Failure of Cerebellar Patients to Time Finger Opening Precisely Causes Ball High-Low Inaccuracy in Overarm Throws

D. Timmann, S. Watts, and J. Hore

Physiology Department, University of Western Ontario, London, Ontario N6A 5C1, Canada


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Timmann, D., S. Watts, and J. Hore. Failure of Cerebellar Patients to Time Finger Opening Precisely Causes Ball High-Low Inaccuracy in Overarm Throws. J. Neurophysiol. 82: 103-114, 1999. We investigated the idea that the cerebellum is required for precise timing of fast skilled arm movements by studying one situation where timing precision is required, namely finger opening in overarm throwing. Specifically, we tested the hypothesis that in overarm throws made by cerebellar patients, ball high-low inaccuracy is due to disordered timing of finger opening. Six cerebellar patients and six matched control subjects were instructed to throw tennis balls at three different speeds from a seated position while angular positions in three dimensions of five arm segments were recorded at 1,000 Hz with the search-coil technique. Cerebellar patients threw more slowly than controls, were markedly less accurate, had more variable hand trajectories, and showed increased variability in the timing, amplitude, and velocity of finger opening. Ball high-low inaccuracy was not related to variability in the height or direction of the hand trajectory or to variability in finger amplitude or velocity. Instead, the cause was variable timing of finger opening and thereby ball release occurring on a flattened arc hand trajectory. The ranges of finger opening times and ball release times (timing windows) for 95% of the throws were on average four to five times longer for cerebellar patients; e.g., across subjects mean ball release timing windows for throws made under the medium-speed instruction were 11 ms for controls and 55 ms for cerebellar patients. This increased timing variability could not be explained by disorder in control of force at the fingers. Because finger opening in throwing is likely controlled by a central command, the results implicate the cerebellum in timing the central command that initiates finger opening in this fast skilled multijoint arm movement.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Although it is often stated that an important function of the cerebellum is to time movements, for the case of arm movements, the situation is unclear. One piece of evidence that is argued to be in favor of the timing proposal (e.g., Ivry 1997) is the finding that cerebellar patients show prolonged agonist and delayed antagonist activity in fast single joint movements (Hallett et al. 1991; Hore et al. 1991). However, cerebellar patients also show a more gradual buildup of agonist electromyographic activity and a decrease in force (Holmes 1917; Hore et al. 1991), which are not readily explained by timing theories. A second piece of evidence used to support the timing role is that cerebellar patients show a delay in the onset of movement (increase in reaction time) (Holmes 1917). Although at first sight this appears to be a timing disorder, it has also been explained as lack of efficient coupling of the stimulus to the motor response (Grill et al. 1997). Similarly, for multijoint movements, the ataxia occurring in cerebellar patients, which could be explained as timing disorders, has been attributed to an inability to control interaction torques (Bastian et al. 1996; Topka et al. 1998). It is unknown to what extent disorders, such as a decrease in initial force production at individual joints and disorders in timing of onset of joint rotations, also contribute to the inaccuracy in multijoint movements (Massaquoi and Hallett 1996).

Our objective was to test the idea that the cerebellum is important for precise timing of fast skilled arm movements. This was achieved by studying a situation where timing precision is required for task accuracy, namely finger opening in overarm throwing (Hore et al. 1995, 1996a,b). Finger opening is of interest for studies of timing because its onset appears to be triggered by central commands to the finger muscles (Hore et al. 1999a). In contrast, onset of more proximal joint rotations, such as elbow extension and wrist flexion, may be determined in part mechanically by interaction torques associated with movements of adjacent segments (Bernstein 1967; Herring and Chapman 1992). Timing of finger opening is important in throwing because it determines the time of ball release on the flattened-arc hand trajectory: balls released early go high, those released late go low. It has been reported previously that cerebellar patients cannot throw accurately (Becker et al. 1990). We therefore tested the hypothesis that for overarm throws made by cerebellar patients, ball inaccuracy in the high-low direction is due to a disorder (increased variability) in the timing of finger opening.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Subjects

Experiments were performed on six right-handed cerebellar patients from the Department of Neurology, University of Essen, Germany, and on six control subjects. The experiments were approved by the local ethics committee, and all subjects and patients gave informed consent. Patient information is given in Table 1. In brief, four patients had right-sided surgical lesions that affected the region of the cerebellar nuclei, one had a right-sided cerebellar infarction (superior cerebellar artery), and one had diffuse cerebellar cortical atrophy. In all cases the extent of the lesion was confirmed by magnetic resonance imaging. All patients had a full neurological examination at the time of the experiments.


