Development of pendulum mechanism and kinematic coordination from the first unsupported steps in toddlers
1 Department of Neuromotor Physiology, IRCCS Fondazione Santa Lucia, via
Ardeatina 306, 00179 Rome, Italy
2 Department of Neuroscience, University of Rome Tor Vergata, Via
Montpellier 1, 00133 Rome, Italy
3 ISEPK, Université Libre de Bruxelles, Brussels 1050,
Belgium
4 Centre of Space Bio-medicine, University of Rome Tor Vergata, Via Raimondo
8, 00173 Rome, Italy
* Author for correspondence at address 1 (e-mail: lacquaniti{at}caspur.it)
Accepted 29 July 2004
![]() |
Summary |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Key words: locomotion, gravity, pendulum, child
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
The principle of dynamic similarity states that geometrically similar
bodies that rely on pendulum-like mechanics of movement have similar gait
dynamics at the same Froude number, i.e. all lengths, times and forces scale
by the same factors (Alexander,
1989). The Froude number (Fr) is given by
Fr=V2g1L1,
where V is the average speed of locomotion, g the
acceleration of gravity, and L the leg length. Fr is
directly proportional to the ratio between the kinetic energy and the
gravitational potential energy needed during movement. Dynamic similarity
implies that the recovery of mechanical energy in subjects of short height,
such as children (Cavagna et al.,
1983
; Schepens et al.,
2004
), Pygmies (Minetti et
al., 1994
) and dwarfs (Minetti
et al., 2000
), is not different from that of normal sized adults
at the same Fr. No overt violations of the pendulum mechanism have
been reported so far for legged walking on land. It has been demonstrated not
only in humans, but also in a wide variety of animals that differ in body
size, shape, mass, leg number, posture or skeleton type, including monkeys,
kangaroos, dogs, birds, lizards, frogs, crabs and cockroaches
(Ahn et al., 2004
;
Alexander, 1989
;
Dickinson et al., 2000
;
Farley and Ko, 1997
;
Goslow et al., 1981
;
Heglund et al., 1982
).
The pendulum mechanism might arise from the coupling of neural oscillators
with mechanical oscillators, muscle contraction intervening sparsely to
re-excite the intrinsic oscillations of the system when energy is lost. But is
the pendulum mechanism an innate property of the interaction between the motor
patterns and the physical properties of the environment? Or is it acquired
with walking experience in the developing child? Previous studies have
demonstrated conclusively that the mechanics of walking of children 212
years old, in particular the pendular recovery of energy at each step, is very
similar to that of the adults when the walking speed is normalised with the
Froude number (Bastien et al.,
2003; Cavagna et al.,
1983
; Schepens et al.,
2004
), though in younger children (from 2 weeks to 6 months after
the onset of independent walking) the mechanical energy exchange occurs to a
lesser degree (Hallemans et al.,
2004
). However, to the best of our knowledge, the pendulum
mechanism has not been investigated in toddlers who are just beginning
independent, unsupported locomotion, roughly around 1 year of age. At that
time, toddlers are faced with the novel task of transporting their body in the
upright position against full gravitational load. If the pendulum mechanism
were an innate property, one would expect to discover it at the onset of
unsupported locomotion.
Here we studied walking mechanics in toddlers at their first unsupported steps and in older children (overall age range, 113 years). We report that the pendulum mechanism is not implemented by newly walking toddlers, but it develops over the first few months of independent locomotion along with the inter-segmental kinematic coordination. Thus we argue that the pendulum mechanism is not innate, but is learnt through walking experience.
![]() |
Materials and methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Walking conditions
For the recording of the very first steps, one parent initially held the
child by hand. Then, the parent started to move forward, leaving the child's
hand and encouraging her/him to walk unsupported on the floor. For each
subject, about ten trials were recorded under similar conditions. Children
generally performed 23 steps on the force platform in each trial. They
were encouraged to look straightforward and to walk as naturally as possible.
Short trials (up to 3 min, depending on endurance and tolerance) were recorded
with rest breaks in between. The mean walking speed in toddlers was
1.4±0.7 km h1 (mean ±
S.D.). Adult subjects were asked to walk at a natural,
freely chosen speed (on average it was 3.8±0.4 km
h1), and in additional trials at faster speeds
(7.3±0.8 km h1) and lower speeds (2.4±0.8 km
h1).
Two infants were recorded between 1.5 and 4 months before the onset of unsupported walking while they walked firmly supported by the hand of one of their parents.
Data recording
Kinematics of locomotion (Fig.
1A) was recorded at 100 Hz by means of either the ELITE (BTS,
Milan, Italy) or the VICON (Oxford, UK) motion analysis systems. The position
of selected points was recorded by attaching passive infrared reflective
markers (diameter 1.5 cm or 1.4 cm, for the ELITE and the VICON, respectively)
to the skin overlying the following bony landmarks on the right side of the
body (Fig. 1A): gleno-humeral
joint (GH), the tubercle of the anterosuperior iliac crest (IL), greater
trochanter (GT), lateral femur epicondyle (LE), lateral malleolus (LM), and
fifth metatarso-phalangeal joint (VM). In half of the children we measured
kinematics bilaterally (with the VICON system).
|
In children and at low speeds in adults, the ground reaction forces (GRFs; Fx, Fy and Fz) under both feet (Fig. 1C) were recorded at 1000 Hz by a force platform (0.9 mx0.6 m; Kistler 9287B, Zurich, Switzerland). At natural, higher speeds in adults, the GRFs under each foot were recorded separately by means of two force platforms (0.6 mx0.4 m; Kistler 9281B), placed at the centre of the walkway, spaced by 0.2 m between each other in both the longitudinal and the lateral directions. Because of the longitudinal spacing between the two platforms, the left foot could step onto the first platform and the right foot could step onto the second platform. The lateral spacing between the platforms ensured that one foot only stepped on each of them. Sampling of kinematic and kinetic data was synchronized.
At the end of the recording session, anthropometric measurements were taken
on each subject. These included the mass (m) and stature of the
subject, the length and circumference of the main segments of the body (17
segments, according to the procedure of
Schneider and Zernicke
1992).
