Exp Brain Res (2006) 168: 88–97
DOI 10.1007/s00221-005-0070-6
R ES E AR C H A RT I C L E
Slobodan Jaric Æ Jeffrey J. Collins Æ Rahul Marwaha
Elizabeth Russell
Interlimb and within limb force coordination in static bimanual
manipulation task
Received: 20 March 2005 / Accepted: 13 May 2005 / Published online: 3 August 2005
Springer-Verlag 2005
Abstract The aim of the study was to compare the
coordination of hand grip (G) and load force (a force
that tends to cause slippage of a grasped object; L) in
static bimanual manipulation tasks with the same data
obtained from the similar dynamic tasks. Based on the
previous findings obtained from dynamic tasks, it was
hypothesized that an increase in the rate of L change
would be predominantly associated with a decrease in
the coordination of the within limb forces (coordination
of G and L of each hand as assessed through the correlation coefficients), while a decrease in coordination of
interlimb forces (between two G and two L) will be less
pronounced. Regarding the pattern of modulation of G,
the same increase in L frequency was also expected to be
associated with a decrease in G gain and an increase in G
offset (as assessed by slope and intercept of the regression lines obtained from G to L diagrams, respectively),
as well as with an increase in average G/L ratio. Subjects
exerted oscillatory isometric L profiles by simultaneous
pulling out two handles of an externally fixed device
under an exceptionally wide range of L frequencies
(0.67–3.33 Hz). The results demonstrated relatively high
correlation coefficients between both the interlimb and
within limb forces that were only moderately affected
under sub-maximal L frequencies. Furthermore, the
hypothesized changes in G gain and offset appeared only
under the highest L frequency, while the G/L ratio remained unaffected. We conclude that, when compared
with the dynamic tasks based on the unconstrained
movements of hand-held objects that produce similar
pattern of L change, the static manipulation tasks
demonstrate a consistent and highly coordinated pattern
of bilateral G and L under a wide range of frequencies.
S. Jaric (&) Æ J. J. Collins Æ R. Marwaha Æ E. Russell
Department of Health, Nutrition, and Exercise Sciences,
Human Performance Lab, University of Delaware,
547 S. College Av., Newark, DE 19716, USA
E-mail: jaric@udel.edu
Tel.: +1-302-8316174
Fax: +1-302-8313693
However, the neural mechanisms that play a role in the
revealed differences need further elucidation.
Keywords Hand Æ Grip force Æ Load force Æ
Correlation Æ Frequency Æ Oscillatory pattern
Introduction
\A number of daily activities involve bimanual manipulation, such as repositioning hand-held objects, operating
tools, or using external supports. This manipulation requires coordination of both the interlimb and within limb
forces for successful task performance. The interlimb
coordination refers to the coordination of forces applied
by two hands against the load imposed through a handheld object or objects, which is required for successful
manipulation (Kelso et al. 1979; Scholz and Latash 1998).
The within limb coordination refers to the requirement of
keeping the grip force (G) of each hand within a certain
range relative to the acting load (in further text, load force;
L) that not only prevents slippage, but also avoids
excessive G that can crush the object or cause rapid fatigue
(Johansson and Westling 1988; Flanagan and Wing
1995). The following three paragraphs will specifically
address the basic properties of the within limb force
coordination, the interlimb force coordination, and the
pattern of G modulation regarding changes in L. Particular attention will be given to the effects associated with an
increase in frequency of L change.
If G is limited to the normal force component acting
upon the surface of a hand-held object, while L is the
tangential force tending to cause slippage, a continuous
adjustment of G–L variations caused by vertical shaking
and point-to-point movements (Flanagan and Wing
1995, 1997; Nowak et al. 2002; Zatsiorsky et al. 2004),
or gravity changes due to parabolic flight (White et al.
