Development of displacement of centre of mass during independent walking in children Frédéric Dierick MSc; Caroline Lefebvre PT, Rehabilitation and Physical Medicine Unit, Université catholique de Louvain; Adélaïde van den Hecke PT, Department of Physical Medicine and Rehabilitation, Cliniques universitaires Saint-Luc; Christine Detrembleur* PhD, Rehabilitation and Physical Medicine Unit, Université catholique de Louvain, Brussels, Belgium. *Correspondence to last author at Rehabilitation and Physical Medicine Unit, Université catholique de Louvain, Tour Pasteur 5375, Avenue Mounier 53, 1200 Brussels, Belgium. E-mail: [email protected]

The aims of this study were to assess the characteristics of three-dimensional displacement of the centre of mass of the body (CMb) during walking in healthy children and to compare it with those of young adults. Twenty-one children (11 males, 10 females; age range 1 to 9 years) were recruited from the nursery and school attached to the Université catholique de Louvain, Brussels, Belgium; and three young adults (one male, two females; mean age 26 years 4 months) were recruited from the Rehabilitation and Physical Medicine Unit of the same university. Displacement of CMb was assessed at different walking velocities in the children and adults by two successive mathematical integrations of ground reaction forces, measured by a large strain-gauge force platform. Displacement of CMb was controlled for leg length of the participant to eliminate the scaling effect that is dependent on growth. Results showed that vertical and lateral amplitudes of the CMb when controlled for leg length were greater for children before 4 years of age and that the forward amplitude when controlled for leg length was greater for children before 7 years of age. We conclude that the development of mature human CMb displacement during independent walking is a gradual neural process, evolving until the age of 7 years.

See end of paper for list of abbreviations.

The development of independent walking has been studied for a long time (McGraw 1940, Scrutton 1969, Burnett and Johnson 1971, Statham and Murray 1971, Sutherland et al. 1980, Forssberg 1985). Locomotor development can result from a multidimensional, gradual process (Thelen and Cooke 1987) involving not only musculoskeletal growth and biomechanical factors but also maturation of the central nervous system (Sutherland et al. 1980, Forssberg 1985, Sutherland 1997). The challenge in studying the development of independent normal walking is to understand which locomotor changes are related to anthropomorphic development and which are due to the maturation of neural control. To take size and morphology into account, dimensionless numbers are used widely in biology; this normalization method has proven to be useful in comparing walking patterns of different species (Alexander 1989) and of differently sized participants (Cavagna et al. 1983, Minetti et al. 1994). To appreciate quantitatively the subtle changes in walking that occur during locomotor development, numerous variables associated with walking (time–distance parameters, footprint sequences, kinematics, electromyography, kinetics, metabolic cost, centre of mass of the body [CMb] acceleration and mechanics) have been widely explored (Scrutton 1969, Sutherland et al. 1980, Beck et al. 1981, Cavagna et al. 1983, Brenière and Bril 1998, DeJaeger et al. 2001). Although some of these studies showed that the development of walking is mainly complete by about 3 years of age (Sutherland et al. 1980), several studies have shown that the development of locomotor function takes up to about 7 years of age to be refined (Cavagna et al. 1983, Preis et al. 1997, Brenière and Bril 1998, Hausdorff et al. 1999) depending on the variables analyzed. None of the many studies of the development of walking has measured three-dimensional displacement of CMb from the onset of independent walking. Nevertheless, the displacement of CMb during walking, which represents and characterizes the whole body system in movement, is classically used to explain CMb mechanics, metabolic energy expenditure, postural adjustments, and dynamic equilibrium. The aims of this study were: (1) to study the characteristics of three-dimensional displacement of CMb during walking in children at ages between 1 and 9 years, and to compare it with those of young adults; and (2) to determine when children achieve an adult-like three-dimensional displacement of CMb. Method PARTICIPANTS

