1Department of Physiology, University of Western Ontario London, Ontario N6A 5C1; and 2Department of Physiology, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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ABSTRACT |
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Hore, J., S. Watts, and D. Tweed. Prediction and Compensation by an Internal Model for Back Forces During Finger Opening in an Overarm Throw. J. Neurophysiol. 82: 1187-1197, 1999. Previous studies have indicated that timing of finger opening in an overarm throw is likely controlled centrally, possibly by means of an internal model of hand trajectory. The present objective was to extend the study of throwing to an examination of the dynamics of finger opening. Throwing a heavy ball and throwing a light ball presumably require different neural commands, because the weight of the ball affects the mechanics of the arm, and particularly, the mechanics of the finger. Yet finger control is critical to the accuracy of an overarm throw. We hypothesized that finger opening in an overarm throw is controlled by a central mechanism that uses an internal model to predict and compensate for movement-dependent back forces on the fingers. To test this idea we determined whether finger motion is affected by back forces, i.e., whether larger back forces cause larger finger extensions. Back forces were varied by having subjects throw, at the same fast speed, tennis-sized balls of different weights (14, 55, and 196 g). Arm- and finger-joint rotations were recorded with the search-coil technique; forces on the middle finger were measured with force transducers. Recordings showed that during ball release, the middle finger experienced larger back forces in throws with heavier balls. Nevertheless, most subjects showed proximal interphalangeal joint extensions that were unchanged or actually smaller with the heavier balls. This was the case for the first throw and for all subsequent throws with a ball of a new weight. This suggests that the finger flexors compensated for the larger back forces by exerting larger torques during finger extension. Supporting this view, at the moment of ball release, all finger joints flexed abruptly due to the now unopposed torques of the finger flexors, and the amplitude of this flexion was proportional to ball weight. We conclude that in overarm throws made with balls of different weights, the CNS predicts the different back forces from the balls and adjusts finger flexor torques accordingly. This is consistent with the view that finger opening in overarm throws is controlled by means of an internal model of the motor apparatus and the external load.
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INTRODUCTION |
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Fast, goal-directed movements are often too brief
to be controlled by sensory feedback. For overarm throwing, it has been proposed that finger opening could be triggered by proprioceptive feedback from elbow extension (Cordo 1990; Cordo
et al. 1994
). However, the time interval between the onset of
elbow extension and onset of finger opening is ~20 ms for a fast
throw, which does not leave sufficient time for feedback from elbow
extension to enter the CNS and emerge again to trigger the finger
extensors (Hore et al. 1999
). In agreement, this
previous study also showed that perturbations during throwing that
blocked elbow extension did not block finger opening or change its timing.
If a movement is too fast for sensory feedback, what guides it to its
goal? One possibility is a feedback system entirely within the CNS. The
clearest example of this idea is perhaps Robinson's (1975) internal-feedback theory of saccades, the rapid eye
movements that shift the line of sight from object to object. In
Robinson's theory, a neural circuit called the oculomotor integrator
monitors the neural commands being sent to the eye muscles and predicts the resulting changes in eye position before they happen. When the
eye-position estimate from the integrator matches the desired eye
position, the saccadic system switches off, and the eye comes to rest.
As long as the integrator is accurate in its estimates, the saccade
will stop on target.
Something similar may underlie fast arm movements: an internal
predictor or model may monitor motor commands to the arm muscles and
predict the resulting motion (e.g., Flanagan and Wing
1997; Jordan 1995
; Kawato 1996
;
Windhorst 1996
; Wolpert et al. 1995
). Later occurring joint motions could then be triggered with respect to
these central signals without reference to sensory feedback. In keeping
with this idea Hore et al. (1999)
proposed that the timing of finger opening in an overarm throw was likely controlled by
means of an internal model that could predict hand trajectory.
The internal model for arm movements must be more complicated than the internal model for eye movements. For the case of the eye, any given neural command always produces the same motion, whereas for the arm, one and the same neural command will produce different motions depending on the load. If a pitcher threw a light ball and then a heavy ball, using the same neural activity both times, the flight paths of the two pitches would be very different. To maintain accuracy, the internal model would have to take into account the weight of the ball and adjust its predictions of arm and ball motion accordingly.
