INTRODUCTION

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BEHAVIOR OF MUSCLE-TENDON COMPLEX (MTC) during dynamic human movement has often been studied through vertical jumps. In vertical jump studies, the movement of the whole body, based on the body center of gravity and the ground reaction force, is first compared with and without countermovement from the viewpoint of the store and utilization of elastic energy (6). Second joint moments about hip, knee, and ankle are determined during jumping by inverse dynamics (23). Many biomechanical studies have been based on this technique for the quantification of mechanical output from MTCs. Estimated net joint moment is often processed to calculate the tendon force, considering the moment arm of corresponding muscle at the joint and the physiological cross-sectional area (PCSA) of the muscles involved (9, 10, 40, 41). Direct measurement of tendon force by use of the special techniques with buckle type transducer and optical fiber (30, 31) was more often difficult from an ethical point of view. On the other hand, change in length of MTCs during human movement has been estimated from the angular displacement of joints (18). Many researchers have been interested in knowing the behavior of muscle fibers and tendinous structures with respect to force and length during the body's dynamic movement. Modeling studies have been used to separate muscle fiber and tendinous structures in MTC during human dynamic-complex movements (5, 9, 10, 40, 41). However, it should be noted that such modeling requires knowledge of the magnitude of a great number of variables, which are usually not known for human muscles, for the obvious reason that human muscles are not usually accessible for controlled experimentation (24).

Ultrasonography is a tool that allows structural information of the MTC to be obtained in vivo during muscle contraction (14). We can measure the lengthening and shortening of fascicles and tendinous structures (external tendon and aponeurosis) by using an ultrasonic apparatus in vivo and comparing those data to previous modeling studies. The purpose of the this study was to measure the change in length of muscle fiber (fascicle) and tendinous structures of gastrocnemius medialis muscle in vivo and to discuss their function during vertical jumping.

	METHODS

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Subjects and Experimental Protocol

Kinematic and Kinetic Measurements

With a motion analyzer (Frame-DIAS, DKH, Japan) the positions of five anatomical landmarks and two landmarks on the force platform were automatically digitized. The coordinates of the digitized landmarks were low-pass filtered at 8 Hz (bidirectional Butterworth filter), as in a previous study (41). After synchronization of kinematic and kinetic data, instantaneous net joint moments about the ankle and knee were calculated using inverse dynamics (44). For convenience, net joint moments having a plantar-flexing and knee-extendong influence were defined as positive and were referred to as plantar-flexing and knee-extendong moments, respectively. Net joint power was calculated by multiplication of net joint moment and joint angular velocity.

Ultrasonography

The length of the fascicle was measured as the length of the echo that runs diagonally from the superficial to the deep aponeurosis along the fascicle (see Fig. 2). The fascicle angle was obtained as the averaged value of two angles; i.e., one was the angle between the deep aponeurosis and the line drawn tangentially to the fascicle; another was the angle between the superficial aponeurosis and the tangential line to the fascicle. These measurements were performed frame by frame by means of an image-processing and analysis application (NIH image 1.60 b; National Institutes of Health). The reliability of fascicle length and angle measurement has been confirmed elsewhere from a comparison with manual measurements on human cadavers as well as from the reproducibility of measurement in resting and static contraction (28, 14). In the present study, measurements of fascicle lengths and fascicle angles were repeated three times on each ultrasonic image obtained during SQJ, and the averaged value of the these measurements was used as a representative for the image. The coefficients of variation (CV) of the three measurements were in the range of 0-3%. The reproducibility of the fascicle length and angle measurements was assessed on two jump trials. The intraclass correlation coefficient for test-retest of fascicle length and angle was r = 0.994 (P < 0.001) and r = 0.998 (P < 0.001), respectively.