Twenty-one healthy children (11 males, 10 females; age range 1 to 9 years) and three healthy young adults (one male, two females; mean age 26 years 4 months) participated in the experiments. Children were recruited from the nursery and the school attached to the Université catholique de Louvain, Brussels, Belgium. Adults were recruited from the Rehabilitation and Physical Medicine Unit of the same university. Participant characteristics are listed in Table I. The local ethics committee approved the study procedure. From the initial potential sample (n=410), 50 parents and the adult participants gave informed consent. The healthy children were able to walk independently, and toe-walkers were excluded. Children were divided into three age groups: group 1, 1 to 3 years; group 2, 4 to 6 years; and group 3, 7 to 9 years. These groups were formed according to studies on locomotor development (Sutherland et al. 1980) which shows that variables associated

Developmental Medicine & Child Neurology 2004, 46: 533–539 533

with walking are completely mature after 3 to 4 years of age, and more recent literature demonstrating, on the contrary, that development of walking is only complete after 6 to 7 years of age (Brenière and Bril 1998, Hausdorff et al. 1999). From the residual group of 50 children, we randomly selected 30 children, 10 in each age group, but only seven children in each group were able to walk at a steady speed. The young adults formed group 4. INSTRUMENTATION

A strain-gauge force platform (1.8m long × 0.6m wide; Pharos System Inc., MA, USA; Fig. 1a), sensitive to the three-dimensional components of the ground reaction force, was mounted at ground level in the centre of a walkway that was 10m in length (Fig. 1b). The platform signal was sampled at 50Hz and recorded on an IBM compatible computer. Two photoelectric cells and reflectors were placed at either end of the platform to trigger data and provide the mean forward walking speed of participants (Fig. 1b). PROCEDURE

All participants walked wearing their clothes and normal shoes (heel height no greater than 2cm) over the force platform (Fig. 1b). The children in group 3 (7 to 9 years) and the adult group were instructed to look straight forward and to walk as naturally as possible at different constant forward speeds on the platform. Information from the photocells, which were placed at the level of the neck of the participant to avoid interference with the movements of the upper limbs, was used to give feedback to the children and adults about their forward walking speed during the experiments.

No instruction was given to the children in groups 1 and 2, who spontaneously walked at different forward speeds. Two wooden boards were placed on the sides of the platform to ensure that the youngest children walked straight forward and to ensure that they stayed on the platform during the measurement period (Fig. 1b). DATA ANALYSIS

From the vertical, lateral, and forward components of the ground reaction force, three-dimensional accelerations of CMb were calculated. The vertical, lateral, and forward displacement of CMb (Sv, Sl, Sf) were obtained by two successive mathematical integrations. This methodology was tested and validated by Willems et al. (1995). The criterion for rejecting a stride was the demonstration during the selected stride of a clear trend (more than 10%) towards an increase or decrease in the average speed of CMb (Cavagna et al. 1983). In total, 129 of 800 trials corresponding to this criterion were selected. For each selected stride the amplitude of CMb in the vertical, lateral, and forward directions (Av, Al, Af) was calculated as the absolute value of the difference between the maximum and minimum values on the Sv, Sl, and Sf curves. In addition, the total length of the path (Lpath) of CMb in the frontal plane (Sl versus Sv) during one stride was calculated as i=n–1

Lpath = ∑

(Svi – Svi+1)2 + (Sli – Sli+1)2

i=1

where Svi, Svi+1, Sli, and Sli+1 denote the values of Sv and Sl at the instants i and i+1.

Table I: Characteristics of participants Group

Number of participants

Mean (SD) age, y:mo

Mean (SD) weight, kg

Mean (SD) height, m

Mean (SD) leg length, m

7 7 7 3

1:11 (0:11) 4:8 (0:11) 8:4 (1:2) 26:4 (4:7)

15.15 (3.4) 20.57 (2.7) 31.59 (7.4) 73.32 (21.2)

0.93 (0.09) 1.12 (0.09) 1.36 (0.07) 1.70 (0.06)

0.42 (0.03) 0.54 (0.04) 0.71 (0.05) 0.87 (0.04)

Group 1 (1–3 years) Group 2 (4–6 years) Group 3 (7–9 years) Group 4 (adults)

a

b

Reflector Photoelectric cell

0.6m

0.6m

0.6m

0.6m

Force platform

Wooden board

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Figure 1: Experiment set up. (a) Top view of large force platform made of seven plates of different sizes. (b) Young participant walking over force platform during a trial. Note two wooden boards placed at sides of platform and photoelectric cells and reflectors at either end of platform, which allowed acquisition of ground reaction forces to start and stop.

number, Fr=Vf2/(gL), where Vf is the mean forward walking speed, g is acceleration due to gravity, and L is leg length of the participant. Fr is particularly appropriate when comparing participants of different size, but who are geometrically and kinematically similar, moving in situations where mainly inertia and gravity interact, such as walking (Alexander 1989, Hof 1996).

