Exp Brain Res (2005) 164: 120–132
DOI 10.1007/s00221-005-2216-y
R ES E AR C H A RT I C L E
Isaac Kurtzer Æ Paul A. DiZio Æ James R. Lackner
Adaptation to a novel multi-force environment
Received: 26 April 2004 / Accepted: 15 December 2004 / Published online: 16 April 2005
Springer-Verlag 2005
Abstract Humans display accurate limb behavior when
they move in familiar environments composed of many
simultaneously-acting forces. Little is known about how
multi-force environments are represented and whether
this process partitions between the underlying force
components, reflects the net forces present, or is cued to
the force-context. We tested between these three main
alternatives by examining how reaching movements
adapt to a novel multi-force field composed of a velocity-dependent force and a constant force. These hypotheses were dissociated first by making the constant
force larger and oppositely-oriented to the velocity-dependent force; thereby, the net force was always opposite the velocity-dependent component. Second, we
tested adaptation with all novel forces removed to
eliminate any potential cues for the force-context. In two
experiments that used forces perpendicular or parallel to
the forward movement direction, we found adaptation
aftereffects consistent with a mechanism that partitioned
the velocity-dependent component from the net force
field. Specifically, we found aftereffects opposite the
rightward or resistive velocity-dependent component of
the multi-force field, even though the net force imposed
was leftward or assistive, respectively. An additional
experiment suggested that the velocity-dependent component is partitioned relative to the background load in
a limb-based coordinate frame.
I. Kurtzer Æ P. A. DiZio Æ J. R. Lackner
Ashton Graybiel Spatial Orientation Laboratory,
Volen Center for Complex Systems,
Brandeis University, 415 South St. Waltham,
MA 02454, USA
I. Kurtzer (&)
Department of Anatomy and Cell Biology,
Queen’s University, Kingston, ON,
Canada, K7L 3N6
E-mail: isaac@biomed.queensu.ca
Tel.: +613-533-2600
Fax: +613-533-6880
Keywords Motor learning Æ Force partitioning Æ
Reaching Æ Modularity
Introduction
Accurate motor control is supported by neural mechanisms that adaptively anticipate the force requirements of the task. These anticipatory mechanisms are
evident during the introduction, repetition, and removal
of a novel movement-dependent force as a canonical
pattern of movement disruption, return of accurate
performance, and compensatory aftereffects (Lackner
and DiZio 1992; Lackner and DiZio 1994; Shadmehr
and Mussa-Ivaldi 1994). Such force adaptation paradigms have been intensively utilized over the past decade
in examining adaptation of reaching movements across
movement direction (Gandolfo et al 1996; Sainburg et al
1999; Thoroughman and Shadmehr 2000), movement
speed (Goodbody and Wolpert 1998), limb configuration (Shadmehr and Mussa-Ivaldi 1994; Shadmehr and
Moussavi 2000; Malfait et al 2002), in relation to visual
and proprioceptive feedback (Lackner and DiZio 1994;
Cohn et al 2000; DiZio and Lackner 2000), and transfer
between limbs (DiZio and Lackner 1995; Wang and
Sainburg 2004). These studies focused on adaptation to
single force fields and demonstrated that adaptive force
representations are encoded within a limb-based coordinate system dominated by proprioceptive inputs and
displaying limited generalization over the tested dimensions. It remains unknown how force adaptation occurs
within environments composed of multiple simultaneously acting forces, as is typical in natural settings that
include the inertial dynamics of the limb, the background force of gravity, and forces associated with
wielded objects and surrounding media.
We considered three basic hypotheses for how multiforce environments could be adaptively represented.
First, the nervous system could adaptively partition the
net force into its underlying components, for example,
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between the ‘‘static’’/gravity-related and ‘‘dynamic’’/
movement-related components. Second, the nervous
system could adapt to the net force without regard to its
underlying components. Lastly, the nervous system
could utilize a context-dependent force representation
that is engaged by some salient cue.
The force partitioning hypothesis is the most likely
candidate, as several studies suggest that ‘‘static’’/
gravity-related and ‘‘dynamic’’/movement-related forces are separately represented by the motor system.
First, modeling studies demonstrate that such a partitioned organization could simplify the control of
reaching over a range of movement speeds and background loads (Hollerbach and Flash 1982; Atkenson
and Hollerbach 1985). Second, empirical studies report
that unconstrained reaching trajectories tend to minimize the peak dynamic forces (Nishikawa et al 1999;
Soechting et al 1995) and possess joint-torque and
EMG patterns consistent with separate dynamic- and
gravity-dependent neural drives (Flanders and Herrmann 1992; Gottlieb et al 1997). Lastly, altered-gravity
studies do not report largely deranged movement
patterns upon the rapid transitions to hypo- or hypergravity in parabolic flight. Instead, the accuracy of
reaching (Fisk et al 1993), object lifting (Kingma et al
1999), and movements of the torso (Vernazza-Martin
et al 2000) are near to those on Earth, suggesting that
dynamic forces are planned independently of the forces
that counteract gravity.
