Chapter 12 Adaptation of arm movements to altered loads: Implications for sensorimotor transformations

Motor Control and Sensory Motor Integration: Issues and Directions D.J. Glencross and J.P. Piek (Editors) 9 1995 Elsevier Science B.V. All rights reserved.

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Chapter 12

ADAPTATION OF ARM MOVEMENTS TO ALTERED LOADS: I M P L I C A T I O N S FOR S E N S O R I M O T O R T R A N S F O R M A T I O N S .

G.K. Kerr

School of Human Movement Studies, Queeensland University of Technology Department of Human Movement, The University of Western Australia University Laboratory of Physiology, Parks Road, Oxford, OX1 3PT, UK

R.N. Marshall

Department of Human Movement, The University of Western Australia

In th& chapter we consider how arm movements may be adapted in response to alterations in proprioceptive information. The first part of the chapter introduces issues related to the planning and control of arm movements and the coordinate space that these processes may be represented in. The second part describes how arm movements are performed when propriocepfive information is altered by the addition of loads to the hand. In the final part we describe how methods of computer simulation may be applied to the examination of these questions.

1.

COORDINATE SPACE

When we move through our environment we continuously interact with objects within it. The location of these objects, whether they be located in peripersonal or extrapersonal space, is determined by the central nervous system (CNS) from many sources of sensory information. Although visual information is predominantly used to derive the location of objects, auditory and to some extent somaesthetic and kinaesthetic information may be utilised. Our movements may also be visually guided within peripersonal space. Thus they can be considered to be controlled within a coordinate system that is relative to the external world; that is in extrinsic coordinates. In contrast, in the absence of vision, the position and orientation of our limb, both statically and during movement, are predominantly derived from somaesthetic and

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kinaesthetic information. This information is expressed in terms of joint angles and muscle lengths (Stein, 1989). Because such a coordinate system is relative to the body it is referred to as an intrinsic coordinate system. There is, however, some controversy as to how sensory and motor information are represented within the central nervous system. For each of the above coordinate systems there are a number of possible representations. For example, an extrinsic coordinate system might use Cartesian or polar coordinates. An intrinsic coordinate system might use limb angles or muscle lengths (Lacquaniti, 1989). Knowledge of the shape, size and mass of our limbs is also necessary if we are to produce coordinated movement. To some extent this is a dynamic process as we acquire a knowledge of our "body image" during our development. The ability to modify this "body image" is also important if we are to use tools, manipulate objects, adapt to different external environments, and to rehabilitate from traumatic body injury. In this sense a coordinate system that represents the positions of our limb in space may be considered to be enmeshed with the mechanical properties of the limb (Kugler & Turvey, 1987). Ascertaining what type of representation or coordinate system is utilised by the CNS for movement control is difficult because the numerous muscular and mechanical degrees of freedom involved allow movements to be performed in a number of different ways. However, ann movements display a number of regularities in their kinematic prof'des and from these have been inferred variables essential to representation and control of movement. Descriptions of both the path and time prof'de of a movement may therefore provide insight as to how movements are planned, programmed and performed (Bernstein, 1967; Lacquaniti, 1989). 2.

EXTRINSIC COORDINATE CONTROL

If planning of an arm movement is performed at the level of the hand, that is in extrinsic coordinates, then essentially straight movement paths are predicted. Such a strategy, in which a coordinate system that is relative to the external world is used, is teleologicaUy appealing because it allows for greater ease of interaction between the biological system and the external environment (Atkeson & Hollerbach, 1985; Hildreth & HoUerbach, 1986). This assumption has implications in terms of the computations that must be performed. In order that the hand may be controlled along a particular path an inverse dynamics computation is required so that the correct magnitude and sequencing of joint torques may be produced. This imposes a considerable computational burden on a biological (or robotic) control system but has the advantage in that it allows the trajectory of the hand to be planned independently of the specific joint and muscle patterns (Morasso, 1983).

