Lower limb sagittal kinematic and kinetic modeling of very slow walking for gait trajectory scaling
Lower limb sagittal kinematic and kinetic modeling of very slow walking for gait trajectory scaling
Andrew J. J. SmithID 0 1 2
Edward D. LemaireID 0 1 2
Julie Nantel 0 2
0 Funding: Ontario Centres of Excellence Voucher for Innovation and Productivity II
1 Ottawa Hospital Research Institute , Ottawa , Canada , 2 University of Ottawa, Department of Human Kinetics, University of Ottawa , Ottawa , Canada , 3 Faculty of Medicine, University of Ottawa , Ottawa , Canada
2 Editor: Steven Allen Gard, Northwestern University , UNITED STATES
Lower extremity powered exoskeletons (LEPE) are an emerging technology that assists people with lower-limb paralysis. LEPE for people with complete spinal cord injury walk at very slow speeds, below 0.5m/s. For the able-bodied population, very slow walking uses different neuromuscular, locomotor, postural, and dynamic balance control. Speed dependent kinetic and kinematic regression equations in the literature could be used for very slow walking LEPE trajectory scaling; however, kinematic and kinetic information at walking speeds below 0.5 m/s is lacking. Scaling LEPE trajectories using current reference equations may be inaccurate because these equations were produced from faster than real-world LEPE walking speeds. An improved understanding of how able-bodied people biomechanically adapt to very slow walking will provide LEPE developers with more accurate models to predict and scale LEPE gait trajectories. Full body motion capture data were collected from 30 healthy adults while walking on an instrumented self-paced treadmill, within a CARENExtended virtual reality environment. Kinematic and kinetic data were collected for 0.2 m/s Ð0.8 m/s, and self-selected walking speed. Thirty-three common sagittal kinematic and kinetic gait parameters were identified from motion capture data and inverse dynamics. Gait parameter relationships to walking speed, cadence, and stride length were determined with linear and quadratic (second and third order) regression. For parameters with a non-linear relationship with speed, cadence, or stride-length, linear regressions were used to determine if a consistent inflection occurred for faster and slower walking speeds. Group mean equations were applied to each participant's data to determine the best performing equations for calculating important peak sagittal kinematic and kinetic gait parameters. Quadratic models based on walking speed had the strongest correlations with sagittal kinematic and kinetic gait parameters, with kinetic parameters having the better results. The lack of a consistent inflection point indicated that the kinematic and kinetic gait strategies did not change at very slow gait speeds. This research showed stronger associations with speed and gait parameters then previous studies, and provided more accurate regression equations for gait parameters at very slow walking speeds that can be used for LEPE joint trajectory development.
Data Availability Statement: All relevant data are
within the paper and its Supporting Information
Competing interests: The authors have declared
that no competing interests exist
Motor adaptation to different gait speeds are relevant to lower extremity powered exoskeletons
(LEPE) since predefined gait control strategies are typically used for persons with complete
]. Consistent with patients receiving neurological rehabilitation [
], persons using
a LEPE walk at speeds between 0.1m/s and 0.55 m/s [3±13], with an average speed of 0.26 m/s
]. However, LEPE predefined joint trajectories are typically developed from able-bodied
individuals walking within a normal range of walking speeds. Since walking slowly is
considered to be more complex [
] and uses different locomotor and postural control strategies
], LEPE may be improved with predefined joint trajectories based on
speed-appropriate slow gait biomechanics.
Despite a wealth of biomechanics literature on a range of gait speeds [2,18±27], the slowest
walking speed in studies that predicted kinematic and kinetic parameters was 0.5 m/s, and
averaged greater than 0.9 m/s. From some of these works, kinematic peak sagittal parameters
were found to be positively correlated with gait speed, but that correlation coefficients from
simple linear (R2<0.60) and quadratic (R2<0.45) regressions were weak [
]. As well,
kinematics were significantly less accurate when calculated from regression equations produced
from gait speeds outside those being modeled . Contrary to kinematics, gait kinetics have
shown strong relationships with gait speed [
], with correlation coefficients greater than
0.90 for knee flexion  and extension [
] moments. However, if regression equations are
inaccurate at walking speeds outside the range they were produced from, even highly
correlated kinetic equations may be inaccurate at very slow walking speeds.