However, these strongly suggestive studies are not
definitive. Foremost, there is no clear understanding of
how the background force conditions prior to movement
onset are integrated into the patterning of force commands during movement. Second, studies of ‘‘normal
performance’’ are arguably studies of highly overtrained behavior over a lifetime of interacting constraints. Third, behaviors observed under altered-gravity
conditions include vestibular representations of the
gravity force as well as motor and somatosensory
sources (Lackner and DiZio 2000), and given its
universal presence in terrestrial evolution, gravity might
Fig. 1a–c Diagrams of force fields. a Velocity-dependent.
b Constant. c Multi. The multi-force field is the combination of
the velocity-dependent and constant force fields. X-axis: forward
hand velocity ( mm/s); for clarity, only the forward component is
indicated. Y-axis: imposed force (N). Experiment 1: +/ is
leftwards/rightwards force; Experiment 2: +/ is assistive/resistive
force. Gray shading for multi-force field indicates hand velocities
above 600 mm/s threshold, where net force reverses sign
be associated with specialized adaptive mechanisms.
Lastly, several authors have reported context-dependent
force adaptation (Gandolfo et al 1996; Blakemore et al
1998; Wada et al 2003), although others have shown
contextual ‘‘cueing’’ to be ineffective (Karniel and
Mussa-Ivaldi 2002).
Here we were able to predict categorically different
aftereffects for the three alternative hypotheses by (1)
programming a robot manipulandum to impose both a
velocity-dependent force and a larger, oppositely-oriented constant force, and (2) by testing adaptation with
both the velocity-dependent and constant forces
removed (Figs. 1 and 2). We chose a velocity-dependent
force because it has been widely used for inducing
adaptation and a co-planar constant force since it is
the simplest additional force and is reminiscent of the
force of gravity. Importantly, the programmed constant
force was larger and opposite to the velocity-dependent
force throughout the movement, so the net force imposed was always opposite the underlying velocity-dependent component.
Consider a forward movement in which we simultaneously impose one force that acts rightward
proportional to the hand’s forward velocity and a larger force that acts leftward independently of hand
motion. During a forward movement the summation of
the two forces (the net force) would begin at a maximal
leftward value at movement onset, decrease proportional to the hand’s forward velocity, and return to the
same maximal leftward value at the movement’s completion. After removal of all the forces, each hypothesis
predicts a categorically different aftereffect. A net force
hypothesis predicts a rightward aftereffect opposite the
net leftward force. In contrast, the force partitioning
hypothesis predicts a leftward aftereffect opposite the
rightward velocity-dependent component. Lastly, the
context-dependent hypothesis predicts no aftereffect
upon removing both forces, as any force-cue has also
been removed. (As a first step, we will only focus on
the potential adaptation to the underlying velocity-dependent component, since subjects are already known
to adapt to velocity-dependent forces with a null force
background.)
This logic was utilized in two principal experiments
with particular attention paid to the middle portion of
the movement, where cumulative feedback effects
and voluntary intervention is expected to be minimal
(Shapiro et al 2002, 2004). The first experiment examined adaptation to a multi-force field applied lateral
to the hand’s forward movement as described above.
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Material and methods
Subjects
Twenty-four subjects (Experiment 1: n=8; Experiment
2: n=8; Experiment 3: n=8) from Brandeis University
participated in three separate experiments. Subjects included both males (n=13) and females (n=11) ranging
in age from 18 to 33 years. All were right-handed,
neurologically normal, fluent English speakers, and naive to the purpose of the experiment. Subjects participated in one 90-min session and were compensated for
their time. Before beginning, each gave their informed
consent to the procedure approved by the Brandeis
University IRB.
Apparatus
Fig. 2 Outline of experiments. All experiments followed the same
design with three force fields. Note the constant condition was
always followed first by the multi or velocity-only condition. The
baseline was comprised of the mean of all reaches in the no-force
blocks, surrounded by a green rectangle. The initial effect for a
force perturbation was comprised of the first reach (Experiments 1
and 3) or the mean of first two reaches (Experiment 2) occurring on
the transition from a no-force block to a force field block, three
black arrows for three force conditions. The average behavior
during the last black with the force field (Final) is indicated by an
oval, three ovals for three force conditions. The post aftereffect of
the force field was comprised of the first reach (Experiments 1 and
3) or mean of first two reaches (Experiment 2) occurring on the
transition from a force field block to a no-force block, three red
arrows for three force conditions
The second experiment examined adaptation to a similar
multi-force field applied parallel to the hand’s forward
movement. A velocity-dependent resistive force was
paired with a constant assistive force so that the net
force was always assistive (decreasing proportional to
the forward hand velocity). The adaptation patterns
predicted by the different hypotheses were tested by
examining the aftereffects when both forces were removed: net force hypothesis—a speed undershoot reflecting compensation of the assistive net force; force
partitioning hypothesis—a speed overshoot reflecting
compensation of the resistive force component; forcecontext hypothesis—no aftereffect as the context-cue is
absent.
In both experiments, subjects unambiguously exhibited trajectory aftereffects linked to the velocity-dependent component of force; rather than the net force,
or the force-context alternatives. An additional experiment involving a velocity-dependent and position-dependent force suggests that the velocity-dependent
component is partitioned relative to the background
load within a limb-based coordinate frame.
Hand motion was recorded at the fingertip by a
WATSMART or OPTOTRACK 3020 (Northern Digital, Waterloo, Ontario) motion detection system sampling at 200Hz while subjects reached with a
PHANToM device (Sensable Devices, Cambridge, MA).
This robotic device is lightweight, mobile in three dimensions, and was connected to a custom-molded cuff
that encased the metacarpal region of the hand without
obstructing the fingers.