                              
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Table 1. Patient information

Control subjects and cerebellar patients were matched for age, sex, handedness, and self-assessed throwing ability (for patients before the lesion). Patients rated their prelesion throwing ability on a score from 1 to 5 (1, very bad; 2, bad; 3, reasonable; 4, good; 5, very good thrower; Table 1). Self-assessed throwing ability was verified by asking patients how far they threw in the standardized test for athletic ability given every year to German school children. Although young, cerebellar patient Hv was large and strong for her age, was active in ball sports, and rated herself as a reasonably good thrower before the lesion. For cerebellar patient Sc, prelesion throwing ability could not be assessed, because a cerebellar tumor was removed at the age of six.

General procedures

Subjects and patients sat in a chair with the trunk fixed by straps over the shoulder so that translational position (hand trajectory) could be computed with reference to a fixed position in space (the sternum). They threw tennis balls at a 162-cm square grid of numbered 6-cm squares, aiming for a central square that was at eye level 3 m from the chest. They were instructed to throw accurately 50 balls at a medium speed, 50 at a slow speed, and 50 at a fast speed, in all cases using an overarm motion that involved horizontal adduction of the upper arm. The experimenter, located behind the subject, scored the number of the target square hit by the ball. Often throws in cerebellar patients missed the aimed target. Nevertheless these throws were scored in terms of their approximate high-low level including when they hit a high cross bar located on the magnetic field coils near the ceiling 1.8 m from the subject (extreme high) and when they hit a low crossbar near the floor (extreme low). Subjects threw on a verbal command given approximately every 15 s.

Ball release and throwing speed

In previous experiments, ball release was signaled by microswitches (triggers) taped to the proximal and distal phalanges of the middle finger that signaled the start of the ball rolling along the finger (proximal trigger) and the moment of final ball release from the finger tip (distal trigger) (e.g., Hore et al. 1996a,b). The time of the distal trigger is important because it represents the last moment that the finger can influence the ball. The time of the proximal trigger is also of interest because in recreational ball players the velocity vector of the hand at this moment is related to ball direction (unpublished observations). Because the time interval between the proximal and distal triggers is proportional to throwing speed and because it was easier to grip the ball without the proximal trigger, this trigger was not used in the present experiments. Instead the time of the proximal trigger was estimated by subtracting a fixed time, which was proportional to throwing speed, from the time of the distal trigger; e.g., for throws of 10 m/s, the estimated time of the proximal trigger was 30 ms before the distal trigger (final ball release). In some patients, the ball did not always activate the distal trigger (presumably because it rolled along the side of the middle finger). Therefore the moment of final ball release from the fingertip was determined by a number of criteria including the time of the distal trigger (when present), the moment of a deflection or peak in finger extension (that we have shown correlates with ball release), and the moment when finger torsion or finger horizontal motion, both with respect to the hand, suddenly changed direction (as a result of a reactive force associated with the ball leaving the fingertip). The few throws not meeting these criteria were omitted. In all experiments, throwing speed was measured as hand peak angular velocity in space, which in control subjects was related tightly to ball speed. Hand angular velocity was used instead of ball speed because it could be measured for throws that missed the target and for which ball speed was unavailable.

Timing windows

As before (Hore et al. 1995, 1996a,b), we defined variability in the timing of ball release and timing of onset of finger extension in terms of the SD about the mean times with respect to the moment in the throw that the hand was vertical in space. For timing windows, time of ball release was defined as the moment of final ball release from the finger tip (the distal trigger). Time of finger extension onset was determined when finger extension velocity crossed a high threshold, which was usually 20% of the mean finger extension peak velocity for that subject. For a normal distribution, 95% of observations occur in the interval defined by the mean ± 1.96 × SD (Sokal and Rohlf 1981). Thus timing windows for ball release and finger onset for 95% of the throws were calculated by multiplying the respective SDs by 3.92.

Recording angular and translational arm position

As previously, arm segment orientations were measured with the use of a modification of Robinson's (1963) magnetic-field search-coil technique (Tweed et al. 1990). Arm movements were sampled at 1,000 Hz by means of a pair of orthogonal search coils taped to each arm segment: scapula, upper arm, forearm, hand, and tip of the middle finger. A reference arm position was recorded where the upper arm was held horizontal and the forearm and fingers were held vertical. In all figures, hand angular position in space is the amplitude of vertical rotation from the reference position around a space-fixed horizontal (pitch) axis. Calculations also were performed to obtain rotations of the fingertip with respect to the hand. Hand translation was computed with the use of the measured length of each arm segment and its angular position with respect to the distal end of the adjacent proximal segment. Only hand trajectories in the vertical plane were analyzed in detail.