2005) has been reported with virtually no time lag
between them (Flanagan and Wing 1995; Scholz and
Latash 1998; Blank et al. 2001; Gysin et al. 2003;
89
Zatsiorsky et al. 2004). Based on these observations, it
has been concluded that the coordination of G and L is
controlled by predictive, feed-forward mechanisms (Johansson and Westling 1984; Flanagan and Wing 1995)
providing a relatively stable grip-to-load (G/L) ratio
with a small safety margin that prevents slippage (Johansson and Westling 1984; Serrien and Wiesendanger
2001c, d). Both the low level of the G/L ratio and a high
level of modulation of G with respect to L proved to be
difficult to maintain under increased difficulty of the task
performed, such as an increase in frequency of vertical
point-to-point movements or vertical shaking of handheld objects or dissimilar actions of two hands (Flanagan and Wing 1995; Blank et al. 2001; Serrien and
Wiesendanger 2001a, b, c, d; Bracewell et al. 2003;
McDonnell et al. 2004; Zatsiorsky et al. 2004). Nevertheless, it has been suggested that G/L ratio could be a
controlled variable that is adjusted to the friction of the
contact surface (Flanagan and Wing 1995; Burstedt
et al. 1999; Serrien and Wiesendanger 2001c). There are
several under-explored aspects of the within limb force
coordination regarding potential differences between the
static and dynamic tasks. For example, most of the
mentioned studies have been based on unrestricted
movements of a hand-held object, while there are virtually no data on static tasks that allow for better control of the experimental conditions. Although the
important role of glabrous skin receptors in assessment
of sufficient G (Johansson and Westling 1984; Monzee
et al. 2003) may be unaffected by switching from static
to dynamic task conditions, Zatsiorsky et al. (2004)
suggested partly independent mechanisms for the
adjustment of G to static and dynamic components of L.
In addition to the within limb coordination of G and
L, bimanual manipulations also require interlimb coordination of two G and two L exerted by each hand. The
interlimb force coordination has been demonstrated in
both similar and dissimilar tasks performed with two
hands (Scholz and Latash 1998; Ohki and Johansson
1999; Perrig et al. 1999; Li et al. 2001; Serrien and
Wiesendanger 2001a, b, c, d; Bracewell et al. 2003).
When applied on the dissimilar bimanual tasks, an increase in the frequency is also believed to lead to
‘bimanual assimilation’ causing either gradual or abrupt
switching to similar bimanual actions (Kelso et al. 1979;
Kelso 1984; Spijkers and Heuer 1995; Serrien and
Wiesendanger 2001d; Bracewell et al. 2003). A number
of authors explained these phenomena by neural contralateral interactions that particularly affect dissimilar
tasks performed by two hands (Swinnen et al. 1991). As
a consequence, one could expect that the coupling of two
lateral G or L could be relatively stronger at higher
frequencies. However, the interlimb coordination of two
lateral G and L has not been compared with the within
limb coordination of the same forces exerted in a
bimanual manipulation task. Importance of this comparison has been either explicitly or implicitly stressed in
a number of recent studies. For example, the level of
interference between motor commands for one and both
arms is generally unknown (de Oliveira et al. in press).
Although it could be task specific (Bracewell et al. 2003),
and characterized by various transient phenomena
(Ohki and Johansson 1999; Steglich et al. 1999), the
question remains whether the G/L ratio is a ‘local’ (i.e.
specified for each hand separately) or ‘global parameter’
(specified for both hands; Serrien and Wiesendanger
2001c, d).
Regarding the pattern of G modulation with respect to
change in L, an increase in frequency of vertical shaking of
an object leads to a gradual decrease in both the consistency and range of G modulation with respect to L, while
the overall G/L ratio increases (Flanagan and Wing 1993,
1995; Zatsiorsky et al. 2004). As a result, the frequency
associated changes in the regression lines calculated from
the G–L diagrams demonstrate a decrease in slope (G
gain) associated with an increase in intercepts (G offset) of
G modulation with respect to changes in L, as well as an
increase in the average G/L ratio (increase in G offset).
This phenomenon has been explained in different ways.
Flanagan and Wing (Flanagan and Wing 1993, 1995)
suggested that the G gain and the G/L ratio vary independently across the conditions. In particular, to economize muscular effort, the CNS keeps a high G gain in low
frequency tasks, which results in a low and stable G/L
ratio (Johansson and Westling 1984). Due to a high cost of
G modulation in rapid (e.g. high frequency) movements,
the system reduces G gain but, therefore, increases the G
offset and G/L ratio to prevent slippage. Note that the
hypothesized behavior could apply to both the static and
dynamic manipulation conditions. Conversely, Zatsiorsky et al. (2004) decomposed the grip force into a ‘static
fraction’ that is responsible for counteracting L solely
originating from the object’s weight (and, thus, assessed
from static conditions), a ‘stato-dynamic fraction’ that
reflects a steady increase in static fraction due to shaking
the object, and a ‘dynamic fraction’ originating solely
from modulation of G with respect to the inertial component of L. They proposed these fractions to be controlled partly independently, presuming that the CNS was
able to distinguish among them. However, the hypothesized behavior applies only to the tasks performed under
dynamic conditions since static manipulation does not
produce the inertial component of L.
