Exp Brain Res (2008) 187:509–523
DOI 10.1007/s00221-008-1321-0
R ES EA R C H A R TI CLE
Kinetic analysis of arm reaching movements during voluntary
and passive rotation of the torso
Simone B. Bortolami · Pascale Pigeon · Paul DiZio ·
James R. Lackner
Received: 9 January 2007 / Accepted: 11 February 2008 / Published online: 11 March 2008
© Springer-Verlag 2008
Abstract Reaching movements made to targets during
exposure to passive constant velocity rotation show signiWcant endpoint errors. By contrast, reaching movements
made during voluntary rotation of the torso are accurate. In
both cases, as a consequence of the simultaneous motion of
the arm and the torso, Coriolis forces are generated on the
arm tending to deXect its path. Our goal in the present paper
was to determine whether during voluntary torso rotations
arm movement accuracy is preserved by feed forward compensations for self-generated Coriolis forces. To test this
hypothesis we analyzed and quantiWed the contribution of
torso rotation and translation to arm dynamics and compared the kinematics and kinetics of pointing movements
during voluntary and passive torso rotation. Coriolis
torques at the shoulder increase nearly sixfold in voluntary
turn and reach movements relative to reaches made without
torso rotation, yet are equally accurate. Coriolis torques
during voluntary turn and reach movements are more than
double those produced by reaching movements during passive body rotation at 60°/s. Nevertheless, the endpoints of
the reaches made during voluntary rotation are not deviated, but those of reaches made during passive rotation are
deviated in the direction of the Coriolis forces generated
during the movements. We conclude that there is anticipatory pre-programmed compensation for self-generated
S. B. Bortolami · P. Pigeon · P. DiZio · J. R. Lackner
Ashton Graybiel Spatial Orientation Laboratory,
Brandeis University, Waltham, MA, USA
S. B. Bortolami (&)
The Charles Stark Draper Laboratory, Inc.,
555 Technology Square, Cambridge,
MA 02139-3563, USA
e-mail: simborto@brandeis.edu
Coriolis forces during voluntary torso rotation contingent
on intended torso motion and arm trajectory.
Keywords Arm model · Arm reaching ·
Inverse dynamics · Coriolis perturbation ·
Voluntary movement · Passive movement
Introduction
When a reaching movement is made while the torso is
simultaneously turning, an inertial Coriolis force is generated on the reaching arm (see Fig. 1). The elementary Coriolis force (dFcor) on a particle is proportional to its mass
(dm), its velocity (v) relative to the rotating environment,
and the rotation velocity () of the environment, and acts
orthogonally to the particle velocity direction:
dFcor = ¡2dm( £ v). The total Coriolis force on the arm
is given by the integration of the elementary forces dFcor
over the volume of the moving segments. Coriolis forces
can arise during passive or active rotation. If a reaching
movement to a target is made during passive, constant
velocity rotation in a fully enclosed slow rotation room, its
trajectory and endpoint will be signiWcantly deviated in the
direction of the Coriolis force generated on the arm (Lackner and DiZio 1992, 1994). If the individual makes additional reaches to the target, even without visual feedback of
hand motion, subsequent reaches will become straighter
and more accurate until they are indistinguishable from prerotation reaches. When a reach is then made with the room
again stationary, a mirror image aftereVect will be apparent
reXecting an anticipatory compensation for a Coriolis force
that is no longer present during the reaching movement. It
is fairly well accepted that adaptation to Coriolis forces
during passive rotation is accomplished through plastic
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Exp Brain Res (2008) 187:509–523
Fig. 1 Illustration of the Coriolis force perturbation of the arm relative
to the torso produced during a Simple Reach made in a rotating room
turning counterclockwise at a constant velocity. The Coriolis force
(Fcor) magnitude is twice the product of the arm mass (m), arm velocity
relative to the torso (v) and body angular velocity in space, , and its
direction is orthogonal to both v and changes in internal models of the muscle activations associated with intended kinematics (Lackner and DiZio 1994,
2005). Adaptation of reaching movements to mechanical
analogs of Coriolis forces, planar curl Welds imposed by a
robotic manipulandum, is also thought to reXect the structure and formation of an internal model (Shadmehr and
Mussa-Ivaldi 1994).
In a fully enclosed slow-rotation-room (SRR), the Coriolis acceleration is due to the passive rotation, SRR, of the
torso delivered in a way which eliminates sensory and cognitive cues signifying rotation. The subject always feels
perfectly stationary. In robotic force Weld experiments
(Shadmehr et al. 1993; Shadmehr and Mussa-Ivaldi 1994),
the torso does not move. In both paradigms, the reaching
task presented to the CNS is equivalent in torso and world
frames of reference, both paradigms initially evoke reaching errors, and both involve feed forward control through
adaptable internal models. Voluntary torso rotations in a
stationary environment also generate Coriolis accelerations
on the moving arm (see Fig. 2). During voluntary turn and
reach (T&R) movements, the peak velocity of the arm relative to the torso and the peak rotational velocity of the
torso, Torso, occur very close together so that Coriolis
forces on the arm are actually maximized (cf. Pigeon et al.
2003a, b). However, the accuracy of reaching movements
made at diVerent speeds with and without voluntary torso
rotation is not aVected by the Coriolis forces.
The goal of the present paper is to test the hypothesis that
during voluntary T&R movements, the CNS compensates in
a feed forward fashion for the torso-relative Coriolis forces
that are generated on the reaching arm, thus preventing the
forces from disrupting performance. Because of the additional degrees of freedom of free torso rotation in the T&R
paradigm relative to the SRR and robotic force Weld
paradigms, it is by no means certain that the modes of
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Fig. 2 Experimental set-up, showing the subject’s starting position
and the locations of the targets for T&R movements, requiring a torso
turn and an arm reach, and Simple Reach movements, requiring mostly
arm reaching with little torso rotation
compensation will be identical. For example, one component
of compensation in the T&R paradigm is a potentially plastic
representation of torso rotation relative to world coordinates
(Hudson et al. 2005). This factor is not relevant for the SRR
and robotic manipulandum paradigms because neither
involves sensory or motor activity related to torso rotation.
Our approach was to compare the kinematic and kinetic characteristics of reaching movements made under diVerent
speeds of voluntary torso rotation in a stationary environment
and during passive torso rotation in a rotating environment.
To determine the speciWc patterns of joint torques associated
with reaches made during active and passive rotation, it was
necessary to develop an inverse dynamics model of the arm
and torso appropriate for our test conditions. This model, its
rationale, and underlying assumptions are presented in detail
in the companion paper (Bortolami et al. 2008).
Methods
Subjects
Six subjects (four males, two females) participated in the
SRR experiments and seven subjects (Wve males, two
females) participated in the T&R test conditions. Their ages
ranged from 19 to 55 years, and they were without physical
or neurological deWcits that could have impaired their performance on the experimental tasks. Each subject signed an
informed consent form approved by the Brandeis Human
Subjects Committee.
