Exp Brain Res
DOI 10.1007/s00221-007-0932-1
R ES EA R C H A R TI CLE
Prospective dynamic balance control in healthy children
and adults
Hanne Austad · Audrey L. H. van der Meer
Received: 26 June 2006 / Accepted: 27 February 2007
© Springer-Verlag 2007
Abstract Balance control during gait initiation was
studied using center of pressure (CoP) data from force plate
measurements. Twenty-four participants were divided into
four age groups: (1) 2–3 years, (2) 4–5 years, (3) 7–8 years,
and (4) adults. Movement in the antero-posterior (CoPy)
direction during the initial step was tau-G analyzed, investigating the hypothesis that tau of the CoPy motion-gap
(CoPy), i.e., the time it will take to close the gap at its
current closure rate, is tau-coupled onto an intrinsic tau-G
guide (G), by maintaining the relation CoPy = KG, for a
constant K. Mean percentage of tau-guidance for all groups
was ¸99%, resulting in all r² exceeding 0.95, justifying an
investigation of the regression slope as an estimate of the
coupling constant K in the tau-coupling equation. Mean K
values decreased signiWcantly with age and were for 2- to
3-year-olds 0.56, for 4- to 5-year-olds 0.50, for 7- to 8-yearolds 0.47, and for adults 0.41. Therefore, the control of
dynamic balance develops from the youngest children
colliding with the boundaries of the base of support
(K > 0.5) to the older children and adults making touch
contact (K · 0.5). The Wndings may provide us with a
measure for testing prospective balance control, a helpful
tool in assessing whether a child is following a normal
developmental pattern.
Keywords Dynamic balance · Gait initiation ·
Movement control · Prospective control · Tau-G analysis ·
Children
H. Austad · A. L. H. van der Meer (&)
Developmental Neuroscience Laboratory,
Department of Psychology, Norwegian University
of Science and Technology (NTNU), Trondheim, Norway
e-mail: [email protected]
Introduction
A major milestone in a child’s life is to no longer have to
hold on to any of the surrounding surfaces to balance the
body in an upright position and attain independent walk. In
the process of achieving this, the child has to learn to use
sensory information and motor action together to orient his
or her presence in the environment. The child also has to be
able to stabilize the body’s center of gravity (Barela et al.
1999), the point where the body is in perfect balance. Stable
control of posture and balance is an integral component of
all motor abilities (Ferdjallah et al. 2002). A common
method for measuring postural stability is to obtain
movement of center of pressure (CoP) data from force
plates (Cherng et al. 2003).
Independent walking is a highly complex series of
actions. It changes style as we grow older and become more
skilled walkers, and will, by adulthood, be characterized by
smooth, regular, and repetitive movements (Vaughan
2003). The speciWc ankle displacement in mature walking,
resulting in a prominent heel strike and push oV, is absent
in new walkers (Dierick et al. 2004). Young children walk
with a wide base of support. As they mature, they are better
able to control their body weight over the supporting limb,
due to greater coordination and improved balance
(Sutherland 1997). The pelvic span/ankle spread ratio
increases steadily from the beginning of walking until
about the age of 3½ after which it remains constant. Age
and more practice improve balance control, leading to
better postural control and decreased postural sway (Rival
et al. 2005).
Some researchers have observed that children under the
age of 4 have relatively longer steps than older children and
adults when the step length is compared to leg length
(Dierick et al. 2004; Sutherland 1997). New walkers also
123
Exp Brain Res
use a high and middle guard posture of the arms which has
been found to be correlated to step width, as well as a natural factor in helping to move the body forward at a time
when the child’s muscles in the lower limbs are not strong
enough to cause movement on their own (Kubo and Ulrich
2006; Ledebt 2000). Ledebt (2000) reported that children
will lower their arms and progressively start moving them,
Wrst in the shoulder joint, and then also the elbow, supporting Bernstein’s (1967) theory of initially freezing the
redundant degrees of freedom in motor skill learning. Then,
as the new skill is practiced, “freeing” of degrees of freedom allow more movement as new tasks are performed
with less restrictions, while still maintaining body posture
(Newell and Vaillancourt 2001).
