Exp Brain Res (2006) 172: 331–342
DOI 10.1007/s00221-005-0340-3
R ES E AR C H A RT I C L E
Médéric Descoins Æ Frédéric Danion
Reinoud J. Bootsma
Predictive control of grip force when moving object with an elastic load
applied on the arm
Received: 17 October 2005 / Accepted: 14 December 2005 / Published online: 1 February 2006
Springer-Verlag 2006
Abstract Skilled object manipulation relies on the
capability to adjust the grip force according to the
consequences of our movements in terms of the resulting
load force of the object. Such predictive grip force
control requires (at least) two neural processes: (1) predicting the kinematic characteristics of the unfolding
arm trajectory and (2) predicting the load force on the
object resulting, among other factors, from the arm
movement. The goal of this study was to examine whether subjects can still anticipate the resulting load force
on the object when the moving arm is submitted to a
type of load that does not contribute to the object load.
To this end, 12 subjects were asked to rhythmically move
a 0.4 kg object under three different conditions. In the
first condition (ARM), an elastic cord was attached to
the upper arm. In the second condition, the elastic cord
was attached to the object (OBJECT). In the third
condition, the elastic cord was absent (NO ELAST). At
the kinematic level, results showed no influence of the
elastic cord on the pattern of movement of the object. At
the kinetic level, cross-correlation analyses between grip
force and load force acting on the object revealed significant correlations with minimal delays. In addition,
grip force profiles were similar under the ARM and NO
ELAST conditions, both differing from the OBJECT
condition. Overall, we interpret these results as evidence
that the neural processes involved in the prediction of
the arm trajectory and those involved in the prediction
of the load on the object held can take into account
different external force fields, thereby preserving the
functionality of the behaviour.
M. Descoins Æ F. Danion (&) Æ R. J. Bootsma
UMR 6152 ‘‘Mouvement et Perception’’,
Université de la Méditerranée, CNRS,
Faculté des Sciences du Sport, 163 avenue de Luminy,
13288 Marseille cedex 09, France
E-mail: [email protected]
Tel.: +33-491-172278
Fax: +33-491-172252
Keywords Grip-load force Æ Predictive control Æ
Human Æ Elastic loading Æ Rhythmical movement
Introduction
When holding an object with a precision grip, a minimal
grip force (GF) (normal to the contact surfaces) must be
applied to prevent the object from slipping under the
influence of external forces. In other words, GF needs to
be large enough to compensate for the total load force
exerted at the object–finger interface (tangential to
contact surfaces). According to Newton’s second law,
accelerating an object creates an inertial force. When
acting in a gravitational field, the total load force increases when an object is accelerated upward, while it
decreases when the object is accelerated downward.1
How does the central nervous system (CNS) deal with
such mechanical constraints? Earlier studies have shown
that, for self-produced hand-and-arm movements, GF
adjustments occur simultaneously with (or slightly
ahead of) movement-induced fluctuations in object load.
It has been suggested that the CNS uses the motor
command of the arm in conjunction with an internal
model of both the arm and the object to anticipate the
resulting load force and thereby adjusts GF appropriately (Johansson and Cole 1992; Flanagan and Wing
1995; Blakemore et al. 1998; Flanagan and Lolley 2001;
Flanagan et al. 2003).
Although the complex relation between arm movement motor commands and the load experienced at the
finger depends, among other things, on the type of load
being moved, experimental studies have revealed that
predictive control is effective in a wide variety of external
force fields. For instance, it has been shown that a tight
coupling between grip and load force was preserved in
both hyper- and micro-gravity (Hermsdorfer et al. 2000;
1
For a downward deceleration of 1 g, the total load force is equal
to zero. When the downward acceleration exceeds 1 g, the load
force re-increases.
332
Nowak et al. 2001; Augurelle et al. 2003; White et al.
2005). Similarly, it has been shown that subjects could
still successfully anticipate the resulting load force, when
the displacement of the object was constrained by an
elastic or a viscous force field (Flanagan and Wing
1997). Overall, these studies demonstrate that the mapping between arm motor commands and GF commands
can be tuned to accommodate various types of external
force fields. In other words, the internal representation
of the arm and the object dynamics can be updated with
respect to the physical environment in which the arm
and the object are to be moved.
Despite a considerable body of evidence in support of
the existence of a predictive mechanism dedicated to the
control of GF, a number of questions remain. In particular, it remains unclear whether the CNS uses identical or separate internal models of the physical
environment to predict the behaviour of the arm and the
object. Indeed, in order to anticipate the resulting load
force of the object, (at least) two successive neural processes are required: (1) to predict the kinematic characteristics of the unfolding arm trajectory (arm dynamics),
and (2) to predict the load force on the object associated
with this arm trajectory (object dynamics). The former
operation requires knowledge about the force field in
which the arm is moved, whereas the latter requires
knowledge about the force field in which the object is
moved. Because, in most studies, the arm and the object
were simultaneously exposed to the same external force
field (elastic, viscous, and/or gravitational), it is currently not clear whether the object and the arm dynamics
were predicted on the basis of a unique model of the
physical environment of the arm and object or on the
basis of separate models. One way to address this issue is
to investigate whether humans can still anticipate adequately the resulting load force on the object, when the
external force fields acting upon the arm and the object
become dissimilar.