In gait analysis, a good practice is to try to correct as much as possible for unequal weight and stature of participants, and to compare measurements of participants without the effect of scaling. Many solutions to the scaling problem exist. A method based on non-dimensional quantities is very useful in correcting for size differences (Hof 1996). However, these numbers are more difficult to interpret than SI units. In human gait analysis it is natural to choose the leg length of the participant (the distance from hip to ground; L) to eliminate the scaling effect. Then values of Sv, Sl, Sf, Av, Al, Af, and Lpath are expressed as dimensionless numbers by relating to L. We also expressed walking speed as a dimensionless number. However, a dynamic comparison is not based simply on the geometrical scale factor, therefore the walking speed cannot be simply related to L. For example, if we are interested in calculating the angular speed of a smaller pendulum from that of a large one, a scale factor would no longer apply because the natural frequency of oscillation is not the same, being higher for the smaller pendulum. Then the ideal scaling method for speed is to use the Froude (Fr)

Statistically, we analyzed Av, Al, Af, and Lpath. Values of the variables were arbitrarily grouped into three different speed groups: speed group I, 2 to 2.99km/h; speed group II, 3 to 3.99km/h; and speed group III, >4km/h. The dimensionless data were grouped in three Fr groups: Fr group I, 0 to 0.09; Fr group II, 0.1 to 0.19; and Fr group III, 0.2 to 0.29. Data were also grouped in the four different age groups: groups 1 to 4 (see Participants). A two-way measures analysis of variance (ANOVA) with post hoc Dunnett’s method (SigmaStat V, version 2.0) evaluated the effect of age on variables at a probability level of 0.05 without neglecting the effect of speed or Fr.

a

b

0.04

Sv(m)

Sv /L

0.04

Sl (m)

Sl /L 20% stride

Al

Sv (m) 0.04

Figure 2: Typical centre of mass of body (CMb) displacement during one stride in vertical and lateral directions and phase portraits: (a) traces were obtained from a male child age 3 years (height, 1.07m, weight, 21kg; leg length (L), 0.42m) walking at 0.54m/s, and (b) traces from a male adult of 25 years of age (height, 1.78m; weight, 96kg; L, 0.86m) walking at 0.75m/s. Upper and middle traces show typical displacement of CMb in vertical and lateral directions during one stride (expressed as per cent) for a similar Fr (0. 07). Grey lines indicate raw data, and black lines data controlled for L. Bottom traces show phase portraits between Sv and Sl during one stride, representing displacement of CMb in frontal plane. Sv(m), displacement of CMb in vertical direction; Sv/L, displacement of CMb in vertical direction controlled for L; Sl(m), displacement of CMb in lateral direction; SlL displacement of CMb in vertical direction controlled for L.

STATISTICAL ANALYSIS

Av

Sv /L 0.04 Sl (m)

Sl /L

Child 3y

Adult 25y

0.54m/s – Fr=0.07

0.75m/s – Fr=0.07

Development of Displacement of Centre of Mass Frédéric Dierick et al. 535

Results The subgroups were mixed in sex because no significant difference was observed between males and females. Figure 2 shows, from top to bottom, typical traces of Sv, Sv controlled for L (Sv/L,) in the vertical direction; Sl and Sl controlled for L (Sl/L,) in the lateral direction during one stride; and phase portraits between Sv/Sl and (Sv/L)/(Sl/L) during one stride. Left traces were obtained from a male child of 3 years of age walking at 0.54m/s, and right traces from a male adult of 25 years of age walking at 0.75m/s. Lower limb length of the child was 0.41m and for the adult 0.86m. Fr was equal to 0.07 for child and adult. Sv describes a pseudo-sinusoidal curve in the vertical direction. The

