1School of Health Related Professions,
Sainburg, R. L.,
C. Ghez, and
D. Kalakanis.
Intersegmental dynamics are controlled by sequential anticipatory,
error correction, and positional control mechanisms. The purpose of this study is to examine the mechanisms underlying control
of intersegmental dynamics during reaching movements. Two experiments
were conducted to determine the relative contributions of anticipatory
and somatosensory feedback mechanisms in controlling intersegmental
dynamics and whether adaptation to novel intersegmental dynamics
generalizes across a range of movement directions. The mechanisms used
to control interaction torques were examined by altering the inertial
load of the forearm. Movements were restricted to the shoulder and
elbow and supported on a horizontal plane by a frictionless air-jet
system. Subjects made rapid out-and-back movements over a target line
presented on a computer screen. The screen cursor disappeared at
movement onset, and hand paths were displayed after each movement.
After subjects adapted to a novel inertial configuration, the position
of an attached mass was changed on pseudorandom trials. During these
"surprise" trials, movements were initiated with the torque
patterns appropriate to the previously learned inertial condition. As a
result, characteristic errors in initial movement direction were
predicted by an open-looped forward simulation. After these errors
occurred, feedback mediated changes in torque emerged that,
surprisingly, further decreased the accuracy of movement reversals.
Nevertheless at the end of movement, the hand consistently returned to
the starting position. It is plausible that the final position was
determined completely by feedback-mediated changes in torque. In a
second experiment, adaptation to a novel inertial load during movements
made in a single direction showed limited transfer across a range of
directions. These findings support and extend those of previous
reports, which indicated combined anticipatory and postural mechanisms
to coordinate rapid reaching movements. The current results
indicate a three-stage control system that sequentially links
anticipatory, error correction, and postural mechanisms to control
intersegmental dynamics. Our results, showing limited generalization
across directions, are consistent with previous reports examining
adaptation to externally applied forces and extend those findings to
indicate that the nervous system uses sensory information to
recalibrate internal representations of the musculoskeletal apparatus itself.
To produce a desired hand trajectory, the nervous
system must coordinate muscle forces with both external forces imposed
by the environment and internal forces that arise within the
musculoskeletal system itself. Internal forces include those produced
by stretch and compression of noncontractile tissues, and
"interaction forces" imposed on each limb segment by motion of
the segments attached to it. Adaptation to perturbations arising from
outside the musculoskeletal system has been postulated to occur through
the learning and recalibration of neural representations or
"internal models" of the perturbing forces (Gandolfo et
al. 1996 The externally applied forces described in the previous paragraph can
be detected directly through muscle spindles and tactile receptors in
the hand. However, because interaction forces vary with segment
accelerations and are transferred across the segments through bony and
ligamentous connections, they cannot be detected in this way. Although
the nervous system can detect changes in muscle length and its first
derivative through muscle spindles, the rotational effect of
interaction forces at the joint (interaction torque), which varies most
substantially with joint angular accelerations (Hollerbach and
Flash 1982 Mechanisms for controlling limb movements without explicitly
representing musculoskeletal dynamics have been proposed by equilibrium point theories of control (Bizzi 1987 Imamizu and coworkers (1995) The purpose of the current paper is to examine the mechanisms
underlying control of intersegmental dynamics. Two experiments were
conducted to examine whether control of intersegmental forces normally
occurs through anticipatory mechanisms based on internal representations of limb dynamics and whether adaptation to novel intersegmental dynamics transfers across a range of movement
directions. The mechanisms used to control interaction torques were
examined by altering the inertial load of the forearm. By comparing our experimental results to an ideal open-looped forward simulation, we
could assess the contributions of somatosensory feedback to the control
of intersegmental dynamics. Furthermore we examined whether control
strategies learned during adaptation to one load remained evident when
the load was unexpectedly changed.