Exp Brain Res (2008) 187:509–523
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SRR apparatus and procedure
lifted to begin a reach. The target positions were chosen so
that one required substantial leftward trunk rotation and
arm extension (T&R) and the other involved comparable
arm extension relative to the trunk without signiWcant trunk
rotation (Simple Reach). The height of the target surface
and locations of the targets were chosen so that subjects
could perform the T&R movements with a minimum of
torso translation and bending and with a reasonably planar
arm movement while avoiding the arm joint limits. The
T&R target was located at an angle of 105.8° left of midline
about the start button and 56.1 cm from the start button; the
Simple Reach target was 25.4° left of midline and 30.6 cm
from the start position. The table surface was set for each
subject at about the height of the T3 spinal segment.
Trials were run in blocks of 18, with the two types of
movements (T&R and Simple Reach) in random order.
Blocks were run at two movement speeds (slow and fast).
The slow movements were instructed to be at a pace to pick
up an object on the table, the fast movements were meant to
be at the speed and accuracy necessary to trap a Xy. All
movements were made in complete darkness to prevent
diVerences in visually based corrections across movement
speeds. An Optotrak™ motion analysis system was used to
record at 200 Hz the positions of infrared emitters attached
to the tip of the right index Wnger, the styloid process of the
ulna (wrist), the lateral epicondyle (elbow), the left and
right acromion processes (left and right shoulders), the sternal notch (sternum), and above the left and right eyes.
The test subject sat in a chair surrounded by a wrap-around
Plexiglas table with a uniform, smooth surface (see Fig. 1)
located at the center of the Brandeis SRR, which is a fully
enclosed chamber 23 ft in diameter. A start button was
located near the proximal edge of the table, near the body
midline. A light emitting diode embedded in the underside
of the transparent surface served as target. The target was
illuminated when the subject depressed the start button with
his/her right index Wnger and extinguished when the Wnger
was lifted to begin the reach. The target was located 35 cm
in front of the start button (target distance) and 5.7° left of
the body midline (target longitude). The height of the target
surface was approximately 10 cm above the waist. The subject’s head was at the center of rotation.
Reaching movements to the target were run in blocks of
8, with 6 blocks for each of the three conditions: pre-, per-,
and post-rotation, for a total of 144 reaches per subject.
During the pre- and post-rotation conditions: the SRR was
stationary. For the per-rotation condition, the SRR was
accelerated at 1°/s2 to a constant angular velocity of 60°/s
or 120°/s. Three subjects were tested with a per-rotation
rate of 60°/s and three at 120°/s. After two minutes had
elapsed at constant velocity (to allow any semicircular
canal activity to decay) the subject performed the per-rotation reaches. Before the post-rotation reaches, the SRR was
decelerated to rest and 2 min were allowed to elapse. Rotational speeds of 60 and 120°/s were chosen because they
bracket the speeds of torso rotation seen in natural, voluntary T&R movements.
All movements were made in complete darkness (to
avoid subjects using visual feedback to correct their movements) and the subjects were instructed to reach rapidly to
the target while trying to be accurate. At all stages of the
experiment, subjects always felt completely stationary.
They kept their body still except when making the pointing
movements. An Optotrak™ motion analysis system was
used to record at 200 Hz arm motion relative to the rotating
room. It tracked the positions of infrared markers attached
to the tip of the right index Wnger, the styloid process of the
ulna (wrist), the lateral epicondyle (elbow), the left and
right acromion processes (left and right shoulders), and the
sternal notch (sternum).
T&R apparatus and procedure
The test subject stood at a wrap-around Plexiglas table with
a smooth uniform surface (see Fig. 2). A start button was
located at the near edge of the table on the body midline,
and light emitting diodes served as targets. A target was
illuminated when the subject depressed the start button with
his/her right index Wnger and extinguished when the Wnger
Kinematics data processing, T&R data
Marker frequency content was negligible above 20 Hz.
Arm marker positions were numerically diVerentiated twice
with a LaGrange Wve-point central approximation formula
to obtain marker velocities and accelerations and Wltered
before and after each diVerentiation with a seven point, zero
lag averaging Wlter. To determine the beginning and end of
each movement, we employed a threshold equal to 5% of
the peak Wnger velocity or peak trunk angular velocity,
whichever occurred Wrst and last, respectively. DiVerences
in movement duration across subjects (§10% on average)
were compensated for by re-sampling the time series to the
average length of the set. For each subject, we averaged
together, sample by sample, repetitions within the same
conditions (nine T&R slow, nine Simple Reach slow, nine
T&R fast, and nine Simple Reach fast). Hereafter, we will
simply refer to these averaged time series as arm marker
positions.
Kinematics data processing, SRR data
The same procedures were followed as for the T&R data
except for the pooling of data within conditions. We
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averaged, sample-by-sample, the last eight pre-rotation and
the last eight per-rotation reaches to constitute the preexposure baseline and the adapted baseline, respectively.
The Wrst per-rotation reach and Wrst post-rotation reach
were unique trials, which are emphasized in our analyses
because they reveal the eVects of unexpected introduction
and removal of Coriolis forces.
Kinematics data processing, torso rotation and shoulder
position
Trunk angular velocity, Torso, was calculated from the
motions of the markers on the sternum and both shoulders.
The companion paper (Bortolami et al. 2008) describes
how we derived Torso from these three points, which as a
group rotate, and in addition may moderately deform due to
shoulder protraction. We obtained torso angular acceleration by numerical diVerentiation and Wltering of the angular
velocity as was done with the marker positions. Torso
angular position was obtained by integration of Torso.
Arm model
The variations of the velocity vectors of the hand and forearm markers in our T&R and SRR data were nearly planar.
However, the motion of the upper arm had an oV-plane component due to shoulder abduction during reaching. For T&R
movements, the hand and forearm had oV-plane velocity
components within 10% rms of their respective peak velocities (the projected hand and forearm length variations were
approximately 4 and 2% rms of their respective mean values). For the SRR paradigm, the corresponding length variations with respect to average values were 1 and 0.5% rms,
respectively, for the forearm and hand. Consequently, we
modeled the forearm and hand as rigid bodies in planar
motion. The variation of the projected length of the upper
arm for the T&R paradigm was approximately 19% of its
maximum during Simple Reaches and approximately 25.5%
during T&R movements. For the SRR, the variation of the
projected length of the upper arm was about 19%. Therefore, we modeled the upper arm as an extendable planar
link, which enabled us to account for the eVect of upper arm
abduction and shoulder protraction (shoulder protraction is a
much smaller component than the upper arm abduction) on
the horizontal plane dynamics. The details are presented in
the companion paper (Bortolami et al. 2008).
To obtain the reduced planar equations of motion of the
upper arm, we projected the 6 degrees of freedom dynamics
equations of the upper arm onto the horizontal plane. We
used rigid body models in planar motion for the forearm
and hand. Masses, inertias, and center of mass locations of
the arm segments were calculated by means of a regression
model (Zatsiorsky and Seluyanov 1985).
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Exp Brain Res (2008) 187:509–523
Inverse dynamics
To calculate the multisegmental inverse dynamics from the
kinematics data we used the Cartesian Coordinate approach
(Nikravesh 1988). We expressed the kinematics of the arm
with respect to a moving, torso-Wxed reference frame with
the origin S located at the shoulder. Figure 3 shows the
environment frame, which is the frame with respect to
which the kinematics data are collected (EXEY) and the
torso reference frame (XY) with respect to which the kinematics of the arm motion are calculated.
