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J Appl Physiol 89: 1352-1359, 2000;
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Vol. 89, Issue 4, 1352-1359, October 2000

Dynamic viscoelastic behavior of lower extremity tendons during simulated running

M. De Zee1, F. Bojsen-Møller2, and M. Voigt1

1 Center for Sensory-Motor Interaction, Aalborg University, 9220 Aalborg; and 2 Laboratory for Functional Anatomy, Biomechanics and Motor Control, Panum Institute, 2200 Copenhagen N, Denmark


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The aim of this project was to see whether the tendon would show creep during long-term dynamic loading (here referred to as dynamic creep). Pig tendons were loaded by a material-testing machine with a human Achilles tendon force profile (1.37 Hz, 3% strain, 1,600 cycles), which was obtained in an earlier in vivo experiment during running. All the pig tendons showed some dynamic creep during cyclic loading (between 0.23 ± 0.15 and 0.42 ± 0.21%, means ± SD). The pig tendon data were used as an input of a model to predict dynamic creep in the human Achilles tendon during running of a marathon and to evaluate whether there might consequently be an influence on group Ia afferent-mediated length and velocity feedback from muscle spindles. The predicted dynamic creep in the Achilles tendon was considered to be too small to have a significant influence on the length and velocity feedback from soleus during running. In spite of the characteristic nonlinear viscoelastic behavior of tendons, our results demonstrate that these properties have a minor effect on the ability of tendons to act as predictable, stable, and elastic force transmitters during long-term cyclic loading.

digital tendon; Achilles tendon; creep; dynamic creep


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

THE ROLE OF TENDON COMPLIANCE on group Ia afferent-mediated length and velocity feedback from muscle spindles has received some attention in studies of cat and human motor control. It is still a controversial issue, however, whether tendon mechanical properties have an important influence on the length and velocity feedback during natural movement. Because of tendon compliance, length changes in the muscle spindles do not necessarily reflect length changes of the whole muscle-tendon unit in walking cats (7, 10). This topic has been investigated in the human elbow and ankle joint (5, 19) and by human hopping (27), showing that a compliant tendon might have an influence on what muscle spindles "see." This could make the task for the feedback system more complex compared with a situation with an infinitely stiff tendon. On the other hand, Elek et al. (4) reject the claim that tendon stretch during movement possesses a serious difficulty for the feedback system. However, all these studies assume that the mechanical properties of the tendon remain constant. This might not be the case during long-term cyclic loading because of the time-dependent viscoelastic properties of the tendon. If a tendon experiences the same loading pattern in vivo for a long period (for example during a marathon run), the tendon might show a change in length; in other words, the tendon shows creep. If we assume that the whole muscle-tendon length remains the same during a certain phase of the step cycle while the tendon experiences a significant elongation, the muscle fibers will be shorter. This could have three consequences: 1) the muscle fibers would work in a shorter range of their length-force curve, 2) the group II output from the spindles would be lower, and 3) the group Ia output from the spindles might change depending on whether the fusimotor drive has changed. This all depends on whether the tendon really shows a significant elongation during long-term cyclic loading. Another important thing is the storage and release of energy in the tendon during locomotion (1). The contribution of elastic work from the tendons to the total work during movement will be affected by a significant change in the viscoelastic behavior, e.g., stiffness and hysteresis.

Creep is one of the viscoelastic properties for tendon tissue (25). Normally creep is defined as the length change during a constant load. Wang and Ker (30) described static creep as a combination of primary creep (decelerating strain) and tertiary creep (accelerating strain). Primary creep is nondamaging, but tertiary creep is accompanied by accumulating damage characterized by a loss of stiffness. In their paper, Wang and Ker were mainly concerned with later stages of creep, in which significant damage occurs, the so-called creep rupture. Wang et al. (31) noticed throughout their fatigue tests of wallaby tail tendons a strain increase with a sinusoidal force pattern, but the strain increase was much faster just before rupture. The strain increase during dynamic loading will be referred to as "dynamic creep." The dynamic creep was partly due to damage, because the tendon stiffness decreased gradually throughout each fatigue test. They used a minimum stress in each cycle of 11.5 MPa, and the peak stress was between 20 and 80 MPa. Also, dynamic creep can be divided in a nondamaging creep (primary creep) and a damaging creep (tertiary creep). In the present study, the stresses were chosen in a range in which no damage was expected, which we assume to be in the physiological range.

