Human Movement
North-Holland
Science 3 (1984) 51-76
51
KINEMATIC AND KINETIC PATTERNS IN HUMAN
VARIABILITY AND COMPENSATING
EFFECTS
David A. WINTER
GAIT:
*
urlt1w-s1t):
of Warerloo,Canada
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 considerable
variability
at the kinetic level. Intra-subject
variability of joint moment patterns over the stride
period was high at the knee and hip, but low at the ankle and in a recently defined total limb
pattern, called support moment. A similar profile of variability was evident for inter-subject
trials
at slow, natural and fast cadences, with the percentage variability at the knee and hip decreasing as
cadence 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 these
joints. Also shown was the fact that these compensating
patterns were highly predictable from link
segment theory.
1. Introduction
In the assessment of motor patterns of walking the joint kinetics are
fundamental
to the understanding
of that movement and are extremely
powerful in the diagnosis of pathological
gait. The moments of force
represent the net effect of all agonist and antagonist activity, and can
therefore be considered as the final desired motor pattern at that joint.
Both the clinical and basic researcher are interested in these motor
patterns and if sufficient analyses are available the following questions
can now be posed:
(1) How do these patterns
alter with cadence
* Author’s address:
Canada N2L 3Gl.
D.A. Winter,
Dept. of Kinesiology.
0167-9457/84/$3.00
0 1984, Elsevier Science Publishers
changes?
University
of Waterloo,
B.V. (North-Holland)
Waterloo,
Ont.,
(2) Is there evidence of a consistent synergistic pattern across the joints
of 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
using data from a normal population
examples of pathologies.
2. Literature
answers to the above questions
supplemented
by case study
review
In the large volume of literature of gait analyses the number of studies
that have addressed the reaction forces and moments of force have been
quite limited (Winter 1980). Since 1980 only a few additional
case
histories have been added (Boccardi et al. 1981). This is unfortunate
because it is at the kinetic level we can see the cau.se of the movement
rather than at the kinematic level at which scores of papers have
described the final effect of all these forces. Because of the complex
interaction of the link segment system it is almost impossible to infer
from the kinematics alone as to what forces are acting to cause the
observed pattern. This was demonstrated
in a case study reported by
Winter (1980) in which a knee replacement
patient had a dominant
knee flexor moment during the entire stance period yet still walked with
a stiff knee. In the presence of this flexibility at individual joints there
was still a consistent total pattern of support during stance by all three
of the joints of the lower limb. The total extensor pattern, called the
support moment, was defined (Winter 1980) as:
Ms=Ma+Mk+Mh
(0
where: Ma, Mk and Mh are the moments of force at the ankle, knee
and hip, and are positive for extension and negative for flexion. The
polarities of Ma and Mh have been reversed from the original formula,
which was written to satisfy the polarity conventions
of link segment
mechanics, rather than functional convention.
MS was found on all
subjects and patients to be positive during stance and negative during
swing. This consistent total extensor pattern also means that there can
be considerable
inconsistency
in the moment patterns of the three
joints, and, in actual fact, this is regularly demonstrated.
From a link
D.A.
Wtnter / Kinenzut~c and kinettc
patternsin
hums
guit
53
segment mechanics point-of-view
we know that a consistent kinematic
pattern 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 of
joint moments of force that could result in exactly the same ankle and
knee angle histories.
3. Theory
and methodology
3. I. General
Data for this paper have been collected over the past six years in the
Gait Laboratory in the Department
of Kinesiology at the University of
Waterloo. Details of the data collection, processing and analysis appear
in previous publications (Winter 1980, 1983a), and yields the kinematic
and kinetic patterns over the stride period. The moments of force at the
ankle, knee and hip, were calculated using equations developed by
Bresler 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 by
neglecting the medial-lateral
movement certain errors will result. There
will be no error in the moments of force as calculated, they will be a
true representation
of the moments in the plane of progression. However, if bone-on-bone
forces were to be analysed,
there could be
significant
errors generated
by muscles acting in the medio-lateral
plane. This is especially true at the hip joint during single support when
abductor muscle forces would add to the already existing compressive
forces of the hip flexors and extensors. However, since articulating
forces were not part of the analyses reported here a 3-D analysis was
not necessary.