Statistics

To determine whether there was a relation between any two variables, a scatter diagram was plotted and the slope of the regression line and the correlation coefficient r were computed. The null hypothesis, that the slope of this line was 0, was tested by an ANOVA procedure (F test of regression ANOVA). Analysis of variance with repeated measures was performed for those dependent variables that were analyzed under all three velocity conditions (i.e., time of ball release, throwing accuracy, peak hand angular velocity, and onset of finger extension; repeated measures ANOVA; SPSS 8.0 for Windows statistical package). Repeated measures factors were: instruction to throw at three different speeds (slow, medium, and fast) or actual throwing speed; between group factor was the control and cerebellar group. In addition to different speed instructions, throws of individual subjects were divided into three groups (slow, medium, and fast) based on the actual throwing speed (i.e., peak hand angular velocity). Greenhouse-Geisser's adjustment of degrees of freedom was applied to correct for small departures from the assumption of normality and equality of variance in the three-factors design. All other parameters (i.e., trajectory length, height, and direction, finger amplitude, and velocity) were analyzed under the medium-speed instruction only and unpaired t-tests were used to show group differences (controls vs. cerebellar patients). P values for effects were set at <0.05.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Accuracy and speed of throws

All patients felt that they were much less accurate at throwing after the cerebellar lesion. In agreement with this self-assessment, cerebellar patients threw less accurately than the matched control subjects. Figure 1 shows the height of ball impact on the target plotted against the point of impact in the left-right direction for throws made by a 15-yr-old male cerebellar patient (Ol) and for throws made by a matched control subject. Groups of 50 throws are plotted according to the instruction to throw at a slow speed (Fig. 1A), a medium speed (Fig. 1B), and a fast speed (Fig. 1C). Mean throwing speeds (hand peak angular velocity in space) for each group are shown on each graph. Two results are clear. First, in all cases, throws made by the cerebellar patient were more variable on the target in height and in width than those made by the control. Second, throws for each group were much slower for the patient. The cause of the high-low inaccuracy will be examined in the present paper; the cause of the left-right inaccuracy will be described elsewhere.



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Fig. 1. Ball accuracy on the target for throws made by a cerebellar patient (Ol) and a matched control (Mr). In both cases, the instruction was to make 50 throws at a slow, medium, and fast speed. Mean ± SD of peak hand angular velocity in space (a measure of throwing speed) is shown for each set of throws.

All cerebellar patients threw less accurately in the high-low direction than their matched controls. We assessed accuracy by calculating the mean impact height of the ball on the target and used the SD as a measure of throwing variability. Figure 2 shows the mean impact height ± SD (where 0 is the aimed level) for throws made under each speed instruction. For cerebellar patients, SDs were on average five times larger than those for controls. The effect of the instruction to throw at different speeds or of the actual throwing speed on ball accuracy was determined using a repeated measures factors design. As expected, ANOVA revealed significant group effects (cerebellar vs. control) for ball accuracy (both P values = 0.001). There were no significant effects of instruction or throwing speed on ball accuracy. The interactions of group and instruction or throwing speed effects did not reach statistical significance. Thus neither the speed instruction nor throwing speed significantly influenced throwing accuracy. This presumably reflects the instruction to the subjects to throw accurately at each of the three speeds. Therefore for simplicity, in the following only results are illustrated for experiments made under the instruction to throw accurately at a medium speed, unless indicated otherwise.



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Fig. 2. Ball accuracy in the high-low direction for all cerebellar patients and controls. Each point is the mean ± SD for ball impact height on the target for 50 throws where 0 is the aimed height. Throws are grouped by the instructed speed. Patients and their matched controls are in equivalent positions from left to right.

Patients threw more slowly than the matched controls especially for the fast-speed instruction. Mean throwing speeds for the different speed instructions were fast: 3,901 ± 923, 2,084 ± 472; medium: 2,930 ± 655, 1,897 ± 519; and slow: 2,204 ± 528, 1,671 ± 437 (SD) °/s, respectively, for controls and cerebellar patients. Across subjects, mean throwing speeds were decreased significantly in the cerebellar group compared with the control group (P = 0.005; ANOVA).

Variability in hand trajectory

Each control subject and each cerebellar patient threw with a slightly different throwing motion and a slightly different hand trajectory. Figure 3 shows a side view of the forward part of one throw from patient Ol that hit near the aimed target. Hand trajectory is indicated by the curved line, i.e., it gives the path of the distal end of the middle finger metacarpal to ball release. This throw had a flattened-arc (curved) trajectory as has been described previously for normal subjects (Hore et al. 1996a,b).



