The cerebellum-mediated latency-duration balance minimizes the endpoint variability in saccadic eye movements

A large consensus in literature indicates that the cerebellum not only integrates and process sensory and motor information, but it is also involved in sensorimotor learning and control (Doya, 2000; Gao et al., 1996). Complex sensorimotor functions that include cognitive processes in planning, attention, and language have also been reported to be mediated by the cerebellum (Schmahmann, 1991; Thach, 1998; Kim, Uğurbil, and Strick, 1994). Indeed, the cytoarchitectonic uniformity of the cerebellum would facilitate its ability to process sensory information (Ramnani, 2006), while the existence of  connections from prefrontal and posterior parietal areas to the cerebellum gives evidence for its possibility to process abstract information too (Ramnani, 2012; Koziol et al., 2014). Moreover, it has been suggested that the lateral cerebellum would be implicated during the phase of acquisition and pre-processing (i.e., selection) of sensory information (Gao et al, 1996), as well as in volitional oculomotor control (Rosini et al., 2017). Actually, eye movements have been thoroughly studied as a reliable model of motor control, but have also large implications in processes beyond the motor domain. Specifically, the anti-saccade task is known to be a reliable indicator of volitional control implying top-down inhibition of reflexive saccade (Munoz and Everling, 2004; Coe and Munoz, 2017), and therefore it can enable to investigate the role of cerebellum in the non-motor domains of sensory information integration and action planning. For saccadic eye movements the spatial information about the starting and endpoints of the eyes’ position is translated by the cerebellar cortex into time information about the duration of the trajectory (Kornhuber, 1971). In other words, since saccades cause anticipatory non-visual signals (Railo et al., 2017), visual information of the initial eyes’ position would be remapped into space-time converted information about the duration of the possible saccade towards the anticipated endpoint  location. Thus, spatial localization would be estimated through this remapping process, which was suggested to occur during the saccadic latency, that is, the time interval between the stimuli presentation and the motor action initiation (Melcher and Colby, 2008). Consequently, inaccuracies in predicting the target localization is expected to produce error prone space-to-time conversion during the latency interval, and eventually deviations from the desired target. In this sense, the endpoint variability is duration-dependent and is already known to be optimized by the amplitude-duration main sequence (Harris and Wolpert, 2006). 

In a recent research (Piu et al, 2019) it has been studied the relationship between latency and duration, such that the durations of the  programmed saccades would scale with the time necessary for the sensory representation of the visual signal and for the action planning.  The hypothesis under study was that the cerebellum has a role also on the initiation of saccadic movement by regulating the perception and integration of sensory information  and the action planning stages during the latency interval of visual tasks. In order to investigate more deeply the latency-duration relationship a decomposition of the latency into the sensory-planning time (i.e., decision time) and a residual time (i.e., non-decision non-motor execution time) was considered in the study. The saccadic latency-duration-amplitude joint distributions of healthy subjects and cerebellar patients suffering from idiopathic cerebellar ataxia (ICA) were generated from real data and compared. The comparative analysis was useful to evaluate whether and to what extent impairments in the cerebellum might affect the stability of the space-time conversion process carried on by the cerebellum. The major finding was that both healthy controls and ICA showed a similar, although time-shifted, strategy for optimizing the endpoint variability-duration trade-off , which relied on inversely relating the saccadic duration to the time taken by the pre-motor stages of sensory perception and integration and of motor action planning in order to maximize the probability of getting closer to the target. In addition, the dynamics of this pattern resulted entropy-driven, so as maximum information was most likely learned in correspondence of the optimal latency-dependent time windows of duration.      

The major findings were the following: a) in both groups it was observed a trade-off between duration and decision time (duration reduced as decision time increased) for optimizing the probability of getting closer to the target, and a pick of entropy within the range of this trade-off where the information flow was maximized; b) cerebellar patients showed a significant longer latency, a greater reduction of duration as the time of decision increased, and constant low entropy outside the optimal time window, with respect to controls; c) the decomposition of the latency distributions into a decision time and a residual time through the Ex-Wald convolution suggested two driving forces for explaining the difference of latency between  the two groups: decision-related factors concerning the response caution and the reliability of the sensory evidence, and extra-decision (sensory) factors depending on the stimulus encoding; d) the decision time, along with duration, significantly shaped the probability distribution of the near-to-target saccade endpoints, whilst the residual time did not.      

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