Other methodological
short-cuts
were not done, however. Some
researchers have used a quasi-static approach to the analysis of joint
reaction forces and joint moments of forces. Such an approach ignores
the inertial forces of the segments of the limb. During stance the error
of this approach is negligible for the foot (because the mass acceleration
products for the foot are small), but become noticeable at the knee and
significant at the hip (Wells 1981) especially at weight acceptance and
push-off.
3.2. Within-subject
triuls
One subject underwent 9 repeat trials spaced over three days so that
measures of within-subject
variability
might be obtained.
for each
walking trial the subject was asked to “walk her natural cadence” as
she walked along the walkway over the force plate as she was tracked
by a 16mm tine camera. No metrome or other timing device was used
for the repeat trials. Ensemble average patterns over the stride period
were 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%. At
each 2% interval from heel contact to heel contact an average and
standard deviation of the 9 trials on each of the three variables was
calculated.
The ensemble average for this subject’s joint angles are
presented in fig. 1, the ground reaction force patterns appear in fig. 2
and 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 subject’s natural cadence was determined with slow cadence being
defined as a subject’s 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
Cadence
Cadence
N
classification
x
groups
Mass
SD.
x
(kg)
SD.
Height
Age
X
S.D.
X
(cm)
SD.
Stance
time
(B stride)
x
S.D.
SIOW
14
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
84.7
D.A. Winter / Ktmmutrc
cmd ktnetic
patternsin human gait
55
Prior to calculating
the average kinetic patterns for each cadence
group two normalizations
were required. The first normalization
was to
make the stance time = loo%, and to set the stance period = 62%. For
the natural cadence group this meant a linear adjustment of all data
over stance and compressing it from a time base of 63.3% to 62%. For
the 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 from
61.0% to 62%. These minor adjustments in the time base were necessary
to emphasize the similar timing in the patterns especially prior to
toe-off. The second normalization
was required to reduce the inter-subject variability that results when ensemble average profiles are calculated over the stride period. Averaging the moment of force patterns
(Nm) resulted in tremendous
variability.
Two techniques
were attempted. Normalizing
to the maximum support moment, as was done
previously in jogging (Winter 1983a), reduced the variability but was
not as effective as dividing the moment of force by body mass. Thus an
ensemble average pattern (Nm/kg)
was calculated
for each subject
within each cadence group, the average was calculated
at each 2%
interval over the stride period. At each of these intervals the standard
deviation was also calculated. The moment patterns at each joint plus
the total support moment pattern were plotted (figs. 4, 5, 6) along with
a 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 average
patterns a coefficient
of variation (CV) was calculated = root mean
square 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 amplitude
of 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 pattern
itself.
The CV scores for each joint moment profile do not tell us whether
the variability is merely random biological perturbations,
or whether
there is some correlation between what is happening at one joint with
the motor patterns at other joints. One way of determining
this is to
calculate the covariance between the individual joint moment patterns
and the total support moment pattern. If the moment of force patterns
are completely independent
then the predicted variance in the support
moment should be the sum of the variances in each joint moment
pattern, or
where the subscripts s, a, k and h represent the support, ankle, knee
and hip, respectively.
However, we actually have an estimate of the
variance in the support moment, 6x = r.m.s. S.D. of Ms. The difference, a, - es,, is an estimate of the total covariance amongst the three
joint moment patterns. If a, > 6s then the experimental
results show
that there is a correlation between the three moments as a result of a
cancellation
(i.e., a subject increased his flexor moment at one joint
while at the same time increased his extensor moments at one or both
of the other joints). If a, < 6s then the reverse correlation is indicated.
To ascertain where most of the correlation occurs a further analysis was
undertaken to partition the covariance and this was done by computing
u,‘s for paired summations
of the hip + knee, and ankle + knee moments of force. Then, to calculate the covariance between the hip and
knee patterns, ehk we use the formula:
-2
uhtk
where: t!ii+k is the average variance of the sum of the hip and knee
moment patterns across the same subject or cadence group. Similar
formulae 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
one subject with 9 trials walking at her natural
from the tine film of
cadence. The average
D.A. Winter / Kinematrc and krnetrt patterns m human gad
JOINT
0 7’
,’
RNGLES
WM22
57
(N=9)
1
‘.
.‘: : :
20
;
2
0
-20
Fig. 1. Average ankle, knee and hip angle for nine repeat trials on the same subject spread
three separate days. Coefficient
of variation (CV) reflects the average standard deviation
stride period (dotted line) as a percent of the mean curve (solid line).
over
over
cadence for these 9 trials was 110 steps/mm
with a standard deviation
of only 2 steps/min.