Figure 3: Results of amplitudes of centre of mass of body (CMb) in three directions for different age groups. Left column, amplitudes of CMb (in metres) in vertical, lateral , and forward directions, and Lpath (in metres) during one stride for different age groups (▲, 1 to 3 years; ■, 4 to 6 years; ●, 7 to 9 years, ● , adults) as a function of different speed (m/s) groups. Right column, dimensionless data, i.e. threedimensional amplitudes of CMb and Lpath controlled for L as a function of different Froude (Fr) groups. Each symbol represents mean value of trials obtained for a same range of speed or Fr and age group. Vertical bars, standard deviations. Av (m), amplitudes of CMb in vertical direction; Al , amplitudes of CMb in lateral direction; Af , amplitudes of CMb in forward direction; Av/l/f/L, amplitude directions controlled for leg length of participant; Lpath, total length of path of CMb in frontal plane.

Av /L

0.08

0.03

0.04

0

0.06

0.10

Al /L

0

0.03

0.05

0

1.5

2

Af /L

0

1

1.5

0.5

1

0

0

0.2

0.3

Lpath /L

Lpath (m)

Af (m)

Al (m)

Av (m)

0.06

minima of the Sv curve took place at about the middle of the double-stance phases, and the maxima at about the middle of the single-stance phases. Sl also described a sinusoidal curve but in the lateral direction. The minimum and maximum of Sl nearly occurred when Sv was maximum. The phase portrait combining Sv and Sl described the path of CMb in the frontal plane during one stride of walking. This path, in shape of an infinity symbol (∞ ), varied with age for a similar Fr. For the young child, ∞ was closer to a ‘U’ shape than for the adult. The left column in Figure 3 shows, from top to bottom, Av, Al, Af , and Lpath (expressed in metres) as a function of walking speed (in metres per second) for the different age groups. The right column in Figure 3 shows the three-dimensional

0.2

0.1 0

0 0

0.6

0.9

1.2

1.5

0

Walking speed (m/s)

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0.1

0.2

Froude number (Fr)

0.3

amplitudes of CMb and Lpath controlled for L as function of Fr. Each symbol represents the mean value of trials obtained for a same range of speed and Fr in each age group; vertical bars indicate standard deviations. The vertical amplitude of CMb increased with walking speed as Av/L increased with Fr for all age groups. Av was significantly smaller (p=0.007; Table II) for children of age groups 1 (1–3y; 0.029m) and 2 (4–6y; 0.028m) than for the adult group (0.038m). By eliminating the scaling effect to underline the maturation effect, we observed that Av/L was significantly greater (p=0.018; Table II) for children of age group 1 (0.068) than for the adult group (0.049). Note that in the typical trace (Fig. 2), Av was nearly equal for the young child (0.021) and the adult (0.019), depending on the low speed adopted by the adult. However, Av/L (Fig. 2) was 2.4 times greater for the young child (0.052) than for the adult (0.022). Lateral amplitude decreased with speed, and lateral amplitude controlled for L decreased with Fr for all age groups. Al increased with age and was significantly lower (p<0.001; Table II) for children of age groups 1 (0.026), 2 (0.026), and 3 (0.030) than for the adults (0.043). After eliminating the scaling effect, we observed that Av/L was significantly greater (p<0.001; Table II) between age group 1 (0.058) and the adult group (0.037). Note that in Fig. 2, Al for the young child (0.033) was 60% that of the adult (0.055). Av/L was 1.3 times greater for the young child (0.081) than for the adult (0.064). Forward amplitude of CMb increased with speed, and Af/L increased with Fr for all age groups. Af was significantly affected by the scaling effect (p<0.0001; Table II), being lower between age group 1 (0.71m), group 2 (0.87m), group 3 (0.98m), and the adult group (1.09m). By eliminating the scaling effect, we observed that Af/L was significantly greater (p=0.004; Table II) for age groups 1 (1.57) and 2 (1.56) than for the adult group (1.37). Finally, Lpath was significantly lower (p=0.02; Table II) for children of age groups 1 (0.12m) and 2 (0.11m) than for the

