1Psychology Department, Indiana University, Bloomington, Indiana 47405; and 2NeuroMuscular Research Center, Boston University, Boston, Massachusetts 02215
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ABSTRACT |
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Zaal, Frank T.J.M., Kristin Daigle, Gerald L. Gottlieb, and Esther Thelen. An Unlearned Principle for Controlling Natural Movements. J. Neurophysiol. 82: 255-259, 1999. Recently, Gottlieb and colleagues discovered a linear relation between elbow and shoulder dynamic torque in natural pointing movements in the sagittal plane. The present study investigates if the process of learning to reach involves discovering this linearity principle. We inspected torque data from four infants who were learning to reach and grab a toy in front of them. In a longitudinal study, we collected data both in the period before and after they performed their first successful reaches. Torque profiles at the shoulder and elbow were typically multipeaked and became more and more biphasic toward the end of the first year of life. Torques at the shoulder and elbow were correlated tightly for movements in the prereaching period as well as for reaches later in the year. Furthermore, slopes of a regression of shoulder dynamic torque on elbow dynamic torque were remarkably constant at a value ~2.5-3.0. If linear synergy is used by the nervous system to reduce the controlled degrees of freedom, it will act as a strong constraint on the complex of possible coordination patterns for arm movement early in life. Natural reaching movements can capitalize on this constraint because it simplifies the process of learning to reach.
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INTRODUCTION |
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A central issue for understanding human movement
is how the excessive degrees of freedom of the neuromotor system are
controlled (Bernstein 1967). Even the most common,
everyday movement requires coordinating numerous skeletal joints and
muscles. Additional complexity comes from the nonlinear interactions
between the active and passive forces generated by movements in a
linked system. Because the control and coordination of a system of such
an anatomic and dynamic complexity would seem to be exceedingly
demanding, motor neuroscientists have devoted major efforts to
discovering principles by which this problem might be simplified.
Recently, Gottlieb and his colleagues (Gottlieb et al. 1996a,b
,
1997
) described a simple rule that reduces the degrees of freedom for some multijoint pointing movements. They studied pointing movements in the sagittal plane and noted a proportionality between muscle torques at the shoulder and muscle torques at the elbow
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(1) |
The discovery of a linear relation between shoulder and elbow torque in
natural pointing movements led to a number of experiments investigating
the effects of speed differences, added weights, and changes in
pointing direction (Gottlieb et al. 1996b, 1997
). In
these studies, Gottlieb and colleagues focused on the transient qualities of the muscle torque and restricted their investigation to
the so-called dynamic muscle torques, the portion of muscle torque not
concerned with resisting gravity (the latter being static muscle
torque). As in the earlier results, there was a linear relation between
shoulder dynamic muscle torque and elbow dynamic muscle torque for
pointing movements in the sagittal plane. Neither speed manipulations
nor added weight changed the parameters of this linear relation,
whereas the gain constant, Kd, was
related directly to the direction of pointing.
That a linear covariance of shoulder torque and elbow torque is seen in natural pointing movements, but not when people point in a less comfortable way, suggests that the linear relation serves movement economy by linking the timing of torque pulses. In the pointing movements studied, torque profiles typically exhibit a biphasic form. A linear relation between two biphasic torque profiles results from a strict temporal coupling of the torque pulses. The slope of the regression of shoulder torque onto elbow torque (i.e., Kd) indicates the relative size of the torque pulses at shoulder and elbow. Because deviations from linearity sometimes are observed, this relation cannot be simply a hard-wired biomechanical artifact of a moving linked system. Rather linearity may be a natural organizing principle for decreasing the degrees of freedom at the level of muscle torques, at least for those movement tasks that can be accomplished under such a constraint.
The relation between these muscle torque constraints and regularities
at the level of endpoint kinematics is not clear, however. For
instance, linear joint torques do not guarantee the straight reaching
paths seen in many planar reaches. Indeed, "comfortable" reaches
may not be straight at all (Atkeson and Hollerbach
1985). Curiously enough, Gottlieb et al. (1996a)
found that more uncomfortable reaches could exhibit straighter
handpaths as well as deviations from a linear torque-torque relation.