Thus the normalization
of the time base for each
trial to loo%, which is necessary to achieve a cyclical average, has
negligible change on the pattern for any individual trial. The solid line
indicates the mean curve and the dotted lines are one standard deviation either side of the mean. The r.m.s. standard deviation over the
stride was 1.5” at the ankle, 1.9” at the knee and 1.8” at the hip. Such a
low variability over the complete stride at all three joints is a strong
indicator that she had learned a very repeatable kinematic pattern and
could replicate this same pattern day after day.
Fig. 2 shows similar curves for the ground reaction forces for these
same 9 trials. Both vertical and horizontal forces are a reflection of the
total mass-acceleration
product of all body segments and therefore
represent the total of all net muscle and gravitational
forces acting at
each instant of time over the stance period. The horizontal reaction
58
D.A. Wtnter / Kinemattc and krnerrc
GROUND
200
-
100
-
REACTION
FORCES
HORIZONTAL
VERTICRL
patternsm human pit
WM22
(N=9)
CV=2W
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 10.6
Nm and in the vertical direction it was 30.8 Nm. When the magnitudes
of these horizontal and vertical forces are considered the coefficients of
variation 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 both
vertical 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 brief
description of this subject’s average pattern shows that she is within the
range seen for normals (as will be seen later in fig. 7). The ankle
initially had a small dorsiflexor
moment to lower the foot to the
ground, followed by a major build-up of plantarflexor
activity reaching
a 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 a
coefficient of variation of 22%.
D.A.
W/nrer / Kir~emuric and kinerr
parterns
rn human guir
59
WM22FIVERAGED
JOINTIIOMENTS
- NOR/MLWRLK (n=9)
I
......
KNEE
CV=67%
Fig. 3. Average moments of force at the ankle, knee and hip for same nine repeat trials. Support
moment (eq. 1) is algebraic sum of three joint moments and represents the total extensor/flexor
pattern of the lower limb.
The knee moment shows a momentary flexor pattern during the first
few percent of stance, followed by an extensor response to assist in
arresting knee flexion as full weight bearing takes place. During the
latter half of stance a flexor moment is evident and just before and
after toe-off the knee extensors turn on to decelerate the backward
rotating leg and minimize heel rise just after toe-off (at about 65%
stride). Finally, at the end of swing the knee flexor activity serves to
decelerate the swinging leg prior to the next heel contact. This motor
pattern at the knee represents a higher percentage variability ( Y.WZ.S.
60
D.A. Winter / Kinemnrrc and kinetrc potrerns rn human go/r
S.D. = 10.2 Nm and a coefficient
of variation of 67%) than at the
ankle, especially during the time of push-off. The much larger CVat the
knee compared with the ankle is partially due to a larger absolute
variability
but more so because the average magnitude of the knee
moment is considerably
less than that generated at the ankle. Such
variability is likely higher at the knee because of the large number of
biarticulate muscles crossing that joint.
The hip patterns demonstrate that this subject has an extensor motor
pattern for the first half of stance which assists in keeping the knee
from collapsing and also decelerates the forward rotating trunk. During
the latter half of stance the hip flexors serve to decelerate the backward
rotating thigh and then reverse it and cause its forward rotation prior to
swing through of the lower limb. This forward rotating flexor moment
continues well into swing and is followed by an extensor burst to
decelerate the forward swinging thigh. The highest variability is seen in
this hip motor pattern (mean S.D. = 13.2 Nm, CV = 72%) and this
appears to be due to the number of biarticular muscles crossing the hip
joint.
Finally, in the support moment we see the net extensor/flexor
pattern of the total lower limb. During stance there is a major total
extensor pattern which reverses rapidly to a small flexor pattern during
early swing and back to extensor as the limb is extended prior to heel
contact. The variability in the support moment is quite low (CV = 25%)
which strongly indicates that the total extensor/flexor
pattern at all
three joints of the lower limb is quite reproduceable
in spite of large
individual variations, especially at the knee and hip joints.
