variability and compensating effects

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Human Movement Science 3 (1984) 51-76North-Holland

51

KINEMATIC AND KINETIC PATTERNS IN HUMAN GAIT:

VARIABILITY AND COMPENSATING EFFECTS

David A. WINTER *urlt1w-s1t): f Warerloo, anada

Winter, D. A., 1984. Kinematic and kinetic patterns in human gait:variability and compensating effects. Human Movement Science 3,51-76.

In the presence of fairly well defined kinematic patterns in human walking there was considerablevariability at the kinetic level. Intra-subject variability of joint moment patterns over the strideperiod was high at the knee and hip, but low at the ankle and in a recently defined total limbpattern, called support moment. A similar profile of variability was evident for inter-subject trialsat slow, natural and fast cadences, with the percentage variability at the knee and hip decreasing ascadence increases. These moment of force patterns were not random, but were highly correlated.

Such a finding points to compensating mechanisms by the biarticulate muscles crossing thesejoints. Also shown was the fact that these compensating patterns were highly predictable from linksegment theory.

1 Introduction

In the assessment of motor patterns of walking the joint kinetics arefundamental to the understanding of that movement and are extremely

powerful in the diagnosis of pathological gait. The moments of forcerepresent the net effect of all agonist and antagonist activity, and cantherefore be considered as the final desired motor pattern at that joint.Both the clinical and basic researcher are interested in these motorpatterns and if sufficient analyses are available the following questionscan now be posed:

(1) How do these patterns alter with cadence changes?

* Authors address: D.A. Winter, Dept. of Kinesiology. University of Waterloo, Waterloo, Ont.,Canada N2L 3Gl.

0167-9457/84/$3.00 0 1984, Elsevier Science Publishers B.V. (North-Holland)


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2) Is there evidence of a consistent synergistic pattern across the jointsof the lower limb during stance and swing?

(3) How variable are these patterns across the normal population?

The purpose of this paper is to present answers to the above questionsusing data from a normal population supplemented by case studyexamples of pathologies.

2. iterature review

In the large volume of literature of gait analyses the number of studiesthat have addressed the reaction forces and moments of force have beenquite limited (Winter 1980). Since 1980 only a few additional casehistories have been added (Boccardi et al. 1981). This is unfortunatebecause it is at the kinetic level we can see the cau.se of the movementrather than at the kinematic level at which scores of papers havedescribed the final effect of all these forces. Because of the complexinteraction of the link segment system it is almost impossible to infer

from the kinematics alone as to what forces are acting to cause theobserved pattern. This was demonstrated in a case study reported byWinter (1980) in which a knee replacement patient had a dominantknee flexor moment during the entire stance period yet still walked witha stiff knee. In the presence of this flexibility at individual joints therewas still a consistent total pattern of support during stance by all threeof the joints of the lower limb. The total extensor pattern, called thesupport moment, was defined (Winter 1980) as:

Ms=Ma+Mk+Mh 0

where: Ma, Mk and Mh are the moments of force at the ankle, kneeand hip, and are positive for extension and negative for flexion. Thepolarities of Ma and Mh have been reversed from the original formula,which was written to satisfy the polarity conventions of link segmentmechanics, rather than functional convention. MS was found on allsubjects and patients to be positive during stance and negative duringswing. This consistent total extensor pattern also means that there can

be considerable inconsistency in the moment patterns of the threejoints, and, in actual fact, this is regularly demonstrated. From a link


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D.A. Wtnter / Kinenzut~c and kinettc patterns n hums guit 53

segment mechanics point-of-view we know that a consistent kinematicpattern at the knee and ankle during stance does not guarantee a

consistent motor pattern at each of the joints of the support limb.Theoretically, during single support there are an infinite number ofjoint moments of force that could result in exactly the same ankle andknee angle histories.

3. Theory and methodology

3. I. General

Data for this paper have been collected over the past six years in theGait Laboratory in the Department of Kinesiology at the University ofWaterloo. Details of the data collection, processing and analysis appearin previous publications (Winter 1980, 1983a), and yields the kinematicand kinetic patterns over the stride period. The moments of force at theankle, knee and hip, were calculated using equations developed byBresler and Frankel (1950).

