Energy Cost of the HumanWalk

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Nonlinear Optics and Qua ntum Opt ics,Vol. 39, pp. 177183 2009 Old City Publishing, Inc.

Reprints available directly from the publisher Published by license under the OCP Science imprint,

Photocopying permitted by license only a member of the Old City Publishing Group

Energy Cost of the Human Walk: Assessment

Methods and Devices

Silvia N. Miu1, Doina Bucur1 and Georgeta M. Capris2

1University Politehnica of Bucharest, Dept. of Precision Mechanics and Mechatronics,

Spl. Independentei no.313, sect. 6, Bucharest, Romania2Institute for Research and Development in Fine Mechanics, Bucharest, Romania

E-mail: [email protected]

Human gait on a horizontal plane is characterized by a power expenditureexpressed by both an external power due to the ground reaction forces thatallow the vertical and horizontal movement of the body centre of massand an internal power due to the muscular activity. The authors workedout a new way of assessing the external work of the forward horizontalground reaction forces. The sum of these can express the energy cost ofhuman walk on a horizontal surface. The evaluation of the energy costwas done by an original software derived by the authors. Comparativetests were performed on several healthy subjects equipped both with ourdevice and with the portable device Cosmed K4b. The validation of themeasured values of the healthy subjects vertical ground reaction forcesand their graphical display in time was achieved by comparing these withthose given by the PEDAR-NOVEL equipment.

Keywords: Human gait, energy cost, ground reaction force, kinematic parameters,

plantar pressure.

1 INTRODUCTION

The gait energetic cost is composed by the external power (the power resulted

from the work done by the external forces) and the internal power (resulted

from the work associated to the limbs movement relative to the COM). The

method proposed and the equipment realized in a Romanian CEEX project,estimate both the external power - by measuring the vertical component of the

ground reaction force and by applying a patented mathematical algorithm and

the internal power (proposed by A.E. Minetti). The method and the equipment

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178 S. N. Miuet al.

were validated by comparing the experimental results got using the system

PEDAR Novel Germany both with the gait energetic cost measured by us

through indirect calorimetry and with similar results.

2 METHOD

2.1 Assessment of the vertical powerPz

The ground reaction forces are Fzi. These forces are measured at different

moments of timeti , andn measurements are done for each step with a 50 Hz

frequency. The vertical speed of the body center of mass changes during a

time gaptwith the value:

Vzi =[(Fzi G)/m] t (1)

The value of the initial vertical speed Vz0 :

Vz0 = n Vz1 +(n 1) Vz2 +(n 2) Vz3 + +Vzn

n+1(2)

The power needed by the two legs, left and right, to do the external work

is given by:

Pzsi =Fzsi Vzi; Pzdi =Fzdi Vzi (3)

wherePzsiand Pzdiare the external powers corresponding to the left and right

feet. The external work done by the vertical ground reaction force of each

foot is:

Lzsi =Pzsi t; Lzdi =Pzdi t (4)

The positive work expresses the work needed to replace the energy lost by

this leg and it is done by the active leg, called as the leading leg. The positive

works done by both left and right leg are as follows:

L+zs =

n=n+psn=1

L+zsi and L+

zd =

n=n+pdn=1

L+zdi

(5)

where L+zsand L+

zdis the positive work done by the left and right leg, as shown

in Figure 1. The total positive work is the sum of these two values of positivework, calculated with (5). In order to evaluate the power during the measured

gait cycle, the total positive work is going to be divided into the duration of a

step [1].


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Energy Cost of the Human Walk 179

FIGURE 1Positive and negative work of the GRF during three steps of the right leg.

FIGURE 2Ground reaction forces at the moment of heel strike: A = initial contact point of the left foot;B = initial COPs, of the left foot; E = initial COPd, of the right foot; D = initial projectionof the COM on the horizontal plane; F = ACF = hip joint; Fs = GRFacting on the left foot;Fzs =VGRFacting on the left foot;Fys = HGRFacting on the left foot; Fd = GRFacting onthe right foot;Fzd =VGRFacting on the right foot;Fyd =HGRFacting on the right foot.

2.2 Assessment of the rear-anterior power Py

Assumptions: At the initial moment of the double stance, the two hip joints

are at the same high relative to the ground, point F in the Figure 2, the rear

and the anterior leg are perfectly straight, the ground reaction force followsthe line that unites the instantly COP and the knee joint, and DE = Lp/2,

whereLp is the step length, as shown in Figures 2 and 3. The instant angles

of the two legs, expressed in the relationships (6), depend on the leg lengthL


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180 S. N. Miuet al.