In Experiments 1 and 2, the PHANToM was programmed to deliver a constant force, a velocity-dependent force, or a multi-force field to the hand during
forward reaching. Force is expressed in Newtons (N),
hand velocity in m/s ð_xÞ; and viscosity (V) in Ns/m.
During Experiment 1, the applied forces primarily
acted lateral to the hand’s forward motion (Fig. 1a–c).
The velocity-dependent force field acted rightward relative to the hand motion. Thereby, forward/backward
movements induced right/left forces, while right/left
movements induced backward/forward forces. We focused on the primary forward hand motion and the
associated rightward force; note that the hand trajectories showed some changes in their forward motion
(forward peak velocity and movement time) due to the
secondary backward/forward forces, but these were
quite variable and weak (p>0.05). The constant force
was always a constant leftward force, so its magnitude
and direction were independent of the hand motion.
The multi-force field was the combination of these two
forces.
Multi - force Velocity - dependent force Constant force
V x_ þf0;6gT N V x_ ; where V ¼f0;10;10;0g
f0;6gT N
During Experiment 2 the applied forces acted parallel
to the hand’s forward motion (Fig. 1a–c). The velocitydependent force field resisted the forward hand motion.
The constant force assisted forward hand motion with
a magnitude and direction independent of the hand
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within the movement time. Subjects were informed that
throughout the experiment they would encounter three
force conditions whose presence or absence would be
indicated after the first trial. This information was acMulti - force Velocity - dependent force Constant force curate and presented as such. Lastly, when the force
V x_ þf6;0gT N V x_ ; where V ¼ f0;0;0;10g
f6;0gT N
fields were removed, subjects were informed of the
transition, re-stabilized their limb, and were instructed
In Experiment 3, the robot applied a velocity-de- to ‘‘reach naturally, as if you had no prior experience
pendent rightward force identical to that in Experi- with the force field’’. All subjects indicated that they
ment 1 and a leftward position-dependent force that understood the instructions.
generated an approximately constant torque at the
elbow and shoulder; the multi-force field was the
combination of these two forces. An approximately Experimental design
constant joint torque was created by decreasing the
lateral force as the limb’s forward distance, and hence All experiments followed the same design as outlined in
moment arm, increased: Torque = Force · Moment Fig. 2. Each subject participated in a single session
Arm. The position-dependent leftward force began where he or she reached in blocks of ten separated by a
at a maximum value of 6 N and decreased with short rest period (1 min); a total of 210 reaches were
the forward hand position at a rate depending on the made during the experiment. Four force conditions were
initial distance between the hand and shoulder. The utilized: no-force, constant-only, velocity-only, and
initial hand–shoulder forward distance was determined multi-force. All subjects performed 30 consecutive
on a subject-by-subject basis (24–38 cm) such that the reaches in the no-force condition followed by 40 conlateral force at the hand decreased to 50–60% of its secutive reaches in the constant-only force condition.
initial value at the final forward position of hand: x¢ is The velocity-only and multi-force conditions were prethe ratio of the initial hand–shoulder forward distance sented either third or fourth and balanced across subover the current hand–shoulder forward distance.
motion. The multi-force field was the combination of
these two forces.
Multi - load Velocity - dependent force Torque - Conserving force
V x_ þP x’ V x_ ; where V ¼f0;10;10;0g
P x’,where P ¼f0;6g
Procedure
In all experiments, subjects reached forward to a single
square target 5 mm across, impressed on a tabletop
and along a line roughly in the parasagittal plane of their
right shoulder. The target placement required a mediumsized movement ranging from 22 to 24 cm across subjects. Reaches were completed under full visual feedback
in a well-lit room and always began with the entire arm
not contacting the table so that subjects would have to
actively stabilize the manipulandum against any forces
applied before reaching.
Our instructions were designed to allow unhurried
and naturalistic reaching movements. Subjects were
instructed to reach in a ‘‘single continuous movement’’
and ‘‘if you feel you are making a mistake do not
stop, slow down, or ‘stiffen up’; rather continue towards the target as best you can’’. Reaches were selfinitiated and required to remain within a window of
movement times, 800±100 ms. Therefore, the movements were moderately slow, but well within the range
used to study motor adaptation (Lackner and DiZio
1994; Goodbody and Wolpert 1998). This feature allowed the peak forward hand velocities to remain
under 600 mm/s so that the net force would always be
in direction of the constant force component in Experiments 1 and 2.
Subjects were given no strict criterion on their endpoint accuracy; they were simply told to land on target
jects. Two blocks of no-force trials separated all force
field conditions.
Analysis
Position signals were low pass-filtered offline at 10Hz and
again after each differentiation. Movement duration was
measured using a 5% peak velocity criterion for the start
and end. We examined both middle and terminal measures of the movements although we were primarily interested in the middle portion of the trajectory.
Therefore, all hypotheses are evaluated with regard to the
middle parts of the trajectory aftereffects. During Experiments 1 and 3 with the orthogonal perturbations, we
examined the hand’s lateral position (perpendicular displacement from a line connecting the start and target) at
the peak forward velocity and at the endpoint. In Experiment 2 with the parallel perturbations, we examined
the hand’s peak forward velocity and the endpoint along
the fore-aft axis. In all experiments, the critical information was the change from baseline during different
learning periods of the constant, velocity-only, and multiforce conditions. Unless otherwise specified, reported
measurements of the different learning periods are mean
and standard error deviations from the baselines.