A summary of what we now see for this one subject regarding how
robot-like here motor patterns are reveals the following. All the kinematic patterns (fig. 1) and the total kinetic patterns (fig. 2 plus the
support moment in fig. 3) are quite repeatable. However, the individual
joint motor patterns (fig. 3) especially at the hip and knee, are quite
variable and presumably a measure of the flexibility of the individual
muscles as they adapt to produce the same kinematic pattern. This
adaption demonstrates
the fine motor tuning that takes place over
strides in order to correct for minor deviations
from the desired
kinematic pattern. For example, on one stride the trunk may be leaning
1” or 2” too far forward, thus the hip extensors increase during the
stance period to correct the error. Because the upper part of the body
represents
2/3 mass of the body the hip extensors,
including the
D.A. Wlnter / Klnematrc und kinettc
Table 2
Variability
Moment
Support
of moments
of force: within-subject
of force
= hip + knee + ankle
putternsin human gait
trials
Coeff. of
variation (CV)
S. D.
Pm)
25.1%
10.6
Hip
Knee
Ankle
71.6%
67.0%
22.1%
13.2
10.2
8.15
Hip + knee
Hip + ankle
Ankle + knee
27.7%
46.4%
16.4%
5.98
19.3
6.72
19.7
15.6
11.2
cv (eq. 3)
s,, (eq. 4)
& (eq. 4)
hamstrings, would be significantly more
string, being knee flexors as well, would
but in the opposite direction. Thus the
ment at one joint can manifest itself
increasing the variability at both joints.
4.2. Synchronization
61
active than normal. The hamalter the knee moment pattern
flexibility to make an adjustat an adjacent joint, thereby
of motor patterns
Table 2 summarizes the variability measures for the 9 repeat trials on
the same subject as before. Both the coefficient of variation and the
r.m.s. of the standard deviation over the stride period are tabulated.
The CL’ values have been discussed earlier and reflect the variability at
each 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 must
compare 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 a
finding is not surprising when one considers the number of biarticulate
muscles that have opposite functions at adjacent joints: hamstrings,
rectus femoris, gastrocnemius.
To ascertain where most of the cancellation occurs a further analysis was undertaken
to partition the covariante, and table 2 shows the computed 8’s for paired summations of the
hip + knee, hip + ankle and ankle + knee moments of force. Then the
covariance between the hip and knee, and ankle and knee patterns was
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 the
linked patterns of opposite moments of force at those two joints, and is
a dramatic indication of the role of the double joint hamstring and
rectus femoris muscles. The lower, but still significant negative covariante between the knee and ankle is likely due to the only biarticulate
muscle crossing those joints, the gastrocnemius.
In order to dramatize
this trade-off between hip and knee muscles fig. 4 was plotted to show
3MPHRISONOF MAX/MINAND AVERAGEMOMENTS
-1001
200r
-flVERAGE
-
Fig. 4. Averaged moment of force pattern
selected to represent extreme compensating
details.
-
(n=9)
-Wfl22D
plus patterns from two of the nine trials that were
motor patterns seen at the hip and knee. See text for
D.A. W~nrer / Kinenwtrc
and krnerrc patterns ITI human gorr
two extreme strides from this subject whose kinematic
quite consistent. The average moment of force curves
trials (solid line) is the same as shown in fig. 3 and two
(WM22D and WM22J) are labelled. Trial WM22D had
63
patterns were
for these nine
extreme trials
a hip pattern
SENSITIVITY
OF JOINTMOMENTS
TO Fh
,
_
i
7
I
100
l-
')
5
j
KNEEWENT
-normal
... ... . -10%
fh-Horizontal
reaction
ground
force
RULEHolENT
X of STRIDE
4
Fig. 5. Theoretical
moment of force patterns
that would have resulted in same lower limb
kinematics but with altered horizontal ground reaction forces. Such stride-to-stride
alterations of
the hip moments of force to correct for the trunk’s posture can be quite large compared with the
resultant ground reaction force change.
64
D.A. Winter / Kinematic
und krnetrc
patterns,n humutl gort
that was biased and predominantly
flexor during stance while WM22J
was extensor. The opposite was true at the knee: WM22D was mainly
extensor and WM22J had a dominant flexor pattern. Thus we could
conclude that WM22D trial was accomplished
with rectus femoris
dominant and for WM22J trial the hamstrings prevailed. As indicated
in the opening comments of this paper the trade-off that has just been
described falls well within theoretical prediction. This is now demonstrated quite readily if we re-analyse one of the trials with identical
lower limb kinematics but with slightly altered ground reaction forces.
Although this is a form of sensitivity analysis it also serves to demonstrate how a subject could maintain identical limb kinematics but with
different
moment of force patterns.
In effect, we can answer the
question “could the subject walk the same way (kinematically)
but with
an entirely different combination
of muscle force patterns at each
joint?“. The answer is, yes.
