Abstract
Visual scan paths exhibit complex, stochastic dynamics. Even during visual fixation, the eye is in constant motion. Fixational drift and tremor are thought to reflect fluctuations in the persistent neural activity of neural integrators in the oculomotor brainstem, which integrate sequences of transient saccadic velocity signals into a short term memory of eye position. Despite intensive research and much progress, the precise mechanisms by which oculomotor posture is maintained remain elusive. Drift exhibits a stochastic statistical profile which has been modeled using random walk formalisms. Tremor is widely dismissed as noise. Here we focus on the dynamical profile of fixational tremor, and argue that tremor may be a signal which usefully reflects the workings of oculomotor postural control. We identify signatures reminiscent of a certain flavor of transient neurodynamics; toric traveling waves which rotate around a central phase singularity. Spiral waves play an organizational role in dynamical systems at many scales throughout nature, though their potential functional role in brain activity remains a matter of educated speculation. Spiral waves have a repertoire of functionally interesting dynamical properties, including persistence, which suggest that they could in theory contribute to persistent neural activity in the oculomotor postural control system. Whilst speculative, the singularity hypothesis of oculomotor postural control implies testable predictions, and could provide the beginnings of an integrated dynamical framework for eye movements across scales.
Highlights
During fixation the eye is not still
We identify signatures reminiscent of a certain flavor of transient neurodynamics; toric traveling waves which rotate around a central phase singularity
Seung (1996) described a model of how persistent neural activity could be maintained through positive feedback, and showed how FEM drift-tremor could reflect a random walk along the line attractor created by the positive feedback dynamics in the motor memory of eye position
Summary
During fixation the eye is not still. Three main classes of fixational eye movement ( FEM) have been identified (MartinezConde et al, 2004). Little detailed information was given, but it was reported that the drift-tremor combination took a complex, curling trajectory These high resolution data may enable new insight into the underlying generative mechanisms of fixational eye movements. Rotational waveforms (aka spiral waves, vortices, tori) are a commonplace, universal dynamical form which play an organizing role in dynamical systems at all scales, from galaxies to weather to evolution to organisms to organs to cells to photons (Toomre, 1969; Da-sheng, 1980; Boerlijst and Hogeweg, 1991; Gray and Jalife, 1996; Winfree, 2001; Molina-Terriza et al, 2007; Schecter et al, 2008; Taniguchi et al, 2013) This generality led Winfree (2001) to suggest toroidal temporal structure as Frontiers in Systems Neuroscience www.frontiersin.org.
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