Kinematics and Dynamics

Kinematics and Dynamics 271

Kinematics and Dynamics A d’Avella, Santa Lucia Foundation, Rome, Italy ã 2009 Elsevier Ltd. All rights reserved.

Introduction To behave adaptively under novel and changing circumstances, many animals extend and adapt their movement repertoire. Humans and other primates in particular have an extraordinary capacity for learning skilled arm and hand movements. Reaching and grasping are crucial components of the movement repertoire of all primates and the foundations of many sophisticated human skills. While these basic skills are learned early in life, changes in the motor apparatus due to growth or injury require continuously monitoring and recalibrating the neuronal control system for maintaining adequate performance. Moreover, using tools and performing sports often requires learning new reaching and grasping skills. Consider, for example, reaching with a cursor on a computer screen using a ‘mouse,’ grasping a small object with a forceps under a microscope, or hitting a ball with a racket. In this article, recent advances in the study of the characteristics and the neural basis of motor learning are reviewed. The focus is on learning and adaptation of reaching skills as a specific but very significant case of motor learning. To control reaching, as for many other goaldirected movements, the central nervous system (CNS) has to map sensory input into motor output. Vision and audition provide information about the movement goal, that is, the spatial location to be reached. Vision and proprioception are used to determine the location of the hand and the arm joints configuration. The activations of shoulder and arm muscles constitute the motor output. This sensorimotor mapping involves both kinematic and dynamic transformations. Kinematics is the description of the motion of the limb joints or the motion of the limb endpoint, while dynamics is concerned with the forces acting on the limb segments and the segment masses that produce or affect those motions. The overall mapping can be decomposed into different transformations. First, proprioceptive information has to be aligned with visual information in a common reference frame. This alignment process is likely accomplished through transformation of proprioceptive information about the limb configuration into a vision-based coordinate frame and requires a direct kinematic transformation: the mapping of joint angles and muscle lengths into end-effector spatial

location. Second, a motor error, formulated as a difference vector between the location of the target and the location of the hand, must be transformed into a motor plan, possibly expressed as the joint displacements necessary to zero the error and bring the hand to the target. This is an inverse kinematics transformation: from end-effector to joints. Finally, the motor plan must be mapped into muscle activations, an inverse dynamic transformation. When learning a new reaching skill, such as moving a cursor on a computer screen by moving an object (a ‘mouse’) with the hand or reaching with a stick, a new kinematic mapping between the end-effector motor error and the motor plan must be acquired. For example, the motor error may be on a vertical plane (the computer screen) while the hand moves on a horizontal plane (the desk surface). In situations involving perturbations of the alignment of vision and proprioception, as when vision is distorted by prism glasses (see the section titled ‘Adapting to prism glasses’), the existing kinematic mappings must be adjusted. Finally, when learning to reach while holding an object with unusual dynamic properties, a new dynamic mapping between motor plan and motor output must be acquired, or when adapting to novel dynamic behavior of the arm, the existing mapping must be modified.

Learning Kinematics Adapting to Prism Glasses

The adaptation processes induced by a perturbation of the visual input has been investigated experimentally using prism glasses. When people wear glasses with wedge prisms in place of regular lenses, the path of light is deviated by a certain angle, and the visual field is rotated accordingly. Initially, participants are unable to reach a nearby target in front of them with their hand or to hit a more distant target by throwing a clay ball (Figure 1). For example, participants wearing prisms that bend the light path to their right, so that objects appear shifted to the left of their actual location, initially reach to the left of the target. With practice, participants progressively change the movement direction until they reach accurately in the direction of the target. When the prisms are removed, participants miss again the target by reaching to its right, a phenomenon called negative aftereffect. Within a few trials, this aftereffect disappears. The existence of aftereffects indicates that some changes have occurred in the kinematic transformations used for controlling reaching movements in

