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First published online June 7, 2004
Journal of Experimental Biology 207, 2417-2431 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.01040

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Mechanical energy in toddler gait A trade-off between economy and stability?

Ann Hallemans^1,2,*, Peter Aerts¹, Bert Otten³, Peter P. De Deyn⁴ and Dirk De Clercq²

¹ Laboratory for Functional Morphology, University of Antwerp, Antwerp, Belgium
² Department of Movement and Sport Sciences, University of Ghent, Ghent, Belgium
³ Institute of Movement Sciences, University of Groningen, The Netherlands
⁴ Hoger Instituut voor Kinesitherapie en Ergotherapie, Antwerp, Belgium

View larger version (26K): [in a new window]   Fig. 1. Adult Ep and Ek oscillations are plotted as a function of gait cycle duration. The shaded area indicates the periods of double support. The IP mechanism, as observed in adult gait, shows an out-of-phase oscillation of kinetic and potential energy, allowing energy exchange to occur from Ep to Ek and partially from Ek to Ep. Though 70% of the required mechanical energy can be recovered due to this energy saving mechanism, 30% of energy is lost and must be re-supplied by the muscles. It is primarily used to redirect the centre of mass from one pendular arc to the next. HC, heel contact; OTO, opposite toe-off; OHC, opposite heel contact; TO, toe-off.

View larger version (98K): [in a new window]   Fig. 2. A modified Helen-Hayes marker set-up was used for measuring full body kinematics. Markers were attached to a tight fitting suit since the children did not tolerate sticking markers on their skin. Foot markers were attached to socks or soft leather shoes.

View larger version (15K): [in a new window]   Fig. 3. (A) The Individual Limbs Method (ILM), proposed by Donelan et al. (2002), models the legs as two rigid struts joined by the centre of mass (COM). Single support is considered as a pendular phase during which the COM moves over the stiff supporting limb. Energy exchange is allowed between Ep and Ek. Double support is a transition state during which the COM is redirected from one pendular arc to the next. To maintain a constant walking speed, the propulsive back leg (black lines) has to perform work to overcome the braking action of the front leg (grey lines) on the COM. When using the classical method of calculating work performed on the COM (i.e. by integration of the resultant of forces underneath both feat) simultaneous positive (Wy,back) and negative (Wy,front) work is cancelled out and work during double contact is underestimated. The ILM calculates the amount of positive work performed by the front and back limb separately, consequently opposite work of both limbs during double contact is not cancelled out. (B) Bastien et al. (2003) proposed an alternative method for calculating internal work during double contact (Wint,dc). The legs are seen as two oscillating actuators performing work on the COM. Since both are performing work on the same structure, they can also perform work on each other. Consequently the energy absorbed when the downward movement of the COM is slowed down after foot contact, (Wv is decreasing during the first half of double support) can be used by the propulsive back limb to accelerate the COM forward (transfer of energy from Wv to Wy,back). Also, the energy absorbed by the front limb (Wy,front) can be used during the second half of double support to lift the COM against gravity (transfer from Wy,front to Wv, which is increasing during the second half of double support). Allowing for this energy transfer between the front and back limb will reduce the amount of work that has to be performed by the back limb to overcome the braking action of the front limb. F, force component.

View larger version (18K): [in a new window]   Fig. 4. (A) Toddlers' mean oscillations in Ep and Ek (± S.D.), are plotted as a function of gait cycle duration. The shaded bars indicate the double support phase. Both Ep as Ek show a sinusoidal oscillation with two maxima and two minima occurring during one gait cycle. The oscillations in Ep are largest and almost completely determine the total mechanical energy fluctuations. (B) The average kinetic energy fluctuations in the forward (y), lateral (x) and vertical (z) directions are plotted as a function of gait cycle duration. Ek is entirely determined by the forward kinetic energy fluctuations.

View larger version (20K): [in a new window]   Fig. 5. (A) Recoveries R are plotted as a function of walking speed for both adults (triangles) and toddlers (circles). (Adult data were reproduced from Willems et al., 1995.) In both age groups R shows an inverted U-shape relationship with walking speed. R reaches a maximum at lower speeds in toddlers. (B) Adult (triangles) and toddler (circles) R-values are plotted as a function of the dimensionless froude number. In both age groups R is maximal around froude number 0.4. In toddlers, however, R is smaller than in adults. (C) % Congruity expresses the % of the gait cycle during which Ek and Ep are oscillating in-phase. % Congruity shows a U-shaped relationship with speed, reaching a minimum at the speed when R was maximal. (D) % Congruity shows a U-shaped relationship with froude number and is minimal at froude number 0.4. (E,F) Relative amplitude RA. The amplitude of Ek is much larger than the amplitude of Ep. With increasing walking speed (or froude number) the Ek oscillations increase. However, they never exceed the fluctuations in Ep (cf. RA always >1). r2 values apply to toddlers only.