It is well known that adults prepare for the Wrst step, in
part, by leaning forwards, which sets oV a controlled fall
and the initiation of gait (Mann et al. 1979). When controlling posture and balance during gait, the task is to maintain
the movement of the CoP within the boundaries of the base
of support (MacKinnon and Winter 1993). Brenière and
Bril (1998) found that young toddlers are not able to control
the disequilibrium which characterizes the single support
phase. Their study showed that during the Wrst 6 months of
independent walking children displayed negative values of
the vertical acceleration of the center of mass at foot contact, while adults displayed positive values. They concluded that toddlers can walk, despite lacking the strength
required to maintain balance, but that they are “walking by
falling”. It is not until the age of 4–5 years that children are
able to control this fall by controlling gravity forces and the
inertia forces induced by movement (Brenière and Bril
1998). Assaiante et al. (2000) studied the development of
postural adjustment during gait initiation from kinetic and
EMG as well as kinematic analyses. They reported that
anticipatory postural adjustments that shift the weight
towards the stance leg preceded the integrative postural
adjustments that take care that balance is stabilized during
the swing phase of gait when the body is supported by one
leg. Both processes, however, did not mature before the age
of approximately 4–5 years.
A common problem in movement control is that of stabilizing an eVector within the boundaries of a goal zone. For
example, in balance control this would involve stabilizing
the vertical projection of the centre of gravity within the
boundaries of the base of support. Movement can be
described as a goal-directed action. The intention is to get
from state A to state B, which necessitates the closure of the
gap between the two states. The gap between the two states
is called a motion-gap. Thinking of a step as the closure of a
motion-gap leads to the theory, which will be used in this
study, to estimate the prospective control of balance in the
transitional stage between standing still and starting to walk:
General tau theory (Lee 1998, 2005; Lee et al. 2001).
123
Tau, , of a motion-gap is the time it will take to close
the gap at its current closure rate. A gap can be either a spatial or a force gap (Lee 1998). Lee (1998) writes that at the
root of general tau theory is the idea of prospective control.
The movement has to be controlled ahead of time to allow
for such factors as inertia. Prospective guidance of a selfpaced movement (such as taking a step, or reaching for a
stationary object) requires intrinsic information generated
in the central nervous system and perceptual information,
but it is not necessary to know the size of the gap, neither
the rate of closure (Lee et al. 2001). It is, however, necessary to monitor the progress of the movement perceptually
so that appropriate muscular adjustments can be made (Lee
2005), which in turn will minimize the risk of falling when
walking (Vaughan 2003). Intrinsic tau guidance is goal-oriented, aiming at closing the motion-gap between the current
state and the desired state. The dimension which underlies
the process of change in any motion-gap is time, and it is
necessary to be able to perceive the motion-gap and estimate the time it will take to close the motion-gap at the current closure rate without falling short of, or crashing into
the target or goal state (Lee 2005; Slobounov et al. 1997).
When used to guide a self-paced movement to a goal, the
motion-tau would be constantly tau-coupled onto an intrinsic tau-G guide (Craig et al. 2000a). The general tau theory
can be applied to any kind of gap closure. If we imagine an
upright cylinder surrounding us when we walk, the walls of
this cylinder can be thought of as guiding upright posture.
When walking or running, the task is to control the movement of the CoP to stay within the walls of the cylinder, i.e.,
within the boundaries of the base of support.
The present study
This study investigated, by measuring the abilities of children in three diVerent age groups, the levels of postural
control during the transitional stage between standing still
and walking, i.e., when taking the initial step. The results
were compared to those of an adult group. It was expected
that as children become more skilled walkers, their control
of the movement of the CoP would improve. It was postulated that controlling the movement of the CoP in the
antero-posterior direction (CoPy) entails controlling the closure of the motion gap between the current position of the
CoPy and a goal position lying within the cylinder; and that
this is achieved by tau-G guiding the motion-gap, i.e., keeping the changing tau of the motion-gap proportional to an
intrinsically generated changing tau value, tau-G. It was
expected that the youngest children would overshoot the
goal position (rather than making touch contact with it, as
the oldest children and the adults would), because their tauG guidance of CoPy was underdeveloped. This study aimed
to identify and map out the developmental stages of gait
Exp Brain Res
initiation so as to create a barometer for predicting prospective balance control, a helpful tool in assessing if a child is
following a normal developmental pattern.