adult group (0.14m). By eliminating the scaling effect, we observed that Lpath/L was significantly greater (p<0.001; Table II) for children of age group 1 (0.27) than for the adult group (0.17). The evolution of Av, Al, and Af as functions of walking speed (Fig. 3, left column) and the evolution of CMb amplitudes controlled for L as a function of Fr (Fig. 3, right column) have the same tendency in children and adults. For the same age group and increasing Fr, we systematically observed an increase in Av/L and Af/L, and a decrease of the Al/L. With the increase of Fr, Av/L increases when Al/L decreases nearly in the same proportion, and consequently values of Lpath/L were not modified by changes in Fr among children and adults (p=0.144; Table II). Discussion The main aim of this study was to assess the characteristics of the three-dimensional displacement of CMb during walking in children from 1 to 9 years of age, and to compare it with those of young adults, in order to underline the changes related to the development of mature CMb displacement. Therefore, to eliminate scaling differences between children and adults, results for Av, Al, Af, and Lpath were controlled for L and expressed as dimensionless numbers. Results have shown that the values of Av/L, Al/L, and Lpath/L are mature for children from the age of 4 years, whereas the values of Af/L are only mature from the age of 7 years. SCALING EFFECT

Why have we chosen to express the three-dimensional amplitudes of CMb controlled for L to obtain dimensionless results? First, in the sagittal plane, the validity of the inverted pendulum model during walking, L dependent, has been previously demonstrated for adults (see Cavagna et al. 1976) and children (see Cavagna et al. 1983). Hence, in this model, the magnitudes of vertical and forward displacements of CMb are related to the length of the pendulum, represented by the value of L of the participant. Secondly, in the frontal plane, an

Table II: Statistical results of a two-way measures ANOVA and post-hoc Dunnett’s method on amplitudes of centre of mass of the body displacement Amplitude

Av Al Af Lpath

p

0.007 <0.001 <0.001 0.016

F

4.2 10.4 68.3 3.6

Age factor

Speed factor

Group 4 (Adults) Reference Mean (95% CI)

Group 1 (1–3 years) Mean (95% CI)

Group 2 (4–6 years) Mean (95% CI)

Group 3 (7–9 years) Mean (95% CI)

p

0.038 (0.034–0.042) 0.043 (0.038–0.047) 1.09 (1.05–1.12) 0.14 (0.12–0.16)

0.029 (0.025–0.034) 0.026 (0.021–0.031) 0.71 (0.69–0.75) 0.12 (0.11–0.13)

0.028 (0.023–0.034) 0.026 (0.019–0.032) 0.87 (0.82–0.91) 0.11 (0.09–0.12)

0.035 (0.031–0.39) 0.030 (0.026–0.034) 0.98 (1.05–1.12) 0.14 (0.13–0.15)

0.002 <0.001 <0.001 0.58

Age factor Av /L Al /L Af /L Lpath/L

0.018 <0.001 0.004 <0.001

3.5 5.9 4.8 11.9

0.049 (0.041–0.058) 0.037 (0.029–0.045) 1.37 (1.29–1.45) 0.17 (0.13–0.21)

0.068 (0·06–0.075) 0.058 (0.05–0.065) 1.57 (1.5–1.65) 0.27 (0.25–0.29)

0.055 (0.047–0.063) 0.046 (0.037–0.053) 1.56 (1.48–1.64) 0.19 (0.17–0.21)

Fr factor 0.060 (0.053–0.066) 0.036 (0.029–0.042) 1.48 (1.42–1.55) 0.20 (0.18–0.22)

<0.001 <0.001 <0.001 0.144

Significant differences for ANOVA and post-hoc analysis on age factor (adult group: reference) are shown in bold. Fr, Froude number; Av/l/f,vertical/lateral/forward amplitudes; Lpath, total length of path of centre of mass of body in frontal plane; L, participants’ leg length.

