INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Cerebellar lesions impair the control of single-joint limb movements, producing systematic errors (e.g., hypometria or hypermetria) and increased variability of performance parameters (e.g., angular displacement) (for review, see Brooks and Thach 1981). However, it is well known that the control of multijoint movement is considerably more impaired (Thach et al. 1992). This disproportionate effect on multijoint movement could reflect cumulative defects at individual joints, as suggested by Holmes (1939), or a specific disorder in interjoint control (Luciani 1915; Thach et al. 1992). A compelling reason why multijoint movements are more impaired is that the mechanics of segmented limbs impose control problems for multijoint movements that have no analogue in single-joint movements; inertial interactions due to motion at other joints produce large torques at each joint. For the endpoint of a multijoint movement to be accurate, limb muscle contraction needs to be adapted to these interaction torques at each joint (Ghez et al. 1996; Hoy et al. 1985; Sainberg et al. 1995; Smith and Zernicke 1987). The cerebellum could play a crucial role in producing control signals that take the various torques into account during movement planning. The study of ataxic reaching in patients by Bastian et al. (1996) suggests an important role for the cerebellum in controlling interaction torques.

We have approached the problem of cerebellar control of multijoint movement by studying the strategies used by cats to perform a prehension task (Cooper 1995; Martin et al. 1995). During performance of this task, we have shown that cats use visuo-spatial information from the target to scale elbow joint excursions and velocity to control reach height, which is similar to multijoint strategies that have been described in other prehension tasks in cats (Perfiliev and Pettersson 1998; Pettersson et al. 1997) as well as in humans (e.g., Jakobson and Goodale 1991; Jeannerod 1984). We have found that this control of scaled elbow excursions is coordinated with motions at the other forelimb joints, which keeps the paw path straight as the limb is lifted to the height of the target (Martin et al. 1995). Straight distal joint and hand paths are general characteristics of reaching in our task as well as reaching in humans (Morasso 1981).

In a previous study (Martin et al. 2000) we showed that inactivating the anterior interpositus nucleus (AIP), which receives the output of the C1-C3 paravermal zones (Trott and Armstrong 1987), impaired performance in this task; paw paths became hypometric and path curvature was increased. The purpose of the present study was to determine the impairments in joint trajectory control that underlie these path defects. Hypometric paw paths could be due to weakness or, alternatively, to a scaling defect in which the transformation from target information to movement parameters is altered. To distinguish these alternatives, it is necessary to study movements to a range of targets. The changes in path curvature produced by AIP inactivation could be due to a failure to control intersegmental interjoint interaction torques during movement, as occurs in human deafferentation (Gordon et al. 1994; Sainberg et al. 1995). Analysis of the temporal variations in joint torques is necessary to distinguish the possible effects of altered neuromuscular control from the effects of biomechanical interactions in inaccurate movements.

To analyze joint torques, we developed a four-segment model of the cat forelimb (Cooper 1995) similar to the three-segment cat hindlimb model of Hoy et al. (1985). These authors expressed limb movement in terms of limb segment angles; we followed instead the convention of Hollerbach and Flash (1982) and used joint angles. Since the nervous system has proprioceptive information about joint motion available to it, but lacks a direct measure of segment angles, we felt that the equations of motion in terms of joint angles would more accurately represent the control problem from the point of view of the brain.

We partitioned torques into three computed components: "interaction" torque, which corresponds to the torque at one joint produced by motion at the other joints; "self" torque, which is an acceleration-dependent torque reflecting inertial resistance; and gravitational torque. The sum of these torques is equal and opposite to a residual term that we refer to as "generalized muscle" torque or "muscle torque." This corresponds to the summed net mechanical contributions of muscle contraction acting at the joint and the "passive" resistance of soft tissue deformation. When the limb is in contact with external objects, muscle torque also includes torque exerted on the limb by those objects (e.g., ground reaction force). We computed those torques to determine the relative contributions of muscle and interaction torques to normal and ataxic movements. We were particularly interested in identifying changes in the way animals used muscle torque to compensate for interaction torque during AIP inactivation.

We began with an analysis of joint kinematics, examining the relations between individual joint angular motions and target height. We next examined the relation of shoulder and wrist motions to those at the elbow, both through kinematic and joint torque analyses. AIP inactivation slowed movements at all joints but did not disrupt the scaling of elbow excursions to the target. Inactivation impaired substantially the anticipatory control of interaction torques at each joint. Some of the results were presented in an abstract (Cooper and Ghez 1991), a doctoral thesis (Cooper 1995), and a review (Ghez et al. 1996).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Three cats were used for the kinematic and two for the dynamic analyses of normal and dysmetric reaching during AIP inactivation. These cats were also subjects in our prior study (Martin et al. 2000). All procedures were approved by the New York State Psychiatric Institute Animal Care and Use Committee.