Fig. 5 shows the result of such an analysis. The solid lines plot the
actual moments of force, the dotted line was when the horizontal
ground reaction force was decreased lo%, and dashed line shows what
motor patterns would have caused a 10% increase in the horizontal
reaction force pattern. As can be seen there are insignificant changes in
ankle moments, small changes in knee moments and significant hip
moment changes. Thus we can conclude that an alteration in the hip
moment pattern (mainly to correct for the position of the trunk)
combined with compensating changes at the knee and ankle could yield
identical ankle and knee angle patterns. Note that the ground reaction
force changed only lo%, but the average hip moment changed more
than 40% of its mean value. Thus it is not surprising that relatively low
variability seen in this subject’s ground reaction forces and in her joint
kinematics were the result of fairly large variations in the hip and knee
motor patterns. From a practical point of view it is worth a note of
caution that gait disorders analysed solely with joint kinematic data
could never lead to definitive conclusions regarding underlying motor
disfunction.
A final comment should be made concerning the fact that the data
from only one subject was presented in this paper. The cost in time and
money for each complete biomechanical
analysis is quite high so only 9
trials on one subject were attempted. Thus these variability measures
are to be interpreted
as a first indicator of the results that might be
expected if similar analyses were performed on additional subjects.
D.A.
Winrer /
4.3. Between-subjects
Kmemtrric
and kinetrc putterns
65
in human gait
variability
The three cadence groups’ kinetic curves plotted in figs. 6-8 can now be
discussed to identify general similarities and differences. In figs. 9-12
the average moment of force patterns at each joint are superimposed
so
that cadence-related
differences can be readily identified.
In general, at all three speeds at the ankle (fig. 9) we see a small
dorsiflexor
moment at heel contact followed by a major build up of
plantarflexor
moment reaching a maximum
at about 50% (during
AVERflGED
MOMENTSBODYMASS
- SLOWWALK (N=141
m
1.5[
,....“_,
-..,,.:
/““.~ .,,.
_.
W
El
1
:
1.
5 ...
KNEE
-
._......_..._.._..,,..
..,..’
,;,.~
;.“._
1.5
I
I
,..‘.,
_:’
.’
Fig. 6. Average moment of force/body
hip and knee joints was very high.
:
‘,
:
mass for 14 subjects
walking
slowly. Variability
(CV)
at
VERAGEDllOHENTS/BODY
HflSS- NORrmLWFlLK(N=161
I.5
ti
*
w .5
e
-.5
I
x .5
0
-.5
-I
I-
IA
I
Ix .5
KNEE
IA e
-.5
2
$5
’
f
i .5
8
Fig. 7. Average moments/body
mass for 16 subjects walking their natural cadence. CV for ankle
and support moments were about same as for slow walking but have reduced significantly
at the
hip and knee.
push-off). It then reduces to 0 at toe-off. The knee pattern (fig. 10) is
generally extensor during early stance (5525%), as the knee flexes to
absorb energy during initial weight bearing and to extend the knee
slightly toward mid-stance (Winter 1983b). During mid-stance (25-40%)
the knee has a tendency to show a small flexor moment, but the
variability is very high such that some subjects could maintain a small
flexor moment during all of stance while others had an extensor pattern
at this time. Then late in stance during push-off (40-60%) the knee
extensors turned on again in an attempt to control the knee flexion
D.A. W/nter / Kinemmrc
and ktnetic patterns ,n human gait
67
AVERAGED
MOMENTSBODY
MASS- FASTWALK(N=141
I
N
m
0
-
Fig. 8. Average moments/body
mass
moments remained the same magnitude
for 14 subjects walking fast. CV for ankle and support
but reduced even further at the hip and ankle.
(knee flexion increases from 10” to 40” during this time). A surprising
amount of mechanical energy absorbed by the quadriceps accompanies
this eccentric contraction
(Winter 1983b). Finally, after toe-off this
same extensor moment serves to arrest the backward swinging leg and
foot, and at the end of swing a small but consistent flexor moment by
the eccentrically contracting hamstrings decelerates the swinging leg. At
the hip the pattern (fig. 11) is also extremely variable but has a general
trend. There is an initial extensor pattern during weight bearing followed by a flexor pattern which continues
through mid-stance
to
mid-swing. The initial extensor pattern is partly responsible
for the
68
D.A.
