Skip to main content
NCBI home page
The Journal of Physiology logoLink to The Journal of Physiology
. 2001 Feb 15;531(Pt 1):277–288. doi: 10.1111/j.1469-7793.2001.0277j.x

Load–displacement properties of the human triceps surae aponeurosis in vivo

S Peter Magnusson *, Per Aagaard *, Sofie Rosager *, Poul Dyhre-Poulsen *, Michael Kjaer *
PMCID: PMC2278435  PMID: 11179410

Abstract

  1. The present investigation measured the Load–displacement and stress-strain characteristics of the proximal and distal human triceps surae aponeurosis and tendon in vivo during graded voluntary 10 s isometric plantarflexion efforts in five subjects.

  2. During the contractions synchronous real-time ultrasonography of aponeurosis displacement, electromyography of the gastrocnemius, soleus and dorsiflexor muscles, and joint angular rotation were obtained. Tendon cross-sectional area and moment arm were obtained from magnetic resonance (MR) images. Force and electromyography data from dorsiflexion efforts were used to examine the effect of coactivation.

  3. Tendon force was calculated from the joint moments and tendon moment arm, and stress was obtained by dividing force by cross-sectional area. Aponeurosis and tendon strain were obtained from the displacements normalised to tendon length.

  4. Tendon force was 3171 ± 201 N, which corresponded to 2.6% less than the estimated force when coactivation was accounted for (3255 ± 206 N). Aponeurosis displacement (13.9–12.9 mm) decreased 30 % (9.6–10.7 mm) when accounting for joint angular rotation (3.6 deg). Coactivation and angular rotation-corrected stiffness yielded a quadratic relationship, R2= 0.98± 0.01, which was similar for the proximal (467 N mm−1) and distal (494 N mm−1) aponeurosis and tendon. Maximal strain and stress were 4.4–5.6 % and 41.6 ± 3.9 MPa, respectively, which resulted in a Young’s modulus of 1048–1474 MPa.

  5. The mechanical properties of the human triceps surae aponeurosis and tendon in vivo were for the first time examined. The stiffness and Young’s modulus exceeded those previously reported for the tibialis anterior tendon in vivo, but were similar to those obtained for various isolated mammalian and human tendons.

The force from muscle contraction is transferred to bone via tendons to produce joint movement. Tendons are, however, not inextensible, but have non-linear spring-like characteristics, which allows for a dynamic mechanical interaction between the muscle and tendon (Griffiths & Selesnick, 1998; Lieber et al. 2000). During locomotion the tendon is stretched and energy is stored which is subsequently converted into kinetic energy upon release (Alexander & Vernon, 1975; Ker et al. 1988).

Although it has been recognised that tendon properties contribute to the complex interaction of the central nervous system, muscle-tendon unit and bony structures to produce joint movement, there is scarce information on human tendon behaviour in vivo. Moreover, investigations of human tendon behaviour have largely been limited to biomechanical testing of isolated cadaver tissue specimens (Rack & Ross, 1984; Goldstein et al. 1987; Loren & Lieber, 1995; McGough et al. 1996), or invasive in vivo methods (Amis et al. 1987; Fellows & Rack, 1987). Therefore, the recent advance of using real-time ultrasonography to non-invasively determine fascicle movement during muscle contraction has provided a method for studying human aponeurosis and tendon tissue behaviour during isometric muscle contraction in vivo (Fukashiro et al. 1995a; Ito et al. 1998).

Thus far, the mechanical properties of the tibialis anterior in the leg have been examined using ultrasonography during voluntary (Ito et al. 1998) and electrically induced (Maganaris & Paul, 1999) contractions, with considerably different results with respect to both tendon force and deformation. The dissimilarities may in part be explained by the different methodologies. In this context, it should be noted that previous studies (Ito et al. 1998; Maganaris & Paul, 1999) have not accounted for the potential error in tendon displacement due to joint angular rotation, or the tendon load attributed to coactivation of the antagonist muscles during the isometric contraction.

Since the aponeurosis of the triceps surae complex and Achilles’ tendon is subject to appreciable stresses during human locomotion, the in vivo study of their mechanical properties is of considerable interest and relevant to loading history and ageing. Furthermore, the Achilles’ tendon is frequently associated with various pathologies related to loading history (Kannus et al. 1997), including complete tendon ruptures (Kannus & Jozsa, 1991). While several studies have estimated Achilles’ tendon force during various activities (Scott & Winter, 1990; Fukashiro et al. 1995b; Finni et al. 1998; Giddings et al. 2000) aponeurosis deformation of the triceps surae has thus far not been measured. Therefore, the purpose of the present investigation was to (1) measure the load- displacement and stress-strain characteristics of the human triceps surae aponeurosis and tendon in vivo, during graded maximal voluntary plantarflexion efforts and (2) examine whether the Load–displacement characteristics of the proximal and distal aponeurosis differed.

METHODS

Subjects

The study conformed to the Declaration of Helsinki and was approved by the Copenhagen Ethics Committee (KF 01-277/99). Five healthy male subjects gave written informed consent to participate in the study. The mean ±s.d. age, body mass and height were 37 ± 3 years, 72.4 ± 5.0 kg and 1.8 ± 0.03 m, respectively.

Experimental set-up

The mechanical properties of the proximal and distal aponeurosis and tendon of the left leg were examined with the ankle in the neutral position and with the tibia at right angles to the sole of the foot. The subjects were seated in a rigid steel frame (Fig. 1) with the knee fully extended and the hip flexed to 90 deg. The foot rested against an adjustable steel foot plate with a mechanical axis of rotation that corresponded to the lateral malleolus. To register plantarflexion force (N) a strain gauge load cell was attached between the foot plate and the steel frame. The backrest of the frame was adjusted to prevent displacement between the foot and foot plate, and between the back and the backrest during maximal plantarflexion efforts.

Figure 1. Measurement set-up.

Figure 1

Open in a new tab

A, the subjects were seated in a rigid steel frame with the knee extended and the hip flexed to 90 deg. The foot rested against an adjustable steel foot plate with a mechanical axis of rotation that corresponded to the lateral malleolus. (1) EMG activity of the medial gastrocnemius (not shown), soleus and dorsiflexor muscles were registered. (2) Joint angular change was monitored with an electrical goniometer. (3) To register plantarflexion force (N) a strain gauge load cell was attached between the foot plate and the steel frame. One computer was used to sample 1-3, while a separate computer was used to sample the ultrasound data. The two computers were interconnected electronically to ensure that all signal sampling was synchronous. Synchronisation between the computers was achieved with a custom-built device that provided a visual marker on the ultrasound image and simultaneously initiated data sampling of force, EMG and joint angular change via the A/D converter. B, the connective tissue length (Lo) of the triceps surae complex (free tendon and aponeurosis) was obtained by measuring the distance from the sole of the foot to the proximal (a) and distal point (b) of the fascicle aponeurosis cross-point on the ultrasound image at rest.