Within the present study, a bimanual static manipulation task was tested, while both G and L of two hands
were recorded. Specifically, the subjects exerted laterally
symmetric pulling L in an oscillatory fashion under a wide
range of frequencies paced by a metronome. The first aim
was to explore the interlimb and within limb coordination
of G and L in the tested task. We hypothesized that the
within limb coordination (as assessed through the correlation coefficients between G and L of each hand) will be
more affected by an increase in L frequency than the interlimb coordination (i.e. the correlation between two G
and two L). The second aim of the study was to explore the
pattern of G modulation, in particular, the effect of the L
frequency on the G gain, G offset and the average G/L
ratio. Specifically, results in line to those observed under
90
dynamic conditions would support the suggested frequency related trade-off between the G gain and G offset,
and the G/L ratio as a general strategy of the CNS
applicable to both dynamic and static manipulation tasks.
Alternatively, a difference from the previous findings
based on the unconstrained movements would suggest
that the within limb force coordination of manipulative
tasks could be task specific regarding the static and dynamic manipulation conditions.
Methods
Participants
The study was performed on ten healthy human volunteers (six women and four men) aged between 19 and
29 years. Subjects completed the ten-point Edinburgh
Inventory to quantify their handedness (Oldfield 1971).
Nine subjects appeared to be right handed and one left
handed, all showing the maximum scores on the applied
scale. The experimental procedure was conducted in
accordance to Declaration of Helsinki and approved by
the Human Subjects Review Board of the University of
Delaware.
Experimental device
The experimental device is shown schematically in
Fig. 1. It consists of two coupled handles covered by
nylon and four force transducers (miniature strain gauge
Fig. 1 Schematic
representation of the
experimental device. The circles
illustrate the positions of four
fingers and the thumbs applying
a precision grip on two lateral
handles of the device. The
transducers recording both the
right and left grip force, as well
as the right and left load force
(L indicated with arrows)
exerted horizontally in the
direction of compression/
tension are depicted with
squares and while the direction
of the recorded force is
indicated with arrows
load cells WMC-50, Interface Inc., Atlanta, GA, USA)
allowing simultaneous recording of the two independent
contralateral compression/tension forces (in further text
‘load force’ (L)) exerted along the long axis of the device
and the grip forces (G) of each hand. The device was
fixed in a horizontal position, symmetrically with respect
to the subject’s sagittal plane, while the height of the
device was individually adjusted for each subject to
provide a ‘comfortably position’. Subjects sat comfortably in a chair and held the device in front of them with
the tips of all five fingers (‘pinch grip’) with the elbows
supported by pads positioned on the top of the table in
front of the subject and forearms oriented vertically. The
same handle aperture of 4.5 cm was applied in all subjects. Note that we were interested in the overall L frequency effects rather than the across the subject
comparisons. Therefore, we adjusted the aperture to a
‘comfortable size’ for our subject instead of recording
the hand sizes and adjusting the device aperture to each
subject individually.
Experimental procedure
The experimental procedure consisted of three consecutive steps. First, the minimum G/L ratio that prevents
slippage (‘slip point’) was assessed according to methods
applied in previous studies (Flanagan and Wing 1995).
In short, subjects held the a distal end of the device’s
handle stationary in vertical position with one hand
while gradually reducing their grip force. The ratio between G at the moment slippage began (recorded as an
91
abrupt decrease in L) and the weight of the device
(corresponding to L) was calculated as the slip point.
