Unraveling nonlinear electrophysiologic processes in the human visual system with full dimension spectral analysis

Abstract

Natural sensory signals have nonlinear structures dynamically composed of the carrier frequencies and the variation of the amplitude (i.e., envelope). How the human brain processes the envelope information is still poorly understood, largely due to the conventional analysis failing to quantify it directly. Here, we used a recently developed method, Holo-Hilbert spectral analysis, and steady-state visually evoked potential collected using electroencephalography (EEG) recordings to investigate how the human visual system processes the envelope of amplitude-modulated signals, in this case with a 14 Hz carrier and a 2 Hz envelope. The EEG results demonstrated that in addition to the fundamental stimulus frequencies, 4 Hz amplitude modulation residing in 14 Hz carrier and a broad range of carrier frequencies covering from 8 to 32 Hz modulated by 2 Hz amplitude modulation are also found in the two-dimensional frequency spectrum, which have not yet been recognized before. The envelope of the stimulus is also found to dominantly modulate the response to the incoming signal. The findings thus reveal that the electrophysiological response to amplitude-modulated stimuli is more complex than could be revealed by, for example, Fourier analysis. This highlights the dynamics of neural processes in the visual system.

A Hilbert-based method for processing respiratory timeseries

“…The Hilbert transform is convenient, but splitting one time-varying signal into two time-varying quantities is an underdetermined problem that admits different solutions [Boashash 1992a]. Similarly, the interactions between the two quantities can themselves carry meaningful information [Huang et al 2016;Nguyen et al 2019]. Therefore, it may be that other decompositions or regularisation strategies improve performance.…”

“…As we describe in more detail later, current methods typically characterise the recordings from respiratory bellows via peak detection, but this has issues in terms of both robustness and temporal resolution. Here, we use a decomposition based on the Hilbert-transform to characterise the respiratory recordings; this is a technique that has been more widely used in the context of characterising complex oscillatory waveforms from electrophysiological data [Brookes et al 2011;Hipp et al 2012;Luckhoo et al 2012;Engel et al 2013;Voytek et al 2013;Cole and Voytek 2017;Nguyen et al 2019]. The crucial link is that the quantities that we need to define RVT, breathing depth and rate, are simply the amplitude and (instantaneous) frequency of the breathing-related oscillation in the bellows recordings.…”

Waveform changes with the evolution of beta bursts in the human subthalamic nucleus

“…Computation of the EMD, unlike convolution filters such as Fourier and Wavelet decompositions, captures intra-waveform changes in IMFs without dispersing their waveform characteristics into higher-frequency decompositions (Wu et al, 2007;Yang et al, 2018;Yeh et al, 2016). This feature of IMFs enables decompositions that are virtually free from harmonic artifacts, an important characteristic when evaluating PAC (Lopes- Dos-Santos et al, 2018;Shi et al, 2018;Yeh et al, 2016;Nguyen et al, 2019;Pittman-Polletta et al, 2014;Aru et al, 2015). The broadband nature of IMFs which follows the dyadic filter bank also ensures that higher-frequency IMFs include information about amplitude modulation indicative of PAC (Flandrin et al, 2004;Pittman-Polletta et al, 2014).…”

Holo-Hilbert Spectral-based Noise Removal Method for EEG High-Frequency Bands

“…Then, the amplitude envelope of each of the IMFs is decomposed into a set of amplitude modulated IMFs (IMFs AM ), constituting the second layer. Although HHSA can go through multiple iterations until the amplitude functions bear no more cyclic characteristics in the envelopes, in practice only two iterations are performed [6,33,35,[37][38][39].…”

“…The HHSA method has been used in a number of EEG applications, including the examination of oscillatory brain activity and interactions amongst EEG frequency bands (alpha and beta bands) [6], the study of human visual system processing [37], and the derivation of time-frequency spectrum matrices to characterize sleep stages [39]. However, previous studies have not applied the second layer of EMD to the FM components of IMFs computed by the first layer; the AM frequency represents the slow-changing envelope of intermode frequency variations and can be used to analyze intermode interactions [6].…”