Identifying dynamic transactions between brain regions has become increasingly important. Measurements within and across brain structures, demonstrating the occurrence of bursts of beta/gamma oscillations only during one specific phase of each theta/alpha cycle, have motivated the need to advance beyond linear and stationary time series models. Here we offer a novel measure, namely, the "dual frequency RV-coupling coefficient", for assessing different types of frequency-frequency interactions that subserve information flow in the brain. This is a measure of coherence between two complex-valued vectors, consisting of the set of Fourier coefficients for two different frequency bands, within or across two brain regions. RV-coupling is expressed in terms of instantaneous and lagged components. Furthermore, by using normalized Fourier coefficients (unit modulus), phase-type couplings can also be measured. The dual frequency RV-coupling coefficient is based on previous work: the second order bispectrum, i.e. the dual-frequency coherence (Thomson 1982; Haykin & Thomson 1998); the RV-coefficient (Escoufier 1973); Gorrostieta et al (2012); and Pascual-Marqui et al (2011). This paper presents the new measure, and outlines relevant statistical tests. The novel aspects of the "dual frequency RV-coupling coefficient" are: (1) it can be applied to two multivariate time series; (2) the method is not limited to single discrete frequencies, and in addition, the frequency bands are treated by means of appropriate multivariate statistical methodology; (3) the method makes use of a novel generalization of the RV-coefficient for complex-valued multivariate data; (4) real and imaginary covariance contributions to the RV-coherence are obtained, allowing the definition of a "lagged-coupling" measure that is minimally affected by the low spatial resolution of estimated cortical electric neuronal activity.

Pascual-Marqui, R D; Faber, Pascal L; Kinoshita, T; Kitaura, Y; Kochi, Kieko; Milz, Patricia; Nishida, K; Yoshimura, M (2016). *The dual frequency RV-coupling coefficient: a novel measure for quantifying cross-frequency information transactions in the brain.* Quantitative Biology > Neurons and Cognition 1603, University of Zurich.

## Abstract

Identifying dynamic transactions between brain regions has become increasingly important. Measurements within and across brain structures, demonstrating the occurrence of bursts of beta/gamma oscillations only during one specific phase of each theta/alpha cycle, have motivated the need to advance beyond linear and stationary time series models. Here we offer a novel measure, namely, the "dual frequency RV-coupling coefficient", for assessing different types of frequency-frequency interactions that subserve information flow in the brain. This is a measure of coherence between two complex-valued vectors, consisting of the set of Fourier coefficients for two different frequency bands, within or across two brain regions. RV-coupling is expressed in terms of instantaneous and lagged components. Furthermore, by using normalized Fourier coefficients (unit modulus), phase-type couplings can also be measured. The dual frequency RV-coupling coefficient is based on previous work: the second order bispectrum, i.e. the dual-frequency coherence (Thomson 1982; Haykin & Thomson 1998); the RV-coefficient (Escoufier 1973); Gorrostieta et al (2012); and Pascual-Marqui et al (2011). This paper presents the new measure, and outlines relevant statistical tests. The novel aspects of the "dual frequency RV-coupling coefficient" are: (1) it can be applied to two multivariate time series; (2) the method is not limited to single discrete frequencies, and in addition, the frequency bands are treated by means of appropriate multivariate statistical methodology; (3) the method makes use of a novel generalization of the RV-coefficient for complex-valued multivariate data; (4) real and imaginary covariance contributions to the RV-coherence are obtained, allowing the definition of a "lagged-coupling" measure that is minimally affected by the low spatial resolution of estimated cortical electric neuronal activity.

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## Additional indexing

Item Type: | Working Paper |
---|---|

Communities & Collections: | 04 Faculty of Medicine > Psychiatric University Hospital Zurich > Clinic for Psychiatry, Psychotherapy, and Psychosomatics
04 Faculty of Medicine > The KEY Institute for Brain-Mind Research |

Dewey Decimal Classification: | 610 Medicine & health |

Language: | English |

Date: | 17 March 2016 |

Deposited On: | 22 Mar 2016 16:36 |

Last Modified: | 05 Apr 2016 20:11 |

Series Name: | Quantitative Biology > Neurons and Cognition |

Number of Pages: | 14 |

Free access at: | Related URL. An embargo period may apply. |

Related URLs: | http://arxiv.org/abs/1603.05343 |

Other Identification Number: | arXiv:1603.05343 [q-bio.NC] |

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