On the accuracy of center ... estimation during high-impact movement GeWu *

ELSEWIER
Human Movement
Science 16 (1997) 323-336
On the accuracy of center of mass acceleration
estimation during high-impact movement
GeWu
*
Department of Physical Therapy, lJniversi@ of Vermont, 305 Rowe11Building, Burlington, VT 0540.5, USA
Abstract
Injuries in the lower limb occur mainly at the transition from swing to stance phase during high
impact movements. Because body kinematics and kinetics at this transition has higher frequency
components than that during other portions of the movement, the traditional biomechanical
approaches in quantifying these variables, such as image-based motion analysis system, are not
satisfactory. This paper reports on the use of the Integrated Kinematic Sensor (IKS) for studying
kinematics of high-impact activities such as heel-strike during running. The accuracy of estimating
segmental center of mass acceleration (COM) in the lower limb using the traditional differentiation approach and the IKS approach was investigated. The results suggested that the COM
acceleration estimates using the differentiation approach is not able to capture the true kinematic
details, while the IKS approach is less dependent on the frequency range and provides detailed,
high quality description of the COM acceleration. Furthermore, the relative contributions of the
different components of the IKS was examined and the results suggested that by adding either
angular velocity or linear acceleration measurement to the traditional differentiation approach, the
impact acceleration at heel strike can be discovered for either proximal or distal body segments.
Therefore, it is possible to reduce the complexity of the IKS approach and yet to achieve an
acceptable quality of the information.
PsyclNFO classification:
2260
Keywords: Center of mass acceleration:
Three-dimensional
measurement
Ir E-mail: [email protected],
0167-9457/97/$17.00
Copyright
PII SO167-9457(96)00059-O
Differentiation:
Fax: + 1 802 656-2191,
High impact movement;
Integrated
Tel.: + 1 802 656-2556.
0 1997 Elsevier Science B.V. All rights reserved.
Kinematic
Sensor:
324
G. Wu / Human Mouement Science 16 (19971323-336
1. Introduction
Lower limbs of human body experience large loads during locomotion. These
loads are necessary to support the entire body, to perform the desired motion
and to sustain the impact from foot-floor contact. An accurate knowledge of
three-dimensional joint loads during high impact activities is necessary to assess
musculoskeletal
dysfunction and to prevent joints in the lower limb from
injuries. In fact, it has been shown that acute injuries in the lower limb are
caused mainly by the impact shear forces at the joints during foot-floor contact
(Steele, 1990; McConkey, 1986, Yasuda et al., 1993; Robinovitch et al., 1991;
Parkkari et al., 1994).
Unfortunately, there have been limited, and inconsistent reports on the joint
reaction forces and moments in the lower extremity of human body during
walking and running. This is perhaps mainly due to the difficulty in directly
measuring the acceleration at the center of mass (COM) of a body segment
during gait. One of the common procedures of obtaining segmental COM
acceleration involves measurements of the displacements of body segments, and
the calculation of the velocities and accelerations via numerical differentiation.
The amplification of high frequency noise that is inherent to this process
produced joint load estimates that depended closely on data processing schemes.
This resulted in not only a wide range of joint load estimates reported by
different research groups (Patriarco et al., 1981; Schot et al., 1989; etc.), but also
a rather smooth transition at the foot-floor contact (Bresler and Frankel, 1950;
Winter, 1980). Therefore, it is difficult to conclude whether the differences
represent true biomechanical findings or merely reflect the different instrumentation and processing techniques used to derive those estimates.
On the other hand, attempts to replace the above acceleration estimation
procedure by direct measurements using linear accelerometers were reported by
a few groups (Morris, 1973; Seemann and Lustick, 1981; Gilbert et al., 1984;
Sabelman et al., 1988). However, because the accelerometers
could not be
attached directly to the segmental COM, and were sensitivity to the field of
gravity, it was necessary to use between four accelerometers (Hayes et al., 1983)
and twelve accelerometers
(Kane et al., 1974) to resolve the full segmental
kinematics. Nevertheless, these measurement schemes proved sensitive to low
frequency errors (reported as drift of the segmental orientation) and depended on
estimates or approximations of the initial conditions. As a result, the direct
human body segmental acceleration measurements
during locomotion were
limited to the sagittal plane and either swing or stance phase of gait (Morris,
1973; Gilbert et al., 1984).
