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.