INTRODUCTION

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MUSCLE FIBERS ARE PACKED in bundles (fascicles) that extend from the proximal to distal tendons, comprising a whole muscle. In many cases, when investigators refer to muscle fiber length, they are actually referring to fascicle length (4, 11, 12, 24, 25, 29), although some muscle fibers have been shown to terminate midfascicularly (17, 31). Intrafascicle muscle fibers are, however, serially connected to make one functional unit, which has the same length as that of a fascicle (31). Changes in fiber length by contraction are thus expressed as fascicle length changes.

In pennate muscles, fascicles are arranged obliquely with respect to the tendon, and this angulation (pennation angle) changes by contraction. The forces exerted by muscle fibers are therefore modified at the fascicle level to characterize the force-generating capabilities of a muscle. Pennate muscles also have long tendons and aponeuroses with substantial compliance (9), which modulate the force-generating capabilities of a muscle by causing changes in fascicle length as force is exerted at a given joint angle. These factors make it difficult to estimate muscle actions from sole observation of joint performance (6).

Attempts have been made to determine the geometric arrangement of muscle fibers or fascicles (muscle architecture) in humans, and many attemtps have been based on measurements of cadaver specimens (3, 4, 11, 12, 29, 32). However, it has been shown in animals (9) as well as in humans (6) that muscle architecture changes by contraction even in isometric actions. Therefore, available data on human muscle architecture based on human cadaver specimens might not accurately represent the profile of actively contracting muscles; consequently, there are particular advantages in using noninvasive techniques to determine the muscle architecture in living subjects.

The triceps surae muscles are the main synergists for plantar flexion (6, 18), but they have different architectural properties, such as muscle length, fascicle length, and pennation angles (3, 4, 32). In addition, the gastrocnemius muscles are two-joint muscles crossing both the knee and ankle joints, whereas the soleus is a single-joint plantar flexor. Consequently, the relationships among joint angles (knee and ankle), muscle (fascicle) lengths, and pennation angles are highly specific to individual muscles. Information on muscle architecture related to joint positions is essential for the study of muscle functions, but to date very few data are available in humans in vivo (16). The purpose of the present study is to quantitatively describe the relationships between joint angles and muscle architecture (lengths and angles of fascicles) of human triceps surae muscles in vivo in passive (relaxed) and active (contracting) conditions and to discuss their functional implications.

	METHODS

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Subjects. Six healthy men [age, 21-53 yr; height, 175 ± 5 (SD) cm; and weight, 71 ± 7 kg] participated as subjects. The nature and possible consequences of the study were explained to each subject before informed consent was obtained.

Joint position settings and torque measurement. Each subject's right foot was firmly attached to an electric dynamometer (Myoret, Asics), and the lower leg was fixed to a test bench. The ankle joint was fixed at 15° dorsiflexion (15°) and 0, 15, and 30° plantar flexion. The knee joint was positioned at 0 (full extension), 45, and 90°. Thus the following measurements were performed in 12 conditions. In each condition, the subject was asked to relax the plantar flexor muscles (passive condition), and passive plantar flexion torque was recorded from the output of the dynamometer by a computer (PC-9801, NEC). The passive plantar flexion torques were greater when the ankle joint was in a less flexed position and the knee joint was in a less flexed position [0 (ankle, 30°; knee; 90°) vs. 12 (ankle, 15°; knee, 0°) N · m; average of 6 subjects]. We assumed that there was no muscle activity in the passive condition.

Measurement of lengths and angles of fascicles. In each position, longitudinal ultrasonic images of the triceps surae [medial (MG) and lateral (LG) gastrocnemius and soleus (Sol) muscles] were obtained (SSD-2000, Aloka) (Fig. 1) at the proximal levels 30 (MG and LG) and 50% (Sol) of the distance between the popliteal crease and the center of the lateral malleolus. Each level is where the anatomic cross-sectional area of the respective muscle is maximal (7). At that level, mediolateral widths of MG and LG were determined over the skin surface, and the position of one-half of the width was used as a measurement site for each muscle. For Sol, the position of the greatest thickness in the lateral half of the muscle was measured at the level mentioned above. Figure 2 shows the calf with planes of ultrasonograms for the three muscles. The echoes from interspaces of fascicles and from the superficial and deep aponeuroses were visualized, and the ultrasonic images were printed onto calibrated recording films (SSZ-305, Aloka). By visualizing the fascicles along their lengths from the superficial to the deep aponeuroses, one can be convinced that the plane of the ultrasonogram is parallel to the fascicles (14); otherwise, the fascicle length would be overestimated and the fascicle angle would be underestimated (25). The echoes from interspaces of the fascicles were sometimes imaged more clearly along the length of fascicles when the plane was changed slightly diagonally to the longitudinal line of each muscle, in which case the recreated image was used. In the printed images, the length of the fascicles and fascicle angles [the angle at which the fascicles arose from the deep (MG and LG) and superficial (Sol) aponeuroses] were measured, the former by the use of a curvimeter (Comcurve-8, Koizumi) and the latter by the use of a protractor. The fascicles were somewhat curvilinear in all muscles (particularly MG) at shorter lengths. The length of a fascicle was always measured along its path, with the curvature, if present, taken into consideration. For the fascicle angle, a line was drawn tangentially to the fascicle at the contacting point onto the aponeurosis. The angle made by the line and aponeurosis was measured as the fascicle angle. Some authors have approximated a fascicle as a straight line between its origin and insertion to determine fascicle angles (10), but we considered that the angle defined in the present study would be more appropriate for studying the impact of pennation on the force transmission from fascicles to aponeuroses. The reliability of fascicle length and angle measurement have been confirmed elsewhere from a comparison with manual measurements on human cadavers (14, 19) as well as the reproducibility of measurement (7, 14, 15). In the present study, ultrasonic measurement was repeated three times for each subject and averaged values were used. The coefficients of variation of three measurements were in the range of 0-2%.

