Spatial resonance: A mechanism for spatial selectivity in the human visual system

Jason Pina

Humans are known to exhibit responses to static visual stimuli that vary based on the spatial frequencies that are present, often showing greater sensitivity to stimuli with dominant wavenumbers in the range of ∼2-4 cycles per degree (cpd). Studies of contrast sensitivity, so-called visual discomfort, and pattern-sensitive epilepsy (PnSE) all have shown that subjects are much more sensitive to spatial modes in this band of wavenumbers. In particular, at low contrast levels, subjects are better able to distinguish visual stimuli in this spatial frequency band, while at high contrast levels, such stimuli cause visual discomfort in healthy individuals and induce seizures in those with PnSE. Indeed, very similar response sensitivities are observed in all three cases, suggesting a common underlying cause. However, while some studies have examined neuronal population responses to these stimuli, the dynamic mechanisms leading to these neural and perceptual responses remain unknown.

We propose that spatial resonances in visual-cortical tissue provide a plausible explanation of these spatial selectivities, and support this hypothesis using a combination of simulation-based, numerical continuation, and analytical analyses. We first set a spatially extended neural field model of primary visual cortex near a Turing-Hopf bifurcation, where spatially uniform stable equilibria are lost to spatially heterogeneous oscillations of the natural spatial frequency of the system. We then find that the neural field exhibits similar bandpass activity as found in humans, displaying spatially heterogeneous oscilliatory activity when driven by stimuli with dominant wavenumbers in a band away from zero, but steady, non-oscillatory activity with wavenumbers outside of this band. Surprisingly, the system is most sensitive to wavenumbers at twice the natural frequency of the system. Using perturbation techniques near the Turing-Hopf bifurcation, we find that the system responds linearly in the stimulus amplitude to small-amplitude perturbations with a wavenumber of twice the natural frequency, while only responding quadratically to other nonzero wavenumbers, helping to explain this interesting result and providing a strong, testable prediction for our model.

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