A thorough investigation of the elastic properties of tendons has been carried out in the past. The dynamic tests focused mainly on obtaining Young's modulus of tendon tissue (3, 13, 14, 21). The loading patterns used were sinusoidal loading patterns. However, under natural circumstances, the force on tendons during stretch-shortening cycles clearly has a more complex shape than a sinusoid (6, 15). A complex loading pattern might affect the elastic and viscoelastic behavior of the tendon.

The aim of this project was to see how much a tendon would show dynamic creep during long-term dynamic loading with a natural loading profile. Digital pig tendons were used for the experimental part of the study. The experimental information was used to estimate the dynamic creep of the human Achilles tendon during a marathon race. The pig tendon data were used as an input of a model to predict this dynamic creep. A comparison of the time-dependent properties between the "trained" flexor and "untrained" extensor digital tendons was made. Woo et al. (34) showed that training increases the collagen content and the total weight of digital extensor pig tendons, but the effect of training on pig digital flexor tendons is minimal (33). Shadwick (22) used pig digital flexor and extensor tendons to show a difference in elastic properties and also in the amount of hysteresis between mature flexor and extensor tendons due to different physiological functions. The flexor tendons in pigs generally experience more physical loading than the extensor tendons. Therefore, the flexor tendons can be considered as "trained" tendons in contrast to the extensor tendons. The human Achilles tendon is a load-bearing tendon and can therefore be considered as a trained tendon. For the model input of the human Achilles tendon, we used the data from the trained pig digital flexor tendons.

Furthermore, the ability of the tendon to store and release energy during long-term loading will be discussed. Contrary to most other studies, the pig tendons were loaded with a force profile as in human running, which will give information about the influence of a more complex loading pattern on the tendon characteristics. The amplitude of the applied stresses was in a range in which tertiary dynamic creep was avoided.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Tendon Preparation

Pig front feet were obtained from the local slaughterhouse a few hours after the animals were slaughtered. Ten digital extensor tendons and 21 deep digital flexor tendons were dissected out. To overcome clamp-induced failure, the ends of the tendon specimens were air dried; the rest of the specimen was wrapped in plastic film moistened with paraffin oil as described in earlier work (8, 30). The prepared tendon specimens were stored at 5°C until tested.

Mechanical Testing

Mechanical tests were performed with an Instron 8501+ material testing machine with adaptive tuning controlled by the software MAX (version 4.2, Instron) running on a personal computer. The tendon specimens were clamped on both ends in clamps like those used by Riemersma and Schamhardt (20), but the tendon ends were not frozen down. Length changes were measured on the central portion of the tendon specimen by an electronic extensometer. The extensometer was custom made according to the principles described by Ker (13) and calibrated carefully with a micrometer. In midposition, the gauge length was 37.8 mm with a range of movement of ±2.5 mm. The nonlinearity was 0.5% of full range. During all tests, a simultaneous recording of the force and extension signals was carried out with a sampling rate of 100 Hz.

Experiments

To obtain a stable response, the specimens were preconditioned for a period of 1 min with a haversine load of 350 N for flexor tendons and 100 N for extensor tendons at a frequency of 1.5 Hz before the tests started. Between the tests, the tendon specimen was kept in slack position for 5 min to recover. The following tests were performed after the preconditioning.

Test 1: Obtaining peak force. The tendon specimen was preloaded with a force of 5 N. This was done to overcome the problems with defining the resting length. The tendon was then stretched 3% with the system in strain control, and the force necessary to produce this initial stretch (Fmax) was noted. Fmax was used for the rest of the tests on the given specimen. A strain of 3% is in the physiological range (14).

Test 2: Static creep. The tendon specimen was loaded for a period of 60 s with the constant Fmax with the material testing machine in load control. The rising and falling times were 3 s (Fig. 1B).


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  		Fig. 1.   Example of creep of an extensor tendon specimen during a constant force. A: creep curve characteristic for creep as a result of the loading pattern as showed in B. The vertical lines in B at 4 and 62 s indicate the points between which the amount of creep was quantified. F, force; Fmax, force necessary to stretch preloaded tendon 3%.