The analyses presented here are confined to the sagittal plane, or,more correctly, to the plane of progression. It is recognized that byneglecting the medial-lateral movement certain errors will result. Therewill be no error in the moments of force as calculated, they will be atrue representation of the moments in the plane of progression. How-ever, if bone-on-bone forces were to be analysed, there could besignificant errors generated by muscles acting in the medio-lateralplane. This is especially true at the hip joint during single support whenabductor muscle forces would add to the already existing compressive

forces of the hip flexors and extensors. However, since articulatingforces were not part of the analyses reported here a 3-D analysis wasnot necessary.

Other methodological short-cuts were not done, however. Someresearchers have used a quasi-static approach to the analysis of jointreaction forces and joint moments of forces. Such an approach ignoresthe inertial forces of the segments of the limb. During stance the errorof this approach is negligible for the foot (because the mass accelerationproducts for the foot are small), but become noticeable at the knee and

significant at the hip (Wells 1981) especially at weight acceptance andpush-off.


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3.2. Within-subject triuls

One subject underwent 9 repeat trials spaced over three days so thatmeasures of within-subject variability might be obtained. for eachwalking trial the subject was asked to walk her natural cadence asshe walked along the walkway over the force plate as she was trackedby a 16mm tine camera. No metrome or other timing device was usedfor the repeat trials. Ensemble average patterns over the stride periodwere obtained for three sets of variables:

(i) joint angles - ankle, knee and hip;(ii) ground reaction forces - horizontal and vertical;(iii) joint moments of force and support moment.

The ensemble average for any given variable was derived as follows.Firstly, the stride period for each of the 9 trials was set to 100%. Ateach 2% interval from heel contact to heel contact an average andstandard deviation of the 9 trials on each of the three variables wascalculated. The ensemble average for this subjects joint angles arepresented in fig. 1, the ground reaction force patterns appear in fig. 2and the moment of force profiles are plotted in fig. 3.

3.3. Between-subjects and cadence related trials

For the inter-subject comparisons three cadence groups were examined.Each subjects natural cadence was determined with slow cadence beingdefined as a subjects natural cadence -20 steps/min and fast cadence= natural cadence + 20 steps/min. In the population group reported in

this paper the cadence, mass, height and age is reported in table 1.

Table 1

General information on cadence groups

Cadence N Cadence Mass (kg) Age Height (cm) Stance time

classificationx SD. x SD. X S.D. X SD.

(B stride)

x S.D.

S OW 14 84.7 10.4 71.5 9.0 22.2 1.8 177 8.6 63.5 1.9

Natural 16 105 7.7 69.1 X.8 25.6 6.2 175 7.8 63.3 1.0

Fast 14 121.6 5.3 71.5 8.9 22.2 1.8 177 8.8 61.0 1.5


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D.A. Winter / Ktmmutrc cmd ktnetic patterns n human gait 55

Prior to calculating the average kinetic patterns for each cadencegroup two normalizations were required. The first normalization was to

make the stance time = loo%, and to set the stance period = 62%. Forthe natural cadence group this meant a linear adjustment of all dataover stance and compressing it from a time base of 63.3% to 62%. Forthe slow cadence group it was necessary to reduce it from 63.5% to 62%and for the fast cadence group the stance period was increased from61.0% to 62%. These minor adjustments in the time base were necessaryto emphasize the similar timing in the patterns especially prior totoe-off. The second normalization was required to reduce the inter-sub-ject variability that results when ensemble average profiles are calcu-lated over the stride period. Averaging the moment of force patterns(Nm) resulted in tremendous variability. Two techniques were at-tempted. Normalizing to the maximum support moment, as was donepreviously in jogging (Winter 1983a), reduced the variability but wasnot as effective as dividing the moment of force by body mass. Thus anensemble average pattern (Nm/kg) was calculated for each subjectwithin each cadence group, the average was calculated at each 2%interval over the stride period. At each of these intervals the standarddeviation was also calculated. The moment patterns at each joint plusthe total support moment pattern were plotted (figs. 4, 5, 6) along witha band of kl S.D.

