Center for Neurobiology and Behavior, Columbia University; and the
New York State Psychiatric Institute, New York, New York 10032
 |
INTRODUCTION |
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 |
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).

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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
i
k, 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 |
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.

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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.
|
|
The ensemble averages in Fig. 1 show differences in the time course of
both elbow and shoulder movement during AIP inactivation; whereas the
shoulder extensor phase was reduced in duration (Fig. 1,
left; control, a-b interval; inactivation, a-c
interval), elbow flexion was prolonged (Fig. 1; control, a-d interval;
inactivation, a-e interval). Normally, the shoulder and elbow
reversals were nearly synchronous (Fig.
3, open histogram). During inactivation, the mean interval from shoulder to elbow reversal increased as did its
variability (20 ± 12 to 42 ± 37 ms; P < 0.001; Fig. 3, filled histogram; see also Fig. 1,
left; control, c-d interval; inactivation, b-e
interval).

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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).
|
|
In both normal and inactivated conditions, as target height was
increased, shoulder reversal from extension to flexion occurred at
increasingly flexed elbow angles. Since the elbow flexion varied with
both target height and inactivation state, we calculated the fraction
of the maximal elbow excursion when shoulder joint angle reversed from
extension to flexion. For control reaches, such reversal in shoulder
angle occurred at 79% of maximal elbow flexion, independent of target
height (r = 0.003; not significant). During
AIP inactivation, reversal occurred significantly earlier at 54% of
maximal elbow flexion (P < 0.0001). The reduction
in shoulder extension, which retracts the paw early during lift, with
relative preservation in shoulder flexion causes the paw to ultimately
collide with the undersurface of the target.
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.
Along with the increased dependence of wrist flexor velocity on target
height, there was a systematic change in the timing of the wrist
plantarflexion-dorsiflexion reversal (i.e., wrist flexion to extension)
relative to elbow flexion across target heights. During preinjection
control trials, as animals reached to higher targets, the wrist
reversed direction progressively later in the reach (i.e., at elbow
angles that were increasingly flexed). During AIP inactivation, wrist
reversal occurred prematurely. Computation of the fraction of elbow
flexion completed at the time of wrist reversal showed that, like as
for the shoulder, it occurred at a decreased fraction of peak elbow
flexion (65% vs. 54%; P = 0.0001). Kinematic changes
at the wrist during inactivation, as with the shoulder, contributed to
bowing of the paw path.
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.

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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.
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AIP inactivation.
As noted earlier, the main kinematic effect of AIP inactivation at the
shoulder was a pronounced decrease in amplitude, speed, and duration of
the initial extension. Figure 4 (right) shows that both peak
muscle and interaction torques were substantially reduced (open
arrows). Significant decreases were present across all experiments
(P < 0.001). The intervals between the peaks in interaction and muscle torques were unchanged during AIP inactivation. These findings suggest that the reduction in interaction torque was an
important cause of the reduction in shoulder extension since this
torque was the major determinant of this phase of motion.
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.

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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.
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|
AIP inactivation.
The data in Fig. 5 (right) show a substantial reduction in
elbow flexor interaction torque during inactivation. Although the amplitude of the elbow flexor muscle torque was similar to controls, its duration was clearly increased (dark gray area). Across cats, interaction torque was reduced 47% on average (P < 0.0001) whereas peak muscle torque was reduced only slightly (6%;
P = 0.039). In contrast to this relatively unchanged
amplitude, the duration of the flexor muscle torque increased. The time
from movement onset to reversal from flexor to extensor muscle torque
increased from 101 ± 2 to 144 ± 4 ms (P < 0.0001) (Fig. 6). This prolongation occurred disproportionately as flexor muscle torque was declining (10 ms increase in the time from movement onset to peak as compared with 33 ms increase in the time from peak to zero cross; both significant at
P < 0.001). The prolongation in flexor muscle torque resulted in a significant increase in the duration of elbow flexion (see Fig. 7D) and acted to
bring the paw farther toward the food well. Thus it could reflect a
compensatory adjustment for the reduced muscle and interaction torques.

