Multifractal Functional Connectivity Analysis of Electroencephalogram Reveals Reorganization of Brain Networks in a Visual Pattern Recognition Paradigm

Multiscale detrended cross-correlation coefficient: estimating coupling in non-stationary neurophysiological signals

The brain consists of a vastly interconnected network of regions, the connectome. By estimating the statistical interdependence of neurophysiological time series, we can measure the functional connectivity (FC) of this connectome. Pearson's correlation (r P) is a common metric of coupling in FC studies. Yet r P does not account properly for the non-stationarity of the signals recorded in neuroimaging. In this study, we introduced a novel estimator of coupled dynamics termed multiscale detrended cross-correlation coefficient (MDC3). Firstly, we showed that MDC3 had higher accuracy compared to r P and lagged covariance using simulated time series with known coupling, as well as simulated functional magnetic resonance imaging (fMRI) signals with known underlying structural connectivity. Next, we computed functional brain networks based on empirical magnetoencephalography (MEG) and fMRI. We found that by using MDC3 we could construct networks of healthy populations with significantly different properties compared to r P networks. Based on our results, we believe that MDC3 is a valid alternative to r P that should be incorporated in future FC studies.

Postural control in gymnasts: anisotropic fractal scaling reveals proprioceptive reintegration in vestibular perturbation

Dexterous postural control subtly complements movement variability with sensory correlations at many scales. The expressive poise of gymnasts exemplifies this lyrical punctuation of release with constraint, from coarse grain to fine scales. Dexterous postural control upon a 2D support surface might collapse the variation of center of pressure (CoP) to a relatively 1D orientation-a direction often oriented towards the focal point of a visual task. Sensory corrections in dexterous postural control might manifest in temporal correlations, specifically as fractional Brownian motions whose differences are more and less correlated with fractional Gaussian noises (fGns) with progressively larger and smaller Hurst exponent H. Traditional empirical work examines this arrangement of lower-dimensional compression of CoP along two orthogonal axes, anteroposterior (AP) and mediolateral (ML). Eyes-open and face-forward orientations cultivate greater variability along AP than ML axes, and the orthogonal distribution of spatial variability has so far gone hand in hand with an orthogonal distribution of H, for example, larger in AP and lower in ML. However, perturbing the orientation of task focus might destabilize the postural synergy away from its 1D distribution and homogenize the temporal correlations across the 2D support surface, resulting in narrower angles between the directions of the largest and smallest H. We used oriented fractal scaling component analysis (OFSCA) to investigate whether sensory corrections in postural control might thus become suborthogonal. OFSCA models raw 2D CoP trajectory by decomposing it in all directions along the 2D support surface and fits the directions with the largest and smallest H. We studied a sample of gymnasts in eyes-open and face-forward quiet posture, and results from OFSCA confirm that such posture exhibits the classic orthogonal distribution of temporal correlations. Head-turning resulted in a simultaneous decrease in this angle Δθ, which promptly reversed once gymnasts reoriented their heads forward. However, when vision was absent, there was only a discernible negative trend in Δθ, indicating a shift in the angle's direction but not a statistically significant one. Thus, the narrowing of Δθ may signify an adaptive strategy in postural control. The swift recovery of Δθ upon returning to a forward-facing posture suggests that the temporary reduction is specific to head-turning and does not impose a lasting burden on postural control. Turning the head reduced the angle between these two orientations, facilitating the release of postural degrees of freedom towards a more uniform spread of the CoP across both dimensions of the support surface. The innovative aspect of this work is that it shows how fractality might serve as a control parameter of adaptive mechanisms of dexterous postural control.