Four learning periods were examined for each force
condition and for each measure: baseline, initial, final,
and post (Fig. 2). The baseline period included no-force
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blocks before the perturbations and sufficiently after the
perturbations to ensure complete re-adaptation to
normal conditions, in other words 9–16 reaches beyond
the first aftereffect (Lackner and DiZio 1994; Thoroughman and Shadmehr 2000). This period was considered the unbiased level of performance. The initial
period included the first reach for Experiments 1 and 3
and the mean of the first two reaches for Experiment 2
upon introducing the force perturbation. We utilized the
mean of the first two reaches for Experiment 2 because
on-axis components of trajectories show considerable
more variability than off-axis measures (Gordon et al
1994; Messier and Kalaska 1999). The final period was
measured as the average final block performance to the
force perturbation; this was taken as the most complete
learning during the brief exposure with the perturbation.
Lastly, the post period was comprised of the first reach
for Experiments 1 and 3 and the mean of the first two
reaches for Experiment 2 after removal of the force
perturbation. The post period was taken to reflect the
force representation underlying adaptation.
Repeated measures ANOVAs examined the stabilities
of the blocks that compose the baseline period (6
blocks · time) and the effect of each force field across
the learning periods (4 periods · 1 force field). These
were conducted separately for the middle and terminal
measures. t-Tests compared baseline vs initial, initial vs
final, and baseline vs post values to determine whether
the initial reaches were perturbed from baseline, whether
any adaptation occurred from the initial to final reaches
with the force present, and whether any adaptive afterFig. 3a–i Summary of
Experiment 1. a–c Rightward
velocity-dependent force
condition. d–f Leftward
constant force condition.
g–i Multi-force condition. Each
row has a cartoon of the subject
and robot-imposed force during
an idealized bell-shaped velocity
profile on the left; the middle
panels show the initial (black)
and post (red) hand trajectories
of individual subjects, green
trajectory is the group baseline;
the right panels show the mean
change in lateral position (mm)
from baseline measured at the
maximum forward velocity for
the initial, final, and post
periods; standard errors for
experimental and baseline
periods are indicated by error
bars and width of green lines,
respectively. Comparisons are
baseline vs initial, initial vs
final, and baseline vs post:
* p<0.05, ** p<0.01,
*** p<0.001
effects occurred upon removing the force. Significance
was set at p<0.05.
Results
Experiment 1: Perpendicular force fields
The baseline reaching pattern was characterized by
moderately straight and accurate hand paths with
smooth and single peaked velocity profiles. Subjects
reached quite accurately. Over all baseline trials, the
mean lateral bias and standard deviation from target
center was 1.4±2.4 mm. The maximum deviation
from a straight line averaged 3% of the movement amplitude (7/227 mm), the peak forward velocity averaged 470 mm/s, and the movements lasted 860 ms
on average. Importantly, the hand’s lateral position was
not significantly altered across blocks that formed the
baseline (see Fig. 2). This was the case at the hand’s
peak velocity (F(5,35)=0.94, p>0.45) and at the endpoint
(F(5,35)=0.32, p>0.8) indicating that a stable baseline
was achieved.
Perpendicular velocity-dependent force
The rightward velocity-dependent force (Fig. 1a), resulted in significant changes in the lateral position of the
hand measured at the peak forward velocity
(F(3,21)=98.3, p<0.001), while no effect was seen at the
endpoint (F(3,21)=0.8, p>0.5) (Fig. 3a–c; Table 1).
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Table 1 Deviations from baseline across learning periods with velocity-dependent and constant forces perpendicular to forward movement. Significant comparisons (p<0.05) of baseline vs initial, initial vs final, and baseline vs post values are in bold face
Velocity-dependent force
Constant force
Multi-force
Lateral deviation at peak velocity (mm)
Lateral deviation at endpoint (mm)
Initial
Final
Post
Initial
Final
Post
19.5±2.0
11.8±2.5
7.7±1.7
6.6±1.7
1.3±1.4
3.5±1.3
20±2.0
5.9±2.5
7.9±1.3
1.1±2.4
4.2±3.6
6.4±2.0
0.1±0.9
0.2±0.6
0.8±0.7
1.9±1.4
6.5±1.9
7.8±1.9
The initial behavior included significant rightward
deviations at the peak velocity (p<0.001). These lateral
deviations were largely absent by the movement’s completion; the endpoint of the first reach did not differ
from baseline (p>0.25).
Throughout the force exposure period, subjects
reached with single peaked velocity profiles that attained
a maximum of 490 mm/s on average and, consequently,
induced an average maximum rightward force of
4.9 N. The perpendicular force was increasingly compensated with continued exposure; the final deviations at
the peak velocity were significantly smaller than the initial deviations (p<0.001).
Upon removing the force, the subjects’ hand trajectories deviated left of baseline at the peak velocity
(p<0.001), opposite the previous velocity-dependent
force, and achieved an accurate endpoint (p>0.2).
Perpendicular constant force
The leftward constant force (Fig. 1b) induced significant
lateral changes of the hand at both the peak forward
velocity (F(3,21)=20.1, p<0.001) and endpoint
(F(3,21)=3.8, p<0.05) across learning periods (Fig. 3d–f;
Table 1). Although subjects accurately stabilized prior
to reaching, their initial reaches exhibited undercompensations to the constant force; the resulting leftward deviations from baseline were significant at the
peak velocity of the reaches (p<0.01), but not at the
endpoint (p>0.25).
