Journal of Biomechanics 35 (2002) 1639–1646

Tensile properties of the in vivo human gastrocnemius tendon Constantinos N. Maganarisa,*, John P. Paulb a

Centre for Biophysical and Clinical Research into Human Movement, Manchester Metropolitan University, Alsager ST7 2HL, UK b Bioengineering Unit, University of Strathclyde, Glasgow G4 0NW, UK Accepted 17 July 2002

Abstract In the present experiment we obtained the tensile properties of the human gastrocnemius tendon, a high-stressed tendon suitable for spring-like action during locomotion. Measurements were taken in vivo in six men. The gastrocnemius tendon elongation during tendon loading
unloading induced by muscle contraction
relaxation was measured using real-time ultrasonography. Tendon forces were calculated from the moment generated during isometric plantarflexion contraction, using tendon moment arm length data obtained in vivo with the tendon travel method. Tendon stiffness data were calculated from the slope of the tendon force
elongation curve, and were then normalized to the tendon’s original dimensions, obtained from morphometric analysis of sonographs, to estimate the tendon Young’s modulus. Mechanical hysteresis values were obtained from area calculations by numerical integration. The elongation of the tendon increased curvilinearly with the force acting upon it, from 1.771 mm (0.870.3% strain) at 87.578.5 N to 11.173.1 mm (4.971% strain) at 875785 N. The tendon Young’s modulus and mechanical hysteresis were 1.1670.15 GPa and 1873%, respectively. These values fall within the range of values obtained from in vitro experiments and are very similar to the respective values recently obtained from in vivo measurements in the less highly stressed human tibialis anterior tendon (1.2 GPa and 19%), thus indicating that the material properties of tendon are independent of physiological loading and function. Combining the present tendon force
elongation data with previously reported Achilles tendon force data recorded during walking indicates that the gastrocnemius tendon would provide B6% of the total external work produced by the locomotor system. This estimate illustrates the contribution of passive elastic mechanisms on the economy and efficiency of walking. The contributions would be greater in more active exercise such as running. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Ultrasonography; Young’s modulus; Mechanical hysteresis; Viscoelasticity; Locomotion

1. Introduction The function of tendons can be classified into two categories: Tensile force transmission, and storage and release of elastic strain energy during locomotion (Ker et al., 1988, 2000; Shadwick, 1990; Pollock and Shadwick, 1994). The action of tendons as force transmitters corresponds to the contractile forces elicited while shortening the in-series muscle to generate joint displacement. On the other hand, they may act as springs when subjected to higher loads associated with initial ground contact forces. Since tendons exhibit adaptive responses to chronic use and disuse (Butler et al., 1978; Woo et al., 1980, 1982), it may be speculated *Corresponding author. Tel.: +44-161-247-5428; fax: +44-161-2476375. E-mail address: [email protected] (C.N. Maganaris).

that they develop over time different material properties in response to differences in physiological loading and function. Results supporting this hypothesis have been reported by Shadwick (1990), who showed that the swine digital flexor tendons (high-stressed tendons involved in spring-like actions) are intrinsically stiffer and more rebound resilient than the digital extensor tendons (low-stressed tendons whose main function is force transmission). However, in a later study, Pollock and Shadwick (1994) examined several mammals and showed that the material properties of tendon are independent of physiological loading and function. Similarly, Ker et al. (2000) and Pike et al. (2000) showed that the Young’s modulus of several wallaby and sheep tendons is independent of the maximal isometric stress that these tendons would be subjected to in real life. The above experiments have been performed on animal tendons, some of which may have undergone

0021-9290/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 0 2 ) 0 0 2 4 0 - 3

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material changes associated with storage and preservation (Matthews and Ellis, 1968; Smith et al., 1996). Moreover, the clamps used may have allowed specimen slippage, thus introducing artifactual elongations (Ker, 1981; Bennett et al., 1986). We recently reported a tensile testing method that avoids the above limitations (Maganaris and Paul, 1999, 2000). The method is based on displacement measurements of ultrasound echoes generated from the tendon during muscle contraction under in vivo conditions. In our first experiments, we applied this method to the human tibialis anterior tendon, a relatively low-stressed tendon, and we found that its Young’s modulus and mechanical hysteresis are 1.2 GPa and 19%, respectively (Maganaris and Paul, 1999, 2000). In the present study we have applied the same method to the more highly stressed human gastrocnemius tendon. The measurements taken allow: (1) examination of the hypothesis that the material properties of in vivo tendon are independent of physiological loading and function; and (2) estimation of the mechanical work done by the elastic recoil of gastrocnemius tendon during locomotion.

