Ankle plantar flexor force production is an important determinant of the preferred walk-to-run transition speed
Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712, USA
* Author for correspondence (e-mail: rneptune{at}mail.utexas.edu)
Accepted 13 December 2004
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Summary |
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Key words: gait, intrinsic muscle properties, modeling and simulation
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Introduction |
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Examining various biomechanical factors, Hreljac
(1995a) proposed that critical
levels of high ankle dorsiflexion angular velocity occur during swing that
cause the dorsiflexors to operate near their maximum capacity at the PTS.
While he suggested that the transition from walking to running occurs to
prevent dorsiflexor overexertion during the swing phase, his data would also
be consistent with preventing overexertion of the plantar flexors. His data
shows that the highest ankle angular velocity actually occurs in plantar
flexion during the push-off phase, which is the region of highest ankle
plantar flexor activity and muscle power output during walking (e.g.
Neptune et al., 2001
). Because
of the increased plantar flexion angle and velocity with walking speed, the
contractile state of the plantar flexors may be greatly impaired due to
intrinsic muscle properties (i.e. the muscle forcelengthvelocity
relationships) as walking speed approaches the PTS. The ankle plantar flexor
muscles have been shown to be important contributors to support, forward
progression and swing initiation during normal walking
(Neptune et al., 2004a
;
Zajac et al., 2003
) and
various clinical studies have suggested that the plantar flexors are a
limiting factor in achieving higher walking speeds (e.g.
Mueller et al., 1995
;
Nadeau et al., 1999
;
Olney et al., 1994
).
We hypothesize that plantar flexor muscle force production is greatly
impaired at walking speeds near the PTS due to poor contractile conditions
and, therefore, necessitates a change in gait mode. Previous analyses of the
walkrun transition have suggested that for a variable to be considered
as a determinant of the transition, the variable should be near its maximum
value as walking speed approaches the PTS, and then decrease to an acceptable
level when gait is changed to a run (e.g. Hreljac,
1993b,
1995a
). However, with our
hypothesis we predict that the plantar flexor force would actually increase
after the transition to a run due to an improved contractile state (assuming
the muscle activation remains similar), which would make running at the PTS
more effective in satisfying the increasing energetic demands of faster
movement speeds.
To test this hypothesis, the anterior/posterior and vertical ground
reaction forces (GRFs) across a wide range of walking speeds, including the
PTS, were analyzed. Previous studies have shown that the peak GRFs increase
with walking speed (e.g. Hreljac,
1993b; Nilsson and
Thorstensson, 1989
) and recent modeling and simulation studies
have shown that the ankle plantar flexors are the primary contributors to the
peak anterior/posterior and vertical GRFs during the propulsion phase in late
stance (Anderson and Pandy,
2003
; Neptune et al.,
2004a
). Thus, if the plantar flexor force production decreases
near the PTS as hypothesized, then the peak GRFs during the propulsion phase
at the PTS would also be expected to decrease. The GRF data presented in
Nilsson and Thorstensson
(1989
) across a wide range of
walking speeds provides evidence that such a phenomenon may occur; however,
the data in that study were not analyzed relative to the PTS of their
subjects. In addition, forward dynamics simulations actuated by individual
musculotendon actuators were generated that emulated human subjects walking at
increasing speeds and running at the PTS to examine the contractile state and
force production of the ankle plantar flexors. The combination of the
experimental and simulation analyses would provide important insight into the
influence of the ankle plantar flexors on the walk-to-run PTS.