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The use of an extrinsic coordinate system implies that some form of positional control may be exerted during movement. This has most convincingly been demonstrated by applying perturbations to single-joint arm movements performed by deafferented monkeys. Their movement trajectories were able to be reassumed despite large perturbations to their limb (Bizzi, Polit & Morasso, 1976; Bizzi et al., 1981, 1982; Polit & BiTzi, 1978, 1979). Results of perturbations to forearm movements performed by humans (Cooke, 1979, 1980a, 1980b) are also consistent with this hypothesis. The trajectories of two degree of freedom arm movements in the horizontal plane of both monkeys (Georgopoulos et al., 1981) and humans (Morasso, 1981) are also consistent with some form of positional control. Hand paths of these movements are straight or slightly curved and the tangential hand velocities of these movements generally show a single peaked bell-shaped curve. In contrast, joint angular velocities exhibit variable patterns which are direction dependent. Curved hand movements also tend to be controlled in short segments of shallow curvature with velocity maxima that coincide with local curvature minima. These relationships remain unaltered despite the use of different movement spaces, the tracing of curved outlines, and additional movement of the wrist. Such observations indicate that control is manifest via the trajectory of the hand and involves the precise coordination of joint torques and compensation for interactional forces (Abend, Bizzi & Morasso, 1982; Atkeson & Hollerbach, 1985; Flash, 1990). A feature of observed movement paths, for both single (Hogan, 1984; Nelson, 1983; Stein, Oguztoreli & Capaday, 1985) and multi-joint movements (Abend, Bizzi & Morasso, 1982; Atkeson & Hollerbach, 1985; Morasso, 1981) has been that, providing spatial and temporal accuracy constraints of the movement are not high, the tangential velocity profile of the hand is unimodal. Moreover, alterations in the speed of unconstrained movements are able to be accomplished by appropriate scaling of the tangential velocity profile, irrespective of the path of the hand (Atkeson & Hollerbach, 1985). This observation provides support for planning in terms of hand coordinates, but it has further implications as to additional constraints applied to the planning and control of movements. These velocity profdes have been found to adhere to a minimum-jerk cost function which is related to minimum energy expenditure. Such movement optimisation criteria appear to apply to both single (Hogan, 1984; Nelson, 1983; Stein et al., 1985) and multi-joint movements (Flash, 1983). Optimisation of movement control by the minimisation of jerk cost (Hogan, 1984; Hogan & Flash, 1987) or minimum torque-change (Uno, Kawato & Suzuki, 1989) also appears to enable a movement to be performed more smoothly and efficiently. However, other variables such as time, force, impulse or energy (Nelson, 1983), and joint stiffness (Hasan, 1986) may also provide an appropriate minimisation term, depending on the task and environmental context of the movement (Nelson, 1983; Stein et al., 1985).

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Problems For Extrinsic Coordinate Control

However, trajectory may not necessarily be the only controlled feature of the movement. As Atkeson and Hollerbach (1985) have noted, arm movements in the horizontal plane, from which much of the evidence for trajectory control has been obtained, are not typical of naturally occurring movements. In addition, limiting movements to one plane of movement in contact with a surface restricts them within a class of compliant motions and implies that atypical control strategies may be used in their performance (Atkeson & Hollerbach, 1985; Brady, 1982; Saltzman, 1979). Movement trajectories also differ depending on the context within which a movement is performed (Marteniuk et al., 1987). Even when unconstrained three dimensional movements are examined it is still unclear as to which coordinate system movements are planned and controlled within. Hand paths may be straight or curved depending on the workspace within which movements are performed (Atkeson & Hollerbach, 1985; HoUerbach & Atkeson, 1986, 1987a,b; Hollerbach, Moore & Atkeson, 1987). At the extreme ranges of movement, and when movements are performed in a straight line through the shoulder, both straight-line hand trajectories and constant jointangle ratios are obtained 0_,acquaniti & Soechting, 1982; Soechting & Lacquaniti, 1981). Under these conditions it is possible to attribute control to both endpoint Cartesian interpolation

(extrinsic

coordinates)

and joint

interpolation

(intrinsic

coordinates)

(Hollerbach & Atkeson, 1987a). Experimental attempts to distinguish between the different coordinate systems that might be employed in controlling movements have therefore proven difficult to achieve. 2.2

Adaptation To Altered Visual Extrinsic Coordinates

One method that has been used to study the coordinate system in which we control our movements, at least in the visual world, has been to systematically alter or bias the available visual information. If visual information is delayed (Smith & Bowen, 1980) or prismatically altered (e.g. Held, 1965; Held & Freedman, 1963) there are considerable deviations from normal trajectories. In these circumstances we are faced with the challenge of modifying our internal representation of the externally perceived world such that it matches with the known intrinsic coordinates of our body; that is, those aspects of our movement that are not visually derived. Experiments in which the visually perceived world is altered therefore provide a means by which we can examine the coordinate systems in which our movements are planned and controlled. In the situation of prism adaptation the visual representation of an object is displaced to one side. Consequently there is a misreaching by the arm as it strives to accomplish its initial visually def'med path. Over a number of attempts at this task, however,