Experimental design

After positioning the subjects performed minimally three and maximally eight forceful plantarflexion efforts that served as pre-conditioning of the muscle-tendon complex. Thereafter, the subjects performed a slow isometric force ramp by gradually increasing plantarflexion effort over a 10 s period (Trial 1) while proximal aponeurosis displacement, plantarflexion force, electromyography signals and ankle joint angle were measured. After a 1 min rest the plantarflexion effort was repeated (Trial 2). The ultrasound probe was then positioned over the most distal portion of the aponeurosis overlying the soleus muscle and the above-described procedure was repeated (Trials 1 and 2). Thereafter, two separate 4 s maximal voluntary contractions (MVCs) were performed for ankle dorsiflexor muscle strength.

Measurement of electromyographic activity

Electromyographic (EMG) activity of the medial gastrocnemius, soleus and dorsiflexor muscles was registered using bipolar Ag-AgCl surface electrodes (Medicotest, Type QN-10-A, Olstykke, Denmark) with a 3 cm interelectrode distance. Custom-made amplifiers with a frequency response of 20 Hz to 10 kHz and 1:1 pre-amplifiers were used for the EMG signal measurements. The EMG signal was full-wave rectified, integrated and averaged with a time constant of 200 ms and expressed in microvolts (Basmajian & DeLuca, 1985). The EMG was normalised to the maximal amplitudes during the trials. The EMG for the dorsiflexor muscles was normalised to the maximal amplitude during the dorsiflexion effort (see below).

Measurement of tendon displacement

A 7.5 MHz linear array B-mode ultrasound probe (Sonoline Sienna, Siemens, Erlangen, Germany) with a width and depth resolution of 0.51 and 0.34 mm, respectively, was used for imaging. For the measurement of distal aponeurosis displacement the probe was placed in the saggital plane over the most distal identifiable portion of the soleus muscle. When the distal aponeurosis is followed in the proximal (cephalic) direction it continues underneath the gastrocnemius muscle. For the measurement of proximal aponeurosis displacement the probe was placed in the saggital plane over the most distal (caudal) part of the medial gastrocnemius head. The ultrasound probe was tightly fitted into a block of rigid polystyrene plastic (Styrofoam) that was taped onto the skin of the subjects. In accordance with previous reports (Maganaris & Paul, 1999), pilot work demonstrated that the ultrasound probe did not shift position during muscular contraction in relation to an echo-absorptive marker placed on the skin.

The parallel echoes that can be observed on the ultrasound image correspond to the aponeurosis between muscle fascicles (Fukashiro et al. 1995a; Ito et al. 1998) (Fig. 2). The cross-point of ultrasound echoes from a fascicle and the aponeurosis was defined as the position where the fascicle was affixed. The displacement of this fixation point was considered to represent the magnitude of displacement (mm) of the aponeurosis. The ultrasound image was displayed in real time on the ultrasound monitor. The S-VHS output video signal from the ultrasound apparatus was fed to a computer (Fig. 1) for data collection at a rate of 50 Hz. The ultrasound image was also visualised in real time on the PC monitor.

Figure 2. Sonography of the proximal aponeurosis.

Figure 2

Open in a new tab

GA, gastrocnemius muscle; SO, soleus muscle. The measurement was performed along the length of aponeurosis from the white vertical bar to the end of the ultrasound (US) field. Note the shift in the displacement of the aponeurosis to the left during the graded isometric contraction effort from rest to 2000 N of tendon force. The US data presented correspond to subject a in Fig. 8. The aponeurosis between the gastrocnemius and the soleus muscle was seen on the ultrasound as two distinct entities with a small separating space. This was noted in all subjects.

Measurement of angular ankle joint rotation

It has been shown that passive angular rotation about a joint results in considerable tendon displacement (Spoor et al. 1990), and that the relationship between tendon displacement and joint angular rotation is linear (Fukunaga et al. 1996). Therefore, should any angular joint rotation occur in the direction of plantarflexion during an ‘isometric’ contraction, tendon displacement will be attributed to both angular rotation and contractile tension. It is extremely difficult to completely prevent any joint angular rotation during a forceful muscular contraction with external strap fixation, especially during plantarflexion, which can yield very large forces. Thus, angular joint rotation needs to be accounted for to avoid an overestimation of tendon displacement during an isometric contraction. Therefore, to monitor ankle joint angular rotation an electrical goniometer (Penny and Giles, Biometrics Ltd, Gwent, UK) was placed on the lateral aspect of the foot. The electrical goniometer end blocks were secured with tape over the distal part of the fifth metatarsal and the posterolateral aspect of the fibula. The ratio of tendon displacement (Δmm) to angular rotation (Δrad) about a joint corresponds to the estimated tendon moment arm (Spoor et al. 1990; Fukunaga et al. 1997; Ito et al. 1998). Therefore, the product of the tendon moment arm and angular rotation (rad) yielded the estimated tendon displacement caused by joint rotation alone. The tendon moment arm was measured from MR images (see details below). Thus, for each subject the tendon displacement obtained from the ultrasound images could be corrected for that attributed to joint rotation alone.

Measurement of maximal plantarflexion and dorsiflexion moment

In addition to the plantarflexion displacement trials the subjects performed two dorsiflexion MVC efforts. Each effort lasted for ∼4 s with a 1 min rest period. Dorsiflexion was performed with the subject in a seated position with the hips and knees in 90 deg of flexion. A strap was placed over the distal part of the metatarsals and connected to the load cell, which was secured to the floor. The foot was placed in the neutral position (90 deg) for the dorsiflexion effort. The product of the distance from the strap to the centre of rotation (obtained from MR images, see below) and the registered force yielded the dorsiflexion moment (N m). The force and moment generated due to dorsiflexor muscles coactivation during the plantarflexion efforts was estimated assuming a linear relationship between EMG amplitude of the dorsiflexor muscles and tension (Lippold, 1952).

