In vivo mechanical properties of the human Achilles tendon during one-legged hopping
1 Structure and Motion Laboratory, Institute of Orthopaedics and
Musculoskeletal Sciences, University College London, Royal National
Orthopaedic Hospital, Brockley Hill, Stanmore, Middlesex, HA7 4LP,
UK
2 Structure and Motion Laboratory, The Royal Veterinary College, Hawkshead
Lane, North Mymms, Hatfield, Herts, AL9 7TA, UK
* Author for correspondence (e-mail: g.lichtwark{at}ucl.ac.uk)
Accepted 25 October 2005
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Summary |
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Key words: elasticity, biomechanics, stress, strain, elastic modulus, human
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Introduction |
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The mechanical properties of tendon have been shown to be relatively
uniform across a range of vertebrate animals
(Bennett et al., 1986;
Pollock and Shadwick, 1994
).
Many ex vivo mechanical tests have been carried out on tendon to
determine how much energy it can store and return, its ultimate tensile
strength and how repetitive loading affects the tensile strength
(Bennett et al., 1986
; Ker et
al., 1986
,
2000
;
Wang and Ker, 1995
). However,
much of this work has been carried out on cadaveric animal material, which may
have undergone material changes as a result of the preservation process
(Smith et al., 1996
).
In vivo measurements of mechanical properties of the AT have
demonstrated mixed results compared to those measured ex vivo.
Measures of the mechanical properties of the AT have demonstrated that there
is variation in tendon stiffness and elastic modulus between individuals
(De Zee and Voigt, 2001;
Hof, 1998
;
Maganaris and Paul, 2002
;
Maganaris, 2002
).
Ultrasonography and magnetic resonance imaging (MRI) studies have recently
reported strains of the AT ranging from 510% during isometric
contractions at forces below the maximum possible force during dynamic
movements (Finni et al., 2003
;
Muramatsu et al., 2001
;
Maganaris and Paul, 2002
). It
has previously been thought that such high strain would cause tendon rupture
and failure; however real-life activities such as one-legged hopping can
induce much larger stresses and strains on the AT without inducing acute
rupture (Komi, 1990
).
We seek to understand the amount of energy stored and returned from the AT under in vivo conditions where high strain is achieved. This will give an indication of the capacity for the AT to recycle mechanical energy during real-life movements and determine whether there is individual variation in the mechanical properties. We hypothesise that the AT acts like a classic energy storing spring, which stores and returns a substantial proportion of the energy required for the hopping movement. In addition, we hypothesise that the high strain movement will provide further evidence for variation in AT stiffness between individuals and more accurate measurements of tendon stiffness due to the greater range of strain data available.
To test this hypothesis it is necessary to determine the length of the
tendon and the force exerted during a dynamic activity that will induce large
tendon strains. Therefore the aim of the experiment was to determine the
in vivo AT length and force changes during one-legged hopping and
hence the stressstrain relationships of individual ATs. We introduce a
method that combines ultrasonography and motion analysis to make an estimate
of the mechanical properties of tendons during the dynamic movement of
one-legged hopping. This high force movement will allow a greater range of the
forcelength properties to be explored. Although it is likely that
differential strain patterns will occur along the tendon
(Finni et al., 2003;
Lyman et al., 2004
), in this
paper we aim to determine the absolute forcelength relationship during
the high force activity of one-legged hopping. Unlike previously discussed
ultrasound techniques for estimating tendon strain, this technique is the
first that directly measures tendon length changes during dynamic movements
and can potentially be applied to any movements, including locomotion.
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Materials and methods |
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The position of the MT junction and the calcaneous relative to the global coordinate system was determined by a combination of ultrasonography and motion analysis. The MT junction was imaged by ultrasound whilst synchronously determining the position and orientation of the ultrasound image. Therefore the position of the MT junction could be projected into three-dimensional (3D) space and the distance from this point to the calcaneous marker determined as the AT length (Fig. 1B). Details of the methodology and potential sources of error of this method are discussed further below. Tendon strain at any time was determined by dividing the instantaneous length of the tendon by the length of the tendon at approximately 5% of the average maximum force achieved during the hopping movements (200 N). Due to the rapid rise in tendon force and the relatively low rate of strain measurement, as well as noise in the measurement, resolving the toe region in a single trial was not possible. Therefore when averaging trials, whilst a toe region would appear, this would be an artefact of the timing of individual points and the associated smoothing effect of averaging. We therefore preferred to cut off the data at 200 N, which would result in a slight underestimate of strain. The magnitude of this underestimate is difficult to quantify as published values vary, but it is likely to be less than 1%.
