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First published online November 19, 2007
Journal of Experimental Biology 210, 4159-4168 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.002204
Passive mechanical properties of human gastrocnemius muscle–tendon units, muscle fascicles and tendons in vivo
1 School of Physiotherapy, Faculty of Health Sciences, University of Sydney,
2141, Australia
2 School of Molecular and Biomedical Science, University of Adelaide, 5005,
Australia
3 Prince of Wales Medical Research Institute University of New South Wales,
Cnr Barker Street and Easy Street, Randwick, NSW 2031, Australia
* Author for correspondence (e-mail: s.gandevia{at}unsw.edu.au)
Accepted 21 August 2007
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Summary |
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Key words: gastrocnemius, muscle, strain, tendon
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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; Swanstrom et al.,
2005; Whitehead et al.,
2001).
The passive length–tension properties of whole muscle–tendon
units are often explained in terms of a simple mechanical model in which
muscle fibres (or, perhaps more accurately, muscle fascicles) are arranged in
series with tendons. According to this model, as muscle–tendon units are
lengthened, muscle fascicles and tendons contribute to the total change in
muscle–tendon length in proportion with their compliances
(Zajac, 1989).
It has often been assumed that relaxed muscle fascicles are much more
compliant than tendons and that therefore, when muscle–tendon units are
lengthened, most of the increase in length occurs in the muscle fascicles
(e.g. De Deyne, 2001;
Tardieu et al., 1982). But
this view may be incorrect for several reasons. First, in many muscles, the
tendons are very long compared to the muscle fascicles, so at any given strain
the tendons typically experience much greater changes in length than do muscle
fascicles. Second, while it has often been claimed that tendons undergo only
small strains, and fail at strains of about 10%
(Zajac, 1989), the true
strains experienced by whole tendons in vivo may actually be quite
large. Estimates of failure strains are usually based on measurements made on
extramuscular tendon, but it is possible that intramuscular tendon experiences
greater strains than does extramuscular tendon
(Lieber et al., 2000;
Zuurbier et al., 1994). Also,
studies of failure properties of tendons often measure gauge lengths with the
tendon under significant tension (Ker,
1981), causing the strain numerator to be underestimated and the
strain denominator to be overestimated
(Herbert and Crosbie, 1997). A
further complication, articulated recently by Epstein and Herzog
(Epstein et al., 2006), is that
muscle fascicles and tendons are not arranged simply in series but instead are
arranged partly in series and partly in parallel. This may explain why the
tendons of contracting muscles appear to be shorter and possibly stiffer than
the tendons of relaxed muscles (Ettema and
Huijing, 1989; Lieber et al.,
2000).
Elegant methods have been used to quantify contributions of changes in
tendon length to changes in length of contracting muscle–tendon
units (Biewener et al., 1998;
Elek et al., 1990;
Griffiths, 1991;
Morgan, 1977;
Rack and Westbury, 1984;
Roberts et al., 1997) but
relatively few studies have examined contributions of changes in tendon length
to changes in length of relaxed muscle–tendon units. Herbert
and Crosbie measured displacement of markers placed on the ends of the muscle
fascicles of rabbit soleus muscle–tendon units and showed that when the
relaxed muscle–tendon unit was stretched through a physiological range
of lengths about half of the total change in length occurred in the tendon
(Herbert and Crosbie,
1997).
In humans, ultrasonography can be used to obtain non-invasive measures of
muscle fascicle length (De Monte et al.,
2006; Fukashiro et al.,
1995; Fukunaga et al.,
1997; Herbert et al.,
2002; Lichtwark et al.,
2007; Loram et al.,
2004; Maganaris et al.,
1998; Magnusson et al.,
2001; Muraoka et al.,
2002; Narici et al.,
1996), and several groups have measured muscle fascicle lengths of
relaxed human lower limb muscles at a range of joint angles
(De Monte et al., 2006;
Herbert et al., 2002;
Kawakami et al., 1998;
Maganaris et al., 1998;
Muraoka et al., 2005;
Muraoka et al., 2002;
Narici et al., 1996). The
change in length of muscle fascicles that occurs as the relaxed gastrocnemius
or tibialis anterior muscle is lengthened through its physiological range is
much less than the total change in muscle–tendon unit length. This
suggests that the tendon contributes substantially to the total length changes
in these muscle–tendon units (De
Monte et al., 2006; Herbert et
al., 2002).