3.4. Variability measures - intra and inter subject trials

As a measure of total variability in any of these ensemble averagepatterns a coefficient of variation CV) was calculated = root meansquare of standard deviation of the moment over stride period t mean

of absolute moment of force over stride period.

(2)

where: N is the number of intervals over the stride, M, is the amplitudeof the normalized moment of force (Nm/kg) at the i th interval, and u,is the standard deviation of M, at the i th interval.

Thus CV represents the r.m.s. width of the standard deviation

band expressed as a percent of the magnitude of the signal patternitself.


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The CV scores for each joint moment profile do not tell us whetherthe variability is merely random biological perturbations, or whether

there is some correlation between what is happening at one joint withthe motor patterns at other joints. One way of determining this is tocalculate the covariance between the individual joint moment patternsand the total support moment pattern. If the moment of force patternsare completely independent then the predicted variance in the supportmoment should be the sum of the variances in each joint momentpattern, or

where the subscripts s, a, k and h represent the support, ankle, kneeand hip, respectively. However, we actually have an estimate of thevariance in the support moment, 6x = r.m.s. S.D. of Ms. The dif-ference, a, - es,, is an estimate of the total covariance amongst the threejoint moment patterns. If a, > 6s then the experimental results showthat there is a correlation between the three moments as a result of acancellation (i.e., a subject increased his flexor moment at one jointwhile at the same time increased his extensor moments at one or bothof the other joints). If a, < 6s then the reverse correlation is indicated.To ascertain where most of the correlation occurs a further analysis wasundertaken to partition the covariance and this was done by computingu,s for paired summations of the hip + knee, and ankle + knee mo-ments of force. Then, to calculate the covariance between the hip andknee patterns, ehk we use the formula:

2uhtk

where: t ii+ k is the average variance of the sum of the hip and kneemoment patterns across the same subject or cadence group. Similarformulae apply for the knee + ankle.

4. Results and discussion

4 1 Within-subject variability - kinemutics and kinetics

Fig. 1 presents the joint angle plots as obtained from the tine film ofone subject with 9 trials walking at her natural cadence. The average


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D.A. Winter / Kinematrc and krnetrt patterns m human gad 57

JOINT RNGLES WM22 (N=9)1

0

20

;2 0

-20

7 ., .: : :

Fig 1 Average ankle, knee and hip angle for nine repeat trials on the same subject spread overthree separate days. Coefficient of variation (CV) reflects the average standard deviation overstride period (dotted line) as a percent of the mean curve (solid line).

cadence for these 9 trials was 110 steps/mm with a standard deviationof only 2 steps/min. Thus the normalization of the time base for eachtrial to loo%, which is necessary to achieve a cyclical average, hasnegligible change on the pattern for any individual trial. The solid line

indicates the mean curve and the dotted lines are one standard devia-tion either side of the mean. The r m s standard deviation over thestride was 1.5 at the ankle, 1.9 at the knee and 1.8 at the hip. Such alow variability over the complete stride at all three joints is a strongindicator that she had learned a very repeatable kinematic pattern andcould replicate this same pattern day after day.

Fig. 2 shows similar curves for the ground reaction forces for thesesame 9 trials. Both vertical and horizontal forces are a reflection of thetotal mass-acceleration product of all body segments and therefore

represent the total of all net muscle and gravitational forces acting ateach instant of time over the stance period. The horizontal reaction


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58 D.A. Wtnter / Ki nemattc and kr nerrc patterns m human pit

GROUND REACTION FORCES WM22 N=9)200 -

100 -

HORIZONTAL CV=2W

VERTICRL CV-7

0

Fig. 2. Average horizontal and vertical ground reaction force curves for same nine trials

force had an r.m.s. standard deviation over the stance period of 10.6Nm and in the vertical direction it was 30.8 Nm. When the magnitudesof these horizontal and vertical forces are considered the coefficients ofvariation in the horizontal direction (20%) and vertical direction (7%)are quite low. The vertical ground reaction force is dominated by

gravitational forces, but the muscularly generated accelerations in bothvertical and horizontal directions show a consistent net pattern.Fig. 3 shows the average moments of force curves ( c 1 S.D.) for

these same trials calculated at the ankle, knee and hip joints. A briefdescription of this subjects average pattern shows that she is within therange seen for normals (as will be seen later in fig. 7). The ankleinitially had a small dorsiflexor moment to lower the foot to theground, followed by a major build-up of plantarflexor activity reachinga peak at push-off (50% stride). This ankle pattern is quite consistent

and has an r.m.s. standard deviation of only 8.2 Nm which represents acoefficient of variation of 22%.


