|
| |
|
|
|
|
||||
| Home Help Feedback Subscriptions Archive Search Table of Contents | ||||
First published online May 29, 2009
Journal of Experimental Biology 212, 1965-1970 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.026153
The independent effect of added mass on the stability of the sagittal plane leg kinematics during steady-state human walking
1 Laboratory of Integrated Physiology, University of Houston, Houston, TX 77004,
USA
2 University of Nebraska Medical Center, Munroe-Meyer Institute for Genetics and
Rehabilitation, Omaha, NE 68198, USA
* Author for correspondence (e-mail: mkurz{at}unmc.edu)
Accepted 16 March 2009
 |
Summary |
|---|
 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Key words: inertia, gait, Floquet multipliers, nonlinear
|
INTRODUCTION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
).
Furthermore, the velocity of the center of mass is transitioned from a
downward to an upward direction by the legs during double support
(Donelan et al., 2002). Hence,
humans must perform external work by the legs to control the acceleration of
the body's mass during walking (Cavagna and
Margaria, 1966). The ability to change the acceleration of the
body is governed by the body's inertial state or resistance to change in its
motion. If the body's inertia grows too large, then it is possible that the
leg kinematics become less stable because the legs may not be able to
accelerate properly and redirect the body's mass throughout the gait cycle.
Although this seems plausible, the influence of added mass on the stability of
the leg kinematics during walking remains unknown.
The influence of mass alone on the biomechanics of walking has been
experimentally explored by first adding weight to the subject and then
counteracting the forces due to gravity with a body weight suspension system
(De Witt et al., 2008;
Grabowski et al., 2005). The
upward lifting force provided by the suspension system compensates for the
gravitational forces such that the subject's weight is maintained but the
subject's overall mass is increased. Thus, adding mass without adding weight
increases the amount of mass that the legs must redirect and accelerate
throughout the gait cycle. Using the combination of body weight support and
added weight, it has been demonstrated that walking under the influence of
added mass alone increases metabolic cost and affects the velocity of the
center of mass (De Witt et al.,
2008; Grabowski et al.,
2005). These results suggest that the acceleration and redirection
of the body's mass throughout the gait cycle is important for the maintenance
of the steady-state walking pattern. Potentially, these factors may also play
a role in the stability of the leg kinematics.
Human walking is constantly subjected to local disturbances that arise in
the natural couplings of the lower extremity dynamics and neural noise
(Dingwell and Kang, 2007;
Faisal et al., 2008;
Hasan, 2005). These local
disturbances must be dissipated within or across several strides to maintain a
stable walking pattern. If the locomotor system fails to dissipate these
disturbances, they will grow uncontrollably and may result in a loss of
stability (Dingwell and Kang,
2007). The amount of variation in the walking pattern is often
used as a metric for assessing stability
(Dingwell et al., 2001;
Dingwell and Marin, 2006;
Gabell and Nayak, 1984;
Hausdorff, 2007). However,
there is less experimental evidence to support the notion that changes in the
amount of variability are equated with the ability of the legs to dissipate
the local instabilities that arise in the walking pattern
(Dingwell et al., 2001;
Dingwell and Marin, 2006). The
difficulty in making this connection most probably lies in the fact that
variability measures (i.e. standard deviation and coefficient of variation) do
not provide insight into how the motor system responds to local disturbances
over continuous strides.
Floquet analysis is a well-established technique from theoretical mechanics
that has been used to quantify the rate at which local disturbances, which are
naturally present in the walking kinematics, are dissipated
(Dingwell and Kang, 2007;
Full et al., 2002;
Granata and Lockhart, 2008;
Hurmuzlu and Basdogan, 1994;
Hurmuzlu et al., 1996;
McGeer, 1990). The walking
pattern is considered to have greater stability if it is capable of
dissipating these small disturbances at a faster rate. The rate at which
disturbances are dissipated is quantified by the magnitude of the largest
eigenvalue of the Jacobian which defines the evolution of the walking pattern
from one stride (or section of the Poincaré map) to the next
(Guckenheimer and Holmes,
1983). An eigenvalue that is close to zero indicates that the
walking pattern will rapidly dissipate small disturbances. Alternatively an
eigenvalue that is further away from zero indicates a slower dissipation of
the disturbances that occurred during the walking pattern. For example, an
eigenvalue of 0.24 means that 24% of a disturbance remains after a stride and
that the disturbance will be asymptotically reduced over several strides
(Fig. 1). A walking pattern
with a larger eigenvalue (e.g. 0.54 versus 0.24) is considered less
stable because it takes longer to dissipate the local disturbances.