Our aim was to see whether the neural circuitry that controls finger
opening in overarm throws takes into account the ball's mass. We
concentrated on the fingers, because they are the smallest, lightest
parts of the motor apparatus, and therefore the parts most easily
deflected by force from the ball. But at the same time, finger control
is especially important for the accuracy of an overarm throw
(Calvin 1983; Hore et al. 1996b
). We
proposed the hypothesis that finger opening is controlled by means of
an internal model that predicts the movement-dependent back forces on
the fingers and adjusts the neural commands to the finger muscles to
compensate for the differing loads. Without such correction, finger
motion would be strongly affected by forces from the ball, with heavier
balls producing larger finger extensions. To test the hypothesis, we
therefore determined whether finger extension amplitude was larger in
throws with balls of heavier weights.
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METHODS |
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General procedures
Measurement techniques were similar to those used previously
(e.g., Hore et al. 1996a-c
). Experiments were approved
by the local ethics review board, and all subjects gave informed
consent. Subjects were right-handed male recreational ball players who were accurate throwers. Three series of experiments were performed: 1) to examine the mechanism of finger opening, 2)
to determine whether back forces occurred on the fingers, and
3) to determine the kinematics of finger opening with balls
of different weights. In each series, throws were made from the sitting
position with the trunk fixed by straps so that hand translation could
be computed (this required that the sternum was fixed in space), and
from the standing position to verify that results applied for a more natural throw. In the first series, six subjects threw tennis balls
while seated, and four subjects threw tennis balls from a standing
position with the left foot forward without moving their feet. In the
second series, six subjects threw balls of three different weights from
the sitting and standing positions while back forces were recorded on
the middle finger by means of a force transducer taped to the distal
phalanx. And in the third series, six subjects threw balls of different
weights from the sitting and standing position. In all experiments
subjects were instructed to throw accurately at a medium to fast speed (~15 m/s) using an overarm style (i.e., with a motion involving horizontal adduction of the upper arm) and to grip the ball primarily with the middle finger (whose joint angles we measured) so that in the
process of ball release the ball rolled along that finger. In the
second and third series of experiments, balls were of different weights
and diameters: a tennis ball (55 g, 65 mm), a tennis ball filled with
concrete (196 g, 65 mm), and a hard hollow plastic ball (14 g, 70 mm).
Subjects made a total of 40 throws with each ball in blocks of 20 throws in the order of normal tennis ball, light ball, and heavy ball,
then repeated the sequence. They were instructed to throw these balls
at the same speed at a grid of 6-cm, numbered target squares, and to
aim for the central colored square, which was at eye level ~3.5 m
away. Subjects were handed the balls that they then held on or above
the right leg in anticipation of the command to throw. The weight of
the ball was obvious to the subject, and when a change was made, e.g.,
from the light to the heavy ball, they usually commented that the
weight of the ball was different. Subjects threw with a backswing that
took the hand behind the head. Each throw was scored for accuracy by the subject calling out the square that was hit, which was verified by
an experimenter.
Ball release was detected by offset of pressure switches attached to the proximal and distal phalanges of the middle finger (see Fig. 1A). If these signals were unavailable, e.g., because the ball rolled along the side of the finger, ball release was defined as the moment when the distal interphalangeal joint reversed its direction from extension to flexion, an event that coincides with departure of the ball from the finger tip (Fig. 1A). Throwing speed was monitored on-line as the peak angular velocity of the hand in space. In the experiments with seated throwers, this latter parameter was found to be strongly linearly related to ball speed (calculated from the flight distance and flight time to ball impact on the target measured by pressure detectors). For the standing throwers, because flight distance was uncertain, hand angular velocity was used as the measure of throwing speed.
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Recording angular positions of arm segments
Angular positions of five arm segments were measured using a
modification of Robinson's (1963) search-coil technique
(Tweed et al. 1990
). Skalar search coils, embedded in
plastic for protection, were taped securely to the back of the distal
phalanx of the middle finger, back of the hand, forearm proximal to the
wrist, lateral aspect of the upper arm and acromion process.
Alternatively, when rotations at each finger joint were required,
search coils were taped to the back of each of the three phalanges of
the middle finger, the hand and the forearm close to the wrist.
Subjects sat or stood in three orthogonal alternating magnetic fields
of frequencies 62.5, 100, and 125 kHz, generated by 3 × 3 × 4-m-wide Helmholtz coils, and uniform to within 2% over the working
range. Coil voltages, sampled at 1,000 Hz, were used to calculate the simultaneous angular positions of the five segments in
three-dimensional space.
