The cerebellum has been hypothesized to provide internal models for limb movement control. If the cerebellum is the site of an inverse dynamics model, then cerebellar neural activity should signal limb dynamics and be coupled to arm muscle activity. To address this, we recorded from 166 task-related Purkinje cells in two monkeys performing circular manual tracking under varying viscous and elastic loads. Hand forces and arm muscle activity increased with the load, and their spatial tuning differed markedly between the viscous and elastic fields. In contrast, the simple spike firing of 91.0% of the Purkinje cells was not significantly modulated by the force nor was their spatial tuning affected. For the 15 cells with a significant force effect, changes were small and isolated. These results do not support the hypothesis that Purkinje cells represent the output of an inverse dynamics model of the arm. Instead these neurons provide a kinematic representation of arm movements.

The cerebellum plays an essential role in pursuit tracking with the eye and with the hand. During smooth pursuit eye movements, both tracking position and velocity are signaled by Purkinje cells. Purkinje cell simple spike discharge is also modulated by direction and speed during linear manual tracking. This study evaluated how all three parameters, position, movement direction, and speed, are signaled in the simple spike discharge of Purkinje cells during circular manual tracking. Three rhesus monkeys intercepted and then tracked a target moving in a circle in both counterclockwise and clockwise directions across a range of constant target speeds. Two sets of analyses of the simple spike firing of 97 Purkinje cells examined the effects of position, movement direction, and speed. The first approach was the incremental improvement of regression models, initially modeling a pure position dependence, then incorporating movement direction, and finally incorporating speed dependence. The second was a modelindependent approach, without any explicit assumptions about the character of the directional tuning or speed effects. Both analyses revealed the same three results: (1) Purkinje cell discharge is spatially tuned, to both the position and direction of movement, and (2) this spatial tuning is not altered by the speed, except (3) the speed scales the average firing and/or depth of modulation.The results suggest that the population of Purkinje cells forms a representation of the entire position-direction space of arm movements, and that the speed modulates the scale of that representation. This speed scaling provides insights into the cerebellar processing of movement-related timing.

Roitman, A. V., S. G. Massaquoi, K. Takahashi, and T. J. Ebner. Kinematic analysis of manual tracking in monkeys: characterization of movement intermittencies during a circular tracking task. J Neurophysiol 91: 901-911, 2004. First published October 15, 2003 10.1152/jn.00261.2003. Segmentation of the velocity profiles into the submovements has been observed in reaching and tracking limb movements and even in isometric tasks. Submovements have been implicated in both feed-forward and feedback control. In this study, submovements were analyzed during manual tracking in the nonhuman primate with the focus on the amplitude-duration scaling of submovements and the error signals involved in their control. The task consisted of the interception and visually guided pursuit of a target moving in a circle. The submovements were quantified based on their duration and amplitude in the speed profile. Control experiments using passive movements demonstrated that these intermittencies were not instrumentation artifacts. Submovements were prominent in both the interception and tracking phases and their amplitude scaled linearly with duration. The scaling factors increased with tracking speed at the same rate for both interception and pursuit. A cross-correlation analysis between a variety of error signals and the speed profile revealed that direction and speed errors were temporally coupled to the submovements. The cross-correlation profiles suggest that submovements are initiated when speed error reaches a certain limit and when direction error is minimized. The scaling results show that in monkeys submovements characterize both the interception and pursuit portions of the task and that these submovements have similar scaling properties consistent with 1) the concept of stereotypy and 2) adding constant acceleration/force at a specific tracking speed. The correlation results show involvement of speed and direction error signals in controlling the submovements.

Complex limb movements exhibit segmentation into submovements characterized as bell-shaped speed pulses. Submovements have been implicated in both feedback and feedforward control, reflecting an intermittent error-correction process. This study examines submovements occurring during a circular manual tracking task in humans, focusing on the amplitude-duration scaling of submovements and the properties of this scaling across changes in movement speed and external force load. The task consisted of intercepting and tracking a circularly moving target using a two-jointed, robotic arm that allowed external force fields to be imposed during tracking. Different speed levels and different levels of three types of force field were examined. Submovements were defined as fluctuations in the speed profile. The properties of the amplitude-duration ratio of the speed pulses were examined in relation to target speed and external force fields. The results show that the amplitude and duration of the submovements scale linearly in human manual tracking. The slope of the scaling was independently influenced by both target speed and external force fields. A common element in the increase in the scaling slope was increased tracking errors. Control experiments using passive movements and power spectral analysis showed that the submovements were not artifacts of the mechanical/acquisition system or the imposed force field. These results are consistent with the concept of stereotypy in which movements are constructed of scaled versions of a single prototype. Furthermore, the results support the hypothesis that submovements are integral to an error detection and correction control process.

The simple spike firing of cerebellar Purkinje cells encodes information on the kinematics of limb movements. However, these conclusions have been primarily based on averaging the discharge of Purkinje cells across trials and time and there is little information on whether Purkinje cell simple spike firing encodes specific motor errors during limb movements. Therefore, this study investigated single-trial correlations between the instantaneous simple spike firing of Purkinje cells with various kinematics and error signals. Purkinje cells (n = 126) were recorded in the intermediate and lateral zones centered on the primary fissure while three monkeys intercepted and tracked a target moving in a circle. Cross-correlation analysis was performed between the instantaneous simple spike firing rate and speed, the directional component of the velocity vector, and error signals during single movement trials. Significant correlations at physiologically relevant lags of ±250 ms were observed with tracking speed for 37% of Purkinje cells, with the velocity component in 39%, with direction error in 6% and speed error in 25%. Simple spike firing of the majority of Purkinje cells with significant correlation showed a negative lag with respect to speed and a positive lag with respect to error signals. We hypothesize that the cerebellum is involved in movement planning and control by continuously monitoring movement errors and making intermittent corrections that are represented as fluctuations in the speed profile.