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there is adaptation to this altered visual field such that the object to which the action is directed is reached with a movement path that is similar to that of movements in the normal visual field (Jakobson and Goodale, 1989). When the prisms are removed the process is reversed with the initial misreaching occurring in the opposite direction. Overall these experiments are highly supportive of movement planning and control in terms of visually defined coordinates. 3.

INTRINSIC COORDINATE CONTROL

Movement planning performed in terms of joint variables, that is in intrinsic coordinates, implies the existence of curved hand paths. In computational terms, the control of movement in terms of joint coordinates requires an integral dynamics calculation. This is used to produce a trajectory based on a time sequence of torque inputs to the joints. However, this method of control does not allow the trajectory of the hand to be explicitly determined between each new joint position. Rather, hand position is an a posteriori consequence of a change in joint angle. This level of planning and control has been equated with a muscle oriented mechanism of trajectory formation where a cognitive level, responsible for planning the movement, continuously and directly controls the action of the muscles (Morasso & Ivaldi, 1982). Controlling movement in terms of intrinsic coordinates may confer certain advantages to a biological system. Because such a system exerts control 'closer' to the actual implementation of a movement it is potentially more responsive to the different forces generated throughout the course of a movement. These include joint and limb inertia interactions, centripetal and centrifugal forces, all of which must be compensated for if the desired movement trajectory is to be maintained (Hollerbach & Flash, 1982). Different movement speeds require different dynamics and result in different magnitudes of interactional forces (Atkeson & Hollerbach, 1985) which, given that the motor control system is trying to maintain a particular movement path, further complicate the control of multi-joint ann movements. Such a control system is potentially more responsive to external perturbations. Thus, if obstacles are encountered during the course of a movement or, for example, when an object is lifted that is heavier or lighter than is anticipated, the nervous system is able to rapidly adapt to these localised disturbances. Such rapid alterations have been well documented in 'reflexive' patterns of EMG activity, although these mechanisms may not be sufficient to maintain the limb on its intended course (Soechting, 1988). If the perturbation is predictable, however, then over a number of repetitions the movement is able to be 'adapted' to these constraints such that the same end point trajectory is maintained.

326 3.1

G.K. Kerr & R.N. Marshall

Adaptation To Altered Intrinsic Coordinates Thus another way to examine how the nervous system plans and controls movements is

to alter the kinaesthetic and somaesthetic sources of information that contribute to intrinsic coordinates. One method that we have used is to alter the inertial characteristics of the limb and thereby cause a modification of the limb dynamics required to perform a movement. Such a method should produce a mismatch in the relationship between the intended and actual movement and result in an alteration of the movement trajectory. Insight as to the controlled features of ann movements may therefore be obtained from observed changes in the kinetic and kinematic prof'des of a movement. In a recent experiment (Kerr & Marshall, 1990, submitted) we examined the effects of adding a load to the hand during a pointing movement.

We were interested in how the

nervous system used proprioceptive information to control these movements and whether this information was sufficient to maintain a particular movement trajectory.

For this

experiment we required subjects to make movements from a set starting position to a 2.5 cm. sphere situated at the subject's eye level and at a horizontal distance from the subject equal to their shoulder to wrist distance; this ensured a standard reaching distance for each subject relative to their ann length (Figure 1). A screen prevented vision of the limb except when the finger appeared in front of the target. The positioning of subjects was such that arm movements were predominandy located in a vertical plane. Subjects were allowed to practice without any load attached to their limb until they were comfortable in performing the movement. Data were then collected on eight consecutive trials. A one kilogram object

F

Figure 1. Experimental arrangement for load adaptation

Adaptation of Arm Movements to Altered Loads

327

with uniformly distributed mass was then attached to the subject~ hand. This was done in such a manner that the subject was prevented from ascertaining the magnitude of the mass prior to the next sequence of trials. Data were then collected on eight consecutive handweighted trials. Examples of movements performed in the unweighted condition are contrasted with those of weighted movements in Figure 2. This figure shows the f'mger paths for one subject in 8 consecutive trials. Of note in the unweighted condition (Figure 2A) is the consistency of the f'mger path across trials. In contrast the first weighted trial shows a large deviation from the original trajectory (Figure 2B).

