Spontaneous traveling waves naturally emerge from horizontal fiber time delays and travel through locally asynchronous-irregular states

Abstract Sensory neuroscience has focused a great deal of its attention on characterizing the mean firing rate that is evoked by a stimulus, and while it has long been recognized that the firing rates of individual neurons fluctuate around the mean, these fluctuations are often treated as a form of internally generated noise1. There is, however, evidence that these “ongoing” fluctuations of activity in sensory cortex during normal, waking function shape neuronal excitability and responses to external input2,3. We have recently found that spontaneous fluctuations are organized into waves traveling at speeds consistent with the speed of action potentials traversing unmyelinated horizontal cortical fibers (0.1-0.6 m/s)4 across the cortical surface5. These waves systematically modulate excitability across the retinotopic map, strongly affecting perceptual sensitivity as measured in a visual detection task. The underlying mechanism for these waves, however, is unknown. Further, it is unclear whether waves are consistent with the low rate, highly irregular, and weakly correlated “asynchronous-irregular” dynamics observed in computational models6 and cortical recordings in vivo7. Here, we study a large-scale computational model of a cortical sheet, with connections ranging up to biological scales. Using an efficient custom simulation framework, we study networks with topographically-organized connectivity and distance-dependent axonal conduction delays from several thousand up to one million neurons. We find that spontaneous traveling waves are a general property of these networks and are consistent with the asynchronous-irregular regime. These waves are well matched to spontaneous waves recorded in the neocortex of awake monkeys. Further, individual neurons sparsely participate in waves, yielding a sparse-wave regime that offers a unique operating mode, where traveling waves coexist with locally asynchronous-irregular dynamics, without inducing deleterious neuronal correlations8.