Analysis of variability in pylon transducer signals*
D . J O N E S a n d J. P. P A U L
Bioengineering Unit, University of Strathclyde, Glasgow
Abstract
A pylon transducer has been used to provide
force a n d m o m e n t d a t a relating to the stance
phase of gait of below-knee amputees fitted
with m o d u l a r types of P T B prostheses.
T h e d a t a has been collected a n d modified
using digital processing systems with particular
interest in quantifying shape differences in the
loading information curves. Earlier tests illus­
trated the need for m o r e d a t a t o provide
statistical s u p p o r t for conclusions. However, the
requirements for m o r e d a t a greatly increased
the d a t a handling a n d storage problems. A
m e t h o d was devised whereby those features
considered significant from an information
point of view could be extracted from the trans­
ducer signals a n d then combined. T h e statistical
combination of features was m a d e t o allow
objective comparisons of strides for a particular
subject.
Introduction
T o formulate a useful locomotion study it is
necessary t o answer several
fundamental
questions :
a) W h a t d a t a should be collected in
study?
the
D a t a which is collected, but n o t essential for
the success of a study is c o m m o n l y referred to
as " r e d u n d a n t " . S h a n n o n (1948) defined the
concept of redundancy a s : " T h a t fraction of a
message which is unnecessary and hence
repetitive in the sense that if it were missing
the message would still be essentially complete;
o r at least could be completed".
T h e study t o be described attempts to reduce
the redundancy amongst collected pylon trans­
ducer data. T h e nature of the required informa­
tion is controlled by the aims of the study.
Aims of the study
Previous pylon transducer studies h a v e
a t t e m p t e d t o examine the effects of, for example,
prosthetic alignment changes u p o n the loading
signals, without first establishing that these
signal patterns exhibit statistical consistency
u n d e r conditions of fixed alignment.
At the University of Strathclyde the stride t o
stride loading signals obtained from pylon
transducer tests were examined with a view t o
quantifying the stride t o stride differences. W i t h
the signal variability established, this would
form a basis for comparison once the conditions
of the prosthetic experiment differ.
b) H o w will it be collected?
c) W h i c h part of the collected d a t a con­
stitutes information valuable to the aims
of the s t u d y ?
These three elements are mutually dependent.
Unfortunately, the p r o b l e m of extracting useful
information from masses of d a t a often seems
t o be treated as an "after t h o u g h t " in spite of
o u r enthusiasm in d a t a acquisition. T h e
evidence of this enthusiasm can be seen in m a n y
locomotion laboratories where m o u n t a i n s of
c o m p u t e r o u t p u t lie unused.
The mechanism of redundancy reduction
T h e details of d a t a acquisition is given later
but it is convenient t o note at this t i m e that the
conversion of the analogue transducer signals
t o their sampled d a t a equivalents was conducted
at a sample rate of 200 samples per second u p o n
each channel.
T w o simple observations of the d a t a a r e
helpful :
a) Any single stance p h a s e period will, at the
*Based on a paper presented at the Second World
Congress, ISPO, New York, 1977.
acquisition stage, be represented by m a n y
samples of the original continuous-time
signal.
b) Successive stance phase periods m a y
occupy significantly different total times.
T h e first point raises worries over the a m o u n t
of l a b o u r needed in a sample t o sample com­
parison of successive stance phase periods,
whilst the second point poses d o u b t s as to
whether that process would be valid.
A n a p p r o a c h that could be used for d a t a
reduction involves the fitting of mathematical
functions with orthogonal properties t o the
successive stride data. T h e best k n o w n of these
m e t h o d s involve polynomial expansion, Taylor
series or Fourier series approximations.
Jacobs a n d Skorecki (1972) examined the
differences in the vertical force records from a
force plate, a m o n g s t subjects exhibiting b o t h
" n o r m a l " a n d " p a t h o l o g i c a l " (in appearance)
gaits. C o m p a r i s o n s were m a d e by using the
F o u r i e r series spectra of the stance period data.
A p r o b l e m with the m e t h o d arises with a loss
of all phase information. Also the use of this
type of representation, termed " P e r i o d o g r a m " ,
can provide unreliable spectral magnitude d a t a
when only a limited signal record is available
(Jenkins, 1961; Tukey, 1967; Richards, 1967;
Rayner, 1971).
T h e examination of curvature t o define a
shape has received m u c h support.