The reasons for kinematics having lower correlations than kinetics may be gait speed
variability and experimental methods [
]. An inherent problem with interpreting
biomechanical results is that gait variable differences can often be partially or entirely explained by speed
. One method for controlling speed mediated effects on gait is the use of an instrumented
treadmill to reduce outcome measure variability when researching task specific biomechanics
]. However, treadmills that dictate constant walking speeds by reducing variability
compared to over ground walking  may not reflect the joint's natural mechanical environment
]. However, this methodology would be sufficient for modeling kinematic and kinetic
speed dependent changes in gait for LEPE development because a LEPE also imposes a
consistent and less variable walking pattern. Recently, we assessed extremely slow walking speeds of
abled bodied adults to determine if changes in strategy were required at LEPE walking speeds
]. A consistent inflection point at 0.5 m/s was found for step time, stance time, and double
support time, suggesting a change in strategy at very slow speeds that favours increased ground
contact time. The effect of these slow walking speeds on common sagittal plane kinematic and
kinetic parameters has yet to be determined.
The primary goal of this research was to produce a set of reference equations derived from
very slow gait speeds to improve modelling accuracy of peak sagittal gait parameters for gait
trajectory scaling and LEPE development. This research included very slow walking speeds
that are common for exoskeleton users. Since gait speed is the product of cadence and stride
length, we examined these three stride parameters for their relationship with sagittal kinematic
and kinetic gait parameters. The research outcomes determined which stride parameter had
the best relationships between very slow walking and peak sagittal kinetics and kinematics.
Based on previous literature, we hypothesized that kinetics would have stronger associations
with temporal spatial parameters. From our previous research on stride parameters [
hypothesised that a change in gait strategy would occur at 0.5m/s, indicated by an inflection
point for parameters with non-linear relationships with speed, cadence, or stride-length. An
improved understanding of gait kinematics and kinetics at speeds achievable by exoskeleton
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device users, by identifying how able-bodied people biomechanically adapt to very slow gait
speeds, will provide LEPE developers with better models for predicting and scaling exoskeleton
Materials and methods
Thirty able-bodied (AB) volunteers were recruited from staff, students, and volunteers at The
Ottawa Hospital Rehabilitation Centre and University of Ottawa (15 males, 15 females;
mass = 75.8±13.2 kg, height = 1.73±0.12 m; age = 30±10 years). To be enrolled in the study
participants did not have health issues that would affect walking on a treadmill. Prior to
testing, volunteers were notified of potential risks of participating in this research and signed an
informed consent form. This study, including consent forms, was approved by both the
Ottawa Health Science Network and the University of Ottawa Research Ethics Boards.
The CAREN-Extended virtual environment (Motekforce Link, Amsterdam, NL) was used for
the movement activities and data collection. This system included 3D motion capture (Vicon,
Oxford, UK), six degree of freedom (6-DOF) moving platform with an embedded dual-track
treadmill (Bertec Corp., Columbus, OH) with force plates under each track sampled at 1000
Hz, 180Ê screen for 3D virtual world projection. Full body kinematics were tracked at 100 Hz,
using a 6-DOF, 57-markerset [
Participant's height, weight, and leg dominance were collected. Height and weight were used
to scale the biomechanical model to each participant for three dimensional motion analysis.
Leg dominance was determined by the participants answer to ªwhat leg would you use to kick
a ball as far as possibleº. Participants were given time to acclimate to the seven slow walking
speeds (0.2±0.8 m/s, incremented by 0.1) and to self-pace treadmill walking [
walked 40 meters at each walking speed (total 320 m), through a virtual park scene that
provided realistic optic flow. At least 10 successful left and right strides of level walking where the
participant cleanly contacted the two force plates with their right and left feet were collected
for each speed. Walking speeds were randomised to avoid learning bias.
Three-dimensional marker data were filtered with a 4th order, low pass Butterworth filter
(10Hz). A 10-segment model was defined using Visual3D (C-Motion) [
] scaled to the
participant's height and weight. Ground reaction force data were filtered with a zero lag
Butterworth filter with a cut off frequency of 20 Hz. Matlab software (2016a, Mathworks, Matwick,
MA) was used to identify 33 common peak sagittal kinematic and kinetic parameters
(Table 1). Repeated measures analysis of variance (ANOVA) was performed to determine if
leg dominance had an effect on very slow sagittal gait kinematics and kinetics, with a p <0.05
considered to be statistically significant.