Ultrasonography can provide descriptions of length changes in human muscle
fascicles, but unless ultrasonographic measures of muscle fascicle lengths are
combined with measures of muscle tension they cannot be used to determine
length–tension properties. Some authors have estimated tension in a
single human muscle by dividing joint torque by the moment arm of the muscle
(Muraoka et al., 2002), but,
because many structures usually contribute to passive joint torque, this
approach is likely to overestimate tension in the muscle. Without a measure of
tension it is not possible to measure slack length, so it is difficult to
estimate strains. Slack length is usually assumed to be the length measured
with the joint in its mid-position
(Magnusson et al., 2003) or
when the net joint torque is zero (De Monte
et al., 2006; Muraoka et al.,
2002), but there is no compelling reason to believe that either
joint position should correspond to the true slack length.
In the present study, we combine ultrasonographic measures of fascicle
lengths and measures of the length–tension properties of the human
gastrocnemius muscle–tendon unit obtained with a recently developed
method (Hoang et al., 2005).
By combining these methods it is possible to obtain non-invasive measures of
the length–tension properties and strains of relaxed human muscle
fascicles and tendons without having to assume that the passive torque is
entirely attributable to the gastrocnemius and without making arbitrary
assumptions about which joint angles correspond to slack length.
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Materials and methods |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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Testing equipment
Subjects lay prone on a device designed to enable both the knee and ankle
to move freely within their available ranges without moving the lower leg
(Fig. 1B). The axes of the
device were aligned with the presumed axes of the subject's ankle and knee,
using laser pointers built into the device's axes
(Fig. 1A). Potentiometers
recorded knee and ankle angles. The foot was strapped to a footplate that
`floated' on a footplate balance mechanism to accommodate changes in location
of the ankle axis of rotation as well as the subjects' different foot shapes
(an enhancement of the device initially described for this application
(Hoang et al., 2005). A
calibrated force transducer measured passive ankle torque (XTran, Melbourne,
Australia: linear to 250 N). The analogue outputs from the force transducer
and potentiometers were sampled at 50 Hz.
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). Once
the images were considered optimal, the transducer was manually stabilized
while the ankle was rotated. To maintain optimal images, markers were placed
on the skin to maintain a constant orientation of the ultrasound head with
respect to the muscle fascicles. The images were displayed in real time and
digitally sampled at 25 Hz. Surface electromyography was used to monitor muscle relaxation during ankle movement. Bipolar surface electrodes (Ag–AgCl, 10 mm diameter) were placed over the muscle bellies of the lateral gastrocnemius, soleus and tibialis anterior with an inter-electrode distance of 3 cm. The signals were amplified (x1000), bandpass filtered (100–1000 Hz; Grass, IP 511, West Warwick, RI, USA) and sampled at 2000 Hz.
Measurement
Passive ankle torque-angle relations were measured at eight knee angles
(0°, 10°, 20°, 50°, 60°, 70°, 90° and 100° in
random order; 0° represents full knee extension). With the subject's right
foot firmly strapped to the footplate, the footplate was manually cycled from
plantarflexion to dorsiflexion and back at 
0.05 Hz (average angular speed
of 6 deg. s–1) (Fig.
1B). Subjects were asked to remain as relaxed as possible
throughout measurements. Occasionally, brief bursts of electromyographic
activity were observed [see fig.
3 of Hoang et al. (Hoang et
al., 2005)], but these were small: typically of the order of
1–3% of the amplitude observed during a maximal voluntary contraction.
Such low-level contractions have little effect on passive length–tension
curves (data not shown). Nonetheless, all passive ankle torque-angle data
associated with observable electrical activity were excluded from the
analyses.
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Data analysis and statistics
Here, we use the term `tendon' to mean both intramuscular tendon
(aponeuroses) and extramuscular tendon (free tendon) and the term
`gastrocnemius' to mean both medial and lateral parts of the muscle. The
gastrocnemius is treated as a functional unit, although there are some
anatomical differences between the two components
(Huijing, 1985).
Passive length–tension relation of the muscle–tendon unit
The analysis used to derive the passive length–tension relation of
the gastrocnemius muscle–tendon unit has been presented in detail
(Hoang et al., 2005). Key
features of the analytical approach are repeated here.
The method is based on the assumption that the passive torque measured at
the ankle depends on torques due to (1) single-joint structures such as
single-joint muscles and ligaments that cross the plantar (posterior) and
dorsal (anterior) aspects of the ankle joint but not the knee joint and (2)
the two-joint muscle, gastrocnemius, which crosses the plantar aspect of the
ankle and the posterior aspect of the knee (see
Fig. 2A for a schematic diagram
of these structures). The key proposition is that, therefore, differences in
the passive ankle torques measured at different knee angles are due to changes
in the length of the gastrocnemius (Fig.