|
|
MATERIALS AND METHODS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
To begin the experiment, each subject put on neoprene wetsuit bottoms
followed by a support vest (Biodex Medical Systems, NY, USA) that was secured
around the torso and upper thighs. The neoprene wetsuit bottoms helped reduce
chafing during walking and improved the comfort and fit of the support vest.
The subjects initially selected a comfortable walking speed that could be
maintained for a long duration by manually increasing and decreasing the
treadmill speed. Once their self-selected speed was chosen, the subjects
warmed up while walking on the treadmill for a total of 6 min. A self-selected
speed was used in this investigation because it best represented the subject's
natural walking dynamics. This notion is based on previous experimental data
that has shown that changes in walking speed above or below a preferred gait
influences the dynamic stability of the walking pattern
(Dingwell and Marin, 2006;
England and Granata, 2007).
The self-selected speed (0.98±0.24 m s–1, mean
± s.d.) was maintained for all the respective inertia conditions.
The subjects completed walking trials with 0%, 10%, 20% and 30% of added body mass. Each of the mass conditions was presented in a random order. First, thin lead strips (0.45 kg each) were firmly attached symmetrically around the hips using a modified hip belt (Fig. 2). By adding the lead strips to the subject, we increased both weight and mass. To compensate for the increased forces due to weight, an upward vertical force was applied (i.e. equal to the amount of added weight) by a customized body weight suspension system that easily attached to the support vest worn by each subject. The subject stood quietly on the treadmill while in line with the overhead pulley as the upward lifting force was applied in the direction of gravity. A strain gauge load cell (Omega Engineering, Stamford, CT, USA) was placed in parallel with a cable-spring-pulley and supplied a voltage proportional to the applied lifting force. The lifting force recorded by the strain gauge load cell was monitored in real-time with the aid of a desktop computer. To apply the lifting force to the subject, rubber springs were stretched using a hand winch. Once the desired lifting force was achieved, the hand-winch was locked in place to allow the lifting force to be constantly applied throughout the entire duration of each walking trial. The average lifting force (mean ± s.d.) applied to each subject was 14.27±2.06 lbs, 27.26±3.83 lbs and 40.40±6.22 lbs while walking with 10%, 20% and 30% added mass, respectively.
|
For each condition, the subjects walked for a total of 4 min and we
collected lower extremity kinematics during the last 3 min. A high speed (120
Hz) six-camera motion capture system (ViconPeak, Centennial, CO, USA) was used
to record the three-dimensional positions of marker triangulations that were
placed on the right foot, shank and thigh segments. A 5 s standing calibration
was collected to determine the anatomical reference system for each segment.
Subjects were instructed to stand upright, distribute their weight evenly on
both feet, and keep both knees in a locked position. The location of the
markers during the standing calibration trial was used to correct any
misalignment of the local reference vectors that defined each of the
respective lower extremity segments (Nigg
et al., 1993). The position data for all markers were filtered
using a zero-lag Butterworth filter, and the selected cutoff frequencies were
determined using the Jackson Knee Method with a prescribed limit of 0.01 m
Hz–1 Hz–1
(Jackson, 1979). The range for
the optimal cutoff frequency in the x, y and z coordinates
ranged from 5–7, 3–5 and 4–7 Hz, respectively. The Jackson
Knee Method was used because it allowed for the maximum attenuation of noise
in each respective coordinate while still preserving the relevant content of
the signal.