Group means and standard deviations for each parameter were calculated at each speed.
Linear and quadratic (second and third order) regressions were calculated to determine group
mean equations for each of 33 sagittal gait parameters and 3 stride parameters (speed, cadence,
stride-length). Pearson correlations were applied to determine the strength of association
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between each stride parameter and mean peak sagittal gait parameters. Correlation coefficients
(R2) greater than 0.90 were considered strong, 70±89 moderate, 40±69 weak, and <39 poor.
For parameters with R2<0.9, linear regressions between each sagittal gait parameter and
speed, cadence, or stride-length were used to determine if a consistent inflection point occurred
for faster and slower walking speeds. For each parameter, linear regressions were performed for
the following six gait speed sets (m/s): SP, 0.8, 0.7; SP, 0.8, 0.7, 0.6; SP, 0.8, 0.7, 0.6, 0.5; SP, 0.8,
0.7, 0.6, 0.5, 0.4; SP, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3; SP, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2. If the correlation
coefficients from a parameter's speed sets dropped and remained below 0.90 for subsequent
sets, a non-linear change was identified. An inflection point was identified if a non-linear
change occurred consistently at the same speed for greater than 50% of participants.
The group mean equations were applied to each participant's data to assess how well
the equations represented the participant's peak sagittal kinematics and kinetics. The best
performing equations (i.e., individual correlation coefficients) fit the largest number of
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participants with a correlation coefficient greater than 0.90 and had the highest average
correlation coefficient. If correlation coefficients were equally as high for the same number of study
participants, the simpler equation was chosen.
To determine the difference between regression equations calculated outside the speed
range of exoskeleton gait and our regression equations that were within the range, the
predicted range between sagittal kinematics and kinetic parameters at 0.2m/s and 0.8m/s were
computed using the best performing equations from Table 2 and 24 corresponding regression
equations published by Lelas et al. [
]. The difference in the predicted range and difference as
a percentage of the maximal range were compared between the two studies.
At each speed interval, an average of 24 ± 8 steps were analyzed. Thirty-three common sagittal
parameters were evaluated at the ankle, knee, and hip from the last 10 successful steps
(Table 1). Peaks included 14 kinematic measures (joint angles, ranges) and 19 kinetic measures
(joint moments, powers). No significant differences were observed between dominant and
non-dominant limbs, therefore only the dominant limb was used for analysis.
From Pearson correlations of group mean data, gait speed had stronger correlations than
stride-length and cadence for 18 of 33 parameters (KAx2, KAx4, HAx2, HAx3, KMx1, KMx2,
KMx3, HMx1, HMx2, HMx3, APx1, APx3, KPx1, KPx3, KPx4, HPx1, HPx2, HPx3).
Stridelength had the strongest association with five parameters (AAx3, AAxRG, AMx1, AMx2,
KMx4), and cadence only two parameters (KAxRG, APx2). Hip flexion during early stance
(HAx1) and hip range of motion (HAxRG) were associated equally with gait speed and
stridelength. For all 33 parameters, correlation coefficients were highest using second order
quadratic equations. No consistent point of inflection was identified for any sagittal gait
From Pearson correlations of group mean regression equations fit to individual participant
data, the same 12 sagittal gait parameters (AMx2, HMx1, APx1, KPx1, KPx2, KPx4, HPx2,
HAxRG, HMx2, HMx3, APx3, HPx3) had strong associations with cadence, gait speed, and
stride-length. Gait speed had the strongest associations, thus only results for speed were
reported in Table 2. Equations for cadence and stride-length can be found in supporting
information (S1 and S2 Tables). Of the 12 strongly correlated parameters for gait speed, all but one
(HAxRG) were a kinetic parameter and most were best fit using a second order quadratic
(AMx2, HMx1, APx1, KPx1, KPx2, KPx4, HPx2). Linear equations strongly predicted
HAxRG, HMx2, HMx3, and APx3 while third order quadratic formulas strongly fit the kinetic
Parameters with moderate correlation coefficients (0.7<R2<0.9) that fit at least 50% of
participants with individual correlation coefficients > 0.90 were: KAxRG, HAx1, and HAx2
(kinematic parameters) and AMx1, KMx2, APx2, KPx3, and HPx1 (kinetic parameters). Moderate
correlation coefficients that fit less than 50% of participants were AAx3, AAxRG, KAx2, KAx4,
HAx3 (kinematic parameters) and KMx1 and KMx4 (kinetic parameters). Weak and poor
correlation coefficients were found for kinematic parameters AAx1, AAx2, AAx4, KAx1, KAx3
and kinetic parameter KMx3.