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Fig. 3. Side view of stick figure of forward arm trajectory for a single medium-speed throw made by cerebellar patient Ol. Throw progresses from left to right and hit near the aimed target. Final ball release indicates when the ball left the fingertip. Arm segments shown every 2 ms. Curved line shows hand trajectory in space to final ball release.

A feature of throws made by cerebellar patients was that they had more variable hand trajectories than controls. For example, Fig. 4 (top right) shows that for 10 consecutive throws made under the medium-speed instruction by cerebellar patient Ol, there was slightly greater variability in hand trajectory height and much greater variability in length to ball release () than for the control subject (Mr). Similar increased variability, especially in trajectory length, can be seen for all cerebellar patients. The mean ± SD of hand trajectory lengths and heights measured 20 cm in front of the sternum for throws made under the medium-speed instruction can be seen in Table 2. Across subjects, SDs of hand trajectory lengths for cerebellar patients were 3.5 times those of controls, whereas SDs of hand trajectory heights were 1.5 times larger. This was also the case for trajectory heights measured at 10 and 30 cm in front of the sternum. Variability of trajectory length was increased significantly in the cerebellar group as compared with the control group (P < 0.01), but variability of trajectory height did not reach statistical significance (P = 0.09; unpaired t-tests). Mean values of trajectory height and length were not significantly different between groups.



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Fig. 4. Side view of hand trajectory for 10 consecutive throws made under the medium-speed instruction in cerebellar patients and controls. Traces begin at start of forward hand translation (left side of each column) and end at final ball release (black circle). Throws are aligned on the sternal notch, which is indicated by a small circle and vertical line.


                              
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Table 2. Hand trajectory parameters

Does variability in hand trajectory height or direction cause ball inaccuracy?

This was investigated by plotting ball impact height on the target against the height of the hand trajectory measured at a point that was a fixed distance forward from the sternum. Figure 5A shows that in two representative cerebellar patients, for the throws made under the medium-speed instruction, no relation occurred between ball accuracy and trajectory height at 20 cm in front of the sternum. This was also true for all patients for trajectory heights measured at 10 and 30 cm in front of the sternum. Thus ball high-low inaccuracy cannot be explained by variable high-low locations of the hand trajectory.



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Fig. 5. Relations in 2 cerebellar patients between ball impact height on the target and different kinematic parameters. Hand trajectory parameters in A and C were measured at a fixed point forward from the sternum. In B, a relationship occurs between ball impact height and hand trajectory direction in the up-down direction at the time the ball first starts to roll along the fingers (30 ms before final ball release, see METHODS).

In a throw, the direction of the ball will follow the direction of the tangent of the hand trajectory at ball release (i.e., the velocity vector of the hand trajectory). We have found that this is true in recreational ball players not for the moment of final release from the fingertip (distal trigger) but for the moment that the ball is first released from the grip and begins to roll along the fingers. This is because once the hand releases its grip, it no longer dictates the direction of the ball, although the possibility remains that the fingers can deflect the ball to some degree. It follows that the orientation of the velocity vector of the hand trajectory at this first release point should be related to ball direction (see METHODS). The direction of the velocity vector was defined as the angle between the tangent of the hand trajectory at this first release point in the vertical plane and a fixed horizontal zero-vector. As expected, all cerebellar patients showed a strong relation between the height of ball impact on the target and the direction of the velocity vector of the hand measured for medium-speed throws 30 ms before final ball release (all P values < 0.001; see Fig. 5B for 2 representative patients).

However, the question of functional interest is: do differences in direction (orientation) of the hand trajectory from throw to throw cause the ball to go high and low? In keeping with this possibility, cerebellar patients had a greater variability in the direction of the hand trajectory from throw to throw than controls. For example, for medium-speed throws, across subjects the mean SD of the angle of the velocity vector for cerebellar patients was twice that of controls, measured at 20 cm in front of the sternum in the vertical plane (Table 2). If the ball impact height on the target is determined by hand trajectory direction, then at a fixed point in the throw, the velocity vector will be related to ball impact height. Figure 5C shows for the two representative cerebellar patients that when the angles of velocity vectors at a fixed point 20 cm forward from the sternum were plotted against ball impact height on the target no relation was found. Similarly, no relation was found for any of the six cerebellar patients (all P values >0.05) despite significantly increased variability of trajectory direction as compared with the control subjects (P < 0.01; unpaired t-test). The same was true for other fixed forward positions (i.e., at 10 and 30 cm in front of the sternum).

In summary, for throws made by cerebellar patients, ball inaccuracy in the high-low direction was not related to differences from throw to throw in hand trajectory height or to differences in hand trajectory direction.