Method
Participants
The children in this study were divided into three age
groups: (1) 2- to 3-year-olds, mean age 2.9 years (§0.2),
(2) 4- to 5-year-olds, mean age 4.8 years (§0.6), and (3)
7- to 8-year-olds, mean age 7.3 years (§0.2). A total of 21
children were recruited to participate in this study. However, only six children from each age group were analyzed
due to technical problems (1), insuYcient data (1), and a
history of ear infections (1). In addition, a total of six adults
participated. The mean age for the adults was 27.8 years
(§3.3). Each group consisted of four females and two
males.
Participants for the two youngest age groups were
recruited from the University nursery where the parents of
the children were given letters informing them about the
research and requesting consent for their children to be
brought to the Developmental Neuroscience Laboratory,
Department of Psychology, Norwegian University of Science and Technology (NTNU), during the day, by a nursery
worker. The 7- to 8-year-olds were recruited among
friends’ children and their friends, and all were pupils at
one of the primary schools nearby. All the adult participants were volunteers from master level classes in psychology. All child participants involved in this study were
conWrmed born to term. None of the parents reported any
developmental problems with balance or other motor control behaviors, vision or auditory problems, or anything else
which could have an inXuence. All adult participants had
normal or corrected to normal vision. One of the adults
reported some childhood ear infections. None of the adult
participants reported having experienced any motor control
diYculties. Parents and adult participants gave their
informed written consent prior to inclusion in the study
according to the Helsinki Declaration.
Apparatus and procedure
Center of pressure data were collected using custom-built
force plates. There were four plates (92 £ 83 cm each)
lined up in a row, creating a walkway. The two plates in the
middle were used for data collection. The force plate data
were sampled at 100 Hz. In addition, all trials for all the
participants were recorded on video.
A trial consisted of a period where the participant was
standing still, after which s/he was asked to walk across
both force plates. The youngest children were looking after
a raisin, which they had to put in a cup at the opposite end
of the platform. The raisins were given as a reward at the
end of the experiment. In addition, all children received a
diploma for their participation. Each participant completed
between 7 and 10 trials. The adult participants were given
instructions at the beginning of the session and asked to
adopt a quiet two-legged stance. They were also asked to
start their walking with intention, as if they had a purpose
with the walk across the force plates. All participants wore
socks during testing.
Data analysis
The video recordings were inspected to extract from
the data step initiation until the foot was placed back on the
platform. Since walking occurs, to a large degree, in the
antero-posterior direction, only movement of CoPy was
analyzed for step initiation. The data were Wltered using a
Gaussian sigma 3 Wlter. The displacement of CoPy and its
velocity (rate of closure of CoPy motion-gap) were plotted
against time (see Figs. 1b, 2b). The peak velocity of each
Wrst step was identiWed and the movement of CoPy was
demarcated at 10%, or as close to 10% as possible, of this
value. The CoPy (i.e., the tau of the gap between the beginning and the end of the movement of CoPy) was calculated
and plotted against the tau-G guide (G) for the movement,
using the formula G(TG,t) = TG(1 + tn)tn/(1 + 2tn), where
TG is the CoPy motion duration, which starts at time t = 0,
for ¡TG · t · 0, or ¡1 · tn · 0 (Lee 2005). Finally, a
recursive linear regression analysis was run on the plot to
determine the strength of the coupling between CoPy and G
(measured by the r² value of the regression) and to estimate
the value of the constant K in the tau-coupling equation
CoPy = KG (measured by the slope of the regression), by
removing the leftmost points in the plot one by one until the
r² of the regression exceeded the criterion level which was
set at 0.95. The percentage of the movement during which
it has intrinsic tau-G guidance was calculated by dividing
the remaining points in the plot by the total number in the
movement, providing an estimate of how much the CoPy
movement was prospectively controlled. Thus, for the fragment identiWed in each movement three measures were
given: (1) the percentage of the movement that was tau-G
guided to the criterion of r² ¸ 0.95, (2) the value of r², and
(3) the regression slope, which estimates the K value in the
tau-coupling equation. High percentages of tau-G guidance
of the movement and high r² values allow for the regression
slope to be a good estimator of the K of the movement.