The general methods for behavioral training and testing, data acquisition, basic kinematic analysis, the inactivation procedure, and histological identification have been described in detail (Martin et al. 2000). Here, we briefly summarize the methods. Cats were trained to reach to the back of a narrow food well to grasp a cube of meat (for details see Martin and Ghez 1993; Martin et al. 1995). The food well was instrumented with photocells to detect paw entry. To minimize trial-to-trial variability in the position of the shoulder relative to the food well, cats were restrained in a cloth vest attached to a hammock. Cats were required to stand on narrow supports to minimize paw placement variability at the start of the reach. The forepaw supports were instrumented with a strain gauge for signaling the time when the reaching paw lifted off of the support (toe off). Reaching was elicited during discrete trials that were initiated when the cat placed all four paws on the supports (Martin et al. 1995). After a period of 0.5-1.5 s of stable stance, the animal was permitted to reach to the food well. Trials were run in blocks. In the present study, we present data on reaching to a range of target heights (8, 11, 14, 17, and 20 cm from the foot plate) at a standard anteroposterior location (14 cm forward of the foot plate). Sessions consisted of 100-150 control (i.e., preinjection) trials and 100-300 test or inactivation (i.e., postinjection) trials.

Surgical procedures

Prior to surgery for implanting the chamber, the head fixation device, and the shoulder pin for mounting the elbow and shoulder markers (see Analysis), cats received atropine (0.5 mg/kg im) and an antibiotic (benzathine penicillin, 300,000 units im). They were sedated with ketamine (20 mg/kg im) and anesthetized with sodium pentobarbital (30 mg/kg iv). Additional doses of sodium pentobarbital (5 mg iv) were administered as needed. During surgery, lactated Ringer was administered intravenously and body temperature was maintained at 39° with a heating pad. Following surgery, animals received buprenorphine (0.03 mg/kg im) for analgesia. Animals were mounted in a stereotaxic head holder (Kopf Instruments Inc.), a craniotomy was made over the cerebellum ipsilateral to the trained limb, and a chamber was implanted (at 30° posterior angulation) for mounting the recording and inactivation apparatus.

Electrophysiological procedures and reversible inactivation

Sites for nuclear injection were identified by recording the presence of units with large somatic spikes at the appropriate stereotaxic coordinates (for details see Martin et al. 2000). We recorded unit activity in response to skin contact, movement of limb joints, etc., and evoked muscle contraction and joint movement of the contralateral limbs at threshold currents (<40 µA threshold, 0.5 M etched tungsten electrode, 330 Hz, 45 ms train, 200 µsec balanced biphasic pulses). Muscimol (0.25-1.0 µg/µL in isotonic saline) microinjections were made using a custom-designed cannula (33 gauge stainless steel hypodermic tubing; for details see Martin and Ghez 1993, 1999) connected to a Hamilton microliter syringe with Teflon or polyethylene tubing. Injected volume was checked by measuring movement of the drug-oil meniscus with a microscope and calibrated graticule. For most injections, we mixed Evans blue dye or fluorescent-labeled latex microspheres with the muscimol solution to mark the injection site for later histological reconstruction.

For muscimol microinjection, the cat's head was mechanically fixed to a rigid support using an implanted device and, by means of a hydraulic microdrive, the cannula was lowered to the injection site. Following a four-minute wait, the solution was injected over a period of 4-6 min. We typically used 0.25-0.5 µg muscimol in 0.5 µL saline. The cannula was left in place after the injection for an additional four minutes, to minimize drug spread, and was then withdrawn. The cat's head was then released from fixation and behavioral testing resumed. The total delay between control and postinjection testing was 15-20 min; the delay between the start of injection and resumption of behavioral testing was no more than 12 min. Behavioral testing after injection lasted one hour or less. We made muscimol injections adjacent to (i.e., within 1 or 2 mm) the AIP inactivation sites (posterior interpositus, fastigial nucleus, white matter) to verify the specificity of effects (see Martin et al. 2000).

At the conclusion of experiments, we made electrolytic marking lesions (10 µA × 15 s, 0.5 M etched tungsten microelectrode) (see also Martin et al. 2000). Cats were administered a lethal dose of pentobarbital sodium and perfused through the left ventricle with saline followed by 4% paraformaldehyde solution. The brain was stereotactically blocked in situ, postfixed, and cryoprotected. Frozen sections (40 µm) were cut parasagittally or in a coronal plane with the same posterior angulation (30°) as the injection cannulae. Even-numbered sections were mounted unstained for fluorescence microscopy of the microspheres and odd-numbered sections were processed using either Nissl-myelin (Klüver-Barrera) or plain Nissl methods. Injection sites were reconstructed and nuclear boundaries were drawn in accordance with cytoarchitectonic criteria (Berman 1968; Berntson et al. 1978). These AIP injection sites corresponded to those presented in our previous report (Martin et al. 2000).