Data acquisition

The goniometer, EMG, strain gauge load cell and ultrasound image signals were continuously recorded immediately prior to and during the 10 s plantarflexion effort (Fig. 3). The goniometer, EMG and force signals were sampled at 50 Hz using an A/D converter (DT 2801A, Data Translation), and stored on a computer for subsequent analysis. The ultrasound images were simultaneously and continuously sampled on a separate computer. The two computers (a and b in Fig. 1) were interconnected electronically to ensure that all signal sampling was synchronous. Synchronisation between the two computers was achieved with a custom-built device that provided a visual marker on the ultrasound image and simultaneously initiated data sampling of force, EMG and the goniometer via the A/D converter.

Figure 3. The synchronised data recorded during a 10 s plantarflexion effort for one subject.

Figure 3

Open in a new tab

A, the dorsiflexor EMG activity normalised to its maximum amplitude during maximum isometric dorsiflexion. B and C, the gastrocnemius (B) and soleus (C) EMG activity normalised to its maximum amplitude during maximum isometric dorsiflexion. D, the proximal aponeurosis displacement recorded with the ultrasonography, and corrected for joint angular motion. E, joint angular motion (deg). F, the tendon force (N) has been calculated using tendon moment arm data from MR images, and corrected for antagonist coactivation.

Calculation of moment arm

Saggital plane MR images (GE Signa horizon LX 1.5T, T2 weighted FSE, TR/TE: 4000/88; FOV 12; matrix 256 × 192, slice thickness 3 mm) were obtained with the ankle in the neutral position (90 deg) to estimate the Achilles’ tendon moment arm using a modified Reuleaux method (Voigt, 1994). Briefly, the method assumes that the joint surface of the talus is circular and by using geometric rules obtains a centre of rotation at a specific point distal to the joint surface of the talus. The tendon moment arm was obtained by measuring the perpendicular distance from the Achilles’ tendon to the centre of rotation. The measurement of the moment arm from the MR images was performed 3 times for each subject and the mean was used as an estimate for the moment arm. The mean coefficient of variation for repeated measures across subjects was 1.9 %.

Calculation of tendon force

The tendon (and aponeurosis) force in triceps surae during the plantarflexion effort was calculated by dividing the externally measured moment by the tendon moment arm. Separately, the contribution from the dorsiflexor moment was added to the externally measured moment to compensate for coactivation.

Measurement of tendon cross-sectional area and calculation of tendon stress

Tendon cross-sectional area was obtained from MR images (T1 weighted SE, TR/TE: 400/15; FOV 12; matrix 512 × 512, slice thickness 6 mm). The cross-sectional area of the Achilles’ tendon was measured 3 cm proximal to its insertion onto the calcaneus, which corresponds to the narrowest portion of the Achilles’ tendon (Voigt, 1994). The measurement was performed 3 times for each subject and the mean was used as the cross-sectional area. The mean coefficient of variation for repeated measures across subjects was 5.8 %.

Measurement of tendon length and calculation of tendon strain

For the purpose of this study the connective tissue length (Lo) of the triceps surae complex (free tendon and aponeurosis) was obtained by measuring the distance from the sole of the foot to the proximal and distal point of the fascicle aponeurosis cross-point on the ultrasound image at rest (Fig. 1B). Strain (ε) was calculated by dividing aponeurosis cross-point displacement (ΔL, mm) during plantarflexion by Lo.

Calculation of tendon stiffness and Young’s modulus

A quadratic fit was applied to the Load–displacement data for each person. Thereafter the structural stiffness (N mm−1) was calculated from the Load–displacement relationship in the final 10 % of the force range, i.e. from 90 to 100 %. Stiffness was calculated (1) without correction for ankle rotation, (2) with correction for ankle rotation, and (3) with correction for ankle rotation and coactivation of dorsiflexor and plantarflexor muscles (Fig. 4). Similarly, the Young’s modulus (MPa) of the Achilles’ tendon (3 cm from the insertion) was estimated by dividing the stress (σ, N m−2) by the strain (ε) obtained at the level of the soleus in the final 10 % of stresses (90-100 %).

Figure 4. The Load–displacement curve for one subject.

Figure 4

Open in a new tab

○, without any correction for ankle joint rotation; •, corrected for tendon movement attributed to ankle joint rotation. ▵, corrected for ankle joint rotation and antagonist coactivation. The mechanical stiffness (N mm−1) was calculated from the Load–displacement relationship in the final 10 % of the force range, i.e. from 90 to 100 % based on the quadratic fit.

Data reduction and statistics

All signals were considered at baseline with the subject completely relaxed in the experimental set-up. The ultrasound images were identified and analysed at tendon force intervals of 200 N. The displacement for each ultrasound image was measured 3 times and the mean was used for analysis. Student’s two-tailed t tests were used to examine if displacement for proximal and distal aponeurosis at 2000 N differed between trials 1 and 2, and if the Load–displacement properties of proximal and distal aponeurosis differed. Pearson’s correlation coefficient was used to examine the strength of the relationships between the variables in trials 1and 2. A P value of 0.05 was considered significant. Results are reported as population means (± standard error of the mean, s.e.m.) unless otherwise indicated.

RESULTS

The maximal isometric plantarflexion effort yielded a moment about the ankle of 161 ± 11 N m with a corresponding EMG activity of 194 ± 21 μV for the gastrocnemius muscle, and 231 ± 29 μV for the soleus muscle. The maximal isometric dorsiflexion effort yielded a moment about the ankle of 38 ± 3 N m with a corresponding EMG activity of 282 ± 48 μV for the dorsiflexor muscles. The maximal dorsiflexor muscle activity during the plantarflexion effort was 16 ± 3 % of its amplitude during dorsiflexion.

The data from the MR images yielded an Achilles’ tendon moment arm of 51 ± 1 mm, and a tendon cross-sectional area of 78.1 ± 5.6 mm2. The calculated tendon force was 3171 ± 201 N, which corresponded to 97.4 ± 0.4 % of the estimated tendon force when dorsiflexor muscle coactivation was accounted for (3255 ± 206 N).

There was no difference in the angle-corrected aponeurosis displacement at 2000 N in trial 1 (7.6 ± 0.8 mm) and trial 2 (7.4 ± 0.9 mm). There was a significant relationship between the two trials (proximal and distal, n= 10; r= 0.96, P < 0.001), and the coefficient of variation for repeated measures was 11.3 %.