To our knowledge, only two studies have examined
predictive GF control under a ‘‘force dissociation’’
protocol (Danion 2004; White et al. 2005). While holding an object in one hand, Danion (2004) investigated a
bimanual task that consisted in alleviating the arm by
lifting, with the other hand, a second, suspended object
attached to the arm by a string. It was found that when
the subjects lifted the suspended load (alleviating the
arm), they tended to behave as if the held object was
lighter (reducing the GF), a result indicating against
separate models of the physical environment, since the
load acting on the arm tended to be incorporated in the
anticipated load on the object. However, a number of
limitations should be noted. First, it was a bimanual task
and subjects may have difficulty in partitioning hand
actions (Li et al. 2002; Rinkenauer et al. 2001; Serrien
and Wiesendanger 2001a, b). Second, because several
prime movers of the wrist and fingers also cross the
elbow joint (flexor digitorum superficialis, extensor
digitorum communis; see Kendall et al. 1971), a pure
mechanical coupling could be suspected. Third, changes
in load were of a short duration (about 700 ms) and the
swiftness of the loading/unloading actions may be partly
responsible for the observed inappropriate GF adjustments.
More recently, White et al. (2005) compared GF
adjustments during cyclic vertical arm movements under
different gravity fields. Depending on the experimental
conditions, a ballast brace could be placed around the
wrist of the subject, so as to increase the inertia of the
limb, without changing the inertia of the held object.
Under each gravitational environment (0, 1, 1.8 g), it
was found that wearing the brace had virtually no effect
on the GF exerted, a result indicating in favour of a
separate assessment of the external loads acting on the
arm and the object. However, a number of limitations
should be noted. First, subjects were highly experienced
with parabolic flights and may therefore have developed
adaptive strategies. Second, while wearing the brace
magnified the inertial and gravitational loads exerted on
the moving arm, in the parabolic flight protocol the load
on the object is also determined by gravito-inertial
constraints. The change is therefore quantitative rather
qualitative. It remains unclear whether subjects can
adequately adjust GF when the moving arm is submitted
to a type of load that does not contribute to the object
load.
Overall the experiments of Danion (2004) and White
et al. (2005) appear to yield conflicting results. A subsidiary goal of the present study was therefore to reinvest the ‘‘force dissociation’’ paradigm in the context of
a task that would not suffer from the limitations inherent to these earlier studies (Danion 2004; White et al.
2005). To this end, we designed a uni-manual prehensile
task in which subjects were instructed to perform horizontal, oscillatory movements with an elastic cord
attached to their upper arm (condition ARM). In this
experimental condition, the moving arm is submitted to
an elastic load that does not contribute to the object
load. Therefore when a subject moves the arm slowly,
the external load applied on the arm changes as a
function of its current position, whereas the external
load of the object does not (i.e., GF does not need to
change). In order to evaluate behaviour in the ARM
condition, and for comparison purposes, we examined
two other experimental conditions. In the first condition,
referred to as OBJECT, the elastic cord was detached
from the arm and connected directly to the object, so
that both the arm and the object experienced the elastic
load. In the second condition, referred to as NO
ELAST, we removed the elastic cord all together, so that
the arm and the object were no longer exposed to the
elastic load. We reasoned that if GF profiles observed in
the ARM condition remained identical to those
observed in the NO ELAST condition, this implies that
neural processes involved in the prediction of the arm
trajectory and those involved in the prediction of the
resulting load on the object can take into account different external force fields. By contrast, if GF profiles
observed in the ARM condition resembled those of the
333
OBJECT condition, this implies that the object and the
arm dynamics are predicted on the basis of a unique
internal model of the environment (in which the external
force field acting on the arm overrules the one acting on
the object). Of course, the interpretation of the characteristics of the GF profiles depends on the characteristics
of the movement produced and we therefore also analysed the pattern of motion of the object.
Materials and methods
Subjects
Twelve unpaid healthy volunteers, six males and six
females (25.0±2.4 years of age; data are presented
henceforth as the mean ± inter-individual standard
deviation), participated in the experiment. All were
right-handed according to their preferential use of the
right hand during writing and eating. The mean body
height and mass were 1.73±0.08 m and 65.8±9.2 kg,
respectively. The subjects had no previous history of
neuropathies or trauma to the upper extremities. Subjects gave informed consent according to the procedures
approved by the University of the Mediterranean.
Apparatus
The grip device was basically the same as in the study of
Danion (2004). Five unidirectional sensors (ELPMT1M-25N, Entran) were used to measure the forces
exerted by each of the fingers. With subjects grasping the
object between the thumb and the four remaining
fingers, each sensor measured the normal force component (i.e., the force perpendicular to the sensor’s
surface). The sensors were mounted on an aluminium
handle (see Fig. 1a), with the four finger sensors separated by 25 mm intervals in the direction of finger
Fig. 1 Schematic drawing of the apparatus. a The handle was used
as grasping device. It was equipped with five unidirectional force
sensors, one unidirectional accelerometer, and one infrared LED. b
On its upper part, the grasping device was suspended from the
ceiling by a compliant elastic cord. During OBJECT, a stiffer set of
elastic cords was placed between the grasping device and the wall
adduction-abduction. This configuration was comfortable for all subjects. The surface of each transducer was
covered with medium grain sandpaper. To measure the
horizontal acceleration induced by the oscillatory
movement, the object was equipped with an accelerometer (EGAS-FS-5, Entran, ±5 g range). The signal of
this accelerometer was positive when the object was
accelerated toward the subject. An infrared camera
(C2399, Hamamatsu) tracking an infrared LED mounted on the upper part of the object served to measure the
horizontal (X) and vertical (Y) displacement of the object in the sagittal plane (X increased when the object
moved toward the subject, and Y increased when the
object moved upward). The total mass of the grip device
was 0.4 kg (or 3.92 N). However, within the task space,
the weight of the device was neutralized: the object was
suspended from the ceiling by a long compliant elastic
cord (stiffness = 3.8 N m1). This elastic cord was
present in all experimental conditions. By contrast,
depending on the experimental conditions another set of
elastic cords, much stiffer (stiffness = 37.2 N m1),
could be attached to the object or to the subject’s upper
arm (see Fig. 1b). In the latter condition, a rigid plastic
cuff, attached to the dorsal side of the subject’s upper
arm, allowed the elastic cords to be connected very close
to the axis of rotation of the elbow. A force sensor
(ELPM-T1M-125N, Entran) was placed between the
wall and the elastic cords to determine the traction force
exerted by the subject. The output of the sensors was
sent to a multi-channel signal conditioner (MSC12,
Entran). The analogue signals were sent to a BNC panel
(BNC 2090, National Instrument, Austin, TX, USA)
and were then input into a 16 channels 16-bit analogueto-digital converter (PCI-MIO-16XE50, National
Instrument, Austin, TX, USA). The accuracy of accelerometer, infrared tracking system, load cells for the
finger forces, and load cell for the elastic force was,
respectively, 0.002 g, 0.2 mm, 0.02 N, and 0.1 N. A
computer (Dell, Optiplex 240, USA) was used to control
facing the subject. During ARM, the set of elastic cords was
attached to the back to the subject’s upper arm. During NO
ELAST, the set of elastic cords was removed. During OBJECT and
ARM, the elastic load was measured by a unidirectional force
sensor. See ‘‘Materials and methods’’ for further details
334
the experiment, acquire, and process the data. A LabView (National Instrument, Austin, TX) program was
used to collect the signals from each sensor at the sampling frequency of 1000 Hz.