Electromyography

Calculations of Variables

Estimation of instantaneous length of MTC and tendinous structures and moment arm at the ankle for MG during jumping. The instantaneous length of MTC for MG (L_MTC), i.e., the distance between origin and insertion, was calculated by substituting instantaneous ankle and knee joint angles into the equations developed by Grieve et al. (18) and multiplying the segment length of the shank. The instantaneous length of tendinous structures was determined on the basis of a geometric MTC model proposed by Allinger and Herzog (4). The MTC was modeled as two tendinous structures (distal and proximal) on either side of each fascicle with a fascicle angle. Properties of the fascicles and tendon fibers were assumed to be uniform along the length of the MTC. It was also assumed that all fascicles were parallel and inserted at the same fascicle angle along the muscle. Therefore, the length of tendinous structures (L_TS) was defined as the sum of the proximal and distal tendinous structures (i.e., distal and proximal external tendons plus two parts of both superficial and deep aponeuroses or either one of the whole aponeurosis). The length of tendinous structures was calculated from the equation (1)

(1)

where L_fascicle, , and L_MTC are fascicle length, fascicle angle, and MTC length, respectively. Basically, the instantaneous moment arm of MG at the ankle was calculated by differentiating the length change of the MTC with the corresponding angle change of the joint, concerning biarticularity of MG.

Estimation of instantaneous force of tendon and fascicles generated by MG. The force applied to the Achilles tendon was calculated as the quotient of the plantar-flexing moment and the moment arm of MG at the ankle. It was assumed that the relative contribution of the force developed by MG to the Achilles tendon force was equal to the relative physiological cross-sectional area (PCSA) of MG to the plantar flexors at any time during SQJ. Furthermore, it was assumed that the ratio of tendon cross-sectional area of MG to the Achilles tendon coincided with the ratio of PCSA for MG to the plantar flexors and that its fraction of MG was separate in the Achilles tendon. According to Fukunaga et al. (15), the averaged relative PCSA of MG was 15.4% of total plantar flexors. Therefore, the instantaneous tendon force generated by MG (F_tendon MG) and the force of the fascicles in the direction of the fascicle of MG (F_fascicle MG) were calculated as follows

(2)

(3)

where M_ankle and d indicate the plantar flexing moments produced by a single leg and the moment arm of MG at the ankle, respectively.

Estimation of velocity, mechanical power, work of MTC, fascicles, and tendinous structures. The velocity in the MTC, fascicles, and tendinous structures was calculated by differentiating the corresponding length change value with time; the shortening of the MTC, fascicles, and tendinous structures was defined as positive. The mechanical power produced by the MTC and tendinous structures was calculated as the product of F_tendon MG and the velocity in the MTC and tendinous structures, respectively. F_fascicle MG was multiplied by the velocity in the fascicle to calculate the mechanical power produced by the fascicles. Negative and positive mechanical work done by the MTC, fascicles, and tendinous structures was calculated by numerical integration of the corresponding power values.

Treatment of Data

	RESULTS

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As shown in Fig. 1, ankle and knee joint angles and moment arm of MG at the ankle were almost constant until 150 ms before toe-off (150 ms) and thereafter increased progressively (maximum values of 2.5, 2.8 rad and 0.053 m, respectively). After 250 ms, the plantar-flexing moment generated by both legs increased gradually (peak value of 245 ± 20 Nm at 75 ms) and then rapidly decreased. EMG activities of Sol, MG, and LG began to increase gradually from 300 ms and reached a plateau, which lasted until about 75 ms. Reciprocal EMG activities were observed between the agonists and the antagonist for plantar flexion. The joint power about the ankle generated by both legs reached a peak of 2,000 W at approximately 50 ms, when the angular velocity of plantar flexion was about 10 rad/s. The angular velocities of plantar flexion and knee extension attained peak values of 12.8 ± 1.5 and 12.4 ± 1.3 rad/s around 25 ms and decreased thereafter.