Analysis

We used the MacReflex motion analysis system (Qualisys, Inc.) for the kinematic and dynamic analysis of reaching (Martin et al. 1995, 2000). Markers were placed directly on the lateral surface of the distal phalanx of the fourth digit (paw tip), on the skin directly over the metacarpalphalangeal (MCP) joint of the fifth digit, and on the styloid process of the ulna (wrist joint). To accurately monitor shoulder and elbow joint locations, since the skin slides over the shoulder and elbow joints during forelimb motion, we implanted an orthopedic pin through the bone of the greater tuberosity of the humerus and into the medullary cavity prior to behavioral training. The pin protruded 1 cm from the skin surface to provide a stable attachment site for a light-weight metal rod on which markers corresponding to the shoulder and elbow joints were mounted (see Surgical procedures for general surgical procedure; see Martin et al. 1995 for details). The MacReflex cameras were controlled with National Instruments TTL I/O hardware and custom software. Force plate and photocell signals were acquired at 100 Hz using 16-bit A/D converters (Macintosh II computer with National Instruments I/O and DMA boards) synchronized with the video cameras by the software. Joint and paw-tip x-y coordinates, sampled at 100 Hz, were computed and analyzed with custom software written in Matlab programming language. Upper arm, forearm, and metacarpal limb segments were defined as joining the shoulder, elbow, wrist, and MCP joints. The most distal part of the limb was treated as a single phalangeal segment joining the MCP and the paw tip. Shoulder angle was computed as the angle between the arm segment and the horizontal plane (see Fig. 1, inset).

View larger version (31K): [in this window] [in a new window]   Fig. 1. Ensemble averages of shoulder (A), elbow (B), and wrist (C) joint angles (left) and angular velocities (right) for reaches to a standard height (14 cm) and distance (11 cm). Gray lines, preinjection control reaches; black lines, postinjection reaches. Averages synchronized with wrist speed onset (see METHODS). Top inset: stick figures at four sequential times during representative single control (gray) and test (black) reaches. a, movement onset; f, peak wrist flexor joint angle; b, control and c, test peak shoulder extensor joint angles; d, control and e, test peak elbow extensor joint angles. Bottom inset: joint angle conventions (n = 22 before inactivation and 32 during inactivation).

Elbow angle was computed as the angle between the arm and forearm segments, wrist angle as the angle between the forearm and metacarpal segments, and MCP as the angle between the metacarpal segment and the tip of the fourth digit. Time derivatives (e.g., joint angular velocities) were computed with a three-point central difference filter and accelerations were computed by differentiating twice. For the ensemble averages shown in Fig. 1, trials were aligned on the time at which the wrist speed crossed a threshold of 10% of its peak value on that trial. This criterion was chosen empirically as representing the earliest reliably detectable movement at the beginning of the reach. A percentage of peak rather than an absolute level was chosen to avoid an artifactual delay in onset for slower movements. For the ensemble averages of torque data (and associated kinematic data) shown in Figs. 4, 5, and 8, trials were aligned with the time the paw broke contact with the force plate on which it rested. Toe off has the disadvantage of occurring later in the movement than the 10% peak wrist speed, but we used it for the dynamic analysis because it demarcates the portion of the movement where generalized muscle torque excludes ground reaction force.

Amplitudes and the times of occurrence of peaks (local maxima and minima) and onsets in time series of individual trials were measured by operator-assisted custom Matlab software routines. To avoid a bias toward underestimating the amplitude of narrow peaks, a second-order polynomial was fit to the three samples spanning the maximum (or minimum) sample value and the maximum (or minimum) of the polynomial determined.

Onset and peak data for both kinematic and torque data were assembled into two multi-experiment databases, one for target-height variations in normal cats, which contained 714 reaching movements, and another for inactivation, which contained 1,957 reaching movements to various target heights before and after muscimol injection. Statistical analysis of these databases was done using the programs Statview 4 and Super ANOVA. For tests of significance, we used a least-squares general linear model
where K = constant, Expt = experiment number, TDV = target dorsoventral position, and Inact = 1 during inactivation, 0 as control.

Dynamic analysis

Equations of motion for a four-segment planar limb are given in the APPENDIX. These expressions describe the torque required at a given joint to produce a particular pattern of limb motion. Equivalently, they describe a motion-dependent torque at that segment that must be overcome by muscle contraction, tendon stretch, etc. (d'Alembert's principle) (Cooper 1995). We partitioned the biomechanical effects in the equation of motion (see APPENDIX) into three components: self, interaction, and gravitational torques. Muscle torque is defined as equal and opposite to the sum of the other three torques and includes the net mechanical contribution of muscle contraction acting at the joint. It also includes the "passive" resistance of soft tissue deformation and, at the beginning and end of movement, contact with external objects (e.g., ground reaction forces prior to the time the paw broke contact with the force plate). As discussed in the INTRODUCTION (see also APPENDIX), we follow the convention of Hollerbach and Flash (1982) and use joint angles for describing torques.