2B). Contributions to the passive ankle torque from other
two-joint structures such as the plantaris muscle, nerves and blood vessels
were assumed to be negligible. For discussion of the assumptions, see Hoang et
al. (Hoang et al., 2005).
|
 | (1) |
ankle{
a,k} is the
passive torque at the ankle, which is a function of both ankle and knee joint
angles;
apekp(a–p)–ap
is the torque due to single-joint structures on the plantar aspect of the
ankle;
adekd(D–a)–ad
is the torque due to single-joint structures on the dorsal aspect of the
ankle;
mg[agekg(lg–lG)–ag]
is torque due to the gastrocnemius; a and
k are ankle angle and knee angle, respectively;
ap, kp, ad,
kd, ag and kg are
parameters that determine the stiffness of structures that cross the plantar
aspect (ap, kp) and dorsal aspect
(ad, kd) of the ankle, and the
gastrocnemius (ag, kg);
P and D are ankle angles at which ankle
plantar flexors and dorsiflexors, respectively, are slack;
mg is the moment arm of the gastrocnemius at the ankle;
lg is the length of the gastrocnemius muscle–tendon
unit; and lG is the slack length of the gastrocnemius
muscle–tendon unit.
In Eqn 1, two variables
– ankle torque (ankle) and ankle angle
(a) – were known from measurement. Two further
variables – the moment arm (mg) and length
(lg) of the gastrocnemius – were derived using
published anthropometric data. The length of the gastrocnemius varied as a
function of knee and ankle angles (Grieve
et al., 1978), and the moment arm at the ankle was calculated by
differentiation of the gastrocnemius length with respect to ankle angle. The
remaining parameters in Eqn 1
(ag, kg, lG,
ap, kp, P,
ad, kd and D) are
unknown and were estimated during the analysis process. Of these parameters,
the three of interest were ag, kg and
lG, as they determine the gastrocnemius
length–tension properties.
Before analysis, raw data of passive ankle torque-ankle angle relations
were transformed as follows. First, torques due to the weight of the footplate
and estimated weight of the foot (both functions of ankle angle) were
subtracted from the measured ankle torques. The weight of the foot was
estimated using anthropometric data
(Winter, 1990). Second, we
used data from the dorsiflexion half of each cycle. We focused on the
dorsiflexion portion of the curve as this direction mimics clinical
examination of the ankle to assess the plantarflexor muscles, and dorsiflexion
is the direction that lengthens the gastrocnemius. This also avoids the
complexity associated with the hysteretic behaviour of the muscle–tendon
unit.
Derivation of passive length–tension properties of the gastrocnemius
muscle–tendon unit involved two steps. First, the parameters in
Eqn 1 were estimated using the
quasi-Newton algorithm with Statistica [StatSoft, Inc., Tulsa, OK, USA,
version 6; for details see Hoang et al.
(Hoang et al., 2005)]. The
quasi-Newton class of algorithms involves iterative estimation of parameters.
The parameter search is guided by approximations to the first and second
derivatives of an error function. The approach is generally robust but shares
with other non-linear optimization techniques the risk that it may fail to
converge or may converge on local rather than global minima. Second, estimated
values of the three gastrocnemius parameters ag,
kg and lG were used to construct
passive length–tension curves of the gastrocnemius using the formula:
 | (2) |
)].
Sensitivity analysis
As passive length–tension curves rely on the precision of the
estimated parameters ag, kg and
lG, we assessed the sensitivity of the curves from one
randomly selected subject to errors in model parameters by analyzing changes
in length–tension curve associated with a 5% error in each of the model
parameters. For each sensitivity analysis, we fixed one parameter at its new
value (its initial value ±5%) and then used the quasi-Newton algorithm
to estimate the values of the remaining eight parameters. The new values of
parameters ag, kg and
lG were used to re-plot the length–tension curves.
In addition, we tested the sensitivity of the length–tension curve of
the same subject to biases in passive ankle torques or weight torques of the
foot or ankle. To do this, we re-ran the analysis after systematically adding
biases (±2% or 5%) to recorded ankle torques and after adding 5% to the
weight torque of the footplate and 25% to the weight torque of the foot. In
all of the above analyses, differences between the re-plotted curves and the
initial curve were calculated as root-mean-square errors (RMSEs) and expressed
as a percentage of the maximal tension of the initial length–tension
curve. The new values of lG obtained from all of the above
sensitivity analyses were also used to estimate the sensitivity of measures of
strains of the whole muscle–tendon unit, the muscle fascicles and the
tendon.