The value of K in the tau-coupling equation regulates the
kinematics of closure of the CoPy motion-gap. In particular,
for K values lying between 0 and 1, the larger the value of
K, the longer the duration of the acceleration phase of the
123
Exp Brain Res
Start
a
End
Start
80
80
60
60
Displacement of CoPy (cm)
Displacement of CoPy (cm)
a
40
20
0
-20
-40
40
20
0
-20
-40
-60
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-60
1.6
0.0
Time (s)
End
300
20
250
0
-10
200
Displacement of CoPy
Velocity of CoPy
150
100
-20
-30
50
-40
0
0.2
0.4
0.6
0.8
Time (s)
1.0
1.2
Start
1.4
1.6
End
30
300
20
250
10
0
-10
200
Displacement of CoPy
150
Velocity of CoPy
100
-20
-30
50
-40
0
Velocity of CoPy (cm/s)
10
b
Displacement of CoPy (cm)
Start
30
Velocity of CoPy (cm/s)
Displacement of CoPy (cm)
b
End
-50
0.0
0.2
0.4
0.6
0.8
-50
0.0
Time (s)
0.2
0.4
0.6
0.8
Time (s)
Fig. 1 a Displacement of CoPy during normal gait in a typical 2-yearold, where the CoPy oscillates between the medial borders of the
supporting feet (dashed lines). The vertical solid lines mark the start
and the end of the CoPy movement during gait initiation. b Zooming in
on the displacement of CoPy and its corresponding velocity curve
during the initial step. The resulting K value was 0.53, indicating that
the movement of CoPy is colliding with the boundaries of the base of
support
movement and the more abrupt the deceleration to the goal
(Lee 1998). The three ranges of K give rise to distinct types
of movement (Lee 2005). When 0 < K · 0.5, the CoPy
movement starts at rest and moves away with increasing
acceleration from a zero value; the movement then decelerates at a decreasing rate and stops at the goal. Thus, when
0 < K · 0.5, the movement ends with touch contact. When
0.5 < K < 1, the CoPy movement starts at rest and moves
away with a high initial acceleration, which decreases to
zero. Then the movement decelerates at an increasing rate
until maximum deceleration is achieved, which is
maintained until the goal is reached. Thus, when
0.5 < K < 1, the movement ends with hard contact while the
movement is decelerating. A controlled collision is the consequence. When K ¸ 1, the CoPy movement starts moving
away at speed, decelerates at a decreasing rate and then
accelerates at an increasing rate until maximum acceleration is achieved, and Wnally hits the goal at high velocity.
123
Fig. 2 a Displacement of CoPy during normal gait in a typical adult,
where the CoPy oscillates between the medial borders of the supporting
feet (dashed lines). The vertical solid lines mark the start and the end
of the CoPy movement during gait initiation. b Zooming in on the
displacement of CoPy and its corresponding velocity curve during the
initial step. The resulting K value was 0.41, indicating that the movement of CoPy is heading for the boundaries of the base of support with
touch contact
The eVect is a non-controlled collision. So, K values greater
than one indicate that the movement is still accelerating
when it reaches its goal.
Results
A total of 202 trials were recorded. One of these was
deWned as an outlier [value larger/smaller than mean
§2.5 SD, see Field (2005)] and was therefore excluded
from the analysis. Figure 1a illustrates the displacement of
CoPy during gait in a typical 2-year-old, and Fig. 1b zooms
in on the initial step and illustrates displacement of CoPy
and its corresponding velocity during gait initiation until
the swinging foot is placed back on the force plate.
Figures 2a and b show the same for a typical adult.