Some of these results have previously been reported in abstract form
(Sainburg and Ghez 1995 Subjects and apparatus
Subjects were 13 neurologically intact adults (8 females, 5 males), aged 28-46. Five subjects (3 females, 2 males) participated in
experiment 1, whereas eight participated in experiment
2 (5 females, 3 males). Figure 1
illustrates the experimental setup. All subjects provided informed
consent before participation in this study, which was approved by the
institutional review board of Columbia University. Subjects sat facing
a computer screen with their dominant arm supported over a digitizing
tablet by a frictionless air-jet system. A thermoplastic splint was
fitted to the subject's forearm and hand, immobilizing all joints
distal to the elbow. A magnetic pen (200 Hz), attached to the tip of the splint, allowed the hand position to be monitored and displayed as
a screen cursor. Vision of the arm and table was blocked using a
horizontal screen. An outrigger was fixed to the splint for the
attachment of a 1.2 kg mass placed 25 cm medial or lateral to the
forearm. Two precision, single-turn, linear potentiometers (Beckman
Instruments) were used to monitor the elbow and shoulder joint angles,
and data were digitized using a Macintosh computer equipped with an A/D
board (National Instruments PCI-MIO-16 × E-50). The experimental tasks
and hand position feedback were presented to the subjects using a
second computer connected to the digitizing tablet. Computer routines
for data analysis were written in Igor (Wavemetrics).
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
ELBOW JOINT TORQUES.
RESULTS
DISCUSSION
REFERENCES
INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
ELBOW JOINT TORQUES.
RESULTS
DISCUSSION
REFERENCES
; Goodbody and Wolpert 1998
;
Imamizu et al. 1995
; Jordan and Rumelhart
1992
; Lackner and Dizio 1994
; Shadmehr
and Mussa-Ivaldi 1994
). Recent reports have shown that, with
practice, subjects adapt to coriolis forces (Lackner and Dizio
1994
) and viscous forces applied to the hand by a manipulandum (Gandolfo et al. 1996
; Goodbody and Wolpert
1998
; Shadmehr and Mussa-Ivaldi 1994
). The
development of neural representations of applied forces was
demonstrated by the persistence of hand-path curvatures that mirrored
the directions and magnitudes of such forces after they had been
removed ("after effects"). After effects even occurred for
movements made in different regions of space (Shadmehr and
Mussa-Ivaldi 1994
), in different directions (Gandolfo et
al. 1996
), and at different speeds than that of practice
(Goodbody and Wolpert 1998
). These reports indicate that
during practice of novel tasks, the nervous system gradually develops
an internal representation of the associated environmental dynamics.
This internal model is subsequently used to control movements made under identical or similar task conditions.
; Hoy and Zernicke 1986
;
Sainburg et al. 1995
; Schneider et al.
1989
; Winter 1990
), is not directly encoded by
muscle and tendon proprioceptors (Hasan 1983
;
Hasan and Houk 1975
; Matthews 1981
).
Because of the differences in available sensory information, it is not
known whether intersegmental forces and extrinsically applied forces
are controlled through the same neural mechanisms.
; Bizzi et
al. 1976
, 1984
; Feldman 1986
; Flash
1987
; Polit and Bizzi 1979
). According to these
ideas, once a single endpoint or a sequence of desired positions is
specified, the springlike properties of the muscles are exploited. Joint torque emerges as a function of the difference between the muscle
lengths for the current and the desired limb positions. Equilibrium
point mechanisms thus do not require that the controller explicitly
represent or predict the effects of musculoskeletal dynamics. Other
authors (Gottlieb et al. 1995
; Hirayama et al. 1993
) incorporated this type of controller into hybrid
mechanisms that initiate movements through open-looped processes,
subsequently employing equilibrium-type mechanisms to specify the end
posture and compensate unexpected loads. In this way, equilibrium point mechanisms can compensate for inaccuracies in learned control strategies.
described methods for
experimentally discriminating between alternative representations
of learned control strategies based on patterns of generalization. They
proposed that different patterns of generalization could differentiate between pure analytic representations and tabular representations. The
former would predict complete transfer of learning anywhere in space
because the precise dynamic or kinematic transformation would be
represented in abstract terms. The latter implies a simple recording of
input-output relationships, such as a memory of a muscle-activation/sensory-feedback pattern, and as such does not predict generalization. A third type of representation is characterized by neural network models, which do not directly represent physical parameters and can result in intermediate patterns of generalization.