Angular positions (orientations) of arm segments in space were calculated directly from search-coil voltages. For the seated subjects, translational positions were computed using these orientations and the measured lengths of the arm segments. Locations in space were expressed with respect to the sternal notch, which was held stationary by the straps over the shoulders.
Finger and hand configurations were also described in terms of joint angles. Flexion-extension at each finger joint was obtained from the angular position of the corresponding phalanges, and for the metacarpophalangeal joint, the angular position of the proximal phalanx and the hand. All joint angles were defined as being 0 when the arm was in reference position, with the subject facing the target with the upper arm horizontal and lateral, and forearm, hand, and fingers vertical with the palm forward.
Statistics
To determine whether the amplitude of finger extension was different for throws with balls of different weights, a one-way ANOVA was performed with Duncan's multiple range test. Post hoc regression analysis determined whether there was a finger amplitude increase or decrease with the balls of different weights.
Photography
To verify the accuracy of measurements computed from the coil signals, hand paths were also recorded with long-exposure photography (Fig. 1C). Six subjects threw from the seated position with a light-emitting diode attached to their hand. This diode was wired so that it went off for a few milliseconds at the time of offset of the switch on the proximal phalange and went off permanently at the time of final offset of the switch on the distal phalanx, i.e., at final ball release. This latter signal was also used to trigger a stroboscope that flashed at final ball departure and 50 ms later, thereby giving the ball path.
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RESULTS |
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Ball release from the hand
In an overarm throw, ball release occurs by a mechanism that
involves opening the fingers as the hand moves in a flattened arc
underneath the ball (Hore et al. 1996a,b
).
Correspondingly, with respect to the hand, the ball rolls up the
fingers and is released from the fingertips. The steps involved in this
process are illustrated in Fig. 1A for a throw made by a
seated thrower (Jn) at a medium speed (12.5 m/s). Zero angle
for the finger joints indicates when the finger was in a straight line
with the hand, and for the hand when it was vertical in space. At
point 1, the start of the forward and upward angular motion
of the hand in space, both distal and proximal switches (on the distal
and proximal phalanges) are on as the hand grips the ball. At
point 2, the distal switch goes off as the proximal and
distal interphalangeal joints start to extend and the distal phalanx
lifts off the ball. This early extension is clearly seen in the
bottom trace, which shows the angle of the distal phalanx
with respect to the hand. This finger extension is illustrated in Fig.
1B (point 2), which is a reconstruction of the
finger and hand angular position in space. The switches are shown as
small rectangles (filled shows switch on; open switch off). At
point 3 the proximal switch goes off as the ball starts to
roll up the finger, and at point 4 the distal switch goes on
again as the ball rolls over it. At point 5 the distal
switch goes off as the ball loses contact with the finger tip. The
flattened arc of the hand is shown in Fig. 1C, a tracing
from a long-exposure photograph of another throw from the same subject
(see METHODS). The gap in the trace at point 3 indicates offset of the proximal switch, and the end of the trace
indicates final offset of the distal switch at final ball release
(point 5). At this point the direction of the hand path (dashed line) is not the same as the direction of the ball path (solid line).
Inspection of the individual finger-joint motions (Fig. 1A) reveals that in this sequence there is relatively little motion at the metacarpophalangeal joint and a relatively large extension at the proximal interphalangeal joint. The distal interphalangeal joint shows different components: an early small extension (which was not always present) followed by a faster extension whose timing was consistent with it occurring in part as a result of back force from the ball as it rolled up the finger. This was followed by a small flexion occurring after ball release, which was presumably due to the sudden loss of back force from the ball.
A back force from the ball occurs on the finger during finger opening
In an overarm throw, as the hand propels the ball forward, the
ball exerts a back force on the hand. This force is described by
Newton's third law of motion: to every action there is an equal and
opposite reaction, or in other words if the hand pushes on the ball,
the ball pushes back equally hard on the hand. The push can be deduced
from the ball's mass and motion: the ball's total translational
acceleration, minus the acceleration due to gravity, equals the
acceleration imparted by the hand. This acceleration, multiplied by the
mass of the ball, is the force exerted by the hand on the ball. The
same force vector, multiplied by 1, is the force exerted by the ball
on the hand.