After this initial "perturbation" however, the path

assumed by the finger was adapted over subsequent trials until it matched that of the finger path in the unweighted condition.

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Figure 2. Movement paths of the finger for unweighted (a) and hand-weighted (b) movements for one subject. Arrow indicates first loaded trial.

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G.K. Kerr & R.N. Marshall

Similar trends can be observed for the finger tangential velocity profiles illustrated in Figure 3. The shape of these profdes was quite different for the first one or two trials of the hand weighted condition. The profdes exhibited either an increase or decrease in peak tangential velocity and these adjustments covaried with respective decreases and increases in movement duration.

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Hgure 3. Tangential velocity profiles of the fmger for unweighted (a) and hand-weighted (b) movements for one subject. Arrow indicates fwst loaded Irial. These results, in which differences due to the addition of a load occur in the first trial of a loaded movement, are similar to those of other studies (Atkeson & Hollerbach, 1985; Bock, 1990). After this initial deviation, hand paths of pointing movements with external loads remain similar to those of unloaded movements (Atkeson & HoUerbach, 1985; Bock, 1990; Lacquaniti et al. 1982). However, some slight biases in the hand paths of loaded

Adaptation of Arm Movements to Altered Loads

329

movements have been reported (Uno et al., 1989). Thus the nervous system appears to have compensated for the increased load by maintaining a similar endpoint trajectory. This consistency of endpoint trajectory independent of load offers further support for planning and control of movements in terms of extrinsic coordinates. 4. SIMULATION The stereotyped hand trajectories observed during ann movements suggest that the motor system is able to simplify control by scaling some parameters of the movement while leaving others unchanged. Hollerbach and Flash (1982) have suggested that the inertial and gravitational resulting joint moments (RJM) are separately controlled. Inertial RJMs are the forces due to acceleration and velocity of body segments involved in the movement. Gravitational RJMs are the forces due to the action of gravity on the masses of the body segments involved. For example, an increase in speed could be achieved by scaling the inertial RJMs while the gravitationalRJMs remained constant (Atkeson & Hollerbach, 1985; Hollerbach & Flash, 1982). Explanations of mechanisms involved in compensating for external loads have also distinguished between adjustments to the torques necessary to move the limb or the load. Atkeson and HoUerbach (1985) proposed that adjustments in some components of these torques were required in proportion to the increased mass in order that similar movement trajectories could be maintained. Thus increasing mass by a factor 'r' resulted in an increase in the inertial ('drive') and gravity torques for the load component by a similar proportion, that is, Tload unweighted = Tload drive + Tload gravity Tload weighted = rTload drive + rTloaa gravity These modified torques were then used as drive parameters to their "phantom ann". Thus a simple scaling of some of the dynamic components of the torques would produce the required trajectory. In contrast, translating the trajectory of the hand into torques via an inverse dynamics relationship would be computationally more intensive. Bock (1990) also proposed that load adaptation was achieved by scaling inertial and gravitational terms. The scaling factor derived by Bock was obtained from a ratio of the apparent mass (MA) of the limb to the actual load (ML), at the instant of peak hand velocity. Apparent mass was defined as the mass associated with a unit vector force producing a specified acceleration. It should be noted that the ratio as calculated changes continuously through the movement.