Calculation of slack lengths and changes in the length of muscle fascicles and tendon
Muscle fascicles lengthen and shorten during ankle rotation. Changes in the
length of muscle fascicles were tracked automatically using the following
procedure. Three video files of the images of muscle fascicles of the medial
gastrocnemius (each with the knee at a different angle: 20°, 60° or
90°) were analysed. In the first frame of each file, three sets of three
points were identified: one set lay along the superficial aponeurosis, one set
lay along the deep aponeurosis and one set lay along an identifiable muscle
fascicle (Fig. 3). The DgeeMe
program (freeware available at
www.geeware.com)
was used to track the coordinates of the three sets of points on the video
files during ankle rotation. The tracking was then checked manually frame by
frame.
Subsequently, three lines were fitted to the three sets of points. The
regression equations were used to identify the coordinates of the
intersections of the muscle fascicle line and the two aponeurosis lines, and
therefore also both the (straight line) length of the muscle fascicles and
fascicle pennation (
, the acute angle between the muscle fascicles and
the deep aponeurosis) (Fig.
3).
The relationship between the length of muscle fascicles and the length of
the muscle–tendon units was modeled as a third-order polynomial:
 | (3) |
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The slack length of the tendon (lT) was calculated by
subtracting the longitudinal displacement of the muscle fascicles
[lFcos(s), where s is
fascicle pennation at slack length] from the slack length of the
muscle–tendon unit (lG). The maximal tendon length
was calculated by subtracting the maximal longitudinal displacement of the
muscle fascicles [lf,maxcos(max), where
the `max' subscript indicates the longest in vivo length] from the
maximal muscle–tendon length. The contribution of tendon lengthening to
the maximal change in muscle–tendon length above slack length was
calculated by dividing the maximal change in tendon length by the maximal
change in muscle–tendon length. Maximal strains of the
muscle–tendon unit, muscle fascicles and tendon were calculated by
dividing maximal changes in lengths by slack lengths. Passive
length–tension curves of the fascicles and tendon were derived by
plotting lf and
Lg–lfcos() against
tension. All data are presented as means ± s.d.
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In Table 2, we present complete results for only six of the nine subjects because the slack lengths of the gastrocnemius muscle–tendon unit in the remaining three subjects were shorter than the minimum length of muscle–tendon unit that we were able to attain in vivo. In these three subjects, we could not use Eqn 3 to derive the slack length of muscle fascicles.
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The shortest in vivo length of the gastrocnemius muscle–tendon unit in the six subjects was 40.1±1.8 cm (mean ± s.d.). The slack lengths of the muscle–tendon units, muscle fascicles and tendons were 42.3±1.5 cm, 3.3±0.5 cm and 39.5±1.6 cm, respectively. The slack length of the muscle–tendon unit exceeded the shortest in vivo length by 2.3±1.2 cm, or about one-quarter of the total length range (maximum in vivo length minus minimum in vivo length) of the muscle–tendon unit.
The mean maximal change in length of the whole gastrocnemius muscle–tendon unit, from slack length to the longest length measured in vivo, was 6.7±1.9 cm. The mean maximal change in the longitudinal displacement of the muscle fascicles (with correction for changes in pennation angle) was 3.1±0.9 cm, and the mean maximal change in the length of the tendon from slack length was 3.6±1.6 cm. This indicates that tendon contributes slightly more than muscle fascicles (means of 52.4% for tendon and 47.6% for muscle fascicles) to the maximal change in length of the whole muscle–tendon unit under passive conditions. Changes in fascicle pennation (32.2±7.7° at slack length, 17.2±4.8° at the maximal length) were accounted for in these calculations, but they make little difference to estimates of the contribution of muscle fascicles and tendons to total changes in muscle–tendon unit length.
Fig. 5 shows a typical example of passive length–tension curves of the gastrocnemius muscle–tendon unit, muscle fascicles and tendon from one subject, and length–tension curves of the muscle fascicles and tendons of the six subjects. Most of the change in length of the whole muscle–tendon units, muscle fascicles and tendons occurs at low tensions.
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The potential errors in our analysis have been quantified. Fig. 6 shows that forcing errors into any one of the estimated parameters produces small to moderate changes in the length–tension curves (RMSEs of 1.2–8.9% of initial maximal tension). Adding biases to either ankle torque data or weight torques of the footplate and the foot produces only small changes in length–tension curves. For the subject randomly chosen for the sensitivity analysis, adding 5% errors to the parameters and biases to the ankle torque and weight torques produced only small changes in the maximum strains of the muscle–tendon unit, the fascicles and the tendon. The means of all changes (absolute deviations from the control values) were 2%, 9% and 3% for muscle–tendon unit, muscle fascicles and tendon, respectively. This is well within one standard deviation of the means from six subjects (Table 2). These data are presented fully in Table 3. Table 4 also gives a summary of the nine parameters fit from each subject.