Arm kinetics were apportioned to force components
associated with torso and arm motions as follows:
RSHOULDER TRAN torso translation and shoulder protraction;
RTORSO ANG ACC torso and environment angular acceleration;
RRELATIVE
arm motion relative to the torso;
torso and environment angular velocity;
RCENTRIFUGAL
RCORIOLIS
environment and torso Coriolis accelerations.
These are generalized joint forces that have the following structure (R = Rx1, Ry1, 1, Rx2, Ry2, 2, Rx3, Ry3, 3)
where the components Rx and Ry represent the forces
exchanged at a speciWc joint while represents the related
joint torque components. In our Results and Discussion sections we present the joint torque components of the Rs, which
are labeled here, respectively, SHOULDER, TORSO ANG ACC,
Fig. 3 Multibody representation of the torso and arm during reaching.
The Wgure indicates the orientation of the torso reference frame with
respect to the frame of the enviroment. S symbolizes the shoulder (see
text) and origin of the torso reference frame with respect to which the
motion of all of the other links is referred. The segments are drawn separated to indicate the joint torques and forces exchanged between the
segments, which constitute the inverse dynamics of the arm motion.
Each other segment’s reference frame is Wxed with respect to the segment, located at its center of mass and oriented along its longitudinal
axis. The link-Wxed references are in planar motion with respect to the
torso reference
Exp Brain Res (2008) 187:509–523
RELATIVE, CENTRIFUGAL, and CORIOLIS. The sign of the
torques is representative of the muscle action. For example, Coriolis forces during a leftward T&R movement tend
to extend the right upper arm and forearm, therefore, a Xexing torque developed at a joint to counteract the Coriolis
perturbation is deWned as a positive . RELATIVE represents
the torque components that are computed by inverse
dynamics equations using the accelerations of the arm segments measured in the frame of reference of the torso.
TORSO ANG ACC represents torques due to torso and environment angular acceleration. It causes tangential accelerations
on the arm. CENTRIFUGAL includes torques due to angular
velocity of the torso and of the environment. It causes
centrifugal accelerations on the arm. SHOULDER represents
the torque due to shoulder translation, which results from
torso translation and shoulder protraction. CORIOLIS is the
Coriolis component caused by the simultaneous translation
of the arm and rotation of the environment or the torso. The
sum of SHOULDER TRAN + TORSO ANG ACC + RELATIVE +
CENTRIFUGAL + CORIOLIS will be referred to as “total
torque”. These total torques are indicated in Fig. 3, respectively, for shoulder, elbow, and wrist as s, e, and w.
Sainburg (2002) uses the term “muscle torque” for what we
call total torque.
Our analysis is designed to show the segmental forces
caused by external inertial forces attributable to voluntary
or passive torso rotation and translation. For this reason, we
do not partition out the inter-brachial forces entirely attributable to arm segment motions in relation to one another.
Our relative torque includes what Hollerbach and Flash
(1982) called “normal inertial interaction” plus their “Coriolis” and “centripetal torques”. Our TORSO ANG ACC, SHOULDER TRAN, CENTRIFUGAL, and CORIOLIS are the additional
torques generated at the shoulder, elbow, and wrist by the
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translation and rotation of the torso. These torques were not
treated by Hollerbach and Flash nor by later investigators
whose paradigms typically involve a stationary torso.
All inverse dynamics calculations are aVected by uncertainty. Uncertainty arises from the variability of the data
used and its interaction with the non-linear nature of the
inverse dynamics equations (cf. Bortolami et al. 1997a, b).
The Optotrak™ system we used to track marker positions is
accurate to within 0.5 mm £ 0.5 mm £ 0.5 mm rms.
Masses, inertias, and center of mass locations of the subject’s arm segments were calculated by means of the
regression model of Zatsiorsky and Seluyanov (1985). To
evaluate the reliability of our inverse dynamics calculations
we applied the numerical procedure to the average kinematics data of eight fast T&R movements for one subject. Then
we fed the algorithm the same average position data plus
and minus one standard deviation. Figure 4 shows that the
resulting torques vary somewhat in magnitude and shape
and location of their maxima, but that their basic patterns
are quite well preserved.
Results
Accuracy
The statistical analysis of movement endpoint began with
separate one-way ANOVAs of the T&R and SRR lateral
endpoint errors. The T&R ANOVA included two factors,
movement type (Simple Reach, T&R) and movement speed
(slow, fast), and it showed no main eVects or interaction
eVects on movement endpoint. Bonferroni corrected t tests
comparing across conditions indicated that the endpoint
accuracy of T&R slow and fast movements did not diVer
Fig. 4 Evaluation of the sensitivity of the inverse dynamics
calculations due to the intrinsic
variability of measurements,
data processing, and calculation.
The data utilized are also plotted
in Fig. 5
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Exp Brain Res (2008) 187:509–523
from each other or from that of slow and fast Simple Reaches
either in distance or lateral position. Although nonsigniWcant
diVerence can be due to a lack of power, these nonsigniWcant
results are consistent with a previous study (Pigeon et al
2003a) that had greater statistical power and found no diVerences. Throughout this paper, wherever an ANOVA is followed by pair-wise comparisons, those comparisons were
conducted with t-tests corrected for the number of comparisons with the Bonferroni method. Unless otherwise stated,
the criterion for signiWcance was P < 0.05, adjusted.
The SRR ANOVA included two factors, SRR speed (60
and 120°/s) and rotation period (baseline pre-rotation, initial
rotation and Wnal per-rotation), and it showed signiWcant
main eVects of both factors as well as a signiWcant interaction of the two factors (P < 0.05, at least). Movement lateral
endpoints were signiWcantly diVerent (P < 0.001) for the initial per-rotation reaches at 60 and 120°/s from baseline nonrotating conditions. The deviations were in the direction of
the Coriolis forces generated. Endpoint distance was not
aVected. The endpoint of the Wnal per-rotation reaches, both
at 60 and 120°/s, were not diVerent from baseline (P > 0.05).
The endpoints of the initial but not Wnal post-rotation
reaches were signiWcantly diVerent from baseline, 60 and
120°/s (P < 0.001). Table 1 summarizes the Wndings.
These Wndings indicate that reaching movements made
during voluntary rotation of the torso are accurate while
those made during passive rotation are not. To see whether
feed forward compensations for anticipated Coriolis forces
account for the accuracy of reaching during voluntary rotation it is necessary to examine the kinematic and kinetic
properties of the reaches in the diVerent conditions. The
Wndings would not be surprising if much smaller Coriolis
forces were generated during T&R movements than during
reaching in the SRR.