Is there any back force on the fingers while they are opening? The answer is not obvious because, in a fast throw, the ball rolls along the fingers only briefly (<20 ms, Fig. 1A), and it is not known whether the fingers undergo translational acceleration toward the ball during this period. Therefore we measured the translational acceleration of the fingers as the hand moved forward and the fingers opened. Subjects were asked to sit and throw balls of different weights at the same speed. Hand angular velocity was monitored on-line, and feedback was given to subjects if a throw was faster or slower than the predetermined speed.
Figure 2 shows averages from subject Jn of 10 throws with each of the 3 balls (light ball, thin line; normal tennis ball, medium line; heavy ball, thick line). Figure 2A shows computer reconstructions of the flattened-arc trajectory of the finger in space aligned on the moment the hand was vertical and viewed from the side (the same view as in Fig. 1C). Figure 2, B and C, shows the backward-forward and down-up components of the translational acceleration of the finger in space, and Fig. 2D shows the corresponding finger extension (motion of the distal phalanx with respect to the hand). Figure 2, B-D, was aligned on ball release so that finger acceleration occurring before ball release would not be confused with that occurring in association with the finger flexion that occurred after the ball left the finger tip. These traces show two important points. First, on average, the trajectories of the finger in space (Fig. 2A) are similar for throws with the different balls. This shows that the subject did not change his throwing style with the different balls. Second, finger translational acceleration occurs during the time of finger opening to ball release: as the fingers extend (Fig. 2D) they accelerate first forward (Fig. 2B) and then also downward (Fig. 2C). Our reconstructions overestimated the downward component of acceleration at the expense of the forward component because they were based on the angular position of the distal phalanx and assumed that the finger was straight. Nevertheless, it is clear that during the time of finger extension the finger underwent forward and downward translational acceleration, and therefore the ball exerted a back force on the finger. Further, because these accelerations were similar in magnitude for throws with the three balls, but the ball weights were markedly different (e.g., the heavy ball was 14 times as heavy as the light ball), it follows that the heavy ball exerted a larger back force on the fingers.
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This result was confirmed in a separate series of experiments by direct measurement of forces on the distal phalanx during finger opening. Figure 3 shows averages of recordings from a force transducer taped to the distal phalanx of the middle finger as a subject made 10 throws with each of the 3 different balls from both sitting and standing positions. For both sets of throws, during the time of finger extension (Fig. 3A), there was first a decrease in force on the distal phalanx (Fig. 3B), followed by an increase, then a rapid decrease. This corresponds to the sequence in Fig. 1, in which the distal phalanx first lifts off the ball (force decrease), then the ball rolls up over it (force increase) before losing contact (rapid decrease). For both sitting and standing throws, the force on the finger was proportional to the weight of the ball, being largest with the heaviest balls. In summary, the ball pushes back on the finger during finger opening, the back forces are larger for the heavier balls, and they are similar for throws made from the sitting and standing positions.
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Effect of back forces on finger extension amplitude
Do these larger back forces cause the fingers to open wider? We measured the amplitude of rotation at the different joints of the middle finger as 6 subjects stood and made 40 throws with each ball at the same speed. We concentrated on the proximal interphalangeal joint because it is largely responsible for finger opening (Fig. 1A). Figure 4 shows averages from two subjects of rotations at the three finger joints, and the distal phalanx with respect to the hand, aligned on the moment the ball left the fingertip (vertical line; see Fig. 1A, point 5). For subject Jn, inspection of the extensions at the proximal interphalangeal joint (Fig. 4A) shows that before ball release the traces overlap: on average, this joint moved much the same way regardless of the weight of the ball. For subject De (Fig. 1B), the average amplitude of extension of this joint decreased slightly with the heavy ball. For each subject we compared the amplitude of extension of both the proximal interphalangeal joint and the distal phalanx with respect to the hand. Figure 5A shows that for the proximal interphalangeal joint there was an increase in extension amplitude with ball weight in subject Co and a decrease in the other five subjects. This was statistically significant in all cases at the P < 0.001 level (see METHODS). For the amplitude of extension of the distal phalanx with respect to the hand, there was no increase with ball weight in any subject and a statistically significant decrease in four subjects (Jn, De, Nv, and Ak; P < 0.001). In short, there was no overall increase in the amplitude of finger opening with heavier balls: increased back force did not increase finger extension.
