Toward a proper estimation of phase–amplitude coupling in neural oscillations

BACKGROUND The phase-amplitude coupling (PAC) between distinct neural oscillations is critical to brain functions that include cross-scale organization, selection of attention, routing the flow of information through neural circuits, memory processing and information coding. Several methods for PAC estimation have been proposed but the limitations of PAC estimation as well as the assumptions about the data for accurate PAC estimation are unclear. NEW METHOD We define boundary conditions for standard PAC algorithms and propose "oscillation-triggered coupling" (OTC), a parameter-free, data-driven algorithm for unbiased estimation of PAC. OTC establishes a unified framework that treats individual oscillations as discrete events for estimating PAC from a set of oscillations and for characterizing events from time windows as short as a single modulating oscillation. RESULTS For accurate PAC estimation, standard PAC algorithms require amplitude filters with a bandwidth at least twice the modulatory frequency. The phase filters must be moderately narrow-band, especially when the modulatory rhythm is non-sinusoidal. The minimally appropriate analysis window is ∼10s. We then demonstrate that OTC can characterize PAC by treating neural oscillations as discrete events rather than continuous phase and amplitude time series. COMPARISON WITH EXISTING METHODS These findings show that in addition to providing the same information about PAC as the standard approach, OTC facilitates characterization of single oscillations and their sequences, in addition to explaining the role of individual oscillations in generating PAC patterns. CONCLUSIONS OTC allows PAC analysis at the level of individual oscillations and therefore enables investigation of PAC at the time scales of cognitive phenomena.

[1]  Sonja Grün,et al.  How local is the local field potential? , 2011, BMC Neuroscience.

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

[3]  Adriano B. L. Tort,et al.  Theta–gamma coupling increases during the learning of item–context associations , 2009, Proceedings of the National Academy of Sciences.

[4]  J. Csicsvari,et al.  Oscillatory Coupling of Hippocampal Pyramidal Cells and Interneurons in the Behaving Rat , 1999, The Journal of Neuroscience.

[5]  Christoph von der Malsburg,et al.  The Correlation Theory of Brain Function , 1994 .

[6]  J. Csicsvari,et al.  Organization of cell assemblies in the hippocampus , 2003, Nature.

[7]  Song Liu,et al.  Variable Bandwidth Filtering for Improved Sensitivity of Cross-Frequency Coupling Metrics , 2012, Brain Connect..

[8]  A. Fenton,et al.  Key Features of Human Episodic Recollection in the Cross-Episode Retrieval of Rat Hippocampus Representations of Space , 2013, PLoS biology.

[9]  W. Penny,et al.  Testing for nested oscillation , 2008, Journal of Neuroscience Methods.

[10]  C. Schroeder,et al.  Low-frequency neuronal oscillations as instruments of sensory selection , 2009, Trends in Neurosciences.

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

[12]  György Buzsáki,et al.  Neural Syntax: Cell Assemblies, Synapsembles, and Readers , 2010, Neuron.

[13]  W. Singer,et al.  Dysfunctional Long-Range Coordination of Neural Activity during Gestalt Perception in Schizophrenia , 2006, The Journal of Neuroscience.

[14]  Hindiael Belchior,et al.  On High-Frequency Field Oscillations (>100 Hz) and the Spectral Leakage of Spiking Activity , 2013, The Journal of Neuroscience.

[15]  Ankoor S. Shah,et al.  An oscillatory hierarchy controlling neuronal excitability and stimulus processing in the auditory cortex. , 2005, Journal of neurophysiology.

[16]  William W Lytton,et al.  Unmasking the CA1 Ensemble Place Code by Exposures to Small and Large Environments: More Place Cells and Multiple, Irregularly Arranged, and Expanded Place Fields in the Larger Space , 2008, The Journal of Neuroscience.

[17]  Jose M Hurtado,et al.  Statistical method for detection of phase-locking episodes in neural oscillations. , 2004, Journal of neurophysiology.

[18]  Adriano B. L. Tort,et al.  On cross-frequency phase-phase coupling between theta and gamma oscillations in the hippocampus , 2016, eLife.

[19]  W. Singer,et al.  Temporal binding and the neural correlates of sensory awareness , 2001, Trends in Cognitive Sciences.