Development of Displacement of Centre of Mass Frédéric Dierick et al. 537

inverted pendulum model was also used to assess the mechanism of equilibrium control during walking (MacKinnon and Winter 1993) and the magnitude of lateral displacement of CMb was, thus, also related to the value of L of the participant. Moreover, leg length was chosen rather than the child’s height, as it represented the static lever length of the limb (Scrutton 1969). Previous studies have shown that the mechanics between differently sized participants can be compared better if the locomotion speeds of the different groups are normalized for dynamic similarity by transforming them into dimensionless speed: the so-called Froude number (Cavagna et al. 1976, 1983). This normalization method has been successfully used in the past to compare walking patterns of different species (Alexander 1989) and differently sized participants (see Cavagna et al. 1983, Minetti et al. 1994). DEVELOPMENT OF MATURE VERTICAL DISPLACEMENT

Results obtained in this study have shown that in taking into account the scaling effect, the vertical amplitude of CMb controlled for L is greater for children before 4 years of age than for the adults. Our results are in good agreement with the only previous study on the mechanics of CMb in children (see Cavagna et al. 1983). The greater Av/L by children and the maturation of this parameter from the age of 4 years could result from a lack of maturation of three mechanisms systematically observed during mature plantigrade walking: (1) heel strike and push off; (2) knee–ankle kinematic coordination; and (3) reciprocal arm swing. Heel strike and push off Mature human walking is characterized by a specific ankle displacement in the sagittal plane, with a prominent heel strike at foot contact owing to a strong dorsiflexion of the foot at the end of the swing phase and a push off at the end of the stance phase. This ankle displacement, resulting from a particular temporal pattern of pretibial and calf muscles, enables the path of displacement of the knee to remain relatively horizontal during the entire stance phase (Saunders et al. 1953). This in turn allows smoothing of the path of the hip and the vertical path of CMb and, consequently, minimization of its vertical displacement (Saunders et al. 1953). The child who begins to walk independently shows neither initial heel strike nor push off; rather, the child places their foot flat on the ground (Statham and Murray 1971, Sutherland et al. 1980, Forssberg 1985). Initial heel strike is absent at 1 year of age, is only slightly developed between 11⁄2 and 2 years of age (Sutherland et al. 1980), and prominent heel strike does not occur until after 2 years of age (Forssberg 1992). The transformation to a mature ankle displacement in children allows a progressive smoothing of the vertical displacement of CMb because this transformation to mature plantigrade walking continues in children until about 4 years of age (Forssberg 1992). Knee–ankle kinematic coordination Mature human walking also needs a specific knee–ankle coordination based on out-of-phase knee and ankle joint displacements during the stride. In a study of the ontogeny of human locomotor control, Forssberg (1985) noticed the lack of knee– ankle kinematic coordination in children beginning to walk independently. We hypothesized that this lack of coordination during the single-stance phase could induce a reduction

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of the virtual-stance limb compression that is present in mature walking and which allows reduction in the magnitude of the vertical excursion of CMb (Lee and Farley 1998). Reciprocal arm swing It has been shown that reciprocal arm swing is an important factor in minimizing the vertical displacement of CMb (Murray et al. 1967). Hence, the absence of reciprocal arm swing could be, to a lesser extent, responsible for the greater relative vertical displacement of CMb in the youngest children. This active reciprocal arm swing first appears at 11⁄2 years of age and is systematically produced by the age of 11⁄2 years (Sutherland et al. 1980). DEVELOPMENT OF MATURE LATERAL DISPLACEMENT

In taking into account the scaling effect, the lateral amplitude of CMb controlled for L is also greater for children before 4 years of age than for adults. This immature lateral displacement of CMb during walking before the age of 4 could be mainly explained by: (1) a wider supporting base; (2) an increase in the included angle of the foot; and (3) an immature temporal activity pattern of the gluteus medius muscle. Wider supporting base Previous studies emphasized the wider supporting base adopted by children during walking before the age of 4 years (Sutherland 1997). This wider supporting base could explain the greater lateral amplitude of CMb (Saunders et al. 1953). Several previous studies have shown that a decrease in the supporting base width during walking in children was related to the development of the equilibrium system (Woollacott et al. 1996). Increase in the included angle of the foot Scrutton (1969) showed little alteration of the dynamic base in children between 1 and 4 years, but the dynamic base may be reduced as the infant matures by a reduction in the included angle of the foot. Younger infants, having a larger included angle, find themselves with a good base and, therefore, have no need to widen it to improve their stability. Immature temporal activity pattern of the gluteus medius The temporal activity pattern of the gluteus medius, of which the most important functions are to stabilize the hip and prevent excessive drop of the opposite part of the pelvis during single-stance phases of walking, is adult-like from the age of 4 years (Sutherland et al. 1988). DEVELOPMENT OF MATURE FORWARD DISPLACEMENT