G. Wu /Human Movement Science 16 f 19971323-336
325
Recently, a new kinematic measurement
approach called the Integrated
Kinematic sensor (IKS) was developed (Wu and Ladin, 1993). It combines
spatial position, linear acceleration, and angular velocity measurements, with
six-degrees of freedom analysis of rigid body motion to fully characterize the
segmental kinematics. The validity and accuracy of this approach has been
tested under a controlled environment using a two degree of freedom mechanical
pendulum, and the results have been published elsewhere (Wu and Ladin, 1993).
However, it is obvious that the IKS involves integration of three different
measurements
which are more complex and expensive than the traditional
differentiation approach. The questions remain to be answered are: (1) Are there
advantages of using IKS approach, comparing to the traditional differentiation
approach, in estimating body kinematics and kinetics during high impact human
movement? (2) How does each of the direct measurements in an IKS unit (i.e.,
angular velocity and linear acceleration) contribute to improving the quality of
body kinematics and kinetics during high impact movement?
The purpose of this study is to address the above questions. First, a theoretical
analysis was conducted on the noise of determining the segmental COM
acceleration based on the IKS and traditional differentiation approaches. Numerical values of the maximum noises for each approach were then calculated to
demonstrate the effect of the frequency band on these noise components. Last,
experiments on human subjects running were performed and three-dimensional
linear accelerations at the COM of the lower limb segments were calculated
using four approaches: IKS, differentiation, differentiation plus angular velocity,
and differentiation plus linear acceleration. The results were compared with a
focus on the transition phase from swing to stance.
2. Noise in the calculation
of segmental
COM acceleration
The relation between the accelerations at the COM (acorn) and at an arbitrary
point p (a,) of a rigid body is described by the following equation:
a corn=tZ ,-_(jXr,--wX(wXr,),
(1)
where w is the angular velocity of the rigid body, and rp is the distance of point
p to the COM. Assuming that the measurement
by each transducer (i.e.
accelerometer, angular rate sensor, and optoelectronic system) contained a white
noise:
aj:=a,+n,,
(2)
G. Wu/Human
326
Mowment
Science 16 (1997) 323-336
w m= o+nw,
8”=
(3)
(4)
tl+n,,
where superscript m stands for measured, the calculated
based on Eq. (1) has a noise component Aucom as:
A%n
COM acceleration
= II, -~wXr,-wX(n,Xr,)--n,X(oXr,)--n,
(5)
x(%PJ
It should be pointed out that the variables in the above equations are vectors
expressed in the body-fixed coordinate system (BCS). Without loosing generality, we assume that: (1) the origin of BCS is at the COM with its three
orthogonal axes (x, y, z) along the medial-lateral,
anterior-posterior,
and proximal-distal directions of the body segment; (2) the arbitrary point p is in the
x-y plane (i.e., ri = 0, r,” = rJ = r,,); (3) the angular velocity of the body
w”=wZ=0);and(4)the
segment is mainly in the sagittal plane (i.e., o-‘=w,
noises in three axes of each measurement are the same (i.e., ni = nz = nl; = n,,
ni= nZ=n” =n w, n;T=n? H= ni = no>. The three components of Aacorn in Eq.
(5) then beclme:
Aa~~om=nn+iz,r,-(o-n,)n,r,,
Aa~~,=n,-~~r,+(w+n,)n,r,,
Au&,
(6)
= ~1, - (o + 2n,)n,,,r,,.
We further assume that the noises for all the measurements are white with a
magnitude of N and a maximum dynamic range of 0,. For the traditional
differentiation approach in which only the body movement is directly measured,
the maximum magnitude of the noise in each of the three components of the
COM acceleration is proportional to the square of the dynamic range w,:
( k&l
>,,X
( Aa:“, Lx
=
=
( AGIl >nl,,
=
wrpNw,, + N(l + 2Nr,,)w,f
wr,No,
+ N( 1 + rp + Nr,,) w,’
(7)
For the IKS approach, however, the maximum magnitude of the noise in each of
the three components of the COM acceleration is less dependent on w,~, as
described by the following equation, than the previous method:
(AaXcorn) max
(Au- corn) max
=
(Au?’corn) max
zx
N( 1 + wr,, + Nr,,) + r,, No,
=
N(l + 2Nrp)
(8)
G. Wu / Human Movement Science 16 (1997) 323-336
Table 1
Maximum magnitude of noise in COM acceleration
calculation (in m/s21 using
differentiation approach or the IKS approach (w = 15 rad/s, I-,, = 0.1 m, N = 0.1)
o,, (Hz)
0
2
4
6
8
IO
12
14
16
18
20
Differentiation
IKS
321
either
the traditional
Ratio (Diff./IKS)
x and y
z
x and y
z
x and y
z
0.0
0.7
2.4
4.9
8.3
12.6
17.8
23.9
30.8
38.7
47.4
0.0
0.7
2.2
4.6
7.7
11.7
16.5
22.1
28.5
35.7
43.8
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.4
0.5
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0
3
8
16
25
36
48
61
75
90
105
7
22
45
76
115
162
217
280
350
429
0
A numerical example of these noises as a function of o, is illustrated in
Table 1. Clearly, as the dynamic range of body movement increases the noises
with the differentiation approach increase dramatically. For example, at 6 Hz
which is typically considered as the maximum dynamic range for human
walking (Winter, 1990), the maximum noises from the differentiation approach
are about 16 and 45 times of the noise from the IKS approach in the frontal
plane and in the proximal-distal
direction, respectively.