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Figure 1 Adaptation to prism glasses. In the adaptation study illustrated here, a participant wearing wedge prisms bending the light path to the left (a) initially throws a ball to the left of the target ((b), II, where the horizontal displacement of the impact points from the target are shown as a function of the trial number). With practice, the participant progressively adapts to the visual perturbation and hits the target with the same accuracy ((b), III) than before wearing the prisms ((b), I). In the first trial after the removal of the prisms, the participant misses the target by throwing to its right ((b), IV), that is, making an error in the opposite direction to the error observed in the first trial with the prisms (aftereffect). Within a few trials without the glasses, the participant hits the target accurately again ((b), V). (c) Gaze and throw directions in the different phases of the experiment schematized with arrows. Adapted from Martin TA, Keating JG, Goodkin HP, Bastian AJ, and Thach WT (1996) Throwing while looking through prisms. II. Specificity and storage of multiple gaze-throw calibrations. Brain 119: 1199–1211, with permission from Oxford University Press.

normal conditions. The adaptation is specific to the trained arm: participants who have adapted and reach correctly with one hand while wearing the prisms do not show aftereffects when reaching with the other hand after removing the prisms. Thus, the adaptation cannot be accounted for by a shift of the mapping of the visual input to the reference frame where a motor error is encoded. Instead, the specificity of adaptation is compatible with a shift in the kinematic transformations that map proprioceptive input into a visual reference frame. This proprioceptive shift can be interpreted as a shift in the ‘felt’ hand location in the visual field. However, while this proprioceptive shift allows the CNS to compute the correct motor error even when the hand is not in sight, accurate reaching with the prisms requires that the kinematic mapping between motor error and motor plan be adjusted as well. In fact, the original mapping of motor errors in visual coordinates into joint displacements would generate a correct motor plan only if the physical world were shifted along the visual field. Thus, the kinematic mapping between motor error and motor plan is adjusted during adaptation to compensate for the shift of the visual field. Learning Visuomotor Transformations

In the experiments with prism glasses, the CNS interprets a mismatch between vision and proprioception

and between motor error and motor plan as an error in the implementation of the normal sensorimotor transformations used for reaching and recalibrates those transformations. However, in other conditions the CNS may interpret a visuomotor mismatch as due to the kinematic characteristic of an object or tool being manipulated. In this case, a new visuomotor transformation is learned instead of adapting the existing transformation used for normal reaching. For example, learning to reach with a computer mouse does not affect normal reaching movements, and it is possible to switch from one transformation to the other instantaneously. Visuomotor recalibration, as in the case of prism adaptation, and visuomotor skill learning, as in the case of tool-specific skills, generalize differently to untrained conditions. Generalization has been studied in experiments using novel visuomotor transformation. In these experiments, visual feedback provided by either a computer screen or a virtual reality display allowed simulating either a novel tool whose end-effector movements did not coincide with the hand movements, as in the case of a computer mouse, or a precisely controlled prismlike perceptual distortion of the movement of a person’s own hand. In both cases, by training study participants in a single reaching condition, such as reaching in one direction, and testing them on multiple conditions, it was possible

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Figure 2 Visuomotor rotation learning. In this experiment, participants sat facing a computer monitor at eye level and controlled a screen cursor by moving a hand-held indicator in a horizontal digitizing tablet. Participants were required to move the cursor from one central location to different peripheral targets. After practicing without any visual perturbation, participants were trained to perform the task while the direction of cursor movement relative to the hand movement on the tablet was rotated counterclockwise by 30 . Training with a single target (a), the directional error was quickly reduced with practice. When generalization to other targets was tested, the amount of adaptation resulted very small except for directions very close to the trained direction ((b), where the curves representing the percent adaptation as a function of the angular difference between trained and tested targets, bottom, are shown with different symbols for different trained targets, top). Adapted from Krakauer JW, Pine ZM, Ghilardi MF, and Ghez C (2000) Learning of visuomotor transformations for vectorial planning of reaching trajectories. Journal of Neuroscience 20(23): 8916–8924, Copyright (2000) by the Society for Neuroscience.

