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First published online July 23, 2003

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The double contact phase in walking children

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

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

View larger version (18K): [in a new window]   Fig. 1. Methods. (A) Ground reaction forces (F; measured in N), velocity (V; m s-1), displacement (S; cm), energy of forward movement (Ek,f; J), energy of vertical motion (Ep+Ekv; J) and total mechanical energy (Eext=Ekf+Ep+Ekv; J) of the centre of mass (COM) during a walking step. Vertical and forward components are indicated by the subscripts v and f, respectively. Bold continuous lines represent the back leg; broken lines represent the front leg, and thin continuous lines represent the sum of both legs. Back and front legs are indicated by the subscripts back and front, respectively. Increments of each energy curve are, respectively, +Ef, +Ev (a+b) and Wext (c+d), representing the positive work done by the muscles to increase the level of each energy curve. The work done to maintain the motion of the COM is Wext. (B) Work curves for each leg independently (Wf,front, Wf,back, Wv,front and Wv,back) and curve Wv (sum of Wv,front and Wv,back) during a step. Work curves are also presented during the double contact (DC) phase, Wback=Wf,back + `transfer from Wv' (see equation 3); Wfront=Wf,front + `transfer from Wv' (see equation 4); Wcom=Wback+Wfront. The work done by one leg against the other during DC (+Wint,dc) is equal to (+Wback++Wfront)-+Wcom (see Materials and methods; equation 6). Data are from a 10.5-year-old boy walking at 1.32 m s-1. The step duration is 0.485 s and DC lasts for 0.14 s. DC is delimited by the vertical dotted lines.

View larger version (30K): [in a new window]   Fig. 2. Typical accelerations (m s-2) and ground reaction forces (N) in the forward (Ff) and vertical (Fv) direction during a step at a low (A), intermediate (B) and fast (C) speed in a young child (left column) and an adult (right column). The double contact (DC) phase is delimited by the vertical dotted lines. Arrows indicate the peak of the forward ground reaction force on the back leg (peak Ff,back). Left column: a 4.9-year-old female, mass of 17.75 kg, leg length of 0.535 m, walking at 0.72 m s-1, 1.21 m s-1 and 1.56 m s-1 (A to C). Right column: a 20.2-year-old male, mass of 64.90 kg, leg length of 0.919 m, walking at 0.84 m s-1, 1.37 m s-1 and 2.58 m s-1 (A to C). Other indications are as in Fig. 1.

View larger version (20K): [in a new window]   Fig. 3. Description of the double contact (DC) phase as a function of speed and age. (A) In each age group, the step length (Lstep; measured in metres) and the forward displacement of the centre of mass taking place at each step when both feet contact the ground (Ldc; m) are given as a function of the walking speed. Ldc was calculated as the mean forward speed during DC multiplied by the fraction of the step during which both feet contact the ground. (B) The angle of contact with the ground during a step was computed from Lstep and the leg length as shown in the Materials and methods. (C) The relative importance of DC (Ldc/Lstep) is shown as a function of the walking speed. The symbols represent mean values of data grouped into the following intervals along the abscissa: 0.28 m s-1 to <0.42 m s-1, 0.42 m s-1 to <0.56 m s-1...2.5 m s-1 to <2.64 m s-1. N is from low to high speed classes for 3-4 years: 2, 1, 7, 8, 6, 13, 7, 9, 7, 2, 3; for 5-6 years: 4, 3, 11, 7, 13, 10, 9, 18, 18, 12, 2, 1; for 7-8 years: 1, 4, 1, 9, 14, 8, 16, 20, 10, 13, 10, 13, 2, 10, 5, 3, 1; for 9-10 years: 3, 9, 16, 22, 19, 23, 19, 12, 12, 11, 17, 10, 8, 3, 3 and for 11-12 years: 1, 4, 5, 6, 8, 13, 18, 18, 12, 13, 19, 14, 16, 8, 6, 3. Bars indicating the S.D. of the mean are drawn when they exceed the size of the symbol. The broken lines indicate the adult trend.

View larger version (18K): [in a new window]   Fig. 4. (A) The mass-specific work per distance (Wint,dc; J kg-1 m-1; filled circles) done by one leg against the other during the double contact (DC) phase and the mass-specific external work per distance (Wext; J kg-1 m-1; open circles) done to maintain the centre of mass (COM) motion in the sagittal plan are given for each age group as a function of the walking speed. (B) The ratio Wint,dc/Wext is given for each age group as a function of speed in the lower panels. Other indications are as in Fig. 3.

View larger version (9K): [in a new window]   Fig. 5. The phase angle between the peak in the forward push (peak in the Ff,back curve) and the beginning of the double contact (DC) phase is shown as a function of walking speed for the different age groups. The phase angle (rad) is calculated as 2(t/T), where t is the difference between the time at which Ff,back is maximal and the beginning of DC, and T is the duration of the step. A positive value means that peak Ff,back occurs during DC; a negative value means that peak Ff,back occurs during the single contact phase preceding the DC phase. Other indications as in Fig. 3.

View larger version (15K): [in a new window]   Fig. 6. The components of Wint,dc (Wf,front, Wf,back, Wv, Wback, Wfront and Wcom; in J kg-1) are presented as a function of time during double contact (DC) for a slow speed step at 0.84 m s-1 (A), a medium speed step at 1.37 m s-1 (B) and a high speed step at 2.58 m s-1 (C). The Wint,dc curve is obtained by subtracting instant-by-instant the positive increments in Wcom from the positive increments in Wback and Wfront (see Materials and methods). +Wint,dc is the total increment in the Wint,dc curve (fine broken line) and is the work done by one leg against the other during DC. Note that the scale of the Wint,dc curve is 2.5 times that of the other curves. Other indications are as in Fig. 1. Data are from a 20.2-year-old 64.9 kg male subject.

View larger version (16K): [in a new window]   Fig. 7. (A) The phase angle (rad) between the peak in the forward push of the back leg (peak Ff,back) and the beginning of the double contact phase is presented as a function of the walking speed expressed as a Froude number. Each age group is presented with a different symbol (filled circles, 3-4 years; squares, 5-6 years; diamonds, 7-8 years; triangles, 9-10 years; inverted triangles, 11-12 years). (B) The mass-specific work per distance done by one leg against the other (Wint,dc; J kg-1 m-1) is presented as a function of the Froude number for all age groups. The broken lines show the adult trends.