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First published online February 13, 2009
Journal of Experimental Biology 212, 738-744 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.023267
The relationships between muscle, external, internal and joint mechanical work during normal walking
1 Department of Mechanical and Biomedical Engineering, Boise State University,
Boise, ID 83725, USA
2 Department of Mechanical Engineering, University of Texas at Austin, Austin,
TX 78712, USA
3 Brain Rehabilitation Research Center, Malcom Randall VA Medical Center,
Gainesville, FL 32611, USA
4 Brooks Center for Rehabilitation Studies, University of Florida, Gainesville,
FL 32611, USA
5 Department of Physical Therapy, University of Florida, Gainesville, FL 32601,
USA
* Author for correspondence (e-mail: rneptune{at}mail.utexas.edu)
Accepted 9 December 2008
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Summary |
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 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Key words: gait, musculotendon work, musculoskeletal model, simulation
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INTRODUCTION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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;
Detrembleur et al., 2003;
Devita et al., 2007;
Donelan et al., 2002;
Minetti et al., 1995;
Saibene and Minetti, 2003),
analyze energy generation, absorption and/or transfer within body segments
(Caldwell and Forrester, 1992;
Willems et al., 1995), compare
mechanical and metabolic cost (Burdett et
al., 1983; Frost et al.,
2002; Griffin et al.,
2003; Martin et al.,
1993; Massaad et al.,
2007; Ortega and Farley,
2005; Umberger and Martin,
2007), examine locomotor efficiencies
(Aissaoui et al., 1996;
Winter, 1979), determine how
muscles function (Jacobs et al.,
1996; Winter and Eng,
1983), and identify impairments associated with neurological
deficits (Mansour et al.,
1982; Olney et al.,
1991; Parvataneni et al.,
2007).
Historically, mechanical work has been quantified using a number of methods
and generally classified as external, internal or joint work. External work is
the mechanical work done on an external load [e.g. during pedaling
(van Ingen Schenau et al.,
1990)] and/or the body's center of mass [e.g. during walking
(Cavagna et al., 1963)].
Internal work is the work necessary to move the body segments relative to the
body's center of mass and is computed as the sum of the absolute changes in
body segment kinetic and potential energy
(Cavagna and Kaneko, 1977;
Winter, 1979). Although used
extensively to estimate mechanical energy expenditure, either alone or as a
sum (Burdett et al., 1983;
Detrembleur et al., 2003;
Minetti et al., 1995;
Ortega and Farley, 2005;
Saibene and Minetti, 2003),
external and internal work both have several limitations. For example, there
exists ambiguity regarding energy transfer within and among body segments
(Willems et al., 1995) and
lack of independence between external and internal work that prevents the
total mechanical work from being estimated as a simple sum of the two measures
(Aleshinsky, 1986a;
Kautz and Neptune, 2002). In
addition, these estimates provide little insight into the mechanical work
generated by individual muscles during locomotor tasks of interest
(Aleshinsky, 1986b;
Kautz and Neptune, 2002).
Joint work, computed as the time integral of net joint power calculated
using standard inverse dynamics techniques, is thought to represent
musculotendon work more accurately than external or internal work. The
advantages of joint work over the external/internal work approach have been
documented in previous studies of pedaling, walking and running
(Caldwell and Forrester, 1992;
Kautz et al., 1994). Kautz and
colleagues showed in pedaling that the change in internal work is not
concomitant with the change in joint work, and therefore there is little
correlation between these measures (Kautz
et al., 1994). However, the joint work approach is not without
limitations. The primary limitation is its inability to account for individual
muscle contributions to mechanical work, primarily due to co-contraction
causing the net moment to be less than the sum of the individual muscle flexor
and extensor moments and muscle tendon energy storage and release that allows
negative work in one phase to be recovered as positive work in a subsequent
phase. For example, human walking involves substantial muscle co-contraction
at the knee and ankle joints (Centomo et
al., 2007; Falconer and
Winter, 1985; Schmitt and
Rudolph, 2007) and elastic energy storage and release in the
calcaneus tendon (Fukunaga et al.,
2001; Hof, 1998),
both of which are difficult to account for using joint work calculations. In
addition, the various methods used to account for intercompensation of joint
power by biarticular muscles (i.e. power can appear to be absorbed at one
joint and generated at the other joint) means that joint work only provides an
estimation within upper and lower bounds
(Kautz et al., 1994). This was
highlighted in a previous analysis of pedaling that showed joint work
including biarticular muscle intercompensation greatly underestimates muscle
fiber work, while the joint work neglecting intercompensation estimates the
muscle work relatively well (Neptune and
van den Bogert, 1998). However, whether these relationships hold
in other locomotor tasks such as walking is unclear. Walking differs from
pedaling in several ways. The feet collide with the ground, which leads to
energy losses from friction and damping while, unlike pedaling, little work is
done on the environment. Instead, mechanical work is required primarily to
provide body support (i.e. to stop the body's downward motion and accelerate
it upward during each step), forward propulsion and leg swing.