to study how the learned visuomotor transformation generalizes to untrained conditions. When the transformation between the hand movement on a horizontal plane, recorded by a mouse or a pen on a digitizing tablet, and the movement of a cursor on a vertically mounted computer display is altered by a rotation or a shift, with practice people learn the novel visuomotor transformation (Figure 2(a)). Learning this skill does not affect the accuracy of normal reaching movements, and if only one movement condition is trained, the generalization to other untrained conditions is modest (Figure 2(b)). In contrast, when a novel visuomotor transformation is introduced in a virtual reality display, where participants initially see a virtual representation of the position in space of their fingertip matching its actual location (Figure 3(a)), learning to reach in one movement condition generalizes to other conditions (Figures 3(b) and 3(c)). Moreover, immediately after the removal of the visual perturbation, normal reaching is affected and aftereffects are observed. Thus, the perception of the coincidence of the source of visual feedback and the end effector may be a crucial element in determining whether motor learning occurs through recalibration of an existing visuomotor mapping or by acquisition of a new mapping.

Learning Dynamics When adapting to altered visual feedback or learning new visuomotor skills, the CNS needs to deal only

with kinematic transformations. However, in many circumstances the forces necessary to generate a desired movement may change, and thus the CNS must recalibrate or acquire a new dynamic transformation that maps motor plans to muscle activations. Adapting to Novel Inertial Forces

The dynamics of the arm change during trunk rotations. Moving the arm with respect to a rotating reference frame generates velocity-dependent inertial forces (Coriolis forces) that alter the hand trajectory generated by a given muscle activation pattern. This effect is fully compensated for when normal reaching movements are combined with active trunk rotations so that it is possible to reach accurately during wholebody turning. However, exposure to artificially generated Coriolis forces, during passive trunk rotations, causes reaching errors. The adaptation process required to compensate for these unusual inertial forces has been investigated in experiments in which participants performed reaching movements in a rotating room. If the heads of the participants are close to the rotation axis and the angular velocity is constant, participants do not perceive the effect rotation if they do not move. When a participant moves, Coriolis forces act on the whole arm without any external mechanical contact (Figure 4(a)). Initially, reaching toward a remembered location, without vision of the arm, is inaccurate (Figure 4(b)). The trajectory of the hand deviates from the straight line connecting start to target which would normally

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Figure 3 Learning a local visuomotor transformation in a virtual reality environment. A three-dimensional virtual visual feedback setup ((a), constituted by a mirror, a rear projection screen, and shuttered glasses synchronized with the display for stereoscopic perception) was used in this experiment to overlay images onto the arm workspace. Participants could not see their arm but were shown a target location and their finger location as a 1 cm-edge cube. A computer-controlled discrepancy between the finger and the cube position could be introduced. After a familiarization phase, during which participants pointed to 36 different targets with continuous veridical feedback, pointing errors without visual feedback of the finger location were assessed in a preexposure phase. During the following exposure phase, participants pointed to one target only while the finger position was displaced, gradually across trials, up to 6 cm to the right of the average preexposure position, and the visual feedback of finger position was displayed only within 3 cm from the target. As a control condition, visual feedback was altered so that participants had to point to their average preexposure position to see their finger on the target. Changes in pointing due to the exposure of the visuomotor remapping were assessed in a postexposure phase by testing all targets without visual feedback. In the control condition (b), changes in pointing due to the exposure to the remapping when pointing to the target indicated by a square were not significant. In contrast, remapping of the visual feedback at one target ((c), exposure target indicated by a square) induced significant changes over the whole workspace. Adapted from Vetter P, Goodbody SJ, and Wolpert DM (1999) Evidence for an eye-centered spherical representation of the visuomotor map. Journal of Neurophysiology 81(2): 935–939, used with permission from the American Physiological Society.