Procedure
The procedure is illustrated in Fig. 1b. During testing,
the subject was seated on a chair facing the apparatus. At
the beginning of each trial, the arm posture was the following: the shoulder was at about 50 of flexion, and the
elbow at 40 of flexion (0 corresponding to full extension). Using the right hand, the subjects grasped the
instrumented object between the thumb and the four
remaining fingers. The task was to move the object at a
prescribed frequency of 1.2 Hz over an amplitude of
20 cm, indicated by two targets. The movement was
performed along a horizontal axis that was parallel to the
sagittal plane. Subjects were instructed to synchronize
movement reversals in the vicinity of the targets with the
beeps of the metronome. The duration of a trial was 20 s.
Depending on the experimental conditions two
experimental factors were manipulated. The first factor
(TYPE) corresponded to the type of external load
applied. In the first condition, the elastic cord was
attached to the upper arm (ARM), so that the elastic
load was applied uniquely on the upper arm. In the
second condition, the elastic cord was attached to the
object (OBJECT), so that both the arm and the object
were submitted to the elastic load. The length of the
cords was adjusted so as to equalize the magnitude of
the elastic load in ARM and OBJECT. In the third
condition, the elastic cord was removed (NO ELAST),
so that no elastic load was applied on the object or on
the arm (apart from the elastic cord neutralizing the
weight of the object). The second experimental factor
(ZONE) was determined by the location in space where
the movement was performed. The rationale was that
manipulating the magnitude of the elastic load allowed
testing whether this factor influenced the coordination
between arm movement and GF. Two sets of targets
were used (see Fig. 1b). When the subject performed the
task between the first set of targets (Zone Z1), the
average elastic load was about 9 N (range: 5–13 N); in
Zone Z2, the average elastic load was about 13 N
(range: 9–17 N). The overlap between Z1 and Z2 was
10 cm. When the subject switched from one zone to the
other, the chair was displaced by 10 cm so as to preserve
a constant posture of the arm.
In order to estimate the effects of our experimental
manipulations on the magnitude of the net muscle torque required at the shoulder level, we used a two-link
inverse dynamics model (see Appendix). Because the
movement was performed with the hand and arm in
front of the longitudinal plane through the shoulder, the
effect of the gravitational forces acting on the two arm
segments was to pull the arm in. Because the contribution of inertial forces was relatively small (as compared
to gravitational forces), the net muscle torque required
at the shoulder was thus positive for both the forward
and backward movement of the object. With the elastic
cords attached to the arm or to the object creating a
force oriented in the opposite direction (pulling the arm
outward), the net effect of the elastic force field was to
reduce the magnitude of the required net muscle torque
at the shoulder. According to the model, a harmonic
motion of 20 cm amplitude at a frequency of 1.2 Hz in
Z2 implied a net muscle torque at the shoulder varying
between 3.4 and 7.9 Nm at the movement extremes in
the NO ELAST condition. Under the effect of the elastic
force field these variations were reduced to 1.4 and
3.6 Nm in the ARM condition and 1.3 and 4.3 Nm in
the OBJECT condition.
Each subject performed a block of five trials in each
of the six (3 TYPES · 2 ZONES) experimental conditions. The order of the blocks was pseudo-randomized
and counterbalanced across subjects. Prior to the
experiment, each subject performed two practice trials
(NO ELAST · Z1) to become familiarized with the task.
Subjects were neither suggested useful strategies nor
were they given instructions regarding suitable normal
forces (Ohki et al. 2002).
Once the main experimental conditions described
above had been completed, subjects performed several
post-experimental trials in order to evaluate the minimal
GF needed to hold the object. During these trials, the
elastic cord was connected to the object and the elastic
load was close to 6 N. Subjects were asked to gradually
release their grasp until the object slipped.
Data analysis
Several MATLAB routines were developed to analyse
the data. The kinematic and kinetic signals were first
filtered using a second-order dual-pass Butterworth
digital filter with a low-pass cut-off frequency of 10 Hz.
For the present purposes, GF was defined as the sum of
all finger forces. The total load force on the object
(LFO) was computed as the absolute value of the algebraic sum of the elastic (EL) and inertial loads (IL), that
is LFO =ŒEL + ILŒ. During OBJECT trials, EL was
considered as positive (during ARM and NO ELAST
trials, EL=0). By contrast, depending on the phase of
the movement IL could be either positive or negative.