Test 3: Dynamic creep. The loading pattern data used in the present study were obtained during an earlier experiment on a human subject during heel-toe running while a buckle force transducer was implanted around the Achilles tendon (15, 29). The tendon specimen was loaded with this natural force profile (Fig. 2A) with a frequency of 1.37 Hz for a period of 1,600 cycles (approx 20 min) with the material testing machine in load control. The chosen frequency is equal to the step frequency of elite runners running with a speed of 19 km/h (28). The force profile was scaled so that the peak force was equal to Fmax.


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  		Fig. 2.   A: normalized Achilles tendon force profile of one step cycle during human heel-toe running (29). HC, heel contact; TO, toe off. There is a drop in force directly after heel contact. After that, the force increases until maximum during the push-off. The force does not return to zero in the swing phase because of cocontraction of the muscles around the ankle joint during natural running. This force profile was used to load the tendon specimens. B: typical stress-strain curve of a flexor tendon specimen as a result of the loading pattern presented in A. The double hysteresis loop, which is characteristic, is caused by the drop in force in the loading pattern directly after the imaginary heel contact. The strain does not return to zero because of the cocontraction in the swing phase.

Test 4: Static creep. This test was the same as test 2.

Additional tests. Test 3 was repeated in two flexor tendon specimens and in one extensor tendon specimen, but with a frequency of 2 Hz.

After the tests, the parts of the tendon specimens enclosed by the extensometer were cut out and kept frozen for later analysis.

Measurement of Cross-Sectional Area

To express the load on the tendon specimens in stress values (MPa), the cross-sectional area had to be measured in each specimen. Volumes of the tendon samples were measured gravimetrically by using 0.9% saline, the temperature of the saline was measured simultaneously for calculating the density of the saline, and the lengths of the samples were defined as the gauge length before test 1 started at 5 N preload. The cross-sectional area was then calculated by dividing the volumes by the lengths.

Calculations

Young's modulus. Young's modulus was calculated as the slope of the supposed linear part of the stress-strain curve. The linear part was defined as the curve between 50 and 95% of the maximum stress.

Hysteresis. The hysteresis was calculated as the ratio of the area in the stress-strain loop to the area beneath the load portion of the curve.

Static creep. The amount of creep in tests 2 and 4 was calculated as the difference between the strain after 62 s and the strain after 4 s (see vertical lines in Fig. 1B). In this way, the dynamic effects of loading and unloading the tendon were avoided.

Dynamic creep. The dynamic creep curves from test 3 were obtained by taking the maximum strain and minimum strain of each cycle and plotting them against the time. A typical curve is presented in Fig. 3. The amount of dynamic creep was obtained by subtracting the first point of the dynamic creep curve from the last point of the curve.


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  		Fig. 3.   Example of dynamic creep of a flexor tendon specimen. The first 3 cycles were recorded continuously; after that, every second cycle was stored. The dynamic creep curve was obtained by taking the maximum (max) and minimum (min) strain of each cycle and plotting them against time (inset).

Dynamic Creep Model

The dynamic creep curves in Fig. 3 have a shape comparable with the classic creep under constant load. This creep can be described as an exponential function of time (24). In analogy with the classic creep, the dynamic creep can be described as a function of the amount of cycles with Eq. 1
ϵ=<FR><NU>&sfgr;</NU><DE>E<SUB><IT>1</IT></SUB></DE></FR><IT>+</IT><FR><NU><IT>&sfgr;</IT></NU><DE>E<SUB><IT>2</IT></SUB></DE></FR> [<IT>1−</IT>exp(−<IT>c/&tgr;</IT>)] (1)
where varepsilon  is strain, sigma  is stress, E1 is initial stiffness, E2 is a constant in the time-dependent stiffness, c is cycle number, and tau  is a dynamic creep constant.

The constants E1, E2, and tau  were obtained by a nonlinear curve fit to the experimentally obtained dynamic creep curve from the flexor tendons. For each tendon specimen, two sets of constants were obtained: one for the curve for the phases of maximum stress and one for the curve for the phases of minimum stress.