Second, the maximum pinch force of each hand was
recorded by a pinch dynamometer (JAMAR, range
200 N). Finally, the subjects were tested on a bimanual
manipulation task performed under isometric conditions. They were asked to hold the device with the tips of
their fingers and pull the handles laterally equally with
both hands (i.e. to produce L in the direction of tension)
and, thereafter, to relax, which was expected to provide
an oscillatory L pattern. To provide a feedback, the
current average of the two lateral L exerted by the
subject’s right and left hand was shown on a computer
screen, as well as two horizontal lines depicting the
target levels for the peaks of L. The target level for the
minimum peak of L was zero, while the target level of
the maximum peak of L corresponded to 25% of the
tested maximum pinch G since a pilot experiment suggested that exerting L below 30% of the maximum pinch
G would not cause fatigue. The rationale of this approach was the findings that for the given body position
the subjects’ ability to exert high L was limited by their
G, as well as the presumption of proportionality of the
subjects’ ability to exert G and L. To familiarize with the
task, the subjects were allowed to practice for 15 min
prior to the experiment.
The main experimental factor applied was the frequency of the oscillatory L profile paced by a metronome. Preliminary experiments revealed that most of the
subjects start switching from feed-forward to feedback
control of the exerted L at the frequencies below 0.6 Hz,
which presumably causes a change in involved neural
mechanisms. Specifically, the subjects reported that they
were able to ‘‘draw entire cycle of the force’’ using online corrections based on the current visual feedback,
instead on just relying on previous L peaks for correcting the forthcoming ones. In addition, the highest L
frequency that the subjects were able to follow was between 3.33 and 4 Hz. Therefore, five frequencies were
selected to cover the interval between these two limits
(specifically, 0.66, 1.33, 2, 2.67 and 3.33 Hz) presumably
providing feed-forward control mechanisms of the tested
trials. The order of the corresponding five experimental
trials (i.e. one trial per each frequency) was randomized.
Data processing
The duration of each trial was 12 s. However, to avoid
analyzing the initial adjustment to the instructed L level,
the final 9 s were taken for further analysis. The signals
from all four force transducers were digitized on line at
the rate of 200 Hz, low-pass filtered (10 Hz) and stored
on a computer disk for further analysis.
To assess the task performance, constant and variable
errors were calculated from the differences between the
consecutive peaks of the averaged L and the aimed
maximum level of force depicted at the screen. To assess
the coordination of the recorded forces, the cross cor-
relations between the pairs of both the interlimb (G
versus L of each hand) and within limb (G versus G and
L versus L) forces were calculated. The cross correlation
between two lateral G/L ratios was also calculated.
However, the time lags proved to be small relative to the
durations of particular L cycles. In particular, when
averaged across the subjects and hands, the L frequencies 0.67, 1.33, 2, 2.67 and 3.33 Hz revealed the time lags
(Mean ± SD) 3.6±7.3, 1.6±7.1, 2.8±3.9, 4.4±5.5 and
6.4±5.2 ms (positive sign meaning that G precedes L),
respectively. Therefore, we decided to present only the
Pearson’s correlation coefficients instead. In addition to
the G versus L correlation coefficients, we also assessed
the pattern of G modulation by calculating G gain and
offset relative to L changes, as well as the average G/L
ratio. The G gain and offset were obtained from the
slope and intercept, respectively, of the linear relationship between G and L assessed from a linear regression
model (see (Flanagan and Wing 1995) for similar approach; see also right hand panels of Fig. 2 for illustration).
A standard software package STATISTICA for
Windows (SoftStat) was used for statistical analysis. In
addition to descriptive statistics, repeated measures
ANOVAs were applied to test the effects of force pair (G
versus L of each hand, G versus G and L versus L), hand
dominance, and frequency on the Z-transformed correlation coefficients, while the Schefee test was applied as a
post hoc test. The effect of frequency on variable errors,
slope, intercept and G/L ratio was assessed by repeated
measures one-way ANOVA. Lateral differences between
two G and two L, as well as between two lateral G/L
ratios were assessed by paired t test.
Results
Force profiles and task performance
Maximum pinch force (averaged across the subjects and
hands) was (Mean ± SD) 52±13 N demonstrating no
effect of hand dominance.