When the acceleration of the object was directed toward
the subject, IL (the product of object mass and acceleration) had a positive value. As the amplitude of vertical displacements was small as compared to horizontal
displacements (less than 1 vs. 21 cm), we neglected the
contribution of the vertical displacements in the evaluation of IL.
Following the procedure described above, Fig. 2
presents the main signals used in this study; a typical
set of trials performed by the same subject is shown for
each TYPE. For analysis purposes, each trial was segmented into cycles on the basis of the horizontal po-
335
Fig. 2 Records of trial sections of subject S5 executing the
rhythmical task in zone Z2 with the elastic cord attached to the
upper-arm (ARM), with the elastic cord attached to the object
(OBJECT) and without the elastic cord (NO ELAST). From top
to bottom the panels show grip force (GF), total load force on
the object (LFO), acceleration of the object (A), and position of
the object (X). A and X vary smoothly in anti-phase, indicating
the harmonic nature of the movement pattern. In the absence of
an elastic force acting on the object (ARM and NO ELAST),
LFO varies as a function of the absolute value of A, with two
peaks per half-cycle of movement. In the presence of an elastic
force acting on the object (OBJECT), LFO is essentially
determined by this force, leading to a halving of the main
LFO frequency
sition signal. By definition, a cycle corresponded to a
movement of the object performed toward the subject,
followed by a movement away from the subject (see the
example in Fig. 2). Only the first 20 cycles of each trial
were retained for further analysis. Thus, with five trials
per condition, for each subject a total of 100 cycles was
analysed for each experimental condition. The following dependent variables were extracted within each
cycle. The amplitude of the horizontal displacement
and the duration of each cycle served to evaluate
whether subjects abided by the task instructions. To
characterize the kinematic characteristics of the oscillatory movement, we determined the positive and negative peaks of the velocity and acceleration signals; the
velocity signal was obtained by differentiating the signal
position using a three-point central difference method.
At the kinetic level, we computed the mean and
amplitude of LFO and GF signals. We also analysed
LFO and GF at the middle of each movement cycle
(i.e. maximal arm flexion), as the inverse dynamics
model presented in the Appendix indicated that the
largest differences between condition in shoulder muscle
torque were located there. To evaluate the strength of
the coupling between grip and total load force, crosscorrelations were computed between GF and LFO.
When the correlation was significant (90% of the
cycles), the lag was kept for further analysis; a positive
lag indicated that GF preceded LFO. Before statistical
analysis, each dependent variable was averaged over
100 values (100 cycles per condition).
In the post-experimental control trials, we sought to
identify the minimal GF (GFmin) necessary to prevent
the object from slipping between the fingers. Initiation of
slipping was determined with respect to the first time
derivative of the accelerometer signal. We used a critical
value of 1 g s1 to determine whether the object was
slipping or not (see Danion 2004). The GF at that specific value was taken as an estimate of GFmin. Over the
group of subjects, GFmin=6.4±1.1 N for an average
LFO = 5.7±0.4 N. For each Gmin value, an individual
estimate of the friction coefficient (l) was obtained by
dividing the load of the object by GFmin. We found
l=0.89±0.14, a value comparable to those reported
elsewhere for sandpaper (Burstedt et al. 1999; Danion
2004).
Statistical analysis
Two-way repeated measures analyses of variance
(ANOVA) were used as the main tool for statistical
analysis of the data. The first factor (TYPE) allowed
comparisons across types of constraint (ARM, OBJECT, NO ELAST). The second factor (ZONE) was
included in the analyses to assess differences between Z1
and Z2. Post hoc tests (Newman Keuls) were used
whenever a main effect of TYPE (or an interaction) was
found. Because coefficients of correlation do not follow
a normal distribution, we used a logarithmic transformation (z score) before conducting any statistical procedure. All tests were performed with P<0.05 as
significance criterion.
Results
Mean values (and inter-individual standard deviations)
of the variables discussed in the subsequent sections
are presented in Table 1 for all the experimental
conditions.
336
Table 1 Mean values and inter-individual standard deviations for all dependant variables in each experimental condition
TYPE
NO ELAST
OBJECT
ARM
Effects
ZONE
Z1
Z2
Z1
Z2
Z1
Z2
Variables
Xamp (cm)
Dur (ms)
LFO mean (N)
LFO amp (N)
LFO Xmax (N)
GF mean (N)
GF amp (N)
GF Xmax (N)
r
LAG (ms)
Vmin (cm s1)
Vmax (cm s1)
Amin (m s1)
Amax (m s1)
20.9±0.8
827±4
1.5±0.1
2.3±0.2
2.4±0.2
10.2±4.4
2.1±1.2
10.2±4.2
0.51±0.11
10±25
65±3
68±4
6.07±0.50
5.59±0.39
20.9±1.1
824±15
1.5±0.1
2.3±0.2
2.4±0.1
9.6±4.5
2±1.2
9.7±4.3
0.54±0.13
8±19
66±4
69±4
6.00±0.55
5.58±0.49
21.2±0.8
826±4
9.6±0.2
2.9±0.3
10.9±1.5
28.6±5.7
4±1.3
29.7±5.7
0.85±0.19
40±28
67±3
67±3
6.92±0.48
5.53±0.35
21.3±0.9
826±2
13±0.2
3.8±0.4
15.5±1.6
39.9±7.7
5.9±1.9
42.1±7.9
0.90±0.21
32±24
68±4
69±3
7.05±0.57
5.39±0.43
21±0.8
823±10
1.51±0.1
2.3±0.2
2.5±0.2
10.5±4.6
1.9±1.2
10.5±4.6
0.49±0.10
1±39
67±4
67±3
6.28±0.40
5.57±0.36
21.3±0.9
829±8
1.49±0.1
2.4±0.2
2.5±0.2
10±4
1.5±0.8
10.1±3.9
0.52±0.10
4±35
68±4
69±3
6.23±0.48
5.48±0.57
–
–
T,
T,
T,
T,
T,
T,
T,
T
Z
Z
Z
–
Z,
Z,
Z,
Z,
Z,
Z,
Z,
TZ
TZ
TZ
TZ
TZ
TZ
TZ
Two-way ANOVA was performed for each dependant variable. Significant effects of the experimental factors are shown on the right side
of the table (T = TYPE, Z = ZONE, TZ = TYPE · ZONE interaction)
Task performance
Amplitude of movement
The amplitude of movement (along the x-axis) did not
vary across experimental conditions. An ANOVA
revealed no significant main effects of the factors TYPE
(F(2,22)=0.9; ns) or ZONE (F(1,11)=2.8; ns), nor an
interaction between the two (F(2,22)=0.5; ns). On the
average, the amplitude of movement was 21.1±0.9 cm.