Based on the filtered marker positions, we calculated the sagittal plane
joint angular positions and velocities of the ankle, knee and hip. We
evaluated the stability of only the sagittal plane leg kinematics because they
represent the dominant plane of motion during walking
(Mah et al., 1994). The joint
angles and velocities from the continuous time series were extracted for each
instance of heel-contact and mid-swing that occurred during the gait cycle
using customized laboratory software. The instant of heel-contact was defined
as the maximum position of the heel marker in the forward direction for each
stride. The instant of mid-swing was defined as the maximum knee flexion that
occurs during the swing phase of the gait cycle. These discrete points were
used to construct Poincaré maps that were used to determine the
stability of the leg kinematics at these instances of the gait cycle. Several
technical articles on the use of Floquet analysis have indicated that the
eigenvalues of the Jacobian will not depend on the choice of the
Poincaré section for steady-state walking
(Dingwell and Kang, 2007;
Hurmuzlu and Basdogan, 1994).
We chose to partition the stability of the leg kinematics into the stance and
swing because previous biomechanical studies have indicated that these phases
of gait may be under different balance control mechanisms
(Frenkel-Toledo et al., 2005;
Gabell and Nayak, 1984).
Additionally, the instances of heel-contact and mid-swing were selected
because they represent repeatable features of the leg kinematics that can be
reliably extracted from the kinematic data for the construction of the
Poincaré maps.
The eigenvalues of the Poincaré map were used to measure the
stability of the leg kinematics at the instant of heel-contact and mid-swing
during the gait cycle (Granata and
Lockhart, 2008; Hurmuzlu and
Basdogan, 1994; Hurmuzlu et
al., 1996; McGeer,
1990; Tedrake et al.,
2004). The sagittal plane joint positions and velocities of the
right ankle, knee and hip were used to define the a state vector that defined
the dynamics of the leg as:
 | (1) |
123) and angular velocities
(456) at the ankle, knee and
hip respectively. For steady-state human locomotion, the walking pattern
achieves dynamic equilibrium. This property was defined by the following
relationship:
 | (2) |
; Hurmuzlu
et al., 1996).
Perturbations were linearized about the equilibrium state vector
x* according to the following equation:
 | (3) |
denotes the deviation from the equilibrium state vector, and
J is the Jacobian which defined the rate of change of the state
variables from one stride (n) to the next (n+1).
xn and xn+1
were defined as:
 | (4) |
 | (5) |
) was used to solve for J
(Eqn 6), and the stability of the
leg's kinematics were determined by calculating the eigenvalues of J:
 | (6) |
To be cautious in our Floquet analysis, we tested the possibility that the
calculated eigenvalues were a result of correlated noise in the walking
pattern rather than instabilities within the leg kinematics. We used an
algorithm developed by Theiler et al.
(Theiler et al., 1992) to
generate surrogate data sets from the original discrete points that were used
to construct the Poincaré maps. The surrogation algorithm is based on a
phase randomization process that destroys any deterministic features of the
data but maintains the mean, variance and power spectra
(Miller et al., 2006;
Theiler et al., 1992). The
maximum eigenvalue (βSUR) was computed for each surrogate, and
a paired t-test was used to test if the original (β) and
surrogate (βSUR) values were significantly different. A
significant difference would provide evidence that the β values from the
original data were not due to correlated noise in the walking pattern.
The number of subjects used in this investigation was based on an a
priori power analysis. Based on a sample size of twenty subjects and a
conservative effect size of 0.8, the power analysis revealed a type II error
rate equal or lesser than 0.20 (i.e. power 
80%) to detect differences in
stability (the largest eigenvalue, β) between inertia conditions. The
conservative effect size of 0.8 was based on the data from Hurmuzlu et al.