2. Materials-methods 2.1. Experimental design The mechanical properties of the gastrocnemius tendon were examined in six healthy male volunteers [age, height and body mass: 2473 yr, 17474 cm and 7575 kg, respectively (means7SD)], with the approval of the ethical committee of Manchester Metropolitan University. The following four parameters were measured or calculated in the right leg at an ankle angle of 01 (the sole of the foot at right angles to the tibial axis): (1) the isometric plantarflexion maximal voluntary contraction (MVC) moment, (2) the gastrocnemius tendon elongation during MVC, (3) the gastrocnemius tendon moment arm length, and (4) the gastrocnemius tendon original cross-sectional area and length. 2.1.1. Measurement of MVC moment MVCs were elicited in the prone position on the bench of an isokinetic dynamometer (Lido Active, Loredan Biomedical, Davis). The ankle joint axis was visually aligned with the pivot point of the dynamometer lever, and the foot was firmly secured at the dynamometer footplate with Velcro straps. Plantarflexion moment measurements were taken after compensating for the effect of gravity by dynamic weighing of the foot using the dynamometer manufacturer’s procedure. MVCs were elicited by requesting the subject to increase the plantarflexion moment gradually over a 3-s period (ascending phase); the subject then relaxed

the contracting muscles (descending phase). Visual feedback of the plantarflexion moment generated and time elapsed was provided. Three MVCs were elicited with the knee fully extended (1801) and two MVCs were elicited with the knee flexed at 601. MVCs were generated at 2-min intervals in a randomized order of knee angle. Measurements were taken 2 min after three submaximal contractions were performed 1 min apart. MVCs were measured 2–3 days after a familiarization trial and repeated on a second occasion 2–3 days later. No difference was found in the measurements taken at each knee position either within each testing session or between the two testing sessions (P > 0:05; two-way ANOVA). 2.1.2. Measurement of tendon elongation Tendon elongation measurements were taken in two of the three MVCs performed in the knee extension position using a 7.5 MHz, linear, B-mode ultrasound probe (Esaote Biomedica, AU3 Partner, Florence; width and depth resolutions: 1 and 0.62 mm, respectively). Details of the methodology employed have been described elsewhere (Maganaris and Paul, 1999, 2000). First, consecutive axial-plane scans were taken along the belly of the gastrocnemius medialis muscle with a 2-cm interscan gap. The medial and lateral borders of the muscle in each scan were identified, and the midpoint between the two borders was marked on the skin. Sagittal-plane scans were then taken at the level of the heel to identify the insertion point of the Achilles tendon in the calcaneus, which was also marked on the skin. A straight line connecting the Achilles tendon insertion with all midpoints marked along the muscle was assumed to be the midlongitudinal axis of the muscle– tendon unit. The scanning probe was displaced along this axis to locate the distal myotendinous junction of the muscle, and subsequently the probe was clamped over the myotendinous junction on a fixed bracket. MVCs were then elicited while at the same time videorecordings were made at 30 Hz of the sonographs taken (Fig. 1). The displacement of the gastrocnemius tendon end in the myotendinous junction (hereafter designated as the tendon origin) during the ascending and descending phases of MVC was digitized using computerized image analysis (NIH Image, National Institute of Health, Bethesda, MD). To correct the measurements taken for displacements of the tendon bony attachment (hereafter designated as the tendon insertion) due to imperfect fixation of the foot on the footplate and compliance of the heel-pad, ligaments and dynamometer lever, additional measurements were taken in the third MVC elicited with the knee fully extended. These measurements involved sagittal-plane scanning of the proximal edge of the calcaneal posterior surface using the ultrasound probe mounted on the bracket used for scanning the tendon