Table 1 Averages and standard
deviations of kinematic characteristics of slow and fast T&R
and Simple Reach movements
(N = 7), and averages and standard deviations of kinematic
characteristics of baseline reaching in the SRR (N = 6)
Kinematics
Table 1 summarizes the kinematic parameters of the T&R,
Simple Reach, and SRR reaching data. On average, across
subjects and movement speeds, T&R involved 77° of
shoulder Xexion, 88° of elbow extension, and 60° of trunk
rotation. Simple Reaches involved a similar range of arm
motion (62° of shoulder Xexion, 83° of elbow extension),
but very little trunk rotation (9°). T&R movements displaced the Wnger further in external space and lasted longer
than Simple Reach movements. The average durations were
0.45 and 0.72 s, respectively, for fast and slow T&R movements and 0.33 and 0.60 s, respectively, for fast and slow
Simple Reaches. The peak velocity of the Wnger relative to
the torso was 1.7 and 0.86 m/s for fast and slow T&R
movements and 1.88 and 1.07 m/s for fast and slow Simple
Reaches. These diVerences within speed conditions were
not signiWcant. For the SRR data, baseline reaches (combined baselines of 60 and 120°/s rotation sessions) involved
54° of shoulder Xexion, 94° of elbow extension, and 12° of
torso rotation. For 60 and 120°/s, respectively, the average
durations of the movements were 0.41 and 0.37 s for baseline reaches, 0.37 and 0.38 s for the Wrst per-rotation
reaches, 0.42 and 0.38 s for adapted per-rotation reaches,
and 0.45 and 0.39 s for Wrst post-rotation reaches. The peak
velocity of the Wnger in relation to the torso was 1.48 m/s in
the SRR baseline trials and did not diVer signiWcantly in
any of the per- and post-rotation movements for either the
60 and 120°/s conditions.
Kinetics
We calculated the complete set of component torques for
subjects in the T&R and SRR experiments (See Figs. 5, 6, 7).
Turn and Reach
Simple Reach
Fast
Fast
Slow
Finger peak vel. relative
to torso (m/s)
1.71 § 0.06 0.86 § 0.17
Torso peak ang. vel. (°/s)
204 § 47
Torso ang. displ. (°)
136 § 22
SRR
Slow
1.88 § 0.42
1.07 § 0.16
1.48 § 0.38*
54 § 24
35 § 17
9.5 § 10*
59 § 9
62 § 11
9§5
11 § 6
12.0 § 11.5*
510 § 270
216 § 68
429 § 149
210 § 44
186 § 66*
Shoulder peak Xexion (°)
81 § 23
73 § 20
66 § 13
60 § 14
54 § 13*
Elbow peak ext. vel. (°/s)
430 § 216
191 § 49
504 § 169
255 § 43
322 § 101*
Shoulder peak Xexion vel. (°/s)
Elbow ext. displ. (°)
93 § 17
86 § 20
86 § 9
83 § 13
94 § 15*
Finger reach distance error (cm)
0.0 § 2.6
0.8 § 2.4
1.7 § 2.4
2.4 § 2.3
¡0.2 § 1.8*
¡1.0 § 2.4a
a
Per-rotation reaches in SRR @
60°/s
b
Per-rotation reaches in SRR @
120°/s
* Baseline reaches in SRR
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2.2 § 2.5b
Finger reach longitude error (°)
¡5.2 § 3.5
¡4.2 § 3.7
¡0.8 § 4.9
¡0.5 § 4.4
0.1 § 2.7*
5.9 § 3.6a
11.8 § 7.6b
Exp Brain Res (2008) 187:509–523
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Fig. 6 Torques produced at the shoulder and elbow joints during
reaching at 60°/s in the SRR. The Wgure shows the torques related to
baseline reaching when the room is not rotating, during the Wrst reach
while the room is rotating, during the Wnal, adapted reach while the
room is rotating, and during the Wrst reach after the room has stopped.
The total torque (black) is plotted as well as the same torque components described in Fig. 5. The plotted torques are the compensations
exerted by the muscles to the listed actions
Fig. 5 Torques produced at the shoulder and elbow joints during fast
and slow T&R movements and Simple Reaches. The total torque
(black) is plotted as well as the components due to simultaneous arm
translation relative to the torso (Relative, blue) and torso angular velocity (Coriolis, red) and acceleration (Torso Angular Acceleration, cyan), centrifugal forces (Torso and Environment Centrifugal, violet),
and shoulder translatory acceleration (Shoulder Translation, green).
The plotted torques are the compensations exerted by the muscles to
the listed actions
For each subject in the T&R experiment we averaged the
kinematics for each movement type, T&R slow and fast
and Simple Reach slow and fast. These values were the
input for the torque calculations. For each SRR subject, we
used the average kinematics of the baseline, Wrst per-rotation, adapted per-rotation, and Wrst post-rotation reaches as
the input for torque calculations.
For statistical purposes, each shoulder and elbow torque
time series was characterized in terms of peak Xexion
(maxima) and extension (minima) torque. A complete summary of the composite torques for the diVerent test conditions is presented in Tables 2, 3 and 4. In the tables, the
peak total torques are not simple sums of the peaks of the
individual torque components because the maxima and
minima of the components do not occur at the same time.
For the T&R paradigm we performed a MANOVA on
all of the torque components to assess the eVects of movement type (T&R versus Simple Reach) and movement
speed (fast versus slow). For the reaches in the SRR, twoway repeated measure MANOVAs were performed to evaluate the eVects of rotation speed (60°/s vs. 120°/s) and
reach type (baseline versus Wrst per-rotation versus perrotation adapted versus Wrst post-rotation) on the torque
components. Both MANOVAs showed signiWcant main
eVects and interaction eVects (P < 0.05, at least), so they
were followed by speciWc pair-wise comparisons, reported
below.
Total torque
T&R paradigm: peak Xexion values more than double at the
shoulder (P < 0.01) and elbow (P < 0.05) for fast versus
slow movements both for T&R and Simple Reaches.
Shoulder peak torque extension also doubles with increased
speed (P < 0.01), but elbow extension torque is insensitive
to movement speed. Total shoulder Xexion (P < 0.05) and
elbow extension (P < 0.01) torques diVer between T&R
and Simple Reach while their opposite extremes, shoulder
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Exp Brain Res (2008) 187:509–523
to the torso for T&R movements and Simple Reaches. SRR
paradigm: relative torques at the shoulder were not signiWcantly diVerent across movement types and room speeds,
and similarly for the elbow except for elbow Xexion during
movements made at 60°/s versus 120°/s; P < 0.05 (cf.
Table 4).
Coriolis torque
Fig. 7 Torques produced at the shoulder and elbow joints during
reaching at 120°/s in the SRR. The organization of the Wgure is the
same as Fig. 6
extension and elbow Xexion, do not. SRR paradigm:
shoulder Xexion and elbow extension peak torques are
insensitive both to movement type (baseline versus Wrst
per-rotation versus adapted versus Wrst post-rotation) and
SRR speed (60 and 120°/s), while elbow Xexion and shoulder extension values are diVerent (P < 0.01) between movement types, and elbow Xexion values increase with SRR
speed.
Relative torque
T&R paradigm: the size and shape of the apparent joint
torques, i.e., the torques solely required by the relative
motion of the arm with respect to the torso, are comparable
for T&R and Simple Reach movements of the same speeds,
slow or fast (cf. Table 2). The Xexion and extension peaks
of relative torque also occur at approximately the same proportion of movement time for the T&R and Simple
Reaches. Relative shoulder torques more than double for
fast versus slow movements (P < 0.01). Elbow torques are
overall much smaller than shoulder torques and are less for
slow versus fast movements (Table 2). The relative torques
at the shoulder and elbow are insensitive to movement type
(T&R versus Simple Reach). This result was expected and
demonstrates that the targets we chose elicited arm movements having the same kinematics and kinetics with respect
123
The Coriolis torque proWles are unidirectional, always having maxima in the direction of Xexion for both shoulder and
elbow. T&R paradigm: Coriolis torques: (1) are four to
seven times larger in T&R movements than Simple
Reaches at the same speeds (P < 0.01), (2) are more than
double in fast versus slow T&R movements (P < 0.01), and
(3) are greater at the shoulder than the elbow in comparable
conditions (cf. Table 2). Two-way ANOVAs also showed
an interaction eVect of movement type and movement
speed on the Coriolis force at the shoulder (P < 0.01) and
the elbow (P < 0.05). SRR paradigm: Analogous results are
found for reaching movements in the SRR. Coriolis peaks
at both shoulder and elbow are signiWcantly larger
(P < 0.01) during rotation versus baseline movements. The
baseline reaches have minimal Coriolis torques (cf.
