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.

Microsaccades Are Coupled to Heartbeat

“…This in turn would generate a microsaccade if the activity distribution's center of mass deviated significantly from the center of the map. From the perspective of neural dynamics (Engbert et al, 2011), heartbeat drives slow fixational eye movements by oscillatory changes of the movement's potential that constrains the current focus of visual selective attention (Hafed and Clark, 2002;Engbert and Kliegl, 2003). Such a mechanism has been shown to modulate microsaccade rates (Engbert, 2012) and might be implemented in the superior colliculus.…”

“…Moreover, microsaccades effectively counteract perceptual fading (Ditchburn et al, 1959;Martinez-Conde et al, 2006;McCamy et al, 2012); however, fading does not causally trigger microsaccades . There is, however, a higher probability for the triggering of a microsaccade if retinal image motion is slower than average (Engbert and Mergenthaler, 2006;Engbert et al, 2011).…”

Computational Modeling of Collicular Integration of Perceptual Responses and Attention in Microsaccades

“…The walker moves to the lattice position among the four neighboring sites with the smallest value of the sum of selfgenerated activation and potential. We interpret the numerical value of h ij as the neural activation of a local population of SC neurons that drive fixational eye movements (Engbert et al, 2011). A microsaccade is triggered when the walker reaches a lattice site with activation higher than a predefined critical value, i.e., h ij Ͼh c .…”

“…Such a preference could result from the dissociation into horizontal and vertical saccade centers (Sparks, 2002) with independent activity patterns for fixational eye movements. In the model (Engbert et al, 2011), we introduced an additional oculomotor potential to account for the preferences in microsaccade directions. All model parameters were taken from the original publication of the model (Engbert et al, 2011)…”

“…We model the generation of fixational eye movements by neural activity in superior colliculus (Hafed et al, 2009) on a finite square lattice of L ϫ L of continuous activations with periodic boundary conditions. We implement a self-avoiding walk (Freund and Grassberger, 1992) as an explicit model for the generation of neural noise (Engbert et al, 2011). In each time step, activation is added to the current position (i, j) of the walker,…”