Data analysis
Systematic deviations of gait trajectory relative to the
x-direction of the recording system were corrected by rotating the
x, z axes by the angle of drift computed between start and end of the
trajectory. In the following, we will denote the variables in the forward
direction with the subscript f, in the lateral direction with the
subscript l and in the vertical direction with the subscript
v. The body was modelled as an interconnected chain of rigid
segments: GHIL for the trunk, ILGT for the pelvis, GTLE
for the thigh, LELM for the shank, and LMVM for the foot
(Fig. 1A). The main limb axis
was defined as GTLM. The elevation angle of each segment (including the
limb axis) corresponds to the angle between the segment projected on the
sagittal plane and the vertical (positive in the forward direction, i.e. when
the distal marker falls anterior to the proximal one). In addition to the
absolute elevation angles, the relative angles of flexionextension
between two adjacent limb segments were also computed. The abduction angle
corresponds to the angle between the segment projected on the frontal plane
and the vertical (positive in the lateral direction). Walking speed was
measured by computing the mean velocity of the horizontal IL marker movement.
The length of the lower limb (L) was measured as thigh (GTLE)
plus shank (LELM) length.
Gait cycle duration was defined as the time interval T between two
successive maxima of the elevation angle of the main limb axis of the same
limb, and stance phase as the time interval between the maximum and minimum
values of the same angle (Borghese et al.,
1996). Thus, a gait cycle (stride) referred to a cyclic movement
of one leg, and equalled two steps. When subjects stepped on the force
platforms, these kinematic criteria were verified by comparison with foot
strike and lift-off measured from the changes of the vertical force around a
fixed threshold. In general, the difference between the time events measured
from kinematics and the same events measured from kinetics was less than 3%.
However, the kinematic criterion sometimes produced a significant error in the
identification of stance onset in toddlers, due to an unusual forward foot
overshoot at the end of swing (since the trajectory of the foot differed from
that of adults: sometimes the toe reached its maximal height in front of the
body and then the foot just hit the ground; see
Forssberg, 1985
). In such
cases, foot contact was determined using a relative amplitude criterion for
the vertical displacement of the VM marker (when it elevated by 7% of the limb
length from the floor). In all experiments data from each gait cycle were time
interpolated to fit a normalized 200-points time base.
Inter-segmental coordination
The inter-segmental coordination was evaluated in position space as
previously described (Borghese et al.,
1996; Bianchi et al.,
1998a
). In adults, the temporal changes of the elevation angles at
the thigh, shank and foot covary during walking. When these angles are plotted
one vs the others in a 3-D graph, they describe a path that can be
fitted (in the least-square sense) by a plane over each gait cycle. Here, we
studied the development of the gait loop and its associated plane in children.
To this end, we computed the covariance matrix of the ensemble of time-varying
elevation angles (after subtraction of their mean value) over each gait cycle.
The three eigenvectors u1u3,
rank-ordered on the basis of the corresponding eigenvalues, correspond to the
orthogonal directions of maximum variance in the sample scatter. The first two
eigenvectors u1, u2, lie on the
best-fitting plane of angular covariation. The third eigenvector
(u3) is the normal to the plane and defines the plane
orientation. For each eigenvector, the parameters uit,
uis and uif correspond to the
direction cosines with the positive semi-axis of the thigh, shank and foot
angular coordinates, respectively. The orientation of the covariation plane in
each child was compared both across all steps and with the mean orientation of
the corresponding plane of all the adults.
Kinetic and potential energies of the COM in the sagittal plane
To compare our data with those previously obtained in children by Cavagna
et al. (1983) and Schepens et
al. (2004
), we used a similar
method to compute the changes of the instantaneous kinetic and potential
energies of the COM from the force platform data. The vertical
(Fv) and forward (Ff) components of
the ground reaction forces (Fig.
1C) were used to calculate the vertical (av)
and forward (af) acceleration of the COM, respectively:
![]() | (1) |
![]() | (2) |
Equations 1 and 2 were integrated digitally in order to obtain the changes
in the vertical (Vv) and forward (Vf)
velocity of the COM:
![]() | (3) |
![]() | (4) |
The integration constants were found by calculating the mean speed of the IL marker over the analysed stride on the assumption that this parameter is equal to the mean speed of the COM; this is reasonable since the location of the ilium marker is close to the COM and the displacements of the COM within the body are small. The mean vertical velocity (integration constant) was taken equal to zero on the assumption that upward and downwards vertical displacements are equal.
Equation 4 was integrated to obtain the vertical displacement of the COM
(h):
![]() | (5) |
The integration constant is arbitrary and was taken equal to 0. The
instantaneous potential energy (Ep) was calculated as
Ep=mgh. The instantaneous kinetic energy
(Ek) of the COM was calculated as
.
Environmental forces other than gravity (such as air resistance) can be
neglected in low speed locomotion (Cavagna
and Kaneko, 1977
), and were not considered here. The
cross-correlation function (R
ß) between
Ek and Ep waveforms was computed to
quantify their phase shift
by means of the following formula:
![]() | (6) |
Positive external work and recovery of mechanical energy
The total mechanical energy of the COM (Eext) was the
sum of Ek and Ep waveforms over a
stride. The positive external work (Wext) was the sum of
the increments in Eext over a stride
(Cavagna et al., 1976).
Similarly Wv and Wf were the positive
vertical and forward works, respectively, obtained by the summation, over a
stride, of all the increases in vertical
(
)
and forward
(
)
energies of the COM. To minimise errors due to noise, the increments in
mechanical energy were considered to represent positive work actually done
only if the time between two successive maxima was greater than 20 ms. For
older children and adults, the records of Ek and
Ep do not extend to the whole cycle. Therefore, we
replaced a missing initial double support phase at the beginning of stance
using the data from the double-support phase at the end of stance under the
assumption of a symmetrical gait in older children and adults.
