Abstract—Expensive and bulky setups, and center-out whole-arm reaching paradigms have been used extensively in motor control research to explore the neural control of movement in humans and primates. They have led to a number of robust findings about the effect of modified task dynamics onto movement kinematics and motor skill acquisition. A number of controversial findings are related to the role of peripheral reflexes and the effect of practice on motor learning, adaptation, and consolidation A related issue is whether the brain actually uses strategies similar to engineering optimal control. Finally, aspects that typically do not get much attention are the roles of subject motivation and the functional relevance of the task to daily activity.

Here we introduce a suite of virtual environments for motor skill acquisition, running on ubiquitous highly affordable and portable PC hardware. We explore case studies in both a research and a rehabilitation context, and suggest that our observations are compatible with theory by N.A.Bernstein [1] according to which the brain may perform feasibility search. Unlike a robotic system, the brain tries to achieve solutions to the behavioral tasks that satisfy imposed constraints, even if not yet optimal. When more than one solution is identified, the brain retains the better one for future use. In comparison, a robotic system would search (depth- or width-first) throughout the whole parameter space. This difference is not unlike the one between a grand-master and a chess playing program. Based on a rich variety of acquired behavioral data, we demonstrate clearly that the virtual environments we introduced here have a very large potential to: 1) Reproduce individually targeted elements of motor behavior, which are functionally relevant in everyday life; 2) Drive incremental re-acquisition of increasingly complex and adapted motor programs; 3) Achieve the latter goal by selectively augmenting or suppressing particular strategies depending on their compatibility with residual and readapted patient capacity at a particular point of the rehabilitation process.

I. INTRODUCTION ORMAL unperturbed movements are characterized by interesting features such as approximately bell-shaped

velocity profiles, rather constant duration and velocity peaks in a linear proportion to distance, straight paths between targets etc. External perturbations result in deviations from the stereotypical kinematics. At the present time a rather controversial issue in fundamental motor control literature is whether with practice subjects learn to compensate for the effects of the perturbation, which would mean that the motor system is attempting to restore the stereotypical kinematics

Nedialko I. Krouchev is with the GRSNC (FRSQ),

Physiologie,Universite de Montreal, Montreal (Quebec), H3C-3J7 Canada (corresponding author, phone: 514-343-6111 ext 4361; fax: 514-343-6113; e-mail: Krouchen@physio.umontreal.ca).

John F. Kalaska is with the GRSNC (FRSQ), Physiologie, Universite de Montreal, (e-mail: kalaskaj@PHYSIO.UMontreal.CA).

Supported by a CIHR/IRSC-NET Grant in Computational Neuroscience and FRSQ Group Grant.

seen in unperturbed movements [6]. According to Bernstein [1] dexterity is in finding a motor solution for any situation and in any condition. Based on a restricted class of reaching movements [7], motor learning with practice is often understood and modeled in analogy to engineering robotics as unique and stereotyped control output compensating for task conditions, including perturbing force-fields, visuomotor rotations etc, to achieve straight movement paths. Central planning processes and optimization of some cost function is invoked (e.g. [10]). Recent studies [8, 9, 11, 12, 18, 27, 30, 31] suggest that the goals of motor control may, instead of striving for optimality, just be to satisfy behavioral constraints in a given task context. When these are adequately formalized, excellent mathematical predictions of the experimental observations may be obtained.

Multiple sources [2, 5, 13-15, 17, 33, 39] describe beneficial effects of robotic and VR rehab even when applied long after the stroke. VR setups enable patients to safely practice motor acts bearing significant similarity with elements of daily-life. Like a figure skater performing many times a given fall-prone jump, through practice a patient will gain in motivation and self-confidence. Effects could generalize to daily activities and persist. An important feature of this approach, whether devices used are inexpensive or unique pieces of high technology, is the need to customize to the user. Then with proper partial supervision and well-designed tasks, as recovery progresses, assistance provided is likely to diminish in a seamless transition to more adequate motor function even if it does not fully recover. Stroke victims typically receive ER treatment, which may still leave them with profound functional deficits depending on the stroke extents and expediency of medical intervention. The immediate follow-up period of intense rehab according to US statistics is 17 days on average. Even more importantly, once the patients are back home, in Canada they typically receive no more than 1-2 hours of professionally-supervised motor or cognitive 'workout' a week. In this work, we suggest the use of inexpensive devices that the patient can take home and use daily. One useful comparison can be made to an alternative commonly called "Wiihabilitation": Nintendo's Wii game system recently gained popularity among patients. James Osborn (quoted by AP) said: ... many patients say PT [physical therapy] stands for "pain and torture" ... but patients become so engrossed mentally they're almost oblivious to the rigor. This statement clearly explains the two reasons for the success story: 1) Wii is fun; 2) It provides for practicing gross motor skills such as swinging, punching, ball hitting etc. We also rely on the psychological benefits of a gaming context so that patients stay clear of the

