Studies of sensory-evoked neuronal responses often focus on mean spike rates, with fluctuations treated as internally-generated noise. However, fluctuations of spontaneous activity, often organized as traveling waves, shape stimulus-evoked responses and perceptual sensitivity. The mechanisms underlying these waves are unknown. Further, it is unclear whether waves are consistent with the low rate and weakly correlated “asynchronous-irregular” dynamics observed in cortical recordings. Here, we describe a large-scale computational model with topographically-organized connectivity and conduction delays relevant to biological scales. We find that spontaneous traveling waves are a general property of these networks. The traveling waves that occur in the model are sparse, with only a small fraction of neurons participating in any individual wave. Consequently, they do not induce measurable spike correlations and remain consistent with locally asynchronous irregular states. Further, by modulating local network state, they can shape responses to incoming inputs as observed in vivo.

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.