At about 20 Hz,
however, which is typical for some high impact activities such as running or
high jump landing, the differentiation
approach can generate noises that are
hundred times larger than the IKS approach. In fact, these large noises can be on
the same order of magnitude as the acceleration due to body movement.
3. Experiment in human locomotion
In this study, the segmental kinematics of the lower limb during running was
obtained by three IKSs attached to the frontal surfaces of the right shank and
thigh, and to the dorsal surface of the right foot, respectively (Fig. 1). The
interface between the IKS and the surface of the body contained a rigid segment
that was made of thin plastic plate, contoured by the shape of individual body
segment, and could cover the entire frontal surface of the body segment. A
rubber brace was used to completely cover the rigid segment and to press it
against the skin. The maximum ranges for the accelerometers (Entran Devices,
328
Fig.
G. Wu/Human
Mowment
Science 16 (I9971 323-336
1. Three assembled Integrated Kinematic Sensors on the lower limb of a subject.
NJ, USA) were + 1000 g, k 100 g, and f 10 g for the foot, shank, and thigh,
respectively, and the ranges for the angular rate sensors (Watson Industries, Inc.,
WI, USA) were f 1500 deg/s for all the body segments. The marker movements were directly measured by a WATSMART system (Northern Digital,
Ontario, Canada) with two cameras located about 1.5 m apart on both sides of a
15 m runway. In addition, a timer was used to monitor the average speed over a
3.66 m distance around the viewing volume. All the kinematic variables were
low pass filtered at 100 Hz and digitized at 200 Hz.
Four healthy young male subjects were tested. The body segment dimensions
and joint locations with respect to the landmarks on the body were measured in
order to calculate the COM locations (Zatsiorsky and Seluyanov, 1985). The
locations of the IKSs on each body segment were also measured. The anthropometric information for the four subjects is summarized in Table 2.
G. Wu / Hunum Mooement Science 16 (1997) 323-336
Table 2
Anthropometric
information
329
of four subjects
Parameter
Subject 1
Subject 2
Subject 3
Subject 4
Height Cm)
Mass (kg)
Foot length Cm)
Shank length Cm)
Thigh length (m)
1.82
74.5
0.27
0.43
0.39
1.68
73.5
0.24
0.38
0.39
1.I7
70.0
0.27
0.40
0.38
1.88
81.7
0.27
0.46
0.40
After attaching the IKSs, a warm up period of about 10 to 15 minutes was
provided when subjects walked freely in the lab. Then, subjects were allowed to
practice a few times to settle down the running speed and the pace so that the
right foot would be completely within the bounds of the viewing volume for one
heel strike. Multiple trials were collected and only those trials that had the preset
speed and the correct landing were used for further analysis. All the tests were
done with bare feet.
Data processing was done on a DEC-VAX 1 l/750 computer. The segmental
COM accelerations in the lower limb were calculated based on the kinematics
that were directly measured by either the IKSs or by the markers. For the
differentiation approach, a Butterworth low-pass filter was applied with 100 Hz
cut off frequency for the marker displacements and either 60 Hz or 15 Hz cut off
for their time derivatives.