Because we are interested in the problem of interjoint coordination when movements at one joint produce torque at another joint, we chose a form for the equations that distinguishes self torque, which we define as torque at a joint related only to movement at that joint, from interaction torque, defined as torque at a joint caused by the movement of other joints (itself due in part to the contraction of muscles at those joints). As in the two-joint model of Hollerbach and Flash (1982), the terms of the expression include acceleration-dependent torques (proportional to _i), centrifugal torques (proportional to _i²), and Coriolis torques (proportional to _ik, i k). For a given joint i, the _i term is the only one not dependent on motions of joints other than i and so represents the self torque (i.e., inertial resistance to motion). Interaction torque is the sum of all the other terms. Note that interaction torque includes two additional terms proportional to the x and y components of linear acceleration at the most proximal joint. This represents the lumped effect of all the joints in a cat's body proximal to the shoulder and is included for completeness. In these experiments, animals were restrained in a hammock, which minimized this lumped joint effect. Since in the present research we studied limb movements in a vertical plane, we included a term for torque due to gravity; this term is identical to the y-double-dot term, with y-double-dot equal to gravitational acceleration g = 9.8 m/s². Values for limb segment moments of inertia, masses, lengths, and the locations of segment centers of mass were estimated individually for each cat from published regression equations (Hoy and Zernicke 1985). We validated the programs by comparing the generalized muscle torque they computed from experimental data with that computed by a completely independent method (the free-body method) (Cooper 1995).

For computation of torques, joint angles were defined as follows. The proximal segment was extended distally past the joint and an angle was measured counterclockwise from the extension to the next segment (see Fig. 1, inset). A consequence of this convention is that positive torques correspond to flexion at the shoulder and elbow but dorsiflexion at the wrist.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Kinematics of dysmetric movements: hypometria and impaired interjoint coordination

ELBOW AND SHOULDER MOTIONS. The intact cat reaches for targets located over most of the workspace by scaling the elbow displacement and velocity to target height. Shoulder motion, which initially extends during lift to retract the paw and later flexes to protract the paw, exhibits a more complex dependency on target location (Martin et al. 1995). As shown in Fig. 1, both elbow flexion and shoulder extension were reduced in speed and amplitude by AIP inactivation. Figure 2, which presents grouped data from 15 sessions in three cats, shows that AIP inactivation did not alter the dependency of these quantities on target height although, on average, elbow flexor velocity was reduced by 30% and shoulder extensions by 54%. While elbow flexion remained hypometric during inactivation for all target heights, peak angle and angular velocities were related to target height (main effect of inactivation on peak elbow angle and peak elbow angular velocity significant at P  0.0001). Inactivation had no effect on this relationship. Inactivation also produced a reduction in shoulder extension and velocity (main effect on peak angle and angular velocity significant at P  0.0001). Thus hypometria did not result from a change in the strategy normally used for scaling joint trajectories with targets at different heights.

View larger version (25K): [in this window] [in a new window]   Fig. 2. Relation between kinematic changes at the shoulder (A), elbow (B), and wrist (C) before (gray lines) and during (black lines) inactivation. Left: changes in peak shoulder extensor, elbow flexor, and wrist flexor joint angles. Right: angular velocity for the joint angles shown at left.

View larger version (20K): [in this window] [in a new window]   Fig. 3. Histograms showing the distribution of the interval between peak elbow flexor velocity and peak shoulder extensor velocity for control (white) and inactivation (black) trials. Data presented for standard target from 8 sessions in 2 cats (n = 203 before inactivation and 286 during inactivation).

WRIST MOTIONS. As can be seen in Fig. 1C for both the control and inactivated conditions, the wrist undergoes an initial plantar flexion as the paw is lifted from the ground and a later dorsiflexion of approximately equal magnitude as it approaches the food well. Also during both control and inactivation, plantarflexion and dorsiflexion increase with the height of the target (Fig. 2C, left, plantar flexion shown). The slope of the relation of wrist plantarflexor velocity and target height increased during AIP inactivation (Fig. 2C, right). The same appeared to be true of dorsiflexion, but this was difficult to verify statistically since the paw often collided with the food well before peak dorsiflexor velocity occurred.