Determination of the muscletendon junction position
Movement of the MT junction site was determined by ultrasound imaging. A PC
based ultrasound system (Echoblaster 128, UAB `Telemed', Vilnius, Lithuania)
was used to image the junction of the AT and the lateral gastrocnemius muscle
fibres in the sagittal plane (Fig.
2). The junction was imaged approximately 1 cm lateral to the
position where the medial and lateral gastrocnemius muscles join, which
allowed for successful imaging of the MT junction. In this experiment we used
a 128-element, linear, multi-frequency ultrasound probe at a frequency of 7
MHz and with a field of view of 60 mm in B-mode. Images were collected
via USB link to a PC, recorded at 25 frames s1 and
saved as a video file for further analysis. The position of the MT junction
was tracked in the two-dimensional (2D) image at each frame
(Fig. 2).
Synchronous motion analysis allowed the position and orientation of the ultrasound probe in the global coordinate system to be determined. This was achieved by attaching three markers to the probe such that two markers lay along the axis of the ultrasound probe and one in approximately the same plane as the image, a distance of approximately 70 mm away from the line of the other two markers (Fig. 1). The motion analysis data were synchronised with the ultrasound data using a digital output signal from the CODA motion analysis system that signified that the system was collecting data. This signal activated a signal generator that fed a 5 MHz signal to a sonomicrometry crystal (Sonometrics Ltd, Ontario, Canada) attached to the end of the ultrasound probe. This produced a white signal on the edge of the ultrasound image that indicated that the CODA system was collecting data. The motion analysis data were collected at 100 Hz, therefore accuracy of the synchronisation was within 0.04 s.
The position of the ultrasound image relative to the probe coordinate system was required so measurements in the ultrasound image plane could be projected into the 3D global coordinate system. To do this, the point of a metallic wand was tracked in 3D space using three CODA markers attached to the wand. The position of the wand tip relative to the three markers was first determined and the tip of the wand was then immersed into a water bath that was scanned by the ultrasound probe. Because metal is highly echogenic, it was possible to easily identify the point of the wand when it was in the plane of the images being scanned by the ultrasound probe. Three points (relative to the probe axis frame) in the plane of the image are required to translate the 2D coordinate data back into the 3D space. The average coordinate of three corners of the image were chosen to define the image plane relative to the three markers defining the probe axis system.
Points tracked in the 2D ultrasound image could then be embedded back into the laboratory frame of reference to get the 3D position relative to the laboratory. This was a two-step procedure. First the coordinates measured in the 2D image were embedded into the corresponding probe axis system, which was fixed relative to the image. The marked 3D coordinates were then embedded into the laboratory reference frame.
Ultrasound accuracy and sources of error
To determine the accuracy of the calibration and ultrasound measurements,
we scanned a Perspex® phantom located in the laboratory
coordinate system that consisted of two Perspex sheets with grooves cut into
them, which corresponded to an approximate length and position of the muscle
fibres relative to the skin (Fig.
3). The phantom was immersed in a plastic container full of water
so that the phantom grooves could be scanned from the outside of the container
in a direction equivalent to that in which the MT junction is imaged on the
leg (the xz plane of the laboratory coordinate system). The
position of the bottom edge of each of the grooves relative to the laboratory
was determined by running the point of the previously used metallic wand along
the grooves and tracking these points. A 3D regression line was fitted through
the data to represent the position of the grooves in the laboratory space. The
phantom was then scanned with the ultrasound probe and the position of the
image in the laboratory space was tracked synchronously using the previously
mentioned methods. Visible points on the bottom edge of the grooves were
marked in frames where the grooves were visible. These points were then
embedded into the global coordinate space and a comparison between these
points and the fitted regression line made.
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Achilles tendon force and stress
The 3D ground reaction force was measured using a Bertec force plate at
1000 Hz (Bertec Corporation, Columbus, OH, USA) and the motion analysis global
coordinate system was aligned to the force plate so that the ground reaction
vector could be transformed into it. The inertial properties of the foot
segment as defined by Plagenhoef et al.
(1983) were used in an inverse
dynamics solution to calculate the ankle plantar flexor moment at the joint
centre. This was defined as the moment about the axis perpendicular to the
plane defined by the calcaneous marker, the ankle joint centre of rotation and
the insertion of the AT.
The ankle joint centre was estimated by creating a virtual point corresponding to an approximation of the centre of rotation of the ankle. This point was half the distance between the lateral and medial malleoli, perpendicular to the plane created by markers placed on the fifth metatarsal, the calcaneous and the lateral malleolus. This effectively corresponds to a position midway between the lateral and medial malleoli.