Virtual Worlds and Games for rehabilitation and research Nedialko I. Krouchev Student Member, IEEE, and John F. Kalaska

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frustrations due to their limited ability. Moreover, our approach focuses on tuning up the underlying cortical mechanisms that would trigger maintenance and plasticity of the brain's adaptive functions. This approach allows to concentrate very punctually onto a given deficit or side of the body in a way similar to a very strict Constraint-induced movement therapy (CIMT) [33-35, 38, 39] (since the patient can only do a task in an unique way as prescribed). If applied rigorously this approach could in principle promote even better recovery of functional ability in daily motor skills, such as picking up a cup without spilling its contents. One possible implementation, which requires a relatively small investment of time and resources, is outlined below. Control data as well as a case study of a patient tentatively diagnosed with corticobasal degeneration (CBD) [40-42] is presented. The patients could potentially do a lot for themselves using carefully selected personal-computer-assisted diagnostic and practice-exercise programs. A key objective is to demonstrate that dynamic environments, designed to be modular and hence highly customizable, can sufficiently challenge motor control and cognitive function, and guide (re)acquisition of motor skills one simple motor act at a time. These are bound to promote both cognitive and motor health.

II. METHODS On the one hand, this work is related to the principal goals

of the fundamental study of the human control of movement: to elucidate the role of various underlying neural systems, and to describe the dynamics of skill development and

TABLE I

TASK CONDITIONS AND EFFECTS OF PRACTICE BY SUBJECT AND CONDITION:

TASK EFFECTOR (*) CONDITION DEFINITION AND ACRONYMS SUBJECT MET SUBJECT NBC

1.1 Force

transducer (FT) Baseline unperturbed point-mass VR with elastic resistance and viscous friction dynamics

Baseline Baseline

1.2 Virtual External Force perturbations (VEFP) Curl-strategy Spectacular recall after 1 year Rapidly reached plateau performance in the recall

Hook-strategy Spectacular recall after 1 year

1.3 VEFP and Virtual assistance (VA) (**) Precise output timing: Reduced effort Reduced variability

As with MET force output timing is proactively adapted to achieve stable target hold.

1.4 VEFP and proactive VA (VPA) Precise control output timing: Proactive F(t) output strategy

Precise timing: Proactive strategy

2.1 Joystick (J) Baseline unperturbed point-mass VR with elastic resistance and viscous friction dynamics

Skill transfer from 1.1 Skill transfer: Very similar AIR strategy as in task 1.2 and rapidly reached plateau performance

2.2 VEFP, designed to reproduce condition 1.2 in the J-setup Skill transfer from 1.2 Straightened paths Variable (exploration) AIR strategies, similar to task 1.2

Straightened paths Reduced variability

2.3 VEFP and VA Skill transfer from 1.32.4 VEFP and VPA (***) Skill transfer from 1.4

Fatigue - sub-optimal VPA!

We implemented a suite of different VR conditions. Familiarization (baseline) conditions 1.1 and 2.1, respectively for the FT- and J-setups, did not include any perturbation or proactive assistance forces.

(*) Effector-related noise levels were dramatically different between conditions: The FT-device was operating around its maximal range (65N) and hence the effect of physiological tremor did not show in F(t) traces. Conversely the J-device responded to forces inferior to 0.5N (1N for the patient's data).

(**) Subject performance was consistent between subjects, with feasibility search principles. Adapted motion production in perturbed-conditions significantly differed from unperturbed baseline.