4. Results
According to Kerwin and Chapman (19881, the frequency content in barefoot
running can be as high as about 50-60 Hz. However, when the cut off
frequency of the low pass filter was chosen at 100 Hz for the displacements and
60 Hz for their time derivatives, all the components in the lower limb COM
accelerations showed huge peak values, especially at both ends of the time
window from mid-swing to the successive early swing. Representative linear
accelerations at the COM of the foot, shank and thigh are illustrated in Fig. 2. In
contrast, the COM accelerations that were derived from the IKS measurement
(as shown in Fig. 3) showed distinctive impulses at heel strike, indicating the
large impact during the transition from swing to stance. Comparing the results
that were derived from IKS and differentiation approaches, it seemed that unless
a lower cut off frequency is used and the edge effect is overcome, the COM
330
G. WU/ Human MoLtentent Science 16 (19971323-336
swing hs stance
swing hs stance
swing hs stance
Gait Cycle
Fig. 2. A representative trajectories of linear accelerations at the COM of the foot, shank and thigh, using
differentiation approach with the cut off frequencies of 100 Hz for the displacement and 60 Hz for the time
derivatives, respectively. Time axis runs from 200 ms before to 225 ms after heel strike (hs).
swing hs stance
swing hs stance
swing hs stance
Gait Cycle
Fig. 3. A representative trajectories of linear accelerations at the COM of the foot, shank and thigh, using IKS
approach. Time axis runs from 200 ms before to 225 ms after heel strike (hs).
G. Wu / Human Mouement Science 16 (19971323-336
331
foot
Med. loo!
I
-zod
-20
swing hs stance
swmg hs stance
swing hs stance
Gait Cycle
Fig. 4. A representative trajectories of linear accelerations at the COM of the foot, shank and thigh, using
differentiation approach with the cut off frequencies of 1.5 Hz for displacement and the time derivatives. Time
axis runs from 200 ms before to 225 ms after heel strike (hs).
acceleration estimates by the differentiation approach did not indicate even the
basic trajectories.
To further improve the signal to noise ratio of the COM acceleration estimate,
a lower cut off frequency of 15 Hz for the time derivatives of the displacement
data was used. The results are shown in Fig. 4. Clearly, the high frequency noise
as observed in Fig. 2 was eliminated, resulting in rather smooth trajectories.
However, the high frequency impulses at the heel strike as shown in Fig. 3 were
also eliminated.
In order to maintain a high signal to noise ratio at a higher frequency range so
that the heel strike impulses can be revealed, the direct measurement of either
angular velocity or linear acceleration in the lower limb was combined with the
differentiation approach. That is, the segmental COM acceleration was calculated by Eq. (1) in which either the angular velocity (w) or the linear
acceleration (a,) was directly measured (for example, by the sensors in the IKS
unit) while others were derived by differentiation. Fig. 5 shows the mean error
in COM acceleration of lower limb segments between the IKS approach and (a)
pure differentiation
approach, (b) combination of differentiation
and linear
acceleration, and (cl combination of differentiation and angular velocity. The
results showed that the angular velocity and/or linear acceleration played a
different role for different body segment. For the foot, for example, adding the
332
G. Wu/HumanMocementScience
swing hs stance
16 (1997)323-336
swing hs stance
swing hs stance
Gait Cycle
Fig. 5. Mean error in COM acceleration of the lower limb segments between the IKS approach and (a) pure
differentiation approach, (b) combination of differentiation
and linear acceleration, and (c) combination of
differentiation and angular velocity. Time axis runs from 200 ms before to 225 ms after heel strike (hs).
direct measurement of linear acceleration to the differentiation approach showed
a significantly smaller error than the other two approaches. For the thigh,
however, adding the direct measurement of angular velocity resulted in the
smallest error.
5. Discussion
The estimation of segmental COM acceleration in human locomotion has
presented a challenge in the field of biomechanics in the light of the facts that
this parameter is extremely important in the study of joint dynamics and yet it
can not be directly measured (by non-invasive techniques) in human subject. In
this study, both analytical and empirical work were conducted in an attempt to
investigate the accuracy of COM acceleration estimation by various approaches
during high-impact activities such as running. In the human subject experiment,
linear displacements, angular velocities and linear accelerations of the lower
limb during running were directly measured by IKSs, and the linear accelerations at the COM of body segments were derived using those kinematic
variables that were either measured by the IKS or estimated by the time
differentiation approach.
G. Wu / Human Mooemenr Science 16 (19971323-336
333
Overall, the IKS approach is superior to the differentiation
approach in
reporting segmental COM acceleration for high impact movements that have a
wide frequency range. Theoretical analysis demonstrates that the signal to noise
ratio of the calculated segmental COM acceleration using the differentiation
approach increases parabolically with an increase in the frequency band of the
noise. For high impact activities (such as running) with the frequency content of
close to 60 Hz (Kerwin and Chapman, 1988) the COM acceleration estimates
by the differentiation approach are completely lost in the noise. In contrast, the
COM acceleration estimate by the IKS approach has a good signal to noise ratio
over a wide range of frequencies.
