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First published online September 15, 2004
Journal of Experimental Biology 207, 3797-3810 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.01214

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Development of pendulum mechanism and kinematic coordination from the first unsupported steps in toddlers

Yuri P. Ivanenko¹, Nadia Dominici^1,2, Germana Cappellini¹, Bernard Dan³, Guy Cheron³ and Francesco Lacquaniti^1,2,4,*

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

View larger version (43K): [in a new window]   Fig. 1. Kinematic and kinetic recordings. (A) Experimental setup. Kinematic data were measured by monitoring markers on the gleno-humeral joint (GH), ilium (IL), greater trochanter (GT), lateral femur epicondyle (LE), lateral malleolus (LM), and fifth metatarso-phalangeal joint (VM). Trunk, pelvis, thigh, shank and foot are the limb segments identified by these markers. Elevation angles were computed relative to the vertical. Ground reaction forces were measured by force platforms along x,y,z axes. (B) Sagittal stick diagrams and (C) force platform measurements at two stages of early walking in the same child (subject G.M.): at 12.5 months (first independent steps), and at 17 months.

View larger version (24K): [in a new window]   Fig. 2. Kinematics of the pendulum mechanism. (A) Schematic representation of the inverted pendulum: the hip vaults over the stance limb. (B) Ensemble averages (± S.D., N=5 steps) of vertical hip displacement (GTy) and knee joint angle in children of different age, and in a representative adult walking at two different speeds (right panels). Data are plotted vs the normalised gait cycle. Each record begins with the right foot strike. GTy is expressed in relative units (normalised by the limb length L). (C) Percent of variance (± S.D.) of GTy data explained by the second Fourier harmonic is plotted as a function of the time after the onset of independent walking. The values for the adult group were obtained by computing the mean (± S.D.) from the pooled data obtained for walking at natural, freely chosen speed (on average, 3.8±0.4 km h–1). (D) Correlation coefficient between GTy data in children and the corresponding ensemble average in adults during stance. For both C and D, the time course of changes with age was fitted by an exponential function (r=0.93 and 0.87 in C and D, respectively). , the corresponding time constant.

View larger version (23K): [in a new window]   Fig. 3. Changes of vertical hip displacement (GTy,left+GTy,right)/2 (C), gravitational potential energy (Ep) (B) and kinetic energy (Ek) (A,B) of COM during walking in children of different age, and in a representative adult. The upper three traces show the forward (Ek,f), vertical (Ek,v) and lateral (Ek,l) kinetic energies of COM. Ek (B) refers to the kinetic energy in the sagittal plane (sum of Ek,f and Ek,v) that we used to characterize the classic pendulum behaviour in the sagittal plane. Dotted vertical lines correspond to foot contact (FC) of one leg. For older children and adults, the recordings of Ek and Ep do not extend to the whole cycle. Correlation coefficient between Ep and Ek is indicated for each trial.

View larger version (19K): [in a new window]   Fig. 4. Mechanical energy of COM. Mean changes (± S.D.) of selected parameters plotted as a function of the time after the onset of independent walking: correlation coefficient between Ep and Ek (A), phase shift between Ep and Ek (B), percentage of recovery of mechanical energy (C), external work per unit of body mass and per unit distance (Wext; D) and internal work per unit of body mass and per unit distance (Wint; E). The time course of changes with age was fitted by an exponential function (r=0.93, 0.89, 0.87 and 0.92 for A, C, D and E, respectively). Data refer to walking at natural speed.

View larger version (17K): [in a new window]   Fig. 5. Normalisation by the Froude number. Percentage of recovery of mechanical energy (A) and correlation coefficients between Ep and Ek (B) for toddlers at the first unsupported steps (blue), 1–5 months later (cyan), children older than 2 years of age (violet) and adults (red). Data points for individual steps are plotted as a function of Froude number (Fr=V2g–1L–1, where V is the average speed of locomotion, g the acceleration of gravity, and L the lower limb length). Continuous lines represent second-order-polynomial fittings.

View larger version (29K): [in a new window]   Fig. 6. Inter-segmental coordination. (A) Ensemble averages (± S.D., N=5 steps) of thigh, shank and foot elevation angles in children of different age and in a representative adult. (B) Corresponding gait loops plotted in 3-D. A loop represents one gait cycle and is obtained by plotting the thigh waveform vs shank and foot waveforms (after mean values subtraction). Paths progress in time in the counter-clockwise direction, foot strike and lift-off corresponding approximately to the top and bottom of the loop, respectively (swing phase is in red). The interpolation planes result from orthogonal planar regression. The first eigenvector (u1) is aligned with the long axis of the gait loops of B, the second eigenvector (u2) is aligned with the short axis, and the third eigenvector (u3) is the normal to the plane. uit, uis and uif correspond to the direction cosines with the positive semi-axis of the thigh, shank and foot angular coordinates, respectively. (C) Changes with age of percentage of variance accounted for by u1, u2, and u3 (PV1, PV2, PV3 respectively). (D) Direction cosines of the plane normal. (E) Step-by-step variability of the plane normal (exponential fitting, r=0.91).

View larger version (17K): [in a new window]   Fig. 7. Behaviour before and after the onset of independent walking. Percent of variance of GTy data explained by the second Fourier harmonic (A) and step-by-step variability of the plane normal (B) are plotted for experimental sessions performed at different times before and after the first unsupported steps. Triangles, subject R.D.C. data; circles, subject G.M. data.