What, then, is the relation between a linearity constraint at the
torque level and regularities at the level of endpoint kinematics? We
address this question by looking at the developmental origins of
trajectory control. When 3- to 4-mo-old infants first reach out and
grab objects, their hand paths are not straight at all but follow a
tortuous and indirect route to the target. The corresponding speed
profiles are not bell-shaped but show several segments of acceleration
and deceleration, giving the movements a jerky quality. During the
first year the hand path becomes straighter and smoother, and the high
variability of early reaches is reduced (Halverson 1931;
Hofsten 1991
; Konczak and Dichgans 1997
;
Thelen et al. 1993
, 1996
). Infants' reaches become more
and more adult-like, a process that continues at least through the
second year of life (Konczak and Dichgans 1997
).
Is discovery of the linearity principle one the prerequisites for skilled reaching? If this were true, infants' reaches would become smoother only as their torques at elbow and shoulder approached a more linear relation. Alternatively, reach smoothness and torque linearity could be unrelated, with the possibility that linearity is a property of comfortable movements whether they are straight, or even whether they indeed are reaching movements. In this case, we would expect that reach straightness and torque linearity would show no correspondence in infants. Indeed, torque linearity may developmentally predate straight reaching or even reaching itself.
To address these issues, we examined kinematic and torque data
collected longitudinally from four children during their first year,
from weeks 3 to 52, as they were presented with a reachable toy (see
Thelen et al. 1993, 1996
). When the toy captured
infants' attention, they would make movements of the arms that could
be interpreted as attempts at reaching for the attractive object. In
the first few months of life, infants were unsuccessful in such
efforts. As they grew older, however, they became both faster and more
successful in reaching and grabbing the toy. Note that in contrast to
the controlled conditions of adult reaching experiments, infants were
always free to move when and in any direction and at any speed they
chose. This design, and the variability it engendered, allowed a rather
strict test of the linearity constraint. If we find torque linearity
when movements are not constrained by direction, speed, straightness,
or goal, it suggests a fundamental neuromotor organizing principle on
which movements are built.
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METHODS |
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We followed normally developing infants, three boys and a girl.
The longitudinal observations were scheduled weekly from 3 to 30 wk of
age, and biweekly until 52 wk (for details, see Thelen et al.
1993, 1996
). We presented attractive toys to the infants at
midline, shoulder height, and at the distance of their extended arms
while they were seated upright with their torsos secured. We collected
data in 14-s trials, presenting the toy ~5 s after the start of the
trial. Position time data were recorded with a four-camera WATSMART
optical-electronic movement analysis system, sampling at 150 Hz, and
converted to three-dimensional data using direct linear transformation.
Infrared light emitting diodes (IREDs) were placed over each shoulder
joint, elbow joint, and wrist joint as well as on the back of each hand
of the infant. Because infants could move freely in three-dimensional
(3-D) space, continuous visibility of the IREDs was sometimes a
problem. We selected and analyzed portions of trials where spontaneous
movements and reaches occurred based on the following protocol:
1) videocoding of each trial by two coders to exclude
portions of the trial when the infant was not moving, sucking on
fingers, clutching clothing, etc. 2) Determining visibility
of the IREDs and using data only when markers were visible through 70%
of the segments and when gaps of missing data frames were <333 ms. For
the inverse dynamics calculations to be performed, visibility of the
IREDs at hand, wrist, elbow, and shoulder was essential. 3)
Interpolating obscured data with a linear spline and filtering data
based on a 97% cutoff of spectral density profile of each IRED in each
coordinate. 4) Rigorous identification of the reach segment
itself based on object location, infant's gaze at the object, and
matching visually identified start of the reach movement with velocity
minima (see also Corbetta and Thelen 1995
; Thelen
et al. 1993
, 1996
). This selection procedure resulted in 22 instances of prereaching movements and 115 reaches (66 from the early
reaching period and 49 from the stable reaching period), which could be
analyzed for both endpoint kinematics and joint torques. The results
presented later are based on these 137 movement segments. No additional
criteria were used to discard trials for analysis.