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and yields valid results as long as the test does not involve structural deformations leading to substantial elastic strain energy storage (Maganaris, 2000; Maganaris et al., 2000). Hence, the present measurements were taken at rest. The displacement of the tendon origin (dL) caused by rotating the ankle from 51 of dorsiflexion to 51 of plantarflexion (dj; in rad) was digitized in sonographs taken along the midlongitudinal axis of the muscle–tendon unit, as described in the above section. The tendon moment arm length at the ankle angle of 01 was obtained from the ratio dL=dj:

Fig. 1. Typical sagittal-plane sonographs over the heel (left) and over the distal myotendinous junction of the gastrocnemius (GS) muscletendon unit right. A and E, at rest; B and F, at an estimated tendon force of 276 N during muscle contraction; C and G, at the maximal estimated tendon force (920 N); D and H, at an estimated tendon force of 276 N during muscle relaxation. The white arrows in A, B, C and D point to the proximal edge of the calcaneal posterior surface. The white arrows in E, F, G and H point to the end-point echo of the tendon in the myotendinous junction.

origin. The displacement of this reference point along the Achilles tendon axis of traction during the ascending and descending phases of MVC was recorded and digitized. The displacement values obtained were assumed to represent the displacements of the gastrocnemius tendon insertion (Fig. 1). The coefficient of variation of this measurement in eight repeated MVCs performed 2 min apart was 6.4%. For each load level examined (see data analysis section), the elongation of the tendon was obtained by subtracting the displacement of the tendon insertion from the displacement of the tendon origin. 2.1.3. Calculation of the tendon moment arm length The moment arm length of the gastrocnemius tendon was obtained using the tendon travel method (An et al., 1984) under in vivo conditions (Ito et al., 2000; Maganaris, 2000; Maganaris et al., 2000). The tendon travel method is based on the principle of virtual work

2.1.4. Measurement of tendon dimensions The length and cross-sectional area of the gastrocnemius tendon were quantified from sonographs recorded at rest with the probe described above. The distance between the tendon’s origin and insertion along the midlongitudinal axis of the muscle–tendon unit was measured manually to the nearest millimetre and considered to be the tendon’s original length. The Achilles tendon cross-sectional area was digitized in axial-plane scans recorded 1, 2 and 3 cm above the tendon insertion point in the calcaneus, following standard guidelines (Fornage, 1989). The gastrocnemius tendon cross-sectional area was assumed to occupy a fraction of the average Achilles tendon cross-sectional area equivalent to the relative physiological crosssectional area of the gastrocnemius muscle with respect to the entire triceps surae muscle (30%, Wickiewicz et al., 1983; Friederich and Brand, 1990; Fukunaga et al., 1992). The assumption involved in this calculation is that the area ratio between muscle and tendon is constant. This has been shown to hold true for tendons subjected to low physiological loads (Cutts et al., 1991), but further experiments are needed to confirm the applicability of the same principle in high-stressed, spring-like acting tendons (Fig. 1). 2.2. Data analysis For each subject, the gastrocnemius tendon elongation was quantified in the MVC that generated the highest plantarflexion moment. The elongation of the tendon at loads corresponding to 0–100% of the plantarflexion moment generated was measured at 1072% intervals, both in the ascending and descending phases of the MVC. First, the time points corresponding to the above loads were identified from the moment
time relationship, and then the scans corresponding to those time-points were stored in a computer and further processed. The approach followed for identifying the scans corresponding to the loads examined assumes that the moment generated by the gastrocnemius muscle during a ramp isometric contraction with the knee fully extended changes linearly with the gross plantarflexion moment measured. Evidence for the