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D.A. Wlnter / Klnematrc und kinettc putterns n human gait 61

Table 2Variability of moments of force: within-subject trials

Moment of force Coeff. ofvariation CV)

S. D.

Pm)

Support = hip + knee + ankle

HipKneeAnkle

Hip + kneeHip + ankleAnkle + knee

cv (eq. 3)s,, (eq. 4)& (eq. 4)

25.1% 10.6

71.6% 13.267.0% 10.222.1% 8.15

27.7% 5.9846.4% 19.316.4% 6.72

19.715.611.2

hamstrings, would be significantly more active than normal. The ham-string, being knee flexors as well, would alter the knee moment patternbut in the opposite direction. Thus the flexibility to make an adjust-ment at one joint can manifest itself at an adjacent joint, therebyincreasing the variability at both joints.

4.2. Synchronization of motor patterns

Table 2 summarizes the variability measures for the 9 repeat trials onthe same subject as before. Both the coefficient of variation and ther.m.s. of the standard deviation over the stride period are tabulated.The CL values have been discussed earlier and reflect the variability ateach joint as a percent of the joint moment of force. However, in order

to see how the absolute variability varies from joint to joint we mustcompare the r.m.s. S.D. of the moment of force (Nm) at each joint.From eq. (3) a, = 19.7 Nm and 15~ was experimentally determined to

be 10.4 Nm; thus a cancellation of joint moments is indicated. Such afinding is not surprising when one considers the number of biarticulatemuscles that have opposite functions at adjacent joints: hamstrings,rectus femoris, gastrocnemius. To ascertain where most of the cancella-tion occurs a further analysis was undertaken to partition the covari-ante, and table 2 shows the computed 8s for paired summations of the

hip + knee, hip + ankle and ankle + knee moments of force. Then thecovariance between the hip and knee, and ankle and knee patterns was


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62 D.A. Wincer / Kinema/ic and kinetic patterns in humun goit

calculated using eq. (4). For these 9 intra-subject trials SAX = 15.6 Nm.Similarly, for the knee and ankle d,, = 11.2 Nm. Thus the strong

negative covariance seen between the hip and knee is a measure of thelinked patterns of opposite moments of force at those two joints, and isa dramatic indication of the role of the double joint hamstring andrectus femoris muscles. The lower, but still significant negative covari-ante between the knee and ankle is likely due to the only biarticulatemuscle crossing those joints, the gastrocnemius. In order to dramatizethis trade-off between hip and knee muscles fig. 4 was plotted to show

3MPHRI SONOF MAX/ M NAND AVERAGEMOMENTS

-1001

200r

-flVERAGE (n=9)

- - -Wfl22D

Fig. 4. Averaged moment of force pattern plus patterns from two of the nine trials that were

selected to represent extreme compensating motor patterns seen at the hip and knee. See text fordetails.


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D.A. W~nrer / Kinenwtrc and krnerrc patterns ITI human gorr 63

two extreme strides from this subject whose kinematic patterns werequite consistent. The average moment of force curves for these nine

trials (solid line) is the same as shown in fig. 3 and two extreme trials(WM22D and WM22J) are labelled. Trial WM22D had a hip pattern

,_i 100l-7I

' )

5

j

SENSI TI VI TYF J OI NTMOMENTS O Fh

KNEEWENT

-norma. . . -10%

fh Horizontal ground

reaction force

RULE HolENT

X of STRI DE 4Fig. 5. Theoretical moment of force patterns that would have resulted in same lower limbkinematics but with altered horizontal ground reaction forces. Such stride-to-stride alterations ofthe hip moments of force to correct for the trunks posture can be quite large compared with the

resultant ground reaction force change.