View larger version (17K): [in this window] [in a new window]   Fig. 1.   Mean time histories of joint angles, joint angular velocities, joint moments, joint powers, moment arm of gastrocnemius medialis (MG) at ankle and normalized electromyogram (EMG) activities from lower leg muscles during squat jumping (SQJ). Positive joint moment about ankle and knee indicate plantar-flexing and knee-extending moment, respectively. Time is expressed relative to instant of toe-off (time = 0). Thin vertical bars indicate SE; n = 8 subjects. Sol, soleus; LG, gastrocnemius lateralis; TA, tibialis anterior.

Typical longitudinal ultrasonic images of MG during SQJ are shown consecutively in Fig. 2. On the basis of the behavior of MTC (Fig. 3), two distinguishable phases were observed during push-off phase; one was from the onset of push-off (350 ms; start of upward movement of mass center of the body) to 100 ms (phase I); another was from that point to toe-off (phase II). During phase I, MTC remained at an almost constant length of 0.425 ± 0.001 m, whereas the plantar-flexing and knee-extendong moments increased gradually with increasing muscle activities of Sol, MG, and LG throughout the period between 300 and 100 ms. The fascicle length, however, decreased from 56.1 ± 2.2 to 38.7 ± 1.4 mm, the fascicle angle increased from 20.06 ± 0.46 to 32.25 ± 0.40°, and the length of tendinous structures increased from 0.371 ± 0.06 to 0.393 ± 0.06 m during phase I. The changes in fascicle length, fascicle angle, and length of tendinous structures were 26, 71, and 6.0% relative to the corresponding values in the erect standing position, respectively. Although the increase in the plantar-flexing moment was accompanied by fascicle shortening and by tendinous stretching during phase I, during phase II, MTC length decreased to 0.402 ± 0.01 m (5.3% change expressed relative to the corresponding value in the erect standing position). Whereas relatively small changes were observed in fascicle (only 3.6%) and fascicle angle (10%) compared with corresponding changes found during phase I, the length of the tendinous structure decreased steeply to 0.372 ± 0.008 m (5.7%) with a decline of joint moments, tendon force, and fascicle force. Especially after 75 ms in phase II, fascicle length was nearly constant. This indicated that the muscle fibers generated force quasi-isometrically and that the shortening of MTC occurred due to the shortening of tendinous structures during phase II.

View larger version (98K): [in this window] [in a new window]   Fig. 2.   Typical sequence longitudinal ultrasonic images of MG during SQJ. Each longitudinal ultrasonic image was recorded every 25 ms. Time is expressed relative to instant of toe-off. In each image, thin subcutaneous adipose tissue layer and superficial and deep aponeuroses are visualized, between which parallel echoes from the interspaces among fascicles are arranging diagonally. See text for further explanation.

View larger version (19K): [in this window] [in a new window]   Fig. 3.   Mean time histories of muscle-tendon complex (MTC) length, fascicle length, tendinous structure length, and in the fascicle angle during SQJ. Left vertical dotted lines represent the onset of push-off, i.e., start of upward movement of mass center of the body; right vertical dotted lines represent the onset, from which the MTC begins to become remarkably shortened. Time is expressed relative to the instant of toe-off; n = 8 subjects.

As set out in Fig. 4, during phase I, time history of the velocity of fascicles was diametrically opposite to that of tendinous structures with almost the same absolute peak values. During phase II, the velocity of tendinous structures increased rapidly with a maximum value of 0.37 m/s, which was 2.6-fold higher than that of the fascicles. After 75 ms, the velocity of MTC was determined primarily by the velocity of tendinous structures. The differences between the forces generated by fascicles and those transmitted to tendinous structures of MG were, remarkably, around 75 ms, when fascicle angles nearly attained the maximum value. Because the cosine component of the force exerted by muscle fibers/fascicles (F_fascicle MG · cos ) is transmitted to the tendinous structures, during phase I, the power of the fascicles and tendinous structures was positive and negative, respectively. Both peaked at 125 ms with almost the same absolute peak values. The power of MTC was close to zero during this phase, because the energy generated by the fascicles was stored in a series of tendinous structures. During phase II, the power of the fascicles decreased gradually to zero. On the other hand, the power of the tendinous structures turned to positive and peaked at 50 ms. The peak positive power of the tendinous structures reached a higher value than that of the fascicles. The rate at which elastic energy was released by the tendinous structures during phase II was higher than the rate at which it was stored in the tendinous structures by the shortening of the fascicles during phase I, and the peak positive power of MTC corresponded closely to that of the tendinous structures.