Exp Brain Res
Tau-G analyses
The percentage of tau-G guidance of the CoPy movement
was close to 100% in most of the trials. The mean percentage of tau-G guidance was for the 2- to 3-year-olds 99.54%,
for the 4- to 5-year-olds 99.77%, and 100% for both the
7- to 8-year-olds and the adults, which resulted in all the r²
exceeding 0.95, indicating that the tau of CoPy was strongly
coupled onto the tau-G guide. Therefore, further analysis
was only performed on the K values, which show how well
the movement of CoPy was controlled.
Group mean K values (see Fig. 3) were for the 2- to
3-year-olds 0.56 (range 0.51–0.67), for the 4- to 5-year-olds
0.50 (range 0.46–0.51), for the 7- to 8-year-olds 0.47 (range
0.44–0.48), and for the adults 0.41 (range 0.39–0.44).
A one-way ANOVA with group as between factor was carried out on the subject means of the K values, revealing a
main eVect of group, F(3, 20) = 11.02, P < 0.001, indicating lower K values with increasing age. A linear regression
analysis performed to get an estimate of change of the mean
K value with age revealed an r² of 0.57 and a standardized
correlation coeYcient of ¡0.75 (t = ¡5.36, P < 0.001).
The subject mean K values were tested with a one sample t test to see if the results were signiWcantly higher or
lower than 0.5 (see Fig. 3). The 2- to 3-year-olds had K values signiWcantly higher than 0.5, which means that the
youngest children collided with the boundaries of the base
of support (K > 0.5). Both the 7- to 8-year-olds and the
adults had K values signiWcantly lower than 0.5, which
means that they made touch contact with the boundaries of
the base of support (K · 0.5). The 4- to 5-year-olds did not
0.7
K>0.5, p<0.03
Me an K valu e
0.6
K<0.5, p<0.001
0.5
K<0.5, p<0.001
0.4
0.3
2-3 years
4-5 years
7-8 years
Adults
Fig. 3 Group means (and error bars) of the K values of the CoPy
movement during the Wrst step. The 2- to 3-year-olds had K values
signiWcantly larger than 0.5, whereas the 7- to 8-year-olds and the
adults had K values signiWcantly smaller than 0.5. The 4- to 5-year-olds
had K values that were not signiWcantly diVerent from 0.5. The
horizontal line indicates K = 0.5, demarcating the switch from making
a controlled collision with the boundaries of the base of support
(K > 0.5) to making touch contact (K · 0.5)
have K values signiWcantly diVerent from 0.5, placing them
somewhere between the 2- to 3-year-olds and the 7- to
8-year-olds. Typical for the 4- to 5-year-olds was that they
all had K values hovering around 0.5, with K · 0.5 in just
over half of the trials (55%). The corresponding percentages for the 2- to 3-year-olds, the 7- to 8-year-olds, and the
adults were 34, 78, and 100%, respectively.
Discussion
This study investigated the development of postural control
during gait initiation in healthy children aged 2–3, 4–5, and
7–8 years, as well as in a group of adult graduate studentvolunteers. This study, contrary to many other studies
carried out on balance control (Assaiante and Amblard
1992; Cherng et al. 2003; Ferdjallah et al. 2002; Hatzitaki
et al. 2002; Jeka et al. 2000; Peterson et al. 2006), included
no manipulations.
To study postural control, the movement of CoPy was
tau-G analyzed during the Wrst step when gait was initiated. The percentage of total tau-G guidance for the movement was higher than 99% which meant that all the r²
exceeded 0.95. The resulting K values gave an indication
of how well movement of CoPy was controlled. K values
decreased signiWcantly with age, and the control of
dynamic balance during the Wrst step when gait is initiated,
showed a development from the youngest children colliding with the boundaries of the base of support (K > 0.5) to
the oldest children and the adults making touch contact
(K · 0.5).
The present Wndings indicated that the youngest children
have the least control over their movements in dynamic
balance. When K > 0.5 the control of the movement is very
diVerent from that when K · 0.5. If we imagine an upright
cylinder surrounding us when we walk, the walls of this
cylinder can be thought of as guiding upright posture. We
can imagine the youngest children overshooting the goal
position lying within the cylinder and colliding with its wall
when they start walking, but not so hard that they topple
over and fall. The oldest children and the adults, in the
same scenario, will just make touch contact with the wall
when they initiate walking. It has previously been found
that children up to the age of 4–5 years do not show
integrative postural adjustment, which keeps the pelvis
from dropping to the side of the swing leg during foot liftoV. The result is a balance problem for the youngest children during the swing phase of gait (Assaiante et al. 2000).