(***) Use of VPA led to inducing opposite control output from the two subjects within the same behavioral task constraints! (Fig.4 which compares conditions 2.3 and 2.4 - in the latter the computer produced force vectors at a clockwise angle of -π/8 to target direction)

A

B

Fig.1. Task setups

A Force transducer (FT) based VR setup B The dual axis joystick (J) substituting the FT-sensor - Logitech Dual Action(TM) Gamepad, priced below 20$

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retention. Toward this end, we conducted psychophysics experiments, requiring direct control of end-point force (isometric conditions) or position (joystick conditions). output at various levels of resolution amplitude and temporal

On the other hand, here we present a proof of concept,

that simple setups similar to the ones used for fundamental research can be applied to motor rehabilitation in both the young and elderly. To this end, we collected pilot patient data, and compared them to the results obtained for healthy control subjects.

A

F(t)P(t)

Subject MET Subject NBCFig.2. Adapted performance by two representative subjects in the VEFP task 1.2 (see Table 1) A. Experimentally observed curl and hook strategies (left and right respectively). (black) Subject-generated Forces F(t) (red) the computed VO positions p(t). Gray ellipses show the standard deviation of the position vectors at chosen points of the trajectories. The black ellipses inside targets show the standard deviations during THT. B. Simulated control output, for the 12 o'clock trials in Part A, was computed through optimal control with quadratic cost. F(t) output was initialized by a ramp along a straight-line in the Cartesian plane. Position trajectory (lasting 1100ms) for the point-mass VO was sub-divided into 20 episodes of equal duration (55ms). All the episodes' force levels formed a 20-dimensional vector of free parameters u. The VO's p(u,t) vector was obtained by the VR model actually used in the experiment. Quasi-Newton optimization gradients with respect to the controls u were computed through Pontryagin's minimum principle. The 8 distinct solutions we obtained for each target were nearly perfectly symmetrical: Hence, only the profiles for the 12 o'clock target are shown - the optimal F*(t) in orange and the resulting p(t) in green. Two optimal solutions (matching the respective subjects) were obtained for anticipatory initial rotation (AIR) of (curl) 0.59 rad and (hook) 0.19 rad. Inset: Shows a ‘’robotic’’ optimal control solution with no AIR (a 0 rad F-trajectory): It requires a more intricate temporal F(t) profile later in the trial, which no human subject exhibited.

B

F(t)P(t)

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Finally, we conducted a meta-analysis, whose purpose was to investigate the dependence of the motor challenge and resulting subjective motor solution on the actual properties of the interface devices and task paradigm choices. To this end, we implemented a suite of several experimental conditions (Table 1). All of these used a simple two-dimensional virtual reality (VR) environment. However, the reader will easily be able to notice that the ideas laid out below are easy to generalize into more realistic three-dimensional VR setups. In particular toward three important aspects on which we would like to concentrate in our future work: the advantages of a gaming context; the spatio-temporal aspects of neural motor control; the coordination between arms, hands and legs.

In the first set of four VR conditions (Table 1, Tasks 1.1-4), subjects produced an isometric force against the handle of an ATI force transducer in the x and y directions of the horizontal plane (Fig.1A). Required forces were scaled to the ability of each subject, and more importantly, can be automatically and adaptively rescaled with the improvement of the patient's performance, even on a direction by direction basis.

All tasks consisted in displacing a crosshair screen cursor between a center and 8 peripheral targets on a computer monitor. The VR environment was defined as follows: The time-series of forces F(t) generated by a subject, was applied to a virtual object (VO) - a point-mass m, and its moment-to-moment position p(t) was computed in real time, applying Newton's law:

m a(t) = F(t) - p(t) +G(t)⋅ (1) In unperturbed trials (Task 1.1), where G(t)=0, subjects

produced force ramps in different radial directions to displace the cursor from a center of the screen into the corresponding peripheral target. VO motion lasted 600ms on average (from onset to target entry). An additional zero-centered and unit-gained elastic field was introduced in (1) to help the subject with braking at the target. In the perturbed conditions called virtual curl (VC), the dynamics in (1) was altered by G(t) terms proportional and perpendicular (counter-clockwise) to the planar vector of the VO's velocity.