View larger version (24K): [in a new window]   Fig. 6. (A) External work Wext is plotted as a function of walking speed for both adults (triangles) and toddlers (circles). (Adult data were reproduced from Willems et al., 1995.) Wext shows a U-shaped relationship with walking speed, reaching a minimum at speeds around 0.6 m s-1. Toddlers seem to produce a higher amount of external mechanical work to walk at the same speed than adults. (B) Differences between adults and toddlers do not disappear when Wext is plotted as a function of the dimensionless froude number. This suggests that other factors, apart from their small stature, make toddlers consume more energy than adults. (C) Positive mechanical work Wint,k required to move the body segments relative to the centre of mass is plotted as a function of walking speed for both adults (triangles) and toddlers (circles). (Adult data were reproduced from Willems et al., 1995.) Wint,k seems to be larger in toddlers. (D) If Wint,k is plotted as a function of dimensionless froude number, Wint,k is smaller in toddlers. (E,F) Work during double contact. Wext (black line), WILM (circles) and the sum of Wext and Wint,dc (+) are compared as a function of walking speed and froude number. As expected, WILM is larger than the sum of Wext and Wint,dc. However, the shape of the curves and the position of the optimum walking speed do not change, regardless of the method used. (G) Total mechanical work Wtot is plotted as a function of walking speed for both adults (triangles) and toddlers (circles). (Adult data were reproduced from Willems et al., 1995.) Wext shows a U-shaped relationship with walking speed, reaching a minimum at speeds around 0.6 m s-1. (H) If Wtot is plotted as a function of froude number (and differences in size between adults and toddlers are taken into account), Wtot is comparable between adults and toddlers around froude number 0.4. At lower and higher froude numbers sharp increases in Wtot are observed. r2 values apply to toddlers only.

View larger version (22K): [in a new window]   Fig. 7. The kinetic energies of the body segments are plotted as a function of gait cycle duration. The kinetic energies of the head, trunk and arms are small since the upper body is kept relatively stiff during walking and there is no arm swing. The kinetic energies of the thigh and shank are most important.

View larger version (42K): [in a new window]   Fig. 8. To investigate the effect (mechanical energy fluctuations) of walking experience (WE) on the inverted pendulum mechanism, individual mean Ek and Ep profiles (± S.D.) were inspected. The grey bars indicate double support. In the youngest children, the Ek and Ep curves are irregular. The sinusoidal pattern becomes a lot smoother after 3 months of walking experience (28 weeks WE), but variation remains large.

View larger version (24K): [in a new window]   Fig. 9. Preferred walking speed, Wtot, Wext, Wint,k and work during double contact (expressed as a fraction of Wext) are plotted as a function of walking experience. There is a slight increase in preferred walking speed as the children gain more experience in walking. Wtot and Wext show a U-shaped relationship with walking experience. But walking experience showed no relationship with recovery values (and consequently the efficiency of the pendular exchange of energy), Wint,k and work during double contact.

View larger version (31K): [in a new window]   Fig. 10. The fore–aft and vertical ground reaction force traces, COM velocities and instantaneous work traces of one exemplar file are plotted as a function of gait cycle duration. The grey bars indicate double contact. Also in toddlers the front and back limbs are working against each other during double contact (cf. the fore–aft work traces during double contact). But because of the combination of a slow walking speed and large vertical oscillations of the COM, the vertical work traces are most important in determining the amount of work performed during double contact. In the vertical direction, the front and back limb cooperate in performing work on the COM. Consequently, opposite work during double contact is relatively small compared to work performed on the COM.

View larger version (26K): [in a new window]   Fig. 11. The instantaneous work traces of the front and back limb calculated using the individual limbs method (ILM) and the method proposed by Bastien et al. (2003) are plotted as a function of gait cycle duration. The shaded area indicates the double support period. The ILM separately sums the vertical and fore–aft components of each limb to obtain the work performed by the front limb (Wfront) and back limb (Wback). The dark grey area between both curves indicates the amount of opposite work. Using Bastien's method, instantaneous work in the vertical direction performed by the front and back limb is summed (Wz). Then a transfer of energy is allowed from Wz (if Wz is decreasing) to fore–aft work performed by the back limb (Wyback). Another transfer of energy is allowed from the negative fore–aft work of the front limb (Wyfront) to increase Wz during the second half of double support. Allowing for these energy transfers causes a flattening of the instantaneous work curves of the front and back limb. Consequently the amount of calculated opposite work is smaller.