Of 24 corresponding sagittal gait parameter regression equations reported by Lelas et al.
(Table 3), 14 corresponded with the best performing equation types reported in Table 2.
Excluding hip extension moment and hip power generation during loading response, gait
parameters from Lelas et al. equations were all overestimated. Predicted range of peak knee
joint angles during stance and peak ankle plantarflexion angle differed by more than 5Ê, and
by as much as 10.57Ê. Range of peak knee flexion moment during loading response and
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swing, as well as peak ankle dorsiflexion moment predicted by Lelas et al., were more the 62%
greater than values predicted using our equations. Joint power was overestimated by at least
58.8% for hip power generation during pre-swing, knee absorption during loading response,
and ankle peak absorption.
The primary goal of this study was to provide LEPE developers with equations for modelling
speed related changes in sagittal peak joint kinematics and kinetics. These peaks could then be
used to more appropriately scale predefined LEPE joint trajectories. Appropriately scaled
trajectories may enhance LEPE function, making it easier for users to complete steps successfully
], enhancing mobility, balance, cadence, and walking speed of people with complete lower
PLOS ONE | https://doi.org/10.1371/journal.pone.0203934
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(Reg) Regression type: (L) linear, (Q2) second order Quadratic, (Q3) third order quadratic.
limb paralysis. This study compiled a comprehensive reference data set of 33 peak sagittal
kinematic and kinetic parameters at very slow gait speeds that have previously received little
attention in the literature.
The strongest regression equations were between peak kinetics and gait speed. When fit to
participant data, these equations produced correlation coefficients much higher than
previously reported. For example, hip extension moment was reported to have a second order
quadratic relationship with gait speed, with correlation coefficients ranging between 0.72 and 0.89
]. We found that peak hip extension moments in early stance and late swing were
best fit using second order quadratic and linear regressions, with both higher regression
correlation coefficients (0.94 and 0.93) and individually fitted coefficients (87% and 90%). The
strength of correlations in this study may be due to our use of an instrumented treadmill
which may reduce outcome measure variability [
The main limitation to this study was how to control walking speeds. A treadmill was used
rather than vague instructions (e.g., ªwalk fastº, ªwalk slowº) that can result in an unbalanced
dataset where participant may not walk at a given speed for an equal number of stride [
Treadmill studies offer the ability to collect numerous consecutive strides with greater
reproducibility and reduce stride-length variability [
]. The number of consecutive strides and
reduced gait variability associated with fixed-speed treadmill use may explain why our
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regression values were greater than those previously reported; however, treadmill use may
have influenced gait parameters [
] by shortening stride length and cadence, increasing knee
extension and forward trunk lean through stance, and increasing hip and knee flexion through
]. If data from this studies is used for clinical decision making on overground
walking, the potential for less variability in the treadmill data should be considered. However,
since LEPE impose consistent and less variable walking patterns, treadmill gait is appropriate
for developing joint trajectories for powered exoskeleton devices. LEPE stride parameter
variability can occur due to early foot strikes and varying step initiation timing, which are
independent of preset joint trajectories. Therefore, research on short step correction control is also
needed for safe and efficient device use.
Like our results and previous studies [
], sagittal kinematic and kinetic parameters
correlated with speed, but kinematic parameters had poorer correlations. However, regression
types were not always consistent with our results. Of 24 regression equations for peak sagittal
kinematics, reported by Lelas et al. (Table 3), only 14 were consistent with regression equations
types in our research. As well, the range of calculated peak kinematics and kinetics between 0.2
m/s and 0.8 m/s differed between our results and Lelas et al. [
]. Lelas et al. produced
regression equation at 0.5m/s, which was nearly twice the average LEPE user walking speed.