).
METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
ELBOW JOINT TORQUES.
RESULTS
DISCUSSION
REFERENCES
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Fig. 1.
Experimental set-up: X and Y represent
axes of coordinate system originating at shoulder. Shoulder and elbow
angles were measures as and
, respectively. After each trial,
the hand path was displayed on the computer screen, each circle
representing the hand position every 25 ms.
Task
A single target line with the starting circle were presented on the computer screen (see Fig. 1). The hand position was displayed in real time as a screen cursor. Subjects were to hold the cursor within the starting circle for 1 s to initiate each trial. Then an auditory GO signal was given, and the cursor was blanked. Subjects were to trace the line using a rapid overlapping, out-and-back movement of the hand. The movement was to be completed within a 1.5-s sampling window. Subjects were instructed to focus on making their movements straight and to retrace forward and backward motions. Movement paths were displayed on the computer screen at the end of every trial (see Fig. 1).
The two experiments conducted in this study are described in the following text.
EXPERIMENT 1. Each experimental session consisted of three different blocks of trials. The first block consisted of 100 trials performed with the medial load. The second block consisted of 108 trials: 100 trials were made with the medial load, whereas 8 trials, interspersed among the others, were made with the lateral load. Because subjects were not aware of this change, we refer to these trials as "surprise" trials. We used eight surprise trials because pilot data indicated that after approximately nine trials, subjects began to report "expecting" a change in dynamics. Finally, the third block of 100 trials was made with the lateral load. Statistical comparisons were made between the last eight trials of the first block, the eight surprise trials, and the last eight trials of the final block. The surprise trials thereby could be compared with trials performed after the subject had adapted to each mass position.
Because our task was designed to study control of interaction torques, we used a target that required substantial motion at each joint. The target line was 20 cm long, and oriented 135° relative to the horizontal axis. Given the limb dimensions of all five subjects, this target required from 18 to 21° displacements at each joint. We tested reversals in hand motion because joint accelerations and thus inertial interactions are maximized during such movements (Sainburg et al. 1995EXPERIMENT 2. In the second experiment, we investigated whether practice toward one target direction and with a given load configuration influences the accuracy of movements made toward other directions. All eight subjects learned to control movements made toward a single direction and over a single target line. Generalization in this learning was tested for movements made to three different target lines. We chose 10-cm-long targets at directions that differed by 18° (90, 108, and 126°) because they required substantial displacements at both joints. To control for the effect of direction on movement accuracy, half the subjects trained with the 126° target, while the other half trained with the 90° target. Every subject completed two experimental sessions, training with the medial and lateral loads on separate days. On their first day, half the subjects comprising each target group trained with the lateral load, whereas the other half trained with the medial load.
Each daily experimental session consisted of two blocks of trials. In the first block of 100 trials, subjects practiced movements with a single load configuration over a single target line (90 or 126°). In the second block, consisting of 500 trials, subjects continued to make movements over the trained target line. In 50 randomly presented trials, subjects were tested with a different load configuration and/or a different target line. For each of the three directions, 10 trials were performed with the mass in the same position as that of training, whereas for another 10 the position was switched. The effects of training on the accuracy of test trials were assessed by comparing the movements between the two experimental sessions that were made with a given mass position and to a given target. For example, adapted lateral load trials from the lateral mass training session were compared with surprise lateral load trials from the medial mass training session.Kinematic analysis
The primary data consisted of the shoulder and elbow
potentiometer signals that were digitized at 1 kHz, low-pass filtered at 12 Hz (2nd order, no-lag, Butterworth), and double differentiated to
yield angular velocity and acceleration values. Elbow () and shoulder (
) joint angles are defined in Fig. 1.
