Complex Dynamics of Propagating Waves in a Two-Dimensional Neural Field.

Daniel Naoumenko,Pulin Gong

doi:10.3389/fncom.2019.00050

Abstract

Propagating waves with complex dynamics have been widely observed in neural population activity. To understand their formation mechanisms, we investigate a type of two-dimensional neural field model by systematically varying its recurrent excitatory and inhibitory inputs. We show that the neural field model exhibits a rich repertoire of dynamical activity states when the relevant strength of excitation and inhibition is increased, ranging from localized rotating and traveling waves to global waves. Particularly, near the transition between stable states of rotating and traveling waves, the model exhibits a bistable state; that is, both the rotating and the traveling waves can exist, and the inclusion of noise can induce spontaneous transitions between them. Furthermore, we demonstrate that when there are multiple propagating waves, they exhibit rich collective propagation dynamics with variable propagating speeds and trajectories. We use techniques from time series analysis such detrended fluctuation analysis to characterize the effect of the strength of excitation and inhibition on these collective dynamics, which range from purely random motion to motion with long-range spatiotemporal correlations. These results provide insights into the possible contribution of excitation and inhibition toward a range of previously observed spatiotemporal wave phenomena.

Highlights

By varying the relative strength of excitation and inhibition, we find that a variety of propagating waves can emerge from the neural field, including localized rotating and traveling waves, splitting waves, and global waves
We find that there exists a strong relationship between the strength of excitation/inhibition and the behavior of traveling waves: the speed and length of traveling waves increases as excitation increases or inhibition decreases
In this study we have investigated the neural mechanism of the formation of complex propagating wave dynamics in a 2D neural field model

Summary

Introduction

Propagating waves have been observed at different neural levels within multiple recording techniques, including multi-electrode arrays (Freeman and Barrie, 2000; Rubino et al, 2006; Muller et al, 2014; Townsend et al, 2015; Zanos et al, 2015), voltage sensitive dye (VSD) imaging (Wu et al, 2008; Huang et al, 2010; Muller et al, 2014), electroencephalography (EEG), electrocorticography (ECoG), magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI) (Goldman et al, 1949; Ribary et al, 1991; Lee et al, 2005; Patten et al, 2012; Alexander et al, 2013). The phase and amplitude of traveling waves in the motor cortex and visual cortex correlate with reach target location (Rubino et al, 2006) and with saccade size (Zanos et al, 2015), respectively, and the propagation direction of moving waves in the visual cortex is sensitive to visual movement orientation (Townsend et al, 2017) Waves in this visual cortex are implicated in perceptual phenomena like binocular rivalry (Lee et al, 2005), reinforcement of recent visual experience (Han et al, 2008) and visual hallucinations (Ermentrout and Cowan, 1979). This body of evidence indicates that understanding the mechanisms behind the formation and modulation of propagating neural waves is essential for uncovering the principled dynamics of neural population activity and for understanding the working mechanisms of neural circuits (Muller et al, 2018; Townsend and Gong, 2018)

Methods

Results

Conclusion