Table 3) while the adapted reaches during rotation have
maximum Coriolis torques. Coriolis torque is also
increased by SRR room speed (P < 0.05, 120°/s vs. 60°/s)
as expected.
Translation torque
Torso translation and shoulder protraction (to a very small
extent) are responsible for this torque component. T&R
paradigm: For fast and slow reaches translation torque Xexion was signiWcantly greater (P < 0.01) at the elbow and
shoulder for T&R versus Simple Reach movements. SRR
paradigm: shoulder extension and Xexion values are insensitive to movement type or SRR speed.
Torso angular acceleration
T&R paradigm: speed of execution aVected torso acceleration for both T&R and Simple Reach movements. As a consequence, both shoulder and elbow extension and Xexion
peak torque values were signiWcantly diVerent (P < 0.01)
across movement types and speed. SRR paradigm: torso
angular acceleration was statistically indistinguishable
across reaching conditions and SRR rotation speeds, and
there were no torque diVerences among conditions. This is
predictable because in the SRR the torso is rotated passively and reaching movements are comparable in torso
acceleration to the baseline reaches, which also involve
very little torso angular acceleration.
Exp Brain Res (2008) 187:509–523
517
Table 2 Medians and inter-quartile ranges (N = 7) of maxima and minima of joint torques (Nm) of the arm during T&R and Simple Reach movements made in the dark
Turn and Reach
Simple Reach
Fast
Slow
Fast
Slow
Shoulder total torque
7.1 (6.1, 8.9)
2.9 (2.3, 3.4)
4.5 (3.4, 5.7)
1.8 (1.3, 1.9)
Shoulder relative torque
5.0 (4.3, 6.8)
1.9 (1.2, 2.4)
4.4 (3.9, 6.0)
1.9 (1.1, 2.0)
Shoulder torso ang acc torque
1.8 (1.3, 2.3)
0.8 (0.6, 1.0)
0.8 (0.6, 1.5)
0.3 (0.2, 0.4)
Shoulder coriolis torque
3.1 (2.9, 3.7)
1.1 (1.0, 1.2)
0.8 (0.4, 0.9)
0.2 (0.1, 0.4)
Shoulder centrifugal torque
–
–
–
–
Shoulder translation torque
2.0 (1.7, 2.6)
0.8 (0.6, 0.8)
0.6 (0.3, 0.8)
0.1 (0.1, 0.2)
Flexion MAX
Elbow total torque
1.7 (1.5, 2.0)
0.9 (0.8, 0.9)
0.7 (0.6, 0.8)
0.3 (0.3, 0.3)
Elbow relative torque
1.0 (1.0, 1.3)
0.4 (0.4, 0.4)
0.7 (0.5, 0.9)
0.3 (0.2, 0.3)
Elbow torso ang acc torque
0.7 (0.6, 0.8)
0.3 (0.3, 0.3)
0.4 (0.3, 0.6)
0.1 (0.1, 0.2)
Elbow coriolis torque
2.0 (1.7, 2.1)
0.7 (0.7, 0.8)
0.4 (0.2, 0.5)
0.1 (0.1, 0.2)
Elbow centrifugal torque
0.4 (0.4, 0.6)
0.2 (0.2, 0.3)
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
Elbow translation torque
0.9 (0.7, 1.0)
0.3 (0.3, 0.4)
0.3 (0.2, 0.3)
0.1 (0.1, 0.1)
Extension MIN
Shoulder total torque
¡3.9 (¡4.6, ¡3.1)
¡1.6 (¡1.8, ¡1.4)
¡3.1 (¡3.9, ¡2.7)
¡1.4 (¡1.4, ¡1.2)
Shoulder relative torque
¡5.4 (¡6.9, ¡4.8)
¡2.2 (¡2.7, ¡1.4)
¡3.9 (¡4.9, ¡3.1)
¡1.6 (¡1.9, ¡1.2)
Shoulder torso ang acc torque
¡4.5 (¡5.2, ¡3.8)
¡1.8 (¡1.9, ¡1.5)
¡1.4 (¡2.4, ¡1.2)
¡0.5 (¡0.7, ¡0.3)
Shoulder coriolis torque
–
–
–
–
Shoulder centrifugal torque
–
–
–
–
Shoulder translation torque
¡0.1 (¡0.2, 0.0)
0.0 (¡0.1, 0.1)
¡0.3 (¡0.5, ¡0.1)
¡0.1 (¡0.1, ¡0.1)
Elbow total torque
¡0.5 (¡0.6, ¡0.5)
¡0.2 (¡0.2, ¡0.2)
¡1.0 (¡1.1, ¡0.9)
¡0.4 (¡0.5, ¡0.4)
Elbow relative torque
¡1.4 (¡1.7, ¡1.1)
¡0.5 (¡0.6, ¡0.4)
¡1.0 (¡1.2, ¡1.0)
¡0.4 (¡0.6, ¡0.4)
Elbow torso ang acc torque
¡1.7 (¡2.1, ¡1.5)
¡0.7 (¡0.7, ¡0.6)
¡0.5 (¡0.9, ¡0.5)
¡0.2 (¡0.3, ¡0.1)
Elbow coriolis torque
–
–
–
–
Elbow centrifugal torque
–
–
–
–
Elbow translation torque
¡0.6 (¡0.6, ¡0.6)
¡0.3 (¡0.3, ¡0.2)
¡0.2 (¡0.3, ¡0.2)
¡0.1 (¡0.1, ¡0.1)
Centrifugal torque
T&R paradigm: centrifugal torques, were negligible except
at the elbow during fast and slow T&R, where there is a
signiWcant eVect (P < 0.01) of movement speed. SRR paradigm: centrifugal torque increases with room speed, consequently there is a signiWcant eVect (P < 0.01) of movement
type and room speed.
Comparison of torque components of T&R movements
versus SRR movements
A one-way MANOVA was conducted to compare the
torque components in T&R and SRR conditions with signiWcant Coriolis perturbations (Conditions: Initial reaches
in the SRR at 60°/s, Initial reaches in the SRR at 120°/s,
T&R slow reaches, T&R fast reaches). There was a signiWcant main eVect of condition (P < 0.05), so we made pairwise comparisons of SRR and T&R conditions. T&R
movements involved signiWcantly higher shoulder transla-
tion and torso angular acceleration components than movements made at 60 and 120°/s in the SRR. Total torque at the
shoulder was also higher for the T&R movements than the
reaches during 60 and 120°/s rotation in the SRR.