To estimate the ability to save mechanical energy, we used the percentage
of recovery R (Cavagna et al.,
1976):
![]() | (7) |
Energy analysis in the frontal plane
The classical analysis of the inverted pendulum only involves sagittal
components of body motion (Cavagna et al.,
1976,
1983
;
Saibene and Minetti, 2003
). In
normal adults, it has been shown that the lateral component of kinetic energy
of the COM is essentially negligible compared with the sagittal components
(Tesio et al., 1998
). In
toddlers, however, the contribution of the lateral component might be higher
due to postural instability in the frontal plane. Therefore, in addition to
the measurements in the sagittal plane, we also computed the changes in total
mechanical energy of COM including lateral Ek
(Tesio et al., 1998
),
,
where Vl is the instantaneous velocity in the lateral
direction. The mean lateral velocity (integration constant) was taken equal to
zero on the assumption that left and right lateral displacements are equal.
This is reasonable since systematic deviations of gait trajectory relative to
the x-direction of the recording system and ground reaction forces
(x and z) were corrected by rotating the x,z axes
by the angle of drift computed between start and end of the trajectory. The
percentage of recovery of total mechanical energy of COM
(R1) was computed as:
![]() | (8) |
Positive internal work due to segment movements relative to COM
Here the methods were similar to those used by Willems et al.
(1995). Mass
(mi), position of the centre of mass
(ri), and moment of inertia (Ii) in the
sagittal plane of each body segment i were derived using measured
kinematics, anthropometric data taken on each subject (see above), and
regression equations proposed by Schneider and Zernicke
(1992
) for infants less than 2
years, Jensen (1986
) for older
children, and Zatsiorsky et al.
(1990
) for adults. Seven body
segments were included in the analysis of internal work: HAT (head, arms and
trunk), thigh, shank and foot of right and left lower limbs. We computed the
angular velocity (
i) of each segment and the translational
velocity (vi) of its centre of mass relative to COM. COM
position was derived as:
![]() | (9) |
The kinetic energy of each segment (Ek,i) due to its
translation relative to COM and its rotation was then computed as the sum of
its translational and rotational energy:
.
The kinetic energy vs time curves of the segments in each limb were
summed. The internal work due to the movements of the limbs and HAT was then
calculated by adding the increments in their kinetic energy waveforms. As
before, the increments in kinetic energy were considered to represent positive
work actually done only if the time between two successive maxima was greater
than 20 ms. Net internal work (Wint) was finally estimated
as the sum of internal work for each limb and for the HAT. This procedure
allowed energy transfers between segments of the same limb, but disallowed any
energy transfers between different limbs and trunk
(Schepens et al., 2004
;
Willems et al., 1995
).
We could not measure the internal work made by one leg against the other
during double contact (Bastien et al.,
2003), because infants stepped on one platform only. However, this
work contributes less than 10% of total power spent during walking both in
adults and children (Schepens et al.,
2004
). Also, the internal mechanical work done for stretching the
series elastic components of the muscles during isometric contractions, to
overcome antagonistic co-contractions, viscosity and friction, cannot be
directly measured.
Age-related changes
The time course of changes of kinematic and kinetic parameters as a
function of age was fitted by an exponential function:
y=a·et/+b,
where y was the specific parameter under investigation, t
was the time since onset of unsupported walking,
was the time constant,
and a, b, two constants. To avoid an unrealistic fit due to the dispersion of
data corresponding to the very firsts steps in toddlers, data were fitted
using the mean value at t=0.
Statistics
Statistical analysis (Student's unpaired t-tests and analysis of
variance, ANOVA) was used when appropriate. Reported results are considered
significant for P<0.05. Statistics on correlation coefficients was
performed on the normally distributed, Z-transformed values.
Spherical statistics on directional data
(Mardia, 1972) were used to
characterize the mean orientation of the normal to the covariation plane (see
above) and its variability across steps. To assess the variability, we
calculated the angular standard deviation (called spherical angular
dispersion) of the normal to the plane.
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
|
In toddlers at the onset of unsupported locomotion, GTy oscillations were more variable from step to step than in adults. Their mean profile systematically differed from that of the adults (Fig. 2B, leftmost panels). Thus, the first peak in GTy of the adults (corresponding to the stance phase of the ipsilateral leg) was absent in toddlers even though the knee joint was often locked during stance (Fig. 2B, subjects F.A. and G.M.). Instead, the GTy peak corresponding to the second peak of the adults was generally present in toddlers and reflected a lift of the hip joint during swing relative to the contralateral hip joint of the load-bearing leg. This observation was confirmed during bilateral kinematic recordings and it also applied to the IL markers; therefore, it cannot depend on a misplacement of the GT marker relative to the centre of joint rotation. In toddlers, the percent of GTy variance explained was 56±9% (mean ± S.D., N=8) and 22±4% for the first and second harmonic, respectively, indicating a dominance of the first harmonic, in contrast with the dominance of the second harmonic in adults. The hip of the swinging limb was raised by a few centimetres above the hip of the contralateral load-bearing limb. Bilateral coordination of the two hip joints in toddlers, therefore, differs markedly from that of walking adults, and instead is reminiscent of that observed for stepping in place in adults. A few months after the onset of unsupported locomotion, the first peak of GTy at mid-stance became recognizable and was fully developed in older children (see central panels in Fig. 2B).
Age-related changes of kinematic parameters related to the pendulum
mechanism are presented in Fig.
2C,D for the whole population of subjects. Both the power of the
second harmonic of GTy (Fig.
2C) and the correlation coefficient between GTy in
children and GTy in adults (Fig.
2D) were low at the onset of unsupported walking and increased
rapidly afterwards. Changes with age were fitted by an exponential function
(see Materials and methods). The time constant was fast both for the changes
of the second harmonic (=2.2 months) and for the correlation with the
ensemble average in adults (
=4.1 months).
Mechanical energy
The pendulum mechanism has both kinematic and kinetic consequences for
walking (Alexander, 1989;
Cavagna et al., 1976
). We
computed the changes of mechanical energy of COM from force platform
recordings (see Materials and methods). In adults
(Fig. 3B,C, rightmost panel),
kinetic energy (Ek) tends to fluctuate out of phase with
gravitational potential energy (Ep) and with vertical hip
displacements. Between touch-down and mid-stance, the forward velocity of the
COM decreases as the trunk arcs upwards over the stance foot. In this phase,
Ek is converted to Ep. During the
second half of the stance phase, the COM moves downwards as the forward
velocity of the COM increases. In this phase, Ep is
converted back into Ek. Energy exchange by the inverted
pendulum mechanism reduces the mechanical work required from the muscular
system by an amount that depends on walking speed
(Cavagna et al., 1976
).