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G.K. Kerr & R.N. Marshall

This was then used to scale the torques by k and k 2 for the inertial and gravitational terms respectively. Thus Bock's gravitational scaling equates to Atkeson and Hollerbach's (increase the torque by the proportion (MA+ML)/MA), while his inertial term scales the torques by the square root of this ratio. Bock demonstrated a linear increase in the scaling factor with the applied load within the constraints of moving "as quickly and accurately as possible". However, the universality of this scaling factor is questionable, as it was found to change with different instructions: Bock states a scaling factor 3r of approximately 1.4 for the mass of 4.5 lb and the original instruction set, and a 'k' of 1.03 for a mass of 4.5 lb with the new instructions (move at the same speed as in the unloaded condition, regardless of a possible reduction in pointing accuracy). Although these studies have suggested that inertial and gravitational torques may be treated separately with respect to the overall control of the movement, neither group have directly addressed how control is implemented at the individual joints during unweighted and weighted movements. Their models have used a "nett" force rather than the resultant joint moments (RJM) required about individual joints. An aim of this study was to ascertain whether previously described models are implemented by the motor control system at the joint level. We therefore examined how the inertial and gravitational components of the RJMs were scaled in the unweighted and handweighted movements. To achieve this the motion of the upper limb from one trial was simulated using an inverse dynamics approach. The x,y marker coordinate data from one trial were used as the basis for each simulation, and modifications were made to the limb segments and hand weight masses. This technique has the advantage of allowing examination of trials with identical kinematic characteristics while modifying load variables. The inverse dynamics simulation provided RJM time histories for the wrist, elbow and shoulder joints during the motion. These RJMs consisted of the combined armgravity and armdrive RJMs. Initially data from an unweighted trial were used and then the simulation was run twice more, with additional loads of 1 and 2 kg in the hand. These runs produced the nett RJMs at the wrist, elbow and shoulder joints. Finally, two more simulations were performed with the 1 and 2 kg weights where the masses of the upper aim, forearm and hand segments were set to zero. These trials gave the 'phantom' RJMs for the two load conditions (loadgravity and loaddriv e RJMs).

Adaptation of Arm Movements to Altered Loads

S h o u l d e r RJM n o r m a l vs p h a n t o m arms

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--~-----------~---

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2O 18 16 A =. z

14 12 10

-3 n-

8 6 4

20 10

20

30

4'0

50

frame

Figure 4. Resultant joint moments at the shoulder from the simulation for the ann and phantom load components of the RJM, the sum of the arm and phantom load, and the total RJM. Our inverse dynamics simulation results agreed with Atkeson and HoUerbach (1985), that the nett RJM at a joint equals the sum of the arm and load components (Figure 4 shows example results for the shoulder joint). This work also supports their suggestion that a linear relationship exists to scale RJMs for load increases in a movement with identical kinematic

characteristics. Figure 5 shows the combined loadgravity and loaddrive shoulder RJMs for the two weight trials, and it can be clearly seen that the RJM for the 2 kg trial is double that for the I kg trial. Further, as seen in Figure 6 the scaling factor for the load only, in kinematically similar

movements, also holds for the elbow and wrist joints. This result agrees with both Atkeson and Hollerbach (1985) and Bock (1990). One implication from these results is that the control of variables associated with intrinsic joint coordinates is subservient to mechanisms that derive control information from extrinsic coordinates.

5.

E L B O W - S H O U L D E R RELATIONSHIPS

However, further examination of our data show that some changes appear to be required in order that the same movement path can be achieved. Figure 7 shows the elbow-shoulder angle relationships for the unweighted and hand-weighted conditions from one subject.

G.K. Kerr & R.N. Marshall

332

Shoulder RJM p h a n t o m a r m s 1 vs 2 kg

.... o----4---

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Figure 5. Phantom arm load shoulder RJM components from the simulation for loads of 1 and 2 kg.

RJMs

for 1 & 2 kg loads

14 12 10 A

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Figure 6. Phantom arm load elbow and wrist RJM components from the simulation for loads of 1 and 2 kg.

333

Adaptation of Arm Movements to Altered Loads

This clearly shows that the elbow-shoulder angle relationship did not remain invariant under different hand load conditions. This alteration was compensated for at the wrist joint and allowed an invariant finger trajectory to be maintained.

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Shoulder Angle (radians) Figure 7. Relationshipbetween elbow and shoulderangles for unweighted (a) and hand-weighted (b) movementsfor one subject. These alterations in the elbow-shoulder relationship between the unweighted and weighted condition must be associated with altered shoulder and elbow RJMs. Note that the above simulation and the associated 'scaling' models of control all required identical kinematic characteristics to be maintained if such an approach was to be successful. The fact