Next, we conducted a regression analysis (and ANOVA)
of the relationship of shoulder torque to longitudinal (lateral) endpoints of T&R movements and of movements during rotation in the SRR. We used as predictors the peak
values of: (1) total shoulder torque, (2) torque generated at
the shoulder by the torso angular acceleration, (3) torque
generated at the shoulder by torso translation, and (4) Coriolis torque generated at the shoulder. The regression analysis indicated that only the Coriolis torque peak values
across the subjects and conditions were a signiWcant predictor (P < 0.05) of lateral endpoint errors. Figure 8 plots the
relationship between endpoint errors and Coriolis torque
peak values for T&R and Simple Reach, fast and slow. For
the SRR reaches, the endpoint errors are plotted for the
baseline reaches and the initial per-rotation movements at
60 and 120°/s. For both T&R and SRR movements during
123
518
Exp Brain Res (2008) 187:509–523
Table 3 Medians and inter-quartile ranges of maxima and minima of joint torques (Nm) of baseline and Wrst per-rotation reaches made in the SRR
at 60°/s and 120°/s passive rotation
Baseline
First Per-Rotation
60°/s
120°/s
60°/s
120°/s
Shoulder total torque
2.5 (1.6, 2.8)
2.2 (1.6, 2.4)
2.3 (1.9, 2.9)
2.6 (2.5, 3.1)
Shoulder relative torque
2.4 (1.7, 2.7)
2.1 (1.6, 2.5)
1.3 (1.3, 2.0)
1.2 (1.1, 2.7)
Shoulder torso ang acc torque
0.4 (0.3, 0.4)
0.2 (0.1, 0.4)
0.5 (0.5, 0.9)
0.4 (0.4, 1.0)
Shoulder coriolis torque
0.2 (0.1, 0.3)
0.0 (0.0, 0.3)
1.2 (1.0, 1.5)
2.1 (1.8, 2.8)
Shoulder centrifugal torque
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
0.2 (0.2, 0.2)
0.8 (0.8, 0.8)
Shoulder translation torque
0.2 (0.1, 0.3)
0.3 (0.2, 0.5)
0.2 (0.2, 0.4)
0.2 (0.1, 0.5)
Elbow total torque
0.6 (0.5, 0.7)
0.5 (0.5, 1.1)
1.2 (1.2, 1.4)
2.1 (1.9, 2.6)
Elbow relative torque
0.6 (0.5, 0.7)
0.5 (0.5, 1.0)
1.1 (0.9, 1.2)
1.4 (1.1, 2.0)
Elbow torso ang acc torque
0.1 (0.1, 0.1)
0.1 (0.0, 0.1)
0.2 (0.1, 0.3)
0.1 (0.1, 0.3)
Elbow coriolis torque
0.1 (0.0, 0.1)
0.0 (0.0, 0.1)
0.4 (0.4, 0.5)
0.7 (0.7, 0.9)
Elbow centrifugal torque
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
0.1 (0.1, 0.1)
0.3 (0.3, 0.3)
Elbow translation torque
0.1 (0.1, 0.1)
0.1 (0.0, 0.1)
0.2 (0.2, 0.2)
0.3 (0.3, 0.3)
Flexion
Extension
Shoulder total torque
¡1.8 (¡2.2, ¡1.3)
¡1.8 (¡2.4, ¡1.5)
¡1.0 (¡1.3, ¡0.8)
¡0.1 (¡0.5, 0.0)
Shoulder relative torque
¡1.5 (¡1.9, ¡1.2)
¡1.9 (¡2.2, ¡1.6)
¡1.5 (¡1.7, ¡1.4)
¡1.9 (¡2.9, ¡1.6)
Shoulder torso ang acc torque
¡0.8 (¡1.0, ¡0.5)
¡0.2 (¡1.2, ¡0.2)
¡0.5 (¡1.3, ¡0.4)
¡0.5 (¡1.7, ¡0.4)
Shoulder coriolis torque
–
–
–
–
Shoulder centrifugal torque
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
0.2 (0.1, 0.2)
0.6 (0.6, 0.6)
Shoulder translation torque
¡0.2 (¡0.3, ¡0.1)
¡0.2 (¡0.5, ¡0.2)
¡0.3 (¡0.3, ¡0.2)
¡0.3 (¡0.5, ¡0.3)
Elbow total torque
¡1.4 (¡1.6, ¡1.1)
¡1.4 (¡2.1, ¡1.3)
¡1.3 (¡1.4, ¡1.2)
¡1.6 (¡2.0, ¡1.1)
Elbow relative torque
¡1.4 (¡1.5, ¡1.1)
¡1.4 (¡2.1, ¡1.3)
¡1.5 (¡1.6, ¡1.5)
¡2.0 (¡2.5, ¡1.5)
Elbow torso ang acc torque
¡0.2 (¡0.3, ¡0.1)
¡0.1 (¡0.4, ¡0.1)
¡0.2 (¡0.4, ¡0.1)
¡0.2 (¡0.6, ¡0.1)
Elbow coriolis torque
–
–
–
–
Elbow centrifugal torque
0.0, (0.0, 0.0)
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
Elbow translation torque
¡0.1 (¡0.1, ¡0.1)
¡0.1 (¡0.1, ¡0.1)
¡0.2 (¡0.2, ¡0.1)
0.0 (0.0, 0.0)
rotation the Coriolis forces acted in the direction of shoulder extension. The slopes of the regression lines are very
diVerent for the two cases. For T&R movements, the slope
is shallow and negative and there are small errors in the
Xexion direction, the direction opposite the Coriolis force
generated during the movements. The best Wtting regeression line is: Y = ¡0.69 ¡ 0.45 £ X. The slope of the Wt is
not signiWcantly diVerent from zero (P > 0.05, F = 2.39).
By contrast, for the SRR reaches the slope is steep and positive and the errors are in the direction of shoulder extension, the same direction as the Coriolis forces generated by
the movements. The best Wtting regression line is:
Y = ¡2.21 + 4.2 £ X. The slope of the Wt is signiWcantly
diVerent from zero (P < 0.05, F = 31.7).
SRR reaches: adapted versus non-adapted
Figure 6 provides an example of torques for the baseline,
initial per-rotation and Wnal (adapted) per-rotation, and ini-
123
tial post-rotation movements made by subjects at 60°/s.