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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).
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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.
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Figure 7 shows that the increase in peak velocity that occurred with
reaches to higher targets (A) was associated with increases in muscle and interaction torques both before and during inactivation (B and C; similar to Fig. 2). Figure
7D also shows that the duration of flexion did not vary
systematically with target height but was increased overall during
inactivation. This shows that the strategy for controlling the height
of the movement using a scaled command for elbow flexion remained unimpaired.
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.

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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.
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AIP inactivation.
As noted earlier (see Kinematics of dysmetric
movements. WRIST MOTIONS; Fig. 1C),
wrist plantarflexor velocity showed no overall change with
inactivation; however, its dependence on target height increased. The
initial acceleration was significantly reduced in magnitude by 30%
overall (P < 0.0001). As can be seen in Fig. 8
(right), the wrist reversal and the subsequent peak
dorsiflexor acceleration occurred earlier than in control animals.
Overall, the reduction in acceleration was mainly due to a 33%
(P < 0.0001) reduction in plantarflexor interaction
torque although, in one of the cats, there also was a small (10%)
increase in dorsiflexor muscle torque (Fig. 8). Although the
plantarflexor interaction torque driving the initial motion of the
wrist was reduced overall, it remained in the flexor direction for a
longer duration than in controls. (This would be expected if wrist
interaction torque was dominated by torque arising at the elbow, which
is probably the case given that angular velocities and accelerations
were much greater at the elbow than at the shoulder and that the moment of inertia of the phalangeal limb segment was small relative to the
paw.) This effect was shown by the time of reversal from flexor to
extensor interaction torque, which was significantly delayed by 27%
(P < 0.0001) during AIP inactivation. As noted in the
preceding paragraph, dorsiflexor acceleration peaked in the
normal cat when the interaction and muscle torques cooperated to
produce dorsiflexion (Fig. 8, left, boxed region). During
AIP inactivation, there was less cooperation between interaction and
muscle torques and this reduced the dorsiflexor acceleration. Indeed,
in the averages of Fig. 8, the peak plantarflexor interaction torque
occurred near the peak dorsiflexor acceleration. In sum, the changes in wrist kinematics reflected both wrist muscle torque and interaction torque.
These changes in wrist dynamics can be explained by a change in the
relative contributions of active and passive components of muscle
torque. To see how this is so, it should be recalled that after toe
off, ground reaction force no longer contributes to muscle torque,
which is then composed only of active muscle contraction plus passive
viscoelastic torques. We found that, prior to inactivation, wrist
dorsiflexor muscle torque peaked well before the wrist was maximally
plantarflexed (Fig. 8, left). During inactivation, on the
other hand, the two torques reached their peak values simultaneously
(Fig. 8, right). This suggests that wrist extensor muscle
contraction normally contributes substantially to the resistance of the
plantarflexion interaction torque that drives the movement. During
inactivation, the synchronization of peak muscle torque and joint angle
suggests that that simple elastic restoring forces dominated the
variations in muscle torque. We examined this relationship further with
the analysis shown in Fig. 9.

