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Measurement of positive and negative work duration and - The

VIEWS: 4 PAGES: 6

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									                                           Measurement of positive and negative work duration


The difficulty in measuring the increment (tpush) and the decrement (tbrake) of Ecm (Fig. 2 of the manuscript) is mainly due to the blunt attainment


of the Ecm plateau (see black line in Fig. 1 of the manuscript). In order to make this transition more sharp, the derivative dEcm(t)/dt was made


(LabVIEW Derivative x(t).VI). The two graphs below are dEcm(t)/dt records extracted from the custom LabVIEW program we used. On these


graphs, two reference levels were set by the user above (red horizontal line) and below (green horizontal line) the noise of dEcm(t)/dt record during


the Ecm plateau. Push and brake durations were automatically taken by the program (vertical yellow lines) as the time intervals during which the


dEcm(t)/dt record was respectively above and below the mean (blue horizontal line) of the data points comprised between the two reference levels.

       In the graphs below the ordinate is the slope of the black line in Fig. 1, i.e. the instantaneous power in Watt produced during the increment of

the kinetic and gravitational potential energy of the centre of mass of the body (positive values) and absorbed during the decrement of the potential

and kinetic energy of the centre of mass of the body (negative values). The abscissa is the number of analog to digital conversions of the platform

signals (from which the curves in Fig. 1 are derived by computer analysis) made at the rate of 500 Hz (see (b) Data acquisition in 2. MATERIAL

AND METHODS of the manuscript). The time interval between the black circles on the black line in the graphs below is therefore 0.002 s.




                                                                                                                                                        1
Subject running backward at 8.9 km h-1, same step illustrated in the middle left panel of Fig.1.

tpush was measured as the time interval between the two yellow lines on the left when dEcm(t)/dt > average (blue line), that is from 0 to 50.99

conversions equal to 0.102 s.

tbrake was measured as the time interval between the two yellow lines on the right when dEcm(t)/dt > average (blue line), that is from 113.82 to 171

conversions equal to 0.114 s.



                                                                                                                                                   2
Subject running forward at 8.8 km h-1, same step illustrated in the middle right panel of Fig.1.

tpush was measured as the time interval between the two yellow lines on the left when dEcm(t)/dt > average (blue line), that is from 0 to 83.88

conversions equal to 0.168 s.

tbrake was measured as the time interval between the two yellow lines on the right when dEcm(t)/dt > average (blue line), that is from 131.06 to 196

conversions equal to 0.13 s.




                                                                                                                                                   3
                                                           Internal work estimation



       The mass-specific positive internal work done per unit distance, Wint/MbL, has been calculated for each run from the experimental values of

                                                 -1
step length L (m), average running speed Vf (m s ) and step frequency f (Hz) according to the equation derived from data obtained in forward

running (Cavagna et al. 1997):
                                                             -1 -1             -0.200L
                                                Wint/MbL (J kg m )=0.14010                 Vf f        1)



                                                                              
       The data calculated from equation (1) in the forward running group of this study are in good agreement with the experimental data measured

over the same speed range by Cavagna and Kaneko (Fig. 3 of Cavagna & Kaneko, 1977) and by Willems et al. (Fig. 5A, continuous line, of

Willems et al. 1995). Furthermore the internal work calculated from equation (1) is in good agreement with the experimental measurements of

internal work made during forward running at a given speed with different step frequencies dictated by a metronome (Cavagna et al. 1991). This

indicates that equation (1) may safely be used to predict internal work when a given speed is maintained with a higher step frequency as in

backward running (Threlkeld et al. 1989; Devita & Stribling 1991; Wright & Weyand 2001).

       Note, however, that using equation (1) to calculate internal work in backward running, the assumption is made that, for a given step length,

the difference in limb positions between backward and forward running does not affect appreciably the work done to accelerate the limb relative to

the centre of mass, i.e. it assumes equal gait pattern when viewing forward running and reverse backward running film records. The actual internal

                                                                                                                                                      4
work done to accelerate the limbs at a given speed has not been measured directly and could be greater or lower than that calculated using equation

(1).
                                                                                                                                           -1
The 30% increase of the metabolic energy expenditure during backward running was measured by Flynn et al (1994) at a speed of 9.6 km h . In

                                                                                                                           -1 -1                  -
order to have a 30% increase of the total mechanical work at the same speed, the internal work should increase to 1.15 (J kg m ) from 0.74 (J kg

1 -1                                                                                                                         -1
 m ) (see Fig. 4), and the ratio between internal work in backward running and internal work in forward running at 9.6 km h should be 1.77. A

                                                                                                -1                    -1
77% increase in internal work, which would correspond to a forward running speed of ~18 km h , instead of 9.6 km h , does not seem justified by

the relatively small differences in lower limb positions described in the backward and forward running stride (Devita & Stribling 1991).



REFERENCES

1 Cavagna, G.A., Mantovani, M. Willems, P.A., Musch, G. 1997 The resonant step frequency in human running. Pflug Arch Eur J Phy 434,

678-684.

2 Cavagna, G.A., Kaneko, M. 1977 Mechanical work and efficiency in level walking and running. J. Physiol. 268, 467-481.

3 Willems, P. A., Cavagna, G. A., Heglund, N.C. 1995 External, internal and

total work in human locomotion. J. Exp. Biol. 198, 379-393.

4 Cavagna, G.A., Willems, P.A., Franzetti, P., Detrembleur, C. 1991 The two power limits conditioning step frequency in human running. J.

Physiol. 437, 95-108.

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5 Threlkeld, D.A., Horn, T.S., Wojtowicz, G.M., Rooney J.G., Shapiro, R. 1989 Kinematics, ground reaction force, and muscle balance

produced by backward running. J. Orthop. Sports Phys. Ther. 11, 56-63.

6 Devita, P., Stribling, J. 1991 Lower extremity joint kinetics and energetics during backward running. Med. Sci. Sports Exerc. 23, 602-610.

7 Wright, S., Weyand, P.G. 2001 The application of ground force explains the energetic cost of running backward and forward. J. Exp. Biol. 204,

1805-1815.

8 Flynn, T.W., Connerty, S.M., Smutok, M.A., Zeballos, R.J., Weisman, I. 1994 Comparison of cardiopulmonary responses to forward and

backward walking and running. Med. Sci. Sports Exerc. 26, 89-94.




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