Variability in timing of ball release

The remaining possibility is that ball high-low inaccuracy results from variable timing of ball release occurring on a curved hand trajectory. There are a number of ways of testing this possibility. First, a relation should exist between ball impact height on the target and the length of the hand trajectory in the backward-forward direction to ball release, i.e., short trajectories should be associated with the ball going high, long trajectories with the ball going low. Figure 5D shows for two cerebellar patients that such a relation occurred for the medium-speed throws. This relation was significant at the P < 0.001 level in all six patients. Second and most importantly, a relation should exist between ball impact height on the target and the timing of final ball release. As previously (Hore et al. 1995, 1996a,b), we measured timing to the point in the throw when the hand was vertical in space. Figure 6 shows that a strong relation occurred between ball impact height on the target and timing of ball release for all six cerebellar patients (all P values <0.001).



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Fig. 6. Ball impact height on the target was related to timing of ball release in all cerebellar patients. Time of ball release was measured with respect to the time of hand vertical position in space (0). Negative values for time indicate that release occurred before the hand reached vertical position. Extreme high throws e.g., in Hn, hit a high cross bar on apparatus (see METHODS). n congruent  50 throws.

In keeping with their greater throwing inaccuracy, cerebellar patients had markedly more variable times of ball release than controls. Table 3 gives timing windows for ball release in which the SD of the mean release time was multiplied by 3.92 to give the range of variability for 95% of the throws (see METHODS). Overall, timing windows were about five times larger for patients. Analysis of variance revealed significant group effects (cerebellar vs. control) on timing windows for ball release (P = 0.01). There were no significant effects of instruction or throwing speed on timing windows for ball release. The interactions of group and instruction or throwing speed effects did not reach statistical significance.


                              
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Table 3. Timing windows for ball release

Disorders in joint rotations

Which joint rotations caused the errors that produced this variability in timing of ball release? Because timing of ball release was measured with respect to the moment in the throw that the hand was vertical in space and because this hand position arises from the sum of all proximal rotations, there were two major possibilities. First, there could have been correct timing of finger opening with incorrect (variable) timing or velocity of one or more proximal joint rotations. Second, there could have been incorrect (variable) timing of finger opening with correct timing and velocity of proximal joint rotations (and thereby correct hand trajectories). We previously have demonstrated (Hore et al. 1996a) that if there were variable proximal joint rotations (first possibility), then plots of hand angular position against hand translation should separate for high and low throws. However, as shown in Fig. 7A, traces for high (n = 10, lines) and low (n = 10, open circles) throws overlapped in patient Ol. That is, for a particular forward hand translational position, no difference was seen in hand orientation for high and low throws. Similarly, when all throws from patient Ol were considered, plots of ball impact height on the target grid versus hand orientation at a fixed position 30 cm forward from the sternum were unrelated at the P < 0.05 level (Fig. 7B). Similar results were found in four cerebellar patients. Two cerebellar subjects (Hn and Ls) showed a weak correlation (r = 0.38 and 0.29).



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Fig. 7. Relation between hand angular position in space and hand translation in cerebellar patient Ol. A: 10 high and 10 low throws. B: hand angular position measured 30 cm from the sternal notch plotted against ball impact height for all 50 throws in patient Ol.

In summary, no convincing evidence was found that incorrect hand orientation in space, and therefore incorrect timing or velocity of proximal joint rotations, caused high-low accuracy in cerebellar patients.

Variability in finger opening

So far we have established that ball high-low accuracy is related to timing of ball release and that this cannot be explained by variable hand trajectories or variable proximal joint rotations. Instead it seemed likely that variable ball release was related to variable timing of finger opening. But it was unclear whether variability in the amplitude and velocity of finger opening would also contribute to ball high-low accuracy. Figure 8 shows traces of finger opening for 10 consecutive throws in all cerebellar patients and their controls. Each trace represents the angular position of the distal phalanx of the middle finger with respect to the hand aligned on the time of vertical hand position in space (vertical line). Horizontal lines (0°) represent when the fingers were in a straight line with the hand. Finger opening in cerebellar patients appears to be more variable in amplitude, velocity, and time of onset.



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Fig. 8. Timing, velocity, and amplitude of finger opening is more variable in cerebellar patients. Angular positions of the fingertip with respect to the hand, for 10 consecutive throws, aligned to the time when the hand was vertical. Horizontal line indicates reference position when finger and hand were in a straight line.

As expected, time of onset of finger opening in cerebellar patients was related to ball impact height on the target. Figure 9A shows time of onset of finger extension with respect to hand vertical (time 0) plotted against height of ball impact on the target for patient Ol. A strong inverse relation was found between these variables. Similar strong inverse relations were found for all cerebellar patients (all were significant at the P < 0.001 level). Means and SDs were obtained for times of onset of finger opening with respect to time of hand vertical and timing windows were calculated for 95% of the throws. Across subjects, timing windows for throws under the medium-speed instruction were 18 ms for controls (range 6-45 ms) and 68 ms for cerebellar patients (range 22-111 ms). These group means were significantly different for the instruction to throw at different speeds (P < 0.01) and the actual throwing speed (P < 0.01; ANOVA).