Although muscle work and tendon elastic energy storage and release have
been analyzed in walking using muscle-actuated forward dynamics simulations
(Neptune et al., 2008;
Sasaki and Neptune, 2006), the
extent to which muscle work relates to external, internal and joint work has
not been investigated. Therefore, the objective of this study was to use
muscle-actuated forward dynamics simulations of walking to investigate the
relationships between muscle work and external, internal and joint work.
Specifically, we expected that (1) when muscle work was estimated using joint
work, co-contraction would lead to an underestimation of musculotendon work,
while muscle tendon elastic energy storage and release would overestimate
muscle fiber work, and (2) neither external nor internal work (nor their sum)
would accurately estimate musculotendon work.
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MATERIALS AND METHODS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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). The
muscle actuators were combined into 13 functional groups
(Fig. 1), with the muscles
within each group receiving the same excitation pattern. The excitation
patterns were defined using experimentally measured EMG (see `Experimental
data' below). For those muscles where surface EMG were not available, block
patterns were used defined by an onset, duration and magnitude. The muscle
activation dynamics were governed by a first-order differential equation
(Raasch et al., 1997) with
activation and deactivation time constants based on Winters and Stark
(Winters and Stark, 1988). For
those muscles whose time constants were not specified in Winters and Stark,
nominal time constants of 12 and 48 ms were used (seven muscles per leg).
Thirty-eight visco-elastic elements were attached to each foot to model the
foot–ground contact (Neptune et al.,
2000). Passive hip, knee and ankle torques representing ligaments
and connective tissues were applied to each joint based on Davy and Audu
(Davy and Audu, 1987). The
passive torques for the mid-foot and toe joints were defined using the
following equation:
 | (1) |
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Forward dynamics simulations
A forward dynamics walking simulation was generated using Dynamics Pipeline
(MusculoGraphics, Inc., Santa Rosa, CA, USA) and SD/FAST (PTC, Needham, MA,
USA). To generate a well-coordinated walking simulation over a full gait cycle
(i.e. right heel strike to subsequent right heel strike), dynamic optimization
(Neptune and Hull, 1998) was
used to fine-tune the muscle excitation patterns with a cost function that
minimized the difference between the simulation and experimental kinematics
(i.e. the time history of the trunk trajectory and hip, knee and ankle angles)
and ground reaction force (GRF) data (see `Experimental data' below).
Constraints were placed on the excitation magnitude and timing in the
optimization algorithm to ensure the muscles were generating force in the
appropriate region of the gait cycle.
Experimental data
Previously collected experimental kinematic, GRF and EMG data
(Neptune and Sasaki, 2005)
were used and will be briefly described here. Ten able-bodied subjects (five
male and five female; age 29.6±6.1 years, height 169.7±10.9 cm,
body mass 65.6±10.7 kg) walked on a split-belt instrumented treadmill
(TecMachine, Andrezieux Boutheon, France) at 1.2 m s–1.
Kinematic (Motion Analysis Corp, Santa Rosa, CA, USA; 120 Hz sampling rate using a modified Helen Hays marker set), GRF (480 Hz sampling rate) and surface EMG data (Noraxon, Scottsdale, AZ, USA; 1200 Hz sampling rate) from the soleus, tibialis anterior, medial gastrocnemius, vastus medialis, rectus femoris, biceps femoris long head and gluteus maximus were collected for 15 s to acquire 20 consecutive steps. The kinematic and GRF data were then digitally low-pass filtered at 6 and 20 Hz, respectively. Linear envelope EMG data were generated by applying sequentially a band-pass filter (20–400 Hz), full rectification and low-pass filter (10 Hz). All data were then normalized to the gait cycle, and averaged across steps and then across subjects to obtain group-averaged data.
Mechanical work
To identify the various sources of mechanical work during the walking
simulation, various quantities of mechanical work were computed as the time
integral over the complete gait cycle of: (1) external power, (2) internal
power, (3) joint power, (4) joint power with intercompensation, (5)
musculotendon power, (6) muscle fiber power, (7) muscle tendon power, (8)
passive joint power, (9) muscle joint power and (10) mechanical power by the
visco-elastic elements attached at the foot segment (referred to as shoe
elements, hereinafter). Positive, negative, total (absolute sum of positive
and negative) and net (direct sum of positive and negative) work values were
computed. Below, these measures are described in more detail.
External power was computed as the dot product of the GRF and velocity of
the mass center of the body vectors. Internal power was computed as the sum of
time derivatives of rotational and translational kinetic energy and potential
energy of each body segment. Joint power was computed as the product of net
joint torque and corresponding joint angular velocity. Joint power with
biarticular muscle intercompensation was obtained using the method described
by Kautz and colleagues (Kautz et al.,
1994), where power absorbed at one joint was allowed to cancel
power generated at the other joint as if only a biarticular muscle were
active. Musculotendon, muscle fiber and muscle tendon (series-elastic element)
power were computed as the product of corresponding force and velocity vectors
obtained from the Hill-type muscle model. The shoe-element power was computed
as the product of corresponding force and velocity vectors for each ground
contact element, and then summed across elements to obtain the total power.
Passive joint power was computed as the product of the passive joint torque
and corresponding joint angular velocity. Muscle joint power was computed as
the sum of the individual muscle power contributions to each joint power,
which was equivalent to joint power excluding passive joint power. The
influence of muscle co-contraction on joint work was quantified as the
difference between the musculotendon work and muscle joint work.
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RESULTS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Muscle joint work underestimated musculotendon work in all measures. For
example, the total muscle joint work was 
35% (96 J) lower than the total
musculotendon work (Table 1).
This difference represents the influence of muscle co-contraction, which is
not accounted for in joint work. Co-contraction occurred primarily during
early stance and late swing (Fig.
3; e.g. compare HAM with RF and VAS excitation). Overall, the net
joint and musculotendon work was positive
(Table 1), which was necessary
to offset the net negative shoe-element work
(Table 1; net shoe-element
work) such that the net mechanical work over the gait cycle was zero.
The total external and internal work was less than 30% and 40% of the total
musculotendon work, respectively (Table
1). The summation of the total external and internal work still
underestimated the total musculotendon work by 100 J. The net
musculotendon work was substantially higher than both the net external and
internal work, which was near zero (Table
1).
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DISCUSSION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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). When the joint work was quantified only for the stance
phase per leg (hip, knee and ankle joints) in our simulation, the positive and
negative work were 53 J and –35 J, respectively. Thus, the simulation is
representative of normal walking mechanics and sufficient to highlight the
potential limitations of the various methods used to estimate muscle
mechanical work.
The simulation data showed that total joint work with biarticular muscle
intercompensation greatly underestimates the total musculotendon and total
muscle fiber work, which was consistent with a previous analysis of pedaling
(Neptune and van den Bogert,
1998). The underestimation occurs because the intercompensation
model assumes that all the negative power at one joint can be cancelled out by
positive power at the other joint by biarticular muscle action, which does not
properly account for the contributions of uni-articular muscles to the
negative joint power. In general, biarticular muscles act to overestimate
musculotendon work from joint work (e.g.
Prilutsky et al., 1996),
because the muscle joint power is separately time integrated to compute joint
work (e.g. see Fig. 4, areas
under positive and negative RF power near toe-off). The overestimation of the
musculotendon work by the biarticular muscles was 25 J for both positive
and negative work.
|
20 J. The underestimation was due to the
combined contributions of antagonist–agonist muscle co-contraction,
biarticular muscle work and passive joint work to the total joint work. Muscle
co-contraction (i.e. the difference between muscle joint work and
musculotendon work) acted to increase the underestimation of total
musculotendon work, while biarticular muscle work and passive joint work acted
to decrease the underestimation. In our simulation, the total muscle fiber
work was less than the total musculotendon work by 18 J, with the
difference due to tendon elastic energy storage and return. As a result, total
joint work and muscle fiber work were similar in magnitude (254 J and 256 J,
respectively). This result is a coincidence rather than a mechanical
requirement, as the difference between joint work and fiber work is influenced
by many factors including co-contraction, biarticular muscle work, passive
joint work and muscle tendon elastic energy, and these factors vary across
subjects and locomotor tasks. For example, we generated an additional
simulation that walked with the same overall mechanics but had increased
co-contraction (125 J compared with 96 J, i.e. the difference between muscle
joint work and musculotendon work in Table
1) and passive joint work (143 J compared with 101 J in
Table 1) over the gait cycle.
Muscle co-contraction was increased by adding the inverse of the sum of
squared muscle powers to the cost function to be minimized while passive joint
work was increased by increasing the stiffness and damping coefficients in the
model. The total joint, muscle fiber and musculotendon work in this simulation
were 276 J, 301 J and 320 J, respectively. Thus, since there is no mechanical
requirement that the underestimate of work done due to co-contraction equals
the overestimate of work done due to biarticular muscles, passive work and
tendon elastic energy, the similar magnitude of total joint work and total
fiber work observed in this study should not be generalized. However, the sum
of the net musculotendon work and net passive joint work was equal to the net
joint work (Table 1, round-off
error of 1 J) and, therefore, net joint work can estimate net musculotendon
work in locomotor tasks or subjects where net passive joint work is negligible
(e.g. slow walking). Also, as the net elastic energy during the gait cycle is
zero, the net joint work can be used as an estimate of net muscle fiber work.
However, net joint work is not a useful quantity to estimate overall
mechanical work, metabolic cost or efficiency.
Previous studies using inverted pendulum walking models have suggested that
positive work input is primarily required to overcome the energy loss
(negative work) during the step-to-step transition (e.g.
Kuo, 2002), and that the
external work during the step-to-step transition is the primary determinant of
the metabolic cost of walking (Donelan et
al., 2002; Kuo et al.,
2005). However, our data show that muscles perform considerably
more negative work than the negative external work
(Table 1; 122 J vs
–37 J, respectively) and, therefore, the metabolic cost of walking may
not be as strongly related to the work associated with the step-to-step
transition as previously suggested. We also obtained external work using the
individual limbs method of Donelan and colleagues
(Donelan et al., 2002) by
computing the external work for individual limbs separately. Using this
method, the computed negative external work was only –45 J, which was
still substantially lower than the negative musculotendon work. This lack of
correlation is further supported by a simulation analysis showing that muscle
fiber work output is highest when the body's center of mass is raised, not
during the step-to-step transition
(Neptune et al., 2004).
The net musculotendon work (also net joint work) over the gait cycle was
positive (30 J), which is consistent with the results of DeVita and colleagues
(DeVita et al., 2007) and
Umberger and Martin (Umberger and Martin,
2007), who computed joint work using an inverse dynamics approach.
When musculotendon work was quantified only for the stance phase per leg as in
Devita et al. (Devita et al.,
2007), the net positive work was 18 J, which was comparable to the
16 J in their study. Devita and colleagues
(Devita et al., 2007) reasoned
that the positive net work was required to offset energy losses by body
tissues. In our simulation, the net positive work was offset primarily by the
net negative work dissipated in the shoe elements during foot contact, and
secondarily by the energy dissipation in the passive joint torques. Although
not included in the present model, energy could be lost in other body tissues
such as joint cartilage and by muscle damping (e.g.
Boyer and Nigg, 2007;
Nigg and Liu, 1999). If
additional energy-dissipating elements were included in our model, total
musculotendon mechanical work would most likely be higher. However, the
relationship between net musculotendon (or net muscle fiber) and net joint
work would remain unchanged (again, assuming net passive joint work is
negligible).
The positive passive joint work was 35% of the positive joint work.
Previous in vivo studies analyzing the amount of hip or knee passive
joint torque generated during normal walking have produced conflicting results
(Mansour and Audu, 1986;
Silder et al., 2007;
Vrahas et al., 1990;
Yoon and Mansour, 1982). The
positive work by the hip and knee passive torques in our simulation was
approximately 11 J and 3 J, respectively, while the ankle passive work was
negligible. The passive joint torques in our model were based on those of Davy
and Audu (Davy and Audu,
1987), which are lower in magnitude than those of Silder and
colleagues (Silder et al.,
2007). Although further investigation is needed to estimate the
contributions of the passive joint structures to joint work, the relationships
between net joint work and net musculotendon work would remain unchanged
because the net joint torque is the net sum of passive and active muscle
contributions at the joint.