Dynamics of dysmetric movements: impairments in anticipatory control of interaction torques

As noted earlier, for multijoint movements to be accurate, muscle contraction needs to be adapted to the complex, time-varying, inertial interaction and gravitational torques acting at each joint (Ghez et al. 1996; Hoy et al. 1985; Sainberg et al. 1995; Smith and Zernicke 1987). Analysis of the temporal variations in joint torques is therefore necessary to distinguish possible effects of altered neuromuscular control from effects of biomechanical interactions in causing movements to be inaccurate.

SHOULDER DYNAMICS. Normal. Figure 4 shows ensemble averages of shoulder kinematics (top) and joint torques (bottom) for a single representative experiment (left, control trials; right, trials during inactivation). Shoulder muscle torque shows a constant extensor bias, which counters the flexor gravitational torque present throughout the movement. Superimposed on this are phasic extensor muscle and interaction torques, which produce the observed shoulder extension (Fig. 4, left). Because the mass and length of the paw were small, the major determinant of the shoulder extensor interaction torque was the acceleration of the elbow into flexion. The temporal variation in muscle torque paralleled changes in acceleration, which is expected if shoulder muscles contribute to shoulder acceleration. More surprisingly, the timing of changes in interaction torque also paralleled shoulder acceleration; the reversal in shoulder angular acceleration, from extension to flexion (Fig. 4, arrow), was coincident with the reversal in interaction torque and the subsequent peak flexor acceleration and also coincident with the peak interaction torque (Fig. 4). While muscle and interaction torque were similar in their relation to acceleration, they differed in their magnitudes; the extensor peak of muscle torque was consistently smaller and frequently more indistinct than that of interaction torque and was not seen at every target height in every experiment. The extensor peak of interaction torque, on the other hand, was recognizable at all target heights and in every experiment. Interaction and muscle torques acted together to overcome inertial resistance (i.e., self torque) and gravity to accelerate the shoulder into extension. However, since the extensor interaction torque was larger than the phasic extensor component of muscle torque, interaction torque contributed as much or more than muscle torque to shoulder extension.

View larger version (25K): [in this window] [in a new window]   Fig. 4. Ensemble averages of measured joint angle and computed joint torques at the shoulder for reaches during the control (left) and inactivation (right) periods. Top: ensemble averages of shoulder joint angle (thick dashed line), angular velocity (thin dashed line), and acceleration (solid line). Bottom: ensemble averages of gravitation (dotted line), muscle (dashed line), interaction (gray line), and self (solid line) torques. All averages are synchronized with the time the paw breaks contact with the force plate (i.e., toe off). Arrows: reversal from extensor to flexor acceleration (top) and flexor to extensor self torque (and extensor to flexor interaction torque) (bottom). Open arrow: peak extensor muscle torque. Thin vertical lines: acceleration onset (left) and reversal from the extensor to flexor phases of shoulder acceleration (right). I, interaction torque; M, muscle torque; G, gravitational torque; S, self torque (n = 20 before inactivation and 27 during inactivation). Calibration: 4000 deg/s/s; 200 deg/s.

ELBOW DYNAMICS. Normal. Like the initial shoulder extension, flexion of the elbow resulted from the combined effects of muscle and interaction torque, which overcame the extensor actions of gravity and inertia (i.e., gravitational and self torque). As Fig. 5 (left) shows, acceleration and interaction torques peaked at the same time. However, unlike at the shoulder, where muscle and interaction torques changed in parallel throughout the movement, elbow muscle torque remained flexor and continued to rise while interaction torque reversed from flexion into extension. Thus elbow flexor acceleration was prolonged past the end of flexor interaction torque by a prolonged muscle torque. The continued rise in muscle torque after the reversal of interaction torque into extension was a consistent feature of movements to targets in all locations. It can also be seen in Fig. 5 (left) that the transition from elbow flexor to extensor acceleration (right vertical line) occurred just after the peak in muscle torque but well after the transition to extensor interaction torque. Thus the timing of the direction reversal at the elbow, unlike that at the shoulder, appeared to be dependent on changes in elbow muscle torque. At this point in the movement, the elbow was in the middle of its range of motion, where stretch of muscle viscoelastic elements is less than at the extremes of joint motion and where the paw is not in contact with external objects. At this transition, the component of muscle torque caused by passive muscle stretch is least and the component caused by active muscle contraction is greatest. Thus at elbow reversal, elbow muscle torque is likely to be dominated by active muscle contraction. Taken together with the above observations on the relative timing of elbow acceleration and elbow muscle torque, this suggests that reversal in elbow acceleration reflects the timing of active muscle contraction.