be followed in reaching movements, and the hand does not reach the planned location. Within a few trials, accuracy increases, and the trajectories in the rotating room resemble those in a stationary environment (Figures 4(b) and 4(c)). However, the first reaching movement performed after the room rotation is terminated is inaccurate. The hand trajectory is deviated in a direction opposite to the direction of the deviation induced by Coriolis forces. Such aftereffects disappear after a few trials. As for the experiments with prism glasses, the existence of aftereffects indicates that the dynamic transformation used for reaching movements in normal

conditions is adapted during the exposure to novel velocity-dependent noncontacting forces. Since the adaptation occurs without visual or tactile feedback, proprioceptive input is sufficient to adjust the dynamic transformation. A mismatch between expected and actual signals from the muscle spindles conveys the information about an incorrect execution of the motor plan. The resulting changes in the generation of the muscle activations allow for implementing the normal motor plan, a straight hand trajectory from start to target, in the dynamically altered conditions. This dynamic mapping is specific to the arm exposed to the dynamic perturbation, as shown by

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Figure 4 Adapting to novel inertial forces. (a) In this experiment, conducted in a dark room rotating counterclockwise (o: angular velocity), Coriolis forces (Fcor) generated on the reaching arm (v: velocity relative to the torso; m: arm mass) are directed to the right. (b) The trajectory of the first movement to reach a visual target (extinguished at movement initiation) during rotation (10 rpm) was deviated in the direction of the Coriolis force (perrotation, initial, average over 11 participants) and did not reach the target. However, at the 40th movement (per-rotation, final), the trajectory was not different from the trajectory in the stationary room (prerotation). The first movement after rotation (postrotation) showed mirror symmetric endpoint error and curvature to the first movement during rotation (aftereffect). (c) Summary of endpoint error and curvature before (trials 1–40), during (41–80), and after (81–120) rotation. Adapted from Dizio P and Lackner JR (1995) Motor adaptation to Coriolis force perturbations of reaching movements: Endpoint but not trajectory adaptation transfers to the nonexposed arm. Journal of Neurophysiology 74(4): 1787–1792, used with permission from the American Physiological Society.

the fact that the trajectory adaptation does not transfer to the other, unexposed arm. Learning Novel Viscous Force Fields

The dynamics of the reaching arm is also altered when one is grasping an object or manipulating a tool. For objects and tools whose dynamic characteristics are well known, trajectory and endpoint accuracy of reaching while holding the object does not change with respect to reaching with the empty hand, indicating that the CNS is automatically selecting the dynamic mapping appropriate for each condition. The process of learning such tool-specific mappings has been studied experimentally by using a two-link planar robot manipulator (Figure 5(a)) that imposes novel velocity-dependent (viscous) forces on the arm (Figures 5(b) and 5(c)). In a velocity-dependent force field, as in the case of Coriolis forces, no perturbation is applied at the beginning and at the end of the movement, when the

arm is stationary. In a typical experiment, participants make reaching movements while holding the end-effector of the manipulator. As for some of the visuomotor learning experiments described above, participants are first trained to move a cursor on a computer screen by moving the manipulator handle. Trajectories are approximately straight in this baseline condition. Next, a perturbing force is applied to the hand by the manipulator. This force has a magnitude proportional to the hand tangential velocity but a direction which is not always opposite to the movement direction, as is usual with viscous forces. The direction may be always perpendicular to the hand velocity (curl force field) or change as a function of the movement direction. When first exposed to the force field, participants make large errors. Without visual feedback, the trajectory is skewed and deviated from a straight line (Figure 5(d)). With practice, however, the trajectories become straight again, indicating that a dynamic mapping correctly implementing the motor plan has been acquired (Figure 5(e)). Finally, when the perturbing forces are removed, participants initially produce trajectories which are mirror images of the initial trajectories after force field exposure (Figure 5(f)). With practice these aftereffects also disappear. Comparing the adaptation to viscous force fields delivered by a robot manipulator with the adaptation to the Coriolis forces, there are a number of differences. Full adaptation to the perturbation is accomplished after a few tens of repetitions with noncontacting Coriolis forces, but it requires hundreds of movements with the robot manipulator. Moreover, after the adaptation, normal reaching in free space is impaired in the case of Coriolis forces but not with the robot. Thus, the adaptation to noncontacting Coriolis forces and the adaptation to forces applied through mechanical contact appear as different processes. The former is more directly related to an internal calibration process of the dynamic transformation used for reaching with the free arm, whereas the latter is related to the acquisition of a new mapping useful to skillfully control a novel tool.