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Fig. 9. Relationship between kinematics of finger opening and ball high-low accuracy for cerebellar patient Ol. A: relationship between time of finger extension onset and ball impact height on target grid. Time of finger extension onset (determined when velocity crossed a threshold that was 20% of the mean finger extension peak velocity) was measured with respect to time of vertical hand position (0). Negative values indicate that fingers began to extend before the time of hand vertical position. B: absence of relation between finger amplitude and ball impact height on target grid. Finger amplitude was determined by the difference between the angular position of the finger with respect to hand at onset of finger extension and at ball release. C: absence of relation between peak finger extension velocity and ball impact height on target grid. n congruent  50 throws.

Cerebellar patients had greater variability in finger amplitude and velocity. Across subjects finger amplitude was 2.5 times and peak finger velocity two times as variable in the cerebellar group as compared with the controls [SD peak finger amplitude: control group, mean 6.6° (range 3.6-13.6); cerebellar group, 16.3° (9-25.1); SD peak finger velocity: control group, 193°/s (84-299); cerebellar group, 396°/s (117-596); P values <0.05, unpaired t-tests]. In spite of these changes, no evidence was found that either of these parameters made a strong contribution to throwing inaccuracy. For example, for throws made by cerebellar patient Ol under the medium-speed instruction, no significant relation was found between ball impact height on the target and either finger amplitude (Fig. 9B) or peak finger extension velocity (Fig. 9C). Four cerebellar patients (Hs, Hn, Sc, and Ls) did show a weak relation between peak velocity of finger opening and ball high-low accuracy (P < 0.05), and three of them (Hn, Sc, and Ls) showed a weak relation between finger amplitude and ball high-low accuracy (P < 0.01). However, in a multiple (i.e., hierarchical stepwise) regression analysis for each of these patients with time of ball release entered as first independent variable, neither the introduction of peak finger amplitude nor peak finger velocity increased substantially the square of the multiple correlation coefficient (R2). Neither of these two parameters accounted for more than another 1% of the variance of ball high-low accuracy. Therefore, although showing a weak significant simple correlation with ball high-low accuracy in some individual cerebellar patients, neither peak finger amplitude nor peak finger velocity explained a significant amount of the variance of ball high-low accuracy in addition to time of ball release alone. Thus peak finger velocity and amplitude were not making an independent contribution to the prediction.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The results show in an overarm throwing task, that compared with controls, cerebellar patients had increased variability in hand trajectories, in timing of ball release, and in amplitudes, velocities and timing of finger opening. Furthermore cerebellar patients did not throw accurately in the vertical direction because they had increased variability in the timing of ball release, which in turn was caused by increased variability in the timing of finger opening.

Accuracy in overarm throwing requires precise timing of finger opening

Why was ball accuracy in the high-low direction in throws made by cerebellar patients related to timing of ball release and not with variability in other kinematic parameters? There are two likely reasons. First, cerebellar patients could not time finger opening precisely with respect to other joint rotations, and this caused the more variable times of ball release. In the present study, as before, we defined the variability of timing (release windows) in terms of the standard deviation (SD) about the mean of release times with respect to the moment in the throw that the hand was vertical. Expressed in terms of the timing window for 95% of the throws, the variability of ball release was 11 ms in the present control group compared with 10 ms for throws with the right (dominant) arm in recreational ball players (Hore et al. 1996a) and 22 ms for throws with the left (nondominant) arm (Hore et al. 1996b). In contrast, the mean timing window for the cerebellar patients was 55 ms (Table 3), whether the throws were made under the slow, medium, or fast instruction. Similarly, timing windows for onset of finger opening were about four times longer in patients. Thus cerebellar patients had a much greater variability in the timing of finger opening with respect to the moment in the throw that the hand was vertical. Because the hand vertical position represents the sum of rotations at shoulder, elbow, and wrist, it follows that cerebellar patients could not time finger opening precisely with respect to the sum of proximal joint rotations.