Proximal aponeurosis

During the graded plantarflexion effort the maximal ankle joint angular displacement was 3.6 ± 1.1 deg from neutral in the direction of plantarflexion. The measured maximal aponeurosis displacement was 13.9 ± 1.6 mm. There was a significant decrease in displacement when ankle joint angular rotation was corrected for (10.7 ± 1.3 mm, P < 0.001). The Load–displacement curves for the joint angular rotation and coactivation-corrected load yielded a significant quadratic relationship, R2= 0.97± 0.01 (P < 0.0001; Fig. 4). The calculated stiffness for the proximal aponeurosis is shown in Fig. 5A. There was a significant increase in stiffness when ankle joint displacement was accounted for (P < 0.01). There was a further elevation in stiffness when the antagonist muscle coactivation was accounted for (P= 0.05). The displacement for the proximal aponeurosis and the cross-sectional area of the Achilles’ tendon yielded an estimated maximal strain and stress of 4.4 ± 0.5 % (Lo= 248 ± 11 mm) and 41.6 ± 3.9 MPa, respectively, with a resulting Young’s modulus of 1474 ± 100 MPa. Individual subject data are shown in Table 1.

Figure 5. The mechanical stiffness for the proximal and distal aponeurosis.

Figure 5

Open in a new tab

The bars show group means ±s.e.m. The mechanical stiffness (N mm−1) for the proximal (A) and distal (B) aponeurosis (1) without any correction for ankle joint rotation, (2) corrected for tendon movement attributed to ankle joint rotation, and (3) corrected for ankle joint rotation and antagonist coactivation. There was a sigificant increase in the stiffness when ankle joint angular rotation was accounted for (**P < 0.01) and when antagonist coactivation was accounted for (*P < 0.05).

Table 1. Individual data obtained for the proximal aponeurosis during a ramp isometric contraction.

Subject Force (N) Angle (deg) Displacement (mm) Stiffness (N mm-1) CSA (mm2) Stress (MPa) Lo (mm) Strain (%) Modulus (MPa)
1 3603 (3736) 7.6 15.8 (9.3) 470 (469) 76.3 47.4 233 4.0 1362
2 3637 (3695) 2.9 15.4 (12.6) 404 (390) 72.3 50.5 215 5.9 1187
3 2605 (2658) 1.2 8.0 (7.0) 693 (667) 96.7 27.1 260 2.7 1806
4 2804 (2917) 3.8 17.8 (14.2) 394 (371) 69.0 40.6 285 5.0 1556
5 3204 (3271) 2.6 12.7 (10.6) 468 (437) 76.0 42.1 250 4.2 1456
Mean 3171 (3255) 3.6 13.9 (10.7) 486 (467) 78.1 41.6 249 4.4 1474
Open in a new tab

Force is the estimated Achilles’ tendon force. Angle is the joint rotation in the direction of plantarflexion. Displacement is the aponeurosis displacement measured with ultrasound during the contraction. CSA is the cross-sectional area of the Achilles’ tendon. Values in parentheses indicate dorsiflexion coactivation-corrected data for force, ankle joint rotation-corrected data for displacement, and force- and angle-corrected data for stiffness. Strain and stress values are based on the coactivation- and ankle rotation-corrected data. Mechanical stiffness and modulus were calculated in the final 10% of the load–displacement and stress–strain relationships, respectively.

Distal aponeurosis

During the graded plantarflexion effort the maximal ankle joint angular rotation was 3.7 ± 1.0 deg from neutral in the direction of plantarflexion. The measured maximal aponeurosis displacement was 12.9 ± 1.4 mm. When ankle joint angular displacement was accounted for there was a significant decrease in displacement (9.6 ± 0.6 mm, P < 0.001). The Load–displacement curves for the joint angular rotation- and coactivation-corrected load yielded a significant quadratic relationship, R2= 0.98± 0.01 (P < 0.0001). The calculated stiffness for the distal aponeurosis is shown in Fig. 5B. There was a significant increase in stiffness when ankle joint rotation was accounted for (P < 0.01). There was a further elevation in stiffness when the antagonist muscle coactivation was accounted for (P < 0.05). The displacement of the distal aponeurosis and the cross-sectional area of the Achilles’ tendon yielded an estimated maximal strain of 5.6 ± 0.4 % (Lo= 177 ± 7 mm) with a resulting Young’s modulus of 1048 ± 93 MPa. Individual subject data are shown in Table 2.

Table 2. Individual data obtained for distal aponeurosis during a ramp isometric contraction.

Subject Angle (deg) Displacement (mm) Stiffness (N mm-1) Lo (mm) Strain (%) Modulus (MPa)
1 6.8 15.7 (9.9) 374 (394) 180 5.5 891
2 5.0 15.2 (10.4) 349 (404) 160 6.5 756
3 1.4 8.3 (7.3) 741 (756) 166 4.4 1248
4 3.8 14.4 (10.9) 362 (371) 203 6.4 1187
5 1.3 10.7 (9.5) 519 (547) 179 5.3 1159
Mean 3.7 12.9 (9.6) 469 (494) 178 5.6 1048
Open in a new tab

Details as in Table 1.

Distal versus proximal aponeurosis

The mean distance between the measurement sites for the distal and proximal aponeurosis displacement was 71 ± 7 mm. The joint angular rotations during the determination of the proximal and distal aponeurosis displacement were similar. Consequently the calculated stiffness was similar in all instances (Figs 5 and 6). Since the absolute displacement did not differ, but the distance between the proximal and distal aponeurosis differed (71 mm), the estimated maximal strain was greater for the distal aponeurosis (5.6 ± 0.4 %) than for the proximal aponeurosis (4.4 ± 0.5 %; P < 0.01), which in turn resulted in a greater Young’s modulus in the latter (Fig. 7).

Figure 6. Absolute Load–displacement data for the proximal and distal aponeurosis after correction for ankle joint rotatation and antagonist coactivation.

Figure 6

Open in a new tab

Data are group means ±s.e.m. The mechanical stiffness (N mm−1) was calculated from the Load–displacement relationship after a quadratic fit was applied for each person. There was no significant difference between the proximal and distal aponeurosis.

Figure 7. Estimated stress-strain for the proximal and distal aponeurosis after correction for ankle joint rotatation and antagonist coactivation based on the quadratic fit.

Figure 7

Open in a new tab

Data are group means ±s.e.m. The quadratic fit yielded somewhat lower ‘maximal’ values than the maximal values reported in Tables 1 and 2. The maximal strain and the Young’s modulus were significantly different for the distal (5.6 ± 0.4 %, 1048 ± 93 MPa) and proximal aponeurosis (4.4 ± 0.5 %, 1474 ± 100 MPa); P < 0.05.