Neural Basis of Motor Learning Neural plasticity is the likely physiological mechanism underlying the recalibration and acquisition of the kinematic and dynamic transformations involved in the control of reaching. Plasticity may be caused by unmasking of existing connections, synaptic changes, or growth of new connections. The areas of the CNS involved in motor learning are beginning to be identified through lesion and imaging studies. These studies

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Figure 5 Learning novel velocity-dependent forces. Participants made reaching movements while grasping the handle of a two-link planar robot manipulator with their arm on a horizontal plane (a). The location of the handle on the plane was displayed on a monitor placed in front of the participants. The torque motors of the manipulator could be programmed to apply forces to the handle that depended on the handle velocity ((b), handle velocity and force in x–y Cartesian coordinates). Different from normal viscous forces, the applied force was not aligned with the movement direction but, instead, depended on it. This fact is illustrated by the forces acting on the hand during simulated center-out reaching movements from one central location to eight peripheral targets (c). Note that forces at the beginning and at the end of the movement vanish because the velocity is null. After practicing in the null field (torque motors off), participant performed reaching movements in the force field with randomly interspersed trials in the null field (catch trials). In all conditions, a fraction of the movements were performed without visual feedback. At the beginning of the exposure to the force field ((d), average and standard deviation of hand path without visual feedback recoded during the first block of 250 trials in the force field indicated by black dots and gray areas, respectively), the hand path deviated substantially from the null field straight-line trajectory, and there were corrections at the end of the movements. With practice, paths become progressively straighter ((e), average and standard deviation of hand path without visual feedback recoded during the fourth and last block of force field trials). However, during catch trials ((f), average and standard deviation of hand path without visual feedback in the null field recoded during the last block of trials), the hand paths showed aftereffects with deviations opposite to those observed during the initial force field exposure ((d)). Adapted from Shadmehr R and Mussa-Ivaldi FA (1994) Adaptive representation of dynamics during learning of a motor task. Journal of Neuroscience 14(5 Pt 2): 3208–3224, used with permission from Society for Neuroscience.

suggest that motor learning depends on multiple, interconnected cortical and subcortical systems, each contributing to specific aspects and different phases of the process. Moreover, the changes in the neural representation of movement parameters in some of the areas involved in motor learning have been investigated with single cell recordings in monkeys. CNS Structures Involved in Motor Learning

Studies of patients with lesions of the CNS and imagining studies of normal participants have identified

some of the cortical and subcortical areas involved in learning the kinematic and dynamic transformations involved in goal-directed arm movements. Cerebellar dysfunctions impair adaptation of both kinematic (prism) and dynamic (force field) transformations. Positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) studies have also found an increase in cerebellar activation during early phases of visuomotor rotation and force-field learning. The cerebellar involvement during early phases might be related to its role in processing the large execution errors present before adaptation

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is complete. Activation of the posterior parietal cortex has been observed with PET during adaptation to prism glasses and during learning visuomotor hand–cursor rotations. A parietal activation has also been observed with fMRI during early stages of visuomotor learning. This parietal activation might be related to the remapping of the proprioceptive representation of the hand position in a visual reference frame containing the representation of hand and target position. During the learning of a force field perturbation, significant activations have been observed with PET in the dorsolateral prefrontal cortex during early learning phases and in the posterior parietal cortex, premotor cortex, and cerebellum during recall of the learned dynamic transformation. Neural Correlates of Kinematic and Dynamic Learning in the Motor Cortex