Hand paths were calculated from joint angle data by using the measured length of the upper arm and the distance from the elbow to the magnetic pen. The angular data were transformed to a Cartesian coordinate system with origin at the shoulder (see Fig. 1). Movement onset and termination were defined as 1% of the maximum tangential hand velocity, measured before the first peak in velocity (Vmax1) and after the second peak in velocity (Vmax2), respectively.
For ease of presentation, data were segmented into three different acceleration phases, separated by the two main peaks in tangential velocity of the hand (Vmax1, Vmax2): outward acceleration, reversal (outward deceleration and inward acceleration), and inward deceleration (see Fig. 2). The transitions among three phases corresponded well to angular acceleration and torque zero crossings at each joint. These phases will be referred to as outward, reversal, and inward, respectively.
|
Two measures of movement accuracy were calculated from the hand path, initial direction error, and reversal error. The initial direction error was calculated as the angle between the target line and the line originating at the starting location of the hand (at time 0) and terminating at the point at which the first peak in tangential hand velocity (Vmax1) occurred. The reversal error of the hand path was measured as the area circumscribed by the hand path during the reversal phase of motion (see Fig. 4).
Averages of time series data were obtained, first by synchronizing each trial (single time series) to Vmax1, and second by clipping the data so that each trial had an equal number of frames. Corresponding frames from each trial then were averaged and standard errors calculated.
Kinetic analysis
We partitioned the terms of the equations of motion at each
joint into three main components, interaction torque, muscle torque, and net torque (Sainburg et al. 1995). At each segment,
interaction torque represents the rotational effect of the forces
resulting from motion of the other linked segment. The muscle torque
primarily represents the rotational effect of muscle forces. Finally,
net torque represents the inertial resistance of the segments to joint acceleration. This component varies directly with joint acceleration and limb inertia and is equal to the combined muscle and interaction terms.
It is important to note that the computed muscle torque cannot be
considered a simple proxy for the neural activation of the muscles
acting at that joint, as it includes also the passive effects of soft
tissue deformation. The muscle torque does not distinguish muscle
forces that counter one another, such as during contraction.
Additionally, the force generated by muscle to a given neural input
signal is dependent on muscle length, speed of muscle length change,
and recent activation history (Abbott and Wilkie 1953;
Wilkie 1956
; Zajac 1989
).
Torques were computed and analyzed for the shoulder and elbow joints as detailed in the following equations.
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ELBOW JOINT TORQUES. |
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SYMBOLS
A | = | m2L1r2 + mdLdrd |
B | = | mmL1rm |
C | = | I2 + m2r22 + Id + mdrd2 + mmrm2 |
D | = | I1 + m1r12 + [m2 + md + mm]L12 |
m | = | mass |
r | = | distance to center of mass from proximal joint |
L | = | length |
I | = | inertia |
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= | shoulder angle |
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= | elbow angle |
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= | angle between forearm and line connecting attached mass with elbow joint |
SUBSCRIPTS
1 | = | upper arm segment |
2 | = | forearm/hand segment |
d | = | air sled device |
m | = | attached mass |
Simulations
We solved the equations of motion (shown above) for
and
, then forward integrated using a fixed 1-ms time step.
Inputs to each simulation were initial
and
values, subjects'
limb dimensions and inertial values, the configuration of the attached mass, and the joint torque histories calculated from each recorded movement trial. Thus we could predict the effects of an ideal open-looped controller by using the muscle torques computed from a
movement made with a given mass position to drive the simulation with
an "altered" mass position. We calculated the forward integration error by comparing a simulated hand path to that of the actual trial.
The maximum error was 0.61 mm.
Statistical analysis
The individual measures used in this paper were analyzed in separate ANOVAs with experimental blocks (adapted medial, surprise lateral, adapted lateral) as a within subject variable. Post hoc comparison of cell means was done using the Bonferoni/Dunn method.