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G. K. Kerr & R. N. Marshall

that there was an alteration in joint angular relationships raises concerns about the applicability of a theory based upon end point kinematics, when the kinematic redundancy in the system permits a variety of joint RJM combinations to produce the same kinematics. One implication from this result is that scaling of joint RJMs in real-life movements is non-linear. Because the gravitational component of the RJMs are subject to simple linear scaling, we suggest that the scaling for inertial components must therefore be non-linear. This non-linear scaling for inertial components of the RJM assumes even more importance when movements are performed at different speeds. It is worth noting that previous models such as Atkeson and Hollerbach's (1985) necessitate an exponential scaling for inertial effects, even if the same movement trajectories are maintained. These results suggest that control based on an intrinsic coordinate system is crucial for maintaining coordinated movement. Thus changes in joint kinetics and kinematics are able to effected in order that the same movement path can be achieved. 6. INTEGRATING EXTRINSIC AND INTRINSIC COORDINATES It is apparent that the planning and control of movement in either a purely extrinsic or intrinsic coordinate system can not fully account for all of the previous observations. However, because the spatial and temporal movement properties are able to be partially explained in terms of both coordinate systems, it is plausible that some combination of coordinate systems may be effectively used. An overall knowledge of the trajectory of the hand must be available if the appropriate spatiotemporal sequence of proximal joint rotations is to be implemented. In addition, for the final goal to be achieved, an adequate correction for errors in the initial movement is required. For unconstrained arm movements these corrections appear to be related to movements of the distal joints of the limb. Thus control of distal joints is not exerted independently of proximal joints (Lacquaniti, 1989; Soechting & Flanders, 1989a,b). These perspectives indicate that there is an intermeshing of both extrinsic and intrinsic coordinate systems within some mutually accessible spatial representation. In this manner the different sources of sensory information can be thought to have been transformed and represented within a common co-ordinate system (Knudsen, DuLac & Esterly, 1987; Stein, 1989). In fact there is physiological and psychological evidence that the posterior parietal cortex is an area where such transformations occur (Stein, 1989). These notions also speak to the idea of multiple levels of sensorimotor representation (Saltzman, 1979) that may interact in a heterarchical manner (Turvey, Shaw & Mace, 1978). Thus although each sensory modality is represented within its own spatial map these may overlap and become enmeshed with each other.

Adaptation of Arm Movements to Altered Loads

335

Attempting to integrate our results into a unifying model of control is quite a challenge. At present there is no one model that can fully integrate or reconcile positional control with joint torque control. The Fel'dman (lambda) model of equilibrium point control (Ferdman, 1966a,b; 1986) and developments of this model by Latash and Gottlieb (1991a,b), all support a positional control mechanism in terms of the interaction of centrally derived commands with the current state of the peripheral apparatus as signalled by afferent feedback. These approaches do, to some extent, allow for compensation of altered inertial forces during movement. In fact, Fel'dman (1966b) has posited that there are two independent systems of control; one for equilibrium positions of the joint and the other for dynamic parameters which determine a movements acceleration and form. However, a problem for these models is that activity level in participating muscles is not positionaUy unique and is highly dependent on moment arms of the musculo-skeletal system and on the external forces applied to it (Hasan & Enoka, 1985; van Ingen Schenau et al., 1992). The kinematic redundancy observed in multi-joint movements, as described in our experiments, further complicates matters for proposed models because the centrally defined trajectory of the finger must be independent of the muscles and joints involved in the task. In addition, recent work by Shadmehr and Mussa-Ivaldi (1993) indicates that the human nervous system has a strong joint torque dependent mechanism of control and that scaling and adaptation to novel forces occurs at the joint level rather than at the level of the hand. Thus proposed models must integrate mechanisms of planning and control in terms of extrinsic coordinates of the hand and the intrinsic coordinates of the joints and muscles. One of the goals in our research is to quantify the magnitude of the initial alteration in movement trajectory and the time course of the adaptation. In this way we hope to understand more fully how real-life movements are planned and controlled. We also hope to shed some light on the central representations employed by the central nervous system in these processes. Such knowledge is important in understanding how the motor apparatus, which is constrained within a body-centredcoordinate system, is able to produce a movement towards an object localised in a coordinate system with respect to the external world. ACKNOWLEDGEMENTS This research was supported by grants from the Wellcome Trust (U.K.), British Council (Australia), McDonnel-Pew Center for Cognitive Neuroscience (Oxford, U.K.) and the Department of Human Movement, The University of Western Australia. This work was conducted while G. Kerr was a Medical Research Council (U.K.) postdoctoral researcher. We would like to thank John Stein (University Laboratory of Physiology, Oxford, U.K.) for his support and encouragement.

336

G.K. Kerr & R. N. Marshall REFERENCES

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