The second reason why ball accuracy in cerebellar patients was related to timing of ball release and not with other kinematic parameters has to do with the nature of the throwing task. In throwing, ball accuracy is more sensitive to the timing of ball release because the hand and ball travel on a flattened arc and the moment of ball release on this arc determines the ball's direction (Calvin 1983; Simonian 1982). In normal subjects, variability in other parameters such as hand trajectory height and finger amplitude and velocity, has relatively little effect on ball direction compared with the variability in timing of ball release (Hore et al. 1996a,b). Furthermore variability in timing of the fingers has a greater effect on ball accuracy than variability in timing of proximal joints. As described previously (Hore et al. 1996b), the reason that ball accuracy is more sensitive to timing of the fingers than to timing of proximal joints is that finger timing errors are scaled (multiplied) by the larger angular velocities of the hand in space rather than by the smaller angular velocities of the individual proximal joints. Thus throwing is a task in which variability in a number of kinematic parameters (e.g., height and direction of hand trajectory, amplitude of finger opening) can potentially affect ball accuracy; however, any such effects will be overwhelmed by any variability in the timing of finger opening if it is large. In keeping with this, the present results showed variability in hand trajectory height and direction and in the amplitude, velocity, and timing of finger opening in cerebellar patients; however, only the variability in finger timing was related to ball accuracy.

Comparison with other throwing studies

There are few studies of the kinematics of throwing in cerebellar patients. The one related study is that of Becker et al. (1990), who studied the accuracy of dart-like ball throws in three degenerative cerebellar patients. One similarity with the present findings is that in both cases cerebellar patients did not throw as accurately as controls. Becker et al. suggested that the lack of accuracy (in the left-right direction) was due to an inability to coordinate the muscles so as to produce the same hand direction from trial to trial. A difference between the two studies is that Becker et al. did not find any major difference in the timing of hand opening (relative to the time of forearm peak velocity), whereas our major result was impaired timing of finger opening (relative to the moment in the throw that the hand was vertical). Three possible reasons for this difference are that they were not able to sample the rapid finger opening with high resolution (their sampling frequency was 238 vs. 1,000 Hz in the present study), cerebellar patients may show smaller finger timing disorders in the slower and easier dart-like ball throwing task, and their degenerative cerebellar patients with primarily cortical lesions may have had smaller disorders than our patients who primarily had nuclear lesions.

Causes of variable timing of finger opening in cerebellar patients

The present finding of increased variability in timing of finger opening in throwing is in agreement with clinical observations in cerebellar patients of disorders in skilled movements of the fingers. In fact, Holmes (1917, 1922) was of the opinion that ataxia was more pronounced at the distal musculature. In agreement, studies of arm movements in cerebellar patients (Bastian and Thach 1995; Hore et al. 1991), of functional imaging of the cerebellum (Desmond and Fiez 1998; Jenkins et al. 1994; Jueptner et al. 1997; Sadato et al. 1996), and of lesions and recordings in animals (Mason et al. 1998; van Kan et al. 1994) have all emphasized an important role of the cerebellum in the control of finger and hand movements.

Why is it that our cerebellar patients could not time finger opening precisely? We will consider six possibilities. The first is that the patients were very bad throwers before the lesion. However, because patients were matched with controls in terms of throwing skill before the lesion and because their timing windows were five times longer than controls, this does not seem credible. A second possibility is that in daily life patients did not use their affected arm for throwing and this lack of practice caused the variability. Again this is unlikely because it has been our experience that older normal subjects, who had previously been good throwers but who had not practiced throwing for many years, adapted within a few throws to our task and threw with narrow timing windows.

A third possibility is that cerebellar patients could not control forces and interaction torques at individual joints that produced the hand trajectory (cf. Bastian et al. 1996) and that this led to abnormal timing of finger opening. In a throw, during the time of ball release from the hand, back forces occur on the finger from the ball the magnitude of which depends on the sum of the (forward) forces developed at all joints during the throw. If the forward forces, and in turn, back forces were disordered and if finger opening was caused by back forces, then this could potentially cause disorder in timing of finger opening. This possibility can be ruled out because it has been demonstrated that finger opening is not initiated by back forces (Hore et al. 1999a,b). For example, in overarm throws, when forward motion of the hand was blocked or slowed (thereby changing back forces by producing hand translational deceleration rather than hand acceleration), the fingers still opened and at the same time as for unperturbed throws. Alternatively, disordered forward and back forces could produce disordered kinematics of finger opening that could lead to abnormal timing of finger opening. This scenario predicts that early finger onset will be associated with faster initial velocities of finger opening (larger back forces) and late finger onset with slower initial finger velocities (smaller back forces). However, inspection of Fig. 8 shows that this was not the case. For example, late onsets of finger opening in subjects Ol, Hs, and Ls all have large initial velocities of finger opening. Furthermore plots of timing of finger opening against peak velocity of finger extension for all throws did not reveal the predicted relation for any subject.