Several features stand out: (1) the torque proWles of the initial per-rotation movements are “jittery” not smooth like
the pre-rotation movements, (2) the torque proWles of the
Wnal per-rotation movements are as smooth as those of the
pre-rotation movements, and (3) the initial post-rotation
movements are again jittery. The torque proWles for the Wrst
per-rotation and Wrst post-rotation reaches are not smooth
largely because they were computed on kinematic data
from single reaches for each subject, whereas the baseline
and adapted reach torque proWles were each computed on
several reaches per subject. The nature of the initial disruption can be seen by comparing the proWles of the baseline
reaches and the initial per-rotation reaches. The compensation achieved with additional reaching movements that
restores reaching accuracy can be seen by subtracting the
torque proWles of the baseline and Wnal per-rotation,
adapted reaches (see Fig. 9). It is the persistence of this
compensation when no longer necessary in the initial post-
Exp Brain Res (2008) 187:509–523
519
Table 4 Medians and inter-quartile ranges of maxima and minima of joint torques (Nm) of the adapted reaches and Wrst post-rotation reaches in
the SRR at 60 and 120°/s passive rotation
Adapted Reach
First Post-Rotation
60°/s
120°/s
60°/s
120°/s
2.9 (2.2, 3.0)
2.8 (2.4, 3.4)
2.8 (2.0, 3.1)
2.6 (2.1, 3.1)
Shoulder relative torque
2.2 (1.7, 2.3)
1.7 (1.2, 2.4)
2.3 (1.9, 2.8)
2.6 (2.1, 3.1)
Shoulder torso ang acc torque
0.2 (0.2, 0.4)
0.1 (0.1, 0.4)
0.6 (0.5, 0.7)
0.3 (0.3, 0.8)
Shoulder coriolis torque
1.2 (1.0, 1.6)
1.8 (1.7, 2.8)
0.2 (0.1, 0.2)
0.1 (0.1, 0.3)
Shoulder centrifugal torque
0.2 (0.2, 0.2)
0.6 (0.6, 0.7)
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
Shoulder translation torque
0.1 (0.1, 0.4)
0.1 (0.1, 0.3)
0.3 (0.3, 0.3)
0.3 (0.3, 0.5)
Elbow total torque
0.9 (0.9, 1.0)
1.4 (1.4, 2.1)
0.5 (0.4, 0.5)
1.0 (0.8, 1.2)
Elbow relative torque
0.6 (0.5, 0.6)
0.7 (0.6, 1.4)
0.5 (0.5, 0.5)
1.0 (0.8, 1.3)
Elbow torso ang acc torque
0.1 (0.1, 0.1)
0.0 (0.0, 0.1)
0.2 (0.2, 0.2)
0.1 (0.1, 0.3)
Elbow coriolis torque
0.5 (0.4, 0.6)
0.8 (0.7, 1.1)
0.1 (0.0, 0.1)
0.0 (0.0, 0.1)
Elbow centrifugal torque
0.1 (0.1, 0.1)
0.2 (0.2, 0.2)
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
Elbow translation torque
0.1 (0.1, 0.2)
0.3 (0.3, 0.3)
0.1 (0.1, 0.1)
0.1 (0.1, 0.2)
Flexion
Shoulder total torque
Extension
Shoulder total torque
¡0.6 (¡0.9, ¡0.6)
0.3 (¡0.3, 0.3)
¡2.4 (¡2.6, ¡1.9)
¡2.3 (¡3.2, ¡2.1)
Shoulder relative torque
¡1.8 (¡1.9, ¡1.6)
¡1.1 (¡2.0, ¡1.1)
¡2.6 (¡2.8, ¡2.2)
¡2.3 (¡3.0, ¡2.2)
Shoulder torso ang acc torque
¡0.4 (¡0.9, ¡0.4)
¡0.1 (¡0.7, ¡0.1)
¡1.2 (¡1.2, ¡0.9)
¡0.9 (¡1.5, ¡0.7)
Shoulder coriolis torque
–
–
–
–
Shoulder centrifugal torque
0.1 (0.1, 0.1)
0.5 (0.5, 0.5)
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
Shoulder translation torque
¡0.2 (¡0.3, ¡0.1)
¡0.4 (¡0.4, ¡0.3)
¡0.3 (¡0.3, ¡0.3)
¡0.3 (¡0.5, ¡0.3)
Elbow total torque
¡0.9 (¡1.3, ¡0.8)
¡1.1 (¡1.6, ¡0.8)
¡1.1 (¡1.4, ¡1.0)
¡1.4 (¡1.7, ¡1.1)
Elbow relative torque
¡1.2 (¡1.6, ¡1.1)
¡1.5 (¡2.2, ¡1.2)
¡1.1 (¡1.4, ¡1.0)
¡1.4 (¡1.7, ¡1.2)
Elbow torso ang acc torque
¡0.1 (¡0.3, ¡0.1)
0.0 (¡0.2, 0.0)
¡0.3 (¡0.4, ¡0.3)
¡0.3 (¡0.5, ¡0.2)
Elbow coriolis torque
–
–
–
–
Elbow centrifugal torque
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
0.0 (0.0, 0.0)
Elbow translation torque
0.0 (¡0.1, 0.0)
0.1 (0.0, 0.1)
¡0.2 (¡0.2, ¡0.2)
¡0.1 (¡0.2, ¡0.1)
rotation movements that causes renewed lateral endpoint
errors.
Discussion
Our goal was to test the hypothesis that the CNS compensates in a feed forward fashion for the Coriolis forces that
are generated on the moving arm when reaching movements are made during voluntary trunk rotation. Such
movements are as accurate as those made with the trunk
stationary and are little aVected by movement speed. By
contrast, reaching movements made during passive body
rotation are initially inaccurate and errors are even greater
with higher rotation speeds. To determine whether this
diVerence in reaching endpoint accuracy was related to
smaller torques being generated on the arm during voluntary as compared with passive torso rotation it was necessary to compute the torques involved. To achieve this
analysis we developed an inverse dynamics model that
allowed us to compare the total torque and the torque components present on the arm during voluntary and passive
torso rotation. The model is presented in the companion
paper (Bortolami et al. 2008).
We have found that there were a number of large and signiWcant changes in torque components when reaching movements were made during passive or active torso rotation
compared with stationary reaches. These changes are large
both in absolute terms and in relation to torques solely
related to moving the arm relative to the torso. All of the
torques at the shoulder and elbow related to or aVected by
torso rotation (total torque, torso angular acceleration
torque, Coriolis torque) were larger during fast voluntary
T&R movements than during passive rotation in the SRR
(see Tables 2, 3). Our analysis indicated that the crucial
torque aVecting endpoint accuracy in the passive rotation
conditions was the Coriolis torque. In T&R movements relative to Simple Reaches, the Coriolis Xexion torques resulting
123
520
Fig. 8 Regression plots of lateral reaching errors as function of the
Coriolis forces generated by torso and environment rotation. a Reaching errors as a function of self-generated Coriolis torque at the shoulder
produced during fast and slow T&R trials. b Reaching errors as a function of the Coriolis torque at the shoulder produced by baseline reaches
prior to SRR rotation and during rotation in the SRR at 60 and 120°/s
Fig. 9 Torque diVerences between adapted SRR per-rotation reaches
and pre-rotation baseline reaches at 60 and 120°/s
123
Exp Brain Res (2008) 187:509–523
from torso rotation increase greatly, sixfold at the shoulder
and elbow for fast movements and twofold for slow. The
proportion of the relative torque component at the shoulder
resulting from the Coriolis torque increased from 50 to 84%
for slow Simple versus T&R reaches and from 15 to 55% for
fast reaches. The changes were even larger at the elbow.
Nevertheless, movement accuracy was preserved. The magnitude of Coriolis shoulder and elbow torques produced by
torso rotation which we found is an order of magnitude
greater than the Coriolis elbow torques reported by Hollerbach and Flash (1982) due to upper arm rotation.
During T&R movements, subjects voluntarily achieved
much higher torso rotational velocities than subjects who
were passively exposed to rotation in the SRR. Slow T&R
movements involved active peak trunk velocities of t140°/
s, and fast t200°/s, compared with SRR passive velocities
of 60 and 120°/s. As a consequence, considerably higher
Coriolis forces were generated on the reaching arm during
T&R movements compared with reaches in the SRR. The
Coriolis forces at the shoulder were 1.5 times larger in fast
T&R movements than in reaches made at 120°/s in the
SRR. The slow T&R movements had Coriolis torques
equivalent to those during reaches at 60°/s in the SRR.