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Indirect evidence that back forces were different
Forces were not directly recorded during these latter experiments,
but there was indirect evidence that the back forces were larger in
throws with the heavy balls. This evidence came from inspection of
finger motion after the ball left the hand. We have previously reported
that, at the moment the ball leaves the fingertip, the finger flexes
forward (Hore et al. 1995, 1996a
) (see
also Fig. 1A). The new finding is that the amplitude of this
flexion movement is proportional to ball weight in throws of similar
speeds. This can be seen in Fig. 4. Inspection of traces starting at
the moment of final ball release (vertical line) reveals a flexion at
the proximal interphalangeal joint that was larger for the throws with
the heavier balls. Mean amplitudes of flexions of the proximal
interphalangeal joint for all throws with the three balls of different
weights from all subjects are shown in Fig. 6. In some subjects flexion did not occur
for the light (14 g) ball, and this point is missing from the graph. In
all subjects larger flexions occurred with the heavier balls. This
flexion movement presumably resulted from offset of the back force as the ball left the fingertip, thereby leaving a finger flexor torque unopposed. The larger flexions with the heavier balls likely reflected increased torque from the finger flexors, which was required to oppose
larger back forces in these throws.
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First throw with a ball of a new weight
Was finger amplitude controlled precisely in the first throw with a ball of a new weight, or did it take a number of trials to adapt to the new back forces on the fingers? The unequivocal answer for all subjects is that for the first throw with a ball of a new weight (that had not been thrown previously), finger amplitude was adjusted to the new conditions. Figure 7 shows overplots from two representative subjects of finger amplitudes (Fig. 7A) and finger velocities (Fig. 7B) for the first throw with a heavy ball (thick line) and the next nine throws with this same ball (thin lines). Before this, subjects had made 10 throws with the light ball. For both subjects the first throw with the heavy ball was similar in its kinematics to the other throws, i.e., it fell within the range of amplitudes and velocities of the next nine throws. The same result was found for all subjects. Across subjects no statistical difference was found between the mean of finger amplitude for the 1st throw and the mean of the next 9 throws or between the mean of the 1st and the 10th throw (t-test with unequal variance). Similarly, across subjects no consistent trend of either a decrease or increase in finger amplitude was observed across the 10 throws (e.g., Fig. 7C).
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Does finger amplitude affect ball accuracy?
Because in an overarm throw the ball is released from the fingers,
the orientation of the fingers in space can affect the subsequent path
of the ball. And because finger extension amplitude can affect finger
orientation, it might be expected that the decrease in finger amplitude
that occurred in four subjects with the heavy ball (Fig. 5) may have
affected ball accuracy. In previous experiments with seated throwers,
ball accuracy was related to the timing of finger opening and the
timing of ball release, but not to finger amplitude (Hore et al.
1996b). In the present experiments we asked whether this also
applied to throws made with a normal tennis ball while standing, and
whether it applied to those subjects who showed decreased overall
finger amplitudes when standing and throwing with the heavy ball.
First, for standing throws with the normal ball, Fig. 8 shows a representative result (from subject Co). In spite of variability in the amplitude of finger opening (to ball release; Fig. 8A), there was no relation between this variability (over a range of ~25° for all 50 throws) and ball impact height on the target (Fig. 8B). In contrast, as before, a strong relation was found between ball impact height and timing of ball release (Fig. 8C). Similar results were found for all subjects who threw from the standing position. Second, for subjects who showed decreased finger amplitudes for throws with the heavy ball (Fig. 5), no relation was found between finger amplitude and ball accuracy. For example, Fig. 9 shows ball impact heights for all throws made with the light, normal, and heavy tennis balls in subject Nv, who showed decreased finger extension amplitudes with the heavy ball. No relation was found between ball impact height on the target and amplitude of finger extension for throws with each ball separately and for all throws together. Presumably, the relation is absent because such a decrease in finger amplitude has a smaller effect on ball accuracy than does variability in timing, or alternatively, because this subject changed his timing to compensate for the decreased finger amplitude.