With additional reaches, the deviations at the peak
velocity subsided (p<0.001) and by the final block the
trajectories were virtually indistinguishable from their
baseline patterns.
Upon removing the force, the subjects’ movements
were significantly deviated to the right at the peak velocity (p<0.05), opposite the previous constant force,
and ended with a terminal rightward error (p<0.01).
Perpendicular multi-force
The multi-force condition induced significant changes in
lateral displacement at both the peak velocity
(F(3,21)=28.8, p<0.001) and the endpoint (F(3,21)=17.1,
p<0.001) across learning periods (Fig. 3g–i; Table 1).
To achieve their baseline reaching pattern with the
multi-force field, subjects had to counter the velocity-
dependent decrease in leftward force using a matched
decrease in rightward force. Prior to reaching, subjects
achieved an appropriate muscular force to counter the
constant leftward perturbation. However, during the
initial reach, subjects misreached to the right as if perturbed by a rightward force, although actually due to the
decrease in leftward force from the manipulandum
(Fig. 1c). The rightward deviations at the peak forward
velocity were significantly different from the baseline
(p<0.01). In addition, the initial reaches displayed
‘‘over-corrective’’ terminal curvature as their trajectories
curved toward and crossed over the target position and
ended with significant leftward deviations (p<0.01).
The lateral deviations induced by the novel multiforce perturbation were increasingly attenuated with
additional reaches. By the final block, deviations measured at both the peak velocity (p<0.05) and the endpoint (p<0.05) were significantly smaller than those
during the initial reach.
Throughout the exposure period only 3/320 of the
peak velocities (40 reaches per subject) crossed the velocity threshold for inducing a net rightward force. The
average peak velocity of 485 mm/s resulted in an average minimum leftward force of 1.15 N (velocity-dependent force+constant force=4.85 N+6 N).
Upon removing the forces, subjects’ post trajectories
exhibited unambiguous leftward aftereffects at the
maximum velocity (p<0.001), opposite the previous
velocity-dependent component. The post trajectories
also showed an ‘‘over-corrective’’ terminal curvature
such that the hand landed to the right of the target
(p<0.01).
Experiment 2: Parallel force fields
Baseline and main effects
In the baseline blocks, subjects reached in moderately
straight and accurate hand paths with single-peaked and
smooth velocity profiles. Over all baseline trials, the
mean fore-aft bias and standard deviation from target
center was 1.6±3.4 mm. The maximum deviation
from a straight line averaged 3% of the movement amplitude (7/230 mm), the peak forward velocity averaged 490 mm/s, and the movement lasted 840 ms on
average. The blocks of movements forming the baseline
showed no systematic differences in either their peak
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velocity (F(5,35)=1.2, p>0.3) or endpoint (F(5,35)=0.49,
p>0.75), indicating interactions between force periods
were minimal and a stable baseline was achieved.
Parallel velocity-dependent force
Over all four blocks the average peak forward velocity
was 455 mm/s, which induced a peak resistive force of
4.55 N on average (Fig. 1a). Across learning periods,
this resistive force induced significant changes in the
peak velocity (F(3,21)=107.5, p<0.001) although forward endpoint behavior
remained unaffected
(F(3,21)=0.35, p>0.77) (Fig. 4a–c; Table 2).
The initial reaches exhibited a depressed forward
velocity (p<0.001) that necessitated an increase in the
movement duration if the hand were to travel the
baseline distance. In fact, the movement time was appropriately increased (p<0.001) to achieve an accurate
forward endpoint (p>0.1) on the initial reach. By the
final block of reaches, the peak forward velocity
(p<0.001) and movement time (p<0.001) had shown a
significant return toward baseline.
Upon removing the force, reaches exhibited an elevated forward velocity (p<0.01), opposite the previous
resistive force. Since the movement speed was elevated,
subjects needed to decrease their movement time if their
hands were to travel the appropriate distance. Both a
decrease in the movement time (p<0.01) and an accurate movement endpoint (p>0.2) were observed in the
post-force reach.
Fig. 4a–i Summary of
Experiment 2. a–c Resistive
velocity-dependent force
condition. d–f Assistive
constant force condition.
g–i Multi-force condition. Each
row has a cartoon of the subject
and robot-imposed force during
an idealized bell-shaped velocity
profile on the left insets. Left
panels show forward hand
trajectories vs time; the middle
panels show the initial (black)
and post (red) forward velocity
profiles of individual subjects,
green velocity profile is the
group baseline; the right panels
show the mean change in peak
forward velocity (mm/s) from
baseline for the initial, final,
and post periods; standard
errors for experimental and
baseline periods are indicated
by error bars and width of green
line, respectively. Comparisons
are baseline vs initial, initial vs
final, and baseline vs post:
* p<0.05, ** p<0.01,
*** p<0.001
Parallel constant force
The constant assistive force (Fig. 1b) had only a minimal affect on the forward movement (Fig. 4d–f;
Table 2). Across learning periods, neither the forward
peak velocity (F(3,21)=0.07, p>0.95) nor forward endpoint (F(3,21)=2.97, p>0.05) showed a significant effect.
The only significant change occurred upon removing
the force field after training as a small undershoot in the
forward endpoint (p<0.05).