The remaining three isometric VR conditions (Tasks 1.2-4), included virtual curl force field perturbations. Additionally, in the last two tasks (1.3-4) subjects were also provided with virtual proactive assistance. The latter initiated movement along a particular path.

A second set of four VR conditions (Table 1, Tasks 2.1-4) completed the suite of overall eight visuo-motor paradigms. The behavioral paradigms matched exactly the requirements of each task in the first group as described above. However, the FT sensor was replaced by a joystick (Fig.1B) whereby minimal finger motion of either the left or right hand was interpreted as virtual forces (see Table 1 for the full details about the various paradigms, as well as for a summary of the key experimental findings).

In addition to patient data, we acquired full sets of experimental data from eight healthy subjects (age 22-36,

A

P*(t)

F(t)

MET NBC

F(t)

P(t)

P*(t)

B

P(t) F(t)

F(t)P(t)

Fig.3. FT-setup: VA paradigm: Data from task 1.3

A Compensatory control patterns: The inset from Fig.2 is reproduced here for comparisons with actual subject behavior. The colored arrows represent mean subject F(t) output, corresponding to distinct successful trial stages (see Part B, Inset) as follows: RT (mauve), MT-1 (red), MT-2 (green), THT (blue). The two subjects are showing qualitatively similar patterns of F(t) output, which compensates for the VC perturbation and is proactive (starts as early as RT) - thus avoiding to face the complexity of output that focuses on a last-minute change strategy (like the one in the Inset).

B Control strategy blueprints The position and size of circles and squares indicate the mean values and SD of (x,y) value pairs defined for each epoch (see the Inset caption below). Circles and squares relate to the P(t) and F(t) vectors respectively: (y-axis): the y-coordinate of the P(t) or force F(t) vectors; (x-axis) deviation measure: signed means of the sine values of the angle, formed between a current position P(t) or force F(t) vectors at a given time t, and the straight line to the target. Inset: For an actual 12 o'clock trial in the VEFP task, the box introduces time epochs: The colored segments of the F(t) and P(t) profiles define respectively the episodes: mauve: from presentation of the movement target to movement onset (RT), red: first half of the movement-time (MT-1) of the VO's (cursor) path between targets, green: second half of MT (MT-2), blue: target entry and hold time (THT).

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gender balanced). In each session, subjects performed a baseline of 240 unperturbed trials in 2 runs, followed by 360 perturbed trials in 3 runs, and finally another 120 unperturbed trials in a washout run.

III. RESULTS

A. Two distinct solutions (Fig.2) All baseline trials yielded straight p(t) trajectories. In the

VC condition, subjects changed their F(t) output to get the VO into and hold it inside the target.

Bernstein [1] observed that many motor control problems do not have unique solutions, and that motor skill does not mean stereotyped repetition of the same neural commands, but rather a continuous exploration of task space with its multiple degrees of freedom. Consistent with this perspective, after extensive training in the VEFP task 1.2, two distinct strategies (two patterns of dynamic attractor solutions to the VEFP task dynamics, see Fig.2A) emerged in different subjects that had similar success rates. In both cases subjects proactively (anticipating the effects of the perturbation) controlled the approach to the target. Salient features of the curl strategy (Fig.2, subject MET) were the substantially deviated and continuously rotated F(t) path. The initial force output over-compensated proactively, so that the cursor motion curved in the direction opposite to the applied perturbation, in a way that actually exploited the VC perturbation to push the cursor toward the movement goal. Conversely, in the hook strategy (Fig.2A, subject NBC) F(t) output was much less deviated and remained straight for most of the trial. Here subjects managed to produce a hook in the terminal part of the force trajectory, so as to counterbalance an outward radial deviation due to perturbation by the inward action of elastic field. Thus the VO would be stabilized within the target area. The latter strategy was observed more often. Adopted strategies at the end of Day #1 persisted during recall after 1, 2 weeks or more (see Table 1).