A fourth possibility is that cerebellar patients could not produce the appropriate finger force and that this led to increased variability in the timing of finger opening. Disorders in finger force production could occur because of a failure to correctly predict the magnitude of the back forces or because of a failure to generate the correct finger force. The latter possibility is consistent with previous demonstrations in cerebellar patients of disordered buildup and maintenance of finger force (Mai et al. 1988; Müller and Dichgans 1994). If there was disorder in finger force production, then again it would be expected that early finger onset would be associated with faster initial velocities of finger opening (higher finger force) and late finger onset with slower finger velocities (lower finger force). However, as described in the preceding text, the data (e.g., Fig. 8) were not consistent with this possibility.

A fifth possibility, based on the proposal of Cordo et al. (1994), is that finger opening is normally triggered by proprioceptive feedback (e.g., from elbow extension) and that in cerebellar patients these signals were disordered. We have previously found that proprioceptive feedback from wrist flexion and elbow extension can be ruled out as the trigger for finger opening (Hore et al. 1999a). This is because perturbations of these joint rotations do not affect the occurrence or the timing of finger opening and because latencies from onset of these joint rotations to onset of finger opening are too short.

This leaves the sixth possibility, that finger opening is normally controlled by a central command that specifies the timing of finger opening and that in cerebellar patients there is disorder in the timing of this command. We believe that the evidence to date suggests that this is the most likely cause of the increase in variability in the timing of finger opening in cerebellar patients.

Cerebellar mechanisms for timing movements

It has been concluded for normal subjects that because of the fast speeds and short times in an overarm throw, it is likely that finger opening is triggered centrally by means of feedforward control (Hore et al. 1999a). One possible scheme for this is that during a throw descending commands from motor cortex are sent via efference copy to the cerebellum (cf. Hore and Vilis 1984). The cerebellum in turn, using an internal model of the throw, sends a signal back to the motor cortex to trigger finger opening with the correct timing.

The nature of the internal models that contribute to the generation of skilled arm movements and the role of the cerebellum in these models is a matter of considerable current speculation (e.g., Houk et al. 1996; Wolpert et al. 1998). For the case of finger opening in throwing, it has been suggested that both forward and inverse models are likely used for feedforward control (Hore et al. 1999b). This is consistent with a recently proposed model of the cerebellum that contains multiple paired inverse and forward models (Wolpert et al. 1998). However, neither this nor other comparable cerebellar models of limb movements account for the timing of single joint rotations.

Although the mechanisms by which the cerebellum acts as an internal model and performs timing functions are unknown, a number of suggestions have been put forward. Following the early idea that a beam of parallel fiber activity contacting a row of Purkinje cells could be used for timing, Braitenberg et al. (1997) suggested that the output of this structure may be a succession of well-timed inhibitory volleys "sculpting" the motor sequences according to the requirements of a multijoint movement. Similarly, Thach and colleagues proposed that a beam of parallel fiber activity could link Purkinje cells mediolaterally across the somatotopically organized deep nuclei thereby combining actions at several joints into complex coordinated acts. Furthermore they proposed that the cerebellum learns, initiates, continues, and stops complex movements by this mechanism (Thach 1998; Thach et al. 1992). An alternative suggestion is that timing is controlled by a clock-like input from climbing fibers that activates the proper Purkinje cell assemblies at the right time (DeZeeuw et al. 1998 for recent review). However, so far the importance of rhythmic olivary activity for the timing of natural nonrhythmic movements has not been demonstrated experimentally, (e.g., Hartmann and Bower 1998; Keating and Thach 1995, 1997). Houk and colleagues have also argued for an important role for climbing fibers. They emphasized that distal and proximal arm musculature could be coordinated by adaptive influences of climbing fibers onto Purkinje cells (Houk et al. 1996). This idea fits with the observation that small muscimol lesions in the dentate and interpositus affected distal and proximal muscles in the cerebellum in an anterior posterior direction (Mason et al. 1998) rather than the mediolateral direction proposed by Thach et al. (1992).

Whatever the mechanism, the present results show that the cerebellum plays an essential role in enabling precise timing of finger opening to occur in an overarm throw. Lack of this precision in cerebellar patients is an example of a timing disorder at a single joint in a skilled multijoint movement that cannot be attributed to disorder in force control. Because finger opening in overarm throwing is likely controlled by a central command, the results implicate the cerebellum in the timing of this command.


    ACKNOWLEDGMENTS

We thank L. van Cleeff for technical assistance.

This work was supported by Canadian Medical Research Council Grant MT 6773 and Deutsche Forschungsgemeinschaft Grants DFG Ti 239/3-1 and DFG Ti 239/4-1.


    FOOTNOTES

Address reprint requests to J. Hore.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 2 November 1998; accepted in final form 8 March 1999.


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