Positive work is necessary to push forward the COM during early and late
stance, to complete the vertical lift during mid-stance, and to swing the
limbs forward.
|
At the onset of unsupported locomotion, all toddlers failed to demonstrate a prominent energy transfer (Fig. 3B, leftmost panels). In general, the changes of Ep and Ek were very irregular, with a variable phase relation between each other. Peak-to-peak changes of Ek were often smaller than the corresponding changes of Ep (in part due to a low walking speed). A few weeks following the onset of unsupported locomotion, children started to display a clear pendulum-like exchange of Ep and Ek in each step (central panels in Fig. 3B).
To quantify this energy exchange over each step, we computed the
correlation coefficient r between Ek and
Ep waveforms, their phase shift , the percentage of
energy recovery R (Equation 7), and the external work
Wext performed per unit distance and unit mass
(Fig. 4AD). In an ideal
pendulum, Ek changes are exactly equal and opposite to
Ep changes: thus r=1,
=0%,
R=100% and Wext=0. In our sample of adults
walking at natural speed (3.8±0.4 km h1), we found:
r=0.85±0.05,
=1.0±1.7%,
R=64±4% and Wext=0.32±0.04 J
kg1 m1. In toddlers at the onset of
unsupported locomotion (1.4±0.7 km h1), instead, we
found: r=0.39±0.15,
=2.2±8.5%,
R=28±7%, and Wext=0.97±0.20 J
kg1 m1. The mean values of these
parameters in toddlers were significantly
(P<105, Student's unpaired t-test)
different from those in adults, except for
values.
values
exhibited a very large step-by-step variability in toddlers: the mean
S.D. of
values computed over all steps in each
toddler was 27.5±6.2%, whereas it was 1.8±0.9% in adults.
Percentage of energy recovery R computed from Equation 7 only
includes the components in the sagittal plane. We also computed
R1 from Equation 8, including lateral components. The
relative amplitude of changes in the kinetic energy in the lateral direction
(Fig. 3A) was somewhat higher
in the toddlers (31±10% of total kinetic energy oscillations) than in
the adults (6±3%), likely due to a higher instability in the lateral
direction and/or a wider step width
(Assaiante et al., 1993
;
Bril and Brenière,
1993
). The values of the energy recovery R1
were 65±4%, and 36±4% in adults and toddlers, respectively. Also
the internal work Wint performed per unit distance and
unit mass was significantly (P<105) higher in
toddlers (0.74±0.09 J kg1 m1) than
in adults (0.27±0.06 J kg1 m1)
walking at natural speed (1.4±0.7 km h1 in toddlers,
3.8±0.4 km h1 in adults).
|
Age-related changes of parameters related to energy exchange are presented in Fig. 4AD for the whole population of subjects. They were fitted by exponential functions with fast time constants (2.35.1 months, Fig. 4A,C,D), closely comparable to those computed for the changes of kinematic parameters (Fig. 2B,C). The changes of Wint (J kg1 m1) also were well fitted by an exponential (Fig. 4E, time constant of 2.8 months).
Relation with speed
In principle, the low recovery of mechanical energy of COM in toddlers
could be due to their low height and low gait speed. It is known that at a
given speed the net mass-specific mechanical work of locomotion is greater the
smaller the height of the subject, and the slower the speed of locomotion
(Alexander, 1989;
Cavagna et al., 1983
;
Saibene and Minetti, 2003
).
The Froude number (Fr) is a dimension-less parameter suitable for the
comparison of locomotion in subjects of different size walking at different
speed (Alexander, 1989
).
Subjects with a dynamically similar locomotion are expected to output
comparable values of mechanical power when walking with the same Fr.
Thus, children between 2 and 12 years of age
(Cavagna et al., 1983
;
Schepens et al., 2004
), adult
Pygmies (Minetti et al., 1994
)
and dwarfs (Minetti et al.,
2000
) have the same percentage of recovery R (Equation 7)
of mechanical energy as normal-sized adults when they walk at the same
Fr value. Typically, R peaks at
65% at Fr
0.3, and falls off at lower and higher Fr values (see fig. 10 in
Saibene and Minetti,
2003
).
Fig. 5A shows the R vs
Fr function for our toddlers at the first unsupported steps, 15
months later, for children older than 2 years of age, and for adults (the data
of children after the onset of independent locomotion, younger than 2 years of
age are not shown). Adults walked at speeds that covered a wide range of
Fr values, yielding an R vs Fr function comparable to
published data (Saibene and Minetti,
2003). In general, the data points of older children roughly
overlapped those of the adults, in agreement with previous results
(Cavagna et al., 1983
;
Schepens et al., 2004
).
However, on average R values of children were slightly but
significantly lower than those of the adults. Over the 0.070.42 range
of Fr values, R was 62±7% in children and
65±4% in adults. Two-factor ANOVA on R values over that range
of Fr values (discretised in 5 intervals) revealed a significant
effect of subject group (children versus adults, P<0.03), but no
significant effect of Fr value (P=0.14) or interaction
(P=0.31).
|
Toddlers at the first unsupported steps never walked faster than Fr=0.14. Their data points fell systematically below those of both older children and adults for comparable values of Fr. Over the 0.070.14 range of Fr values, R was 35±8% in toddlers and 61±9% in older children (P<107). As for the comparison with the adults, we performed a two-factor ANOVA on R values of toddlers and adults for the 0.040.14 range of Fr values (discretized in 5 intervals), and found a significant effect of both Fr value (P<107) and subject group (toddler vs adult, P<107), as well as a significant interaction (P<0.0005) consistent with the lower slope of the R vs Fr function in toddlers than in adults (Fig. 5A).
As another index of energy exchange, we considered the values of the correlation coefficient r between Ek and Ep (see previous section) plotted vs Fr values (Fig. 5B). Once again, the data points of older children roughly overlapped those of the adults, whereas the data of toddlers were systematically different. Two-factor ANOVA on r values for the 0.040.14 range of Fr values showed a significant effect of subject group (toddler vs adults, P<106), but no significant effect of Fr value (P=0.89) or interaction (P=0.45).