DISCUSSION

The present study demonstrates that the load- displacement of the distal and proximal human triceps surae aponeurosis can be measured in a reproducible manner in vivo, during an isometric contraction. Further, the data show that the absolute displacement (mm) of the proximal and distal aponeurosis did not differ, such that the stiffness (N mm−1) was similar for the two regions. In addition, the measurement method suggests that the ankle joint motion needs to be accounted for during an ‘isometric’ contraction since even small amounts of joint rotation will contribute to tendon movement and thereby incorrectly add to the actual tendon displacement attributed to muscle tensile loading itself. Moreover, the antagonist muscle coactivation influenced the Achilles’ tendon force in a relatively small, but significant, way such that tendon force was underestimated by ∼2.6 %.

A pertinent question to address is whether the Load–displacement data obtained during the isometric plantarflexion effort in the present study are comparable to the loads imposed on the tendon during functional activities. It should be noted that direct measurements of actual human tendon forces in vivo are rather scarce. Using biomechanical models it has been estimated that the human Achilles’ tendon force may reach 4 times body weight (2600 N) during walking (Giddings et al. 2000) and 6-8 times body weight (3100-5330 N) during running (Scott & Winter, 1990; Giddings et al. 2000). Using a fibre optic technique (Finni et al. 1998) an Achilles’ tendon force of 1430 N was measured during walking, while tendon forces of 1895-3786 N were obtained with a buckle transducer during various jumping activities (Fukashiro et al. 1995b). However, tendon deformation was not measured in the above-mentioned studies. In the present study the tendon force during the maximal isometric plantarflexion effort was 4-5 times body weight (∼3200 N), which suggests that the load- displacement data were obtained at a tendon loading comparable to those imposed on the Achilles’ tendon during human locomotion and jumping

The calculation of tendon force may be underestimated in the presence of any antagonist muscle coactivation. During dynamic muscle contraction the relative magnitude of antagonist coactivation may be 15-35 % of its activity as an agonist (Aagaard et al. 2000). Albeit not examined, it has been suggested that the markedly different Load–displacement data of human tibialis anterior aponeurosis in vivo (Ito et al. 1998; Maganaris & Paul, 1999) may be attributed to an underestimation of tendon load due to antagonist coactivation (Maganaris & Paul, 1999). In the present study the isometric antagonist coactivation of the dorsiflexor muscles was 16 % of its activity as an agonist. However, the ability of the dorsiflexor muscle group to generate static moment about the ankle joint is relatively small compared to that of the triceps surae complex. In the present study the mean maximal isometric joint dorsiflexion moment was 24 % of the maximal plantarflexion moment. Therefore, the 16 % coactivation of the dorsiflexor muscles resulted in an underestimation of Achilles’ tendon force by merely 2.6 %. However, it should be noted that although this underestimate was relatively small it contributed significantly to the calculated aponeurosis and tendon stiffness (see Fig. 5), such that the stiffness was elevated by 4.8 % when the coactivation was accounted for.

Joint motion will result in tendon and aponeurosis displacement (Spoor et al. 1990; Fukunaga et al. 1996). Thus, since isometric contraction of muscle about a joint will produce more or less angular joint rotation in the direction of the intended movement, the resulting tendon and aponeurosis displacement is the result of displacement attributed to both joint angular rotation and contractile tensile loading. The present data demonstrate the importance of accounting for even small amounts of joint motion: Despite a rigid frame that was adjusted separately for each subject the average plantarflexion motion was 3.6 deg, which resulted in an overestimation of the displacement by up to ∼30 %. Although it is presumably easier to stabilise the ankle joint during an isometric dorsiflexion contraction, which involves tendon forces considerably smaller than those in the present study, it is possible that the lack of attention to displacement attributed to joint rotation may explain some of the previous differences in tibialis anterior tendon deformation (Ito et al. 1998; Maganaris & Paul, 1999).

The present study showed that the aponeurosis operates as one functional unit during an isometric contraction since the absolute amount of displacement, and consequently the stiffness, is similar throughout, as evidenced by the lack of difference in displacement for the proximal and distal aponeurosis of the triceps surae. This is in accordance with the data of Trestik & Lieber (1993) who demonstrated that the frog aponeurosis had similar mechanical properties throughout its length during passive loading. Thus the aponeurosis may operate as a functional unit during both passive loading and active contraction. Interestingly, it has been shown that the aponeurosis strain properties appear to be influenced by the type of loading, such that strain is lower during active contraction versus passive loading (Lieber et al. 2000). It should be noted that the aponeurosis is a complex structure with the maximal width near its proximal end and width decreasing distally. Moreover, in the cat soleus muscle it has been shown that there is a gradient in the thickness of the aponeurosis, such that it becomes thicker more distally (Scott & Loeb, 1995). It has been suggested that the thickness varies in proportion to the gradient in force transmitted across the structure so that strain will be distributed uniformly (Scott & Loeb, 1995). Although the present model did not not address such morphological complexities, the data appear to support the notion of uniform strain distribution across the aponeurosis of the human triceps surae in vivo.

The transmission of force to bone to produce limb motion is generated by contracting extrafusal muscle fibre, and it is well recognised that afferent feedback to the CNS is important for the control and modulation of movement. The intrafusal muscle spindle is an important ‘sensor’ of muscle length, but the amount of length change that tendinous tissue undergoes during muscle contraction may influence that seen by the muscle spindle and thereby profoundly influence afferent feedback control of movement (Rack & Westbury, 1984; Hoffer et al. 1989; Elek et al. 1990). Nevertheless, data on the amount of tendinous displacement and its role in muscle spindle length changes have been contradictory (Hoffer et al. 1989; Elek et al. 1990; Griffiths, 1991). If the tendinous tissues were essentially inextensible the muscle spindle would sense length changes similar to that of the whole muscle. Conversely, if the tendinous tissue stretched considerably during the contraction the length change sensed by the muscle spindle could be substantially variable (Hoffer et al. 1989; Elek et al. 1990). Hoffer et al. (1989) compared the length of the muscle spindle to the whole length of the muscle for the medial gastrocnemius muscle in the walking cat and observed that the length changes imposed on the muscle spindle did not parallel those of the whole muscle during the step cycle. In fact, the discrepancy between the muscle length and spindle length in the weight-bearing phase of locomotion amounted to 20 % of the overall length change. The considerable divergence was ascribed to the compliant tendinous structures, and the authors suggested that the incongruity would require re-interpretation of fusimotor control (Hoffer et al. 1989). In contrast, Elek et al. (1990) showed that tendinous length change of the medial gastrocnemius in the cat during a normal cat step cycle amounted to ∼2.5-5 % while any discrepancy in muscle spindle discharge was subtle. Accordingly Elek et al. (1990) suggested that, although tendinous displacement may present small inaccuracies, it does not introduce fundamental errors to fusimotor control. In an in vivo human model it was shown that during isometric contractions the tendon of the long head of biceps lengthened by ∼2 % without any intramuscular phase reversals during rapid movements, which suggests that length changes of the muscle spindles are in phase with joint movements (Amis et al. 1987). The data of the present study show that human in vivo tendinous strain of the triceps surae complex at isometric loads comparable to those associated with locomotion is in agreement with the results of Elek et al. and Amis et al. (see Fig. 7), and therefore appears to confirm that any error introduced to fusiomotor control is relatively small during isometric contraction.