We calculated joint torques at shoulder and elbow using inverse
dynamics methods (Schneider and Zernicke 1990). The arm
was modeled as three interconnected rigid links (hand, lower arm, upper
arm), with frictionless joints at the wrist, elbow, and shoulder. We
calculated wrist, elbow, and shoulder angles, as well as their time
derivatives, from the 3-D WATSMART data. Shoulder angle was defined as
the angle between the vertical passing through the shoulder IRED and
the line connecting the IREDs at the shoulder and elbow (180° denotes
a vertically oriented upper arm). Elbow angle was defined as the angle
between the lines connecting the IREDs at the shoulder and elbow, and
the IREDs at the elbow and wrist, respectively (180° denotes a fully
extended elbow). Analogously, we computed wrist angles from the
positions of the IREDs at the elbow, wrist, and hand. We calculated
joint torques using joint angles, their time derivatives, and estimates
of mass, center of mass, and moments of inertia based on measured limb
segment parameters (Schneider and Zernicke 1992
). This
method provides torques about axes normal to the moving-local plane
through the wrist joints, elbow joints, and shoulder joints
(Schneider and Zernicke 1990
). Here, we restricted our
analyses to the magnitudes of those torques, not considering their
directions. At each joint, the net torque (NET) was partitioned into
gravity (GRA), motion-dependent (MDT), and generalized muscle torque
(MUS) components (for more details and examples of the use of this
method applied to infant limb movement, for instance, see
Konczak and Thelen 1994
; Konczak et al.
1997a
; Schneider et al. 1990
). The torque due to
muscle alone is thus MUS = NET
MDT
GRA. Here we
are only interested in the dynamic portion of muscle torque: the
quantity NET
MDT (cf. Gottlieb et al. 1996b
,
1997
). Finally, we normalized torques for body weight, to be
able to compare results among different ages.
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RESULTS |
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Figures
1-3
illustrate typical infant movements in the prereach, early reach and
stable reach periods, in this example at the age of 19, 29, and 42 wk,
respectively (criteria for determining these developmental epochs are
reported in Thelen et al. 1996). The four infants first
consistently touched or grasped the toy at 12, 15, 20, and 20 wk (the
reaches presented in Figs. 1-3 are from the same infant, who first
touched the toy at 20 wk). Before that time, they visually fixated the
toy, and often moved their arms, but were not successful in touching or
grasping it, as suggested by the rather random motion shown in Fig.
1A. Early reaches, typified by Fig. 2A, were
controlled poorly and were extremely variable, as indicated by an index
of hand path straightness, the number of speed accelerations and
decelerations, and the average and contact speed of the hand
(Thelen et al. 1993
, 1996
). Coordination between the
rotations of the shoulder and elbow was also poor and variable, as
shown in Figs. 1C and 2C, reflecting the diverse starting positions of their reaches and the tortuous hand paths. At
~30-34 wk of age, reach control stabilized noticeably, with more
straight and smooth reaches (Fig. 3) and less variable speeds, although
even at 1 yr, infants were not reaching in a fully adult manner.
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Despite infants' poor control of their hand paths and joint
excursions, they adhered strictly to the principle of linear synergy throughout the first year, both in movements before they learned to
successfully reach and afterward. Figure
4 shows distributions of the correlation
coefficients (r) and of the slopes
(Kd) of a linear regression of
shoulder torque onto elbow torque for each inspected movement. The
results are presented separately for the early prereaching period, the
highly variable postreaching onset periods, and the later, more stable
period (Thelen et al. 1996). Correlation coefficients
were uniformly close to unity, showing that the increases and decreases
of force at the two joints were nearly perfectly in synchrony.
Moreover, for these reaches at midline and shoulder height,
Kd remained near 2.5-3.0 [2.68 ± 0.70 (mean ± SD) in the prereaching period; 2.45 ± 0.41 in the early period; 2.83 ± 0.40 in the stable period). Even more
remarkable was that infants appeared to retain this torque invariance
even in their nonreaching movements. The synchrony between forces at shoulder and elbow was nearly perfect, and the slope approximated that
of the reaching movements. The examples from the prereaching period
(Fig. 1), the early reaching period (Fig. 2), and the stable reaching
period (Fig. 3), all from the same infant, illustrate the dramatic
contrast between the variability at the level of hand kinematics and
the dynamic torque-torque stability.