Nevertheless, T&R movements were little aVected by Coriolis force magnitude whereas initial SRR movements
showed signiWcant Coriolis force dependent endpoint errors
in the same direction as the Coriolis forces (see Fig. 8).
These performance diVerences mean that in T&R movements the CNS must be controlling movement in such a
way as to mitigate the consequences of self-generated Coriolis forces related to torso rotation. The nature of this compensation can be computed using the inverse dynamics
model presented in the companion paper. This model
allows us to simulate the dynamics of a reach made during
passive rotation in the SRR and to compare them with the
dynamics of a reach made in a stationary environment during voluntary rotation of the torso. Figure 10 shows the
results of feeding the measured kinematics of an actual fast
Simple Reach (the reach whose dynamics are shown in
Fig. 5, which was a straight and accurate reach) into the
model along with a simulated constant torso rotation velocity of 60°/s CCW. This simulates our actual 60°/s SRR condition. The calculated joint torques are what must be
produced by a subject to achieve the same movement path
in the rotating room during rotation at 60°/s. Note that the
simulated relative torque has the same value as in Fig. 5
because it is determined by the identical arm motion relative to the torso. However, the torques related to torso rotation, e.g., the Coriolis torque, and consequently the total
torque have increased greatly relative to those in Fig. 5
because a reach made at 60°/s in the slow rotation room
would be deviated in the direction of the Coriolis force if
these joint torque adjustments were not generated.
Exp Brain Res (2008) 187:509–523
Fig. 10 Calculated torques necessary during reaching in the SRR to
produce the same accurate movement path as a fast Simple Reach
whose dynamics are shown in Fig. 5
The simulated joint torques of Fig. 10 match what subjects in fact learn to produce when they are fully adapted in
the rotating room (Fig. 6, adapted) and what they fail to
produce in their Wrst reaches during constant velocity rotation. The simulated Coriolis torques are only one third as
large as the torques generated during an actual fast T&R
movement and only half as large as during a slow T&R
movement (see Fig. 5). The change in joint torques between
fast and slow T&R movements, which do not diVer in
movement path or endpoint, is about the same as the torque
which adapted subjects in the SRR produce to prevent deviation of their reach by Coriolis forces. In comparing the
dynamics of the Simple Reach with those of the simulated
reach during 60°/s rotation, it is notable that diVerences in
the dynamics are apparent within 50 ms of movement
onset. This simulated rapid torque onset agrees with the
rapid onset observed in subtracted torque traces of real
adapted and unadapted reaches (see Fig. 9). Similarly, comparing the dynamics of the fast Simple Reach of Fig. 5 with
the fast T&R reach, it is apparent that diVerences are present within 50 ms of movement onset. These diVerences are
the compensations that must be generated to preserve
movement accuracy. We believe that the major proportion
of these compensations are pre-computed rather than due to
passive or reXexive stiVness.
This contention is supported by studies of joint stiVness.
Flash and Mussa-Ivaldi (1990) and Gomi and Kawato
(1996) found shoulder and elbow stiVness during reaching
movements made with the torso stationary to be in the
range of 10–80 Nm/rad. We can reasonably assume from
their results that during a T&R movement shoulder stiVness
may be about 50 Nm/rad when the Wnger is extended
roughly 50 cm from the shoulder. The increment of torque
at the shoulder between fast and slow T&R movements is
approximately 4.2 Nm on average (Table 2). With a shoulder stiVness of 50 Nm/rad, the Wnger should have deXected
in the direction opposite torso displacement at least an extra
521
4 cm during the fast T&R movements but we found no
increase in deXection. The shoulder stiVness would have
had to be at least 500 Nm/rad to prevent a deXection of the
order of 4 mm and virtually inWnite to explain our Wnding
of an absence of a deXection increase. Therefore, passive or
quasi-passive properties of the arm cannot explain the accuracy of T&R movements across diVerent torso rotation
velocities. Instead, our results indicate that muscles must be
activated to produce “pre-computed torques” (cf. Slotine
and Li 1990). This assertion does not necessarily imply that
the CNS has to compute inverse dynamics equations nor
that it has to separately represent the components of torque
we have identiWed and quantiWed.
Several studies have demonstrated that when an arm
movement is combined with trunk translation, kinematic
features of the hand path are preserved (Cockell et al. 1995;
Ma and Feldman 1995; Pigeon et al. 2000; Wang and Stelmach 1998; Marteniuk et al. 2000). In particular, the translation of the trunk in the sagittal plane does not inXuence
the hand trajectory in relation to the target (Kaminski et al.
1995; Ma and Feldman 1995; Saling et al. 1996). The
motion of the trunk and arm are smoothly interrelated to
bring the hand to the target. When trunk motion outlasts
hand motion, the potential inXuence of the continuing trunk
movement on hand position is nulliWed by appropriate compensatory modiWcations of elbow and shoulder angles. This
phenomenon has been likened to the vestibular-ocular
reXex (VOR) that prevents the gaze shift that would otherwise be elicited by head rotation (Pigeon et al. 2000;
Pigeon and Feldman 1998). However, the VOR is a kinematic stabilizing mechanism with relatively simple
dynamic properties. The kinematics and kinetics analysis
that we have presented here shows that any mechanism
responsible for compensating for the inXuence of trunk
motion on the control of the arm has to control multiple
body segments with substantial inertia.
The application of our arm movement model and analysis to kinematics data produced during active versus passive torso rotation also provides an avenue for approaching
the issue of motor planning. It demonstrates that the inertial
loads generated by natural reaching movements involving
torso rotation are orders of magnitude greater than those in
multi-joint movements not involving torso motion. This
unexpected Wnding suggests that to understand normal
unconstrained movements it will be critical to understand
the forces generated by truncal rotation and how they are
controlled. Such information could also illuminate the
study of compensations for unexpected perturbations in
healthy individuals as well as disorders of motor control.
For example, Guillaud et al. (2006) recently showed that
reaching movements to Earth- and body-Wxed targets are
altered if passive yaw body rotation is imposed unexpectedly at movement onset. They suggested that some of the
123
522
compensations they saw were not fully reXexive. A full
analysis of their data with our dynamics model could help
separate vestibular (cf Bresciani et al. 2005) and proprioceptive contributions to their results. A variety of disorders
leads to speciWc deWcits in control of multi-joint movements when inter-segmental interactions are signiWcant.
Subjects without proprioception cannot adequately compensate for naturally occurring inter-segmental forces nor
readily learn to compensate for experimentally introduced
alterations in inter-segmental forces (Ghez and Sainburg
1995; Gribble and Ostry 1999; Sainburg et al. 1993, 1995).
Cerebellar (Bastian et al. 1996; Topka et al. 1998), Parkinson’s (Benecke et al. 1987; Dounskaia et al. 2000; Flash
et al. 1992; Poizner et al. 2000; Seidler et al. 2001) and
hemiparetic (Beer et al. 2000) patients often can produce
normal single joint movements, but when they are required
to make multi-joint movements abnormal trajectories
result. Such observations point to diYculties in representing or actuating the necessary component torque patterns to
achieve desired movement direction and speed during
multi-joint movements.
Acknowledgments We thank Dr. Alberto Pierobon and Dr. Enrico
Chiovetto for technical advice and assistance. Support was provided by
grant from the National Institutes of Health, RO1 AR48546–01.
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