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RESULTS |
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Experiment 1: Control of interaction torques with different loads
KINEMATIC ANALYSIS. When first presented with the medial mass, subjects made consistent deviations in initial movement direction and in reversing the direction of hand motion (see Fig. 3). The initiation of hand movement was deviated counterclockwise and the direction reversed through a wide clockwise curve. Initial direction errors were reduced and direction reversals became sharp, as required by the task, during the first 40 trials of practice. This indicates that accurate control over the medial load requires learning of a unique control strategy.
|
|
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INVERSE DYNAMIC ANALYSIS. Adapted trials. Figure 6 shows the torque profiles from the trials shown in Fig. 4. With both medial and lateral loads, the interaction torque at the elbow acts in the same direction as the net torque, indicating its action in accelerating joint flexion and extension. Muscle torque, however, acts in the opposite direction and thus counters the effects of interaction torque. Note that at the beginning of the reversal phase, initiation of extensor muscle torque coincides with the initiation of flexor interaction torque (Mean time difference across subjects = 5 ± 14 ms). Because the interaction torque for the lateral load trials is substantially larger, muscle torque amplitude increased to maintain similar elbow kinematics between the medial and lateral load conditions.
|
FORWARD SIMULATIONS. We implemented a simple open-looped controller to better understand the origin of the changes in torque that resulted in hand path deviations of surprise trials. The muscle torques calculated from the adapted medial load trials were used as inputs to the dynamic equations of motion. The forward simulation was performed with the inertial values of the distal segment altered to mimic the lateral mass condition. In effect, this predicted what would have happened if the subject had used the torques needed to accurately control the medial load throughout a surprise trial. A forward simulation was obtained for all trials. Figure 7A shows the results for a typical trial, whereas simulated direction and reversal errors are averaged for each subject in Fig. 7B.
|
Experiment 2: Generalization of learning across directions
While it is possible that adaptation to altered intersegmental dynamics occurs through memorization of a single stereotyped muscle activation pattern, it is also possible that subjects develop a more general representation of the altered inertial dynamics. To discriminate between these alternatives, we examined whether learning to control a novel inertial load for movements to a single direction generalizes to movements made in different directions. After adaptation in a single direction (90 or 126°) and with a single mass configuration (medial or lateral), subjects were pseudorandomly tested, every five to eight trials, on movements made to each of the three targets (90, 108, and 126°) with the same or a surprise mass configuration. Subjects completed a training session with each mass configuration on separate days to either the 90 or 126° target. Learning was assessed as the difference in accuracy between trials that were matched for inertial load and target but followed different training sessions.
Figure 8A shows averaged hand paths for trials made with the lateral load from both 126° training sessions. The movements made with the lateral load and to the trained direction, during the lateral load training session, are straight and the direction reversals are sharp. However, in the same direction, surprise lateral load movements made during the medial load training session showed large direction and reversal errors. As the movement direction diverged from that of training, movements performed during the lateral training session became less accurate and more similar to the surprise trials made during the medial training session. Similarly, as movement direction diverged from that of training, the errors in surprise movements made during the medial training sessions were reduced. This decay in the effects of training on movement accuracy was not dependent on movement direction as indicated in Fig. 8B.
|
Figure 8B shows the effects of training, measured as the differences in movement errors between surprise and adapted trials performed with the same load. Whether subjects trained to 126 or to 90°, the effects of training decayed as the movement direction deviated from that of training. On average, differences in direction errors dropped by 29% when movements were made 36° to either side of the trained direction. Similarly, the differences in average reversal areas decreased an average of 26%. Thus regardless of the direction to which subjects trained, the effects of training decayed as movement direction diverged from that of training.