View larger version (17K): [in this window] [in a new window]   Fig. 4.   Mean time histories of velocity, force, and mechanical power of the MTC, fascicle, and tendinous structures. Shortening of the MTC, fascicle, and tendinous structures was defined as positive. Left vertical dotted lines represent the onset of push-off, i.e., start of upward movement of mass center of the body; right vertical dotted lines represent the onset, from which the MTC begins to become remarkably shortened. Positive and negative values in the velocity indicate the velocity of shortening and elongation, respectively. Time is expressed relative to instant of toe-off; n = 8 subjects.

The average mechanical work done by the MTC, fascicles, and tendinous structures of MG is presented in Table 1. During phase I, the positive work done by the fascicles was essentially equivalent to the negative work done by the tendinous structures (4.8 and 4.9 J, respectively), which, in turn, was roughly equal to the value of the positive work done by the tendinous structures during phase II (4.9 and 4.4 J, respectively). To be exact, the positive work done by the tendinous structures during phase II was 89.8% of the corresponding negative work done during phase I. The amount of positive work done by the MTC during phase II was somewhat larger than that of the tendinous structures because of the little positive work done by the fascicles during phase II.

	DISCUSSION

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Recently, a noninvasive technique was developed for determining architectural parameters such as length and angles of fascicles of humans in vivo (14, 27, 28). In the present study, we adopted this technique to determine the change in muscle architecture of the human MG during jumping and elucidated the behavior of fascicles and tendinous structures of human MG during dynamic/complex movement as indicated in RESULTS.

Griffiths (19) showed that the muscle fibers of cat MG shortened by 28% during maximal isometric contraction at optimal muscle length. Also, the internal shortenings of fascicles in humans have been shown during isometric contractions of leg muscles in vivo by using ultrasonography (14, 27, 29). The magnitudes of the internal shortening of human MG fascicles ranged from 13.5 to 40.4% relative to the fascicle length, at which ankle and knee angle was 0° in maximal voluntary isometric plantar flexion at the several combinations of ankle and knee joint (29). Based on the results of Kawakami et al. (29), internal shortening of MG fascicle during isometric contraction of MTC of phase I in this study was extrapolated as 27.3% of the length in the erect standing position. We found the internal shortening of fascicles (0.017 m and 26% relative to the length in the erect standing position) and the stretching of tendinous structures (0.022 m and 6.0% relative to the length in the erect standing position) during isometric contraction of MTC of phase I. The actual internal shortening of fascicles in this phase was slightly lower compared with the extrapolated value. The difference could be attributed mainly to the lower force generated by fascicles of the submaximal muscle activity during phase I (Fig. 1). It was also reported that the fascicles shortened 16% relative to the optimal length during maximal isometric contractions in human tibialis anterior (27). The larger the tendinous structures' length-to-fascicle length ratio, the higher the compliance of the MTC and its ability of storing mechanical energy (3, 46). In other words, fascicles can shorten more during isometric contraction. On the basis of the results of Ito et al. (27) and this study, the tendinous structures' length-to-fascicle length ratios of TA and MG in humans were 3.4 and 5.5, respectively. Therefore, the difference in relative magnitude of internal shortening between MG and TA might be due primarily to the difference of tendinous structures' length-to-fascicle length ratio between these muscles. During phase II, MTC shortened drastically by 5.3% with a decline of tendon force, and so tendinous structures shortened concomitantly by 5.7% (Figs. 3 and 4). Surprisingly, the fascicle length of MG remained almost constant (quasi-isometric condition of fascicle). It follows that shortening of the MTC was due mainly to the shortening of tendinous structures with the peak shortening velocity 2.6 times as high as that of fascicles, and the shortening velocity of fascicles was considerably lower than that of MTC during phase II. These results demonstrate that the tendinous structures of MG are compliant enough to influence the behavior (change in length, shortening velocity) of fascicles substantially. In addition, this fact supports the previous reports that behavior of the MTC would not necessarily be the same as that of muscle fibers/muscle (11, 17, 36).