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Discussion |
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). This
made it possible to quantify in vivo length–tension properties
and strains of fascicles and tendons of the relaxed human gastrocnemius.
We found that the gastrocnemius fell slack close to the shortest length at
which we could obtain measurements. However, the shortest length of the
gastrocnemius measured in this experiment was not necessarily the true
shortest physiological length in vivo because it was not possible to
obtain ultrasound images with the knee in a fully flexed position. The range
of knee angles used in this study was between 0° and 100°. Given that
the physiological range of movement of the knee joint is
0–135°, it was estimated that the `true' shortest physiological
length of the gastrocnemius is 1 cm shorter than the shortest length of
the gastrocnemius measured in this study. This means that although the slack
length of the gastrocnemius muscle–tendon unit in three subjects was
shorter (by a mean of 0.4 cm) than the shortest measured length of the
muscle, the slack lengths in these subjects were probably just within the
`true' physiological range of lengths. On average, the muscle–tendon
unit was slack for about one-quarter of its total excursion.
Our estimate of mean slack length appears to be shorter than the estimate
provided by Muraoka and colleagues
(Muraoka et al., 2005). They
fixed the ankle in a dorsiflexed position (10° more dorsiflexed than the
position in which the sole of the foot is at right angles to the leg) and then
measured the length of the gastrocnemius muscle fascicles with ultrasound
while passively extending the knee from a flexed position. The slack length of
the gastrocnemius muscle fascicles was defined as the length at which the
ankle torque first increased above baseline values, and they found this
occurred when the knee was 43° short of full knee extension. Some simple
calculations show that this implies that the gastrocnemius is slack over more
than half of its physiological range. Our data suggest that the gastrocnemius
is slack over about one-quarter of its range. The differences may reflect
differences in the subjects, or they may reflect the different methodological
approaches.
The muscle–tendon unit underwent strains of about 16% when passively
stretched to its longest physiological length. Tendons experienced much
smaller strains (9%) than muscle fascicles (86%). However, because the tendon
of the gastrocnemius is more than 11 times as long as the muscle fascicles,
the tendons contributed a slightly greater part of the total change in
muscle–tendon length. This is broadly consistent with the findings of
our earlier studies on animal (Herbert and
Crosbie, 1997) and human muscles
(Herbert et al., 2002;
De Monte et al., 2006). The
results from the present study extend the earlier observations by providing
measures of the length–tension properties of the muscle fascicles and
tendons.
The tendon strain reported in this study includes strain of both
intramuscular (aponeurosis) and extramuscular (free tendon) parts of the
tendon. The design of the study did not allow us to differentiate the passive
properties of the two parts. The question as to whether the stiffness of the
aponeurosis is similar to the stiffness of the free tendon is controversial.
Some studies on animal muscles show that the stiffness of aponeurosis and the
free tendon is similar (Rack and Westbury,
1984; Scott and Loeb,
1995; Trestik and Lieber,
1993) while other studies on animal muscles find differences
(Ettema and Huijing, 1989;
Lieber et al., 2000;
Lieber et al., 1991).
Ultrasonographic studies of human muscles also give discordant results. Some
authors report that the strain of the aponeurosis and free tendon of the human
gastrocnemius are similar (Arampatzis et
al., 2005; Muramatsu et al.,
2001) whereas others have concluded that the strain of the
aponeurosis is different from that of the free tendon
(Maganaris and Paul, 2000;
Magnusson et al., 2003). All
of these observations have been made on contracting muscles and, because it is
possible that the aponeurosis changes its intrinsic properties when the muscle
contracts (Ettema and Huijing,
1989; Lieber et al.,
2000), they may not apply to passive muscle.