Parallel multi-force
The multi-force condition (Fig. 1c) induced significant
changes in fore-aft reaching patterns in both peak
velocity (F(3,21)=16.1, p<0.001) and forward endpoint
(F(3,21)=16.9, p<0.001) across learning periods (Fig. 4
g–i; Table 2).
Subjects’ initial reaches exhibited an initial depression
in the peak velocity (p<0.01), as if perturbed by a
resistive force, although it was actually due to the decrease in assistive force from the manipulandum. Since
the perturbation slowed their forward velocity, subjects
needed to increase their movement time to travel the full
distance to the target. In fact, they did increase their
movement time on the initial reach (p<0.05), but
inappropriately such that the hand overshot the baseline
endpoint (p<0.01).
Throughout the exposure period, only 3/320 of the
peak velocities (40 reaches per subject) crossed the ve-
127
Table 2 Deviations from baseline across learning periods with velocity-dependent and constant forces parallel to forward movement.
Significant comparisons (p<0.05) of baseline vs initial, initial vs final, and baseline vs post values are in bold face
Velocity-dependent force
Constant force
Multi-force
Change in peak velocity (mm/s)
Forward deviation at endpoint
(mm)
Change in movement time (ms)
Initial
Final
Post
Initial
Final
Post
Initial
Final
Post
162±14
5±28
42±14
6±5
15±16
6±14
89±19
10±17
50±12
1±1
3.4±2.9
6.7±2.1
0.5±0.9
0.6±0.8
0.8±1.0
1.5±1.8
2.3±0.9
5.7±2.0
355±39
67±47
109±38
6±24
40±19
19±12
94±25
2±28
76±16
locity threshold for generating a resistive force; the
subjects’ average peak velocity of 486 mm/s resulted in
an assistive force of 1.14 N (velocity-dependent+bias=
4.86 N+6 N), on average.
By the final block of reaches, the deviations in peak
velocity (p<0.05), movement time (p<0.01), and the
forward endpoint (p<0.001) had significantly decreased.
Upon removing the forces, the subjects’ post reaches
exhibited a forward velocity elevated from baseline
(p<0.01), opposite the previous resistive component.
Subjects shortened their movement time in a compensatory manner (p<0.001) but this was excessive, resulting in an endpoint that undershot the baseline distance
(p<0.05).
Fig. 5a–i Summary of
Experiment 3. a–c Rightward
velocity-dependent force
condition. d–f Leftward torqueconserving force condition. g–i
Rightward velocity-dependent
and leftward torque-conserving
force condition. Each row has a
cartoon of the subject and
robot-imposed force during an
idealized bell-shaped velocity
profile on the left; the middle
panels show the initial (black)
and post (red) hand trajectories
of individual subjects, green
trajectory is the group baseline;
the right panels show the mean
change in lateral position (mm)
from baseline measured at the
maximum forward velocity for
the initial, final, and post
periods; standard errors for
experimental and baseline
periods are indicated by error
bars and width of green line,
respectively. Comparisons are
baseline vs initial, initial vs
final, and baseline vs post: *
p<0.05, ** p<0.01, ***
p<0.001
Experiment 3: Perpendicular velocity-dependent and
torque-conserving forces
Baseline and main effects
The baseline reaching pattern was characterized by
moderately straight and accurate hand paths with
smooth and single-peaked velocity profiles. Over all
baseline trials, the mean lateral bias and standard
deviation from target center were less than 1 mm and
±3 mm. The maximum deviation from a straight line
averaged 3% of the movement amplitude (6/229 mm),
the peak forward velocity averaged 490 mm/s, and the
movements lasted 860 ms on average. The hand’s lat-
128
eral position was not significantly altered across baseline
blocks—at either the peak velocity (F(5,35)=0.84, p>0.5)
or endpoint (F(5,35)=1.3, p>0.25)—indicating a stable
baseline was achieved.
Perpendicular velocity-dependent force
The initial trajectories were deviated rightward at the
peak velocity (p<0.001) and achieved an accurate endpoint (p>0.15). Throughout the force exposure period,
subjects reached with single-peaked velocity profiles that
attained a maximum velocity of 505 mm/s on average
and, consequently, induced an average maximum rightward force of 5.05 N. With continued exposure, the
perpendicular force was increasingly compensated; the
final deviations at the peak velocity were significantly
smaller than the initial deviations (p<0.001). Upon removing the force, the subjects’ hand trajectories deviated
left of baseline at the peak velocity (p<0.001), opposite
the previous velocity-dependent force, and achieved an
accurate endpoint (p>0.4) (Fig. 5a–c).
Torque-conserving forces
The torque-conserving force was induced by a leftward
force that decreased from 6 N at the movement’s beginning to 3–3.8 N at the movement’s end; this decrease depended on the subject’s initial and final forward
hand position. This load induced minimal systematic
changes in the reaching movement (Fig. 5d–f; Table 3).
We found no significant initial effect, final effect, or
aftereffect, either at the peak hand velocity or at the
endpoint; all comparisons had p>0.05.
Perpendicular multi-force
The combined perturbation condition was composed of
a perpendicular velocity-dependent force and a torqueconserving force. This combined load induced significant changes in the lateral position at the peak
velocity and endpoint of the reaching movement
(Fig. 5g–i; Table 3).
During the initial reach subjects significantly misreached to the right at the peak forward velocity
(p<0.001). In addition, the initial reaches displayed
‘‘over-corrective’’ terminal curvature as their trajectories
crossed over the target position and ended with significant leftward deviations (p<0.001).
Throughout the exposure period, the rightward velocity-dependent force, average peak velocity=520 mm/
s, interacted with the leftward position-dependent force,
resulting in a net force that reversed sign near the hand’s
peak velocity to a rightward force of 0.97 N, on
average.
By the final block, deviations measured at both the
peak velocity (p<0.01) and the endpoint (p<0.001)
were significantly smaller than those during the initial
reach.
Upon removing the forces, subjects’ hand trajectories
exhibited leftward aftereffects at the maximum velocity
(p<0.001), opposite the previous velocity-dependent
component, and achieved an accurate endpoint
(p>0.05).
Discussion
Principal results
Multiple simultaneously-acting forces are ubiquitous in
normal reaching movements and typically include the
inertial dynamics of the limb, the background force of
gravity, and forces associated with wielded objects and
surrounding media. As an initial step for understanding
motor adaptation to such complex conditions, we examined adaptation to a simple multi-force environment
composed of two opposing forces: a velocity-dependent
force and a larger constant force. Depending on whether
the adaptive process partitions between the underlying
force components, reacts to the net forces present, or is
cued to the force-context, the aftereffects could be opposite the velocity-dependent component, opposite the
net force, or absent.
When subjects first encountered the multi-force field
they produced a nominal force pattern to counter the
initial (leftward or assistive) force present prior to
movement onset. Upon moving, the imposed force decreased in magnitude so that subjects’ compensating
muscular force became excessive and (rightward or
backward) trajectory errors resulted. Thereby, subjects
exhibited initial trajectory errors opposite the actual
force imposed by the manipulandum; this relation contrasts with previous studies where the kinematic errors
were in the same direction as the force, since these studies had no significant background loads.
With continued exposure, the trajectory errors were
increasingly minimized, demonstrating that partial
Table 3 Deviations from baseline across learning periods with velocity-dependent and torque-conserving forces perpendicular to forward
movement. Significant comparisons (p<0.05) of baseline vs initial, initial vs final, and baseline vs post values are in bold face
Velocity-dependent force
Torque-conserving force
Multi-force
Lateral deviation at peak velocity(mm)
Lateral deviation at endpoint (mm)
Initial
Final
Post
Initial
Final
Post
23.9±4.8
4.3±2.6
10.1±2.5
5.2±2.0
3.2±2.3
1.9±2.1
21±3.3
4.4±3.2
14±2.1
4.2±2.4
2±2.1
14.2±2.7
0.0±0.7
0.0±1
0.9±1
1.0±1.5
1.3±0.6
2.6±1.3
129
adaptation to a novel multi-force field could occur
within a brief exposure period of 40 reaches. Most importantly, when we removed both forces, subjects exhibited trajectory aftereffects consistent with a
representation of the underlying velocity-dependent
component—leftward aftereffects opposite the rightward velocity-dependent component and speed overshoots opposite the resistive velocity-dependent
component. These aftereffects were typically small but
were observed in every subject’s behavior.
A number of precautions were adopted to ensure a
sound interpretation of the multi-force aftereffects.
First, our paradigm allowed us to dissociate the net force
and force partitioning hypotheses if subjects reached
below a threshold velocity. This requirement was largely
met, as very few (3/320) of the reaches exceeded
threshold in either Experiment 1 or 2. Second, we intended to examine involuntary responses, so subjects
were always informed that the perturbation was removed, re-stabilized their limb before reaching, and were
instructed to reach naturally. Our intention was
achieved insofar as subjects expressed surprise upon
misreaching in the post period and attributed their error
to an involuntary source like ‘‘my arm must have gotten
used to the force’’. Lastly, we utilized measures at the
hand’s peak velocity where cumulative feedback effects
and voluntary intervention is expected to be minimal
(Shapiro et al 2002, 2004). A peak velocity measure also
has the advantage of being linked to an unambiguous
landmark of the trajectory and has been utilized in other
studies (Krakauer et al 2000; Malfait et al 2002). In
addition, even earlier measures of the aftereffects also
showed significant changes, such as the hand’s lateral
deviation at 250 ms (Experiment 1: p<0.005) or changes
Fig. 6a–b Afttereffects from the multi-force and component force
conditions. a Experiment 1: Lateral position deviations of timenormalized trajectories from time-normalized baseline. Mean
deviation and standard errors are shown. All normalized to same
time-base. b Experiment 2: Forward position deviations of timenormalized trajectories from time-normalized baseline. Mean
deviation and standard errors are shown. All normalized to
percentage of baseline. Symbols are velocity-dependent (open
squares), constant (gray triangles), multi-force (black circles)
in the peak forward acceleration (Experiment 2:
p<0.01), which are consistent with force partitioning.
Therefore, force partitioning appears to be a general
strategy for rapidly adapting to multi-force fields either
perpendicular or parallel to the movement direction.