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DISCUSSION |
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We have seen that in an overarm throw the weight of the ball affects the mechanics of its release. That is, for throws of a similar hand translational acceleration, larger back forces occurred on the fingers during finger opening for throws with heavier balls. Because the larger back forces did not produce larger finger extensions, we conclude that the CNS predicted the forces and compensated for them. This compensation appears to occur by the generation of larger finger flexor torques. This was deduced from the finding that the fingers flexed abruptly at the moment of ball release and the amplitude of this flexion was proportional to ball mass.
Presumably, this ability of recreational ball players to throw with small variability in finger amplitude and to adjust immediately to a ball of a new weight is a skill learned from considerable experience in throwing. In agreement, preliminary experiments on three unskilled throwers showed similar mean amplitudes of finger opening for the balls of different weights but larger variability from throw to throw (unpublished observations).
Are finger torques controlled by reflex mechanisms?
Could the compensation for different back forces be controlled by
peripheral feedback? One way this could occur would be if larger back
forces in throws with heavier balls produced larger initial velocities
of finger opening, which in turn, would be signaled by changed
kinesthetic feedback from the fingers. This would then generate, via
spinal cord mechanisms, larger finger flexor activity. This proposal
can be ruled out for two reasons. First, for the standing throwers,
onset of finger opening (extension) occurred on average <40 ms before
ball release (e.g., Figs. 4, 7, and 8). This does not leave sufficient
time for signals from finger movement to pass to and from the spinal
cord and for finger muscles to generate increased torque. Second, such
a proposal predicts that the initial velocity of finger opening will be
greater for throws with heavier balls. However, inspection of kinematic records of finger opening showed that this was not the case (Figs. 2-4). Similarly, changed kinesthetic feedback from wrist flexion and
elbow extension in throws with heavier balls can be ruled out, again
because there is insufficient time between onset of these joints
rotations and onset of finger opening (4 ms for wrist flexion and 21 ms
for elbow extension) (Hore et al. 1999). Although a
contribution from changed feedback during the backswing cannot be ruled
out, this possibility seems to be unlikely because subjects can throw
accurately over short distances with balls of different weights with
the arm starting from a stationary position at the end of the
backswing, i.e., without any backswing motion at all (unpublished observations).
Possible mechanisms for compensation of back forces
Although the mechanism by which the CNS controls finger opening and compensates for back forces cannot be determined by these experiments, some possibilities can be proposed. First, a finger flexion contraction or cocontraction could have occurred that was precisely timed to counteract the back force from the rolling ball. Alternatively, presetting of finger stiffness (grip force) could have occurred at the start of the throw, or progressively throughout the throw, in anticipation of the increase in hand acceleration. The variable degrees of finger flexion after ball release seen in Fig. 6 may reflect intersubject differences in finger flexor activity versus cocontraction. Irrespective of how it is generated, this increase in finger flexor force would presumably be precisely related to the dynamics of the throw, but this remains to be shown.
Whatever the mechanism, finger opening appears to be an active process, i.e., it does not only occur as a result of back forces. Evidence for this can be seen in Fig. 1, A and B. Point 2 shows that during initial finger opening (~30 ms before final ball release) at a time when the hand was undergoing forward translational acceleration (Fig. 2), the fingertip lifted off the ball. This could not occur if finger extension was produced by back force from the ball on the finger. Exactly how the commands for finger stiffness and for timing finger opening, are generated and interact, remains to be determined by further experiments.
Evidence for an internal model
The idea that the CNS predicts and compensates for perturbations
occurring during the throw fits with many observations of anticipatory
responses to expected perturbations in a variety of different motor
tasks. Perhaps the most relevant for throwing are the anticipatory
actions involving the finger and hand that occur when gripping and
lifting small objects (e.g., Johansson and Westling
1988a,b
) and when catching a ball (e.g., Lacquaniti and
Maioli 1989a
,b
).
An interesting conclusion of these finger and hand studies is that the
central control mechanism knows dynamics, i.e., there is an internal
representation that predicts the mechanical consequences of the
perturbation. For example, Johansson and Westling
(1988b) showed that prior knowledge of both the weight of an
object dropped into a cup held by a subject, and the length of the
drop, resulted in the generation of appropriate anticipatory muscle
activation. They concluded that the central control processes possessed
knowledge about the dynamics of the interactions between the held cup
and the dropped weight and this led to anticipatory parameter setting of motor programs. In agreement, Flanagan and Wing
(1997)
concluded that, for a task involving gripping and moving
a manipulandum subjected to a variety of different loads, the grip
force anticipated the load force and that this occurred by means of an
internal model of the loaded limb.