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DISCUSSION |
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Anticipatory control
This study examined the mechanisms underlying control of
interaction torques during reaching movements. Subjects first adapted to a novel inertial load, the position of which altered the magnitude of interaction torques at the shoulder and elbow. After adaptation to
the medial load, the mass was moved lateral on pseudorandom surprise
trials. In these trials, the initial portion of the muscle torque
profiles at the shoulder and elbow remained remarkably similar to that
of adapted medial load trials. As a result, subjects made errors in
initial movement direction that resulted from uncompensated increases
in interaction torque imposed by the new mass configuration. These
deviations in the initial direction of hand motion could be attributed
to open-looped control mechanisms calibrated to the intersegmental
dynamics of the adapted condition. This was demonstrated using a simple
forward simulation that predicted what would have happened had subjects
used the torques needed to accurately control the medial mass
throughout the surprise trials. The simulation predicted initial
direction errors, indicating that the early part of subjects'
trajectories resulted from anticipatory processes. These findings
support those of previous studies examining adaptation to external
coriolis (Lackner and Dizio 1994) and viscous (Gandolfo et al. 1996
; Goodbody and Wolpert
1998
; Shadmehr and Mussa-Ivaldi 1994
) forces
applied to the limb during reaching movements. Those studies indicated
that during adaptation, the nervous system develops internal models of
the applied forces that subsequently are used to specify new movement
commands. The current results extend previous findings, indicating that
the intrinsic dynamics of the musculoskeletal system itself are
controlled through similar anticipatory mechanisms.
Our results support and extend previous findings, indicating that
proprioceptive information is needed to control the intrinsic mechanics
of the musculoskeletal system. In previous studies of unconstrained
reaching (Sainburg et al. 1993) and supported horizontal plane reaching movements (Sainburg et al. 1995
),
deafferented patients showed large errors in movement direction and
curvature that varied with the magnitude of interaction torques. Visual feedback only partially improved movement accuracy, indicating that
proprioceptive information is essential for controlling intersegmental dynamics (Ghez and Sainburg 1995
; Sainburg et al.
1995
). In light of these findings, the results presented here
indicate that control of intersegmental dynamics is normally dependent
on proprioceptive information to update and maintain neural
representations of the musculoskeletal system.
Feedback control
In the surprise trials studied here, differences from the torque
patterns of adapted medial load trials emerged as subjects decelerated
the hand to reverse movement direction. The occurrence of
feedback-mediated responses during movement deceleration is consistent
with reports on single-joint movements (Cooke et al. 1985; Forget and Lamarre 1987
; Gordon and
Ghez 1984
). Although elbow joint muscle torque countered
interaction torque throughout adapted trials, in surprise trials
shoulder flexion deceleration caused elbow flexor interaction torque
that was not countered by extensor muscle torque. As a result, the
elbow flexed in the early part of the reversal phase, desynchronizing
the reversals at the two joints and causing reversal errors. We propose
that this prolonged flexor torque was an attempt to compensate for the
excessive elbow extension that contributed to initial direction errors.
However, because of neural transmission and muscle activation delays,
flexor muscle torque was actuated after interaction torque had become
flexor. As a result, the sharpness of actual direction reversals was
substantially less than that predicted by our forward simulation.
In the final deceleration phase of "return" motion, our forward
simulation no longer predicted the trajectory. Instead, muscle torque
appeared to be determined by feedback-mediated responses that
invariably returned the hand to its starting position. This ability of
subjects to return to the starting position despite large trajectory
errors suggests that movement endpoints are achieved by a mechanism
that is distinct from trajectory control. For example, Feldman and
Bizzi (Bizzi and Abend 1983; Bizzi et al. 1976
,
1982
; Feldman 1974
, 1986
) described an endpoint
control model in which desired positions are achieved by
instantaneously activating antagonistic muscles to specified levels at
the beginning of movement. Because of the springlike properties of
muscles, the final posture is attained independently of the trajectory,
which can vary depending on musculoskeletal and environmental dynamics.
Hirayama and coworkers (1993)
incorporated a similar
postural control mechanism into a two-phase control model in which
initial trajectory features result from open-looped control while final
position is achieved by coactivation of antagonist muscles. The
postural controller used "visual" information about target
location to specify levels of stationary motor commands to groups of
muscles. Our findings support this type of combined anticipatory and
postural controller; however, we expand these ideas to include three
distinct mechanisms that operate successively to control rapid reaching
movements: first, movements are controlled through anticipatory
mechanisms that are adapted to expected mechanical conditions. Second,
as sensory feedback becomes available, corrective modifications are made to the predetermined torque profile. If these corrective mechanisms are not calibrated to the current mechanical conditions, they may result in maladaptive responses. Third, the final position of
the hand is controlled through postural mechanisms that are less
subject to the dynamic conditions of the task.
