Internal Work and Oxygen Consumption of Impaired and

Normal Walking

Sylvain Grenier, M.A.

D.G.E. Robertson, Ph.D.

Biomechanics Laboratory

School of Human Kinetics

University of Ottawa

Purpose

• To compare the absolute work method with absolute power method in calculating work for impaired and normal gait, using physiological oxygen consumption measures as verification.

Methodology

• subjects: 4 male, 4 female;

• Five normal gait trials per subject selected

• one trial each with splinted knee selected

• one trial each with splinted ankle selected

• the conditions were applied in random order

Subject Trials

Methodology

• three-dimensional video (30 Hz)

• markers: both sides all joints

• Ariel digitization (60 Hz)

• Biomech Motion Analysis System

Video

Methodology

• VO2 standing baseline value (Pierrynowski,1980; Stainsby,1980)

• 3 min walking VO2 steady state» speed chosen, then metronome set

• force data collected for a full gait cycle• 2 AMTI force platforms

» data from the first FS was carried over assuming symmetry (Cappozzo et al. 1976)

Treadmill and Force

Work equations

Absolute method Absolute power method

External work:

Internal work:

W E W M t

W E W W M t W

ext Sii

Next i j

j

Ji j

i

N

int Tii

Next int i j i j

j

J

i

Next

E ETf To

( )

'

'

'

1 11

1 11

work

Work equations

• Absolute Power (AP)– integration of joint

moment x angular velocity (power)

– assumes:

» one muscle per joint

» no elastic storage

» pos. and neg. work equal mechanically

• Absolute Work (AW) – change of instanteous

energy

– location of summation limits energy exchanges

» I.e., if types of energy are separated then summed; between and within exchanges are permitted, but between any two segments

Mechanical Efficiency

ME

ME

ME

BIOMECHANICAL COSTPHYSIOLOGICAL COST

OXYGEN COSTINTERNAL work( )EXTERNAL

work outputwork input

outputpower inputpower

x 100 x 100

x 100

x 100

Biomechanical cost: Biomechanical cost: internal work internal work

mass * velocitymass * velocity

Results: Mechanical Efficiency

Table 3:

Method Condition Total Wk.Mech.

Efficiency

M AX%

MIN%

ExternalWk. Mech.efficiency

Max%

Min%

|power| lock ankle 115.4% 150.3 56.1 14.7% 23.7 6.0

lock knee 92.9% 136.5 119.8 15.9% 26.5 0.1

normal 106.7% 184.8 56.4 13.6% 46.0 1.1

|work| lock ankle 66.7% 131.1 38.9 4.2% 10.6 0.27

lock knee 57.03% 91.41 29.2 4.0% 7.9 0.15

normal 59.26% 153.9 19.6 7.6% 26.3 0.36

* Internal Biomechanical Cost = Internal Work/ (mass*speed)

Mechanical Efficiency

• efficiency varies based on these assumptions:– baseline VO2

– value given to negative work

– if internal work is included

– calculation of antisymmetrical movements

– elastic energy storage

– assumption re: biarticular muscles

Mechanical Efficiency

• calculated using AP method– likely overestimates because:

» includes elastic storage twice

» model assumes no intercompensation, • biarticular muscles are not allowed

• negative power at one joint cannot be used to power the neighbouring joint

» Assume negative work = positive work

– all increased Internal work/ O2 cost

Mechanical Efficiency

• calculated using AW method» likely under estimates

– calculates net work vs. produced work

– assumptions of energy transfer limitations contradict Law of Conservation of energy

• I.e., potential to kinetic

– asymmetrical motion does not require energy

– all decreased internal work/ O2 cost

Differences between conditions

Table 1: Re peate d Measures A NOVA: Metho d between conditions

Method F value F signif. F crit. for df(2,14)

Absolute Power 0.55 0.591 3.74

Absolute Work 0.50 0.618 3.74

O2 Consumption 2.31 0.136 3.74

Differences between conditionswithin subjects

Table 7:

Binomial Test distribution P value

Locked ankle power 3 sig 0.0058*

5 non sig

Locked ankle w ork 1 sig 0.3366

7 non sig

Locked knee pow er 2 sig 0.0572

6 non sig

Locked knee work 1 sig 0.3366

7 non sig

Locked ankle VO2 4 sig .0004*

4 non sig

Locked knee VO2 1 sig .3366

7 non sig

* significance at = 0.05 Borderline significance

Direction of Difference

Pairings P value

LAP-NOP 0.674

LKP-NOP 0.049

LAW-N OW 0.484

LKW-N OW 0.889

LAV-NO V 0.124

LKV-NO V 0.575

Wilcoxon signed ranks test

*

Normal Walking

• Normal walking data is similar to previous data from other published research

Mean of subjects: Normal ankleMean Normal Ankle Power

-60-40

-20020

406080100

120140

6 13 20 27 34 41 48 55 62 69 76 83 90 97

Normalized Time

Po

wer

(W

)

avgnm

A1

A2

CFSCTO

A1: eccentric plantar flexor during early to A1: eccentric plantar flexor during early to midstancemidstanceA2: concentric plantar flexor at push-offA2: concentric plantar flexor at push-off

Normal KneeNormal Mean Knee Power

-100

-80

-60

-40

-20

0

20

40

1 8 15

22

29

36

43

50

57

64

71

78

85

92

99

Normalized time

Po

wer

(W)

avgnm

K3 K4

K1K2

CFSCTO

K1: eccentric flexor moment; absorbing impactK1: eccentric flexor moment; absorbing impactK2: concentric extensor; midstance to toe-offK2: concentric extensor; midstance to toe-offK3: eccentric flexor; shortly before toe-off until max knee K3: eccentric flexor; shortly before toe-off until max knee flexionflexionK4: eccentric extensor; late swingK4: eccentric extensor; late swing

Normal HipNormal Hip mean power

-40

-20

0

20

40

60

80

100

6 13

20

27

34

41

48

55

62

69

76

83

90

97

Normalized time

Po

wer

(W)

avgnm

H1H1

H2

H3

CTO CFS

H1: concentric extension; moving CM forwardH1: concentric extension; moving CM forwardH2: eccentric flexor; lowering the CMH2: eccentric flexor; lowering the CMH3: concentric flexor; to swing the leg forwardH3: concentric flexor; to swing the leg forward

Discussion

• Direction of difference: » perhaps humans are optimized for

adaptability rather than efficiency

» LK trials tended to be lower

• induced changes in 3D or rotation not visible to planar analysis (Kerrigan, et al. (1997)

• values similar to other researchers » Winter 1.09 J/kg.m (1979)

» our data: • AW = 1.90 J/kg.m

• AP = 3.05 J/kg.m

Discussion

• Efficiency» obviously > 100% not possible

» subtracting effect of elastic storage, biarticular muscles

» internal work increases, efficiency decreases to about 65-70%

» compared to most efficient engines today: about 60%

Conclusion

• AP IBC seems to indicate that locked knee internal work is less than in the normal case.

• Both AP & AW seem to indicate that locked ankle gait is more efficient than normal

• Binomial test shows that AP method can distinguish between normal and impaired conditions.

• VO2 seems most consistent but not significant

Recommendations

• four or five cameras; increase accuracy

• do a three dimensional analysis; determine if energy lost is in the frontal plane

• use three force plates; increase the accuracy

• have one extreme condition with both ankle and knee of one leg restricted

Acknowledgments

• Thanks to Heidi Sveistrup, Ph.D., for all her assistance and for the use of her lab.

• Thanks to Peter Stothart, Ph.D., for his guidance during my supervisor’s absence.