A similar conclusion came from studies of catching a ball dropped
vertically (Lacquaniti and Maioli 1989a,b
;
Lacquaniti et al. 1992
). By varying the height of the
drop, it was found that anticipatory muscle activation was finely tuned
to the expected properties of the ball's impact with the hand. Again
it was concluded that there was an internal model that took into
account the time to contact, the momentum of the ball's impact and the
limb's geometry. Studies of adaptation of arm movements to externally
applied perturbing forces have also concluded that adaptive learning
occurs by means of an internal model of the dynamics of the environment
(Conditt et al. 1997
; Goodbody and Wolpert
1998
; Shadmehr and Mussa-Ivaldi 1994
).
The concept of an internal model can be used to explain how subjects
compensated for different back forces on the first throw with a ball of
a new weight. According to this idea it would arise from two
mechanisms: first, an accurate internal representation of the mechanics
of throwing built up from extensive previous experience of throwing,
and second, an updating (calibration) of the parameters of this model
before the first throw by means of information obtained from handling
the ball. This scheme is consistent with the finding of
Johansson and Westling (1988b) that sensory
information about the weight of the ball dropped into the cup was
obtained from handling the ball prior to the drop. It is also
consistent with the finding that motor commands were scaled before
lifting common objects on the basis of visual identification and an
accurate estimate of the object's weight (Gordon et al.
1993
).
Although internal models appear to be used in gripping and lifting, in catching a ball and in throwing, the neural mechanism for throwing would appear to be somewhat different. In the lifting and catching tasks, contractions of proximal and distal muscles occur together. In contrast, in throwing, there is a proximal to distal sequence of joint rotations that occurs over hundreds of milliseconds with finger opening being the last rotation to occur. Because the back force that occurs on the fingers from the ball as it rolls up the fingers is proportional to the forward force produced by the hand on the ball, generation of active finger force to oppose the back force requires knowledge of the dynamics of the ongoing hand trajectory. Therefore one possibility is that prediction of finger force in throwing is based on an efference copy of the commands that generate the hand trajectory.
Internal models for throwing
Motor theorists distinguish two types of internal model: inverse
and forward. An inverse model is a neural system that "undoes" something that the muscles do. Perhaps the simplest example is in
Skavenski and Robinson's (1973) theory of the
vestibuloocular reflex (VOR). The VOR counterrotates the eyes when the
head turns, so as to keep the eyes stationary in space. Its aim,
therefore is to make eye velocity equal
1 times head velocity. It has
sensors in the inner ear whose firing rates are proportional to head
velocity, but if it simply relayed this sensory signal, times
1, to
the motoneurons, the resulting eye velocity would be wrong. The
muscles, in transducing the neural command, would distort it. Hence
Skavenski and Robinson proposed that the eye-velocity command passes to the motoneurons both directly and through an integrator. This combination of integrator and direct relay inverts, and hence corrects
for, the subsequent distortion by the muscles, producing a pattern of
motoneuron activity that generates the desired eye velocity.
A similar scheme could work for throwing: signals coding the desired
motion could pass through an inverse model of the arm to generate an
appropriate pattern of motoneuron firing. But a major difference
between the VOR and throwing is that in the VOR the desired motion is
easily computed: the desired velocity of the eye is simply the head's
velocity times 1. For a throw, considerable neural machinery would be
needed to devise a suitable arm trajectory before this could be fed
through the inverse model: the model cannot be the complete mechanism
for generating throws. Another difference is that the inverse model of
the arm would have to contain an adjustable parameter representing the
weight of the ball.
Forward models, in contrast to inverse models, do not undo but rather mimic some aspect of muscle behavior. Feed a pattern of motoneuron firing into a forward model of the arm and it might compute the resulting joint velocities, or the angles of the joints. As in Robinson's model of saccades, a forward model can be used in an internal feedback system: neural commands are fed through the forward model to yield an estimate or prediction of body motion. This estimate is compared with the desired motion, and any difference between the two, called the motor error, is used to adjust the neural commands.