The recorded G and L forces obtained from the
dominant hand of a representative subject under the
lowest (0.67 Hz), medium (2 Hz) and highest (3.33 Hz)
frequency are depicted in Fig. 2 (left panels). Regarding
the L profiles, higher frequencies demonstrate the expected sinusoidal pattern, while the 0.67 Hz trial profile
appears to be somewhat irregular. However, a more
important finding is that the depicted force profiles
suggest a high level of coordination of both the interlimb
and within limb forces. In general, the modulation of G
seems to be both comparable in size and temporally
synchronized with the changes of L, although the depicted force patterns also suggest a moderate decrease in
G modulation associated with an increase in L frequency. Note also that instead of the expected relaxation
of pulling force (i.e. zero L at the end of each cycle), this
particular subject demonstrated a moderate pushing
92
Fig. 2 The data obtained from
a representative subject at the
lowest (top panels), medium
(middle panels) and highest
frequency trial (bottom panels).
Left-hand side panels show the
recorded grip and load forces.
Right-hand side panels depict
the corresponding G versus L
diagrams of the dominant arm
together with the corresponding
regression lines, regression
equations and correlation
coefficients. For illustrative
purposes, the left-hand side
graphs show the data only for
the middle 4 s of the each trial,
while the grip-load diagrams, as
well as the regression data are
based on all 9 s
force. According to our recent results (Jaric et al. 2005),
switching from uni-directional to bi-directional exerting
of L could be associated with both an increase in G/L
ratio and a decrease in the correlation between G and L,
which could affect the important findings of the study
(see further text for details). However, we also found a
similar number of the trials/cycles that demonstrated
somewhat insufficient relaxation. The most important
finding is that this phenomenon was mainly a subject
specific and also not affected by the change in frequency.
Regarding the interlimb differences in the recorded
forces and force ratios, the results (averaged across the
subjects and trials) revealed that the dominant hand
exerted both an 8% stronger G and 9% stronger L than
the non-dominant hand (P<0.001; paired t test).
However, note that these two differences provided a
similar offset of G (i.e. averaged G/L ratio) for the
dominant and non-dominant hand. Since the remaining
data showed neither the main effect of hand dominance
nor the interactions with other factors tested, all of the
data throughout this and the following section will be
presented as averaged across two hands.
The constant errors (averaged across the subjects and
trials) were 0.3±0.9 N suggesting no effect of frequency.
The variable errors recorded from 0.66, 1.33, 2, 2.67 and
3.33 Hz trials were 0.69±0.33, 0.64±0.23, 0.89±0.33,
1.02±0.36 and 1.13±0.45, respectively, revealing a significant effect of frequency [F(4,36)=5.3; P<0.01]. In
93
particular, the variable error recorded in the 3.33 Hz
trial was higher than the same error recorded in 0.66 and
1.33 Hz.
1
Coordination between the interlimb
and within limb forces
Figure 3 shows indices of coordination as assessed
through median correlation coefficients obtained from the
interlimb (G versus G and L versus L) and within limb
forces (G versus L, averaged for two hands) recorded
under five L frequencies. The statistical analysis performed on the Fisher-Z transformed correlation coefficients revealed the effect of force pair [F(2,18)=30,
P<0.001], as well as of frequency [F(4,36)=31, P<0.001].
In particular, L versus L provided higher correlation
coefficients than the remaining two force pairs, while the
0.67 Hz trial provided a higher correlation coefficient and
the 3.33 Hz trial provided a lower correlation coefficients
than the remaining three trials performed at intermediate
frequencies. Note that the non-significant ‘force’ · ‘frequency’ interaction [F(8,72)=0.7; P>0.05] suggested that
the frequency did not affect coordination of interlimb and
within limb forces differently. Also note a lack of difference in the within limb coordination between the dominant and non-dominant hand.
The same figure also shows the correlation coefficients obtained from two lateral G/L ratios that were not
included in the presented statistical analysis (see previous paragraph). When compared with the same coefficients obtained from the pairs of interlimb and within
limb forces, the correlation coefficients obtained between
two lateral G/L ratios appear to be considerably lower
and also not affected by the change in frequency
[F(4,45)=0.2, P>0.05].