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Materials and methods |
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The EMG data were collected using disposable surface bipolar electrodes
(Noraxon, Scottsdale, AZ; 1 cm diameter, 2 cm inter-electrode distance) from
the right soleus (SOL), medial gastrocnemius (GAS), tibialis anterior (TA),
gluteus maximus (GMAX), vasti medialis (VAS), biceps femoris longhead (BF) and
rectus femoris (RF), which were used to assist in the generation of
simulations of walking and running (see Forward dynamics simulations
below). Electrode placements were based on the guidelines provided by Perotto
(1994) and all signals were
checked for clarity and strength of signal during isolated isometric
movements. The data were band-pass filtered (20400 Hz), fully rectified
and then low-pass filtered at 10 Hz using a fourth order zero-lag digital
Butterworth filter. The EMG linear envelope was then normalized to its maximum
value during walking at 120% of each subject's PTS. The body segment motion
data were measured using a modified Helen Hayes marker set and corresponding
joint angles were determined. The GRF and motion data were filtered with a 4th
order zero-lag Butterworth filter with cut-off frequencies of 20 and 6 Hz,
respectively and joint angular velocities were calculated using a
finite-difference approximation. The stance phase was divided into the braking
and propulsion phase as determined from the anterior/posterior GRF (braking
phase when the anterior/posterior force is negative,
030% gait
cycle; propulsion phase when the anterior/posterior force is positive,
3060% gait cycle). The peak anterior/posterior and vertical GRFs
during each phase were determined at each speed. Data were averaged across 10
consecutive walking cycles within each subject at each speed, and then across
subjects to obtain a group average.
A repeated-measures analysis of variance was used to assess whether the peak anterior/posterior and vertical GRFs within the braking and propulsion phases were significantly affected by walking speed (P<0.05). In addition, the peak SOL, GAS and TA EMG magnitudes over the gait cycle were also examined. When significant effects were detected within a quantity, pairwise comparisons with a Bonferroni adjustment to account for the multiple comparisons were performed to identify which speeds were significantly different.
Forward dynamics simulations
Forward dynamics simulations of walking at 60, 80, 100 and 120% PTS and
running at 100% PTS were generated using a previously described
musculoskeletal modeling and dynamic optimization framework (e.g.
Neptune et al., 2004b) to
analyze the contractile state and force production of the major lower
extremity muscle groups. The sagittal-plane biped musculoskeletal model was
developed using SIMM (MusculoGraphics Inc., Evanston, IL, USA) and the
equations of motion of the model were generated using SD/FAST (PTC, Needham,
MA, USA). The equations of motion were then incorporated into simulation code
generated by the Dynamics Pipeline (MusculoGraphics Inc., Evanston, IL, USA).
Details of the musculoskeletal model and dynamic optimization that were used
to produce the forward dynamics simulations emulating the experimentally
collected kinesiological data of walking and running are provided below.
Musculoskeletal model
The musculoskeletal model included a trunk (head, arms and torso combined
as one segment) and right and left legs (each leg containing a femur, tibia,
patella and foot) (Fig. 1). The
model yielded nine degrees-of-freedom including hip, knee and ankle
flexion/extension for both legs, and trunk horizontal and vertical translation
and anterior/posterior tilting. The knee flexion angle was used to prescribe
two translational degrees-of-freedom of the knee joint
(Yamaguchi and Zajac, 1989)
and the position and orientation of the patella relative to the femur
(Delp et al., 1990
). Thirty
visco-elastic elements were attached to the bottom of each foot segment to
model the contact between the foot and ground. Details of the model and
parameter values are provided in Neptune et al.
(2000
). The same
footground contact model parameters were used for both the walking and
running simulations.
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Fifteen Hill-type musculotendon actuators including tendon compliance
(Fig. 2) per leg were used to
actuate the model, which were combined into nine muscle groups based on
anatomical classification with muscles within each group receiving the same
excitation pattern. The nine muscle groups were defined as IL (iliacus,
psoas), GMAX (gluteus maximus, adductor magnus), VAS (three-component vastus),
HAM (medial hamstrings, biceps femoris long head), SOL (soleus), BFsh (biceps
femoris short head), GAS (medial and lateral gastrocnemius), RF (rectus
femoris) and TA (tibialis anterior). The muscle force generating capacity was
governed by normalized forcelength and forcevelocity
relationships (Fig. 3), and a
normalized non-linear tendon forcestrain relationship to describe
tendon force (Delp and Loan,
1995; Zajac,
1989
). All musculotendon parameters were based on the work of Delp
et al. (1990
). The muscle
activationdeactivation dynamics was represented with a first-order
differential equation (Raasch et al.,
1997
) with activation and deactivation time constants of 5 and 10
ms, respectively. Passive joint torques representing ligaments and other
connective tissues were used to limit the joint range of motion at extreme
joint angles (Davy and Audu,
1987
).
