Spurious cross-frequency amplitude-amplitude coupling in nonstationary, nonlinear signals.

Recent studies of brain activities show that cross-frequency coupling (CFC) play an important role in memory and learning. Many measures have been proposed to investigate the CFC phenomenon, including the correlation between the amplitude envelopes of two brain waves at different frequencies - cross-frequency amplitude-amplitude coupling (AAC). In this short communication, we describe how nonstationary, nonlinear oscillatory signals may produce spurious cross-frequency AAC. Utilizing the empirical mode decomposition, we also propose a new method for assessment of AAC that can potentially reduce the effects of nonlinearity and nonstatonarity and, thus, help to avoid the detection of artificial AACs. We compare the performances of this new method and the traditional Fourier-based AAC method. We also discuss the strategies to identify potential spurious AACs.

[1]  Kang K. L. Liu,et al.  Network Physiology: How Organ Systems Dynamically Interact , 2015, PloS one.

[2]  Norden E. Huang,et al.  On Hilbert Spectral Representation: a True Time-Frequency Representation for nonlinear and nonstationary Data , 2011, Adv. Data Sci. Adapt. Anal..

[3]  Men-Tzung Lo,et al.  Novel application of a Wii remote to measure spasticity with the pendulum test: Proof of concept. , 2016, Gait & posture.

[4]  H Eugene Stanley,et al.  Spurious detection of phase synchronization in coupled nonlinear oscillators. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Gang Wang,et al.  On Intrinsic Mode Function , 2010, Adv. Data Sci. Adapt. Anal..

[6]  Chung-Kang Peng,et al.  Posturo-respiratory synchronization: effects of aging and stroke. , 2012, Gait & posture.

[7]  M. Berger,et al.  High Gamma Power Is Phase-Locked to Theta Oscillations in Human Neocortex , 2006, Science.

[8]  A. Schnitzler,et al.  Normal and pathological oscillatory communication in the brain , 2005, Nature Reviews Neuroscience.

[9]  Jeffrey M. Hausdorff,et al.  Fractal dynamics in physiology: Alterations with disease and aging , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[10]  H. Eichenbaum,et al.  Measuring phase-amplitude coupling between neuronal oscillations of different frequencies. , 2010, Journal of neurophysiology.

[11]  Alexei L. Vyssotski,et al.  Selective Coupling between Theta Phase and Neocortical Fast Gamma Oscillations during REM-Sleep in Mice , 2011, PloS one.

[12]  T. Buchman.  The community of the self , 2002, Nature.

[13]  Yi-Lwun Ho,et al.  Outlier-resilient complexity analysis of heartbeat dynamics , 2015, Scientific Reports.

[14]  Josef Parvizi,et al.  Dynamic Changes in Phase-Amplitude Coupling Facilitate Spatial Attention Control in Fronto-Parietal Cortex , 2014, PLoS biology.

[15]  Po-Lei Lee,et al.  Quantifying Spasticity With Limited Swinging Cycles Using Pendulum Test Based on Phase Amplitude Coupling , 2016, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[16]  Amir Bashan,et al.  Network physiology reveals relations between network topology and physiological function , 2012, Nature Communications.

[17]  Biyu J. He,et al.  The Temporal Structures and Functional Significance of Scale-free Brain Activity , 2010, Neuron.

[18]  D. Colella,et al.  Brain chirps: spectrographic signatures of epileptic seizures , 2000, Clinical Neurophysiology.

[19]  Kun Hu,et al.  Multimodal Pressure-Flow Analysis: Application of Hilbert Huang Transform in Cerebral Blood Flow Regulation , 2008, EURASIP J. Adv. Signal Process..

[20]  Kun Hu,et al.  Reduction of scale invariance of activity fluctuations with aging and Alzheimer's disease: Involvement of the circadian pacemaker , 2009, Proceedings of the National Academy of Sciences.

[21]  Thomas Penzel,et al.  Phase transitions in physiologic coupling , 2012, Proceedings of the National Academy of Sciences.

[22]  Thomas Penzel,et al.  Cross-modulated amplitudes and frequencies characterize interacting components in complex systems. , 2009, Physical review letters.

[23]  Boris Podobnik,et al.  Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes , 2007, 0709.0838.