AT force was calculated by dividing the ankle joint moment by the moment arm between the AT and the ankle joint centre. This was calculated at each time point as the perpendicular distance from the ankle joint centre to the line of action of the AT (the direct line from the calcaneous to the projected position of the muscletendon junction). It was assumed that all of the plantar flexor moment was contributed via the AT structure. Tendon stress was calculated for each individual by dividing the instantaneous force by the minimum cross sectional area (CSA) of the AT. CSA was measured by taking an ultrasound scan across the tendon in the coronal plane.
Participants
Ten male participants, average age 30.9 (±8.2) years, gave written
consent to take part in the study, which was approved by a local ethics
committee (RNOH JREC, 04/Q0506/11). The participants were asked to step onto
the force plate and hop continuously on one leg on the spot at a frequency of
approximately 2 Hz (average contact time=0.32 s). An average of 45 hops were
performed across three bouts with rest breaks between every 1520 hops.
Simultaneous force plate, 3D motion analysis and ultrasound data were
collected and synchronised during the hopping periods as previously described.
One participant performed the experiment on 3 separate days so that the
repeatability of the measures could be determined.
Marker positions and measurements
The instrumented ultrasound probe was attached to the leg with CobanTM
tape (3M, St Paul, MN, USA) such that the lateral gastrocnemius
muscletendon junction could be imaged. Further active markers were
placed on the following anatomical landmarks: head of the fifth metatarsal,
proximal calcaneus (at the approximate insertion site of the AT), lateral
malleolus, head of the fibula, lateral femoral epicondyle and on the ilotibial
band (halfway between the greater trochanter and the lateral epicondyle).
Ankle and knee joint angles were calculated in two dimensions (in the plane
of the hopping movement) using the markers previously mentioned. Total
gastrocnemius muscletendon unit (MTU) length was estimated from these
angles by applying the equations of Grieve et al.
(1978). The length change of
the muscle belly (including other series elastic structures like aponeurosis)
was calculated by subtracting the measured AT length change from the MTU
length change.
Data analysis
Individual subject data were used to create an average forcelength
and stressstrain relationship. This was done by filtering the length
data with a fourth order, 5 Hz low-pass Butterworth filter and time
interpolating the force and length measurements to 50 points across the period
of foot contact (when the ground reaction force was above 0 N) on each hop.
The ground reaction force during hopping was symmetrical in time (i.e. the
time course of force rise was similar to the time course of force fall), and
therefore this method of interpolation means that the peak force (and strain)
will occur at very similar times within the hop. The time point where the AT
force was 200 N was taken as the time point of zero length (or slack length)
of the tendon to maintain a consistent measure of tendon length under small
loads (5% of the total average tendon force during the hop). Tendon stiffness
(slope of the forcelength curve) and the elastic modulus (slope of the
stressstrain curve) of the tendon were determined by placing a linear
regression through the averaged forcelength data for each individual.
Hysteresis was calculated by dividing the difference between the area under
the loading and the unloading curves by the area under the loading curve
alone. This provides a measure of the energy converted to heat, an important
feature of the mechanical properties of tendon
(Wilson and Goodship,
1994).
To determine the amount of energy contributed to work of the hop, the
energy recovered from the tendon was determined as the area under the
descending limb of the forcelength curve. The amount of work associated
with each hop was determined as the maximum potential energy for the hop
relative to the lowest point. This was calculated using the vertical ground
reaction force measured with the forceplate using methods described in Cavagna
(1979). The relative
contribution of the AT recoil to the work of the hop was determined by
dividing energy recovered from the tendon by the total work of the hop. This
was averaged across all hops for each participant and a population average was
determined from this.
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Results |
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A scan of the Perspex® phantom with the ultrasound-motion analysis setup allowed for comparison between the predicted position of the grooves of the phantom and regression lines fit to the position of these grooves (as measured by motion analysis) to be made. A 3D reconstruction of the points measured with both techniques can be seen in Fig. 4A, while a comparison in 2D for each Perspex® sheet (in the plane of the sheet) is shown in Fig. 4B. In 3D the error was less than 1.15 mm for 50% of the observations (Fig. 4C); however, much of this error is in the laboratory xy plane. In the xz plane, which is the plane where much of the length change in the AT length was measured, the accuracy was within 0.96 mm for 50% of the cases (Fig. 4C).
|
Achilles stiffness and forcelength properties
An example of the relationship between the instantaneous measurements of AT
force and AT length for an individual during the periods of foot contact is
shown in Fig. 5. The effect of
filtering the AT length is also demonstrated. There is a clear relationship
between the measured length and force, where an increase in force corresponds
to a relatively linear increase in tendon length. On initial increase of AT
force, the length increases at a higher rate than when the tendon is almost
fully loaded (at the highest forces) and generally displays patterns of
hysteresis, where the Achilles force is less for any given length during
unloading compared to loading. The force and length both rise and fall in a
sinusoidal fashion, which is typical of a one-dimensional spring mass
system.
