Surrogate Data Method Requires End-Matched Segmentation of Electroencephalographic Signals to Estimate Non-linearity

The aim of the study is to clarify the impact of the strong cyclic signal component on the results of surrogate data method in the case of resting electroencephalographic (EEG) signals. In addition, the impact of segment length is analyzed. Different non-linear measures (fractality, complexity, etc.) of neural signals have been demonstrated to be useful to infer the non-linearity of brain functioning from EEG. The surrogate data method is often applied to test whether or not the non-linear structure can be captured from the data. In addition, a growing number of studies are using surrogate data method to determine the statistical threshold of connectivity values in network analysis. Current study focuses on the conventional segmentation of EEG signals, which could lead to false results of surrogate data method. More specifically, the necessity to use end-matched segments that contain an integer number of dominant frequency periods is studied. EEG recordings from 80 healthy volunteers during eyes-closed resting state were analyzed using multivariate surrogate data method. The artificial surrogate data were generated by shuffling the phase spectra of original signals. The null hypothesis that time series were generated by a linear process was rejected by statistically comparing the non-linear statistics calculated for original and surrogate data sets. Five discriminating statistics were used as non-linear estimators: Higuchi fractal dimension (HFD), Katz fractal dimension (KFD), Lempel-Ziv complexity (LZC), sample entropy (SampEn) and synchronization likelihood (SL). The results indicate that the number of segments evaluated as non-linear differs in the case of various non-linear measures and changes with the segment length. The main conclusion is that the dependence on the deviation of the segment length from full periods of dominant EEG frequency has non-monotonic character and causes misleading results in the evaluation of non-linearity. Therefore, in the case of the signals with non-monotonic spectrum and strong dominant frequency, the correct use of surrogate data method requires the signal length comprising of full periods of the spectrum dominant frequency. The study is important to understand the influence of incorrect selection of EEG signal segment length for surrogate data method to estimate non-linearity.

[1]  R. Acharya U,et al.  Nonlinear analysis of EEG signals at different mental states , 2004, Biomedical engineering online.

[2]  Eckehard Olbrich,et al.  Dynamics of human sleep EEG , 2003, Neurocomputing.

[3]  Hee Chan Kim,et al.  Automated network analysis to measure brain effective connectivity estimated from EEG data of patients with alcoholism , 2017, Physiological measurement.

[4]  Theiler,et al.  Generating surrogate data for time series with several simultaneously measured variables. , 1994, Physical review letters.

[5]  Shanbao Tong,et al.  Phase synchronization analysis of EEG signals: an evaluation based on surrogate tests. , 2012, IEEE transactions on bio-medical engineering.

[6]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[7]  H. Hinrikus,et al.  Dependence of the EEG Nonlinear Coupling on the Frequency Bands and the Segment Lengths , 2017 .

[8]  Cornelis J. Stam,et al.  Reliable detection of nonlinearity in experimental time series with strong periodic components , 1998 .

[9]  Shanbao Tong,et al.  Phase Synchronization Analysis of EEG Signals: An Evaluation Based on Surrogate Tests , 2012, IEEE Transactions on Biomedical Engineering.

[10]  Roberto Hornero,et al.  Nonlinear analysis of electroencephalogram and magnetoencephalogram recordings in patients with Alzheimer's disease , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[11]  P. Garc,et al.  Analysis of EEG Signals using Nonlinear Dynamics and Chaos: A review , 2015 .

[12]  D. Yao,et al.  A method to standardize a reference of scalp EEG recordings to a point at infinity , 2001, Physiological measurement.

[13]  Slađana Spasić,et al.  Surrogate data test for nonlinearity of the rat cerebellar electrocorticogram in the model of brain injury , 2010, Signal Process..

[14]  Jens Timmer,et al.  Power of surrogate data testing with respect to nonstationarity , 1998, chao-dyn/9807039.

[15]  Ioannis Tarnanas,et al.  Topological Filtering of Dynamic Functional Brain Networks Unfolds Informative Chronnectomics: A Novel Data-Driven Thresholding Scheme Based on Orthogonal Minimal Spanning Trees (OMSTs) , 2017, Front. Neuroinform..

[16]  Nina F. Thornhill,et al.  Finding the source of nonlinearity in a process with plant-wide oscillation , 2005, IEEE Transactions on Control Systems Technology.

[17]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[18]  Abraham Lempel,et al.  On the Complexity of Finite Sequences , 1976, IEEE Trans. Inf. Theory.

[19]  George Zouridakis,et al.  Functional connectivity changes detected with magnetoencephalography after mild traumatic brain injury , 2015, NeuroImage: Clinical.

[20]  Brian Litt,et al.  A comparison of waveform fractal dimension algorithms , 2001 .

[21]  J. R. Moorman,et al.  Accurate estimation of entropy in very short physiological time series: the problem of atrial fibrillation detection in implanted ventricular devices. , 2011, American journal of physiology. Heart and circulatory physiology.

[22]  Roberto Cavoretto,et al.  Two and Three Dimensional Partition of Unity Interpolation by Product-Type Functions , 2015 .

[23]  Michael Small,et al.  Surrogate Test for Pseudoperiodic Time Series Data , 2001 .

[24]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[25]  M. J. Katz,et al.  Fractals and the analysis of waveforms. , 1988, Computers in biology and medicine.

[26]  Hiie Hinrikus,et al.  Lempel-Ziv and multiscale Lempel-Ziv complexity in depression , 2015, 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[27]  C. Stam,et al.  Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets , 2002 .

[28]  F. Zappasodi,et al.  Comparison of connectivity analyses for resting state EEG data , 2017, Journal of neural engineering.

[29]  Cornelis J. Stam,et al.  Synchronization likelihood with explicit time-frequency priors , 2006, NeuroImage.

[30]  Chi K. Tse,et al.  Applying the method of surrogate data to cyclic time series , 2002 .

[31]  T. Higuchi.  Approach to an irregular time series on the basis of the fractal theory , 1988 .

[32]  John R. Terry,et al.  Detection and description of non-linear interdependence in normal multichannel human EEG data , 2002, Clinical Neurophysiology.