Winter
/ K~nemutic
and krnetrc, putterns
,n hunwl
RN,,
DMPARISON
OF FAST,NATURAL
AND SLOWflNKLE
HOMENTS
1.8.
NORHFILIZED
TO BODY H&S
1.6.
; 1.4.
i
w 1.2.
i
u 1.0.
F
g .8Ii
.6.
-NF1T.
-
-
(N=lS)
sLOHM=141
---------fRST(N=l4)
.4 .2 -
2
Fig. 9. Comparison
of average ankle moments for three cadence groups. Moments increased with
speed during the energy-generation
phase (40%-60% stance) but decreased with speed during the
energy-absorption
phase (62-4055 stance).
energy absorption during weight bearing, then the hip flexors serve to
reverse the backward moving thigh and by 50% of stride the thigh
reverses and this continuing
flexor moment serves to concentrically
contract and add energy to the swinging lower limb. During the latter
half of swing the extensor moment (mainly hamstrings)
serves to
decelerate the swinging thigh.
As an indication of the total extensor/flexor
pattern of the lower
limb the support moment is seen to have a major and consistent
D.A. Winter / Kinemarrc and k/m-f/c putterns ,n human gair
69
COMPARISON
OF FAST,NATURALFINDSLOW KNEE MOMENTS
:i
:'
: :
:'
; :
: :
; :
: :
:
:
:
i
!
:
:
:
:
i
Fig. 10. Comparison
same at all cadences
NORHflLIZED
TO BODYms
-NRT.(N=l6)
-
--SLOM(N=14)
----.Ffl6T(N=l4)
of knee moments for three cadence groups. The pattern
and increases in magnitude as cadence increases.
was essentially
the
extensor pattern during stance followed by a small flexor pattern
during swing, (with the exception of the fast walking group (fig. 12)
who showed a small extensor pattern during late swing). Recalling that
the support moment is the algebraic summation of the moments at all
three joints (extensor are + ve and flexor are - ve) we can see that this
small extensor pattern is the result of a hip extension moment (fig. 11)
that is slightly higher than the knee flexor moment (fig. 10) during
latter half of swing (SO-100%).
COtlPRRISON
OF FRST,NATURAL
AND SLOWHIP MOMENTS
NOt?M_IZED
TO BODY MSS
-NI~T.
-
-
(N=16)
*SLOH(N=I4)
--------.fflST(N=]j)
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 in
these 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 stance
with the foot flat on the ground during most of this time (8% to 40% of
stride period). During weight acceptance
and mid stance the sole
function of the ankle plantarflexors
is to control the forward moving
leg and then to cause active plantarflexion
and generate the major
D.A.
Win/w
/ K~nrmrrtic
and klnetlc
puttems
m human gut
71
-t+lT.Wl6)
--
sLow(N=l4)
--------miTW141
Fig. 12. Comparison
of support moment patterns at three walking speeds. Support moment was
positive (extensor) during stance and primarily flexor during swing. Natural cadence group had
equal peaks at weight acceptance and push-off, slow cadence group had small or negligible weight
acceptance
peak. Fast walkers were characterized
by a dominant
weight acceptance peak and a
lower peak during push-off. Major reason for this reduced peak was the increase in hip flexor
moment 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 this
function there is very little room for variability. Similar low variability
has been noted in the EMG patterns of the soleus and gastrocnemius
muscles during slow and natural walking compared with the muscles
crossing the knee and hip (Yang and Winter 1984). In a similar manner
the CV’s for the support moment are low and consistent across all
three speeds (53% to 58%), and this in spite of considerable variability
at the knee and hip. This finding gives credence to the argument that
the neural control during walking involves a total lower limb pattern
rather than control over individual joints.
The hip and knee patterns of variability show a high variability, but
with a distinct trend related to speed. At the slow cadence the CV was
208% 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 fast
cadences. Such a trend indicates a “tightening”
of the neural control as
we increase our cadence. At lower cadences the moments of force are
lower, reaching flexion and extension peaks of no more than 30 Nm.