Pattern of G modulation: offset, gain and G/L ratio
Of particular importance for the study is the frequency
associated changes in the pattern of the G modulation
obtained from G versus L diagrams (for illustration see
right hand panels of Fig. 2). The pattern specifically
refers to the G gain and offset illustrated by the regression lines depicted in the same figures, as well as to the
average G/L ratio. The G gain and offset were assessed
through the linear regressions calculated from G versus
L diagrams (also illustrated in Fig. 2). Specifically, a
high gain (i.e. a high level of modulation of G with respect to change in L) and low offset were expected to be
revealed through a high slope and low intercept,
respectively. Since no effect of hand on the tested variables was recorded (see previous text for details), the
results were averaged across both the subjects and hands
(see top panels of Fig. 4). The one-way ANOVA revealed a significant decrease in slopes [F(4,36)=11,
P<0.001] and an increase in intercepts [F(4,36)=16,
P<0.001] associated with an increase in frequency. The
Correlation Coefficient
0.9
G/L
G/G
L/L
G/L-G/L
0.8
0.7
0.6
0.5
0.66
0.67
1.32
1.33
1.98
2.00
2.64
2.67
3.3
3.33
Frequency (Hz)
Fig. 3 Median correlation coefficients calculated from the interlimb (between two load (L) and between two grip (G) forces), as
well as from the within limb (between G and L, averaged across two
hands). The correlation coefficient between two lateral G/L ratios is
also depicted
post hoc analysis revealed that both findings were based
on the difference between the highest (i.e. 3.33 Hz) and
four lower frequencies (see Fig. 4 for details).
When averaged across the hands, subjects and frequencies, the average G/L ratio was 0.92±0.21
(mean ± SD). Since the slip point (averaged across the
subjects and hands) was 0.64±0.06 (mean ± SD), this
finding suggests a safety margin of 44% (i.e. the G was
on average 44% higher than the minimum G needed to
prevent slippage due to the action of L). However, of
particular importance is the finding that the G offset
suggested no effect of frequency [F(4,36)=0.5, P>0.05;
see bottom panel of Fig. 4 for illustration].
The data presented in Fig. 4 (i.e. slope, intercept and
G/L ratio, averaged across the subjects and hands) were
used to illustrate the effect of frequency on the pattern of
the G modulation (Fig. 5). The depicted regression lines
reveal the results in line with the findings based on the
statistical analysis (see previous paragraph). In particular, except a moderate decrease in G gain and an increase
in G offset obtained under the highest L frequency, the
pattern of G modulation as assessed through G offset,
gain and G/L ratio remained unaffected by change of L
frequency within the most of the tested range.
Discussion
General considerations
Regarding the specific aims of the present study, the
results obtained revealed two major findings. First, the
94
Fig. 4 Indices of the pattern of
G modulation (averaged across
the subjects and hands; error
bars represent standard errors).
The top panels illustrate the
slope and intercept (in N) of the
regression lines obtained from
the G versus L diagrams, while
the bottom panel illustrates the
average G/L ratio (* different
from lower frequencies; +
different from 0.67 Hz). Note
that the slope and intercepts
depict the G gain and offset,
respectively
Intercept
Slope
1
3.5
*
3
0.8
2.5
*
0.6
2
+
1.5
0.4
1
0.2
0.5
0
0.67
1.33
2.00
2.67
0
3.33
0.67
Frequency (Hz)
1.33
2.00
2.67
3.33
Frequency (Hz)
G/L Ratio
1.2
1
0.8
0.6
0.4
0.2
0
0.67
1.33
2.00
2.67
3.33
Frequency (Hz)
coordination of both the interlimb and within limb
forces, as revealed through the correlations calculated
among them, proved to be high, particularly for two L.
In addition, all correlation coefficients decreased at a
similar rate with an increase in L frequency. Second, the
pattern of G modulation appeared to be relatively stable
since the G offset and gain remained only moderately
affected by an increase in frequency, while the average
G/L ratio remained unchanged.