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Achilles material properties and contribution to work
The stressstrain relationships for three individuals representing
the whole range of elastic moduli across the group is demonstrated in
Fig. 9A. A linear regression
was performed through each subject's average data and the elastic modulus
recorded as the slope of this line. Due to interpolation with respect to the
time for each individual hop and the sinusoidal loading pattern, more of the
points acquired in each individual hop were recorded at high loads and
strains. An average stressstrain relationship for all participants is
demonstrated in Fig. 9B. This
figure also shows the standard deviation in both stress and strain measures
during the hopping movements. The greatest deviation in strain measurement is
apparent at lower stress values. An average hysteresis of 26% was recorded
across all subjects, but these values varied greatly with the inter-quartile
range being 1735%.
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Discussion |
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Achilles tendon as an energy saving mechanism
Combining traditional motion analysis with ultrasound imaging to determine
whole tendon length changes during dynamic activities provides an ideal
technique to study muscletendon unit interaction. The results of this
study demonstrated the energy storing capabilities of the AT, whereby the
tendon stretches in proportion to the force applied during the downward motion
of the body and then recoils to release most of the energy stored (74%) during
the upward movement. This provides a substantial amount of the total
mechanical energy of the hop (16%). This mechanism has been thought to provide
an energy saving mechanism during human walking, running and jumping
(Alexander, 1988;
Bobbert et al., 1986
;
Fukunaga et al., 2001
) and has
recently been suggested to account for up to 6% of the total mechanical work
produced during walking (Maganaris and
Paul, 2002
). This research therefore further shows the capacity of
the body to utilise elastic stain energy and provides a valuable technique for
quantifying tendon strain and energy storage capacity in further real-life
movements such as walking and running. However, application of this technique
in lower force activities may result in broader measures of strain due to the
larger variation in strain measured at the low forces in this study.
Most of the length change occurring in the MTU occurs in the AT
(Fig. 6), thereby the return of
elastic energy during tendon recoil provides most of the shortening work
required for take-off. In contrast, the muscle (plus other series elastic
structures such as the proximal tendon and aponeurosis) only stretch and
shorten by small amounts during the hop, thereby reducing the work required by
the muscle fibres. This is energetically efficient because it requires less
work by the muscle fibres and reduces the heat produced from actively
shortening the muscle fibres (Lichtwark
and Wilson, 2005a). The aponeurosis associated with the medial
gastrocnemius has also been found to be highly compliant and therefore some of
the stretch and recoil occurring in the muscle fibres/aponeurosis complex may
be elastic strain energy as well. This would allow the muscle fibres to act
almost isometrically, which has been suggested to be the most efficient manner
to operate (Roberts,
2002
).
Achilles tendon material properties and strain
The strains measured here are at the higher end of those expected before
tendon rupture, based on ex vivo material testing. Typical tensile
testing of tendinous material suggests that it should begin to fail at strains
from 610% (Bennett et al.,
1986; Ker et al.,
1986
); however, here we have measured whole tendon strains of over
10% without failure or injury. One-legged hopping was chosen specifically
because it is an activity that should elicit very high stress and strain in
the tendon. There are also major differences in what is actually measured
between other techniques. For instance, most ex vivo tensile testing
is performed on sections of tendon, typically where the cross-sectional area
is least. In contrast, here we have made a measure of whole tendon length. It
is well documented that large strains can occur in tendinous material with
some estimates of aponeurosis strain during contraction being as high as 50%
(Zuurbier et al., 1994
).
Therefore whole tendon strain is likely to differ from material testing
results for samples of tendon.
Nonetheless, the forcelength and stressstrain properties of
the AT measured are within estimates of animal tendon (elastic modulus,
0.41.7 Gpa; Zajac,
1989) and also in vivo measurements on the AT (stiffness,
150 N mm1; elastic modulus, 1.16 Gpa;
Maganaris and Paul, 2002
). In
addition, we have measured hysteresis values within the normal range
(338%). The average value of 26% is similar to that recently found to
occur in the tibialis anterior and gastrocnemius tendons (19 and 18%,
respectively; Maganaris and Paul,
2002
; Maganaris,
2002
). The lack of a toe-region in our stressstrain data
may be the result of low accuracies at low forces, or because we used a value
of 200 N of tendon force as the cut-off to estimate zero strain. Taking a zero
of 200 N will result in a small (less than 1%) underestimate of actual
strain.