In taking into account the scaling effect, the forward amplitude of CMb controlled for L is greater for the children below the age of 7 years than for adults. Similar results have been described by Cavagna et al. (1983). These authors explained this greater forward displacement at a given speed by a relatively longer step in children than in adults. This explanation raises the following question: why do children make relatively longer steps than adults? During the single-stance phases of independent walking, children do not have the same postural capacity as adults to control their equilibrium with respect to gravitational forces, and consequently they are ‘walking by falling’ whereas the adult falls during walking (Brenière and Bril 1988, 1998). The ‘walk by falling’ in children, associated with a more raised

CMb and consequently a high guard-arm posture, might help them to create the acceleration necessary to move the body forward at a moment when the child is not yet able to propel itself purely by the muscular force of the lower limbs (Ledebt 2000). We hypothesize that this phenomenon could explain the greater amplitude of forward displacement of CMb by children during walking. Conclusion We have shown that the development of mature human CMb displacement during independent walking is a gradual process, evolving until the age of 7 years, depending on the plane of space considered. These data could allow comparisons of children having movement pathology or motor delay with the normative data. Further research is needed to determine the repercussions of neurological or orthopaedic disorders on the displacement of CMb during walking in children, and to evaluate the effects of various surgical interventions and other pharmacological or conservative treatments. However, our results are only exploratory because of the small number of participants. DOI: 10.1017/S0012162204000891 Accepted for publication 25th March 2004. Acknowledgments The authors thank Nicole Boisacq-Schepens for her comments on an earlier version of this manuscript. This research was supported by the Fonds National de la Recherche Scientifique Médicale of Belgium, the Fonds Special de Recherche of the Université catholique de Louvain, the Région wallonne (Programme WallonieDéveloppement-Université, Easyform), and the Fondation Van Goethem-Brichant. References Alexander R McN. (1989) Optimization and gaits in the locomotion of vertebrates. Physiol Rev 69: 1199–1227. Beck RJ, Andriacchi TP, Kuo KN, Fermier RW, Galante JO. (1981) Changes in the gait patterns of growing children. J Bone Joint Surg 63A: 1452–1457. Brenière Y, Bril B. (1988) Pourquoi les enfants marchent en tombant alors que les adultes tombent en marchant? C R Acad Sci Paris 307: 617–622. (In French). Brenière Y, 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. Burnett CN, Johnson EW. (1971) Development of gait in childhood. Part II. Dev Med Child Neurol 13: 207–215. Cavagna GA, Franzetti P, Fuchimoto T. (1983) The mechanics of walking in children. J Physiol 343: 323–339. Cavagna GA, Thys H, Zamboni A. (1976) The sources of external work in level walking and running. J Physiol 262: 639–657. DeJaeger D, Willems PA, Heglund NC. (2001) The energy cost of walking in children. Pflügers Arch 441: 538–543. Forssberg H. (1985) Ontogeny of human locomotor control. I. Infant stepping, supported locomotion and transition to independent locomotion. Exp Brain Res 57: 480–493. Forssberg H. (1992) Evolution of plantigrade gait: is there a neuronal correlate? Dev Med Child Neurol 34: 916–925.

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List of abbreviations Af Al Av CMb Fr L Lpath Sf Sl Sv

Forward amplitude of CMb Lateral amplitude of CMb Vertical amplitude of CMb Centre of mass of the body Froude number Leg length of participant Total length (from hip to ground) of path of CMb in frontal plane Forward displacement of CMb Lateral displacement of CMb Vertical displacement of CMb

Development of Displacement of Centre of Mass Frédéric Dierick et al. 539