captures the integrity of transferred information in the healthy brain. Thus, in this study, 25 schizophrenia patients and 25 controls (8 females/group) were recorded during two five-minutes of resting-state magnetoencephalography (once with eyes-open and once with eyes-closed). We used source-level analyses to investigate temporal dysconnectivity in patients by characterizing LRTCs across cortical and sub-cortical brain regions. In addition to standard statistical assessments, we applied a machine learning framework using support vector machine to evaluate the discriminative power of LRTCs in identifying patients from healthy controls. We found that neural oscillations in schizophrenia patients were characterized by reduced signal memory and higher variability across time, as evidenced by cortical and subcortical attenuations of LRTCs in the alpha and beta frequency bands. Support vector machine significantly classified participants using LRTCs in key limbic and paralimbic brain areas, with decoding accuracy reaching 82%. Importantly, these brain regions belong to networks that are highly relevant to the symptomology of schizophrenia. These findings thus posit temporal dysconnectivity as a hallmark of altered information processing in schizophrenia, and help advance our understanding of this pathology.

Processing of Different Temporal Scales in the Human Brain

While recalling life events, we reexperience events of different durations, ranging across varying temporal scales, from several minutes to years. However, the brain mechanisms underlying temporal cognition are usually investigated only in small-scale periods—milliseconds to minutes. Are the same neurocognitive systems used to organize memory at different temporal scales? Here, we asked participants to compare temporal distances (time elapsed) to personal events at four different temporal scales (hour, day, week, and month) under fMRI. Cortical activity showed temporal scale sensitivity at the medial and lateral parts of the parietal lobe, bilaterally. Activity at the medial parietal cortex also showed a gradual progression from large- to small-scale processing, along a posterior–anterior axis. Interestingly, no sensitivity was found along the hippocampal long axis. In the medial scale-sensitive region, most of the voxels were preferentially active for the larger scale (month), and in the lateral region, scale selectivity was higher for the smallest scale (hour). These results demonstrate how scale-selective activity characterizes autobiographical memory processing and may provide a basis for understanding how the human brain processes and integrates experiences across timescales in a hierarchical manner.

Deterministic characteristics of spontaneous activity detected by multi-fractal analysis in a spiking neural network with long-tailed distributions of synaptic weights

Cortical neural networks maintain autonomous electrical activity called spontaneous activity that represents the brain's dynamic internal state even in the absence of sensory stimuli. The spatio-temporal complexity of spontaneous activity is strongly related to perceptual, learning, and cognitive brain functions; multi-fractal analysis can be utilized to evaluate the complexity of spontaneous activity. Recent studies have shown that the deterministic dynamic behavior of spontaneous activity especially reflects the topological neural network characteristics and changes of neural network structures. However, it remains unclear whether multi-fractal analysis, recently widely utilized for neural activity, is effective for detecting the complexity of the deterministic dynamic process. To verify this point, we focused on the log-normal distribution of excitatory postsynaptic potentials (EPSPs) to evaluate the multi-fractality of spontaneous activity in a spiking neural network with a log-normal distribution of EPSPs. We found that the spiking activities exhibited multi-fractal characteristics. Moreover, to investigate the presence of a deterministic process in the spiking activity, we conducted a surrogate data analysis against the time-series of spiking activity. The results showed that the spontaneous spiking activity included the deterministic dynamic behavior. Overall, the combination of multi-fractal analysis and surrogate data analysis can detect deterministic complex neural activity. The multi-fractal analysis of neural activity used in this study could be widely utilized for brain modeling and evaluation methods for signals obtained by neuroimaging modalities.

Dynamic Functional Connectivity between order and randomness and its evolution across the human adult lifespan

Functional Connectivity (FC) during resting-state or task conditions is not static but inherently dynamic. Yet, there is no consensus on whether fluctuations in FC may resemble isolated transitions between discrete FC states rather than continuous changes. This quarrel hampers advancing the study of dynamic FC. This is unfortunate as the structure of fluctuations in FC can certainly provide more information about developmental changes, aging, and progression of pathologies. We merge the two perspectives and consider dynamic FC as an ongoing network reconfiguration, including a stochastic exploration of the space of possible steady FC states. The statistical properties of this random walk deviate both from a purely "order-driven" dynamics, in which the mean FC is preserved, and from a purely "randomness-driven" scenario, in which fluctuations of FC remain uncorrelated over time. Instead, dynamic FC has a complex structure endowed with long-range sequential correlations that give rise to transient slowing and acceleration epochs in the continuous flow of reconfiguration. Our analysis for fMRI data in healthy elderly revealed that dynamic FC tends to slow down and becomes less complex as well as more random with increasing age. These effects appear to be strongly associated with age-related changes in behavioural and cognitive performance.

Quantifying Functional Links between Brain and Heartbeat Dynamics in the Multifractal Domain: a Preliminary Analysis

Quantification of brain-heart interplay (BHI) has mainly been performed in the time and frequency domains. However, such functional interactions are likely to involve nonlinear dynamics associated with the two systems. To this extent, in this preliminary study we investigate the functional coupling between multifractal properties of Electroencephalography (EEG) and Heart Rate Variability (HRV) series using a channel- and time scale-wise maximal information coefficient analysis. Experimental results were gathered from 24 healthy volunteers undergoing a resting state and a cold-pressure test, and suggest that significant changes between the two experimental conditions might be associated with nonlinear quantifiers of the multifractal spectrum. Particularly, major brain-heart functional coupling was associated with the secondorder cumulant of the multifractal spectrum. We conclude that a functional nonlinear relationship between brain- and heartbeat-related multifractal sprectra exist, with higher values associated with the resting state.

Classification of Brainwaves Using Convolutional Neural Network

Classification of brainwaves in recordings is of considerable interest to neuroscience and medical communities. Classification techniques used presently depend on the extraction of low-level features from the recordings, which in turn affects the classification performance. To alleviate this problem, this paper proposes an end-to-end approach using Convolutional Neural Network (CNN) which has been shown to detect complex patterns in a signal by exploiting its spatiotemporal nature. The present study uses time and frequency axes for the classification using synthesized Local Field Potential (LFP) data. The results are analyzed and compared with the FFT technique. In all the results, the CNN outperforms the FFT by a significant margin especially when the noise level is high. This study also sheds light on certain signal characteristics affecting network performance.

Wavelet p-Leader Non-Gaussian Multiscale Expansions for EEG series: an Exploratory Study on Cold-Pressor Test

Brain dynamics recorded through electroencephalography (EEG) have been proven to be the output of a nonstationary and nonlinear system. Thus, multifractality of EEG series has been exploited as a useful tool for a neurophysiological characterization in health and disease. However, the role of EEG multifractality under peripheral stress is unknown. In this study, we propose to make use of a novel tool, the recently defined non-Gaussian multiscale analysis, to investigate brain dynamics in the range of 4-8Hz following a cold-pressor test versus a resting state. The method builds on the wavelet p-leader multifractal spectrum to quantify different types of departure from Gaussian and linear properties, and is compared here to standard linear descriptive indices. Results suggest that the proposed non-Gaussian multiscale indices were able to detect expected changes over the somatosensory and premotor cortices, over regions different from those detected by linear analyses. They further indicate that preferred responses for the contralateral somatosensory cortex occur at scales 2.5s and 5s. These findings contribute to the characterization of the so-called central autonomic network, linking dynamical changes at a peripheral and a central nervous system levels.