Multifractal Detrended Fluctuation Analysis of Human EEG: Preliminary Investigation and Comparison with the Wavelet Transform Modulus Maxima Technique

Zorick, Todd; Mandelkern, M.

doi:10.1371/journal.pone.0068360

Cited by 105 publications

(79 citation statements)

References 42 publications

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“…The MF-DFA method is the generalization of detrended fluctuation analysis (DFA) [5] and has been widely applied to characterize the properties of various non-stationary time series in different fields such as financial market [23–32], physiology [33], biology [34], traffic jamming [35], geophysics [36] and neuroscience [37]. …”

Section: Methodsmentioning

confidence: 99%

Multifractality and Network Analysis of Phase Transition

Bai¹,

Li²,

Yang³

et al. 2017

PLoS ONE

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Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems.

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Section: Methodsmentioning

confidence: 99%

Multifractality and Network Analysis of Phase Transition

Bai¹,

Li²,

Yang³

et al. 2017

PLoS ONE

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“…Multifractal dynamics are exhibited by complex systems, like the brain (Di Ieva et al, 2013a, 2013b) from macroscopic brain oscillations (Ciuciu et al, 2012; Zorick and Mandelkern, 2013) to an intermediate scale of neuronal spiking (Biella et al, 1999) and to the microscopic scale ion channel fluctuations (Brazhe and Maksimov, 2006). To investigate complex interactions on the intermediate scale, a time series was constructed from the action potential timestamps recorded from individual hippocampal principal cells (CA3 and CA1).…”

Section: Resultsmentioning

confidence: 99%

Multifractal analysis of information processing in hippocampal neural ensembles during working memory under Δ9-tetrahydrocannabinol administration

Fetterhoff

Opriş

Simpson

et al. 2015

Journal of Neuroscience Methods

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Background Multifractal analysis quantifies the time-scale-invariant properties in data by describing the structure of variability over time. By applying this analysis to hippocampal interspike interval sequences recorded during performance of a working memory task, a measure of long-range temporal correlations and multifractal dynamics can reveal single neuron correlates of information processing. New method Wavelet leaders-based multifractal analysis (WLMA) was applied to hippocampal interspike intervals recorded during a working memory task. WLMA can be used to identify neurons likely to exhibit information processing relevant to operation of brain–computer interfaces and nonlinear neuronal models. Results Neurons involved in memory processing (“Functional Cell Types” or FCTs) showed a greater degree of multifractal firing properties than neurons without task-relevant firing characteristics. In addition, previously unidentified FCTs were revealed because multifractal analysis suggested further functional classification. The cannabinoid-type 1 receptor partial agonist, tetrahydrocannabinol (THC), selectively reduced multifractal dynamics in FCT neurons compared to non-FCT neurons. Comparison with existing methods WLMA is an objective tool for quantifying the memory-correlated complexity represented by FCTs that reveals additional information compared to classification of FCTs using traditional z-scores to identify neuronal correlates of behavioral events. Conclusion z-Score-based FCT classification provides limited information about the dynamical range of neuronal activity characterized by WLMA. Increased complexity, as measured with multifractal analysis, may be a marker of functional involvement in memory processing. The level of multifractal attributes can be used to differentially emphasize neural signals to improve computational models and algorithms underlying brain–computer interfaces.

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“…During years different works have been reported in literatures which focused on analysis of neurophysiological time series using fractal theories [1][2][3][4][5][6][7][8][9][10]. In a recent work on prediction of epileptic seizure onset we proposed a new methodology which is based on studying the EEG signals using two measures, the Hurst exponent and fractal dimension.…”

Section: Hamidreza Namazimentioning

confidence: 99%

Fractal Based Analysis, Modeling and Prediction of Neurophysiological Time Series

2016

ARC Journal of Neuroscience

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Neurophysiology is a branch of physiology and neuroscience that is concerned with the study of the functioning of the nervous system. Neurophysiological time series are signal shaped time series which are governed from different processes that are related to nervous system. The most important neurophysiological time series which is directly related to the activity of the nervous system is the EEG signal. Besides EEG time series there are some other neurophysiological signals which are indirectly related to the activity of the nervous system. For instance, the respiratory signal is another type of neurophysiological time series which is governed from the process of the nervous system. In fact, ventilation occurs under the control of the autonomic nervous system from the medulla oblongata and the pons in the brainstem. These areas of the brain form the respiration regulatory center, a series of interconnected brain cells within the lower and middle brain stem which coordinate respiratory movements. We can call other types of neurophysiological time series such as fixational eye movements time series, etc. Analysis, modeling and prediction of neurophysiological time series always have been an important issue between researchers. One of the most important aspects of these modeling and analysis has been from mathematical point of view. In fact, using mathematics for the modeling purpose helps scientists to investigate precisely about the processes. Employing mathematical models can help them in forecasting the processes in the next step where the biological modeling cannot help. Fractals are scale-invariant geometric objects. A scale invariant object can be self-similar or selfaffine. A self-similar object is a union of rescaled copies of itself which is isotropic or uniform in all directions. But in case of self-affine objects, the mechanism is an isotropic or dependent on the direction. Regular fractals have higher self-similarity, but random fractals have a weaker selfsimilarity. The class of regular fractals includes many familiar simple objects, such as line intervals, solid squares, and solid cubes, and also many irregular objects. The scaling rules are characterized by "scaling exponents" (dimension). "Simple" regular fractals have integer scaling dimensions. Complex self-similar objects have non-integer dimension. Therefore, it is completely incorrect to define fractals as geometric objects having "fractional" (non-integer) dimension. Fractals maybe defined as geometric objects whose scaling exponent (dimension) satisfies the Szpilrajn inequality:ℵ ≥ (1) where ℵ is the scaling exponent (dimension) of the object and is its topological dimension, i.e., Euclidean dimension of units from which the fractal object is built. For example, in case of Brownian motion: the path of a particle, a line of dimension one, traveling for a long time over a plane region, eventually covers the entire plane, an entity of dimension two. In case of multi fractal system a single fractal dimension cannot describe its dynamics. In thi...

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Multifractal Detrended Fluctuation Analysis of Human EEG: Preliminary Investigation and Comparison with the Wavelet Transform Modulus Maxima Technique

Cited by 105 publications

References 42 publications

Multifractality and Network Analysis of Phase Transition

Multifractality and Network Analysis of Phase Transition

Multifractal analysis of information processing in hippocampal neural ensembles during working memory under Δ9-tetrahydrocannabinol administration

Fractal Based Analysis, Modeling and Prediction of Neurophysiological Time Series

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