Cycle duration
The duration of a movement cycle did not vary over
experimental conditions. An ANOVA revealed no significant main effects of the factors TYPE (F(2,22)=0.03;
ns) or ZONE (F(1,11)=0.3; ns), nor an interaction
between the two (F(2,22)=2.5; ns). The average duration
of a cycle was 826±8 ms, close to the 833 ms cycle
duration of the metronome.
Grip and load force
ANOVA confirmed a main effect of ZONE
(F(1,11)=8986; P<0.001), as well as a significant TYPE
· ZONE interaction (F(2,22)=6115; P<0.001).
In line with the foregoing, the amplitude of variation
of LFO varied over conditions. An ANOVA revealed
significant main effects of the factors TYPE
(F(2,22)=73.1; P<0.001) and ZONE (F(1,11)=87.0;
P<0.05), as well as a significant interaction between
them (F(2,22)=99.1; P<0.001). While the amplitude of
LFO did not differ between NO ELAST (2.3±0.2 N)
and ARM (2.3±0.2 N), it increased in the OBJECT
condition, reaching 2.9±0.3 N and 3.8±0.4 N, in Z1
and Z2 respectively.
The LFO at maximal flexion of the shoulder (LFO
Xmax) revealed significant main effects of the factor
TYPE
(F(2,22)=525;
P<0.001)
and
ZONE
(F(1,11)=4513; P<0.001) as well as a significant interaction (F(2,22)=3048; P<0.001). Post hoc analysis
revealed that LFO values did not differ between NO
ELAST (2.4±0.2 N) and ARM (2.5±0.2 N), but
increased in the OBJECT condition, due to the maximum lengthening of the elastic cord, reaching
10.9±1.5 N in Z1 and 15.5±1.6 N in Z2.
Total load force on the object (LFO)
Grip force (GF)
Overall, all our LFO indices had similar values in ARM
and NO ELAST, but were significantly greater in OBJECT. Figure 3a presents the mean LFO for all experimental conditions. Of course, with the elastic cord
attached to the object, mean LFO increased
(11.3±1.8 N) relative to the ARM (1.5±0.1 N) and NO
ELAST (1.5±0.1 N) conditions; this view is supported
by a significant main effect of TYPE (F(2,22)=20227;
P<0.001). Similarly, as expected, the factor ZONE
affected LFO in the OBJECT condition only, reaching
9.6±0.2 N and 13.0±0.2 N in Z1 and Z2, respectively;
With respect to GF, its temporal profile was very similar
in the ARM and NO ELAST conditions, but it was
significantly altered in the OBJECT condition. Figure 3b presents the results observed under the different
experimental conditions for the mean GF. An ANOVA
yielded significant main effects of the factors TYPE
(F(2,22)=190; P<0.001) and ZONE (F(1,11)=39.4;
P<0.001), as well as a significant interaction
(F(2,22)=47.0; P<0.001). Post hoc analysis demonstrated that, in both zones, mean GF was similar in the
NO ELAST (9.9±4.4 N) and ARM (10.3±4.3 N)
337
conditions (see Fig. 2b). With the elastic cord attached
to the object, mean GF increased significantly, reaching
28.6±5.7 N in Z1 and 39.9±7.7 N in Z2.
Similar results were observed for the amplitude of
variation of GF. An ANOVA revealed significant main
effects of the factors TYPE (F(2,22)=24.5; P<0.001) and
ZONE (F(1,11)=7.2; P<0.05), with a significant interaction between them (F(2,22)=27.7; P<0.001). Post hoc
analysis demonstrated that, in both zones, the amplitude
of variation of GF was similar for the NO ELAST
(2.1±1.2 N) and ARM (1.7±1.0 N) conditions. In the
OBJECT condition, the amplitude of variation of GF
increased significantly, reaching 4.0±1.3 N in Z1 and
5.9±2.0 N in Z2.
The ANOVA on GF values at maximum shoulder
flexion (GF Xmax) revealed significant main effects of the
factors TYPE (F(2,22)=208; P<0.001) and ZONE
(F(1,11)=45.4; P<0.001), as well as a significant interaction between TYPE and ZONE (F(2,22)=52.5;
P<0.001). Post hoc analysis of the interaction revealed a
similar GF values for the NO ELAST (10.0±4.1 N) and
ARM (10.3±4.2 N) conditions, whereas GF increased
in the OBJECT condition, reaching 29.7±5.7 N and
42.1±7.9 N, respectively, in Z1 and Z2.
