A self-avoiding walk with neural delays as a model of fixational eye movements. Issue 1 (December 2017)

• Record Type: Journal Article
• Authors: Herrmann, Carl; Metzler, Ralf; Engbert, Ralf
• Is Part Of: Scientific reports. Volume 7:Issue 1(2017)
• Page Start: 1
• Page End: 17
• Publication Date: 2017-12
• Subjects: Natural history -- Research -- Periodicals; Biology -- Research -- Periodicals; Physical sciences -- Research -- Periodicals; Earth sciences -- Research -- Periodicals; Environmental sciences -- Research -- Periodicals; 502.85
• DOI: 10.1038/s41598-017-13489-8
• Languages: English
• ISSNs: 2045-2322

Abstract

Abstract Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades.