Slow Cortical Waves through Cyclicity Analysis

Abstract

Fine-grained information about dynamic structure of cortical networks is crucial in unpacking brain function. Here,we introduced a novel analytical method to characterize the dynamic interaction between distant brain regions,based on cyclicity analysis, and applied it to data from the Human Connectome Project. Resting-state fMRI time series are aperiodic and, hence, lack a base frequency. Cyclicity analysis, which is time-reparametrization invariant, is effective in recovering dynamic temporal ordering of such time series along a circular trajectory without assuming any time scale. Our analysis detected the propagation of slow cortical waves across thebrain with consistent shifts in lead-lag relationships between specific brain regions. We also observed short bursts of strong temporal ordering that dominated overall lead-lag relationships between pairs of regions in the brain, which were modulated by tasks. Our results suggest the possible role played by slow waves of ordered information between brain regions that underlie emergent cognitive function.

Signature methods for brain-computer interfaces

“…Interestingly, the cyclic structure or lead-lag relationship (the temporal ordering of cyclic signals) of the multidimensional path can be recovered from the second level signature and has been applied successfully to analyse fMRI data [17][18][19] . Define the lead matrix L by: L := 1 2 (S − S ⊺ ), where S refers to the square matrix formed by level 2 signature S i j = S(X) i, j .…”

Predicting Anorexia Nervosa and Autistic Characteristics in Individuals with Anorexia Nervosa from Resting State Cyclic Connectivity

“…The second drawback of traditional rsfMRI used in previous work in AN, is traditional fMRI explores the synchronous nature of the neural resting state signal but ignores the cyclic dynamic nature of the signal. The resting state signal is known to be dynamic, as the spatio-temporal pattern of neural networks undergoes several reconfigurations during individual rsfMRI scan (Gonzalez-Castillo et al, 2021), due to traveling slow cyclic cortical waves (Baryshnikov & Schlafly 2016; Abraham, Shahsavarani, Zimmerman, Husain & Baryshnikov, 2021). This has been established experimentally from multichannel electroencephalography recordings that demonstrate propagating macroscopic slow cortical waves (Muller, Chavane, Reynolds & Sejnowski, 2018).…”

“…This has been established experimentally from multichannel electroencephalography recordings that demonstrate propagating macroscopic slow cortical waves (Muller, Chavane, Reynolds & Sejnowski, 2018). This wave is cyclic but not periodic, meaning it is invariant to time (Baryshnikov & Schlafly 2016) and has an inherent temporal ordering (Abraham et al, 2021).…”

“…Interest in how the cyclicity and the temporal ordering differs in illness state when compared to healthy controls (HC) has over the past few years led for a search for methods to accurately explore these dynamic changes (Baryshnikov & Schlafly 2016; Abraham et al, 2021). Traditional correlation analysis has drawbacks as it assumes non-autocorrelated time series and is unable to capture temporal ordering (Shahsavarani et al, 2020).…”

“…This led to the development of cyclic analysis (Baryshnikov & Schlafly, 2016). Cyclic analysis derives pairwise temporal relationships between time series using iterated path integrals, to find a lead-follower relationship between these pairwise time series as well as the temporal ordering of the cortical wave (Baryshnikov & Schlafly, 2016; Zimmerman et al, 2018; Shahsavarani et al, 2020; Abraham et al, 2021). Cyclic analysis has advantages over previous methods when exploring rsfMRI signal, for example it does not assume the rsfMRI signal to be stationary (Shahsavarani et al, 2020) and can recover the temporal ordering of the signal (Abraham et al, 2021).…”