Coordination between GF and LFO
Figure 3c presents the mean coefficients of cross-correlation (r) between GF and LFO for each of the experimental conditions. Under all conditions GF covaried
with LFO; however, the strength of this coupling could
change. Indeed an ANOVA revealed main effects of
TYPE (F(2,22)=140; P<0.001) and ZONE (F(1,11)=33.9;
P<0.001), as well as a significant interaction between
them (F(2,22)=9.1; P<0.001). Post hoc analysis demonstrated similar results in the NO ELAST (r=0.53±0.12)
and ARM (r=0.50±0.10) conditions, with the height of
the coefficient not varying over zones. In the OBJECT
Fig. 3 Means of selected
variables under the ARM,
OBJECT, and NO ELAST
conditions when executing the
rhythmical task in zones Z1
(filled squares) and Z2 (open
circles). a Mean grip force (GF).
b Mean load force on the object
(LFO). c Mean (transformed)
coefficient of cross-correlation
between GF and LFO (R). d
Mean lag between GF and
LFO. Error bars indicate interindividual standard deviations
condition, the coefficient of cross-correlation between
GF and LFO increased, reaching 0.85±0.19 in Z1 and
0.90±0.21 in Z2.
Figure 3d presents the lag between GF and LFO for
all experimental conditions. Although the lag was close
from zero under all conditions, the ANOVA revealed a
significant main effect for the factor TYPE only
(F(2,22)=7.7; P<0.005). Post hoc analysis demonstrated
the GF–LFO lag was larger in OBJECT (35.8±25.9 ms)
than in either ARM (2.5±36.4 ms) or NO ELAST
(9.1±21.5 ms) conditions.
Movement kinematics
Peak velocity
Only subtle kinematic changes were observed across
experimental conditions. Peak velocity, whether it be in
the half-cycle with the object moving towards to subject
(Vmax) or away from the subject (Vmin), was not affected
by the factor TYPE (for Vmax: F(2,22)=0.2; ns; for Vmin:
F(2,22)=2.9; ns). As revealed by significant main effects
of the factor ZONE (Vmax: F(1,11)=12.9; P<0.01; Vmin:
F(1,11)=5.2; P=0.043), peak velocities were marginally
larger in Z2 than in Z1 (0.69±0.03 vs. 0.67±0.03 m s1
for Vmax and 0.67±0.04 vs 0.66±0.03 m s1 for
Vmin, respectively).
Peak acceleration
Under all conditions acceleration varied as a linear
function of position (see Fig. 4) so that peak acceleration was reached at movement extremities, indicating a
harmonic (i.e. quasi-sinusoidal) pattern of object
motion. The positive acceleration peak (Amax ; occurring
at maximal arm extension) was not affected by TYPE
(F(2,22)=1.6; ns) or ZONE (F(1,11)=1.6; ns) and reached
338
GF and object load force co-varied consistently in all
experimental conditions. Let us now discuss these results
in more detail and consider their implications for
movement control and GF control.
Kinematic invariance of object motion
Fig. 4 Hooke portraits (acceleration vs. position) of the object
motion under the ARM, OBJECT and NO ELAST conditions in
zone Z1 and Z2 for subject S5. Acceleration varies as a linear
function of position under all conditions, indicating the invariant
harmonic nature of the movement pattern. Note that in the
presence of an elastic force (ARM and OBJECT) the motor
commands to the arm must have changed, relative to NO ELAST,
to produce the same pattern of object motion.
5.52±0.43 m s2 on average. While independent of
ZONE (F(1,11)=0.6; ns), the negative acceleration peak
(Amin; occurring at maximal arm flexion, that is when the
object was close to the subject) was affected by the factor
TYPE (F(2,22)=22.1; P<0.001), with larger negative
accelerations for the OBJECT (6.98±0.52 m s2)
condition than for the ARM (6.26±0.43 m s2) and
NO ELAST (6.14±0.52 m s2) conditions.
Under all conditions moving the arm required dealing
with gravito-inertial constraints. Arm movement was
further constrained by an elastic force field in the ARM
and OBJECT conditions. Nevertheless, in accordance
with the task requirements, amplitude and frequency of
movement did not vary over experimental conditions (see
Table 1). Although not explicitly constrained by the task,
the kinematic form of the movement remained largely
invariant, revealing a quasi-sinusoidal (i.e., harmonic)
pattern, even in the presence of an additional external
elastic force field. Statistical tests revealed no differences
in kinematic characteristics (positive and negative
acceleration peaks, positive and negative velocity peaks)
when comparing the ARM and NO ELAST conditions.
Apart from slight shifts in the magnitude of the negative
acceleration peak, similar results were obtained under the
OBJECT condition. These results are in line with those
obtained by Levin et al. (2003) who studied a stardrawing task performed with or without an elastic load
applied to the forearm. Subjects were only asked to
preserve the amplitude and the duration of each stroke,
but they were found to also preserve the kinematic pattern of the arm movement (for similar results during
discrete arm movements see Bock 1990). In the presence
of an elastic force field (ARM and OBJECT), the patterns of muscle activation around the shoulder had to be
significantly modified in order to produce the same
kinematic pattern as in the NO ELAST condition (see
Fig. 4). These findings thus suggest that movement is
encoded in the brain in a rather abstract form that can be
dissociated from the concrete muscle activations patterns
(Bonnard et al. 1997; Levin et al. 2003).
Grip force regulation in NO ELAST and OBJECT:
confirmation of earlier reports
Discussion
The main goal of this study was to examine how GF is
regulated during object manipulation when the external
force fields acting on the arm and on the object are
dissociated. Overall, the results obtained revealed three
general points. First, at the kinematic level only minor
differences were observed across experimental conditions: the pattern of movement of the arm was relatively
invariant and did not depend on the presence or the
absence of the elastic cord. Second, at the kinetic level
no significant differences were observed between GF
profiles in the ARM and NO ELAST conditions, while
both were different from the GF profiles observed in the
OBJECT condition. Third, at the level of coordination,
In the first control condition (NO ELAST), the external
loads acting on the arm and on the object resulted from
gravito-inertial forces. In the second control condition
(OBJECT), these gravito-inertial forces were complemented by an elastic force. Nevertheless, because in the
OBJECT condition the elastic force acted simultaneously on the arm and the object, the external loads on
the arm and on the object continued to have a common
origin. In both conditions, results showed that GF
adjustments occurred simultaneously or slightly ahead
of the fluctuations in load force acting at the object–
finger interface (LFO). This finding is in agreement with
earlier observations obtained with point-to-point
movements performed against an inertial, viscous, or
339
elastic load (Flanagan and Wing 1997), or with rhythmical movements performed in the horizontal or vertical
plane (Augurelle et al. 2003; Flanagan et al. 1993;
Flanagan and Tresilian 1994; Flanagan and Wing 1997,
Kinoshita et al. 1996; White et al. 2005; Zatsiorsky et al.