Our methods rely on estimates of moment arms obtained from cadavers. In an
earlier paper, we argued that these estimates are likely to be accurate on
average, but we showed that when individuals' moment arms departed
substantially from average values, length–tension curves could be
substantially in error (Hoang et al.,
2005). The estimation of nine non-linear parameters also presents
a potential difficulty. However, we consistently obtain estimates that are
plausible, as demonstrated, for example, by values of muscle–tendon
slack length that are close to the shortest in vivo length. To assess
the sensitivity of parameter estimates to errors in estimation of other
parameters, we conducted an analysis in which we first obtained parameter
estimates in the usual way and then we fixed the value of a single parameter
at 5% above or below its estimated value before re-estimating the remaining
eight parameters. The analysis showed that, while errors of 5% produced small
to moderate changes in length–tension curves, there was no evidence of
an excessive sensitivity of length–tension curves to errors in the
estimates of individual parameters (the largest change was 9% of the initial
maximal passive tension). In addition, to assess the sensitivity of parameter
estimates to biases in the measured ankle torques, we systematically increased
or decreased the final torques used for data analysis by 2% and 5%, and then
re-estimated the nine parameters (see Materials and methods). This analysis
showed that errors of 2% or 5% in the measurement of ankle torques resulted in
approximately proportional changes in the length–tension curve but there
was not an excessive sensitivity to the errors in ankle torque. It also showed
that, for the subject randomly chosen for the sensitivity analysis, adding 5%
errors to the parameters and biases to the ankle torque and weight torques
produced only small changes in the maximum strains of the muscle–tendon
unit, the fascicles and the tendon (Table
3).
Huijing and colleagues have conducted a series of studies on rat muscles
in situ in which they demonstrated length-dependent differences
between forces measured at the distal and proximal insertions of the muscle
(Yucesoy et al., 2003). This
suggests there is some transmission of force to adjacent structures,
presumably by extramuscular connective tissue
(Maas et al., 2005). The
presence of inter-muscular myofascial force transmission would violate the
assumption, made in our analysis, that passive tension in the gastrocnemius
depends only on the knee and ankle angles. However, one observation strongly
suggests that force transmission via extramuscular connective tissue
has negligible effects on passive properties of the human gastrocnemius
muscles in vivo: in all subjects we observed the same relationship
between ultrasonographically measured changes in muscle fascicle length and
the length of the muscle–tendon unit at different knee angles
(Fig. 4). That is, regardless
of whether the lengthening occurred by changing ankle or knee position, we
observed the same relationship between muscle fascicle length and the length
of the muscle–tendon unit. In addition, a recent study
(Lichtwark et al., 2007) shows
that the medial gastrocnemius muscle fascicles act in a similar way along the
length of the muscle belly (distal, midbelly and proximal) during both walking
and running and that muscle fascicle lengths are similar along the length of
the muscle belly throughout the gait cycle (a difference of 4 mm between
distal and proximal fascicles). Our observations and those of Lichtwark and
colleagues (Lichtwark et al.,
2007) suggest there are not functionally important extramuscular
myofascial connections between the human gastrocnemius and adjacent
tissues.
Care needs to be taken with the interpretation of the length–tension
curves in Fig. 5. Tension is
not distributed uniformly in the extramuscular and intramuscular parts of the
tendon, nor is it distributed uniformly in muscle fascicles and intramuscular
tendon (Epstein et al., 2006).
Thus, the length–tension curves do not show the relationship between the
length of each element (muscle fascicles or tendons) and the tension in that
element. Instead, they show the relationship between the length of each
element and the tension at the origin and insertion of the muscle–tendon
unit. Consequently, comparison between our length–tension curves and
those derived from isolated muscle or tendon tissue is not straightforward.
Nonetheless, the data do have a pragmatic interpretation: they indicate how
much each element lengthens, and how much each element contributes to the
total change in muscle–tendon length, when tension is applied to the
muscle–tendon unit.
In conclusion, we have shown that it is possible to quantify length–tension properties of the muscle fascicles and tendons of a relaxed human muscle in vivo. The human gastrocnemius muscle–tendon unit falls slack over about one-quarter of its in vivo length. The muscle fascicle strains are much greater than the tendon strains but, because the tendons are much longer than the muscle fascicles, the tendons contribute more than half of the total passive compliance of the muscle–tendon unit.
List of symbols
a, k using equations of
(Grieve et al.,
1978)]
a)
, s, max
ankle
a, k
P, D
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Acknowledgments |
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References |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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Arampatzis, A., Stafilidis, S., DeMonte, G., Karamanidis, K., Morey-Klapsing, G. and Bruggemann, G. P. (2005). Strain and elongation of the human gastrocnemius tendon and aponeurosis during maximal plantarflexion effort. J. Biomech. 38,833 -841.[CrossRef][Medline]
Biewener, A. A., Konieczynski, D. D. and Baudinette, R. V. (1998). In vivo muscle force-length behavior during steady-speed hopping in tammar wallabies. J. Exp. Biol. 201,1681 -1694.[Abstract]
De Deyne, P. G. (2001). Application of passive
stretch and its implications for muscle fibers. Phys.
Ther. 81,819
-827.