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Dynamic optimization
The experimentally collected EMG linear envelopes were used to define the
muscle excitation patterns in the simulations and dynamic optimization was
used to modify the excitation patterns to produce well coordinated walking and
running motions. For those muscles from which EMG were not measured (IL,
BFsh), a block excitation pattern was used with excitation timing similar to
Perry (1992). A simulated
annealing optimization algorithm (Goffe et
al., 1994
) was used to fine-tune the excitation patterns by
adjusting three parameters per muscle corresponding to the excitation pattern
onset, duration and magnitude until the difference between the experimental
and simulated kinematic and ground reaction force data was minimized (e.g.
Neptune et al., 2001
).
Constraints were placed on the excitation timing in the optimization to
closely replicate the EMG timing (i.e. EMG nominal values ± 10% gait
cycle) to assure that the muscles were active at the appropriate region in the
gait cycle. The muscle excitation patterns were assumed symmetrical between
the left and right legs. The specific tracking quantities used in the
objective function included trunk translation and tilting, all joint angles
and the anterior/posterior and vertical GRFs. The tracking data collected from
the subjects' right side were shifted 50% of the gait cycle to provide data
for the left side. A simulation of 1.5 gait cycles was generated, with the
objective function being evaluated during the final full gait cycle to assure
the initial start-up transients had decayed.
Muscle contractile state
From the walking and running simulations, individual muscle fiber lengths
and velocities over the gait cycle were determined from the model and
normalized to the optimal fiber length and maximum contraction velocity of the
muscle, respectively. The optimal fiber lengths were based on the work of Delp
et al. (1990) and each muscle's
maximum shortening velocity was estimated as ten times the muscle fiber
optimal length per second (Zajac,
1989
). In addition, individual musculotendon forces and activation
levels were quantified.
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Results |
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By contrast, during the propulsion phase the GRFs decreased at and beyond the PTS. The trend for the peak vertical GRF was to increase with walking speed up to 80% PTS, and then to decrease at 120% PTS (P<0.05) (Fig. 5, Table 1). Similarly, the peak anterior/posterior GRF systematically increased with walking speed up to the PTS, with all values being significantly higher than the previous value (P<0.05). By contrast, between 100% and 120% PTS no significant difference in magnitude was observed (Fig. 5, Table 1) (P<0.05). This finding was consistent among subjects as the peak anterior/posterior and vertical GRFs during the propulsion phase were lower at 120% PTS compared with 100% PTS in 8 out of 10 subjects.
Simulation analysis
The dynamic optimization produced walking and running simulations that
emulated the human subject tracking data to within ± 2 S.D.
(e.g. Fig. 6). The simulation
data showed that muscle activation and force both systematically increased
with walking speed in all muscles except for the plantar flexors. Although
both GAS and SOL activation increased with walking speed
(Fig. 7A), as did the other
muscles, the force produced by GAS decreased with walking speed and SOL force
began to decrease after walking speed exceeded 80% PTS
(Fig. 7A). Examination of the
contractile state of the plantar flexors near peak muscle activation and force
production as walking speed increased revealed that the SOL and GAS normalized
fiber lengths systematically shortened and approached 0.6 and 0.7,
respectively (Fig. 7B), and
both normalized shortening fiber velocities systematically increased and
approached 0.25 (Fig.
7B), which were adverse contractile conditions for producing
muscle force (Fig. 3).
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By contrast, all other muscle groups produced greater force as walking speed increased (e.g. TA; Fig. 7A), which was due to an improved contractile state compared with the plantar flexors. For example, the TA normalized fiber length and velocity at peak activation in swing at the fastest walking speed was 0.8 and 0.1, respectively (Fig. 7B). The simulation data of the same subjects running at the PTS revealed that the contractile state of the plantar flexors was greatly improved after the transition from walking to running, which produced greater muscle force for similar levels of activation. SOL produced 90% more peak force and GAS 86% more peak force during their active region even though their activation levels in the simulations only increased by 10% and 27%, respectively (Fig. 8; SOL and GAS).