It might be questioned how the equivalent speeds should be computed. Thus, the toddlers are not geometrically similar to the adults. The COM is located higher in the toddlers (approximately at the level of the sternum) than in the adults (approximately at the level of the ilium). Therefore, we verified whether the R values and the correlation coefficients between Ek and Ep would differ significantly in the toddlers and the adults after normalisation of the walking speed to the distance from supporting foot to COM rather than to the limb length. This procedure shifts the results for the toddlers and the adults towards lower Fr numbers. However, even following this normalization, the R values and the correlation coefficients r between Ek and Ep were significantly lower in the toddlers (R=28±7%, r=0.39±0.15) than in the adults (R=54±10%, r=0.81±0.17) over the 0.020.10 range of newly defined Fr values. In general in the paper we used the limb length normalisation since it is commonly accepted in the literature.
Both the normalised speed (Froude number), the correlation coefficient
between Ek and Ep and energy recovery
increased with age, but 15 months after the onset of independent
walking they were still lower than these values in adults or in older children
(Fig. 5). The recovery of
mechanical energy for this age group (15 months after the onset of
independent walking) was similar to that reported by Hallemans et al.
(2004).
Inter-segmental coordination
The position of the COM in space and therefore the pendulum mechanism
depend on the combined rotation of all lower limb segments. During walking,
the thigh, shank and foot swing back and forth
(Fig. 6A), and in so doing they
carry the trunk along and shift the COM. In adults, the temporal changes of
the elevation angles of lower limb segments co-vary along a plane, describing
a characteristic loop over each stride
(Fig. 6B). The gait loop and
its associated plane depend on the amplitude and phase of the coupled harmonic
oscillations of each limb segment (Bianchi
et al., 1998a).
|
In toddlers, the gait loop departed significantly from planarity and the
mature pattern. Planarity was quantified by the percentage of variance
accounted for by the third eigenvector (PV3) of the data covariance
matrix (Fig. 6C): the closer
PV3 is to 0, the smaller the deviation from planarity.
PV3 was significantly higher in toddlers (4.3±3.5%) than in
adults (0.8±0.3%, P<0.001 Student's unpaired
t-test), in agreement with our previous findings (Cheron et al.,
2001a,b
).
Also, because the amplitude of thigh movement was relatively higher with
respect to that of shank and foot movements in toddlers, the gait loop was
less elongated than in adults, as shown by the smaller contribution of the
first eigenvector (PV1). In toddlers,
PV1=73.2±7.0% and PV2=22.5±6.8%; in
adults, PV1=85.9±1.5% and PV2=13.3±1.5%.
There were no systematic deviations in the orientation of the plane: the mean
normal to the plane in toddlers was similar to that of the adults, but the
individual values of plane orientation varied widely among toddlers
(Fig. 6D). Moreover, the
step-by-step variability of plane orientation (estimated as the angular
dispersion of the plane normal) was considerably higher in toddlers
(18.0±8.1°) than in adults (2.9±1.0°,
Fig. 6E), reflecting a high
degree of instability in the phase relationship between the angular motion of
different limb segments. When the data are compared across children at
different ages, one notices that plane orientation stabilized rapidly after
the onset unsupported locomotion. The time constant of the exponential
function was 3.6 months.
An efficient pendulum mechanism also depends on inter-limb bilateral coordination in the direction of forward progression. When bilateral kinematic recording was available (see Materials and methods), we measured the phase shift between the maximum of the elevation angle of the main axis of left limb and the corresponding value of the right limb, expressed in percent of the gait cycle. Inter-limb phase should be 50% for symmetrical gait involving perfect inter-limb coordination. The measured phase was not significantly different from the ideal value either in toddlers (48.7±2.1%) or in adults (50.2±1.5%). However, toddlers exhibited a large step-by-step variability: the mean S.D. of phase values computed over all steps in each toddler was 6.7±3.9%, whereas it was 1.0±0.4% in adults (P<0.0005).
Toddlers also exhibited a greater amount of oscillations in the lateral direction (in the plane perpendicular to the direction of progression). The peak-to-peak amplitude of the adduction/abduction angle of the main axis of each limb over each stride was 14.9±3.5° in toddlers, as compared with 5.3±1.3° in adults (P<105).
Behaviour before the onset of unsupported locomotion
Progressive changes of gait kinematics and kinetics as a function of child
age presumably depend on the neural maturation of central pathways that are
important for postural and locomotor control. In addition, however, walking
experience under unsupported conditions might act as a functional trigger of
gait maturation. These two developmental factors lead to predictable
differences in the time course of changes of gait parameters. If anatomical
maturation were the only dominant factor, one would expect monotonic changes
of gait parameters beginning before and continuing through the age of the
first unsupported steps. If, instead, walking experience under unsupported
conditions acts as a functional trigger, one would expect that gait parameters
remain more or less unchanged until the age of the first unsupported steps,
and then rapidly mature after that age.
Evidence for the latter behaviour was observed in two infants who were
tested repeatedly over a period between 4 months before and 13 months after
the onset of independent walking (Fig.
7). The infants walked firmly supported by the hand of one of
their parents before they could walk independently. In adults, hand support
does not change gait parameters significantly, as shown in treadmill
experiments where the subjects put their arms on the rollbars
(Ivanenko et al., 2002). In
infants, it could rather improve postural stability and gait kinematics.