This is consistent with another study of young children
where it was found that gait was a result of “walking by
falling” (Brenière and Bril 1998). It has been proposed that
around the age of 6–7 years, a recalibration of the sensory
processes underlying locomotor balance control takes place
123
Exp Brain Res
due to a growth spurt in the trunk, which causes a sudden
shift in the center of gravity. From the age of 7–8 years
onwards the visual, vestibular, and proprioceptive systems
become more eYciently coordinated, resulting in improved
dynamic balance control (Assaiante and Amblard 1992).
Based on this, the tau-G analysis yielded similar results as
other researchers have reported, and the coupling constant
K in the tau-coupling equation gives a good indication of
the diVerences in control between the age groups when initiating gait.
It should be mentioned that the task for the youngest
children was slightly diVerent than for the other participants. In order to engage the youngest children in the task
they were asked to carefully look after a raisin and place it
in a cup at the end of the platform. Although the 2- to
3-year-olds appeared to take this task very seriously, most
likely resulting in more cautious gait initiation, it cannot be
entirely ruled out that the higher K values were a result of
the youngest children being excited about the raisin game
causing them to hurriedly take the Wrst step.
It has been demonstrated here that intrinsic tau-G analysis can successfully be applied to the study of dynamic
balance control. The present study is actually the Wrst study
to take CoP measurements from children during the Wrst
step in gait initiation and apply the general tau theory.
However, the theory has successfully been applied to other
tau-coupling situations, e.g., when studying how professional golfers control the swing of the golf club when
putting (Craig et al. 2000a) and how children with hemiparetic cerebral palsy (CP) control their hitting movements
(Van der Weel et al. 1996). Tau-coupling was also used to
analyze nutritive sucking in healthy infants (Craig and Lee
1999). Those results were compared to results obtained
from preterm infants (Craig et al. 2000b). The results
revealed that some preterm infants displayed irregularities
in sucking control and when compared to an independent
physiotherapist’s assessment 6 months later, the same
preterm infants were found to be delayed in their motor
development. These Wndings suggest that tau-G analysis
can be used as a diagnostic tool.
Many studies have been carried out with both adults and
children suVering developmental delays, or set-backs,
caused by disease or events. A common component
between all these studies is that they have used the measure
of CoP to determine the degree of stability. For example, in
studies with patients diagnosed with Parkinson’s disease
(e.g., Guehl et al. 2006) intrinsic tau-G analysis could be
added, allowing the researchers to study the control of the
CoP movements as well as their position, displacement, and
area. Other postural control studies where the use of intrinsic tau-G analysis could prove valuable is in the search for
better recovery treatment after stroke (e.g., Bayouk et al.
2006), and the treatment of children with developmental
123
coordination disorders (DCD), CP, and idiopathic scoliosis
(e.g., Bennett et al. 2004).
Based on the Wndings from the preterm infants study
(Craig et al. 2000b) as well as the results from the present
study, tau-G analysis applied to motor development studies
seems promising. The analysis would appear to give a good
indication of the level of temporal control involved in performing a movement of the CoP when initiating gait, as
well as diVerentiate between diVerent developmental
stages. More studies should be carried out to establish baselines for motor control development in healthy children in
more age groups, followed by using similar methods to
evaluate the development levels reached by children with
developmental disorders. The ability to estimate prospective control makes tau-G analysis a useful tool in studying
developmental delay problems and motor control deWciencies, possibly making treatment and intervention more
accurate.
Acknowledgments The research reported in this paper was part of a
Master’s thesis by H. Austad. The authors are grateful to all the children and their parents, and the adult participants for taking part in this
study. We also thank Gert-Jan Pepping for providing us with the tau
analysis software and Dave Lee for many fruitful discussions on general tau theory.
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