B. Computational Model We propose a simple optimal control model, which

formalizes adequately the behavioral constraints that the subjects faced in the perturbed task condition. The model just minimizes the distance from p(t) to the movement target p* during the 500ms target hold time (THT). All possible successful force outputs form a superset that includes our optimal solution, since the latter guarantees the goal position was as stable as possible. This formulation reflects accurately the gist of what the subjects were asked to do. E.g. there was no requirement for smoothness of either trajectory, except for low-pass properties of biologically plausible muscle force generation. The model reproduced both curl and hook control strategies we observed (Fig.2B). The latter were distinguished uniquely by their corresponding two magnitudes of Anticipatory Rotation of the Initial part of the F(t) trajectory (AIR) - respectively (curl) 0.59 rad and (hook) 0.19 rad

C. VR Paradigm extensions for applied rehabilitation and fundamental research Subjects were unable to systematically learn and

reproduce arbitrarily complex temporal patterns (like the ones in Fig.2B, Inset) of force output. The VC task was therefore extremely difficult. Table I outlines all task conditions, as well as the key experimental results, using data from two representative control subjects, each exhibiting one of the two control strategies we observed in the main VEFP task 1.2. We designed extensions to the task paradigm to systematically investigate the role of different AIR magnitudes. We programmed the virtual environment so that the task computer automatically initiated cursor movement upon termination of the center-hold time interval, and provided the full extent of the radial component of the force ramp. This virtual assistance (VA) was designed to produce straight movements in the unperturbed task conditions 1.1 and 2.1. By definition, VA force vectors were hence generated at zero deviation to target direction. In the VA-augmented perturbed conditions 1.3 and 2.3, the task computer generated the main motive component, and the subjects had to deal only with the consequences of VEFP on cursor motion. They compensated for angular deviation of the VO's movement trajectory toward the target and stabilized the target hold. This distinction provides for parallels to recent work [8,27,30] that advocates for separate control of postures and movements. While almost the whole work of getting the VO to its desired final position was provided, the VO would still miss the target by a fraction of a central angle due to the velocity dependent counter-clockwise virtual curl field. Moreover, subjects had to refine a process they did not initiate, and which was not natural for them, since it included no AIR (VA force vectors were generated at zero deviation to target). The subjects' motor controllers were engaged from the moment the target was displayed, which can be seen by the time course of changes in the force output's orientation and magnitude (Fig.3) toward more appropriate clockwise proactive rotation, which redirected motion into the target in a more reliable way. Interestingly, the additional VA forces practically unified the F output and VO's kinematics across subjects that had previously (in task 1.2) exhibited different control strategies and different kinematics. Furthermore, when non-zero clockwise AIR was provided in the VPA conditions 1.4 and 2.4 (Fig.4). Here corrective output was produced mainly to prevent the large angular deviation in the final position that would otherwise be caused by the VPA force ramp at a constantly deviated central angle. Once again, the control strategy was proactive, and thus exploited the task context, by exaggerating the initial counter-clockwise deviation of the p(t) trajectory, so that the radial force ramp almost exactly as provided would lead straight into the target (dashed arrow at -π/8 in Fig.4,MET). This observation is qualitatively very similar to the initial 'hook' in the response to perturbing curl forces, as reported in [11]. From a motor rehabilitation perspective, it is also noteworthy to observe the imposed reversal of the subjects' control strategies

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(Fig.4) within exactly the same behavioral context! And this was achieved by manipulating a single scalar parameter of the VR dynamic description.

D. Patient data Persistent sequels of pathologies such as CBD or chronic

stroke are a cause for devastating functional disabilities despite advances in acute stroke treatment. Furthermore, neural mechanisms of spontaneous and induced recovery are still rather poorly understood [2,4,5,14-17, 19-26,28,32]. As proof of concept, here we present patient data acquired at a patient's home, using only an 'outdated' Pentium III computer and the joystick in Fig.1B. Interestingly, the patient presenting right-hand side body weakness symptoms, after exclusive practice in the left-hand task (for 3 sessions of about 30 minutes each) showed significant transfer to right-hand skills. Such transfer is due to cognitive internalization of the task during practice. The patient familiarized with the task's most relevant visual features and joystick-effector controls (similarly to starting to use a new TV remote) and learned to associate with own contribution to VR (e.g. cursor motion) and task performance. Comparisons of patient and control data (as shown in Fig.5) could provide for useful insights into both fundamental principles and pathology. As we see on Fig.5B, the patient initiated movement attempts in the direction of an immediately preceding success trial (consistent with the hand priming effect described in [27]). These attempts resulted in error due to the fully randomized task paradigm. This result is compatible with the marked directional errors reported in hemiparetic subjects by [42]. Even if hand priming effect may have been present in the controls, they also anticipated the changes in target direction that followed every successful trial. A recent paper [27] reviewed evidence supporting Karl Lashley's hierarchical organization of motor behavior. The study describes the remapping, hand path