Prior to interpreting these data within the following
subsections, two potentially important methodological
points need to be stressed. First, due to the nature of the
task, the recorded G and L mainly demonstrated a
sinusoidal pattern, although some visible irregularities
appeared at the lowest frequency (see Fig. 3). This pattern remains preserved when the rate of force change is
calculated (i.e. the derivative of sinusoidal function is
also sinusoidal). Therefore, the findings of the present
study could be compared not only with the studies based
on the G and L forces, but also with those based on the
force derivatives (Ohki and Johansson 1999; Serrien and
Wiesendanger 2001a, b, c; Bracewell et al. 2003; Gysin
et al. 2003). Second, the tested frequency interval 0.66–
3.33 Hz applied in the present study was considerably
broader than the intervals in other studies (e.g. 1.43–
Fig. 5 Illustration of the regression lines depicting G gain, offset
and the average G/L ratio (data averaged across subjects and
hands; based on the data from Fig. 4) obtained from trials
performed under five different frequencies
95
3.13 Hz in (Flanagan and Wing 1995), 1–2 Hz in (Zatsiorsky et al. 2004) and 1.33–2.67 Hz in (Jaric et al.
2005). Since the size of the frequency effect should increase with the range of the applied L frequencies, this
difference needs to be taken into account in further
discussion.
Comparison of the interlimb and within limb
coordination
The coordination of the interlimb forces as assessed by
correlation coefficients was comparable with other data
obtained from static manipulation conditions (Diedrichsen et al. 2003; Jaric et al. 2005), but remarkably
high when compared with a discrete dynamical task
(Bracewell et al. 2003). Regarding the coordination of
the within limb forces, the available data are inconsistent, partly due to differences in the task tested and/or
variables evaluated. For example, most of the experiments have been performed on discrete vertical movements while both the forces and their rates of change
were correlated. In addition, the recorded forces were
correlated through both their time series and their peaks
to assess the within limb force coordination. Taken together, the results revealed relatively low correlation
coefficients between the within limb forces (Flanagan
and Wing 1997; Augurelle et al. 2003; Bracewell et al.
2003; Gilles and Wing 2003; McDonnell et al. 2004)
when compared with the present study. However, the
within limb force control in short-lasting discrete tasks
and continuous oscillation tasks could be different due
to various transient neural processes that particularly
characterize force initiation (Ohki and Johansson 1999;
Steglich et al. 1999). Therefore, of more importance
could be the comparison of the present data with studies
based on the vertical shaking of hand-held objects or
static tasks that provided force profiles similar to those
recorded in the present study. These studies revealed
either a comparable (Flanagan et al. 1993; Zatsiorsky
et al. 2004; Jaric et al. 2005) or a lower level of the
within limb coordination of G and L (Flanagan and
Wing 1995; Gysin et al. 2003).
In addition to high correlation coefficients observed
between both the interlimb and within limb forces, a
relatively weak effect of the task frequency on these
coefficients could also deserve attention. Even the frequency 3.33 Hz revealed the correlation coefficients
regarding both the interlimb and within limb coordination above 0.8, which is well above the same coefficients
observed from discrete movements with lower rate of
force changes (Bracewell et al. 2003; McDonnell et al.
2004). In addition, the frequency-associated effect was
similar for the interlimb and within limb coordination,
although an increase in task difficulty caused by increased frequency (also supported by an increase in
variable errors) is generally expected to lead to a relatively stronger interlimb coordination (see Introduction
for details).
One could speculate that both the high level of force
coordination and a relatively weak effect of frequency
suggest that the tested isometric task could be easier to
control than the tasks based on unconstrained vertical
hand movements. In particular, the high correlation
coefficients observed among the recorded forces could
suggest that all four forces may share the same single
central command. Strong ‘bimanual assimilation’ of two
G/L ratios in a dissimilar bimanual task obtained in a
number of previous studies (Kelso et al. 1979; Perrig
et al. 1999; Serrien and Wiesendanger 2001b, c) also
speaks in favor of this assumption. However, the correlation coefficients observed between the two lateral G/
L ratios appear to be relatively low when compared with
the same coefficients observed between two lateral G and
L, as well as with the correlation coefficients between G
and L of each hand that provide the lateral G/L ratios
[see Jaric et al. (2005) for similar findings). Therefore,
despite a high level of coordination of both the interlimb
and within limb forces, the results suggest that G/L ratios could be partly independently controlled. As a result, the G/L ratio could not be a ‘global parameter’ (i.e.,
specified for two hands; Serrien and Wiesendanger
2001c, d) in the tested task.
Finally, note that it remains possible, that despite a
hypothetically high coordination (i.e., high correlation
coefficient) between two particular forces observed
within each single cycle, the overall coordination obtained from the entire trial could still remain low. This
outcome would be caused by an inconsistent overall G or
L level recorded in consecutive cycles within the same
trial (see right hand panels of Fig. 2 for illustration).
