Ralf Engbert, Konstantin Mergenthaler, Petra Sinn, Arkadij Pikovskij

• 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 aWhen 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.…