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Discussion |
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The experimental and simulation data supported these expectations. The peak
propulsion-phase vertical GRF began to decrease at the PTS and the peak
anterior/posterior force decreased slightly above the PTS
(Fig. 5,
Table 1). By contrast, the
anterior/posterior and vertical GRFs during the braking phase increased over
the whole range of speeds studied. These results are consistent with Nilsson
and Thorstensson (1989) who
performed a comprehensive GRF analysis across a wide range of walking speeds
during overground walking. They found that the peak vertical and
anterior/posterior GRFs during the braking phase increased with walking speed
from 1.0 to 3.0 m s1, but the peak vertical and
anterior/posterior GRFs during the propulsion phase began to decrease near 2.0
to 2.5 m s1, respectively, and continued to decrease up to
3.0 m s1. However, they did not examine the data relative to
the PTS of the subjects in their study. The decrease in their GRFs began at
slightly higher speeds than the present study. For example, the decrease in
the peak vertical GRF occurred at a walking speed of 2.5 m
s1, compared with 2.0 m s1 for the
subjects in the present study. The difference between studies could be related
to subject training (Beaupied et al.,
2003
) or walking on a treadmill versus overground. We chose to
analyze treadmill data because of the methodological advantage of being able
to precisely control walking speed and collect a large number of consecutive
step cycles to establish a steady-state walking pattern.
Li and Hamill (2002) also
observed a decrease in the peak vertical GRF during the propulsion phase in
the step preceding the walk-to-run transition during accelerated treadmill
walking. Although they did not measure the anterior/posterior GRF due to
treadmill limitations, they speculated that the decrease in the vertical GRF
was a reconfiguration of the resultant GRF, and that the magnitude of the
resultant force remains constant. However, our results showed that the peak
anterior/posterior GRF also decreased. Li and Hamill
(2002
) also suggested that the
decrease in the peak propulsive vertical GRF is an active or intentional
behavior in anticipation of the gait transition, which would not occur if
walking speed is increased and a transition is not intended. However, the
results of the present study and those of Nilsson and Thorstensson
(1989
), which show a decrease
in the steady-state GRFs when a transition is not intended, suggest that the
decrease is not an active or intentional behavior, but may be the result of
intrinsic muscle properties influencing muscle force production.
The decrease in the vertical GRFs during the propulsion phase near the PTS
and the decrease in the anterior/posterior GRF immediately after the PTS,
despite an increase in ankle plantar flexor activity
(Fig. 4), suggest that the
ability of these muscles to produce force diminishes as walking speed
approaches the PTS. Both the forcelength and forcevelocity
relationships are intrinsic muscle properties that directly influence a
muscle's ability to generate force, with active force diminishing with
increasing speeds of contraction and as the fiber length deviates from its
optimal (Fig. 3). Thus, if the
plantar flexors are operating at increasingly adverse contractile lengths and
velocities at walking speeds just prior to the PTS, the transition from a walk
to a run at the PTS may place them at a better operating point on the
forcelengthvelocity relationship since the ankle joint
velocities at the PTS are lower in running than walking (e.g.
Hreljac, 1995a). The
transition would thus allow the plantar flexors to generate greater force for
a given activation level to help satisfy the increasing energetic demands of
faster movement speeds.
The simulation analysis supported this hypothesis. The simulation data showed that both activation and force production systematically increased with walking speed in all muscles except for the plantar flexors. The force produced by GAS decreased with walking speed and SOL force began to decrease after walking speed exceeded 80% PTS, despite an increase in GAS and SOL activation with walking speed (Fig. 7A). The contractile state of the plantar flexors near peak muscle activation and force revealed that the SOL and GAS normalized fiber lengths approached 0.6 and 0.7, respectively (Fig. 7B), and both normalized fiber velocities approached 0.25 (Fig. 7B). These velocity values would appear to be conservative estimates as the combined ankle and knee joint angular velocities during the propulsion phase near the PTS were lower in the simulation than the experimental data (Table 2). Thus the capacity of the plantar flexors to produce muscle force as walking speed approached the PTS was greatly impaired (Fig. 3).