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DISCUSSION |
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These results suggest that the principle of linear synergy
is a fundamental property of the human neuromotor system from early in
life and is likely not learned as a means to constrain the kinematics
of the hand into the forms seen in adult reaching. Clearly, the
principle is not responsible for the straightness of the hand path nor
for the unimodal bell-shaped speed profile. Thus following the
principle of linear synergy does not simply lead to the kinematics we
well know in adult reaching. Rather, successful reaching for a target
must be sculpted into the temporal structure of the torque patterns
from this preference of the system to apportion dynamic torque
proportionately and synchronously between shoulder and elbow. Even as
the hand wandered from the path to the toy, or as infants moved in a
seemingly non-goal-directed fashion, the coordination was maintained.
This held across the transition from prereaching to reaching despite
evidence that infants recruited different sets of muscles to move to
the same place in space (Spencer and Thelen 1996). The
principle acts as a constraint in the high-dimensional space of
kinematic and dynamic possibilities, thereby reducing the degrees of
freedom of the problem of learning to control the arm for purposeful
activity (Bernstein 1967
).
Although these results are based on a relatively small population of
four infants, the time series data are remarkably similar to that of
others. For example, Fig. 2 of Konczak et al. (1997a) shows an example of elbow and shoulder torques in a young infant. They
are multiphasic but well synchronized and would probably show a high
degree of colinearity between joints were they plotted as we have in
Figs. 1-3. The joint torques of the older infants shown in that figure
appear to be less linear but this is because the gravitational
component was included.
The invariance of the slope in infants' reaching movements
throughout their first year may be explained by our always presenting the toy to the same place at midline. Although the location of the toy
is certainly an interesting variable to be considered in future
research, the location of the target cannot be a factor for nonreaching
movements, which also showed a strong tendency to have a torque-torque
slope close to the mean of 2.6. More likely, while infants can move to
many areas in their reaching space, limb anatomic and energetic
considerations make certain configurations more attractive than others.
Indeed, during the prereaching period, infants' hands were most likely
to be in front of them or between the midline and shoulder at no higher
than the chest for a majority of the time. Movements at the extremes of
the reaching space were less frequently seen (Spencer and Thelen
1996). Interestingly, Gottlieb et al. (1997)
computed Kd values for various (adult) reaching movements taken from their earlier studies, in which speed and
load, among other things, were manipulated (see Fig. 11 in
Gottlieb et al. 1997
). In their center-out task and
center-crossing task, Kd was related
to movement direction but Kd was
~2.5 for all other movements. These latter movements were all
directed at targets located in front of and above the initial position of the hand as were the infant reaches presented here.
With the linear synergy principle acting as a constraint on the complex
of possible coordination patterns, the infant neuromotor system is
configured to make the acquisition of reaching easier. Thelen et
al. (1993) suggested that infants shifted from spontaneous movements to successful reaching by working on the force dynamics to
initially get the hand in the "ball park" of the visually fixated target. Because each of the four infants differed in the predominant speed of prereaching movements and in the amplitudes of muscle torque
generated, they needed to individually discover torque levels to
approach the object at an appropriate speed. The present results
indicate that shoulder-elbow torque proportion and synchrony is
maintained in this scaling. Movement distance and speed may be
modulated by scalar changes in the muscle activation that generates torques around the joints. Relatively subtle adjustments in the relative apportionment and timing of joint torque, learned by trial and
error, may be sufficient to specify trajectory direction. Natural
reaching movements capitalize on the intrinsic coupled dynamics of the arm.
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ACKNOWLEDGMENTS |
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This work was supported by National Institutes of Health Grants R01 HD-22830 and K05 MH-01102 to E. Thelen and RO1 AR-44388 to G. Gottlieb.
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FOOTNOTES |
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Present address and address for reprint requests: F.T.J.M. Zaal, Faculteit der Bewegingswetenschappen, van der Boechorstsstraat 9, 1081 BT Amsterdam, The Netherlands.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 21 December 1998; accepted in final form 8 March 1999.
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REFERENCES |
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