[24]  H Eugene Stanley,et al.  Cross-correlation of instantaneous phase increments in pressure-flow fluctuations: applications to cerebral autoregulation. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Adriano B. L. Tort,et al.  Sharp edge artifacts and spurious coupling in EEG frequency comodulation measures , 2008, Journal of Neuroscience Methods.

[26]  B. McNaughton,et al.  EEG sharp waves and sparse ensemble unit activity in the macaque hippocampus. , 2007, Journal of neurophysiology.

[27]  Yung-Hung Wang,et al.  On the computational complexity of the empirical mode decomposition algorithm , 2014 .

[28]  H. E. Hurst,et al.  Long-Term Storage Capacity of Reservoirs , 1951 .

[29]  R. G. Medhurst,et al.  Topics in the Theory of Random Noise , 1969 .

[30]  M. Shapiro,et al.  Bidirectional changes to hippocampal theta–gamma comodulation predict memory for recent spatial episodes , 2010, Proceedings of the National Academy of Sciences.

[31]  Men-Tzung Lo,et al.  Suprachiasmatic neuron numbers and rest–activity circadian rhythms in older humans , 2015, Annals of neurology.

[32]  Johanna H Meijer,et al.  Lack of exercise leads to significant and reversible loss of scale invariance in both aged and young mice , 2015, Proceedings of the National Academy of Sciences.

[33]  Markus Siegel,et al.  Phase-dependent neuronal coding of objects in short-term memory , 2009, Proceedings of the National Academy of Sciences.

[34]  Boris Podobnik,et al.  Detrended cross-correlation analysis for non-stationary time series with periodic trends , 2011 .

[35]  Jerry Cavallerano,et al.  Altered Phase Interactions between Spontaneous Blood Pressure and Flow Fluctuations in Type 2 Diabetes Mellitus: Nonlinear Assessment of Cerebral Autoregulation. , 2008, Physica A.

[36]  Norden E. Huang,et al.  Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method , 2009, Adv. Data Sci. Adapt. Anal..

[37]  Men-Tzung Lo,et al.  Nonlinear phase interaction between nonstationary signals: a comparison study of methods based on Hilbert-Huang and Fourier transforms. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Kun Hu,et al.  A Nonlinear Dynamic Approach Reveals a Long-Term Stroke Effect on Cerebral Blood Flow Regulation at Multiple Time Scales , 2012, PLoS Comput. Biol..

[39]  J. Fell,et al.  Cross-frequency coupling supports multi-item working memory in the human hippocampus , 2010, Proceedings of the National Academy of Sciences.

[40]  Men-Tzung Lo,et al.  Nonlinear pressure-flow relationship is able to detect asymmetry of brain blood circulation associated with midline shift. , 2009, Journal of neurotrauma.

[41]  H. Stanley,et al.  Quantifying cross-correlations using local and global detrending approaches , 2009 .

[42]  Kun Hu,et al.  Detecting phase-amplitude coupling with high frequency resolution using adaptive decompositions , 2014, Journal of Neuroscience Methods.

[43]  R. Knight,et al.  The functional role of cross-frequency coupling , 2010, Trends in Cognitive Sciences.

[44]  Men-Tzung Lo,et al.  Investigating the interaction between heart rate variability and sleep EEG using nonlinear algorithms , 2013, Journal of Neuroscience Methods.

[45]  Kun Hu,et al.  Noninvasive fractal biomarker of clock neurotransmitter disturbance in humans with dementia , 2013, Scientific Reports.

[46]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[47]  Marek Czosnyka,et al.  Nonlinear Assessment of Cerebral Autoregulation from Spontaneous Blood Pressure and Cerebral Blood Flow Fluctuations , 2008, Cardiovascular engineering.

[48]  Bryan C. Souza,et al.  Theta-associated high-frequency oscillations (110–160Hz) in the hippocampus and neocortex , 2013, Progress in Neurobiology.

[49]  U. Stephani,et al.  Detection and characterization of changes of the correlation structure in multivariate time series. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  Men-Tzung Lo,et al.  Detrended fluctuation analysis predicts successful defibrillation for out-of-hospital ventricular fibrillation cardiac arrest. , 2010, Resuscitation.