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validity of this assumption has previously been taken from EMG measurements (Hof and van den Berg, 1977; Magnusson et al., 2001; Muramatsu et al., 2001). Estimates of the moment generated by the gastrocnemius muscle alone during the MVC were derived by subtracting the higher of the two MVC moments generated with the knee flexed from that generated with the knee extended (Herzog et al., 1991). This approach assumes that the gastrocnemius muscle–tendon unit is slack at the knee flexion angle and thus it transmits negligible contractile forces to the calcaneus: This has previously been verified by EMG and direct moment measurements (Hof and van den Berg, 1977; Maganaris, 2001). Moreover, it assumes that the moment generated by muscles other than the gastrocnemius muscle during plantarflexion MVC is independent of knee angle. Indeed, since all the major synergist and antagonist muscles of the gastrocnemius muscle span the ankle joint only, their length and therefore contractile force during plantarflexion MVC at any given ankle angle would not change by changing knee angle. The effect of the biarticular plantaris muscle may be ignored because it has a small physiological cross-sectional area and a variable insertion as shown in a study of 100 specimens reported by Cummins et al. (1946). The gastrocnemius muscle moments corresponding to all submaximal plantarflexion moments examined were calculated. To obtain the tendon force
elongation relationship, the gastrocnemius muscle moment values estimated from the above calculations were divided by the tendon moment arm length. Force
elongation data in both ascending and descending phases were fitted with second-order polynomials. Tendon stiffness data were calculated from the slope of the ascending phase of the force
elongation curve over 10% force-intercepts. The respective tendon Young’s modulus data were calculated by multiplying the stiffness values obtained by the ratio of tendon length to tendon cross-sectional area. The work done on the tendon during traction was calculated by numerical integration of the force data in the ascending phase over 0.5-mm intervals. The elastic strain energy released by the tendon during recoil was calculated by numerical integration of the force data in the descending phase over 0.5-mm intervals. The elastic strain energy dissipated in the stretch
recoil cycle was calculated from the area of the loop between the ascending and descending phases of the tendon force
elongation curve. Values of strain energy for each subject were normalized to the mass of the tendon, which was estimated from the volume of the tendon, assumed to be the product of the tendon length and its cross-sectional area, and from the tendon density, assumed to be 1120 kg m
3 (Bennett et al., 1986; Shadwick, 1990; Pollock and Shadwick, 1994). The tendon mechanical hysteresis and rebound resilience were calculated by expressing the values of elastic strain

energy dissipation and release, respectively, relative to the total work done on the tendon during traction.

3. Results The following data present mean7SD values in the six subjects. The MVC moments at the knee extension and flexion positions were 162711 and 10678 Nm, respectively. The ascending and descending phases of the MVC at the knee extension position lasted 2.8570.35 and 0.6670.06 s, respectively (Fig. 2). The estimated moment generated by the gastrocnemius muscle in the above MVC was 5577 Nm. The gastrocnemius tendon moment arm length was 6374 mm, the gastrocnemius tendon original length was 225720 mm, and the Achilles tendon cross-sectional area was 9079 mm2. The tendon insertion shifted proximally during contraction, by between 170.2 mm at 10% of maximal load and 4.171 mm at 100% of maximal load. The tendon elongation and strain (values corrected for the above tendon insertion displacements) increased from 1.771 mm and 0.870.3%, respectively, at 10% of maximal load to 11.173.1 mm and 4.971%, respectively, at 100% of maximal load. The tendon maximal force and stress were 875785 N and 32.472.3 MPa, respectively (Fig. 3). In the descending phase of MVC, the tendon insertion moved distally over the path followed in the ascending phase, but the tendon origin returned back to its original position following a path of larger displacements compared with the ascending phase at any given level of moment, indicating the presence of mechanical hysteresis in the tendon (Figs. 1 and 3). The quadratic models used to fit the force
elongation data yielded an R2 value of 0.9870.01. The tendon stiffness and Young’s modulus increased curvilinearly from 49712 N mm
1 and 0.3870.06 GPa, respectively,

Fig. 2. The plantarflexion moment
time relationship in the ascending (open symbols) and descending (filled symbols) phases of MVC in the present experiment. Values are means7SD (n ¼ 6).

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Fig. 3. The gastrocnemius tendon force
elongation relationship in the present experiment. Arrows indicate loading and unloading directions. Values are means7SD (n ¼ 6).

at 0–10% of maximal load to 150728 N mm
1 and 1.1670.15 GPa, respectively, at 90–100% of maximal load (Fig. 4 and Table 1). The estimated mass of the tendon was 6.971.2 g. The estimated work done on the tendon during traction was 4.271.8 J (5957171 J kg
1) and the strain energy released by the tendon during unloading was 3.471.5 J (4887146 J kg
1). The estimated mechanical hysteresis and rebound resilience in the tendon were 1873% and 8273%, respectively (Table 1).

