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First published online January 12, 2004
Journal of Experimental Biology 207, 587-596 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.00793

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Mechanical work and muscular efficiency in walking children

B. Schepens, G. J. Bastien, N. C. Heglund and P. A. Willems^*

Unité de Physiologie et Biomécanique de la Locomotion, Université Catholique de Louvain, 1 Place Pierre de Coubertin, B-1348 Louvain-la-Neuve, Belgium

View larger version (23K): [in a new window]   Fig. 1. Fluctuations of the external and internal mechanical energy during one stride of walking. The three upper curves present the mechanical energy changes of the centre of mass of the body (COM): Ek is the kinetic energy due to its velocity relative to the surroundings, Ep is the potential energy and Eext is the external energy, which is the sum of the Ek and Ep curves. Due to a pendular-like energy transfer between Ek and Ep, the variations of the Eext curve are smaller than those of the Ek and Ep curves. The increment a represents the work done on the COM during the first double contact phase of the stride. The internal work (Wint,dc) made by one leg against the other is presented as a function of time in the fourth and fifth curves: the positive work done by the back leg during the first double contact phase (increment b) is equal to the negative work (decrement d) absorbed in the front leg. The and curves are the kinetic energy changes of the lower and upper limbs, respectively, due to their velocity relative to the COM. The increment c represents the positive work to accelerate the front lower limb during the double contact phase. The internal energy–time curve of the lower limb () is the sum of the and Wint,dc curves. This procedure assumes that the internal positive work done by the back leg during the double contact phase (increment b in Wint,dc) increases passively the backward velocity of the front leg relative to the COM (see Materials and methods). Consequently, the internal work done by the front leg is reduced (increment e in ). The `stick-man' at the bottom of the figure shows the position of the limb segments each 10% of the stride: thick lines refer to the segments on the right side of the body that were recorded by infrared cameras; thin lines refer to the segments of the left side of the body that were reconstructed on the assumption that the movements of the left segments during one half-stride were equal to the movements of the right segments during the other half-stride. The vertical broken lines delimit the two double contact phases of the stride and were determined from the force traces. The curves are from a 20-year-old woman (mass, 70.1 kg) walking at 1.5 m s–1.

View larger version (22K): [in a new window]   Fig. 2. The mass-specific internal work done per stride to accelerate the limbs relative to the centre of mass of the body (Wint,k) and the stride frequency (f) are shown as a function of speed in each age group (top and middle row, respectively). The mass-specific internal power spent to move the limbs relative to the centre of mass of the body (int,k=Wint,kxf) is presented as a function of speed in the bottom row. Each symbol is the mean of the data grouped into 0.13–0.14 m s–1 (0.5 km h–1) intervals along the abscissa. Bars indicating the S.D. of the mean are drawn when they exceed the size of the symbol. The figures near each symbol in the top row represent N. The broken lines indicate the adult trends: in the top and middle panels, lines represent the weighted mean of the adult data, whereas in the bottom panels, lines are a second-order polynomial fit (KaleidaGraph 3.6). Note that the mass-specific int,k is larger in children due to a higher stride frequency with an approximately equal internal work per stride.

View larger version (34K): [in a new window]   Fig. 3. Energy recovery and mass-specific mechanical work per unit distance as a function of walking speed in different age groups. The pendular recovery of mechanical energy defined by equation 1 (R; circles) and by equation 2 (Rc; crosses) and the external work (Wext) are presented in the two upper rows. The internal work done by one leg against the other (Wint,dc) is presented in the third row. The kinetic internal work (Wint,k; fourth row) is measured, allowing energy transfer between the segments of the same limbs but not between limbs. The internal work (Wint; fifth row) is measured, allowing energy transfer between Wint,dc and Wint,k (see Materials and methods). The bottom row shows the total work (Wtot=Wext+Wint). The broken lines represent the weighted mean of the adult data (other indications are as in Fig. 2). Note that above 1 m s–1, Wext, Wint and Wtot are greater in children than in adults; these differences are greater the younger the subject and tend to disappear after the age of 10.

View larger version (16K): [in a new window]   Fig. 4. Mechanical power, net metabolic power and efficiency of positive work production in walking children. The top row presents the mass-specific total positive mechanical power (tot) as a function of speed in each age group. The second row shows the net energy consumption rate at steady state (net); these data are taken from DeJaeger et al. (2001). The efficiency of positive work production during walking (bottom row) is calculated as Wtot divided by net (equation 6). The values of efficiency are only presented at speeds above 0.75 m s–1 where results are considered to be robust (see text). The continuous and broken lines are fitted through all the data of children and adults, respectively, using a second-order polynomial function (KaleidaGraph 3.6). Efficiency is computed from these polynomial functions. Other indications are as in Fig. 2. Note that in children younger than six, the efficiency of positive work production during walking is lower than in adults.

View larger version (18K): [in a new window]   Fig. 5. Contribution of external and internal power to the total mechanical power spent during walking. In each age group, the mass-specific external power (Wext), internal power (int) and total power (tot) are presented as a function of the walking speed. For tot, the solid line represents the total mechanical power based upon equation 4, which allows reasonable energy transfers (see Materials and methods). The lower broken line shows the total mechanical power computed as the sum of ext and int,k (as has been done in the past). The upper broken line shows the total mechanical power based upon equation 5, which does not allow any energy transfers between ext, int,kand int,dc. Lines represent the weighted mean of the data (KaleidaGraph 3.6). Note that at low speeds, ext is greater than int.

View larger version (17K): [in a new window]   Fig. 6. The mass-specific internal power (Wint) and total mechanical power (tot) are shown as a function of walking speed. The speed is normalised using the dimensionless Froude number [(gl), where f is the forward mean walking speed, g is the acceleration of gravity and l is the leg length], which allows different size subjects to be compared. Each age group is represented by a different symbol (circles, 3–4 years; squares, 5–6 years; diamonds, 7–8 years; triangles, 9–10 years; inverted triangles, 11–12 years). Broken lines represent the weighted mean of the adult data (KaleidaGraph 3.6). Other indications are as in Fig. 2. Note that normalisation of the speed reduces the differences between adults and children.