By kinetic analysis of a one-legged countermovement jumping, it was indicated that the further increase of vertical velocity of mass center of the body after 90 ms, when the difference of vertical component of velocity between mass center of the body and ankle joint had reached its maximum, required not only a high angular velocity of the foot but also a relatively large plantar-flexing moment (10). This implies that both the high shortening velocity of MTC of MG and the relatively large force generated by MG fascicles were required in phase II to jump higher. It is clear that higher shortening velocity of MTC in phase II has been attained not by the shortening velocity of fascicles but by the higher shortening velocity of tendinous structures that could be realized by the elastic recoil. According to the force-velocity relationship, the force generated by a muscle fiber decreases with increasing shortening velocity of muscle fiber (13). Therefore, quasi-isometric contraction of fascicles found in phase II could be advantageous for larger force generation by fascicles because the muscle fibers contract over a high-force region of its force-velocity curve. Additionally, it is well known that the length of sarcomeres in vertebrate striated muscle influences the force that can be generated by that muscle fiber (16). Sarcomere lengths can be estimated by dividing the fascicle length by the average number of sarcomeres in series in fascicles (see Ref. 10). Consequently, the average sarcomere length-fascicle force relationship during SQJ was obtained and compared with the length-force relationship for human muscle (42) (Fig. 5). The results indicate that the working range of sarcomere length during SQJ is over the plateau and the upper part of both descending and ascending limbs of the length-force relationship, where a relatively larger force can be generated. Even in phase II, sarcomere operated over the upper part of ascending limb of the length-force relationship. Although fascicles of MG shortened beyond the plateau during phase II, it could never generate <80% of the force generated at optimal sarcomere length. This finding was in agreement with that of one animal study (34). During jumping, the frog semimembranosus muscle operates mostly over the plateau. It is obvious that operation of muscle fibers quasi-isometrically at sarcomere lengths over the upper part of ascending limb of the length-force relationship increases the force per cross-sectional area of active muscle fibers. This must allow MG muscle to generate a relatively higher force despite the decrease of EMG activity in MG during phase II in human jumping. The delay between EMG and force can be considered the electromechanical delay in the end of this phase (32). If tendinous structures were extremely stiff, the fascicle length would change in phase with MTC length. Thus the present results demonstrated experimentally the suggestion, based on a simulation and animal studies (10, 17), that compliance of tendinous structures was essential to satisfy the combination of high angular velocities and large plantar flexing moments during the late push-off phase. Moreover, it should be stressed that the shortening velocity of muscle fibers is not equal to that of MTC, even in human isokinetic contraction with and without the quick-release technique as suggested by Cook and MacDonagh (11) and as recently shown by Ichinose et al. (25).

View larger version (29K): [in this window] [in a new window]   Fig. 5.   Average sarcomere length-fascicle force relationship during SQJ. Average sarcomere lengths during SQJ (F-LSQJ; thick line) have been estimated and superimposed on a length-force relationship (F-L; thin line) for human muscle derived from the data of Walker and Schrodt (42). During SQJ, MG muscle operates over the shaded portion of sarcomere length-force relationship where >80% of maximum force is generated.

According to Hill's classical model, MTC consists of a contractile component (CC) and a series-elastic component (SEC). Although there is an elastic component even in muscle fiber, the compliance of SEC within the fibers (cross bridge, actin/myosin filaments, Z-lines) is negligible compared with that of the tendinous structures, i.e., external tendon and aponeuroses (2, 26). In this model, the parallel elastic component (PEC) was neglected because a substantial contribution of the PEC is not likely at the muscle lengths occurring during jumping (26). Even if the compliance located in the muscle fibers was considered, this compliance relative to that of tendinous structures might be low during plantar flexion in SQJ, where muscle fibers generate relatively high forces, because the relative compliance of the tendinous structures compared with the compliance located in the muscle fibers increases with increasing muscle force (37). Therefore, elastic strain energy might thus be stored mainly in tendinous structures.