FIGURE 3Geometrical model of the posterior foot (Bi Fi ) and anterior foot (Ei Fi ) at a moment ti (doublestace); Left COP (centre of pressure) is in Bi, and right COP is in Ei ; the device measures theirdisplacements. The hip joint (point Fi ) moves forwardly with the speed vy . The direction of theground reaction force during the simple support phasef

n1is the angle between the direction of

the ground reaction force at the beginning of the simple support and the vertical direction; isthe angle between the vertical direction and the direction of the ground reaction force at the endof the simple support phase.

and the step lengthLp.

i =arc tg

Bi Di

Fi Di

=arc tg

BD+ yi (ysi ys1)

FD + hi

=arc tg

Lp2

y +yi +ys1 ysi

L cos +hi(6)

i =arc tg

Ei Di

Fi Di

=arc tg

DEyi +(ydi yd1)

FD+ hi

=arc tg

Lp2

yi +ydi yd1

L cos +hi(7)

The total rear-anterior ground reaction force is:

fyi =fysi +fydi =fzsi tg

Lp2

y +yi +ys1 ysi

L cos +hifzdi .tgfi (8)


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FIGURE 4The direction of the ground reaction force during the simple support phase Fn1 is the anglebetween the direction of the ground reaction force at the beginning of the simple support and the

vertical direction; is the angle between the vertical direction and the direction of the groundreaction force at the end of the simple support phase.

While only one foot is laid on the ground, the rear-anterior ground reaction

force is:

fydj = fzdj tg

j

(9)

The power in the rear-anterior direction will bePyi = fyi Vyi . The work in

the rear-anterior direction during a step isLyi =Pyi t. The positive workin the rear-anterior direction during a step is the sum of all positive works

evaluated during a step:

L+y total pas =

n=n+pn=1

L+yi (10)

wheren+p the number of ground reaction forces measured when a positive

work is being done.

The power in the rear-anterior direction during a step is:

Pypas =

Ly+totalpas

tpas(11)

wheretpasis the step duration (s).

3 RESULTS

The mathematical algorithm was verified through comparing the results with

those existing in other similar papers. Table 1 shows the measurements done

with the CALORCRO device and the evaluation of the power at different


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182 S. N. Miuet al.

Gait parametersfor a test on atreadmill

Trial no.

1 2 3 4

v[m/s] Sl[cm] v[m/s] Sl[cm] v[m/s] Sl[cm] v[m/s] Sl[cm]No. 1,2 62,73 1,2 63,3 1,2 63,55 1,2 63,03

1 t(s) 87,1474,34 99,6674,34 124,15100,32 112,4100,322 Trial duration (s) 13,6 25,32 23,83 12,083 Walked distance

(m)16,32 30,384 28,6 14,496

4 Step number 26 48 45 235 Mean value of

VGRF [kg]71,93 71,55 70,87 70,6

6 Pzm [W] 60,1 62,3 65,8 68,37 Pym [W] 39,7 40,7 39,4 38,38 Pint [W] 64,4 63,8 63,6 649 Ptot [W] 164 167 169 171

10 Ptot/G [W/kg] 2,1 2,14 2,17 2,1911 Ptot/(G.v)

[W/(kg*m/s)]1,75 1,79 1,8 1,83

TABLE 1Gait parameters and the power consumed during walking: Pzm [W] the mean enternalpower in the vertical direction, Pym [W] the mean enternal power in the rear-forwarddirection, Pint [W] the mean total internal power, Ptot [W] the mean total powerof the gait on a horizontal surface

Tested subject

Gait energy cost evaluated

with ground reaction forcesmeasured with the PEDAR

system [W]

Gait energy cost measuredthrough the indirect

calorimetry method [W]

Subject 1 163.9 172.4

Subject 2 197.6 180.4

TABLE 2Comparison between the gait energy expenditure evaluated by the authors andmeasured through the indirect calorimetry method

gait speeds of the tested subject walking on a treadmill. A more significant

verification was achieved by simultaneously testing several healthy subjects

equipped both with PEDAR device and with portable device COSMED K4b2

(indirect calorimetry). The results can be seen in Table 2.

4 DISCUTIONS

The main difficulty of the power evaluation was the assessment of the rear-anterior ground reaction force, using the vertical ground reaction force, that

can be easily measured either directly with strain gauge sensors (CALOR-

CRO electronic equipment), or through plantar pressure measurements, as the


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PEDAR system does. The physical problem in static undetermined, so the

assumptions we made were necessary to solve this problem. A further verifi-

cation of the mathematical model should be done for the rear-anterior ground

reaction force, using a force platform.

ACKNOWLEDGMENT

The study has been financially supported from the national research projects

CEEX35-Calorcro and PN41064-Simsano.

REFERENCES

[1] Donelan J. M., Kram R and Kuo A. D. Simultaneous, positive and negative externalmechanical work in human walking.Journal of Biomechanics35 (2002), 117124.

[2] Minetti A. E. and Saibene F. Mechanical work rate minimization and freely chosen stridefrequency of human walking: a mathematical model. Journal of Experimental Biology 170(1992), 1934.


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Energy Cost of the HumanWalk

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