However, in all recording sessions performed before the onset of unsupported
locomotion, both the pendulum-related pattern of vertical hip displacement and
the pattern of inter-segmental coordination did not differ significantly from
those recorded at the onset of unsupported locomotion. The percentage of
variance accounted for by the second Fourier harmonic of the vertical GT
displacement (denoting the double-peaked profile of pendular oscillations of
COM, see Fig. 2B) exhibited
inter-step variability but did not change systematically as a function of age
up to the time of onset of unsupported locomotion, when it started to increase
rapidly over the first few months of independent walking experience (compare
Fig. 7A with
Fig. 2C). A similar trend was
exhibited by the step-by-step variability of plane orientation (compare
Fig. 7B with
Fig. 6E), and by the index of
planarity (PV3, not shown).
|
![]() |
Discussion |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
We report for the first time that toddlers at the onset of unsupported
locomotion do not implement the pendulum mechanism. Thus the vertical
oscillations of the hip lack the sinusoidal pattern at twice the frequency of
the gait cycle that is observed in mature gait
(Winter, 1991). A partial
energy exchange may occur during some portions of the gait cycle (probably as
a consequence of physics; see also
Hallemans et al., 2004
);
however, the `classic' inverted pendulum behaviour of a stance limb is lacking
at the transition to independent walking (Figs
2,
3A) and develops within a few
months of unsupported walking experience. Also, the changes of gravitational
potential energy and forward kinetic energy of COM are very irregular, with a
variable phase relation between each other. Normalising the speed with the
Froude number showed that the percentage of recovery of mechanical energy in
toddlers is systematically lower than in older children and adults
(independent of whether normalisation was performed to the limb length or to
the distance between foot and COM). The percentage of energy recovery was
somewhat higher in toddlers when the lateral component was included, probably
due to a greater amount of oscillations in the lateral direction and/or a
wider step width; nonetheless, it remained significantly lower than in adults.
Lack of pendulum may reflect a basic immaturity of the inter-segmental
kinematic coordination.
Determinants of the pendulum mechanism
The finding that toddlers can organize spontaneous walking without using
the pendulum mechanism demonstrates that it is not an inevitable mechanical
consequence of a system of linked segments, cross-coupled by passive inertial
and viscoelastic forces. Instead it must result from active neural
control. What are the determinants of the pendulum mechanism? The simplest
model of the inverted-pendulum for adult walking consists of a rigid rotation
of the COM around a fixed contact point via a stiff supporting limb.
This model has been shown to be incorrect
(Lee and Farley, 1998). During
stance, the contact point between foot and ground translates forward, and the
supporting limb is compressed especially at higher speeds
(Lee and Farley, 1998
;
Winter, 1991
). The trajectory
of the COM in space and the pendulum behaviour also depend on other kinematic
parameters, such as the stancelimb touchdown angle
(Lee and Farley, 1998
).
The deceiving simplicity of the pendulum behaviour hides the inherent
complexity of its neural control
(Lacquaniti et al., 1999). The
problem is that the COM has no anatomical or functional autonomy. It is a
virtual point lying somewhere close to the ilium, but this location changes as
a function of body posture, load carrying, and non-proportional growth of
different body segments in childhood. There is no sensory apparatus that
monitors COM position directly, and computing exactly how much work needs to
be done for its motion may not be an easy task for the nervous system.
However, neglecting possible deformations of the trunk, COM position depends
on the combined rotation of body and limb segments.
Thus if the nervous system encodes a controlled pattern of covariation
between segment rotations, the motion of COM would be specified implicitly.
Such a kinematic covariance between limb and body segment rotations has been
found in adult locomotion. The temporal changes of the elevation angles in the
sagittal plane co-vary along a characteristic gait loop constrained on a plane
(Borghese et al., 1996;
Lacquaniti et al., 1999
). (In
a similar vein, a kinetic covariance has been demonstrated between limb joint
torques; Winter, 1991
). The
specific shape and orientation of the planar gait loop accurately reflect COM
trajectory and its modifications as a function of body posture
(Grasso et al., 2000
). In
addition, the planar orientation changes systematically with increasing
walking speeds (Bianchi et al.,
1998a
), and accurately predicts the net mechanical power output at
each speed by both trained and untrained subjects
(Bianchi et al., 1998b
).
Finally, the planar gait loops of left and right lower limbs are coupled
(Courtine and Schieppati,
2004
), as predicted by the `ballistic walking' model proposed by
Mochon and McMahon (1980
), in
which the swing limb behaves like a compound pendulum, coupled with inverted
pendulum of the stance limb.
In toddlers at the first unsupported steps, pendulum-like behaviour of the
COM, stable planar covariance of the angular motion of the lower limb
segments, and bilateral coordination in both sagittal and frontal directions
are not in place. A lack of the pendulum behaviour was also found in chicks
(Muir et al., 1996): young
chicks do not innately use their leg as a rigid strut during the first 2 weeks
of life and need to acquire the ability to walk in an energy efficient manner.
In toddlers, both the pendulum-like behaviour of the COM and the fixed planar
covariance come into play soon after the onset of independent walking, and
co-evolve toward mature values within a few months. Development of the
pendulum and of the planar covariance have both energetic and stability
consequences, since one of the benefits of pendular rhythmic movements is
cycle-to-cycle stability and reproducibility
(Goodman et al., 2000
). The
percentage of recovery of mechanical energy increases significantly with
walking experience, in parallel with a decrease of the step-by-step
variability of kinematic and kinetic parameters.
Role of walking experience in learning the pendulum mechanism
Walking mechanics depends on the interaction between feedforward motor
patterns and neural feedback, on the one hand, and the physical properties of
the body and the environment, on the other hand
(Dickinson et al., 2000). The
present findings and previous results in infants indicate that this
interaction requires an active tuning of the motor commands through learning.
Basic features of locomotor control are present several months before a child
can walk independently (Forssberg,
1985
). Thus, infants 112 months old can step (either
spontaneously or on a treadmill) at a speed modulated by peripheral inputs, in
different directions (forward, backward, sideways), and with bilateral
coordinated behaviour in response to external perturbations
(Lamb and Yang, 2000
;
Pang and Yang, 2001
;
Yang et al., 1998
). There is
strong evidence that the spinal network of central pattern generators (CPGs)
is already in place at birth, and is rapidly integrated with proprioceptive
feedback to generate appropriate rhythmic patterns for locomotion
(Forssberg, 1985
;
Yang et al., 1998
). On the
other hand, when children start to walk without support, several other
features of locomotion are still immature, such as the stride fluency, head
and trunk stability, amplitude of hip flexion and coordination of lower limb
movements (Assaiante et al.,
1993
; Berger et al.,
1984
; Brenière and Bril,
1998
; Bril and
Brenière, 1993
; Cheron et al.,
2001a
,b
;
Forssberg, 1985
;
Sutherland et al., 1980
).
