title: An integrated model of fixational eye movements and microsaccades.
abstract: When we fixate a stationary target, our eyes generate miniature (or fixational) eye movements involuntarily. These fixational eye movements are classified as slow components (physiological drift, tremor) and microsaccades, which represent rapid, small-amplitude movements. Here we propose an integrated mathematical model for the generation of slow fixational eye movements and microsaccades. The model is based on the concept of self-avoiding random walks in a potential, a process driven by a self-generated activation field. The self-avoiding walk generates persistent movements on a short timescale, whereas, on a longer timescale, the potential produces antipersistent motions that keep the eye close to an intended fixation position. We introduce microsaccades as fast movements triggered by critical activation values. As a consequence, both slow movements and microsaccades follow the same law of motion; i.e., movements are driven by the self-generated activation field. Thus, the model contributes a unified explanation of why it has been a long-standing problem to separate slow movements and microsaccades with respect to their motion-generating principles. We conclude that the concept of a self-avoiding random walk captures fundamental properties of fixational eye movements and provides a coherent theoretical framework for two physiologically distinct movement types.
authors.affiliation: Department of Psychology and Physics, University of Potsdam, 14469 Potsdam, Germany. Ralf.Engbert@uni-potsdam.de
authors.forename: Ralf
authors.initials: R
authors.lastname: Engbert
authors.forename: Konstantin
authors.initials: K
authors.lastname: Mergenthaler
authors.forename: Petra
authors.initials: P
authors.lastname: Sinn
authors.forename: Arkady
authors.initials: A
authors.lastname: Pikovsky
mesh_terms: D006801:Humans; D008962:Models, Theoretical; D012438:Saccades