View larger version (25K): [in this window] [in a new window]   Fig. 5. Ensemble averages of measured joint angle and computed joint torques at the elbow for reaches during the control (left) and inactivation (right) periods. Same format as Fig. 4. Brackets with filled arrowheads: interval between peak flexor interaction torque and peak flexor muscle torque. Open arrow: peak extensor self torque. Gray shaded region (right) identifies difference between average muscle torque prior to and during inactivation. Average during inactivation is primarily prolonged. Thin vertical lines: acceleration onset (left) and reversal from the flexor to extensor phases of the elbow acceleration (right) (n = 20 before inactivation and 27 during inactivation) Calibration: 10000 deg/s/s; 400 deg/s.

View larger version (19K): [in this window] [in a new window]   Fig. 6. Histograms showing that reversal from elbow flexor to extensor muscle torque is prolonged during anterior interpositus nucleus (AIP) inactivation. Data for reaches to standard target height and distance from 6 sessions in 2 cats. Open histogram: preinjection control reaches (mean = 101 ± 23 ms; n = 142); closed histogram: postinjection test reaches (mean = 144 ± 53; n = 173).

View larger version (9K): [in this window] [in a new window]   Fig. 7. Scaling of elbow torques for reaches to higher targets before (gray lines) and during (black lines) inactivation. A: elbow velocity. Data replotted from Fig. 2B, right, but the y scale is inverted to show the same trend as in parts B and C. B: elbow interaction torque; C: elbow muscle torque; D: time to peak elbow joint angular velocity. Data are from 8 sessions in 2 cats.

WRIST DYNAMICS. Normal. We saw earlier (Fig. 1C) that the wrist underwent a biphasic sequence of plantar- and dorsiflexor motions. Figure 8 (left) shows that the initial plantarflexor acceleration was driven by changes in interaction and gravitational torques acting in the same plantarflexor direction. Muscle torque was in the direction opposite to the acceleration for most of the reach and therefore restrained wrist motion. The reversal into dorsiflexion occurred once the plantarflexor interaction torque began to decline from its maximal value. Peak dorsiflexor acceleration occurred during the brief interval when interaction and muscle torques were both in the same (dorsiflexor) direction. This synergy was a consistent feature of ensemble averages of wrist torques in all experiments and is shown by the shaded region in Fig. 8. The timing of reversal from plantar- to dorsiflexion was determined by the interaction torque and the peak dorsiflexion was determined by the synergy between interaction and muscle torques.

View larger version (29K): [in this window] [in a new window]   Fig. 8. Ensemble averages of measured joint angle and computed joint torques at the wrist for reaches during control (left) and inactivation (right) periods. Same format as Figs. 4 and 5. Note that the gravitational torque remains flexor during the flexor and extensor phases of movement. Shaded regions, bottom: period of overlap between extensor muscle torque and extensor interaction torque. Thin vertical lines: acceleration onset (left) and reversal from the plantar flexor to dorsiflexor phases of wrist acceleration (right) (n = 21 before inactivation and 27 during inactivation). Calibration: 10000 deg/s/s; 400 deg/s.

View larger version (19K): [in this window] [in a new window]   Fig. 9. A: relation of peak wrist plantarflexor interaction torque to target height. Data from peak of ensemble averages, aligned on toe off. Data from 2 cats are plotted separately (circles and squares). B: relation between lead of peak wrist extensor muscle torque over peak wrist flexor angle as a function of target heights in 2 cats. Mean ± SE of peaks in individual trials. Data in A and B are from all sessions of two cats, which are plotted separately (circles and squares). Data in B are staggered slightly on the x axis for clarity. C: relationship between wrist muscle torque and joint angle for control (C1) and postinjection (C2) reaches. Data in C are from a single representative session. Dashed arrow: the beginning to the end of the reach.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Our analysis of the motions and torques at individual joints during reaching in the cat demonstrates the complexity of the task faced by the nervous system in multijoint control. Moving a single joint requires primarily accelerating a load against the opposing forces of inertia, gravity, and viscoelastic soft tissue elements. The presence of multiple linked segments introduces significant complications because motions at each joint produce torques that act at the other joints (Hollerbach and Flash 1982). These interjoint interaction torques can assist or resist the torque generated by active muscle contraction so that changes in the former must be compensated by the latter. Thus, in producing a desired paw or hand trajectory, neuromuscular control has to be precisely choreographed with time-varying torques generated by other joints. While accuracy in rapid single-joint torques and movements may require that the nervous system develop an internal model of the musculoskeletal system to program appropriate feedforward commands, with multijoint movement such models would need to be much more complex (Wolpert et al. 1995).