Spinal and brainstem networks are thought to be integrated with
supra-segmental control as automatic stepping evolves into walking. In
particular, the transition to unsupported walking requires that the control of
stepping is integrated with postural control. In human locomotion, this
integration depends on motor cortical control much more heavily than it does
in other mammals (Capaday,
2002
; Dietz,
2002
), and descending cortico-spinal tracts are not mature at the
age of 1 year (Paus et al.,
1999
). It is conceivable that, while the spinal CPG units driving
different limb segments are operational at birth, the phase coupling between
different units may need to be tuned by descending supra-spinal signal during
development.
Progressive changes of gait kinematics and kinetics as a function of child
age depend on the neural maturation of central pathways that are important for
postural and locomotor control, as result from myelination of descending
tracts (Paus et al., 1999) and
from improved cognitive capacity to generate different associations and to
access memory rapidly, which may in turn permit the necessary integrative
capacity for balance and coordination to occur
(Zelazo, 1983
). In addition,
however, walking experience under unsupported conditions acts as a functional
trigger of gait maturation. By repeatedly testing two infants over a period
between 4 months before and 13 months after the onset of independent walking,
we showed that gait parameters remained unchanged until independent walking,
and then rapidly matured after that age. The role of walking experience is
stressed by two other observations. (1) Infants undergoing daily stepping
exercise exhibit an earlier onset of independent walk than untrained infants
(Zelazo et al., 1972
). (2) In
normal untrained children, the rapid developmental changes are clearly
recognized when plotted relative to the time after the onset of independent
walking, but they are blurred when plotted relative to the time after birth,
because of the variability of the age of independent walk
(Sundermier et al., 2001
;
Yaguramaki and Kimura,
2002
).
![]() |
List of symbols |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
![]() |
Acknowledgments |
---|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Ahn, A. N., Furrow, E. and Biewener, A. A.
(2004). Walking and running in the red-legged running frog,
Kassina maculata. J. Exp. Biol.
207,399
-410.
Alexander, R. M. (1989). Optimization and gaits
in the locomotion of vertebrates. Physiol. Rev.
69,1199
-1227.
Assaiante, C., Thomachot, B. and Aurenty, R. (1993). Hip stabilization and lateral balance control in toddlers during the first four months of autonomous walking. Neurorep. 4,875 -878.
Bastien, G. J., Heglund, N. C. and Schepens, B.
(2003). The double contact phase in walking children.
J. Exp. Biol. 206,2967
-2978.
Berger, W., Altenmüller, E. and Dietz, V. (1984). Normal and impaired development of children's gait. Human Neurobiol. 3,163 -170.[Medline]
Bianchi, L., Angelici, D., Orani, G. P. and Lacquaniti, F.
(1998a). Kinematic co-ordination in human gait: relation to
mechanical energy cost. J. Neurophysiol.
79,2155
2170.
Bianchi, L., Angelici, D. and Lacquaniti, F. (1998b). Individual characteristics of human walking mechanics. Pflugers Arch. 436,343 -356.[CrossRef][Medline]
Borghese, N. A., Bianchi, L. and Lacquaniti, F. (1996). Kinematic determinants of human locomotion. J. Physiol. 494,863 879.[Abstract]
Brenière, Y. and Bril, B. (1998). Development of postural control of gravity forces in children during the first 5 years of walking. Exp. Brain Res. 121,255 -262.[CrossRef][Medline]
Bril, B. and Brenière, Y. (1993). Posture and independent locomotion in early childhood: learning to walk or learning dynamic postural control? In The Development of Coordination in Infancy (ed. G. J. P. Savelsbergh), pp.337 -358. Amsterdam: Elsevier.
Capaday, C. (2002). The special nature of human walking and its neural control. Trends Neurosci. 25,370 -376.[CrossRef][Medline]
Cavagna, G. A. (1975). Force platforms as
ergometers. J. Appl. Physiol.
39,174
179.
Cavagna, G. A., Pranzetti, P. and Fuchimoto, T. (1983). The mechanics of walking in children. J. Physiol. 343,323 339.[Abstract]
Cavagna, G. A. and Kaneko, M. (1977). Mechanical work and efficiency in level walking and running. J. Physiol. 268,467 -481.[Medline]
Cavagna, G. A., Saibene, F. P. and Margaria, R. (1963). External work in walking. J. Appl. Physiol. 18,1 -9.
Cavagna, G. A., Thys, H. and Zamboni, A. (1976). The sources of external work in level walking and running. J. Physiol. 262,639 -657.[Abstract]
Cheron, G., Bengoetxea, A., Bouillot, E., Lacquaniti, F. and Dan, B. (2001a). Early emergence of temporal co-ordination of lower limb segments elevation angles in human locomotion. Neurosi. Lett. 308,123 -127.[CrossRef]
Cheron, G., Bouillot, E., Dan, B., Bengoetxea, A., Draye, J. P. and Lacquaniti, F. (2001b). Development of a kinematic coordination pattern in toddler locomotion: planar covariation. Exp. Brain Res. 137,455 -466.[CrossRef][Medline]
Courtine, G. and Schieppati, M. (2004). Tuning
of a basic coordination pattern constructs straight-ahead and curved walking
in humans. J. Neurophysiol.
91,1524
1535.
Dickinson, M. H., Farley, C. T., Full, R. J., Koehl, M. A.,
Kram, R. and Lehman, S. (2000). How animals move: an
integrative view. Science
288,100
-106.
Dietz, V. (2002). Proprioception and locomotor disorders. Nat. Rev. Neurosci. 3, 781-790.[CrossRef][Medline]
Farley, C. T. and Ko, T. C. (1997). Mechanics
of locomotion in lizards. J. Exp. Biol.
200,2177
-2188.
Forssberg, H. (1985). Ontogeny of human locomotor control. I. Infant stepping, supported locomotion and transition to independent locomotion. Exp. Brain Res. 57,480 493.[Medline]
Goodman, L., Riley, M. A., Mitra, S. and Turvey, M. T. (2000). Advantages of rhythmic movements at resonance: minimal active degrees of freedom, minimal noise, and maximal predictability. J. Motil. Behav. 32,3 -8.