Recordings of the activity of single cells in the premotor and primary motor cortex of macaque monkeys during reaching have shown that these cortical areas encode both kinematic and dynamic parameters. The firing rate of most cells in these areas is modulated by the movement direction, with a

directional dependence well captured by a cosine function. Thus, the firing rate of each cell is maximal for some direction of movement, the preferred direction. The population vector, a simple algorithm for decoding the direction of movement from the activity of a population of neurons on the basis of the linear combination of the preferred direction of individual cells, indicates that kinematic parameters are accurately encoded by populations of cortical cells. However, the activity of many cells is also modulated by dynamic parameters, such as the force applied by the hand against a load and the orientation of the arm during reaching. It is likely that different populations of cortical neurons, in parietal and frontal cortical areas, constitute a multilayer recurrent network capable of transforming a population representation of the target and the current limb position, derived from visual and proprioceptive sensory input, into a population representation of the motor output, the appropriate muscle patterns for reaching the target. When learning a new visuomotor mapping, such as the one required to reach with prism glasses or after a rotation of the joystick–cursor transformation, the neural representation of the mapping must also

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Figure 6 Amplitude modulation of the firing rate on neurons in the motor cortex during visuomotor learning. Macaque monkeys were trained to move a manipulandum on a horizontal plane to move a cursor on a vertical monitor from one central location to eight peripheral targets. In the default visuomotor mapping, a rightward (0 ) hand movement (on the horizontal plane) corresponded to a rightward cursor movement (on the vertical plane) and a forward hand movement (90 ) to an upward cursor movement. Monkeys were tested with this mapping before and after learning a novel visuomotor transformation. In the learning epoch, monkeys had to reach only the 90 target, but the direction of hand movement required to reach the target was changed on each experimental session (randomly chosen between 0 , 45 , 135 , and 180 , that is, requiring a rotation of 90 , 45 , 45 , or 90 between hand and cursor movement direction with respect to the default mapping). Neural activity in the default eight-target task was compared before and after learning. (a) Raster plots and peristimulus histograms of the activity of two cells for the eight directions of movements before learning (gray ticks in the raster plots, where each row represents a trial and each tick a spike; gray lines in the peristimulus histogram, showing the sum of the spikes across trials in each time bin after alignment with the onset of the target stimulus) and after learning (black ticks and lines). In the first cell (top row of raster plots and histograms), the learned movement direction necessary to reach the 90 target was 180 (indicated by an arrow) whereas in the second cell (bottom row), it was 45 . The firing rate during the preparatory period (after stimulus onset but before movement onset) is enhanced in the learned-movement direction. (b) Changes in the population averages of normalized firing rates during the preparatory activity before (gray) and after (black) learning. The abscissa shows the angular distance between the cells’ preferred direction and the learned-movement direction; the number of cells in each bin is indicated. Only cells with a preferred direction close to the learned-movement direction showed a significant change in firing rate due to learning. Reprinted by permission from Macmillan Publishers Ltd. (Paz R, Boraud T, Natan C, Bergman H, and Vaadia E (2003) Preparatory activity in motor cortex reflects learning of local visuomotor skills. Nature Neuroscience 6(8): 882–890), copyright (2003).