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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.
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Figure 9A plots plantarflexor interaction torque in relation
to target height. For both control and inactivation trials, interaction torque increases with increasing target height, although torque magnitude is less during inactivation. Figure 9B plots the
interval between peak wrist angle and peak muscle torque. In control
reaches (gray), the lead of peak dorsiflexor muscle torque increased
with target height. This increasing lead time could reflect the
progressively greater contributions of anticipatory muscle contraction
that are needed to compensate for increasing flexor interaction torque (Ghez et al. 1996
). During inactivation, despite the
continued presence of the strong relationship between interaction
torque and target height (Fig. 9A, black symbols), timing
remained invariant, which suggests loss of anticipatory control. Figure
9C illustrates wrist muscle torque-wrist joint angle plots
for movements to a standard target. Control reaches (C1)
showed more hysteresis before than during inactivation (C2),
when the torque-angle relation resembled that of a linear elasticity.
These results suggest that during normal reaches, where there is a
phase lead of muscle torque over joint angle, the cat exploits
interaction torque and dorsiflexes the wrist during a narrow time
interval. During AIP inactivation, the wrist behaves more like a
passive spring and interaction torque does not contribute to
controlling the timing of wrist dorsiflexion.
 |
DISCUSSION |
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.
Equations of motion for a four-segment planar limb appear at the
end of this appendix. They describe the relation between joint torque
and joint motion at any given moment. The equation for each limb
segment has the form
= {term 1 + term 2 + ... term n} + G (shoulder,
1;
elbow,
2; wrist,
3;
MCP,
4).
is the torque that must have been
acting at the joint to produce the motion described by the expression
in curly brackets (G is the torque due to gravity,
proportional to gravitational acceleration g = 9.8 m/s2). Equivalently, the expression in curly
brackets is an inertial torque and is the equal and opposite
torque that must be overcome by muscle contraction (plus tendon stretch
and ground reaction force if any) to produce the observed limb motion
(d'Alembert's principle) (Cooper 1995
). Since in this
experiment we do not measure
directly but compute it from the fact
that the right and left sides of the equation sum to zero, it
corresponds to a residual term. In keeping with commonly-used
terminology (e.g., Bastian et al. 1996
; Smith and
Zernicke 1987
), we call
generalized muscle torque or,
simply, muscle torque.
Each term of the expression for inertial torque consists of a
coefficient (the complicated expression in square brackets) multiplied
by a variable or variables (
) describing the limb motion. The
joint-numbering conventions are the same as for
(
1, shoulder;
2,
elbow;
3, wrist;
4,
MCP). A single dot indicates an angular velocity and double dots
indicate an angular acceleration. There are only three sorts of terms
(Hollerbach and Flash 1982
): dependent on acceleration, dependent on
squared velocity (centrifugal), and dependent on the product of two
velocities (Coriolis). The inertial torque also includes terms
proportional to x and y components of linear
acceleration of the shoulder, effectively lumping together the motion
of all the joints proximal to the shoulder. In the present experiment,
this component was small because linear motion of the shoulder was
deliberately restricted. In is the moment of inertia of the segment distal to joint n,
ln is the length of that segment, and
rn is the distance from joint n
to the segment's center of mass.
The terms in brackets are all functions of limb motion and could
be expressed in terms of segment angles (that is, the angle of the limb
segment relative to an absolute standard; Hoy et al. 1985
) or joint angles (the angle between two adjacent limb
segments) and the corresponding segment or joint angular velocities and accelerations. Because we view these terms as perturbing torques for
which the nervous system must compensate, and because we hypothesize that the nervous system relies on proprioceptors for information about
limb perturbations, we chose to represent them in the coordinate system
closest to what proprioceptors actually sense: joint angle. The choice
of a joint-based coordinate system also affected the meaning of muscle
torque. In a segment-based system, one would speak, for example, of
forearm muscle torque produced by the combined action of elbow and
wrist muscles. In the joint-based description, elbow muscle torque
reflects elbow muscle contraction, which we feel is a more natural
description. In this formulation, wrist muscles still contribute to the
motion of the forearm, but they do so by producing wrist motion, which
causes an interaction torque at the elbow.
The choice of joint-based equations resulted in a larger number of
terms than if we had chosen to represent limb motion in terms of
segment angles; this could have posed a problem for analysis if we had
analyzed each term individually, but we instead grouped the terms into
two components. Torques dependent only on the motion of the joint at
which they act represent the passive inertial resistance of the limb to
rotation of that joint; we called the sum of these torques self
torque. The sum of torques dependent on the motion of other joints
was called interaction torque.
We thank G. Johnson for construction of apparatus. We are grateful
to Dr. Stephen Strain for assistance in deriving dynamic equations and
to T. Hacking for expert technical assistance.
This research was supported by National Institute of Neurological
Disorders and Stroke Grants NS-31391 to C. Ghez and NS-36865 to J. H. Martin, and Medical Scientist Training Program Grant 5T32-GM07367-20
to S. E. Cooper.
Present address of S. E. Cooper: Dept. of Neurology, Columbia
University, 710 W. 168th St., New York, NY 10032.
Address for reprint requests: J. H. Martin, Center for
Neurobiology and Behavior, Columbia University, 1051 Riverside Dr., New
York, NY 10032 (E-mail: jm17{at}columbia.edu) or S. E. Cooper, Dept. of
Neurology, Columbia University, 710 W. 168th St., New York, NY 10032 (E-mail: sec6{at}columbia.edu).
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.