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64 D.A. Winter / Kinematic und krnetrc patterns n humutl gort

that was biased and predominantly flexor during stance while WM22Jwas extensor. The opposite was true at the knee: WM22D was mainly

extensor and WM22J had a dominant flexor pattern. Thus we couldconclude that WM22D trial was accomplished with rectus femorisdominant and for WM22J trial the hamstrings prevailed. As indicatedin the opening comments of this paper the trade-off that has just beendescribed falls well within theoretical prediction. This is now demon-strated quite readily if we re-analyse one of the trials with identicallower limb kinematics but with slightly altered ground reaction forces.Although this is a form of sensitivity analysis it also serves to demon-strate how a subject could maintain identical limb kinematics but withdifferent moment of force patterns. In effect, we can answer thequestion could the subject walk the same way (kinematically) but withan entirely different combination of muscle force patterns at eachjoint?. The answer is, yes.

Fig. 5 shows the result of such an analysis. The solid lines plot theactual moments of force, the dotted line was when the horizontalground reaction force was decreased lo%, and dashed line shows whatmotor patterns would have caused a 10% increase in the horizontalreaction force pattern. As can be seen there are insignificant changes inankle moments, small changes in knee moments and significant hipmoment changes. Thus we can conclude that an alteration in the hipmoment pattern (mainly to correct for the position of the trunk)combined with compensating changes at the knee and ankle could yieldidentical ankle and knee angle patterns. Note that the ground reactionforce changed only lo%, but the average hip moment changed morethan 40% of its mean value. Thus it is not surprising that relatively lowvariability seen in this subjects ground reaction forces and in her joint

kinematics were the result of fairly large variations in the hip and kneemotor patterns. From a practical point of view it is worth a note ofcaution that gait disorders analysed solely with joint kinematic datacould never lead to definitive conclusions regarding underlying motordisfunction.

A final comment should be made concerning the fact that the datafrom only one subject was presented in this paper. The cost in time andmoney for each complete biomechanical analysis is quite high so only 9trials on one subject were attempted. Thus these variability measures

are to be interpreted as a first indicator of the results that might beexpected if similar analyses were performed on additional subjects.


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D.A. Winrer / Kmemtrric and kinetrc putterns in human gait 65

4.3. Between-subjects variability

The three cadence groups kinetic curves plotted in figs. 6-8 can now bediscussed to identify general similarities and differences. In figs. 9-12the average moment of force patterns at each joint are superimposed sothat cadence-related differences can be readily identified.

In general, at all three speeds at the ankle (fig. 9) we see a smalldorsiflexor moment at heel contact followed by a major build up ofplantarflexor moment reaching a maximum at about 50% (during

AVERf l GEDOMENTSBODYMASS SLOWWALK ( N=141m 1.5[ ,...._,

-..,,.:/.~ .,,. KNEE

1.-

W _. 5 ... ._. .._..._.._..,,.. .,..

El 1.5;.._

1: I I ; .~,..., :_: . , :

Fig. 6. Average moment of force/body mass for 14 subjects walking slowly. Variability (CV) athip and knee joints was very high.


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VERAGED l OHENTS/ BODY f l SS NORr mL WFl LK N=161

I.5

ti *w .5

e-.5

II-x .5

IA- . 5

- I

II -x . 5

I A e

- . 5

2

$5

f i . 58

KNEE

Fig. 7. Average moments/body mass for 16 subjects walking their natural cadence. CV for ankleand support moments were about same as for slow walking but have reduced significantly at thehip and knee.

push-off). It then reduces to 0 at toe-off. The knee pattern (fig. 10) isgenerally extensor during early stance (5525%), as the knee flexes toabsorb energy during initial weight bearing and to extend the kneeslightly toward mid-stance (Winter 1983b). During mid-stance (25-40%)the knee has a tendency to show a small flexor moment, but thevariability is very high such that some subjects could maintain a smallflexor moment during all of stance while others had an extensor pattern

at this time. Then late in stance during push-off (40-60%) the kneeextensors turned on again in an attempt to control the knee flexion


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D.A. W/nter / Kinemmrc and ktnetic patterns ,n human gait 67

AVERAGEDOMENTSBODYASS FAST WALK ( N=141I

N m 0

Fig. 8. Average moments/body mass for 14 subjects walking fast. CV for ankle and supportmoments remained the same magnitude but reduced even further at the hip and ankle.

