Even during visual fixation of a stationary target, our eyes perform rather erratic miniature movements, which represent a random walk. These ''fixational'' eye movements counteract perceptual fading, a consequence of fast adaptation of the retinal receptor systems to constant input. The most important contribution to fixational eye movements is produced by microsaccades; however, a specific function of microsaccades only recently has been found. Here we show that the occurrence of microsaccades is correlated with low retinal image slip Ϸ200 ms before microsaccade onset. This result suggests that microsaccades are triggered dynamically, in contrast to the current view that microsaccades are randomly distributed in time characterized by their rate-of-occurrence of 1 to 2 per second. As a result of the dynamic triggering mechanism, individual microsaccade rate can be predicted by the fractal dimension of trajectories. Finally, we propose a minimal computational model for the dynamic triggering of microsaccades.random walks ͉ visual fixation ͉ eye movements ͉ saccade detection

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.

We propose a model for the control of fixational eye movements using time-delayed random walks. Fixational eye movements produce random displacements of the retinal image to prevent perceptual fading. First, we demonstrate that a transition from persistent to antipersistent correlations occurs in data recorded from a visual fixation task. Second, we propose and investigate a delayed random-walk model and get, by comparison of the transition points, an estimate of the neurophysiological delay. Differences between horizontal and vertical components of eye movements are found which can be explained neurophysiologically. Finally, we compare our numerical results with analytic approximations.

Eye-fixation durations are among the best and most widely used measures of ongoing cognition in visual tasks, e.g., reading, visual search or scene perception. However, fixations are characterized by ongoing motor activity (or fixational eye movements) with microsaccades as their most pronounced components. Recent work demonstrated the similarities of microsaccades and inspection saccades. Here, we show that distinct properties of microsaccades and inspection saccades can be found in a scene perception task, based on descriptive measures (e.g., a bimodal amplitude distribution) as well as functional characteristics (e.g., inter saccadic-event intervals and generating processes). Besides these specific differences, microsaccade rates produced by individual participants in a fixation paradigm are correlated with microsaccade rates extracted from fixations in scene perception, indicating a common neurophysiological basis. Finally, we observed that slow fixational eye movements, called drift, are significantly reduced during long fixations in scene viewing, which informs about the control of eye movements in scene viewing.

Astrocytes integrate and process synaptic information and exhibit calcium (Ca2+) signals in response to incoming information from neighboring synapses. The generation of Ca2+ signals is mostly attributed to Ca2+ release from internal Ca2+ stores evoked by an elevated metabotropic glutamate receptor (mGluR) activity. Different experimental results associated the generation of Ca2+ signals to the activity of the glutamate transporter (GluT). The GluT itself does not influence the intracellular Ca2+ concentration, but it indirectly activates Ca2+ entry over the membrane. A closer look into Ca2+ signaling in different astrocytic compartments revealed a spatial separation of those two pathways. Ca2+ signals in the soma are mainly generated by Ca2+ release from internal Ca2+ stores (mGluR-dependent pathway). In astrocytic compartments close to the synapse most Ca2+ signals are evoked by Ca2+ entry over the plasma membrane (GluT-dependent pathway). This assumption is supported by the finding, that the volume ratio between the internal Ca2+ store and the intracellular space decreases from the soma towards the synapse. We extended a model for mGluR-dependent Ca2+ signals in astrocytes with the GluT-dependent pathway. Additionally, we included the volume ratio between the internal Ca2+ store and the intracellular compartment into the model in order to analyze Ca2+ signals either in the soma or close to the synapse. Our model results confirm the spatial separation of the mGluR- and GluT-dependent pathways along the astrocytic process. The model allows to study the binary Ca2+ response during a block of either of both pathways. Moreover, the model contributes to a better understanding of the impact of channel densities on the interaction of both pathways and on the Ca2+ signal.