Therefore, the obtained high correlation coefficients
generally suggest that both the interlimb and within limb
forces demonstrate not only a highly coordinated, but
also a consistent pattern of the recorded forces over a
number of consecutive cycles.
Pattern of G modulation: gain, offset and G/L ratio
In addition to the comparison of coordination of interlimb and within limb forces, we were particularly interested in the effect of frequency on the pattern of the G
modulation. Specifically, the experimental results were
expected to reveal whether the frequency associated
changes in the modulation of G with respect to changes
in L under the tested static conditions correspond to the
same modulation previously observed in the tasks performed under dynamic conditions. We found this correspondence to be only partial. Specifically, an increase
in L frequency was associated with a decrease G gain
(reflected in both decrease in slope of G versus L
regression lines) an increase in G offset. These findings
appear to be generally in line with the findings observed
from dynamic conditions, such as unconstrained vertical
movements or shaking of a hand-held object (Flanagan
and Wing 1995; Zatsiorsky et al. 2004). The recorded
safety margin was also either close to the safety margin
96
obtained from the free movement tasks (Gilles and Wing
2003; Zatsiorsky et al. 2004), or somewhat lower (Serrien and Wiesendanger 2001d; Nowak et al. 2003).
However, we also found a number of discrepancies between our findings and the findings obtained from dynamic tasks. First, note that the recorded changes in G
gain and offset were relatively weak and mainly originated from the data obtained from the highest frequency. This frequency (i.e., 3.33 Hz) was not only
exceptionally high when compared to other studies, but
also close to the physiological limits of the subjects (see
Methods for details). Second, G/L ratio did not demonstrate the expected frequency associated increase.
Therefore, when compared to similar dynamic tasks, we
could conclude that the tested static task revealed a high
interlimb and within limb force coordination, while the
pattern of the G modulation remained predominantly
preserved within a broad range of the L frequency.
Since a number of methodological factors can affect
the studied coordination (e.g. force profiles, range of
frequencies, hand conditions, etc.; see previous text for
details), more research is needed to support the abovementioned conclusion regarding the differences in the
control of static and dynamic manipulation tasks.
Nevertheless, two implications of the discussed findings
deserve to be mentioned. First, since the importance of
the afferent sensory information from skin receptors for
G and L coordination has been both extensively studied
and strongly emphasized (Johansson and Westling 1984;
Monzee et al. 2003), the L profiles acting through the
contact between the skin and hand-held object recorded
in the present study closely correspond to the same
profiles obtained from unconstrained vertical movements. Therefore, it is unlikely that the skin receptors
could play an important role in the observed differences
between the static and dynamic manipulation tasks.
Second, since it appears that the CNS distinguishes between the static and dynamic manipulation tasks, the
suggested pattern of G modulation based on the tradeoff of between the G gain and offset and average G/L
ratio adjusted for different rates of L change (Flanagan
and Wing 1995) cannot be accepted as a control pattern
that applies to all manipulation tasks. Therefore, the
present data indirectly supports the concept of Zatsiorsky et al. (2004) of partly independent fractions of G
modulation originating from coupling with the static
and dynamic components of L.
Concluding remarks
As compared with the similar tasks performed under dynamic conditions, the present study revealed a relatively
high and consistent coordination of both the interlimb
and within limb forces in a symmetric bimanual manipulation task performed under static conditions. A potentially more important and a rather novel finding is that the
pattern of G modulation with respect to L change remains
predominantly unaffected within the most of the range of
L frequencies. Taken together, the results of the present
study suggest that the control mechanisms of the manipulation tasks performed under static and dynamic conditions could be partly different, even when these tasks are
based on a similar pattern of G and L change. However,
taking into account the specificity of the tested task, further research is needed to generalize these findings to other
task conditions, as well as to explore specific neural control mechanisms that play a role in the observed phenomena. Comparisons of discrete and long lasting
continuous tasks, as well as of unimanual and bimanual
tasks performed under both static and dynamic conditions could deserve particular attention.
Acknowledgments The study was supported in part by a grant from
the National Multiple Sclerosis Society (PP1018) and a grant from
the University of Delaware Research Foundation to the first author.
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