(knee flexion increases from 10 to 40 during this time). A surprisingamount of mechanical energy absorbed by the quadriceps accompaniesthis eccentric contraction (Winter 1983b). Finally, after toe-off thissame extensor moment serves to arrest the backward swinging leg andfoot, and at the end of swing a small but consistent flexor moment bythe eccentrically contracting hamstrings decelerates the swinging leg. Atthe hip the pattern (fig. 11) is also extremely variable but has a generaltrend. There is an initial extensor pattern during weight bearing fol-

lowed by a flexor pattern which continues through mid-stance tomid-swing. The initial extensor pattern is partly responsible for the


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68 D.A. Winter / K~nemutic and krn etrc, putterns ,n hunwl RN,,

DMPARI SONF FAST, NATURALND SLOW l NKLEOMENTS

1.8. NORHFLZED TO BODY H S

1.6.

; 1.4.

i-NF1T. (N=lS)

w 1.2. - - sLOHM=141i ---------fRST(N=4)u 1.0.

Fg .8-Ii

.6.

.4 -

.2 -

2

Fig. 9. Comparison of average ankle moments for three cadence groups. Moments increased withspeed during the energy-generation phase (40%-60% stance) but decreased with speed during theenergy-absorption phase (62-4055 stance).

energy absorption during weight bearing, then the hip flexors serve toreverse the backward moving thigh and by 50% of stride the thighreverses and this continuing flexor moment serves to concentricallycontract and add energy to the swinging lower limb. During the latterhalf of swing the extensor moment (mainly hamstrings) serves todecelerate the swinging thigh.

As an indication of the total extensor/flexor pattern of the lowerlimb the support moment is seen to have a major and consistent


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D.A. Winter / Kinemarrc and k/m-f/c putterns ,n human gair 69

:i: '

NORHf l LI ZED O BODY ms

: :: '; :: :; :: :: :

i: - NRT. ( N=l 6)

:: : - - - SLOM( N=14)

i : - - - - . Ff l 6T( N=l 4)

COMPARI SON F FAST, NATURAL I ND LOWKNEE MOMENTS

Fig. 10. Comparison of knee moments for three cadence groups. The pattern was essentially the

same at all cadences and increases in magnitude as cadence increases.

extensor pattern during stance followed by a small flexor patternduring swing, (with the exception of the fast walking group (fig. 12)who showed a small extensor pattern during late swing). Recalling thatthe support moment is the algebraic summation of the moments at allthree joints (extensor are + ve and flexor are - ve) we can see that thissmall extensor pattern is the result of a hip extension moment (fig. 11)

that is slightly higher than the knee flexor moment (fig. 10) duringlatter half of swing (SO-100%).


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COtlPRRISONF FRST, NATURALND SLOWHI P MOMENTS

NO?M_IZED TO BODY MSS

-N~T. (N=16)

- - *SLOHN=4)

--------.fflST(N=)

Fig. 11. Comparison of hip moments for three cadence groups. Pattern remained same at all

cadences with major increases in hip flexor moment at fast speeds during 10%75% stance.

Some discussion should now be directed at the variability seen inthese patterns as summarized in table 3. The ankle pattern (figs. 6-8)shows consistently low variability (CV= 45-46%) at all three speeds.The ankle moments are totally dominated by the requirements of stancewith the foot flat on the ground during most of this time (8% to 40% ofstride period). During weight acceptance and mid stance the sole

function of the ankle plantarflexors is to control the forward movingleg and then to cause active plantarflexion and generate the major


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D.A. Win/w / K~nrmrrtic and klnetlc puttems m human gut 71

- t + T. W 6)

- - sLow( N= 4)

- - - - - - - - m TW141

Fig. 12. Comparison of support moment patterns at three walking speeds. Support moment waspositive (extensor) during stance and primarily flexor during swing. Natural cadence group hadequal peaks at weight acceptance and push-off, slow cadence group had small or negligible weightacceptance peak. Fast walkers were characterized by a dominant weight acceptance peak and alower peak during push-off. Major reason for this reduced peak was the increase in hip flexormoment at this time for the fast walking group.