Attneave (1954) demonstrated that informa­
tion sufficient for the recognition of familiar
shapes was contained in a knowledge of the
points of m a x i m u m absolute curvature on the
boundaries of those shapes a n d their location
and connectivity. M a n y others have employed
these concepts (Zahn and Roskies, 1972; T o m e k ,
1973 a n d 1972).
Macfarlane a n d Lawrie (1972) used a function
termed the "Spatial velocity" t o recognize wave
patterns in E C G signals. If, for example, a force
vector described by its X, Y a n d Z c o m p o n e n t s
in an orthogonal reference frame changes
direction by an a m o u n t SX, SY, SZ in d T
seconds then the spatial velocity is given b y :
SPV = [ ( S X / d T ) + ( S Y / d T ) + ( S Z / d T ) ] '
T h e SPV function was chosen to provide an
indication of a significant event within the time
history of the loading information. T h e sup­
position is that the shapes of the load signals
a r e being examined for similarity.
2
2
2
1
2
Instrumentation
T h e pylon transducer used has been described
previously (Berme etal, 1975). Prior to these tests
the dynamic behaviour of the transducer was
examined using impulse response a n d Fourier
Transform m e t h o d s . T h e results for transverse
a n d longitudinal impulse forces imply (Fig. 1)
that if the activities m o n i t o r e d by the pylon
have n o significant frequency c o m p o n e n t s
higher t h a n 600 H z , then the transducer will be
adequate from a dynamic viewpoint.
Fig. 1. Response to X and Y impulses.
D a t a acquisition was performed using a 12
bit A - D converter operating at 200 samples per
second o n each channel. A P D P - 1 2 computer
was used as a preprocessor for an I C L 1904s
computer system. Prior t o d a t a reduction all
d a t a was filtered using a 4th order Butterworthequivalent digital filter with a 3 d B d o w n
frequency of 20 Hz. Filtered d a t a was corrected
for phase distortion.
Subject data and testing
T h e subject to be considered was a heavy
(96 kg), active below-knee a m p u t e e with a
conventional cuff type suspension P T B pros­
thesis. A Berkeley adjustable alignment unit
was used t o set u p dynamic alignment t o the
satisfaction of the prosthetist. T h e alignment
and shoe type were constant t h r o u g h o u t the
test series.
O n each visit by the subject, six level walking
periods were conducted whilst pylon transducer
a n d knee goniometer signals were recorded.
E a c h level walking period consisted of 20
seconds of free level walking. T h e subject chose
his own walking rate a n d this was measured.
Data reduction strategy
1) T h e n u m b e r of strides needed t o represent
a particular walking occasion were deter­
mined.
2) T h e SPV function g r a p h was p r o d u c e d for
t h e representative strides. T h e ankle force
vector c o m p o n e n t s were used here ( F X A ,
FYA, FZA).
In the case u n d e r examination a range of
n u m b e r s of strides ( n = 4 , 8, 16 and 32) were
combined a n d the statistical
population
estimates for each of the groups were c o m p a r e d
(Fig. 3).
3) T h e points of local extrema in the SPV
function were noted. These points were
considered to indicate a significant feature
in the time history of t h e force vector.
E a c h of the Fi " f e a t u r e s " (i = l
N)
occurs at some time Ti from the start of the
d a t a record. These occurrence times were
n o t e d (Fig. 2).
4) By noting the values of the F X A , F Y A a n d
F Z A c o m p o n e n t s at times Ti the essential
characteristics were determined.
Fig. 3. How n affects the confidence of X as an
approximation to μ.
N o t surprisingly as n increased the confidence
of X (the particular sample mean) as an approxi­
m a t i o n t o μ (the time p o p u l a t i o n mean)
improved. However, the a m o u n t of w o r k
required also increased with n without a p r o ­
p o r t i o n a t e increase in information. A s a com­
promise, for t h e level walking tests, 8 stance
periods were considered sufficient t o describe
an individual walking session.
Fig. 2. SPV function example.
Stride variations
walking session
Results
Estimate
of variability for FXA
component
This estimate was m a d e so that there would
be an idea of h o w m a n y strides would be needed
t o be fairly confident of statistically representing
the measured gait. T h e concept of sampling can
be considered within t h e framework of t h e
c o m m o n sense notion that if all the strides
collected during a walking session were
absolutely identical then only the d a t a for one
stride would be needed t o completely describe
t h a t session. If on the other h a n d all the stride
d a t a were completely dissimilar then it becomes
useless to describe that walking session other
t h a n with consideration of a n extremely large
n u m b e r of strides.
in force
vector within a
level
Eight consecutive strides were extracted from
a level walk conducted by t h e subject. E a c h
stride was examined, processed a n d a set of
features p r o d u c e d for each. Observation of t h e
SPV function for these strides provided 16
features. T h e times of the feature indicators
from the start of the stance periods were
recorded, along with the values of the force
c o m p o n e n t s F X A , F Y A , F Z A at each feature
time.