Resting-state fractal brain connectivity is associated with impaired cognitive performance in healthy aging

Aging affects cognitive functions even in the absence of ongoing pathologies. The neurophysiological basis of age-related cognitive decline (CD), however, is not completely understood. Alterations in both functional brain connectivity and in the fractal scaling of neuronal dynamics have been linked to aging and cognitive performance. Recently, fractal connectivity (FrC) has been proposed - combining the two concepts - for capturing long-term interactions among brain regions. FrC was shown to be influenced by increased mental workload; however, no prior studies investigated how resting-state FrC relates to cognitive performance and plausible CD in healthy aging. We recruited 19 healthy elderly (HE) and 24 young control (YC) participants, who underwent resting-state electroencephalography (EEG) measurements and comprehensive cognitive evaluation using 7 tests of the Cambridge Neurophysiological Test Automated Battery. FrC networks were reconstructed from EEG data using the recently introduced multiple-resampling cross-spectral analysis (MRCSA). Elderly individuals could be characterized with increased response latency and reduced performance in 4-4 tasks, respectively, with both reaction time and accuracy being affected in two tasks. Auto- and cross-spectral exponents - characterizing regional fractal dynamics and FrC, respectively, - were found reduced in HE when compared to YC over most of the cortex. Additionally, fractal scaling of frontoparietal connections expressed an inverse relationship with task performance in visual memory and sustained attention domains in elderly, but not in young individuals. Our results confirm that the fractal nature of brain connectivity - as captured by MRCSA - is affected in healthy aging. Furthermore, FrC appears as a sensitive neurophysiological marker of age-related CD.

Fingerprints of decreased cognitive performance on fractal connectivity dynamics in healthy aging

Analysis of brain functional connectivity (FC) could provide insight in how and why cognitive functions decline even in healthy aging (HA). Despite FC being established as fluctuating over time even in the resting state (RS), dynamic functional connectivity (DFC) studies involving healthy elderly individuals and assessing how these patterns relate to cognitive performance are yet scarce. In our recent study we showed that fractal temporal scaling of functional connections in RS is not only reduced in HA, but also predicts increased response latency and reduced task solving accuracy. However, in that work we did not address changes in the dynamics of fractal connectivity (FrC) strength itself and its plausible relationship with mental capabilities. Therefore, here we analyzed RS electroencephalography recordings of the same subject cohort as previously, consisting of 24 young and 19 healthy elderly individuals, who also completed 7 different cognitive tasks after data collection. Dynamic fractal connectivity (dFrC) analysis was carried out via sliding-window detrended cross-correlation analysis (DCCA). A machine learning method based on recursive feature elimination was employed to select the subset of connections most discriminative between the two age groups, identifying 56 connections that allowed for classifying participants with an accuracy surpassing 92%. Mean of DCCA was found generally increased, while temporal variability of FrC decreased in the elderly when compared to the young group. Finally, dFrC indices expressed an elaborate pattern of associations-assessed via Spearman correlation-with cognitive performance scores in both groups, linking fractal connectivity strength and variance to increased response latency and reduced accuracy in the elderly population. Our results provide further support for the relevance of FrC dynamics in understanding age-related cognitive decline and might help to identify potential targets for future intervention strategies.

Scale-Free Functional Brain Networks Exhibit Increased Connectivity, Are More Integrated and Less Segregated in Patients with Parkinson's Disease following Dopaminergic Treatment

Dopaminergic treatment (DT), the standard therapy for Parkinson's disease (PD), alters the dynamics of functional brain networks at specific time scales. Here, we explore the scale-free functional connectivity (FC) in the PD population and how it is affected by DT. We analyzed the electroencephalogram of: (i) 15 PD patients during DT (ON) and after DT washout (OFF) and (ii) 16 healthy control individuals (HC). We estimated FC using bivariate focus-based multifractal analysis, which evaluated the long-term memory ( H ( 2 ) ) and multifractal strength ( Δ H 15 ) of the connections. Subsequent analysis yielded network metrics (node degree, clustering coefficient and path length) based on FC estimated by H ( 2 ) or Δ H 15 . Cognitive performance was assessed by the Mini Mental State Examination (MMSE) and the North American Adult Reading Test (NAART). The node degrees of the Δ H 15 networks were significantly higher in ON, compared to OFF and HC, while clustering coefficient and path length significantly decreased. No alterations were observed in the H ( 2 ) networks. Significant positive correlations were also found between the metrics of H ( 2 ) networks and NAART scores in the HC group. These results demonstrate that DT alters the multifractal coupled dynamics in the brain, warranting the investigation of scale-free FC in clinical and pharmacological studies.