energy burst during push-off (Winter 1983b). With single joint muscles(with the exception of the gastrocnemius) controlling most of thisfunction there is very little room for variability. Similar low variability

has been noted in the EMG patterns of the soleus and gastrocnemiusmuscles during slow and natural walking compared with the muscles


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crossing the knee and hip (Yang and Winter 1984). In a similar mannerthe CVs for the support moment are low and consistent across all

three speeds (53% to 58%), and this in spite of considerable variabilityat the knee and hip. This finding gives credence to the argument thatthe neural control during walking involves a total lower limb patternrather than control over individual joints.

The hip and knee patterns of variability show a high variability, butwith a distinct trend related to speed. At the slow cadence the CV was208% at the knee and 176% at the hip, this reduced to 150% and 144%respectively at natural cadence and further to 101% and 80% during fastcadences. Such a trend indicates a tightening of the neural control aswe increase our cadence. At lower cadences the moments of force arelower, reaching flexion and extension peaks of no more than 30 Nm.During fast walking those peaks double or triple indicating each musclegroup is getting further into its dynamic range (maximum kneeflexor/extensor moments are 170-300 Nm, (Lesmes et al. 1978) andhip flexor/extensor moments are 150-200 Nm), and therefore has lessflexibility. This flexibility is largely due to the dual roles of severalbiarticulate muscles crossing those joints. For example, contraction ofthe hamstrings during stance causes an extensor moment at the hip andflexor at the knee, and vice versa for the rectus femoris. Thus the sametotal extensor pattern, as seen in the support moment can result frommany different combinations of extensor/flexor combinations at theknee and hip. The variance and covariance analysis of the inter-subjecttrials (table 4) show quite distinctly that there is a considerable correla-

Table 3Coefficients of variation of moment of force profiles for inter-subject cadence groups.

Moment of force Slow cadence (N = 14) Natural cadence (N = 16) Fast cadence (N = 14)

cv T.M.S. cl cv r.m.s 0 cv r.m.s. Ll

(Nm/kg) @m/kg) (Nm/kg)

Support = hip+ knee + ankle

HipKneeAnkle

Hip + kneeKnee + ankleHip + ankle

58% 0.219 56% 0.270 53% 0.226

176% 0.249 144% 0.282 80% 0.290208% 0.216 150% 0.244 101% 0.264

46% 0.217 45% 0.204 45% 0.189

91.3% 0.170 82.7% 0.204 54% 0.18237.5% 0.193 43.3% 0.237 36% 0.23787% 0.399 85.6% 0.409 114% 0.389


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D.A. Winter / Kinemutrc and krnetlc putterns n human put 73

Table 4Variance and covariance of moment of force profiles - inter-subject trials.

Slow 0.170 0.249 0.216 0.282 0.193 0.216Natural 0.204 0.282 0.244 0.312 0.237 0.244Fast 0.182 0.290 0.264 0.348 0.237 0.264

Note: All units in Nm/kg. Subscripts: a = ankle: k = knee: h = hip.

0.217 0.2370.204 0.2110.189 0.222

tion between the moment patterns seen at adjacent joints. The covari-

ante between the hip and knee was chiefly responsible for the corre-lated activity of the total limb. During slow walking the hip/kneecovariance was 0.282 Nm/kg, during natural cadence 0.312 Nm/kg,and 0.348 Nm/kg during fast walking. This means that faster walkingsubjects walk with increased correlation between the muscles crossingthe hip and knee. The presence of any speed-correlation between theknee and ankle is not evident. A fairly constant covariance (0.211 - 237Nm/kg) appears for all three speed-related groups. Such a finding isnot too surprising considering the already high level of ankle motoractivity at slow cadences and the relatively small increase with cadence.

In order to demonstrate the trade-off between hip and knee motorpattern fig. 13 is presented. The average moment of force at the kneeand hip during stance was plotted for all subjects in the 3 cadencegroups. Because of the widely different masses of the subjects theaverage moments of force were divided by body mass. The correlationof the linear regression passing these points is quite high (Y = 0.82, p

variability and compensating effects

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