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change. Single unit recordings in the motor cortex during visuomotor learning have revealed a complex pattern of changes in the neuronal activity. A large fraction of the cells show a change in the magnitude of the activity modulation during adaptation, some increasing and others decreasing. When the visuomotor rotation to be learned is local, that is, in only one direction of movement, changes in the activity modulation are observed only in a subpopulation of cells with a preferred direction near the direction

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Figure 7 Rotation of the preferred direction for different types of cells in the motor cortex during force field learning. Macaque monkeys were trained to move a manipulandum on a horizontal plane to move a cursor on a vertical monitor from one central location to eight peripheral targets. As in the experiment described in Figure 6, a rightward hand movement (0 ) was mapped to a rightward cursor movement and a forward (90 ) hand movement to an upward cursor movement. However, in this experiment two torque motors acting on the manipulandum, during the ‘force field’ epoch, generated a clockwise velocity-dependent curl field, imposing a force on the hand perpendicular to the movement direction. (a) An example of the tuning curves of the movement-related activity of a ‘kinematic’ cell before, during, and after adaptation to the force field. The preferred direction (indicated by a red segment in the polar plot) of this cell does not change across epochs. (b) An example of a ‘dynamic’ cell: Its preferred direction rotates in the direction of the force perturbation during the force field epoch but returns to the initial direction in the washout epoch. (c) An example of ‘memory’ cell: The preferred direction rotates during the force field exposure and does not change back after the force field has been removed. Adapted from Li CS, Padoa-Schioppa C, and Bizzi E (2001) Neuronal correlates of motor performance and motor learning in the primary motor cortex of monkeys adapting to an external force field. Neuron 30(2): 593–607, with permission from Elsevier.

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of the kinematic transformation of motor error into movement plan rather than the dynamic transformation of movement plan into muscle activations. During learning of novel forces applied by a robot manipulator, the neuronal activity of single cells in the motor cortex during movement execution also shows a complex pattern of changes. Macaque monkeys, like humans, learn with practice to reach accurately under a viscous force field, and they show aftereffects when the perturbation is removed. Some cells show no change in magnitude of activity modulation and its directional tuning after learning the force field (Figure 7(a)). These cells might contribute to a kinematic representation of the motor plan. Some cells change their modulation magnitude and directional tuning only during the presence of the force field (Figure 7(b)). This group of cells appears to be involved in the representation of the motor output. In fact, the preferred direction of these cells rotates, similar to the muscles, in the direction of the force perturbation. Finally, other cells change their tuning during the force field but maintain this change after the perturbation is removed (Figure 7(c)). This group of cells might be encoding the learned novel dynamic mapping required for reaching in the force field. At the population level, this persistent change in the directional tuning after the perturbation is removed is balanced by a change in the tuning, in the opposite direction, of a fourth group of cells.

See also: Finger Movements: Control; Motor Skill Learning; Motor Sequences; Neural Coding in Primary Motor Cortex; Premotor Cortex in Primates: Dorsal and Ventral; Premotor Areas: Medial; Reaching and Grasping; Synaptic Mechanisms of Learning.

Further Reading Atkeson CG (1989) Learning arm kinematics and dynamics. Annual Review of Neuroscience 12: 157–183. Clower DM and Boussaoud D (2000) Selective use of perceptual recalibration versus visuomotor skill acquisition. Journal of Neurophysiology 84(5): 2703–2708. Flanagan JR, Nakano E, Imamizu H, et al. (1999) Composition and decomposition of internal models in motor learning under altered kinematic and dynamic environments. Journal of Neuroscience 19(20): RC34. Krakauer JW, Ghilardi MF, and Ghez C (1999) Independent learning of internal models for kinematic and dynamic control of reaching. Nature Neuroscience 2(11): 1026–1031. Lackner JR and DiZio P (2005) Motor control and learning in altered dynamic environments. Current Opinion in Neurobiology 15(6): 653–659. Martin TA, Keating JG, Goodkin HP, Bastian AJ, and Thach WT (1996) Throwing while looking through prisms. II. Specificity and storage of multiple gaze-throw calibrations. Brain 119: 1199–1211. Shadmehr R and Mussa-Ivaldi FA (1994) Adaptive representation of dynamics during learning of a motor task. Journal of Neuroscience 14(5 Pt 2): 3208–3224. Shadmehr R and Wise SP (2005) The Computational Neurobiology of Reaching and Pointing: A Foundation for Motor Learning. Cambridge, MA: MIT Press.