De Monte, G., Arampatzis, A., Stogiannari, C. and Karamanidis, K. (2006). In vivo motion transmission in the inactive gastrocnemius medialis muscle–tendon unit during ankle and knee joint rotation. J. Electromyogr. Kinesiol. 16,413 -422.[CrossRef][Medline]
Elek, J., Prochazka, A., Hulliger, M. and Vincent, S.
(1990). In-series compliance of gastrocnemius muscle in cat step
cycle: do spindles signal origin-to-insertion length? J.
Physiol. 429,237
-258.
Epstein, M., Wong, M. and Herzog, W. (2006). Should tendon and aponeurosis be considered in series? J. Biomech. 39,2020 -2025.[CrossRef][Medline]
Ettema, G. J. and Huijing, P. A. (1989). Properties of the tendinous structures and series elastic component of EDL muscle–tendon complex of the rat. J. Biomech. 22,1209 -1215.[CrossRef][Medline]
Fukashiro, S., Itoh, M., Ichinose, Y., Kawakami, Y. and Fukunaga, T. (1995). Ultrasonography gives directly but noninvasively elastic characteristic of human tendon in vivo. Eur. J. Appl. Physiol. Occup. Physiol. 71,555 -557.[CrossRef][Medline]
Fukunaga, T., Kawakami, Y., Kuno, S., Funato, K. and Fukashiro, S. (1997). Muscle architecture and function in humans. J. Biomech. 30,457 -463.[CrossRef][Medline]
Grieve, D., Pheasant, S. and Cavanagh, P. R. (1978). Prediction of gastrocnemius length from knee and ankle posture. In Biomechanics VI: Proceedings of the Sixth International Congress of Biomechanics, Copenhagen, Denmark (ed. E. Asmussen and K. Jorgensen), pp. 405-412. Baltimore: University Park Press.
Griffiths, R. I. (1991). Shortening of muscle
fibres during stretch of the active cat medial gastrocnemius muscle: the role
of tendon compliance. J. Physiol.
436,219
-236.
Herbert, R. D. and Crosbie, J. (1997). Rest length and compliance of non-immobilised and immobilised rabbit soleus muscle and tendon. Eur. J. Appl. Physiol. Occup. Physiol. 76,472 -479.[CrossRef][Medline]
Herbert, R. D., Moseley, A. M., Butler, J. E. and Gandevia, S.
C. (2002). Change in length of relaxed muscle fascicles and
tendons with knee and ankle movement in humans. J.
Physiol. 539,637
-645.
Hill, A. V. (1952). The thermodynamics of elasticity in resting striated muscle. Proc. R. Soc. Lond. B Biol. Sci. 140,464 -497.
Hoang, P. D., Gorman, R. B., Todd, G., Gandevia, S. C. and Herbert, R. D. (2005). A new method for measuring passive length–tension properties of human gastrocnemius muscle in vivo.J. Biomech. 38,1333 -1341.[CrossRef][Medline]
Huijing, P. A. (1985). Architecture of the human gastrocnemius muscle and some functional consequences. Acta Anat. Basel 123,101 -107.[Medline]
Kawakami, Y., Ichinose, Y. and Fukunaga, T.
(1998). Architectural and functional features of human triceps
surae muscles during contraction. J. Appl. Physiol.
85,398
-404.
Ker, R. F. (1981). Dynamic tensile properties
of the plantaris tendon of sheep (Ovis aries). J. Exp.
Biol. 93,283
-302.
Lichtwark, G. A., Bougoulias, K. and Wilson, A. M. (2007). Muscle fascicle and series elastic element length changes along the length of the human gastrocnemius during walking and running. J. Biomech. 40,157 -164.[CrossRef][Medline]
Lieber, R. L., Leonard, M. E., Brown, C. G. and Trestik, C. L. (1991). Frog semitendinosis tendon load-strain and stress-strain properties during passive loading. Am. J. Physiol. 261,C86 -C92.[Medline]
Lieber, R. L., Leonard, M. E. and Brown-Maupin, C. G. (2000). Effects of muscle contraction on the load-strain properties of frog aponeurosis and tendon. Cells Tissues Organs 166,48 -54.[CrossRef][Medline]
Loram, I. D., Maganaris, C. N. and Lakie, M.
(2004). Paradoxical muscle movement in human standing.
J. Physiol. 556,683
-689.
Maas, H., Meijer, H. J. and Huijing, P. A. (2005). Intermuscular interaction between synergists in rat originates from both intermuscular and extramuscular myofascial force transmission. Cells Tissues Organs 181, 38-50.[CrossRef][Medline]
Maganaris, C. N. and Paul, J. P. (2000). Load-elongation characteristics of in vivo human tendon and aponeurosis. J. Exp. Biol. 203,751 -756.[Abstract]
Maganaris, C. N., Baltzopoulos, V. and Sargeant, A. J.