[20]  L W Leung,et al.  Spectral analysis of hippocampal unit train in relation to hippocampal EEG. , 1983, Electroencephalography and clinical neurophysiology.

[21]  R. Knight,et al.  Shifts in Gamma Phase–Amplitude Coupling Frequency from Theta to Alpha Over Posterior Cortex During Visual Tasks , 2010, Front. Hum. Neurosci..

[22]  G. Buzsáki,et al.  Cellular bases of hippocampal EEG in the behaving rat , 1983, Brain Research Reviews.

[23]  Christof Koch,et al.  The Spiking Component of Oscillatory Extracellular Potentials in the Rat Hippocampus , 2012, The Journal of Neuroscience.

[24]  Adriano B. L. Tort,et al.  Dynamic cross-frequency couplings of local field potential oscillations in rat striatum and hippocampus during performance of a T-maze task , 2008, Proceedings of the National Academy of Sciences.

[25]  T. Hafting,et al.  Frequency of gamma oscillations routes flow of information in the hippocampus , 2009, Nature.

[26]  G. Buzsáki,et al.  Neuronal Oscillations in Cortical Networks , 2004, Science.

[27]  A. Fenton,et al.  Dynamic Grouping of Hippocampal Neural Activity During Cognitive Control of Two Spatial Frames , 2010, PLoS biology.

[28]  O. Jensen,et al.  Cross-frequency coupling between neuronal oscillations , 2007, Trends in Cognitive Sciences.

[29]  G. Buzsáki,et al.  Hippocampal network patterns of activity in the mouse , 2003, Neuroscience.

[30]  G. Buzsáki,et al.  Gamma (40-100 Hz) oscillation in the hippocampus of the behaving rat , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[31]  W. Freeman,et al.  Frequency analysis of olfactory system EEG in cat, rabbit, and rat. , 1980, Electroencephalography and clinical neurophysiology.

[32]  Ch. von der Malsburg,et al.  A neural cocktail-party processor , 1986, Biological Cybernetics.

[33]  Michael X Cohen,et al.  Assessing transient cross-frequency coupling in EEG data , 2008, Journal of Neuroscience Methods.

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

[35]  G. Buzsáki,et al.  Theta Oscillations Provide Temporal Windows for Local Circuit Computation in the Entorhinal-Hippocampal Loop , 2009, Neuron.

[36]  M. Quyen The brainweb of cross-scale interactions , 2011 .

[37]  O. Bertrand,et al.  Oscillatory gamma-band (30-70 Hz) activity induced by a visual search task in humans. , 1997, The Journal of neuroscience : the official journal of the Society for Neuroscience.

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

[39]  J. Pernier,et al.  Oscillatory γ-Band (30–70 Hz) Activity Induced by a Visual Search Task in Humans , 1997, The Journal of Neuroscience.

[40]  Andrey V. Olypher,et al.  Cognitive Disorganization in Hippocampus: A Physiological Model of the Disorganization in Psychosis , 2006, The Journal of Neuroscience.

[41]  G. Buzsáki,et al.  Gamma Oscillations in the Entorhinal Cortex of the Freely Behaving Rat , 1998, The Journal of Neuroscience.

[42]  W. Singer,et al.  In search of common foundations for cortical computation , 1997, Behavioral and Brain Sciences.

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

[44]  Sean M Montgomery,et al.  Relationships between Hippocampal Sharp Waves, Ripples, and Fast Gamma Oscillation: Influence of Dentate and Entorhinal Cortical Activity , 2011, The Journal of Neuroscience.

[45]  L Kellényi,et al.  Depth profiles of hippocampal rhythmic slow activity ('theta rhythm') depend on behaviour. , 1985, Electroencephalography and clinical neurophysiology.

[46]  J. Martinerie,et al.  Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony , 2001, Journal of Neuroscience Methods.

[47]  J. Maunsell,et al.  Different Origins of Gamma Rhythm and High-Gamma Activity in Macaque Visual Cortex , 2011, PLoS biology.

[48]  J E Lisman,et al.  Storage of 7 +/- 2 short-term memories in oscillatory subcycles , 1995, Science.

[49]  Arnaud Delorme,et al.  EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis , 2004, Journal of Neuroscience Methods.

[50]  M. Besserve,et al.  Towards a proper estimation of phase synchronization from time series , 2006, Journal of Neuroscience Methods.

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