Our results show that during AIP inactivation, the linear scaling of kinematic and dynamic parameters to target height was maintained. While decomposition of joint torques into separate components (Cooper 1995) showed that the particular dynamic control impairments produced by AIP inactivation differed at each joint, there were two common defects. First, there was a systematic reduction in initial acceleration and muscle torque at elbow and shoulder and decreased anticipatory muscle torque at the wrist, consistent with disfacilitation of the cerebellar efferent targets (see Impaired single and multijoint control produced by AIP inactivation). Second, there were errors at the beginning of movement and also later, in the adjustments made to correct the initial errors, which suggests that both feedforward and feedback control were affected. Our analysis revealed a lack of compensation for intersegmental interactions similar to that seen in human deafferentation (Ghez et al. 1995; Gordon et al. 1995). We argue below (see Impaired single and multijoint control produced by AIP inactivation) that the lack of compensation was due to impaired use of somesthetic feedback in generating or updating internal models of limb dynamics.

Relation of muscle torque to interaction torque at different joints

At the beginning of movement, there were phasic changes in muscle and interaction torque at each joint that overcame inertial resistance (i.e., self torque). Thus neuromuscular control produced movement in two ways: directly, by acting on the joint(s) spanned by the muscle, and indirectly, by producing interaction torques acting at other joints. Decomposition of joint torques (Cooper 1995) revealed qualitative differences in the roles of muscle and interaction torques during reaching at shoulder, elbow, and wrist. At the elbow, while interaction torque assisted elbow flexion, the amplitude and exact timing of elbow flexion, and its compensation for initial hypometria during AIP inactivation (e.g., Fig. 5), was accomplished by muscle torque. Since this prolongation occurred in mid-reach, when the elbow was in the middle of its range of motion and the paw was not in contact with external objects, muscle torque here would have reflected mostly active muscle contraction.

At the shoulder, the phasic increase in extensor muscle torque was smaller than that of interaction torque and the two were not temporally independent. This suggests that control of shoulder muscles during reaching was dominated by the movement of other joints rather than a stimulus-response transformation for scaling reach height to target height. We have shown (Martin et al. 1995) that movements at the shoulder (and wrist) of the reaching limb are not part of the scaling strategy for controlling the height of the reach but that they operate primarily to linearize the paw path. AIP inactivation disturbed this control resulting in bowing of the paw paths.

At the wrist, a third situation prevailed. Here, muscle torque opposed interaction torque for much of the reach. Even without formal dynamic analysis, it can be appreciated that elbow flexor acceleration followed by deceleration produces a plantarflexor/dorsiflexor "whipping" torque at the wrist (Hollerbach and Flash 1982; Smith and Zernicke 1987). This explains why, among the joints we studied, the wrist alone was not slowed during AIP inactivation. Since wrist motions were resisted rather than produced by muscle contractions, reduction in active muscle contraction by inactivation did not result in slowing as at other joints. As expected in such a situation, the slope of the relationship between wrist plantarflexor velocity and target height actually increased during AIP inactivation.

In the normal cat, wrist muscle torque provided phase-advanced damping of passive wrist motion during reaching and could represent feedforward control (Miall 1998) of wrist muscles, based on anticipation of upcoming interaction torques. Alternatively, it could represent viscous resistance in wrist muscles. However, such viscosity cannot be a purely passive property of muscle but rather an effect that was actively regulated by the CNS, since it was disrupted by cerebellar inactivation.

Impaired single and multijoint control produced by AIP inactivation

Our dynamic analysis indicates that AIP inactivation resulted in a reduction in the muscle torque providing the initial angular acceleration at all joints. These reductions are consistent with disfacilitation of cervical spinal motor neuronal pools through the known projections of AIP to magnocellular red nucleus (Robinson et al. 1987) and through projections via ventrolateral thalamus (Anderson and DeVito 1987) to primary motor cortex (Jörntell and Ekerot 1999). Three reasons indicate that this reduced muscle activation did not reflect simple weakness (i.e., an absolute limitation on the capacity for generating force) over the range studied. First, preservation of scaling and elbow flexor muscle torque compensation indicated that there was a capacity for increasing muscle force. Second, the animals' paws struck the outside of the food well. Had the well not been there, the paw would have passed through the location of the bait; clearly, muscle contractions were adequate to carry the paw to the desired endpoint. Third, the animals were able to extend their shoulder to withdraw the limb and replace it in the food well after contacting the underside of the well. This is similar to our previous finding that, during AIP inactivation, animals could extend the shoulder sufficiently to reach over an obstacle after bumping into it (Martin et al. 2000). However, as in the previous study, the animals were not able to generate sufficient muscle force in an anticipatory, feedforward manner.