2005). Overall, the lag (9–35 ms) between GF and LFO
observed in the present context was close to values reported elsewhere (e.g. 10 ms in Flanagan et al. 1993; 3
to 21 ms in Flanagan and Wing 1997). Similarly our
coefficients of cross-correlation (r values) during OBJECT (0.85–0.90) fall within the range of values reported
elsewhere (e.g. 0.71–0.96 in Flanagan et al. 1993; 0.76–
0.90 in Flanagan and Wing 1997).
Interestingly, the r values during NO ELAST (about
0.5, see also ARM) appeared rather low as compared to
r values obtained in OBJECT and earlier studies
(Flanagan et al. 1993; Flanagan and Wing 1997). We
suggest that this difference is not related to the nature of
the external load, since similar r values were obtained for
inertial and elastic load by Flanagan and Wing (1997).
More likely, the magnitude of LFO could be a determining factor. Note that in OBJECT, the average LFO
was almost ten times larger than in NO ELAST (and
ARM). If we assume that there is an incompressible
amount of noise in the GF signal, possibly due to execution-related neural processes (Van Beers et al. 2004),
the signal to noise ratio becomes more favourable as GF
increases from low to intermediate forces (Slifkin and
Newell 1999). This simple scheme would account, not
only for larger r values in OBJECT (as compared to
ELAST and ARM), but also for the slightly larger r
values in OBJECT-Z2 (0.90) as compared to OBJECTZ1 (0.85), as well as the lack of difference between
inertial and elastic load in Flanagan and Wing (1997) in
which the magnitude of LFO was equalized. However,
further studies need to test this hypothesis.
Grip force regulation in ARM: independent models
of the external environment
The main issue addressed in the present study was to
investigate whether participants can still anticipate the
resulting load force on the object, when the external
force fields acting on the arm and on the object are
dissociated. To achieve this goal our subjects were asked
to grasp an object and to perform rhythmical movements while a spring load was applied to their upper
arm. Anticipating the resulting load force on the object
necessarily requires knowledge of the external force
fields in which the arm and the object are moved. We
distinguished two alternative ways of dealing with the
external environment. Under the first hypothesis, the
arm and object dynamics call upon separate models of
the external environment, whereas under the second
hypothesis, both dynamics refer to a common model,
presumably dominated by the external environment of
the arm. The first hypothesis predicted that in the ARM
condition GF should remain adequately regulated with
respect to the actual load force on the object, whereas
the second hypothesis predicted that GF should be
regulated erroneously (i.e. as if the elastic force on the
arm was also acting on the object).
At least four observations in the present study speak
in favour of separate models of the external environment. Indeed, for all the indices related to GF, we were
unable to demonstrate any significant differences
between ARM and NO ELAST. First, average GF
remained stable in ARM, even in Z2 where the elastic
load could be greater than 15 N. Second, even when GF
was specifically analysed when the elastic load force was
maximal, further comparisons revealed no significant
difference between ARM and NO ELAST. Third, when
confronted with different magnitudes of the elastic force
(Z1 vs. Z2), the amplitude of GF remained comparable
in ARM and NO ELAST. Finally, no significant changes were observed when we analysed either the strength
or the lag of the GF–LFO relationship. Overall, these
results demonstrate that the regulation of GF remained
unaffected by the presence of an elastic constraint
applied to the arm. In other words, subjects continued to
anticipate adequately the load force on the object under
a force dissociation protocol. We are therefore encouraged to conclude that the neural processes involved in
the prediction of the arm trajectory and those involved
in the prediction of the object load take into account
different external force fields. This conclusion confirms
those of White et al. (2005), but our study goes one step
further by showing that the coupling between GF and
LFO is preserved even when the external load acting on
the arm and on the object are structurally different.
A subsidiary goal of the present study was to demonstrate that GF is driven by the mechanical consequences of our arm actions at the object location,
independent of the kinetic (i.e., muscle torque related)
aspects of the arm movement. Results from the comparisons of ARM versus NO ELAST, on the one hand,
and comparisons of ARM versus OBJECT, on the other
hand, support this view. First, as can be seen in Fig. 6,
the net muscle torque necessary to sustain an oscillatory
movement of the shoulder was substantially reduced in
ARM as compared to NO ELAST (the average muscle
torque being almost halved). However, despite this
considerable difference in net muscle torque, subjects
demonstrated similar GF profiles in ARM and NO
ELAST. By contrast, the net muscle torque pattern
required to sustain the oscillation of the shoulder was
(relatively speaking) quite similar in ARM and OBJECT
(see Fig. 6). However, despite this similarity of arm
movements in kinetic (as well as kinematic) terms, GF
profiles in ARM and OBJECT were markedly different
to accommodate the presence (or absence) of the elastic
load at the object site (see Fig. 3). Overall we conclude
that, whether the arm movement is facilitated or not by
an external force is not directly relevant for the modulation of GF. What counts, first and foremost, are the
consequences of the arm movement with respect to the
load on the object.
