Biomedical Engineering Reference
In-Depth Information
DAY-TO-DAY
TRIAL-TO-TRIAL
2
h
=
15.9
2
2
h
=
5.5
2
σ
σ
k
6.9
2
k
4.1
2
hk
19.1
2
(89%)
h
hk
6.5
2
(72%)
h
σ
=
σ
=
σ
=
σ
=
+
+
k
12.6
2
k
5.4
2
σ
=
σ
=
ak
14.3
2
(76%)
ak
5.6
2
(49%)
σ
=
σ
=
2
a
+
k
=
8.1
2
2
a
+
k
=
5.7
2
σ
σ
a
10.5
2
a
5.9
2
σ
=
σ
=
ALL UNITS IN N.m
hk
σ
hk
h
k
h
COV
=
×
100%
σ
=
σ
+
σ
−
σ
+
k
h
k
σ
+
σ
Figure 11.2
Variance and covariance analyses of the joint moments of the subject
shown in Figure 11.1 plus a similar analysis of 10 repeat trials of a second subject
done minutes apart. There is a very high covariance between the hip and knee moments
(89%) and a moderate covariance between the knee and ankle moments (75%). The
trial-to-trial covariances are still moderately high but are reduced because the individual
joint variances are considerably smaller. See the text for detailed calculations. (Repro-
duced with permission from Winter, D. A.
Biomechanics and Motor Control of Human
Gait: Normal, Elderly and Pathological
, 2nd Edition, Waterloo Biomechanics, 1991.)
σ
hk
=
is the mean covariance between hip and knee over
stance.
The term
σ
hk
can be expressed as a percent of the maximum possible,
which would be 100% if
σ
h
+
k
0, meaning that day-to-day changes in
M
h
and
M
k
were completely out of phase and were canceling each other
out completely. Thus, the maximum possible
σ
hk
=
=
σ
h
+
σ
k
, and the %
covariance is:
σ
hk
/(
σ
h
+
σ
k
)
×
COV
=
100%
(11.2)
19
.
1N
.
m
2
,
which is 89% of the maximum; even
σ
ak
is 76% of the maximum. The
trial-to-trial covariances are somewhat reduced, but this is because the indi-
vidual joint variances were drastically smaller over repeat trials minutes apart
compared to repeat trials over days.
As is evident from Figure 11.2 over the 9 days, the
σ
hk
=
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