Characterizing the orientation selectivity in V1 and V4 of macaques by quadratic phase coupling

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

Quadratic Phase Coupling (QPC) serves as an essential statistical instrument for evaluating nonlinear synchronization within multivariate time series data, especially in signal processing and neuroscience fields. This study explores the precision of QPC detection using numerical estimates derived from cross-bicoherence and bivariate Granger causality within a straightforward, yet noisy, instantaneous multiplier model. It further assesses the impact of accidental statistically significant bifrequency interactions, introducing new metrics such as the ratio of bispectral quadratic phase coupling and the ratio of bivariate Granger causality quadratic phase coupling. Ratios nearing 1 signify a high degree of accuracy in detecting QPC. The coupling strength between interacting channels is identified as a key element that introduces nonlinearities, influencing the signal-to-noise ratio in the output channel. The model is tested across 59 experimental conditions of simulated recordings, with each condition evaluated against six coupling strength values, covering a wide range of carrier frequencies to examine a broad spectrum of scenarios. The findings demonstrate that the bispectral method outperforms bivariate Granger causality, particularly in identifying specific QPC under conditions of very weak couplings and in the presence of noise. The detection of specific QPC is crucial for neuroscience applications aimed at better understanding the temporal and spatial coordination between different brain regions.

Measuring Phase-Amplitude Coupling Based on the Jensen-Shannon Divergence and Correlation Matrix

Phase-amplitude coupling (PAC) measures the relationship between the phase of low-frequency oscillations (LFO) and the amplitude of high-frequency oscillations (HFO). It plays an important functional role in neural information processing and cognition. Thus, we propose a novel method based on the Jensen-Shannon (JS) divergence and correlation matrix. The method takes the amplitude distributions of the HFO located in the corresponding phase bins of the LFO as multichannel inputs to construct a correlation matrix, where the elements are calculated based on the JS divergence between pairs of amplitude distributions. Then, the omega complexity extracted from the correlation matrix is used to estimate the PAC strength. The simulation results demonstrate that the proposed method can effectively reflect the PAC strength and slightly vary with the data length. Moreover, it outperforms five frequently used algorithms in the performance against additive white Gaussian noise and spike noise and the ability of detecting PAC in wide frequency ranges. To validate our proposed method with real data, it was applied to analyze the local field potential recorded from the dorsomedial striatum in a male Sprague-Dawley rat. It can replicate previous results obtained with other PAC metrics. In conclusion, these results suggest that our proposed method is a powerful tool for measuring the PAC between neural oscillations.