Whether the free tendon and the aponeurosis have similar mechanical properties has not been firmly established. Trestik & Lieber (1993) showed that in the frog gastrocnemius muscle the proximal aponeurosis and the distal free tendon had similar mechanical properties during passive loading, and were thus considered to be one functional unit. Scott & Loeb (1995) also demonstrated that the free tendon and aponeurosis in the cat triceps surae have similar mechanical properties during isometric contraction. In contrast, it has been suggested that the stiffness of the aponeurosis is less than that of the free tendon during contraction (Delgado-Lezama et al. 1997), while Lieber et al. (1991) showed that the frog semitendinosis tendon strain was 2 % while aponeurosis strain was 8 % during passive loading to a tension equal to maximum isometric tension. The present study found that the absolute displacement of the aponeurosis will be the same regardless of the measurement site. Thus, the initial length (Lo), estimated as the distance from the most distal attachment of the tendon to the initial cross-point on the ultrasound in the present study, will have a pronounced influence on the estimated tendon tensile strain (ΔL/Lo) (see Fig. 7). Previous reports on human in vivo tendon strain of tibialis anterior tendon has defined Lo as the length from origin to insertion (Maganaris & Paul, 1999), and as the insertion to the initial cross-point on the ultrasound (Ito et al. 1998). The dissimilar definitions (Maganaris & Paul, 1999) may have contributed to the reported differences in strain, and consequently calculations of Young’s modulus. Furthermore, it should be noted that strain in the present and the above-mentioned sonography studies is the accumulated strain of the aponeurosis and free tendon.

Previous investigations of human tendon behaviour have mainly been confined to biomechanical testing of isolated cadaver tissue specimens, which may be influenced by a variety of factors, including storage method, fixation technique, strain rate, actual tendon, donor age, and whether the loading is to failure or is under physiological conditions, i.e contractile loading. Previous investigations have reported stress, strain and Young’s modulus to range from 32 to 111 MPa, 2 to 12 % and 421 to 1724 MPa, respectively, for various isolated human tendon specimens (Gratz, 1931; VanBrocklin & Ellis, 1965; Benedict et al. 1968; Blanton & Biggs, 1970; Butler et al. 1984; Loren & Lieber, 1995; McGough et al. 1996; Schechtman & Bader, 1997). In vivo measurements of stiffness for the tibialis anterior aponeurosis and tendon have been reported to be 32-161 N mm−1 with a Young’s modulus of 530-1200 MPa (Ito et al. 1998; Maganaris & Paul, 1999). The present data are the first measurements of the mechancial properties of the aponeurosis of the human triceps surae in vivo. The obtained stiffness was 467 N mm−1 (range 390-667 N mm−1) with a Young’s modulus of 1474 MPa (range 1108-1806 MPa), which is similar to that obtained for several mammalian (Bennett et al. 1986) and human tendons (Butler et al. 1984). In contrast to the tibialis anterior tendon, the substantially larger passive properties of the Achilles’ tendon in vivo are likely to reflect the greater loads placed on it during locomotion. It has been suggested that the fracture stress for tendon is about 100 MPa (Ker et al. 1988). The safety factor, i.e. the stress during strenuous activity divided by the fracture stress, is about 8 for the majority of tendons (Ker et al. 1988). A safety factor of 4 has been reported for the anterior tibialis tendon (Maganaris & Paul, 1999). In the present study a mean stress value of 42 MPa (range 27-51 MPa) was obtained during maximal isometric contraction, which would yield a safety factor of 2.4, assuming a fracture stress of 100 MPa. Thus, it is plausible that the Achilles’ tendon approaches the safety limit if one considers that the tendon strain and stress are likely to be considerably larger during vigorous functional activities that involve eccentric muscle contractions. At the same time it should be noted that there were considerable distinctions between the tendon properties among the subjects, which is also in accordance with animal data (Scott & Loeb, 1995). These differences may well reflect the substantial intersubject variation in Achilles’ tendon loading during locomotion (Finni et al. 1998), and its resulting adaptation. For example, subjects a and b in Fig. 8 had similar tendon forces, but the stress was almost 50 % lower in subject a due to the larger tendon cross-sectional area (Fig. 8B; a, 96.7 mm2; b, 69.0 mm2). That is, the greater tendon cross-sectional area, and thereby lower stress for a given load, provided for a greater ‘safety factor’ against tendon fracture. At the same time the appreciable contrast in aponeurosis and tendon displacement yielded a marked difference (80 %) in stiffness (Fig. 8A; a, 667 vs. b, 371 N mm−1). However, the pronounced difference was reduced when the structural dimensions were accounted for, which yielded a Young’s modulus of 1806 MPa (a) compared to 1556 MPa (b), suggesting that the qualitative material properties were similar. Interestingly, it has been suggested that increased aponeurosis stiffness results in slower sarcomere shortening for a given fixed-end contraction, which in turn may augment muscle force, and possibly contribute to the risk of muscle tissue injury (Lieber et al. 2000). It has also been shown that tendon ruptures after 4.2 h when it is cyclically loaded with its maximum isometric force (Ker et al. 2000), indicating that the duration of loading may be important for the ability of tendon tissue to avoid ‘overuse injuries’. Whether the distinctions in absolute tendon properties in vivo in the present study are related to elastic storage of energy and muscle performance, or to muscle-tendon injury remains to be established. Since the aponeurosis of the human in vivo triceps surae complex and the Achilles’ tendon is subjected to substantial forces during human locomotion, its mechanical properties are of considerable interest and relevant to the study of loading history (activity/inactivity). Furthermore, the Achilles’ tendon is frequently associated with various pathologies related to loading history (Kannus et al. 1997), including complete ruptures (Kannus & Jozsa, 1991). The present method may be used to partly address these questions in a human in vivo model.