(Hurmuzlu et al., 1996), in
which values of β were reported for post-polio patients and normal
healthy subjects. An effect size of 3.75 was computed by taking the difference
in the mean β values between both groups and dividing by the standard
deviation of the healthy group. With an effect size of 3.75, the power
analysis yielded an extremely low sample size of only four subjects. Since our
subject population was healthy and because we expected smaller changes in
stability between mass conditions, we decided to utilize a conservative effect
size of 0.8. With an effect size of 0.8, the power analysis yielded an
objective sample size of twenty or more subjects. We used a general linear
model (GLM) analysis with two within-subjects fixed factors (mass and instant
of the gait cycle) to compare the values of β among the respective mass
conditions (0%, 10%, 20% and 30% of body mass). An additional GLM analysis was
used to test for any possible differences in the equilibrium points at
heel-contact and mid-swing under the respective inertia conditions. All
statistical tests were performed with an 
-level of 0.05.
|
|
RESULTS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Our surrogate analysis revealed a significant difference between the mean values computed for the original data series (β) and the surrogate data series (βSUR, refer to Table 1). The results confirm that the calculated β values were probably not the result of correlated noise in the walking data.
|
The equilibrium values computed at heel-contact and mid-swing are given in Table 2. Compared with normal walking, the equilibrium point for the hip at heel-contact significantly shifted upward (i.e. increased joint flexion) as mass increased from 0% to 10% (P=0.033), 20% (P=0.011) and 30% (P=0.029). The equilibrium point for the knee at heel-contact did not significantly change across mass conditions (P=0.472). However, the equilibrium point for the ankle joint at heel-contact significantly shifted upward at 10% additional mass (P=0.006) compared with walking without added mass, but was not significantly different at 20% (P=0.185) and 30% (P=0.323) added mass.
|
Changes in the equilibrium points were found for the hip and knee joint at mid-swing. Compared with normal walking, the equilibrium points for the hip and knee at mid-swing shifted significantly upward at 10%, 20% and 30% (all values for P<0.001, respectively). The equilibrium points for the ankle at mid-swing did not significantly change with increased mass (P>0.05).
|
DISCUSSION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
).
Changes in the body's inertial state appear to create small disturbances in
the leg kinematics while walking. Based on our results, we suggest that
controlling the acceleration of the body mass throughout the gait cycle may be
essential for maintaining walking stability.
The results presented in this investigation also indicate that the leg
kinematics were more stable at mid-swing than at heel-contact while walking
with additional mass. Most probably the differences in stability of the leg
kinematics may be related to the fact that heel-contact signifies the point in
the gait cycle where the body is undergoing larger changes in velocity as the
body's mass is transferred from the trailing leg to the leading leg
(Donelan et al., 2002).
Alternatively, it is possible that the differences in the stability of the leg
kinematics at heel-contact and mid-swing may be related to the viewpoint that
stance and swing phase dynamics are governed by different balance control
mechanisms (Frenkel-Toledo et al.,
2005; Gabell and Nayak,
1984). This notion is partly supported by experimental evidence
that has shown that humans respond differently to disturbances experienced in
the different phases of the gait cycle
(Dietz et al., 2004). However,
additional studies are necessary to better understand the differences in
stability of the leg kinematics during the stance and swing phase.
Our results indicated that adding an additional 30% of body mass influences
the equilibrium points of the Poincaré sections at heel-contact and
mid-swing. However, it should be noted that the significant changes in the
sagittal plane joint kinematics were quite small (i.e. less than 2 deg.). We
suggest that these slight changes are important given the fact that previous
research has indicated that limb posture plays a crucial role in the
stabilization of gait (Biewener and Daley,
2007). Alternatively, it is possible that the noted changes in the
joint kinematics were small since the largest eigenvalue did not approach one
in any of our experimental conditions. This may indicate that the local
disturbances due to added mass were not sufficiently large enough to require
considerable changes in the joint kinematics.