During phase I, the fascicles were able to shorten because of the compliant nature of the tendinous structures, and so the mechanical energy generated by the fascicles was stored predominantly in the tendinous structures as elastic energy. The total amount of elastic energy stored in tendinous structures was 5.0 J (4.9 plus 0.1 J, phases I and II, respectively), and 88% (4.4 J) of the stored energy was reused in phase II (Table 1). It was presented that, in external tendons of large mammals, the mechanical hysteresis lay between 6 and 11% (8). The mechanical hysteresis (energy dissipation) of MG tendinous structures obtained in this study (12%) is similar to the values reported in previous studies (8). With regard to viscosity, it is unlikely that there are large differences between the tendinous structures and the external tendons and, inevitably, between the aponeuroses and the external tendons.

The important point to note is that the peak positive power of the tendinous structures reached a larger value than that of the fascicle (Fig. 4). Also, the rate at which elastic energy was released by tendinous structures during phase II was higher than the rate at which it was stored in tendinous structures by the shortening of fascicles during phase I. Moreover, the peak positive power of the MTC corresponded closely to that of the tendinous structures (Fig. 4). Essentially, the similar results were predicted previously during stretch-shortening movements such as walking, running, and countermovement-jumping with the use of modeling approaches and the theoretical considerations (2, 9, 46). The aforementioned results of this study might have occurred with the following mechanism. Compliant tendinous structures allow fascicles to shorten before the MTC, and so the fascicles can do mechanical work over a longer period of time compared with the time of shortening of the MTC during the push-off phase in SQJ (Fig. 3). Because the fascicles have a limited rate of mechanical energy generation capability, it might be advantageous for fascicles to have a prolonged shortening time. The reason for this is that this prolongation of fascicle shortening time could decrease the average fascicle power level when the MTC must do a certain amount of mechanical work in a limited period of time. The mechanical work done by the fascicles was stored temporally in tendinous structures and was then released by elastic recoil during the late push-off phase. The rapid release of elastic energy from tendinous structures is well known in previous studies as catapult action (2, 21). As a consequence, the elastic energy stored in tendinous structures contributes to the much higher positive power of the MTC compared with the corresponding value of the fascicles (Fig. 4 and Table 1). Thus the results in this study demonstrate experimentally that the tendinous structures play an important role in redistributing the prestored elastic energy during the late push-off phase and also in functioning as a power amplifier, even in jumping without countermovement. These results would explain the phenomenon that, at higher angular velocities, the triceps surae is capable of greater torque and power generation when contractions are evoked with a stimulated release technique (20). In this context, it should be noted that the isokinetic torque- and power-velocity relationship obtained by use of the quick-release technique does not necessarily reflect intrinsic muscle fiber properties, especially at a high-velocity region, despite several reports that used this technique (11, 20).

To estimate the changes in length of tendinous structures during dynamic movement in humans, the previous studies (40, 41) have generally referred to the morphological and mechanical data obtained from cadaver external tendon (7, 45). However, it is highly probable that the elastic properties of external tendons in living humans differ substantially from those of human cadaver external tendons (38). Furthermore, in vitro animal and in vivo human experiments have demonstrated that compliance of external tendon was lower than that of aponeurosis (12, 33, 35). Therefore, the use of morphological and mechanical data obtained from cadaver external tendon may yield inaccurate results in the study of modeling of muscle function. Figure 6 depicts the average force-elongation relationship of tendinous structures for MG (F-E_actual) actually found during SQJ and that of tendinous structures for MG (F-E_model) calculated with the model in which the force-elongation relationship of tendinous structures was modeled with the use of a quadratic function (26)