With a complex linkage like the arm, however, it will take some computation to figure out how to adjust the neural commands, given a motor-error signal. For example, if the forward model estimates that the hand is veering left of its charted path, what is to be done? Should brachialis, for instance, be more strongly activated or less? The brain needs some device to transform an error signal into motoneuron activity that will reduce the error. Such a device is a type of inverse model: given a desired motor effect, it suggests a neural command. In short, the brain would need an inverse model of the arm to make use of a forward model for on-line feedback control of throwing.
With this idea of a forward model and an inverse model linked in a feedback loop, we have a rough picture of how a complete throw generator could work, based on Robinson's scheme for saccades. Upstream centers set some parameters for the throw: target location, speed of the throw, overarm or sidearm technique, more or less elbow motion than last time, and so on. They also estimate the weight of the ball, sending this information to the forward and inverse models. Something akin to a comparator collects information about the desired parameters of the throw and, from the forward model, the current state of the arm. This information is relayed to the inverse model where it is transformed into a suitable neural command. It is here, in the inverse model, that many of the unconscious details of the throw are determined: the activation pattern for brachialis, the precise arc of the hand, the moment of finger opening and so on.
These internal models of the arm would have to be shaped in early life,
and kept calibrated thereafter, by learning mechanisms such as those
studied by Konczak et al. (1995, 1997
)
and Shadmehr and Mussa-Ivaldi (1994)
. Such adaptation
would presumably affect all aspects of the internal models, including
our ability to adjust them based on an estimate of the weight of a ball
in the hand. Clearly a perfectly accurate, real-time internal model of
arm mechanics would need enormous computational power, but this is not
an objection to the hypothesis of such models. For one thing, there
surely is enormous computational power in vast networks of neurons
where each neuron is a complex information processor in its own right.
And of course the neural computation consists of electrical and
chemical signals flowing through massively parallel networks and
therefore might proceed very quickly. Further, the internal models need
not be perfectly accurate, and of course we know they are not, because
if they were then every throw would strike its mark. Presumably the
networks in the brain, like artificial neural networks, learn
approximations. Their learning is driven by error (i.e., teacher)
signals, in this case perhaps the visually judged errors in recent
throws and the muscular effort of the arm motion. Presumably the
adaptation proceeds until the error signals are reduced as far as
possible, but not apparently to zero.
CNS structures
Two CNS structures that are likely components of the proposed
internal model that controls finger force in overarm throwing are the
motor cortex and cerebellum. The motor cortex is likely involved
because of its special role in controlling precise finger movements and
finger force (Porter and Lemon 1993). The cerebellum is
likely involved, first, because of its role in the generation of
anticipatory (predictive) mechanisms that control the arm, e.g., that
brake single-joint elbow movements (Hore and Vilis 1984
;
Hore et al. 1991
) and that control interaction torques
in multijoint movements (Bastian et al. 1996
), and
second, because of its role in control of finger movements and finger
force (Holmes 1922
; Mai et al. 1988
;
Müller and Dichgans 1994
). Although it is not
known how these two CNS structures interact, a number of models have
recently been put forward that make proposals (see Houk et al.
1996
for a recent review). For example, Kawato and Gomi
(1992)
specifically proposed that the lateral cerebellum functions as the inverse model of the limb's controlled system. Most
others view the cerebellum as the structure that through learning
functions as a predictive controller for limb movement (e.g.,
Barto et al. 1996
; Miall et al. 1993
;
Thach 1996
; Thach et al. 1992
).
Conclusion
Previous studies have shown that the CNS can predict 1) the mechanical consequence of external perturbations applied to the hand and 2) the forces required to produce relatively slow self-generated arm movements under different loads. The present findings add to this by showing in a fast skilled movement, where the fingers are likely entirely controlled by a central process, that finger force is also adjusted according to the mechanics of the movement. We previously proposed that timing of finger opening in an overarm throw is most likely controlled by means of an internal model that can predict the trajectory (kinematics) of the throw. The present results are best explained if finger force is also controlled by an internal model that can predict the dynamics of the throw.
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ACKNOWLEDGMENTS |
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We thank L. Van Cleeff for technical assistance.
This work was supported by Canadian Medical Research Grant MT 6773.
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FOOTNOTES |
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Address for reprint requests: J. Hore, Dept. of Physiology, University of Western Ontario, London, Ontario N6A 5C1, Canada.
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 9 October 1998; accepted in final form 21 April 1999.
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