Figure 8. The Load–displacement of the proximal aponeurosis (A) and stress-strain (B) data for 2 subjects (a and b).

Figure 8

Open in a new tab

Note that 2 two subjects have approximately similar tendon forces, but due to an appreciable difference in aponeurosis displacement subject a has a greater stiffness (667 N mm−1) than subject b (371 N mm−1). On the other hand, the stress was almost 50 % lower in subject a due to the larger tendon cross-sectional area. The Young’s modulus was 1806 MPa for subject a and 1556 MPa for subject b.

In conclusion, in the present study the mechanical properties of the distal and proximal human triceps surae aponeurosis in vivo were examined in a reproducible manner during graded maximal voluntary isometric contractions. The method demonstrates the need to take even small amounts of joint angular rotation and antagonist coactivation into account when stiffness is estimated. The proximal and distal aponeurosis displayed equivalent mechanical properties that exceeded those previously reported for the human tibialis anterior tendon in vivo, but were similar to those obtained for various human and mammalian tendons during isolated biomechanical testing procedures. The similar mechancial properties along the length of the aponeurosis appear to support the notion of uniform strain distribution across the apoeurosis of the human triceps surae in vivo.

Acknowledgments

The research was partially funded by the Danish Medical Research Council (98 02 636), the Team Danmark Research Foundation, and The Danish Sports Research Council. The technical expertise of Jan Brond and Egil Gudbrandsen is greatly appreciated.