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By contrast, all other muscle groups produced higher force as walking speed
increased. For example, TA has an optimal fiber length over two and three
times the length of GAS and SOL, respectively
(Delp et al., 1990), which
provides a more favorable force-generating contractile state compared with the
plantar flexors as walking speed increased
(Fig. 7A). The TA normalized
fiber length and velocity at peak activation in swing was 0.8 and 0.1,
respectively (Fig. 7B). Hreljac
(1995a
) proposed that the
dorsiflexor muscles perform at or near their maximum capacity at the PTS and
may be susceptible to overexertion, and therefore serve as a determinant for
the walk-to-run transition. However, our simulation results indicate that not
only is the forcelengthvelocity state of TA much more favorable
than the plantar flexors for producing force, but TA is activated far below
its maximum. At 120% PTS, peak TA activation was only 60% of maximum
(Fig. 7A), as opposed to the
near 100% activation of the plantar flexors
(Fig. 7A). The differences in
levels of muscle activation are consistent with each muscle's contribution to
the mechanical energetics of walking; TA is primarily responsible for
providing toe clearance during early swing, while the plantar flexors are the
primary contributors to body support, forward progression and swing initiation
in late stance (Neptune et al.,
2001
; Zajac et al.,
2003
). These results suggest that the plantar flexors, rather than
the dorsiflexors, may be over-exerted at the PTS.
The overexertion of the plantar flexors near the PTS may also influence the
walking mechanics. An important task requirement in walking is maintaining the
necessary propulsive impulse over the gait cycle to conserve linear momentum
and maintain a constant average walking speed. With our hypothesis that
plantar flexor force production is impaired at higher walking speeds, we would
predict that the impulse associated with the ankle plantar flexors would also
decrease as walking speed approached the PTS. The planter flexor impulse is
particularly important since the plantar flexors are the primary contributors
to the observed anterior/posterior GRF during the propulsion phase
(Anderson and Pandy, 2003;
Neptune et al., 2004a
). To
test this prediction, we computed the total impulse generated by the plantar
flexors during the propulsive phase in a post hoc analysis of the
simulation data and found that the plantar flexor impulse remained relatively
constant between walking speeds of 60 and 80% PTS, and then began to decrease
dramatically as walking speed approached the PTS
(Fig. 9). These results were
consistent with Nilsson and Thorstensson
(1989
) who found that the
total horizontal GRF propulsive impulse increased until 2.5 m
s1, and then began to decrease at higher speeds. Thus,
considering the important contributions of the plantar flexors to satisfying
the task demands of walking (Neptune et
al., 2001
; Zajac et al.,
2003
), a decrease in the mechanical output of these important
functional muscles as walking speed increases may necessitate a change in gait
mode, and thus serve as a critical determinant for the walk-to-run
transition.
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With our plantar flexor hypothesis, we also predicted that the transition
from walking to running would improve the contractile conditions of the
plantar flexors, allowing them to produce greater muscle force for a given
activation level and make running at the PTS more effective in satisfying the
increasing energetic demands of faster movement speeds. The running simulation
data at the PTS showed that the contractile state of the plantar flexors was
indeed improved after the transition from walking to running. SOL produced 90%
more peak force and GAS 86% more peak force during their active region even
though their activation levels in the simulations only increased by 10% and
27%, respectively (Fig. 8; SOL
and GAS). The increased muscle forces were attributed to improvements in the
contractile state on both the forcelength and forcevelocity
relationships. Thus, the transition from walking to running at the PTS
provides a large increase in plantar flexor force production for a small
increase in activation. By contrast, the TA force levels were similar in both
walking and running (Fig. 8;
TA). Further research is needed to assess whether the increase in force
production during running allows the plantar flexors to perform the same
functional tasks as in walking or if differences in the running mechanics
causes a reorganization of how individual muscles work together in synergy to
satisfy the task requirements. Further, running provides the advantage of
increased elastic energy storage and return in the plantar flexor tendons
(e.g. Hof et al., 2002;
Kram, 2000
), but it is unclear
to what degree other muscle groups exploit similar energy efficient
mechanisms.