4. Discussion In the present study, the tensile response of the human gastrocnemius tendon was obtained in vivo by measuring tendon elongation upon loading
unloading induced by muscle contraction
relaxation. Our results show that the tendon maximal Young’s modulus and mechanical hysteresis are 1.16 GPa and 18%, respectively. The present Young’s modulus value lies within the range of values obtained from experiments on several isolated mammalian tendons stretched by forces equivalent to the isometric force-generating potential of the inseries muscles (0.8–1.5 GPa, Bennett et al., 1986; Ker et al., 1988). The mechanical hysteresis estimate obtained here also falls within the range of values reported from in vitro tests (3–20%, Ker, 1981; Bennett et al., 1986; Pollock and Shadwick, 1994). Almost identical values of maximal Young’s modulus and mechanical hysteresis with the present experiment were recently reported from ultrasound-based experiments in the human tibialis anterior tendon (Young’s modulus: 1.2 GPa, mechanical hysteresis: 19%, Maganaris and Paul, 1999, 2000). The consistency between these results should be considered bearing in mind that the tibialis

Fig. 4. Tendon stiffness (top) and Young’s modulus (bottom) data in the study as a function of tendon load. Values are means7SD (n ¼ 6).

Table 1 Individual data of the gastrocnemius tendon mechanical properties in the study Subject No.

Stiffness (N mm
1)

Youngs modulus (GPa)

Hysteresis (%)

Rebound resilience (%)

1 2 3 4 5 6

171 181 108 161 125 153

1.215 1.159 0.905 1.220 1.101 1.362

14.1 21.2 15.9 18.7 15.8 22.5

85.9 78.8 84.1 81.3 84.2 77.5

Stiffness and Young’s modulus data refer to 90–100% of the gastrocnemius tendon load applied during MVC.

anterior and gastrocnemius tendons are subjected to different physiological forces; the tibialis anterior tendon to the forces generated by controlling plantarflexion in early stance, and the gastrocnemius tendon to the high forces generated in late stance (Procter and Paul, 1982; Finni et al., 1998). Moreover, in contrast to

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the tibialis anterior tendon, the gastrocnemius tendon acts as energy provider during locomotion; most of the work done on the tendon by the initial ground force is recovered as elastic strain energy during push-off, which results in plantarflexing the ankle and thus accelerating the body forward at no metabolic energy cost (Bennett et al., 1986; Ker et al., 1988; Hof et al., 1983; Fukunaga et al., 2001). Notwithstanding these differences between the two tendons, the gastrocnemius tendon was found to be neither intrinsically stiffer nor more rebound resilient than the tibialis anterior tendon. This is in accordance with the findings of Pollock and Shadwick (1994), Ker et al. (2000) and Pike et al. (2000), and contrary to those of Shadwick (1990). Thus, it seems likely that, in general, adjustments in tendon structural properties to physiological loading are accomplished by adding or removing material rather than altering the material intrinsic properties. The present tendon force
elongation data allow calculations to be made of the elastic strain energy provided by the gastrocnemius tendon during locomotion. Finni et al. (1998) used optic fibres inserted in the Achilles tendons of humans walking at speeds of 1.1–1.8 m s
1 and showed that the Achilles tendon load peaks at push-off, reaching a stress of B21 MPa irrespective of walking speed. Since the knee is almost fully extended in the transition from single-stance to push-off (e.g. Winter, 1990; Fukunaga et al., 2001), the maximal values of Achilles tendon stress reported above would also represent the stress carried by the gastrocnemius tendon. From the Achilles tendon crosssectional area data in the subjects examined by Finni et al. (1998) it follows that the gastrocnemius tendon maximal force over the course of a stride would be B470 N, which according to our tendon force
elongaelongation data would result in a tendon elongation of B7.5 mm (Fig. 5). Numerical integration indicates that the strain energy storage associated with the above tendon tensile force and resultant elongation would be 1.6 J (232 J kg
1). From the present mechanical hysteresis data it follows that the strain energy released by recoil in push-off would be 1.35 J (196 J kg
1). To estimate the contribution of this extra elastic work to the total external mechanical work produced by the locomotor system, we considered previously published values of external mechanical work at an average walking speed of 1.5 m s
1 (0.4 J kg
1 m
1, Cavagna et al., 1976; Cavagna and Kaneko, 1977). An average stride length corresponding to the above speed was obtained from the literature (0.8 m, Hinmann et al., 1988), and it was then combined with the subjects’ body mass and the above external mechanical work values to obtain the external mechanical work produced in one stride. These calculations yielded a mechanical work value of 24 J per stride, from which it follows that the elastic work produced by the gastrocnemius tendon