(4)

where k is the constant and l is the length change of tendinous structures. The Young's modulus for human external tendons is reported to lie in the range from 0.6 to 1.8 GPa (1, 22), and the average value of 1.2 GPa was adopted for model calculation. The elastic coefficient k was calculated by use of the Young's modulus of external tendon (1.2 GPa), the cross-sectional area of Achilles tendon for MG (0.96 × 10⁵/m², i.e., 0.625 m² × 10⁴ × 0.154), the ultimate strain (6%), the strain value determing the length of the "toe piece" (2%), and the resting length of the tendinous structures (0.367 m, i.e., L_MTC  L_MB; see Ref. 40).

View larger version (26K): [in this window] [in a new window]   Fig. 6.   Average force-elongation relationship of tendinous structures for MG actually found during SQJ (F-Eactual; thick line) and that calculated with the help of a model (F-Emodel; thin line). Elongation of tendinous structures was considered the difference between tendinous structure length during SQJ and that at the erect standing position. Note that the elastic coefficient of F-Eactual was lower than that of F-Emodel.

Given the variables presented above, the elastic coefficient k of modeled tendinous structures of MG was equal to ~10 × 10⁵ N/m². The area under the curve at any force level represents the amount of stored elastic energy. The amount of elastic energy actually stored in tendinous structures of MG was 5.0 J (4.9 + 0.1 J, phases I and II, respectively), and the 4.4 J (88%) of stored energy were released during phase II (Table 1). This released elastic energy contributes to 86% of the positive work of MTC. On the basis of the model calculations, 3.2 J of the elastic energy were stored in tendinous structures of MG during SQJ, and it accounted on average for 63% of the positive work done by MTC. It follows from this that actually stored and reused elastic energy in MG tendinous structures was larger than that in a simulation study (Fig. 6). In other words, the elastic coefficient was slightly overestimated in the previous simulation study. In fact, when nonlinear regression was applied to the F-E_actual curve, the elastic coefficient of actual tendinous structures for MG was ~6.9 × 10⁵ N/m² (r² = 0.92, P < 0.001). It should be noted that, in the previous simulation studies, researchers did not take into account the compliance of aponeuroses. This discrepancy might be caused by more compliant aponeuroses compared with external tendons (12, 33, 35). To assess the amount of elastic energy stored in tendinous structures and released during complex movement, it is necessary that elastic properties of tendinous structures be determined in vivo.

It has been assumed that the relative force developed by the MG at the Achilles tendon is equal to the relative PCSA of the MG to the plantar flexors at any time. However, all of the muscle in plantar flexors could not be equally affected by changing knee and ankle angle during jumping, even if neural inputs were the same, because, for example, gastrocnemius and soleus are bi- and monoarticular muscle, respectively. In addition, there is a difference in physiological properties between these muscles. Therefore, the proportion of total plantar flexor force contributed by soleus and gastrocnemius must vary with joint position. According to previous animal studies that used tendon transducers (39, 43), the contribution of each medial and lateral gastrocnemius to the total plantar flexion force gradually increased, and that of soleus decreased, during cat jumping. The contribution of LG was somewhat higher than that of MG. These results imply that mechanical power and work derived from force developed by the MG at the Achilles tendon may be underestimated during the late push-off phase in this study, although the difference in species should be considered. Because MTC length and moment arm were calculated as the function of ankle and knee joint angle, interindividual differences in these parameters have been neglected. However, it is likely that this disregard of individuality in muscle-tendon length and moment arm had little effect on the averaged values of these variables.

In conclusion, the present study demonstrated experimentally that elastic energy storage and release by compliant tendinous structures were essential for the MTC to effectively generate relatively large power at the high joint angular velocity region during the late push-off phase in human jumping. Furthermore, this methodology was able to elucidate the interaction between human muscle fiber and tendinous structure in vivo and the mechanism of mechanical efficiency enhancement during stretch-shortening cycle movement like hopping and running.