During fast walking those peaks double or triple indicating each muscle
group is getting further into its dynamic
range (maximum
knee
flexor/extensor
moments are 170-300 Nm, (Lesmes et al. 1978) and
hip flexor/extensor
moments are 150-200 Nm), and therefore has less
flexibility. This flexibility is largely due to the dual roles of several
biarticulate muscles crossing those joints. For example, contraction
of
the hamstrings during stance causes an extensor moment at the hip and
flexor at the knee, and vice versa for the rectus femoris. Thus the same
total extensor pattern, as seen in the support moment can result from
many different combinations
of extensor/flexor
combinations
at the
knee and hip. The variance and covariance analysis of the inter-subject
trials (table 4) show quite distinctly that there is a considerable correlaTable 3
Coefficients
Moment
of variation
of force
of moment
Slow cadence
cv
of force profiles
(N = 14)
T.M.S. cl
for inter-subject
Natural
cv
Hip
Knee
Ankle
Hip + knee
Knee + ankle
Hip + ankle
r.m.s
(N = 16)
0
groups.
Fast cadence
cv
@m/kg)
(Nm/kg)
Support = hip
+ knee + ankle
cadence
cadence
(N = 14)
r.m.s.
58%
0.219
56%
0.270
53%
0.226
176%
208%
46%
0.249
0.216
0.217
144%
150%
45%
0.282
0.244
0.204
80%
101%
45%
0.290
0.264
0.189
0.204
0.237
0.409
54%
36%
114%
0.182
0.237
0.389
91.3%
37.5%
87%
0.170
0.193
0.399
82.7%
43.3%
85.6%
Ll
(Nm/kg)
D.A. Winter / Kinemutrc and krnetlc
Table 4
Variance
Slow
Natural
Fast
and covariance
0.170
0.204
0.182
of moment
0.249
0.282
0.290
Note: All units in Nm/kg.
of force profiles
0.216
0.244
0.264
Subscripts:
0.282
0.312
0.348
putternstn human put
- inter-subject
0.193
0.237
0.237
73
trials.
0.216
0.244
0.264
0.217
0.204
0.189
0.237
0.211
0.222
a = ankle: k = knee: h = hip.
tion between the moment patterns seen at adjacent joints. The covariante between the hip and knee was chiefly responsible for the correlated activity of the total limb. During slow walking the hip/knee
covariance was 0.282 Nm/kg,
during natural cadence 0.312 Nm/kg,
and 0.348 Nm/kg during fast walking. This means that faster walking
subjects walk with increased correlation between the muscles crossing
the hip and knee. The presence of any speed-correlation
between the
knee and ankle is not evident. A fairly constant covariance (0.211 - 237
Nm/kg)
appears for all three speed-related
groups. Such a finding is
not too surprising considering
the already high level of ankle motor
activity at slow cadences and the relatively small increase with cadence.
In order to demonstrate the “trade-off”
between hip and knee motor
pattern fig. 13 is presented. The average moment of force at the knee
and hip during stance was plotted for all subjects in the 3 cadence
groups. Because of the widely different masses of the subjects the
average moments of force were divided by body mass. The correlation
of the linear regression passing these points is quite high (Y = 0.82, p <
0.005).These findings re-emphasize
the tight link between the knee
extensor/flexor
motor pattern with the reverse pattern at the hip. For
example, one subject (labelled A) walked with a dominant (hip extensor/knee
flexor) motor pattern. Another subject (labelled B) chose
the opposite pattern (hip flexor, knee extensor). And both these subjects, plus all other, accomplished
a similar kinematic gait pattern.
A look at the speed-related changes in these moment patterns is quite
revealing (figs. 9-12). In general the patterns were quite similar. The
flexor and extensor peaks occurred at the same times during stride, and
with one exception the magnitudes of the peaks increased as cadence
increased. The ankle patterns (fig. 9) are particularly
interesting. All
three cadence groups reached peak moment at 48% of stride. During
D.A. Wmter / Kinematic
AVERAGE
KNEE
and kinetic
patterns,n human pit
FIND HIP
MOMENTS/BODYMRSS
DURING
STRNCE
PC.0005
r=
-.82
EXTENSOR
J
KNEE
MOMENT/BODYMASS
(N,
m/Kg
1
Fig. 13. Average hip vs knee moments/body
mass during stance for 44 trials on slow. natural and
fast walking subjects. Correlation shows that subjects chose a pattern that is biased towards a knee
extensor/hip
flexor motor pattern or a knee flexor/hip
extensor combination.
active push-off (40-60% stride) the faster walking group had the highest
moment, which was expected if the plantarflexors
were to shorten more
rapidly and generate more energy. During early stance, when these
same muscles were absorbing energy (6-4% stride) the faster walking
group had the lowest moments of force. Also, there was a cross-over of
all three moments at the point in the stride (40%) when these muscles
switch from eccentric to concentric. Thus one of the major reasons why
the faster cadence group maintains its higher speed was that they brake
less during weight acceptance and accelerate more during push-off.