priming and end-state comfort effects observed during adaptation to tasks, requiring specific modifications of the feedforward neural commands' amplitude and timing. The first two effects are related to the consideration that central controls are not formed de novo for each successive movement, but instead are reshaped by making the appropriate changes needed to accomplish the movement at hand using to the fullest the previous motor state that resulted from a previous motor act or postural adjustment in the immediate movement history. The third effect distinguishes between the different control organization of postures and movements (see also [8,30]), and argues that stable and behaviorally-beneficial goal postures are achieved through subordination of the motion production subsystem to the postural one. Hence it may transiently require more effort for the sake of stable terminations. Here we observed very similar effects.

IV. DISCUSSION At this point, the utility of properly selected robotic and

VR therapies to promote recovery in multiple (chronic and acute) rehabilitation contexts has been scientifically and rigorously demonstrated. Due to their high associated costs such therapies have also invoked a lot of resistance and questioning by health-care authorities which compromise the extent of their practical applicability. The approaches we suggest here are directly derived from these same scientific and rigorous premises, but imply only a fraction of the cost. Motor rehabilitation bears multiple (to date, underused) parallels to learning of novel skills by professional athletes. Just like the latter learning a new type of vaulting or yet faster tennis serve, a patient needs special strategies to recrute potentially different brain areas and muscle synergies in order to recover functional use of contra- or ipsi-lesional limbs. The process is long and progress is measured in infinitesimal increments. Reward may only be a partial

A NBCMET

F(t)

P(t)

B

F(t)P(t)

Fig.4. J-setup: Contrast between VPA and VA paradigms: same format as Fig.3. Data from task 2.4 (MET) and 2.3 (NBC). A Compensatory F(t) output B Control blueprints: Forced strategy reversal: VPA in task 2.4 led subject MET to anticipate the large bias in the provided assisting virtual force toward the end of the trial. By appropriately timing corrective output, the subject managed to even exploit the bias, instead of waiting until the THT epoch to counteract it. It is noteworthy that similar behaviors was associated with force outputs of similar magnitude and opposite direction in each of the compared two conditions.

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recovery of function for the multiple hours of repetitive practice, which could still be potentially boring until recovery of function reaches a stage where the paradigms may become more challenging and hence more entertaining. E.g. most of the protocols used in the research of neural control of movement concentrate on single straight movements in Cartesian space around one or two joints. In this respect, novel paradigms need to be developed in to address specific motor deficits and functional challenges in daily and work routines - such as driving or maintaining postural balance. Familiarization with the tasks can start with easy (non-demanding) parameter setups, and the task programs can gradually adapt the parameters to a patient's skill level, prodding and supporting the process of improvement. Internet connections would provide for monitoring of progress by professional PT's and could enable scheduled integration with other therapies. A good VR rehabilitation system can be very successful if it finds ways to be entertaining and have just the right-level of challenge to the current recovery stage of a given patient. E.g. by appropriate inclusion of sensory-motor control and cognitive elements in its paradigms. Such tasks are also expected to have a very beneficial effect on the general cognitive performance in the elderly and, for the sake of both rehab and research, could be made publicly available. Suites of paradigms (variations on a similar theme, such as the one presented here as a proof of concept) would incrementally develop repertoires of motor primitives, using different limbs or their parts. Similarity to daily practice may therefore depend on the imagination of paradigm developers to set up a rich variety of VR environments and behavioral constraints.

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Fig.5. J-setup: Patient data A Success trials in task 2.1: Data from a control subject are compared to patient's on the right; the presentation in the same format as Fig.3B & 4B B Error trials in task 2.1: Slow MT data by the patient on the right. Initial variability is more than twice larger in control subject data due to the twice higher actuator gain and hence noise (see the foot notes in Table 1). The high deviation during the patient's MT is due to initiation of movements in the direction of a preceding success trial, consistent with [27] and esp. [42], whose patients made wrist movements with marked directional errors requiring corrective responses.

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