Goslow, G. E. Jr, Seeherman, H. J., Taylor, C. R., McCutchin, M. N. and Heglund, N. C. (1981). Electrical activity and relative length changes of dog limb muscles as a function of speed and gait. J. Exp. Biol. 94,15 -42.[Abstract]
Grasso, R., Zago, M. and Lacquaniti, F. (2000).
Interactions between posture and locomotion: motor patterns in humans walking
with bent posture versus erect posture. J.
Neurophysiol. 83,288
-300.
Hallemans, A., Aerts, P., Otten, B., De Deyn, P. P. and De
Clercq, D. (2004). Mechanical energy in toddler gait. A
trade-off between economy and stability? J. Exp. Biol.
207,2417
-2431.
Heglund, N. C., Cavagna, G. A. and Taylor, C. R. (1982). Energetics and mechanics of terrestrial locomotion. III. Energy changes of the centre of mass as a function of speed and body size in birds and mammals. J. Exp. Biol. 97, 41-56.[Abstract]
Ivanenko, Y. P., Grasso, R., Macellari, V. and Lacquaniti,
F. (2002). Control of foot trajectory in human locomotion:
role of ground contact forces in simulated reduced gravity. J.
Neurophysiol. 87,3070
-3089.
Jensen, R. K. (1986). Body segment mass, radius and radius of gyration proportions of children. J. Biomech. 19,359 -368.[CrossRef][Medline]
Lacquaniti, F., Grasso, R. and Zago, M. (1999). Motor patterns in walking. News Physiol. Sci. 14,168 174.[Medline]
Lamb, T. and Yang, J. F. (2000). Could
different directions of infant stepping be controlled by the same locomotor
central pattern generator? J. Neurophysiol.
83,2814
-2824.
Lee, C. R. and Farley, C. T. (1998).
Determinants of the center of mass trajectory in human walking and running.
J. Exp. Biol. 201,2935
-2944.
Mardia, K. V. (1972). Statistics of Directional Data. London: Academic Press Inc.
Minetti, A. E., Ardigo, L. P., Saibene, F., Ferrero, S. and Sartorio, A. (2000). Mechanical and metabolic profile of locomotion in adults with childhood-onset GH deficiency. Eur. J. Endocrinol. 142,35 41.[Medline]
Minetti, A. E., Saibene, F., Ardigo, L. P., Atchou, G., Schena, F. and Ferretti, G. (1994). Pygmy locomotion. Eur. J. Appl. Physiol. Occup. Physiol. 68,285 -290.[Medline]
Mochon, S. and McMahon, T. A. (1980). Ballistic walking. J. Biomech. 13,49 -57.[CrossRef][Medline]
Muir, G. D., Gosline, J. M. and Steeves, J. D. (1996). Ontogeny of bipedal locomotion: walking and running in the chick. J. Physiol. 493,589 -601.[Abstract]
Pang, M. Y. and Yang, J. F. (2001). Interlimb
co-ordination in human infant stepping. J. Physiol.
533,617
-625.
Paus, T., Zijdenbos, A., Worsley, K., Collins, D. L., Blumenthal, J., Giedd, J. N., Rapoport, J. L. and Evans, A. C. (1999). Structural maturation of neural pathways in children and adolescents: in vivo study. Science 238,1908 -1911.[CrossRef]
Poppele, R. and Bosco, G. (2003). Sophisticated spinal contributions to motor control. Trends Neurosci. 26,269 -276.[CrossRef][Medline]
Saibene, F. and Minetti, A. E. (2003). Biomechanical and physiological aspects of legged locomotion in humans. Eur. J. Appl. Physiol. 88,297 -316.[Medline]
Schepens, B., Bastien, G. J., Heglund, N. C. and Willems, P.
A. (2004). Mechanical work and muscular efficiency in walking
children. J. Exp. Biol.
207,587
-596.
Schneider, K. and Zernicke, R. F. (1992). Mass, center of mass, and moment of inertia estimates for infant limb segments. J. Biomech. 25,145 -148.[CrossRef][Medline]
Sundermier, L., Woollacott, M., Roncesvalles, N. and Jensen, J. (2001). The development of balance control in children: comparisons of EMG and kinetic variables and chronological and developmental groupings. Exp. Brain Res. 136,340 -350.[CrossRef][Medline]
Sutherland, D. H., Olshen, R., Cooper, L. and Woo, S. L. (1980). The development of mature gait. J. Bone Joint Surg. 62,336 -353.[Medline]
Tesio, L., Lanzi, D. and Detrembleur, C. (1998). The 3-D motion of the centre of gravity of the human body during level walking. I. Normal subjects at low and intermediate walking speeds. Clin. Biomech. 13, 77-82.[CrossRef]
Vaughan, C. L. (2003). Theories of bipedal walking: an odyssey. J. Biomech. 36,513 -523.[CrossRef][Medline]
Willems, P. A., Cavagna, G. A. and Heglund, N. C. (1995). External, internal and total work in human locomotion. J. Exp. Biol. 198,379 -393.[Medline]
Winter, D. A. (1991). The Biomechanics and Motor Control of Human Gait: Normal, Elderly and Pathological. Waterloo, Ontario: Waterloo Biomechanics Press.
Yaguramaki, N. and Kimura, T. (2002). Acquirement of stability and mobility in infant gait. Gait Posture 16,69 -77.[CrossRef][Medline]
Yang, J. F., Stephens, M. J. and Vishram, R.
(1998). Infant stepping: a method to study the sensory control of
human walking. J. Physiol.
507,927
937.
Zatsiorsky, V., Seluyanov, V., Chugunova, L. (1990). In vivo body segment inertial parameters determination using a gamma-scanner method. In Biomechanics of Human Movement: Applications in Rehabilitation, Sports and Ergonomics (ed. N. Berme and A. Cappozzo), pp. 186202. Worthington, OH: Bertec.
Zelazo, P. R., Zelazo, N. A. and Kolb, S. (1972). `Walking' in the newborn. Science 176,314 -315.[Medline]
Zelazo, P. R. (1983). The development of walking: new findings and old assumptions. J. Motil. Behav. 15,99 -137.