There are also measurement reasons why such high strains might have been measured. Firstly, it is likely that the measurement technique introduced some systematic errors in the calculation of the tendon length. The typical rotation of the probe around the tendon (hence changing the region of the muscletendon junction tracked) has been shown to overestimate the Achilles strain by approximately 1.08%. Because this rotation occurs mainly during impact and take-off of the hop, then the estimate of slack length of the tendon may be incorrect (but not tendon stiffness). This may be responsible for the lack of toe-region in the forcelength data for most subjects during the initial loading of the tendon. In addition, the muscle contraction under the skin may distort the junction and alter the results during muscle shortening on impact with the ground.
It is also possible that the 3D structure of the AT allows high strains to be achieved. The structure of the AT varies dramatically along its length, from a uniform, round, cross-sectional area distally to a fan shape more proximally (Fig. 1). It is possible that shape changes of the fan region of the tendon and the muscle may help to achieve such high strains. This could be further explored by making ultrasound measurements of tendon shape change during the movement. This could be achieved with consecutive scans of the tendon at different positions on the muscletendon junction and in different planes, or perhaps by applying new four-dimensional ultrasound techniques that can image volumes of tissue in time.
Numerous other studies have suggested that high levels of strain occur in
the AT and also other elastic structures. Recent ultrasonography studies
during isometric and dynamic movements have reported that strains of the
series elastic element (both the tendon and aponeurosis) can exceed 10%
(Kubo et al., 2002). These
studies do not, however, distinguish between distal tendon, proximal tendon or
aponeurosis. A more direct ultrasound study also achieved strains of 5% (12
mm) during an isometric contraction
(Maganaris and Paul, 2002
);
however, these contractions could only achieve small forces compared to those
obtained here during one-legged hopping. Using phase-contrast magnetic
resonance imaging, strains of approximately 4.7% were achieved during a 40%
maximum isometric contraction (Finni et
al., 2003
), therefore it does seem that the AT can achieve large
levels of strain, at least for a limited number of cycles, without rupture.
Taking these results into account as well as the strain records measured here,
it is apparent that high AT strains are indeed achieved during human movement.
The hopping movement is a particularly high force movement and therefore
should elicit extreme strains, and prolonged one-legged hopping, which rarely
occurs in everyday activities, may well begin to damage the AT.
Individual variation
The individual tendon stiffness and elastic modulus show a relatively broad
range across the subject group measured. Although broad studies of different
animals suggests that there is little variation in the elastic modulus, there
is some evidence that this can vary with training effects
(Buchanan and Marsh, 2001;
Reeves et al., 2003
).
Therefore, with such a small group, the variation may be exaggerated. In
addition, while the technique seems to be reproducible for one participant
(Fig. 7), there is still room
for individual variability that is inherent to the technique. For instance,
the protocol does not control for individual muscle architecture and also
muscle activation during the movement. Individual muscle architecture could
influence the forcelength relationship due to differences in probe
rotation (as previously mentioned) and also the shape of the tendon insertion
relative to the orientation of the probe (and hence image plane). Muscle
activation has also been suggested to influence the stiffness of the series
elastic structures (Hof, 1998
,
2003
), and not controlling for
this may influence the AT stiffness in some way. Finally the contribution of
the soleus and lateral gastrocnemius to the force that strains the AT may
differ between participants and effect the measured whole tendon length
change.
Conclusions
In conclusion, the current study has provided a new technique for the
measurement of whole tendon length during dynamic activities. We have measured
the length of the AT from the muscletendon junction to its insertion to
the calcaneous using a combination of motion analysis and ultrasound. During
the high strain movement of one-legged hopping, the elastic behaviour of the
AT is highlighted, where a substantial amount of the mechanical energy
required to produce the hopping movement is provided by elastic recoil of the
AT. The majority of the strain occurs in the AT compared to the muscle
contractile component and aponeurosis and this allows for rapid recoil of the
muscletendon unit during take-off. Synchronous measurement of AT force
has shown that typically linear forcelength properties of tendons under
high forces can be reproduced. The mechanical properties of the tendon are
within the measured physiological range, despite high measures of whole tendon
strain that result from the high forces. These high strains may be the result
of the complex 3D fan shape of the AT, which may allow for such high whole
tendon strains in the direction of muscle action due to shape change.
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List of abbreviations |
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Acknowledgments |
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Footnotes |
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References |
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