Auxiliary results
In Experiments 1 and 2, we had control conditions involving only the individual force components that together constituted the multi-force field, namely, the
velocity-only and constant-only conditions. The aftereffects of these conditions are relevant to understanding
adaptation to the multi-force condition. For both
perpendicular and parallel force conditions (1) the
velocity-only aftereffects are characterized by the largest
(rightward/forward) errors which peak at the middle of
the movement and are minimal by the movement’s end,
and (2) the constant-only aftereffects include a smaller
(leftward/backward) error that remains at the movement’s end. The aftereffects of the multi-force condition
include initial trajectory errors similar to the velocityonly aftereffect, but smaller, followed by over-compensatory terminal errors. This pattern suggests that the
multi-force aftereffect includes an influence from the
constant-force and becomes readily apparent when
comparing the three aftereffects side-by-side (Fig. 6a,b).
In fact, a linear sum of the separate velocity-only and
constant-only aftereffects is able to closely reproduce the
multi-force aftereffect, r2=0.98, indicting that their influences are largely independent (Fig. 7). We consider
this result consistent with previous studies that posit an
additive combination of separate ‘‘static’’/gravityrelated and ‘‘dynamic’’/movement-related force representations (Hollerbach and Flash 1982; Flanders and
Herrmann 1992; Soechting et al 1995; Gottlieb et al
1997). This process could be driven by a relatively simple
mechanism that measures the contrasting components of
the kinematic error relative to the subjects’ nominal
force pattern. It could be surmised that subjects adapt to
the underlying velocity-dependent component of the
multi-force field because the changing force pattern induces kinematic errors similar to those with only a ve-
130
Fig. 7 Additivity of aftereffects. The mean multi-force aftereffect
(x-axis) of Experiment 1 is plotted against sum of the mean
velocity-dependent and constant force aftereffects (y-axis). Unity
line and regression line are shown with solid and dashed lines
locity-dependent force (Tong et al 2002); likewise, the
aftereffect is smaller because the initial kinematic errors
are smaller. A second, related, possibility is that forces
are registered by sensors ‘‘directly’’ linked to the imposed load, like golgi tendons organs and cutaneous
inputs. We cannot distinguish between these possibilities
as our paradigm did not dissociate the changes in kinematics and changes in kinetics.
Our third experiment examined the adaptive component related to the constant force in Experiment 1. We
suspected adaptation associated with a constant force
might be attributed to encoding the background load
within a limb-based coordinate system such as joint
torque or muscle force—as occurs with velocity-dependent forces (Shadmehr and Moussavi 2000; Malfait et al
2002)—given that a constant force at the hand translates
to a variable joint torque during the course of the
movement. We predicted that if a constant limb-based
Fig. 8a–b Comparing velocity-only and multi-load aftereffects:
constant force or conserved torque background. a Comparing
lateral difference between the multi-load and velocity-only aftereffects normalized to the peak deviation of the velocity-only
aftereffect, mean and standard error indicated. b The mean
velocity-only aftereffect (x-axis) is plotted against the mean multiload aftereffect (y-axis). Symbols are Experiment 1 aftereffects
(open circles) and Experiment 3 aftereffects (black circles)
load does not require predictive adaptation, then a multiload field composed of a velocity-dependent force and a
constant limb-based load should induce adaptation specifically to the velocity-dependent component. Ideally,
the multi-load aftereffect and velocity-only aftereffect
would be identical. Experiment 3 tested this possibility
with a multi-load field composed of a rightward velocitydependent force and a leftward position-dependent force
designed to induce a virtually constant torque at the elbow and shoulder (see ‘‘Material and methods’’). The
resulting multi-load aftereffect was similar, though not
identical, to the velocity-only aftereffect. In comparison
with Experiment 1, the normalized magnitude difference
between the multi-force and velocity-only aftereffects
was smaller with the conserved torque than the constant
force (Experiment 1: maximum difference=74±19%;
Experiment 3: 33±19%) (Fig. 8a). In addition, the
aftereffects of the multi-force and velocity-only conditions showed a more similar temporal evolution with the
conserved torque than with the constant force (Experiment 3: r2=0.94; Experiment 1: r2=0.56) (Fig. 8b).
Therefore, a limb-based representation of loads better
accounts for the process of multi-force partitioning than
an extrinsic representation. Exploring these issues more
completely would require considering movementdependent reflex changes (Bennett 1994; Seki et al 2003)
and an apparatus that can independently apply limbbased perturbations to the movement, such as been done
in recent studies of primary motor cortex (Cabel et al
2001; Gribble and Scott 2002).
Conclusion
We demonstrated that motor adaptation to a multiforce field composed of a velocity-dependent and a
constant force partitions the velocity-dependent component from the net force actually imposed. This was
observed for multi-force fields both perpendicular and
parallel to a forward-directed reaching movement, and
appears to reflect a general mechanism of motor adaptation. These findings are consistent with previous studies suggesting that ‘‘static’’/gravity-related and
‘‘dynamic’’/movement-related components are separately represented by the nervous system (Hollerbach
and Flash 1982; Flanders and Herrmann 1992; Gottlieb
131
et al 1997). Such an organization would account for the
robust control of movement across different gravity
environments (Fisk et al 1993; Berger et al 1997; Papaxanthis et al 1998a; Kingma et al 1999; VernazzaMartin et al 2000; Baroni et al 2001) and at different
orientations to the same gravity environment (Virji-Babul et al 1994; Papaxanthis et al 1998b; Nilsen et al
2003). Here we have shown that the nervous system
possesses adaptive mechanisms which could support the
development of a partitioned organization.
Acknowledgements This research was supported by National
Aeronautics and Space Administration grants: NAG9-1263;
NAG9-1483.
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