The total and net external work were substantially lower than the total and
net musculotendon work, respectively. Similar to external work, the total and
net internal work were markedly lower than the total and net musculotendon
work, respectively. Further, the summation of total external and internal work
was much lower than the total musculotendon work (175 J vs 274 J,
respectively). Previous studies have shown that external and internal work are
not mutually independent and, therefore, total mechanical work cannot be
obtained as the sum of the two measures
(Aleshinsky, 1986a;
Kautz and Neptune, 2002).
Although external and internal work or power have been widely used in previous
studies to estimate mechanical work and metabolic cost
(Burdett et al., 1983;
Cavagna and Kaneko, 1977;
Detrembleur et al., 2003;
Minetti et al., 1995;
Ortega and Farley, 2005;
Saibene and Minetti, 2003;
Winter, 1979), the present
study as well as previous analyses of pedaling
(Kautz et al., 1994;
Neptune and van den Bogert,
1998) clearly show that neither total external nor total internal
work (nor the sum of the two) can be used to estimate total musculotendon
work.
While not the purpose of this study, we recognize that the muscle fiber
work obtained in this study has implications for estimating mechanical
efficiency. There are a number of methods to compute efficiency with different
equations and different quantities to represent mechanical work (joint work,
external work, muscle work). For example, previous studies have suggested that
negative work should be included in the efficiency calculation, in contrast to
the traditionally used measures of mechanical efficiency expressed as the
ratio of positive work to metabolic cost
(Prilutsky, 1997;
Woledge, 1997). Recently,
Umberger and Martin (Umberger and Martin,
2007) looked at the influence of stride rate during walking on
efficiency by including negative joint work (power) in their efficiency
calculation. Using the same equation with our joint work and their net
metabolic rate data to estimate our metabolic cost (243 J), our
efficiency was 0.40 [141 J/(243 J+113 J)], which was comparable with the
data from Umberger and Martin (Umberger
and Martin, 2007), who showed an efficiency of 0.38 when subjects
walked at 1.3 m s–1 using their preferred stride rate. This
value would be higher if negative work was not included in the denominator or
lower if gross, rather than net, metabolic rate data were used. Note that our
individual muscle-based estimate of efficiency would be 0.59 using the ratio
of positive fiber work relative to metabolic cost (143 J/243 J), demonstrating
that net joint work-based measures of mechanical work probably underestimate
positive work due to inevitable co-contraction. However, these efficiency
values are high compared with traditional values of 0.25–0.30 measured
in isolated muscles or muscle fibers (e.g.
Astrand and Rodahl, 1977),
which could be due to a number of factors including an overestimate of muscle
co-contraction in the model, unaccounted or underestimated elasticity in the
muscle fibers, tendon and other tissues, unmodeled stretch-induced force
enhancement, an overestimate of the energy lost at foot–ground contact,
an overestimate of the resting baseline metabolic cost used to determine net
metabolic cost, or the fact that the efficiency measured in isolated muscle
fibers is not the same as whole-body efficiency. For a detailed discussion of
a number of these issues, see target article by van Ingen Schenau and
colleagues (van Ingen Schenau et al.,
1997) and the various responses. While additional research is
clearly needed to validate whole-body efficiency models in human locomotor
tasks such as walking, analyses of individual muscle contributions to
mechanical work as performed in this study are an important step in the
process.
One comment that should be made is that the net external work was not zero over the gait cycle in our study as it should be for steady-state walking, but measured –1 J. This occurred because the walking simulation was not perfectly symmetrical between the right and left steps, although the kinematics and GRFs in the simulations emulated well the experimental data. However, the magnitude of the net external work was much lower than the net musculotendon work (or the net joint work) and, therefore, the overall results would remain unchanged even if the steps were perfectly steady state.
In summary, we found that during walking, (1) total joint work underestimated total musculotendon work due to muscle co-contraction despite the biarticular muscle work and passive joint work that acted to decrease the underestimation, (2) total joint work cannot be used to estimate total muscle fiber work in general because of the influence of tendon elastic energy, muscle co-contraction, biarticular muscle work and passive joint work, (3) net joint work can be used as an estimate of net muscle fiber work over a full gait cycle only if the net passive joint work is known to be negligible, (4) net muscle mechanical work is positive over the gait cycle to overcome energy dissipation during foot–ground contact and other damping effects, and (5) the total and net external and internal work were substantially lower than the total and net musculotendon work, respectively, and therefore cannot be used to estimate the musculotendon work. These results have important implications for studies attempting to estimate metabolic cost from mechanical work measures as external, internal and joint-based work measures do not accurately estimate total muscle work.
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Footnotes |
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References |
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