There are several limitations to our experimental methods that need to be considered. Our method of reducing the gravitational forces was accomplished by applying a vertical lifting force with a fixed pulley system and support vest that was worn around the torso. The vest may have assisted with the stability of the leg dynamics by providing additional torso control. It is also possible that small horizontal forces were introduced if the subject did not stay directly below the fixed pulley. Potentially, these horizontal forces may have influenced our measures of stability. However, we are skeptical that these horizontal forces would have influenced the outcomes of our study because they would be considerably smaller than the vertical lifting forces applied to the body during our experiments. We additionally noted that the vertical lifting forces were more variable as additional mass was added to the subject. It is difficult to determine if these variations were due to the design of the body weight support system or disturbances present in the walking patterns of our subjects. Since we found differences in the largest eigenvalue and the equilibrium points, we suspect that these changes were probably a reflection of the disturbances present in the walking pattern rather than a flaw in the design of our apparatus.
It should also be noted that the participants selected a walking speed that
was slower than that typically reported in the literature (
1.5 m
s–1). This is probably a result of our experimental protocol.
Subjects in this study manually increased and decreased the treadmill speed
while starting from a standing position as opposed to first starting at a slow
walking speed and then at a high walking speed as described by Martin et al.
(Martin et al., 1992). A
faster walking speed would increase the need to accelerate the body mass. As
such, we may have detected differences in the stability of the leg kinematics
for all the experimental conditions by having the subjects walk faster.
Although Floquet analysis has demonstrated that the elderly individuals and
individuals with Polio have a less stable walking pattern, the possible
mechanisms behind these losses of stability has not been identified
(Dingwell et al., 2008;
Hurmuzlu et al., 1996). Our
results might provide initial insights into the understanding how stability in
the leg kinematics may be lost. For example, it is possible that the less
stable walking pattern seen in the elderly may be related to an inability of
the legs to effectively accelerate and redirect the body mass throughout the
gait cycle. Furthermore, our results may be useful for estimating the
stability of the limb kinematics during lunar and Martian extra vehicular
activities where the astronaut may be carrying additional mass while in a
reduced gravity environment. In this case, the additional mass may play a role
in how stable the leg kinematics are while walking across the terrain of
various celestial bodies.
In summary, we found that added mass reduces the stability of the leg kinematics during steady-state walking. These results indicate that the inertial state of the body plays a role in the stability of the leg kinematics and may be related to how the body is redirected and accelerated during walking. Effective acceleration of the body mass throughout the gait cycle appears to be an important factor for stable limb kinematics and possibly walking balance.
|
Footnotes |
|---|
|
References |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Biewener, A. A. and Daley, M. A. (2007).
Unsteady locomotion: integrating muscle function with whole body dynamics and
neuromuscular control. J. Exp. Biol.
210,2949
-2960.
Cavagna, G. A. and Margaria, R. (1966).
Mechanics of walking. J. Appl. Physiol.
21,271
-278.
De Witt, J. K., Hagan, R. D. and Cromwell, R. L.
(2008). The effect of increasing inertia upon vertical ground
reaction forces and temporal kinematics during locomotion. J. Exp.
Biol. 211,1087
-1092.
Dietz, V., Colombo, G. and Muller, R. (2004). Single joint perturbation during gait: neuronal control of movement trajectory. Exp. Brain Res. 158,308 -316.[Medline]
Dingwell, J. B. and Marin, L. C. (2006). Kinematic variability and local dynamic stability of upper body motions when walking at different speeds. J. Biomech. 39,444 -452.[Medline]
Dingwell, J. B. and Kang, H. G. (2007). Differences between local and orbital dynamic stability during human walking. J. Biomech. Eng. 129,586 -593.[CrossRef][Medline]
Dingwell, J. B., Cusumano, J. P., Cavanagh, P. R. and Sternad, D. (2001). Local dynamic stability versus kinematic variability of continuous overground and treadmill walking. J. Biomech. Eng. 123,27 -32.[CrossRef][Medline]
Dingwell, J. B., Robb, R. T., Troy, K. L. and Grabiner, M. D. (2008). Effects of an attention demanding task on dynamic stability during treadmill walking. J. Neuroeng. Rehabil. 5,12 .[CrossRef][Medline]
Donelan, J. M., Kram, R. and Kuo, A. D. (2002).
Mechanical work for step-to-step transitions is a major determinant of the
metabolic cost of human walking. J. Exp. Biol.