Learned representations of musculoskeletal dynamics
In the second experiment, we examined whether adaptation to a
novel inertial load during movements made in a single direction transfers to affect the accuracy of movements made in a range of
directions. We found significant effects of learning over a 36° range
either clockwise or counterclockwise from the trained direction.
However, as the movement direction diverged from that of training, the
effects of training on movement accuracy decreased substantially.
This limitation in generalization agrees with previous reports
examining generalization of learning rotated visual feedback (Ghahramani et al. 1996; Imamizu et al.
1995
) as well as novel viscous force fields applied to the hand
(Gandolfo et al. 1996
; Goodbody and Wolpert
1998
; Shadmehr and Mussa-Ivaldi 1994
). The current results extend these findings by showing that the nervous system uses sensory information to develop and recalibrate internal models of the musculoskeletal system itself.
This does not necessitate that the nervous system explicitly models
physical parameters such as segment geometries and inertias. In fact,
the limitation in generalization suggests that a complete analytic
model of the altered inertial system was not developed. Instead, the
results presented here are consistent with the computational models of
Jordan (Jordan and Rumelhart 1992) and Kawato
(Kawato and Gomi 1992a
,b
) for transforming intended
joint kinematics to joint torques. Those authors demonstrated the
plausibility of using sensory feedback about movement errors to train
the parameters of inverse dynamic models (Jordan and Rumelhart
1992
; Kawato and Gomi 1992a
,b
) that employ
neural network algorithms rather than analytic solutions to dynamic
transformations. In these schemes, the inverse model allows a desired
trajectory to be transformed to appropriate muscle commands only when
the parameters (synaptic weights) of the inverse model are correct.
Both authors have employed forward dynamic models through which errors
in the trajectory can be backpropagated to yield a motor command error.
This command error then is used to train the parameters of the inverse
model. The forward model, which transforms intended movement commands into a trajectory, has the advantage of allowing the system to estimate
the results of a set of movement commands without actually performing
the movement. Discrepancies between predicted and actual trajectories
allow training of the parameters in the forward model. These neural
network models provide plausible alternatives to exact analytic models
and are thus consistent with our findings indicating limited
generalization of learning across a range of movement directions.
It is also possible that instead of network or analytic models of
the musculoskeletal system, the nervous system may use sophisticated tabular models to control intersegmental dynamics. For example, rules
may be used for scaling a template muscle activation pattern developed
through trial and error. This is similar to the ideas developed by
Gottlieb (1996) suggesting scaling of preselected torque
profiles to make movements in different directions under varied speed,
load, and distance requirements. Because of the nonlinear and variable
relationship between muscle activation and joint torque, it is likely
that such rules would govern the relative timing and amplitude of
muscle activations across joints. For example, Hasan and colleagues
(Hasan and Karst 1989
; Karst and Hasan 1987
,
1991a
,b
; Koshland and Hasan 1994
) explained
agonist and antagonist muscle activations at the initiation of planar arm movements in terms of task and limb geometry. The current results
indicate that intersegmental dynamics are controlled by three
sequential processes acting in series: movements are initiated through
anticipatory mechanisms based on learned representations of
musculoskeletal and task-specific dynamics. Later, error corrections based on on-line sensory feedback are followed by positional control mechanisms that determine the final posture for the limb. Further studies are required to determine precisely how anticipatory control is
represented and implemented by the nervous system.
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ACKNOWLEDGMENTS |
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This research was supported by National Institute of Child Health and Human Development Grants 1K01HD-0118601 and HD-07423.
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FOOTNOTES |
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Address for reprint requests: R. L. Sainburg, School of Health Related Professions, State University of New York at Buffalo, 90 Farber Hall, 3235 Main St., Buffalo, NY 14214.
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 18 September 1998; accepted in final form 3 November 1998.
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REFERENCES |
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