(1998). In vivo measurements of the triceps surae
complex architecture in man: implications for muscle function. J.
Physiol. 512,603
-614.
Magnusson, S. P., Aagaard, P., Dyhre-Poulsen, P. and Kjaer,
M. (2001). Load-displacement properties of the human triceps
surae aponeurosis in vivo. J. Physiol.
531,277
-288.
Magnusson, S. P., Hansen, P., Aagaard, P., Brond, J., Dyhre-Poulsen, P., Bojsen-Moller, J. and Kjaer, M. (2003). Differential strain patterns of the human gastrocnemius aponeurosis and free tendon, in vivo. Acta Physiol. Scand. 177,185 -195.[CrossRef][Medline]
Morgan, D. L. (1977). Separation of active and passive components of short-range stiffness of muscle. Am. J. Physiol. 232,C45 -C49.[Medline]
Muramatsu, T., Muraoka, T., Takeshita, D., Kawakami, Y., Hirano,
Y. and Fukunaga, T. (2001). Mechanical properties of tendon
and aponeurosis of human gastrocnemius muscle in vivo. J. Appl.
Physiol. 90,1671
-1678.
Muraoka, T., Muramatsu, T., Takeshita, D., Kawakami, Y. and Fukunaga, T. (2002). Length change of human gastrocnemius aponeurosis and tendon during passive joint motion. Cells Tissues Organs 171,260 -268.[CrossRef][Medline]
Muraoka, T., Chino, K., Muramatsu, T., Fukunaga, T. and Kanehisa, H. (2005). In vivo passive mechanical properties of the human gastrocnemius muscle belly. J. Biomech. 38,1213 -1219.[CrossRef][Medline]
Narici, M. V., Binzoni, T., Hiltbrand, E., Fasel, J., Terrier, F. and Cerretelli, P. (1996). In vivo human gastrocnemius architecture with changing joint angle at rest and during graded isometric contraction. J. Physiol. 496,287 -297.[Medline]
Rack, P. M. and Westbury, D. R. (1984). Elastic
properties of the cat soleus tendon and their functional importance.
J. Physiol. 347,479
-495.
Roberts, T. J., Marsh, R. L.,Weyand, P. G. and Taylor, C. R.
(1997). Muscular force in running turkeys: the economy of
minimizing work. Science
275,1113
-1115.
Scott, S. H. and Loeb, G. E. (1995). Mechanical properties of aponeurosis and tendon of the cat soleus muscle during whole-muscle isometric contractions. J. Morphol. 224, 73-86.[CrossRef][Medline]
Swanstrom, M. D., Zarucco, L., Stover, S. M., Hubbard, M., Hawkins, D. A., Driessen, B. and Steffey, E. P. (2005). Passive and active mechanical properties of the superficial and deep digital flexor muscles in the forelimbs of anesthetized Thoroughbred horses. J. Biomech. 38,579 -586.[CrossRef][Medline]
Tardieu, C., Tabary, J. C., Tabary, C. and Tardieu, G. (1982). Adaptation of connective tissue length to immobilization in the lengthened and shortened positions in cat soleus muscle. J. Physiol. Paris 78,214 -220.[Medline]
Trestik, C. L. and Lieber, R. L. (1993). Relationship between Achilles tendon mechanical properties and gastrocnemius muscle function. J. Biomech. Eng. 115,225 -230.[Medline]
Whitehead, N. P., Gregory, J. E., Morgan, D. L. and Proske,
U. (2001). Passive mechanical properties of the medial
gastrocnemius muscle of the cat. J. Physiol.
536,893
-903.
Winter, D. A. (1990). Biomechanics and Motor Control of Human Movement. New York: Wiley.
Yucesoy, C. A., Koopman, B. H., Baan, G. C., Grootenboer, H. J. and Huijing, P. A. (2003). Effects of inter- and extramuscular myofascial force transmission on adjacent synergistic muscles: assessment by experiments and finite-element modeling. J. Biomech. 36,1797 -1811.[CrossRef][Medline]
Zajac, F. E. (1989). Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit. Rev. Biomed. Eng. 17,359 -411.[Medline]
Zuurbier, C. J., Everard, A. J., van der Wees, P. and Huijing, P. A. (1994). Length-force characteristics of the aponeurosis in the passive and active muscle condition and in the isolated condition. J. Biomech. 27,445 -453.[CrossRef][Medline]
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