Detection of quadratic phase coupling by cross-bicoherence and spectral Granger causality in bifrequencies interactions

Abstract

Quadratic Phase Coupling (QPC) is a crucial statistical tool for assessing nonlinear synchronization within multivariate time series data, particularly within signal processing and neuroscience. This study delves into the accuracy of QPC detection by employing numerical estimates through cross-bicoherence and bivariate Granger causality within a simple yet noisy instantaneous multiplier model. The investigation extends to evaluating the influence of incidental statistically significant bifrequency interactions, introducing key metrics such as the ratio of bispectral quadratic phase coupling and the ratio of bivariate Granger causality quadratic phase coupling, with values close to 1 indicating high level of accuracy in QPC detection. The model is tested using 334 electroencephalographic recordings, encompassing diverse carrier frequencies to explore an extensive array of scenarios. The coupling strength between interacting channels emerges as a pivotal factor introducing nonlinearities that affect the signal-to-noise ratio in the output channel. The bispectral approach outperformed bivariate Granger causality, particularly at weak coupling strengths and with noise biases. Especially noteworthy is cross-bicoherence’s effectiveness in detecting QPC in cases of very weak couplings, making it a reliable method for unveiling subtle nonlinear interactions in noisy signals, a common scenario in brain activity recordings.