205,3717
-3727.
England, S. A. and Granata, K. P. (2007). The influence of gait speed on local dynamic stability of walking. Gait Posture 25,172 -178.[CrossRef][Medline]
Faisal, A. A., Selen, L. P. and Wolpert, D. M. (2008). Noise in the nervous system. Nat. Rev. Neurosci. 9,292 -303.[CrossRef][Medline]
Frenkel-Toledo, S., Giladi, N., Peretz, C., Herman, T., Gruendlinger, L. and Hausdorff, J. M. (2005). Effect of gait speed on gait rhythmicity in Parkinson's disease: variability of stride time and swing time respond differently. J. Neuroeng. Rehabil. 2,23 .[CrossRef][Medline]
Full, R. J., Kubow, T., Schmitt, J., Holmes, P. and Koditschek,
D. (2002). Quantifying dynamic stability and manueverability
in legged locomotion. Integr. Comp. Biol.
42,149
-157.
Gabell, A. and Nayak, U. S. (1984). The effect
of age on variability in gait. J. Gerontol.
39,662
-666.
Grabowski, A., Farley, C. T. and Kram, R.
(2005). Independent metabolic costs of supporting body weight and
accelerating body mass during walking. J. Appl.
Physiol. 98,579
-583.
Granata, K. P. and Lockhart, T. E. (2008). Dynamic stability differences in fall-prone and healthy adults. J. Electromyogr. Kinesiol. 18,172 -178.[CrossRef][Medline]
Guckenheimer, J. and Holmes, P. (1983). Non-Linear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag.
Hasan, Z. (2005). The human motor control system's response to mechanical perturbation: should it, can it, and does it ensure stability? J. Mot. Behav. 37,484 -493.[Medline]
Hausdorff, J. M. (2007). Gait dynamics, fractals and falls: finding meaning in the stride-to-stride fluctuations of human walking. Hum. Mov. Sci. 26,555 -589.[CrossRef][Medline]
Hurmuzlu, Y. and Basdogan, C. (1994). On the measurement of dynamic stability of human locomotion. J. Biomech. Eng. 116,30 -36.[CrossRef][Medline]
Hurmuzlu, Y., Basdogan, C. and Stoianovici, D. (1996). Kinematics and dynamic stability of the locomotion of post-polio patients. J. Biomech. Eng. 118,405 -411.[CrossRef][Medline]
Jackson, K. M. (1979). Fitting of mathematical functions to biomechanical data. IEEE Trans. Biomed. Eng. 26,122 -124.[Medline]
Mah, C. D., Hulliger, M., Lee, R. G. and O'Callaghan, I. S. (1994). Quantitative analysis of human movement synergies: constructive pattern analysis for gait. J. Mot. Behav. 26, 83-102.[Medline]
Martin, P. E., Rothstein, D. E. and Larish, D. D.
(1992). Effects of age and physical activity status on the
speed-aerobic demand relationship of walking. J. Appl.
Physiol. 73,200
-206.
McGeer, T. (1990). Passive dynamic walking. Int. J. Robot. Res. 9,62 -82.[CrossRef]
Miller, D. J., Stergiou, N. and Kurz, M. J. (2006). An improved surrogate method for detecting the presence of chaos in gait. J. Biomech. 39,2873 -2876.[CrossRef][Medline]
Nigg, B. M., Cole, G. K. and Nachbauer, W. (1993). Effects of arch height of the foot on angular motion of the lower extremities in running. J. Biomech. 26,909 -916.[CrossRef][Medline]
Tedrake, R., Zhang, T. W., Fong, M. and Seung, H. S. (2004). Actuating a simple 3D passive dynamic walker. Proc. IEEE Int. Conf. Robot. Autom. 5,4656 -4661.
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. and Farmer, J. D. (1992). Testing for nonlinearity in time series: the method of surrogate data. Physica D 58, 77-94.[CrossRef]
CiteULike 
Complore 
Connotea 
Del.icio.us 
Digg 
Reddit 
Technorati 
Twitter What's this?
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