T h e eight sets of sixteen "critical" values
were combined for these c o m p o n e n t s . Figure 4
shows these c o m p o n e n t s synthesized from their
feature values, their time occurrences and their
95 % confidence intervals from the m e a n values.
Fig. 4a. Synthesized for eight strides with the
features of FXA (16 features used).
Fig. 4b. Synthesized for eight strides with the
features of FYA (16 features used).
Fig. 5. Confidence interval variation during stance
period.
Fig. 4c. Synthesized for eight strides with the
features of FZA (16 features used).
A representation of the magnitude confidence
intervals versus feature n u m b e r is given in
Figure 5. This shows rather m o r e clearly the
places and values of the confidence limits for
each of F X A , F Y A a n d F Z A . Considering the
F X A set, the widest confidence interval is seen
at the 6th feature time a n d has a value of ± 4 2 N .
F r o m a n initial low variability close t o heel
strike the variability increases rapidly between
t h e 3rd a n d 4th features a n d then decreases t o
less t h a n ± 1 0 N at midstance. D u r i n g the roll
over period the variability increases t o a peak
at feature 12 of ± 2 8 N before decreasing again
t o w a r d toe off.
F o r the F Y A set the p e a k variability at feature
time 5 was such as t o allow a confidence interval
of ± 7 0 N a b o u t the sample m e a n . T h e charac­
teristic twin peaks were present with confidence
intervals of less t h a n ± 2 0 N at each peak. T h e
trough between these peaks showed evidence of
a local region of higher variability with a
confidence interval of ± 4 0 N .
T h e F Z A set exhibits one s t r o n g p e a k of
± 3 5 N interval w i d t h at feature time 5, rising
from a region of low variability at feature time
4. T h e rest of the period shows a fairly even
variability distribution without the local high
spots of F X A a n d F Y A .
Overall the region of features 5 a n d 6 displays
the largest stride t o stride variability.
Variations
session
from
walking
session
to
walking
Figure 5 may now be considered to be related
t o the variability of the pylon transducer d a t a
during a single walking session. F o r that session,
at each feature Fi, t h e population mean μl is
estimated by the calculated mean x with a
confidence interval c o m p u t e d from the sample
variance S X (which itself is an estimate of the
population variance O X ) .
Considering a 2nd walking session with again
the averaging being c o m p u t e d over 8 stance
p h a s e periods. This time at t h e F i values, t h e
population m e a n μ2 is estimated by a calculated
m e a n of y with a variance estimate of S Y
(being an estimate of the true variance σ y ) .
A test may then be m a d e for the assumption
that the d a t a from these two level walking
sessions belong to the same statistical p o p u l a t i o n
(that is, that the difference between μl a n d μ2
at the Fi is insignificant).
Taking x a n d y as the estimates for the two
population m e a n s :
2
2
2
2
x—y will be Normally Distributed with a
m e a n μ l — μ 2 a n d a s t a n d a r d deviation of
(SX + SY )/8.
2
2
T h e 95 % confidence intervals are given by :
/
2
2
(x—y) ± 1 •96V (SX + S Y ) / 8 = (x—y) ± K
If these limits d o not include zero then t h e
difference is said t o be significant at the 5 % level.
Figure 6 shows the result of the comparison
of t w o walking sessions conducted with the
subject, expressed as a display of ± K as a
function of feature n u m b e r . T h o s e areas shaded
black correspond t o the areas of significant
differences between the information u p o n the
two walking sessions.
Summary
Fig. 6. Comparison between two level walking
sessions.
T h e variability in pylon d y n a m o m e t e r d a t a
acquired during level walking tests has been
examined. T h e information u p o n variability has
been considered t o lie within the shapes of the
loading signals. T h e extraction of this informa­
tion from the d a t a was performed as indicated
by the local extrema of a spatial velocity curve.
F o r the study example given n o significant
differences could be found for the subject's gait
between time separated walking sessions (with
constant experimental conditions). D a t a re­
duction has provided a statistical template
representing the subject's gait o n a particular
occasion. This template m a y then be used in
comparison with templates p r o d u c e d u n d e r
different experimental conditions (that is,
alignment or footwear changes).
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