The results of this study suggest that normalized intrinsic muscle
properties (i.e. forcelengthvelocity relationships) play an
important role in the determination of the specific neuromotor strategies used
by the nervous system in human locomotion. Previous studies have shown little
success in identifying correlations between various anthropometric
measurements (e.g. body dimensions, inertial characteristics and strength) and
the PTS (Getchell and Whitall,
1997; Hanna et al.,
2000
; Hreljac,
1995b
; Thorstensson and
Roberthson, 1987
). Unlike individual anthropometric measurements,
normalized intrinsic muscle properties are relatively homogeneous across
humans (e.g. Zajac, 1989
), and
therefore would provide a consistent transition mechanism regardless of
variations in anthropometrics, age and gender (e.g.
Hanna et al., 2000
;
Hreljac, 1993b
;
Tseh et al., 2002
). The state
of the plantar flexor's functional capacity in relation to the
forcelength and forcevelocity relationships could be conveyed by
integration of the proprioceptive feedback, which has been previously proposed
as an important feedback mechanism influencing the walk-to-run transition
(Hreljac, 1995a
;
Raynor et al., 2002
;
Thorstensson and Roberthson,
1987
). Hreljac
(1995a
) has suggested that
proprioceptive feedback is used to indicate local discomfort and fatigue in
the ankle dorsiflexors, and Raynor et al.
(2002
) suggested that feedback
is necessary to determine the potential use of stored elastic energy in
tendons. In addition, the state of the plantar flexors on the
forcelengthvelocity relationships would be conveyed through the
integration of sensory information from the muscle spindles (length and
velocity of muscle stretch) and Golgi tendon organs (muscle tension) to
indicate a change in gait mode is necessary. Using such sensory feedback as a
determinant for the walkrun transition is consistent with the idea that
the transition between gait modes is most likely initiated by some
step-by-step criterion (Saibene and
Minetti, 2003
).
A potential confounding factor is that the Hill-type muscle model used in
our simulations did not account for all of the relationships between force,
length, velocity and activation (for review see
Huijing, 1998) and the
time-dependence of muscle force production (for review see
Herzog, 1998
). However, both
the experimental and simulation data support the hypothesis that ankle plantar
flexor force output plateaus or diminishes as walking speed approaches the PTS
due to intrinsic muscle properties, primarily the forcelength and
forcevelocity relationships. As walking speed increases, the plantar
flexion angle and velocity increases in a monotonic fashion (e.g.
Lelas et al., 2003
;
Winter, 1991
), which causes
the plantar flexors to operate at shorter lengths and higher velocities during
the propulsion phase (Fig. 7) when critical levels of plantar flexor force production are required to
satisfy the task demands. Thus, given the need for the plantar flexors to
produce a given level of force to produce the observed kinematics, we believe
muscle activation would change to accommodate the unmodeled complex intrinsic
muscle properties (e.g. force deficit or depression following active
shortening, Herzog, 1998
;
Huijing, 1998
) just as
activation changes to accommodate less force production due to shorter fiber
lengths and faster fiber shortening velocities (Figs
4 and
8). The overall trend of the
plantar flexor contractile state towards becoming increasingly adverse for
producing muscle force as walking speed approaches the PTS would, therefore,
remain.
Although this study does not exclude the many proposed kinetic, kinematic
and energetic determinants for the walk-to-run transition (e.g.
Hanna et al., 2000;
Raynor et al., 2002
), the
analysis of the GRFs and contractile state of the lower extremity muscles do
support the proposed hypothesis that the ankle plantar flexors are operating
under adverse contractile conditions near the PTS. Thus, a change in gait mode
would be necessary to effectively move at higher speeds. These results
highlight the important role intrinsic muscle properties play in determining
the specific neuromotor strategies used in human locomotion. Future work will
be directed at assessing if similar mechanisms hold for the run-to-walk
transition.
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Acknowledgments |
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