Tool Embodiment Is Reflected in Movement Multifractal Nonlinearity

Recent advances in neuroscience have linked dynamical systems theory to cognition. The main contention is that extended cognition relies on a unitary brain-body-tool system showing the expected signatures of interaction-dominance reflected in a multifractal behavior. This might be particularly relevant when it comes to understanding how the brain is able to embody a tool to perform a task. Here we applied the multifractal formalism to the dynamics of hand movement while one was performing a computer task (the herding task) using a mouse or its own hand as a tool to move an object on the screen. We applied a focus-based multifractal detrended fluctuation analysis to acceleration time series. Then, multifractal nonlinearity was assessed by comparing original series to a finite set of surrogates obtained after Iterated Amplitude Adjusted Fourier transformation, a method that removes nonlinear multiscale dependencies while preserving the linear structure of the time series. Both hand and mouse task execution demonstrated multifractal nonlinearity, a typical form of across-scales interactivity in cognitive control. In addition, a wider multifractal spectrum was observed in mouse condition, which might highlight a richer set of interactions when the cognitive system is extended to the embodied mouse. We conclude that the emergence of multifractal nonlinearity from a brain-body-tool system pleads for recent theories of radical tool embodiment. Multifractal nonlinearity may be a promising metric to appreciate how physical objects—but also virtual tools and potentially prosthetics—are efficiently embodied by the brain.

Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes

Assessing power-law cross-correlations between a pair - or among a set - of processes is of great significance in diverse fields of analyses ranging from neuroscience to financial markets. In most cases such analyses are computationally expensive and thus carried out offline once the entire signal is obtained. However, many applications - such as mental state monitoring or financial forecasting - call for fast algorithms capable of estimating scale-free coupling in real time. Detrended cross-correlation analysis (DCCA), a generalization of the detrended fluctuation analysis (DFA) to the bivariate domain, has been introduced as a method designed to quantify power-law cross-correlations between a pair of non-stationary signals. Later, in analogy with the Pearson cross-correlation coefficient, DCCA was adapted to the detrended cross-correlation coefficient (DCCC), however as of now no online algorithms were provided for either of these analysis techniques. Here we introduce a new formula for obtaining the scaling functions in real time for DCCA. Moreover, the formula can be generalized via matrix notation to obtain the scaling relationship between not only a pair of signals, but also all possible pairs among a set of signals at the same time. This includes parallel estimation of the DFA scaling function of each individual process as well, thus allowing also for real-time acquisition of DCCC. The proposed algorithm matches its offline variants in precision, while being substantially more efficient in terms of execution time. We demonstrate that the method can be utilized for mental state monitoring on multi-channel electroencephalographic recordings obtained in eyes-closed and eyes-open resting conditions.

Multiple-Resampling Cross-Spectral Analysis: An Unbiased Tool for Estimating Fractal Connectivity With an Application to Neurophysiological Signals

Investigating scale-free (i.e., fractal) functional connectivity in the brain has recently attracted increasing attention. Although numerous methods have been developed to assess the fractal nature of functional coupling, these typically ignore that neurophysiological signals are assemblies of broadband, arrhythmic activities as well as oscillatory activities at characteristic frequencies such as the alpha waves. While contribution of such rhythmic components may bias estimates of fractal connectivity, they are also likely to represent neural activity and coupling emerging from distinct mechanisms. Irregular-resampling auto-spectral analysis (IRASA) was recently introduced as a tool to separate fractal and oscillatory components in the power spectrum of neurophysiological signals by statistically summarizing the power spectra obtained when resampling the original signal by several non-integer factors. Here we introduce multiple-resampling cross-spectral analysis (MRCSA) as an extension of IRASA from the univariate to the bivariate case, namely, to separate the fractal component of the cross-spectrum between two simultaneously recorded neural signals by applying the same principle. MRCSA does not only provide a theoretically unbiased estimate of the fractal cross-spectrum (and thus its spectral exponent) but also allows for computing the proportion of scale-free coupling between brain regions. As a demonstration, we apply MRCSA to human electroencephalographic recordings obtained in a word generation paradigm. We show that the cross-spectral exponent as well as the proportion of fractal coupling increases almost uniformly over the cortex during the rest-task transition, likely reflecting neural desynchronization. Our results indicate that MRCSA can be a valuable tool for scale-free connectivity studies in characterizing various cognitive states, while it also can be generalized to other applications outside the field of neuroscience.