Simulation of Dynamic Creep in Human Achilles Tendon During Running

The goal of the simulation was to predict the dynamic creep after 11,000 cycles, equal to a run of almost 2 h 14 min. A simple two-dimensional model of the human soleus muscle-tendon complex was used for the simulation. It was adapted from Huijing and Woittiez (12) (Fig. 4) with the following parameters obtained from the literature (26, 32)


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  		Fig. 4.   A simple 2-dimensional model of the human soleus muscle-tendon complex. L0, resting length of the tendon; lF, fiber length; alpha , angle of pennation.


L0   = 364 mm (resting length of tendon)
AT   = 62.5 mm2 (cross-sectional area of the Achilles tendon)
lF   = 20 mm (fiber length)
 alpha    = 25° (pennation angle)
rt   = 50 mm (moment arm of the Achilles tendon)

An average of the dynamic creep model parameters was used for the simulation. The absolute length change of the tendon (Delta L) could be calculated as
&Dgr;L=(ϵ<SUB>11,000</SUB>−ϵ<SUB>0</SUB>)·L<SUB>0</SUB> (mm)
where varepsilon 11,000 and varepsilon 0 are the strains after 11,000 and 0 cycles, respectively.

The next step was to calculate the influence of the length change on the ankle angle beta  (Delta beta ankle) with the following equation
&Dgr;&bgr;<SUB>ankle</SUB><IT>=</IT>(<IT>180·&Dgr;L</IT>)<IT>/</IT>(<IT>&pgr;·</IT>r<SUB>t</SUB>) (degrees)
The last step in the simulation was to estimate the length change in the muscle fibers (Delta lF) for keeping the ankle in the same position to counteract the tendon length change. This could be done by the following equation
&Dgr;l<SUB>F</SUB><IT>=&Dgr;L/</IT>cos<IT> &agr; </IT>(mm)

Statistics

A Student's t-test was used to compare Young's modulus of extensor and flexor tendons. Two-way ANOVA with repeated measures (one-factor repetition) was used to detect significant differences between a before-and-after situation and between extensors and flexor tendons. In the event of significant F values in the ANOVA, a Student-Newman-Keuls post hoc test was used to locate significance between means. A value of P < 0.05 was considered significant. Average values are presented as means ± SD.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Number of Successful Experiments

The number of tendon specimens analyzed was reduced to seven flexor tendon specimens and six extensor tendon specimens because of clamp-induced failure during the long-term cyclic loading.

Cross-Sectional Area and Peak Stress

The tested flexor tendons had a cross-sectional area of 25.5 ± 5.9 mm2 and were tested with a peak stress of 13.0 ± 4.0 MPa. The tested extensor tendons had a cross-sectional area of 10.9 ± 2.7 mm2 and were tested with a peak stress of 12.7 ± 2.7 MPa.

Young's Modulus and Hysteresis

The typical stress-strain curve (Fig. 2B) is the double hysteresis loop due to the natural loading-running profile, which gives a more complex stress-strain curve than during loading with a haversine. The decline in force immediately after heel contact causes the double hysteresis loop (Fig. 2A). In addition, the strain in the tendon specimens does not return to zero during "running." This occurs because the Achilles tendon force does not return to zero due to cocontraction of the ankle dorsiflexors in the swing phase (Fig. 2A). This resulted in the first cycle being different from the following cycles because the stress started at zero but never returned there due to the inherent cocontraction (Fig. 5) in the load signal.


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  		Fig. 5.   Stress-strain curve of the first 3 cycles of an extensor tendon specimen. The first cycle was different from the following cycles because the stress started from zero but never returned to zero, owing to the imaginary cocontraction.

In Table 1, the mechanical properties of the tested tendons are summarized. Young's modulus of the flexor tendon specimens was 0.21 GPa larger (P = 0.043) than Young's modulus of the extensor tendon specimens. However, there was not a significant difference in the hysteresis (P = 0.496) between the flexor and extensor tendon specimens. The hysteresis of the last 10 cycles was significantly lower than the hysteresis of the first 10 cycles (P = 0.022). Stretching the tendons at higher frequency did not seem to change the mechanical properties.