The knee moment patterns (fig. 10) showed drastic speed-related
increases. Especially during weight acceptance,
the quadriceps
contracted eccentrically
to absorb energy and control knee flexion. Maximum knee flexion for this fast cadence group was 24”, 20” for the
natural cadence group and 14” for the slow cadence group. Thus, the
magnitude
of the moments of force were closely correlated
to the
magnitude of the lengthening of the quadriceps, which, in turn, accounts
for the close correlation
between cadence and the power absorption
peaks previously reported (Winter 1983b). The second extensor peak
D.A. Wtnter / Kinemattc
and kinetic patterns rn human gart
75
occurred in later stance into early swing (45575% stride) and served to
control knee flexion that begins at 40% and continues through toe-off
(60%) to its maximum at 70% of stride. Finally, during late swing the
moments of force were directly related to the requirements
of the
flexors to absorb kinetic energy of the faster swinging leg and foot.
The hip moment patterns (fig. 11) demonstrated
the importance
of
the hip extensors as energy absorbers immediately
after heel contact.
The faster cadence group’s extensor activity was high and lasted only
10% of stride while the slower group showed considerably lower activity
but lasting to 23% of the stride period. During the balance of stance
and well into swing the hip flexors were dominant,
with the fast
cadence group having high activity. It appears that this flexor motor
pattern was required to decelerate the backward rotating thigh (lo-SO%
stance) and then reverse it and accelerate it forward (50&80% stance).
Finally, at the end of swing the extensors contracted proportionally
to
absorb kinetic energy from the thigh prior to heel contact.
5. Conclusions
(1) Within-subject
variability in kinematics and ground reaction forces
was quite low, whereas the moment of force patterns at the hip and
knee were highly variable. This high variability was supported by
evidence to demonstrate
that a wide range of moment of force
patterns at the knee and hip could result in identical joint angle
patterns during stance phase of walking.
(2) The basic shape of the moment of force patterns for slow to fast
cadences was basically the same over the stride period and increased
in magnitude as cadence increased. The only exception occurred at
the ankle when the eccentrically contracting plantarflexors
(during
weight acceptance and mid-stance) were least active for the faster
cadence group and most active for the slow cadence group.
(3) The variability of the moment of force patterns at the knee and hip
decreases as speed increases, the ankle moments show constant and
low variability at all cadences.
(4) At all cadences the total extensor/flexor
pattern of the lower limb
(called support moment) was consistent and has low variability.
(5) A considerable
component
of the variability
across the normal
population at all cadences was not random, but shows a high degree
D.A. Winter / Kimmatic
76
and kinetic
patternsm human gait
of covariance, especially between the hip and knee patterns. These
correlated patterns demonstrated
the anatomical links due to the
biarticulate muscles crossing these joints.
References
Boccardi, S., A. Pedotti, R. Rodano and G.C. Santambrogio,
1981. Evaluation
of muscular
moments at the lower limb joints by an on-line processing
of kinematic data and ground
reaction. Journal of Biomechanics
14, 35-45.
Bresler, B. and J.P. Frankel, 1950. The forces and moments in the leg during level walking.
Transactions
American Society of Mechanical Engineers 72, 27-36.
Lesmes, G.R., D.L. Costill, E.F. Coyle and W.J. Fink, 1978. Muscle strength and power changes
during maximal isokinetic training. Medicine and Science in Sports 10, 266-269.
Wells, R.P., 1981. The projection
of the ground reaction force as a predictor of internal joint
moments. Bulletin of Prosthetics Research BPRlO-35,
15-19.
Winter, D.A., 1980. Overall principle of lower limb support during stance phase of gait. Journal of
Biomechanics
13, 923-927.
Winter, D.A., 1983a. Moments of force and mechanical power in jogging. Journal of Biomechanics
16, 91-97.
Winter, D.A., 1983b. Energy generation and absorption at the ankle and knee during fast. natural
and slow cadences. Clinical Orthopaedics
and Related Research 175, 147-154.
Yang, J.F. and D.A. Winter, 1984. EMG amplitude
normalization
methods: on improving its
sensitivity as a diagnostic tool in gait analysis. Archives of Physical medicine and Rehabilitation. (In press.)