Dynamic analyses revealed that the reductions in elbow flexion and shoulder extension were also due to decreases in interaction torque. At both the elbow and shoulder, there was a failure of initial muscle torque to take into account the reductions in interaction torque. At the elbow, compensation for reach height did take place by prolonging the initially hypometric flexion. That duration, rather than amplitude, was adjusted suggests that compensation was accomplished by a feedback mechanism. This is supported by the observation that most of the prolongation took place during the latter half of the movement (~120 ms or more after movement onset; Fig. 5, right; muscle torque, gray area), allowing time for transmission of information around a feedback loop. This latency corresponds to a visual reaction time in the cat (Ghez and Vicario 1978) and is consistent with the hypothesis that the compensation was based on visual feedback. This compensation, however, failed to produce an accurate reach because there was no corresponding increase in extensor muscle torque at the shoulder, which would have been needed to prevent the paw from colliding with the underside of the food well. The reach remained inaccurate because compensation was applied only to scaling and not to control of intersegmental dynamics.

At the wrist, anticipatory control of the plantarflexor interaction torque appeared to be lacking during inactivation because muscle torque behaved like a passive (approximately linear) spring, probably reflecting stretch of passive elastic joint elements. This breakdown in compensation for interaction torque is similar to the defect in ataxic reaching reported by Bastian et al. (1996) in their patients with cerebellar lesions. However, because those experiments were done in humans, lesions were not confined to a single cerebellar nucleus. A similar lack of compensation may have occurred in the study of Milak et al. (1997). These authors reversibly inactivated the interpositus (though without selectively inactivating the anterior interpositus nucleus vs. the posterior interpositus nucleus) in cats performing a reaching task similar to ours. Although they did not explicitly compute joint torques, they made the intriguing observation that limb kinematics during inactivation resembled those of a simple mechanical model in which one joint was moved by hand and the other was allowed to move under the influence of interaction torques alone.

The deficits in kinematic control and their dynamic basis appear similar to those seen in patients lacking proprioception because of large-fiber sensory neuropathy. As in AIP inactivation, these patients show increased hand-path curvature during reaching (Ghez et al. 1990; Gordon et al. 1995) and desynchronization of elbow and shoulder (Sainberg et al. 1995) resulting from a failure to take joint configuration or inertial interactions into account in feedforward control (Gordon et al. 1995; Sainberg et al. 1995). In both cases, dynamic analysis indicated that distal joint motion was effectively slaved to interaction torques developed by proximal joints. In the human, we have also shown that this feedforward control requires learning an internal model of inertial dynamics using proprioceptive information (Krakauer et al. 1999). Since the intermediate cerebellum and the AIP are important receiving areas for proprioceptive and other somatosensory inputs from the limb (Gellman et al. 1983; Gibson et al. 1987; Robinson et al. 1987; for review see Bloedel and Courville 1981), it appears plausible that the defect observed here reflects a similar abnormality. This suggests that these cerebellar circuits either perform the computations needed to establish internal models of limb biomechanics or that they store such models for use in controlling multijoint limb movement. This function of the AIP is consistent with the cerebellar modeling study of Schweighofer et al. (1998a,b) that examined control of a two-joint planar movement. In their model, the presence of feedforward (acceleration) control signals and proprioceptive feedback compensation did not correct for interaction torques and produced curved endpoint trajectories. When their model incorporated the learning of limb dynamical properties by a simulated cerebellum, interaction torques were adequately controlled and trajectories became straighter.

Independence of sensory-motor transformations underlying kinematic scaling and intersegmental dynamics

A striking feature of our results was that the scaling of paw velocity and the elbow motions responsible for the bulk of the lift phase (Martin et al. 1995) were preserved while control over intersegmental dynamics was disrupted by AIP inactivation. This can be interpreted in light of the results of recent studies of the sensorimotor transformations underlying reaching in humans and monkeys. Visual target information, initially encoded in retinotopic coordinates, is remapped into egocentric coordinates and then combined with hand position information to form a simplified, hand-centered vectorial plan of the intended movement trajectory as an extent and direction in extrinsic space (Flanders et al. 1992; Ghez et al. 1999). At this level, extent is specified by linearly scaling a stereotyped bell-shaped trajectory profile (Atkeson and Hollerbach 1985) to the desired target distance according to a learned scaling factor. Our results show that this process is not dependent on AIP.

For movement to occur however, the initial vectorial plan needs to be correctly transformed into intrinsic coordinates that specify the muscle forces and joint torques. This requires that muscle contractions at different joints be adapted to the motions that occur at all other joints. This was disrupted by AIP inactivation. As a result, movements were generated that, while scaled to the external target, did not incorporate the necessary compensation for inertial interactions that occurred within the limb. As a result, the movements were inaccurate.

The dynamic transformation compensating for inertial interactions, which failed during AIP inactivation, depends on an internal model of the limb, which may be adjusted through learning (Ghez et al. 1995; Sainberg et al. 1995; Shadmehr and Mussa-Ivaldi 1994). Recent psychophysical findings indicate that dynamic and vectorial transformations are represented and learned independently by the nervous system (Krakauer et al. 1999). Our findings suggest that the intermediate cerebellum plays a key role in using internal models of limb dynamics to plan accurate reaching movements.