                              
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  		Table 1.   Summary of results from tests 2, 3, and 4 

Creep

The typical creep curve (Fig. 1A) shows the asymptotic curve characteristic for creep. Table 1 summarizes the results of the creep tests. The creep in the extensor tendon specimens was significantly larger than that in the flexor tendon specimens (P = 0.002). Furthermore, the creep in the tests before cyclic loading was significantly larger than the creep after cyclic loading (P = 0.006).

Dynamic Creep

From Fig. 3 it is clear that the tendon showed dynamic creep during both the maximum stress and minimum stress, and the dynamic creep displayed an asymptotic curve. Table 1 shows the results of the dynamic creep test. The tendon specimens showed significantly more lengthening in the phases of minimum stress than in the phases of maximum stress (P < 0.001). There was no significant difference between dynamic creep of the flexor tendon specimens and the extensor tendon specimens (P = 0.582).

Simulation of Dynamic Creep in Human Achilles Tendon

The experimentally obtained dynamic creep curves were fitted by using Eq. 1, and the average parameters for the flexor tendon specimens were obtained and are presented in Table 2. The mean correlation coefficient of the fitting was 0.99 ± 0.005. 

                              
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  		Table 2.   Model parameters for flexor tendons

The simulation was performed over 11,000 cycles, which correspond to a marathon of 2 h 14 min (19 km/h; step frequency 1.37 Hz). The simulation showed dynamic creep in the Achilles tendon of 0.62 mm during the phases of maximum stress. During the phases of minimum stress, the simulation showed dynamic creep of 0.81 mm. An extra shortening of the muscle fibers in the soleus could compensate for the dynamic creep. That would mean an extra shortening of the muscle fibers between 3.3 and 4.5%. In case of no muscle compensation, the angular position of the ankle would change between 0.7 and 0.9°, assuming a moment arm of 50 mm.

Energy Storage in the Tendon

Figure 6 displays the difference between the maximum strain and minimum strain of the Achilles tendon model during simulated running. This difference reflects the ability of the tendon to store and release energy during long-term running; i.e., if the difference increases over time, the tendon stores more energy (assuming a constant hysteresis), and if the difference decreases, the tendon stores less mechanical energy. The simulation shows that the difference is constant after a small decrease in the beginning. The difference shows an asymptote of tendon length change of 2.01% strain.


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  		Fig. 6.   The change in difference between the max and min strain of the Achilles tendon model during simulated running. This difference reflects the constancy of the tendon to store and release energy during long-term loading. Change in difference is small and constant after ~2,000 s (~33 min).


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Pig flexor and extensor tendons selected as a model system for human tendons were cyclically loaded with a natural running-force profile to simulate human marathon running without causing damage in the tissue. We evaluated whether or not elongation of the tendon during the cyclic loading could influence human group Ia afferent-mediated length and velocity feedback from muscle spindles during running. The main results were that all the pig tendons showed a clear dynamic creep in vitro. The dynamic creep was, however, considered to be too small for claiming that dynamic creep in the Achilles tendon might have an influence on the length and velocity feedback during human running. The results also demonstrated the stability of tendons to store and release energy during long-term cyclic loading.

Methodological Considerations

We started out measuring the strain in the tendon specimens with a commercial extensometer (MTS Biomedical Extensometer, model 632.32) designed for measuring strain on soft tissue samples. This type of extensometer is connected to the specimen with a small spring force. It turned out that, during the dynamic loading, the arms of the extensometer started to slip on the specimen. It was therefore necessary to use a custom-made extensometer according to the principles described by Ker (13).

In test 1, Fmax was obtained by stretching the tendon specimen 3%. Originally the specimens should have been stretched to 4% because the peak strain, which could be expected in the Achilles tendon during locomotion, lies between 4-5%, assuming Young's modulus of 1.2 GPa and a peak stress around 50 MPa. In the literature, the estimates of the peak stresses in tendons of mammals during locomotion lie between 15 and 84 MPa (3, 17). The maximum possible stress in the human Achilles tendon was estimated at 67 MPa (14); therefore, a peak stress of 50 MPa in the Achilles tendon during human running seems reasonable. Unfortunately, during the long-term dynamic loading with the obtained Fmax for 4%, we lost seven tendons due to clamp-induced failure after only a few minutes of cyclic loading. Therefore, Fmax was obtained by stretching the tendon specimen 3%. This means that the stress experienced by the tendons during the testing was most probably lower than the stress in the Achilles tendon during actual running. One might expect the values for creep and dynamic creep to be higher when higher values are used for Fmax. Nevertheless, we believe that this would not change our conclusions. As long as the tendons are loaded with stresses that only introduce primary dynamic creep, we assume that our observations are valid.