Fig. 5. Comparison of the gastrocnemius tendon mechanical behaviour in the present study with data from eight subjects while walking at 1.5 m s
1 (Finni et al., 1998). The ratio of the cross-sectional area of the gastrocnemius tendon to that of the Achilles tendon was assumed to be the same as the ratio of the physiological cross-sectional area of the gastrocnemius muscle to that of the triceps surae muscle (0.3, Wickiewicz et al., 1983; Friederich and Brand, 1990; Fukunaga et al., 1992). The estimated gastrocnemius tendon load and resultant elongation’s are B50% and 60%, respectively, of the corresponding values obtained during MVC.

during walking would account for B6% of the total external mechanical work produced. Given that the gastrocnemius tendon is one of several spring-like anatomical structures in the body (a similar mechanical behaviour would be expected from the tendons of the other ankle plantarflexor muscles, the patellar tendon, the aponeuroses of the above tendons and some ligaments in the arch of the foot, Ker et al., 1987; Alexander, 1988), our calculations indicate that passive elastic mechanisms may have a substantial energy contribution in walking, increasing the apparent locomotor efficiency. Similar conclusions have been reached in previous studies (Hof et al., 1983; Fukunaga et al., 2001). The contributions of elastic mechanisms would be much greater in more active exercise such as running. The present method is based on the echoreflectivity of collagenous tissue, and its reproducibilty has been confirmed (Maganaris and Paul, 1999; Muramatsu et al., 2001). Moreover, comparisons with direct measurements on cadaveric material have shown that ultrasonography locates accurately muscular connective tissue in static conditions (Kawakami et al., 1993; Narici et al., 1996), but the validity of the method during dynamic conditions needs to be confirmed. The major advantage of the present method is that the tendon is loaded in its physiological environment, without introducing clamping-induced artifacts (Ker, 1981; Bennett et al., 1986). One limitation of the method is that it involves two-dimensional procedures for calculating tendon forces. The error introduced by this limitation

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depends on the orientation of the axis of rotation in the joint. The tibiotalar joint axis of rotation deviates by only 101 from the perpendicular orientation to the sagittal plane (Isman and Inman, 1969; van den Bogert et al., 1994). Trigonometry-based calculations indicate that neglecting the above angulation would result in underestimating and overestimating, respectively, the actual moment and moment arm length by 1.5%. This would produce an error of only 3% in the tendon force estimated. Substantial errors, however, would be introduced in the calculation of tendon force by failing to distribute the net moment recorded to all agonists and antagonists cocontracting during MVC. The present experimental design takes account of this effect, but other authors have not taken it into account (Kubo et al., 2001; Magnusson et al., 2001; Muramatsu et al., 2001). An additional limitation of the present method is that it may allow application of heterogeneous stress across the tendon. The gastrocnemius tendon would be subjected to this effect because some of its fibres would be pulled further due to the force exerted upon them by the cocontracting soleus muscle. Inevitable errors in the estimate of stress will be therefore introduced, but these are expected to be relatively small because the linkages between the gastrocnemius and soleus tendons (a) are limited to the distal region of the two tendons (Cummins et al., 1946), and (b) would not be fully stretched, since the gastrocnemius and soleus tendons would be pulling simultaneously during MVC. Finally, the present method cannot eliminate (a) the work done on, and the strain energy released by, the myotendinous and osteotendinous junctions, and (b) heat losses induced by surface friction between the tendon and nearby tissues, which would be reflected in the hysteresis values. In fact, our mechanical hysteresis estimates are higher than the average value of B10% obtained from tensile tests on isolated tendons (Ker, 1981; Bennett et al., 1986; Pollock and Shadwick, 1994). However, we do not know whether the above discrepancy can be entirely accounted for by heat losses from sources other than the tendon, or whether it reflects partly differences in tendon material properties between in vivo and in vitro conditions.

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