Kinematic and kinetic regression equations from similar studies can be inaccurate at speeds
achievable by a LEPE user [
Though kinematic parameters had lower correlations, speed associations in this study were
much stronger than correlation results in the literature. Lelas et al. [
] reported a poor linear
relationship (R2 = 0.14) for gait speed and peak hip extension (HAx2) during stance. Our
results produced an average correlation coefficient of 0.85. As well, knee flexion during loading
response (KAx2) and swing (KAx4) had weak relationships with speed (R2 = 0.60 and 0.43,
respectively) in the Lelas et al. study. Our results supported this quadratic relationship with
speed but with moderate correlation coefficients of 0.72 for KAx2 and 0.84 for KAx4.
Kinematic parameters had low correlation coefficients, likely due to the many degrees of freedom
available to the lower limb when adapting to various very slow gait speeds [
gait trajectory choices will differ across people and walking scenarios.
Lower kinematic correlations (i.e., below 0.9) are supported by studies investigating how
able bodied persons adapt to LEPE assisted gait [41±45]. With LEPE assistance, total ankle and
hip moment (muscle plus exoskeleton) were almost identical to passive walking, with both
walking scenarios producing large differences in joint angles and EMG patterns between LEPE
assisted and control steps. Joint kinematic patterns may be less important to nervous system
planning, with the lower limb adapting by prioritising kinetic optimisation [
], unlike the
upper limb prioritises kinematic control during reaching [47±50]. Altering musculoskeletal
mechanics by applying assistive forces results in variable kinematics and invariant moments of
the lower limb, advancing our understanding of how the lower limb optimises motor
adaptation. Kinetic parameters could also be used to predict exoskeleton mechanical output during
different tasks, aiding robotic exoskeleton design.
The goal of this research was to provide better equations for LEPE developers to determine
appropriate peak sagittal kinematics and kinetics for joint trajectory development. Quadratic
models based on walking speed had the strongest correlations with most peak sagittal
kinematic and kinetic gait parameters, with kinetic parameters having the better results. This
research showed that peak sagittal kinematic and kinetic gait parameters, between 0.2 and 0.8
m/s, had a strong non-linear association with speed. The lack of a consistent inflection point
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indicated that the gait kinematic and kinetic strategy did not change at very slow gait speeds.
Inconsistent inflection points may demonstrate how individuals adapt to slow speeds
differently. While these equations should be tested on a separate dataset, within the same gait speed
range, equations produced in this research showed stronger associations with speed then
previous studies. The regression equations defined in this research should provide better results
when modeling LEPE joint trajectories at very slow walking speeds.
S1 Table. Maximum sagittal plane kinematics and kinetics parameter regression equations
for cadence. Cadence (c).
S2 Table. Maximum sagittal plane kinematics and kinetics parameter regression equations
for stride length. Stride length (l).
S1 Supporting Data. This excel document includes means and standard deviations for 33
peak sagittal gait parameters from the 30 able-bodied participants in this study. Each tab is
labled with a gait parameter header defined within the Data Key tab. Data has been provided
for both the dominant (Dom) and non-dominant limbs (NonD). Columns are mean peak data
from level ground (LG) walking at 7 set waking speeds collected for 0.2 m/sÐ0.8 m/s, and a
self-selected walking speed condition. Headers ending in "sd" contain the standard deviations
for the for 33 peak sagittal gait parameters.
Andrew Herbert-Copley and Brandon Fournier are thanked for their help with data collection.
Emily Sinitski is thanked for her help with data processing.
Conceptualization: Edward D. Lemaire, Julie Nantel.
Data curation: Andrew J. J. Smith, Edward D. Lemaire.
Formal analysis: Andrew J. J. Smith, Edward D. Lemaire.
Funding acquisition: Andrew J. J. Smith, Edward D. Lemaire.
Investigation: Andrew J. J. Smith, Edward D. Lemaire, Julie Nantel.
Methodology: Andrew J. J. Smith, Edward D. Lemaire.
Project administration: Andrew J. J. Smith, Edward D. Lemaire, Julie Nantel.
Resources: Edward D. Lemaire.
Software: Andrew J. J. Smith.
Supervision: Edward D. Lemaire, Julie Nantel.
Visualization: Andrew J. J. Smith.
Writing ± original draft: Andrew J. J. Smith.
Writing ± review & editing: Andrew J. J. Smith, Edward D. Lemaire, Julie Nantel.
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