References

  1. Aagaard P, Simonsen EB, Andersen JL, Magnusson SP, Bojsen-Moller F, Dyhre-Poulsen P. Antagonist muscle coactivation during isokinetic knee extension. Scandinavian Journal of Medicine and Science in Sports. 2000;10:58–67. doi: 10.1034/j.1600-0838.2000.010002058.x. [DOI] [PubMed] [Google Scholar]
  2. Alexander RM, Vernon A. The mechanics of hopping by kangoroos (Macropodidae) Journal of Zoology. 1975;177:265–303. [Google Scholar]
  3. Amis A, Prochazka A, Short D, Trend PS, Ward A. Relative displacements in muscle and tendon during human arm movements. Journal of Physiology. 1987;389:37–44. doi: 10.1113/jphysiol.1987.sp016645. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Basmajian JV, Deluca CJ. Muscles Alive. Their Functions Revealed by Electromyography. 5. Baltimore, MD, USA: Williams & Wilkins; 1985. pp. 94–97. [Google Scholar]
  5. Benedict JV, Walker LB, Harris EH. Stress-strain characteristics and tensile strength of unembalmed human tendon. Journal of Biomechanics. 1968;1:53–63. doi: 10.1016/0021-9290(68)90038-9. [DOI] [PubMed] [Google Scholar]
  6. Bennett MB, Ker RF, Dimery NJ, Alexander RM. Mechanical properties of various mammalian tendons. Journal of Zoology. 1986;209:537–548. [Google Scholar]
  7. Blanton PL, Biggs NL. Ultimate tensile strength of fetal and adult human tendons. Journal of Biomechanics. 1970;3:181–189. doi: 10.1016/0021-9290(70)90005-9. [DOI] [PubMed] [Google Scholar]
  8. Butler DL, Grood ES, Noyes FR, Zernicke RF, Brackett K. Effects of structure and strain measurement technique on the material properties of young human tendons and fascia. Journal of Biomechanics. 1984;17:579–596. doi: 10.1016/0021-9290(84)90090-3. [DOI] [PubMed] [Google Scholar]
  9. Delgado-Lezama R, Raya JG, Munoz-Martinez EJ. Methods to find aponeurosis and tendon stiffness and the onset of muscle contraction. Journal of Neuroscience Methods. 1997;78:125–132. doi: 10.1016/s0165-0270(97)00143-x. [DOI] [PubMed] [Google Scholar]
  10. Elek J, Prochazka A, Hulliger M, Vincent S. In-series compliance of gastrocnemius muscle in cat step cycle: do spindles signal origin-to-insertion length? Journal of Physiology. 1990;429:237–258. doi: 10.1113/jphysiol.1990.sp018254. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Fellows SJ, Rack PM. Changes in the length of the human biceps brachii muscle during elbow movements. Journal of Physiology. 1987;383:405–412. doi: 10.1113/jphysiol.1987.sp016416. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Finni T, Komi PV, Lukkariniemi J. Achilles’ tendon loading during walking: application of a novel optic fiber technique. European Journal Applied Physiology. 1998;77:289–291. doi: 10.1007/s004210050335. [DOI] [PubMed] [Google Scholar]
  13. Fukashiro S, Itoh M, Ichinose Y, Kawakami Y, Fukunaga T. Ultrasonography gives directly but noninvasively elastic characteristic of human tendon in vivo. European Journal of Applied Physiology and Occupational Physiology. 1995a;71:555–557. doi: 10.1007/BF00238560. [DOI] [PubMed] [Google Scholar]
  14. Fukashiro S, Komi PV, Jarvinen M, Miyashita M. vivo Achilles’ tendon loading during jumping in humans. European Journal of Applied Physiology. 1995b;71:453–458. doi: 10.1007/BF00635880. [DOI] [PubMed] [Google Scholar]
  15. Fukunaga T, Ito M, Ichinose Y, Kuno S, Kawakami Y, Fukashiro S. Tendinous movement of a human muscle during voluntary contractions determined by real-time ultrasonography. Journal of Applied Physiology. 1996;81:1430–1433. doi: 10.1152/jappl.1996.81.3.1430. [DOI] [PubMed] [Google Scholar]
  16. Fukunaga T, Kawakami Y, Kuno S, Funato K, Fukashiro S. Muscle architecture and function in humans. Journal of Biomechanics. 1997;30:457–463. doi: 10.1016/s0021-9290(96)00171-6. [DOI] [PubMed] [Google Scholar]
  17. Giddings VL, Beaupre GS, Whalen RT, Carter DR. Calcaneal loading during walking and running. Medicine and Science in Sports and Exercise. 2000;32:627–634. doi: 10.1097/00005768-200003000-00012. [DOI] [PubMed] [Google Scholar]
  18. Goldstein SA, Armstrong TJ, Chaffin DB, Matthews LS. Analysis of cumulative strain in tendons and tendon sheaths. Journal of Biomechics. 1987;20:1–6. doi: 10.1016/0021-9290(87)90261-2. [DOI] [PubMed] [Google Scholar]
  19. Gratz CM. Tensile strength and elasticity tests on human fascia lata. Journal of Bone and Joint Surgery - British Volume. 1931;13:334–340. [Google Scholar]
  20. Griffiths GP, Selesnick FH. Operative treatment and arthroscopic findings in chronic patellar tendinitis. Arthroscopy. 1998;14:836–839. doi: 10.1016/s0749-8063(98)70020-9. [DOI] [PubMed] [Google Scholar]
  21. Griffiths RI. Shortening of muscle fibres during stretch of the active cat medial gastrocnemius muscle: the role of tendon compliance. Journal of Physiology. 1991;436:219–236. doi: 10.1113/jphysiol.1991.sp018547. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Hoffer JA, Caputi AA, Pose IE, Griffiths RI. Roles of muscle activity and load on the relationship between muscle spindle length and whole muscle length in the freely walking cat. Progress in Brain Research. 1989;80:75–85. doi: 10.1016/s0079-6123(08)62201-3. [DOI] [PubMed] [Google Scholar]
  23. Ito M, Kawakami Y, Ichinose Y, Fukashiro S, Fukunaga T. Nonisometric behavior of fascicles during isometric contractions of a human muscle. Journal of Applied Physiology. 1998;85:1230–1235. doi: 10.1152/jappl.1998.85.4.1230. [DOI] [PubMed] [Google Scholar]
  24. Kannus P, Jozsa L. Histopathological changes preceding spontaneous rupture of a tendon. A controlled study of 891 patients. Journal of Bone and Joint Surgery - American Volume. 1991;73:1507–1525. [PubMed] [Google Scholar]
  25. Kannus P, Jozsa L, Natri A, Jarvinen M. Effects of training, immobilization and remobilization on tendons. Scandinavian Journal of Medicine and Science in Sports. 1997;7:67–71. doi: 10.1111/j.1600-0838.1997.tb00121.x. [DOI] [PubMed] [Google Scholar]
  26. Ker RF, Alexander RM, Bennett MB. Why are mammalian tendons so thick. Journal of Zoology. 1988;216:309–324. [Google Scholar]
  27. Ker RF, Wang XT, Pike AV. Fatigue quality of mammalian tendons. Journal of Experimental Biology. 2000;203:1317–1327. doi: 10.1242/jeb.203.8.1317. [DOI] [PubMed] [Google Scholar]
  28. Lieber RL, Leonard ME, Brown CG, Trestik CL. Frog semitendinosis tendon load-strain and stress-strain properties during passive loading. American Journal of Physiology. 1991;261:C86–92. doi: 10.1152/ajpcell.1991.261.1.C86. [DOI] [PubMed] [Google Scholar]
  29. Lieber RL, Leonard ME, Brown-Maupin CG. Effects of muscle contraction on the load-strain properties of frog aponeurosis and tendon. Cells Tissues Organs. 2000;166:48–54. doi: 10.1159/000016708. [DOI] [PubMed] [Google Scholar]
  30. Lippold OC. The relationship between integrated action potentials in a human muscle and its isometric tension. Journal of Physiology. 1952;177:492–499. doi: 10.1113/jphysiol.1952.sp004763. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Loren GJ, Lieber RL. Tendon biomechanical properties enhance human wrist muscle specialization. Journal of Biomechanics. 1995;28:791–799. doi: 10.1016/0021-9290(94)00137-s. [DOI] [PubMed] [Google Scholar]
  32. McGough RL, Debski RE, Taskiran E, Fu FH, Woo SL. Mechanical properties of the long head of the biceps tendon. Knee Surgery. Sports Traumatology, Arthroscopy. 1996;3:226–229. doi: 10.1007/BF01466622. [DOI] [PubMed] [Google Scholar]
  33. Maganaris CN, Paul JP. In vivo human tendon mechanical properties. Journal of Physiology. 1999;521:307–313. doi: 10.1111/j.1469-7793.1999.00307.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. Rack PM, Ross HF. The tendon of flexor pollicis longus: its effects on the muscular control of force and position at the human thumb. Journal of Physiology. 1984;351:99–110. doi: 10.1113/jphysiol.1984.sp015235. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Rack PM, Westbury DR. Elastic properties of the cat soleus tendon and their functional importance. Journal of Physiology. 1984;347:479–495. doi: 10.1113/jphysiol.1984.sp015077. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Schechtman H, Bader DL. vitro fatigue of human tendons. Journal of Biomechanics. 1997;30:829–835. doi: 10.1016/s0021-9290(97)00033-x. [DOI] [PubMed] [Google Scholar]
  37. Scott SH, Loeb GE. Mechanical properties of aponeurosis and tendon of the cat soleus muscle during whole-muscle isometric contractions. Journal of Morphology. 1995;224:73–86. doi: 10.1002/jmor.1052240109. [DOI] [PubMed] [Google Scholar]
  38. Scott SH, Winter DA. Internal forces of chronic running injury sites. Medicine and Science in Sports and Exercise. 1990;22:357–369. [PubMed] [Google Scholar]
  39. Spoor CW, Van LJ, Meskers CG, Titulaer AF, Huson A. Estimation of instantaneous moment arms of lower-leg muscles. Journal of Biomechanics. 1990;23:1247–1259. doi: 10.1016/0021-9290(90)90382-d. [DOI] [PubMed] [Google Scholar]
  40. Trestik CL, Lieber RL. Relationship between Achilles’ tendon mechanical properties and gastrocnemius muscle function. Journal of Biomechanical Engineering. 1993;115:225–230. doi: 10.1115/1.2895479. [DOI] [PubMed] [Google Scholar]
  41. Van Brocklin JD, Ellis DG. A study of the mechanical behavior of toe extensor tendons under applied stress. Archives of Physical Medicine and Rehabilitation. 1965;46:369–373. [PubMed] [Google Scholar]
  42. Voigt M. University of Copenhagen; 1994. Muscle-tendon elaticity in vivo and its significance for human performance. PhD Thesis. [Google Scholar]

Articles from The Journal of Physiology are provided here courtesy of The Physiological Society

RESOURCES