Young's Modulus and Hysteresis

Table 1 showed lower values for Young's modulus than for the data obtained by Shadwick (22). It has been shown that mammalian tendons approach asymptotic moduli of ~1.5 GPa at stresses above 30 MPa (3). These high stresses were never reached in our tests, in contrast to the stresses in the tests performed by Shadwick (22), which means that the tendons were never totally out of the toe piece. The lack of difference in hysteresis between the extensor and flexor tendons, contrary to the study by Shadwick, might be due to the loading pattern used. The natural loading pattern used in the present study caused a double hysteresis loop in the stress-strain curve (Fig. 2B). The strain rate in the natural loading pattern (maximal strain rate = 31.7%/s with a peak strain of 3% and a frequency of 1.37 Hz) is higher compared with a haversine (maximal strain rate = 12.9%/s with a peak strain of 3% and a frequency of 1.37 Hz). The higher strain rate plus the double hysteresis loop might be the reason for a lower hysteresis.

Creep and Dynamic Creep

The dynamic creep occurred in all the tendons while Young's modulus was not decreasing during the cyclic loading. Therefore, this dynamic creep was purely a nondamaging primary creep. It is likely that this type of dynamic creep occurs in vivo during repetitive movements such as running, because dynamic creep is a tissue property that hardly changes between the in vivo and in vitro situation insofar as the tendon specimens were properly hydrated. Paraffin oil protected the specimens against dehydration. In this way we are confident that the specimens were always properly hydrated. In the dynamic situation there was unexpectedly no clear difference in the amount of dynamic creep between the flexor and extensor tendon specimens, contrary to the static creep test. This might indicate that different mechanisms are responsible for creep and dynamic creep. Static creep at lower stresses has been suggested to be caused by the straightening out of the crimp in the collagen fibers in the tendon over time (11). As proposed by Shadwick (22), the flexor tendons might have a higher collagen content and more cross-link stabilization than the extensor tendons, resulting in less static creep. In the dynamic situation, the interaction between the water content of the tendon and the collagen might be more important. The water content did not differ between the mature flexor and extensor tendons (22), which might explain the lack of difference in the amount of dynamic creep between the flexor and extensor tendon specimens.

Simulation of Dynamic Creep in Human Achilles Tendon

The purpose of the model was to predict the amount of dynamic creep in the human Achilles tendon during a marathon run. It has been shown that the mechanical properties of the tendons in the extremities of different adult animals are comparable, independent of body mass (3, 17). The measured Young's modulus was on average 1.5 GPa with peak stresses above 30 MPa. In human leg tendons, Young's modulus values were found between 1.0 and 1.5 GPa but measured with lower peak stresses than 30 MPa (2, 18, 23). From the literature and from our data, we believe that the mechanical properties of the trained pig flexor tendon can function as a model for the human Achilles tendon.

The simulation was based on a data set of 20 min, while we tried to simulate a marathon run of 2 h 14 min. However, most of the dynamic creep took place in the first 20-25 min before it reached its asymptote. Hence, the error of the simulation was not dependent on how long the simulation continued.

The simulation of human running showed a small amount of dynamic creep in the equivalent of the Achilles tendon. It has been shown that the kinematics of running does not change after a marathon run (16). This could mean that a change in tendon length has been compensated for by a shortening of the muscle fibers, but it might also be possible that the small angle changes associated with the dynamic creep were smaller than the resolution of the kinematics measurement system. Because of the small amount of dynamic creep in the Achilles tendon, it does not seem necessary for the motor system to change the drive to the soleus muscle.