As a result, not only the fundamental
trajectories are clearly shown, but also the high frequency impulses at heel
strike. Moreover, the signal to noise ratio from the IKS approach is good in all
three directions.
The poor signal to noise ratio problem in the differentiation approach can be
improved by applying a low pass filter with lower cut off frequencies. However,
this approach would result in the elimination of high frequency contents in the
signal such as the impulses at heel strike. Although the knowledge of overall
characteristics of lower limb acceleration is important for understanding the
basic mechanism of human movement, the detailed information about heel strike
impulses will allow us to explore the issues relating to gait transitions. For
example, it has been demonstrated that acute injuries in the lower limb occur
mainly at heel strike (Steele, 1990), and that the impact force applied to the
joints in the lateral direction can cause ligament rupture or joint fracture (Yasuda
et al., 1993; Robinovitch et al., 1991). It may be possible that these impulse
accelerations observed at heel strike be used to study the mechanisms of joint
injuries during high impact activities such as running.
One of the concerns about the IKS approach is its cost and complexity.
Obviously, its high signal to noise ratio over a large range of frequency is
achieved by directly measuring two more variables (i.e., velocity and acceleration) in addition to the displacement. In this study, the possibilities of eliminating one of those two direct measurements was explored. The results suggest
that: (1) the addition of either angular velocity or linear acceleration measurement will reduce error around the heel strike; (2) the effectiveness of adding one
of these two measurements depends on the specific situation. For example, for
the distal body segment such as the foot that experiences larger acceleration
change around heel strike than the proximal body segments, the addition of
linear acceleration measurement is more effective than that of angular velocity
measurement. On the other hand, the addition of angular velocity measurement
helps to reduce the error more effectively than the acceleration measurement in
334
G. Wu / Human Movement Science 16 (19971323-336
the proximal body segments whose angular velocity is relatively large around
the heel strike. Overall, the IKS approach can be simplified, if necessary, to
reduce the cost and complexity but to improve the signal to noise ratio in COM
acceleration estimates during high impact activities.
Another concern about the use of IKS approach is the vibration of soft tissue
to which the IKS unit is attached. Some investigators have questioned the high
peak values observed in the accelerometer’s output at heel strike when the skin
mounted accelerometer is used, and wondered whether it is due to the soft tissue
artifact. However, by comparing the outputs from both bone and skin mounted
accelerometers Light et al. (1980) demonstrated that the tracings from the skin
mounted accelerometer were ‘broadly similar to those from the tibia’, including
the heel strike impulses. In fact, in this study, attempts have been made to
reduce the soft tissue artifact by using a specific mounting interface. The
difference between this configuration
and the one of direct skin-mounted
accelerometer is that it not only increases the unit stiffness of the soft tissue, but
also take into account the entire soft tissue that surrounds the bone and within
the area of the rubber brace.
Overall, the COM acceleration estimates based on the IKS approach show
large high frequency impulses around heel strike during running. This is
consistent with the results reported by others (Gilbert et al., 1984; Light et al.,
1980; Radin et al., 1991; Lafortune, 1991). It is believed that these heel strike
impulses are not artifacts, but true accelerations reflecting the sudden change
from swing to stance.
6. Conclusion
The accuracy of estimating segmental COM acceleration in the lower limb
during high impact activities such as running was investigated. The traditional
differentiation
approach and the IKS approach were compared. The results
suggested that the COM acceleration estimates during running using the differentiation approach depend closely on the bandwidth of the low pass filter.
Obviously, it is not capable of capturing the true kinematic details. The results
are distorted and questionable, although they might be acceptable for slow
activities. On the other hand, the IKS approach is less dependent on the
frequency range and provides detailed, high quality description of the true COM
acceleration. In particular, the high frequency impact accelerations at heel strike
are clearly shown. Furthermore, this study investigated the possibility of using
one of the two direct measurements in the IKS to improve the quality of the
G.
Wu /Human
Mocement Science 16 (I 997) 323-336
335
differentiation
estimates. The results indicated that by adding either angular
velocity or linear acceleration measurement to the traditional differentiation
approach, the impact acceleration at heel strike can be discovered for either
proximal or distal body segments. Therefore, it is possible to reduce the
complexity of the IKS approach.
Acknowledgements
This work was supported by a National Science Foundation
EET-8809060 and by a grant from the Whitaker Foundation.
Grant
No.
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