Slow brain rhythms are attributed to near-simultaneous (synchronous) changes in activity in neuron populations in the brain. Because they are slow and widespread, synchronous rhythms have not been considered crucial for information processing in the waking state. Here we adapted methods from turbulence physics to analyze ␦-band (1-4 Hz) rhythms in local field potential (LFP) activity, in multielectrode recordings from cerebral cortex in anesthetized marmoset monkeys. We found that synchrony contributes only a small fraction (less than one-fourth) to the local spatiotemporal structure of ␦-band signals. Rather, ␦-band activity is dominated by propagating plane waves and spatiotemporal structures, which we call complex waves. Complex waves are manifest at submillimeter spatial scales, and millisecond-range temporal scales. We show that complex waves can be characterized by their relation to phase singularities within local nerve cell networks. We validate the biological relevance of complex waves by showing that nerve cell spike rates are higher in presence of complex waves than in the presence of synchrony and that there are nonrandom patterns of evolution from one type of complex wave to another. We conclude that slow brain rhythms predominantly indicate spatiotemporally organized activity in local nerve cell circuits, not synchronous activity within and across brain regions.

There is growing evidence that population-level brain activity is often organized into propagating waves that are structured in both space and time. Such spatiotemporal patterns have been linked to brain function and observed across multiple recording methodologies and scales. The ability to detect and analyze these patterns is thus essential for understanding the working mechanisms of neural circuits. Here we present a mathematical and computational framework for the identification and analysis of multiple classes of wave patterns in neural population-level recordings. By drawing a conceptual link between spatiotemporal patterns found in the brain and coherent structures such as vortices found in turbulent flows, we introduce velocity vector fields to characterize neural population activity. These vector fields are calculated for both phase and amplitude of oscillatory neural signals by adapting optical flow estimation methods from the field of computer vision. Based on these velocity vector fields, we then introduce order parameters and critical point analysis to detect and characterize a diverse range of propagating wave patterns, including planar waves, sources, sinks, spiral waves, and saddle patterns. We also introduce a novel vector field decomposition method that extracts the dominant spatiotemporal structures in a recording. This enables neural data to be represented by the activity of a small number of independent spatiotemporal modes, providing an alternative to existing dimensionality reduction techniques which separate space and time components. We demonstrate the capabilities of the framework and toolbox with simulated data, local field potentials from marmoset visual cortex and optical voltage recordings from whole mouse cortex, and we show that pattern dynamics are non-random and are modulated by the presence of visual stimuli. These methods are implemented in a MATLAB toolbox, which is freely available under an open-source licensing agreement.

Visual stimuli can evoke waves of neural activity that propagate across the surface of visual cortical areas. The relevance of these waves for visual processing is unknown. Here, we measured the phase and amplitude of local field potentials (LFPs) in electrode array recordings from the motion-processing medial temporal (MT) area of anesthetized male marmosets. Animals viewed grating or dot-field stimuli drifting in different directions. We found that, on individual trials, the direction of LFP wave propagation is sensitive to the direction of stimulus motion. Propagating LFP patterns are also detectable in trial-averaged activity, but the trial-averaged patterns exhibit different dynamics and behaviors from those in single trials and are similar across motion directions. We show that this difference arises because stimulus-sensitive propagating patterns are present in the phase of single-trial oscillations, whereas the trial-averaged signal is dominated by additive amplitude effects. Our results demonstrate that propagating LFP patterns can represent sensory inputs at timescales relevant to visually guided behaviors and raise the possibility that propagating activity patterns serve neural information processing in area MT and other cortical areas. Propagating wave patterns are widely observed in the cortex, but their functional relevance remains unknown. We show here that visual stimuli generate propagating wave patterns in local field potentials (LFPs) in a movement-sensitive area of the primate cortex and that the propagation direction of these patterns is sensitive to stimulus motion direction. We also show that averaging LFP signals across multiple stimulus presentations (trial averaging) yields propagating patterns that capture different dynamic properties of the LFP response and show negligible direction sensitivity. Our results demonstrate that sensory stimuli can modulate propagating wave patterns reliably in the cortex. The relevant dynamics are normally masked by trial averaging, which is a conventional step in LFP signal processing.