340
Finally, the present study did not confirm the
observations of our earlier study (Danion 2004) in which
a ‘‘force dissociation’’ paradigm was also used. However, as already addressed in the Introduction, several
methodological aspects restrict the bearing of those
earlier observations: Danion (2004) used a bimanual
task, involving multi-joint-muscles, and the loading/
unloading procedure was very brief. At this stage, it is
difficult to state which of those factors is responsible for
the conflicting results obtained since they were all
manipulated simultaneously. Interestingly, in the present
study, as well as in the study performed by White et al.
(2005), subjects performed a uni-manual task. Future
research will need to address this issue.
with
ElastT = 0:
in the NO ELAST condition
ElastT = (L1 cos a1L2 sin d)k(x+Dx0):
in the OBJECT condition
ElastT = L1 cos a1k(x+Dx0):
in the ARM condition
Concluding comments
Based on the present set of data, we conclude that the
internal model hypothesized for the predictive control of
GF must include (at least) two separate representations
of the external environment. The first accounts for the
external force field acting on the moving arm, and is
implicated in the process of predicting the ongoing arm
trajectory. The second accounts for the external force
field acting on the object and is involved in the process
of predicting the load force on the object associated with
the predicted arm trajectory. Obviously, whether the
CNS makes use of an internal model of the motor
apparatus in planning and executing goal-directed
movements is still controversial. However, whatever the
exact nature of the neural processes involved in the
regulation of GF, our results demonstrate that those
processes can take into account different external force
fields on the arm and the object without compromising
the overall functionality of the behaviour.
Fig. 5 Geometrical model of the arm. See text for further details
Appendix
A two degrees of freedom model was used to estimate
the net muscle torque acting at the shoulder under the
experimental conditions. The model included shoulder
and elbow joints rotations, uniquely in the sagittal plane
through the shoulder. Net muscle torque acting at the
shoulder joint was computed using standard Newtonian
equations of motions (see below). The set of equations
used closely resembles the set provided by Zatsiorsky
(2002) for the inverse dynamics of a two-link chain. For
the present purposes, we introduced an additional term
to account for the torques generated by the elastic cord.
At the shoulder joint, the net muscle torque is:
MuscT ¼ I1 þ m1 r12 þ I2 þ m2 L21 þ r22 þ 2L1 r2 cos a2 €a1
þ I2 þ m2 r22 þ L1 r2 cos a2 €
a2 ðm2 L1 r2 sin a2 Þa_ 22
ð2m2 L1 r2 sin a2 Þa_ 1 a_ 2 þ ½m1 gr1 sin a1
þ ðm2 m0 ÞgðL1 sin a1 þ r2 sin ða1 þ a2 ÞÞ ElastT
ð1Þ
Fig. 6 Temporal profiles of the resulting net muscle torque at the
shoulder joint during one movement cycle (T1 fi T2 fi T1). The
figure compares the three experimental conditions in ZONE 2 (NO
ELAST, OBJECT, and ARM)
341
m: mass
I: moment of inertia around the proximal joint
r: location of mass centre with respect to the proximal
extremity
k: stiffness of the elastic cord (37 N m1)
Dx0: initial lengthening of the elastic cord at T1 (0.15 m
in ZONE 1, and 0.25 m in ZONE 2)
x: additional lengthening of the elastic cord due to the
task (from 0 to 0.2 m)
m0: mass of the object (0.4 kg)
g: gravity (9.81 m s2)
These equations represent the net muscle torque
produced by all the muscles around the shoulder. The
joint angles (a1, a2, and d) are defined in Fig. 5. The
subscripts ‘1’ and ‘2’ refer to segment 1 and 2. Segment 1
corresponds to the upper arm, and segment 2 corresponds to the system composed by the forearm, hand,
plus the object. The object was considered as a point
mass. Limb segment inertia, centre of mass position, and
mass were computed from regression equations (Zatsiorsky and Seluyanov 1983) in combination with the
group average body height and mass (1.73 m and
65.8 kg). The following values were obtained:
L1 ¼ 0:322 m;m1 ¼ 1:76 kg; r1 ¼ 0:13 m; I1 ¼ 0:0034 kg m2
L2 ¼ 0:376 m;m2 ¼ 1:89 kg; r2 ¼ 0:235 m; I2 ¼ 0:0224kg m2
In the present experiment, we did not record the
instantaneous angles at the elbow and shoulder joints.
However, because our two-link chain is not kinematically redundant with respect to the object position, these
angles can be computed using trigonometric functions.
We assumed that the task was performed in such a way
that when the subject held the object at T1, a1=50 and
a2=40. Given this assumption, trigonometric functions
predict that when the object is at T2 (0.2 m away from
T1), these joint angles become a1=10 and a2=95.
The next stage consisted in computing the angular
profiles (and their time derivatives) associated with a
horizontal sinusoidal movement of the object such that:
xðtÞ ¼
A
A
sin ð2pFt pÞ þ
2
2
ð2Þ
with F=1.2 Hz, and A=0.2 m
Within these conditions, Eqs. 1 and 2 were solved
using a fixed 1-ms step. The result of this simulation is
shown in Fig. 6. The computation of MuscT was performed three times: without the elastic cord (NO
ELAST), with the elastic cord attached to the object
(OBJECT), and with the elastic cord attached to the
elbow (ARM). As can be seen, with respect to NO
ELAST, the overall effect of the elastic cord is to
decrease MuscT. In ZONE 2, we found that MuscT
dropped by 56% in ARM, and by 44% in OBJECT.
Even in ZONE 1, those drops remained substantial
(respectively 41 and 30%).
Acknowledgements The authors would like to thank Vladimir
Zatsiorsky, Guillaume Rao, and Eric Berton for their critical
evaluation of the biomechanical model. The authors are also
grateful to the anonymous reviewers for their helpful comments,
especially with regard to the limitations of this study. Frédéric
Danion is supported by the Centre National de la Recherche Scientifique.
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