TY - JOUR A1 - Engbert, Ralf A1 - Mergenthaler, Konstantin A1 - Sinn, Petra A1 - Pikovskij, Arkadij T1 - An integrated model of fixational eye movements and microsaccades JF - Proceedings of the National Academy of Sciences of the United States of America N2 - 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. Y1 - 2011 U6 - https://doi.org/10.1073/pnas.1102730108 SN - 0027-8424 VL - 108 IS - 39 SP - E765 EP - E770 PB - National Acad. of Sciences CY - Washington ER - TY - JOUR A1 - Romano, Maria Carmen A1 - Thiel, Marco A1 - Kurths, Jürgen A1 - Mergenthaler, Konstantin A1 - Engbert, Ralf T1 - Hypothesis test for synchronization : twin surrogates revisited N2 - The method of twin surrogates has been introduced to test for phase synchronization of complex systems in the case of passive experiments. In this paper we derive new analytical expressions for the number of twins depending on the size of the neighborhood, as well as on the length of the trajectory. This allows us to determine the optimal parameters for the generation of twin surrogates. Furthermore, we determine the quality of the twin surrogates with respect to several linear and nonlinear statistics depending on the parameters of the method. In the second part of the paper we perform a hypothesis test for phase synchronization in the case of experimental data from fixational eye movements. These miniature eye movements have been shown to play a central role in neural information processing underlying the perception of static visual scenes. The high number of data sets (21 subjects and 30 trials per person) allows us to compare the generated twin surrogates with the "natural" surrogates that correspond to the different trials. We show that the generated twin surrogates reproduce very well all linear and nonlinear characteristics of the underlying experimental system. The synchronization analysis of fixational eye movements by means of twin surrogates reveals that the synchronization between the left and right eye is significant, indicating that either the centers in the brain stem generating fixational eye movements are closely linked, or, alternatively that there is only one center controlling both eyes. Y1 - 2009 UR - http://ojps.aip.org/chaos/ U6 - https://doi.org/10.1063/1.3072784 SN - 1054-1500 ER - TY - JOUR A1 - Mergenthaler, Konstantin A1 - Engbert, Ralf T1 - Microsaccades are different from saccades in scene perception N2 - 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. Y1 - 2010 UR - http://dx.doi.org/10.1007/s00221-010-2272-9 ER - TY - JOUR A1 - Engbert, Ralf A1 - Mergenthaler, Konstantin T1 - Statistics of fixational eye movements and oculomotor control Y1 - 2005 SN - 0301-0066 ER - TY - JOUR A1 - Engbert, Ralf A1 - Mergenthaler, Konstantin T1 - Microsaccades are triggered by low retinal image slip N2 - 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 approximate to 200 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 Y1 - 2006 UR - http://www.pnas.org/ U6 - https://doi.org/10.1073/pnas.0509557103 SN - 0027-8424 ER -