The question is whether the small amount of dynamic creep would influence the length and velocity feedback of the soleus muscle spindles. Within a stretch-shortening cycle during running, the Achilles tendon shows a length change due to the compliance of the tendon that is much larger than the dynamic creep that we found. It is still controversial, however, how important the tendon compliance is to the length and velocity feedback during natural movement. In summary, the influence of dynamic creep on the feedback system seems to be limited for two reasons: 1) the slow nature of the dynamic creep phenomenon and 2) the small size of length changes of the tendon over time compared with the length changes of tendon within a cycle. Nevertheless, the tendon length in the first cycle being different from that in the following cycles implies an extra demand on the feedback system at the initiation of running (Fig. 5).

Energy Storage in the Tendon

Earlier work concentrated on the dimensions and mechanical properties of the Achilles tendon to show the ability and the importance of energy storage of the Achilles tendon in humans (9, 26). The simulation showed that the difference between the maximum strain and the minimum strain reaches an asymptote after ~2,000 s (~33 min) during the running of a marathon (Fig. 6). This plus the fact that the hysteresis tends to decrease during long-term loading shows a high constancy of the Achilles tendon to store and release energy during long-term cyclic loading such as running.


    ACKNOWLEDGEMENTS

The Danish National Research Foundation and The National Danish Society for Rheumatism supported this work.


    FOOTNOTES

Address for reprint requests and other correspondence: M. de Zee, Center for Sensory-Motor Interaction, Aalborg Univ., Fredrik Bajers Vej 7-D3, 9220 Aalborg, Denmark (E-mail: mdz{at}miba.auc.dk).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 8 October 1999; accepted in final form 6 May 2000.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

1.   Alexander, RM, and Bennet-Clark HC. Storage of elastic strain energy in muscle and other tissues. Nature 265: 114-117, 1977[Medline].

2.   Benedict, JV, Walker LB, and Harris EH. Stress-strain characteristics and tensile strength of unembalmed human tendon. J Biomech 1: 53-63, 1968.

3.   Bennet, MB, Ker RF, Dimery NJ, and Alexander RM. Mechanical properties of various mammalian tendons. J Zool Lond 209: 537-548, 1986.

4.   Elek, J, Prochazka A, Hulliger M, and Vincent S. In-series compliance of gastrocnemius muscle in cat step cycle: do spindles signal origin-to-insertion length? J Physiol (Lond) 429: 237-258, 1990[Abstract/Free Full Text].

5.   Fellows, SJ, and Rack PM. Changes in the length of the human biceps brachii muscle during elbow movements. J Physiol (Lond) 383: 405-412, 1987[Abstract/Free Full Text].

6.   Finni, T, Komi PV, and Lukkariniemi J. Achilles tendon loading during walking: application of a novel optic fiber technique. Eur J Appl Physiol 77: 289-291, 1998.

7.   Griffiths, RI. Shortening of muscle fibres during stretch of the active cat medial gastrocnemius muscle: the role of tendon compliance. J Physiol (Lond) 436: 219-236, 1991[Abstract/Free Full Text].

8.   Haut, RC. Age-dependent influence of strain rate on the tensile failure of rat-tail tendon. J Biomech Eng 105: 296-299, 1983[ISI][Medline].

9.   Hof, AL. In vivo measurement of the series elasticity release curve of human triceps surae muscle. J Biomech 31: 793-800, 1998[ISI][Medline].

10.   Hoffer, JA, Caputi AA, Pose IE, and Griffiths RI. Roles of muscle activity and load on the relationship between muscle spindle length and whole muscle length in the freely walking cat. Prog Brain Res 80: 75-85, 1989[ISI][Medline].

11.   Hooley, CJ, McCrum NG, and Cohen RE. The viscoelastic deformation of tendon. J Biomech 13: 521-528, 1980[ISI][Medline].

12.   Huijing, PA, and Woittiez RD. The effect of architecture on skeletal muscle performance: a simple planimetric model. Neth J Zool 34: 21-32, 1984.

13.   Ker, RF. Dynamic tensile properties of the plantaris tendon of sheep (Ovis aries). J Exp Biol 93: 283-302, 1981[Abstract/Free Full Text].

14.   Ker, RF, Alexander RM, and Bennet MB. Why are mammalian tendons so thick? J Zool Lond 216: 309-324, 1981.

15.   Komi, PV. Relevance of in vivo force measurements to human biomechanics. J Biomech 23: 23-34, 1990.

16.   Nicol, C, Komi PV, and Marconnet P. Effects of marathon fatigue on running kinematics and economy. Scand J Med Sci Sports 1: 195-204, 1991.

17.   Pollock, CM, and Shadwick RE. Relationship between body mass and biomechanical properties of limb tendons in adult mammals. Am J Physiol Regulatory Integrative Comp Physiol 266: R1016-R1021, 1994[Abstract/Free Full Text].

18.   Rack, PM, and Ross HF. The tendon of flexor pollicis longus: its effects on the muscular control of force and position at the human thumb. J Physiol (Lond) 351: 99-110, 1984[Abstract/Free Full Text].

19.   Rack, PM, Ross HF, Thilmann AF, and Walters DK. Reflex responses at the human ankle: the importance of tendon compliance. J Physiol (Lond) 344: 503-524, 1983[Abstract/Free Full Text].

20.   Riemersma, DJ, and Schamhardt HC. The cryo-jaw, a clamp designed for in vitro rheology studies of horse digital flexor tendons. J Biomech 15: 619-620, 1982[ISI][Medline].

21.   Riemersma, DJ, and Schamhardt HC. In vitro mechanical properties of equine tendons in relation to cross-sectional area and collagen content. Res Vet Sci 39: 263-270, 1985[ISI][Medline].

22.   Shadwick, RE. Elastic energy storage in tendons: mechanical differences related to function and age. J Appl Physiol 68: 1033-1040, 1990[Abstract/Free Full Text].

23.   Van Brocklin, JD, and Ellis DG. A study of the mechanical behaviour of toe extensors tendons under applied stress. Arch Phys Med Rehabil 46: 369-373, 1965[Medline].

24.   Van der Vegt, AK. Polymeren---van keten tot kunststof. Delft, The Netherlands: Delftse Uitgevers Maatschappij, 1991.

25.   Viidik, A. Mechanical properties of parallel-fibred collagenous tissues. In: Biology of Collagen, edited by Viidik A, and Vuust J.. London: Academic, 1980, p. 237-255.

26.   Voigt, M, Bojsen-Moller F, Simonsen EB, and Dyhre-Poulsen P. The influence of tendon Youngs modulus, dimensions and instantaneous moment arms on the efficiency of human movement. J Biomech 28: 281-291, 1995[ISI][Medline].

27.   Voigt, M, Dyhre-Poulsen P, and Simonsen EB. Modulation of short latency stretch reflexes during human hopping. Acta Physiol Scand 163: 181-194, 1998[ISI][Medline].

28.   Voigt, M, and Klausen K. Optimal running economy among elite runners may be related to a low relative level of muscle activation (Abstract). In: Proceedings of the XVI Congress of the International Society of Biomechanics, Tokyo, Japan. Tokyo: Univ. of Tokyo, 1997, p. 204.

29.  Voigt M, Komi PV, Jarvinen M, and Bojsen-Moller F. Electromechanical delay and phase shift between triceps surae EMG and tendon force in man during natural movement (Abstract). In Proceedings of the XIV International Congress on Biomechanics, Paris. Paris: Société de Biomécanique, 1993, p. 1426-1427.

30.   Wang, XT, and Ker RF. Creep rupture of wallaby tail tendons. J Exp Biol 198: 831-845, 1995[Abstract].

31.   Wang, XT, Ker RF, and Alexander RM. Fatigue rupture of wallaby tail tendons. J Exp Biol 198: 847-852, 1995[Abstract].

32.   Wickiewicz, TL, Roy RR, Powell PL, and Edgerton VR. Muscle architecture of the human lower limb. Clin Orthop 179: 275-283, 1983.

33.   Woo, SL, Gomez MA, Amiel D, Ritter MA, Gelberman RH, and Akeson WH. The effects of exercise on the biomechanical and biochemical properties of swine digital flexor tendons. J Biomech Eng 103: 51-56, 1981[ISI][Medline].

34.   Woo, SL, Ritter MA, Amiel D, Sanders TM, Gomez MA, Kuei SC, Garfin SR, and Akeson WH. The biomechanical and biochemical properties of swine tendons---long term effects of exercise on the digital extensors. Connect Tissue Res 7: 177-183, 1980[ISI][Medline].

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