View larger version (77K): [in this window] [in a new window]   Fig. 1.   Ultrasonic images of longitudinal sections of medial (MG; top) and lateral (LG; middle) gastrocnemius and soleus (Sol; bottom) muscles. In each image, thin subcutaneous adipose tissue layer and superficial and deep aponeuroses are visualized, between which parallel echoes from fascicles are arranging diagonally. Fascicle length was determined as length of echoes from fascicles. Fascicle angles were defined as angles at which fascicles arose from deep (MG and LG) and superficial (Sol) aponeuroses.

View larger version (14K): [in this window] [in a new window]   Fig. 2.   Schematic representation of calf with planes of ultrasonograms (heavy black lines; direction of ultrasonic transducer) for MG, LG, and Sol.

Statistical analyses. A three-way ANOVA with repeated measures was used to analyze lengths and angles of fascicles as well as plantar flexion torque (2 × 3 × 4, activation × knee positions × ankle positions). F-ratios were considered significant at P < 0.05. Significant differences among means at P < 0.05 were detected by using Tukey's post hoc tests. The relationships between muscle length change (l_mus; described in RESULTS) and fascicle lengths and torques were examined with linear regression analysis with a significance detected by correlation coefficients at a level of P < 0.05.

	RESULTS

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Table 1 shows average fascicle lengths of MG, LG, and Sol. Fascicle lengths were longest when the ankle joint angle was 15° with the knee fully extended, and shortest when the knee was flexed at 90° and the ankle joint angle was 30°. When the knee was straight and the ankle joint angle was 15°, LG had the longest fascicle lengths, followed by MG and Sol, all significant in this order.

The degree of fascicle length change was not identical for the three muscles. The effects of knee and ankle joint positions on fascicle lengths were significant for MG and LG, and there was also a significant interaction between knee and ankle positions in these muscles. In other words, in MG and LG, changes in fascicle length because of ankle position changes were larger with the straight- compared with the bent-knee condition. In the active condition, when the knee was flexed at 90°, fascicle lengths of MG at four ankle positions were not different, although in the passive condition the difference was significant. The fascicle length of Sol was affected by ankle joint angles, but not by knee joint angles.

The fascicle angles of MG demonstrated the greatest variation in three muscles, ranging from 22° (passive; knee, 0°; ankle, 15°) up to 67° (active; knee, 90°; ankle, 30°) (Table 1). The effects of activation and ankle positions were significant in all three muscles with a significant interaction. The differences in MG fascicle angles because of changes in ankle positions were not significant among 0, 15, and 30° both in the passive and active conditions. Fascicle angles of LG differed among different ankle positions in the active condition but not in the passive condition, except between 15 and 30°. For Sol, fascicle angles were affected by activation and ankle joint angles but not by knee joint angles.

Shorter fascicle lengths and steeper fascicle angles in the active compared with the passive condition show internal shortening of fascicles by contraction. From these parameters, the l_mus was estimated by the following formula, i.e. where l_Fp and l_Fa are fascicle lengths in passive and active conditions, and _p and _a are fascicle angles in passive and active conditions, respectively. The l_mus ranged from 12 ± 4 (SD) to 24 ± 4 mm for MG, from 16 ± 2 to 21 ± 5 mm for LG, and from 11 ± 4 to 15 ± 5 mm for Sol. In each muscle, l_mus was greater when the fascicle lengths were longer (MG: r = 0.73, LG: r = 0.47, and Sol: r = 0.69 for all measurements in 6 subjects and MG: r = 0.92, LG: r = 0.83, and Sol: r = 0.78 for the pooled values of the subjects).

The plantar flexion torque decreased almost linearly as the ankle was plantar flexed (Fig. 3). Knee and ankle positions significantly affected the torque, and there was a significant interaction between knee and ankle positions. There was no significant difference in torque between the knee positions at 45 and 90° at all ankle positions. When the knee was flexed over 45°, torque at ankle joint angles of 15 and 30° did not differ significantly. The torque was greater when the fascicle lengths were longer. The l_mus (averaged for MG, LG, and Sol) was significantly correlated with the plantar flexion torque (r = 0.65 for all measurements in six subjects and r = 0.91 for the pooled values of the subjects; Fig. 3), which suggests that the muscle force and the estimated muscle length change in a similar way.

View larger version (28K): [in this window] [in a new window]   Fig. 3.   Relationship among ankle joint angles, plantar flexion torque, and estimated muscle length change (difference between passive and active conditions) at different knee positions [0 (), 45 (), and 90° (); mean values from 6 subjects]. See text for calculation of muscle length change.

	DISCUSSION

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The relationship between joint angles and torque is influenced by such factors as the length-force relationship of muscle fibers, geometric arrangement of muscles with respect to the joint, and architectural characteristics of the muscle. Muscle architecture, together with intrinsic properties such as fiber composition, also affects functional characteristics of muscle (e.g., maximal shortening velocity and maximal force) (1, 21). Previous studies have not found a clear relationship between muscle architecture and fiber composition (2, 21), but the variation in force-generating capabilities among limb muscles is influenced more by differences in their architecture than those in their fiber types (1, 2, 23). Attempts have been made to determine muscle architecture in humans; however, few of them have related it to joint performance. Furthermore, many of the previous reports have been based on cadaver specimens (3, 4, 11, 12, 29, 32), and little data are available on muscle architecture in living human muscles, especially during contraction. Recently, the authors have developed a technique for determining the length and angles of fascicles in vivo in humans (6, 14, 15). In the present study, we used this technique to determine architectural characteristics of the human triceps surae muscles in passive and active conditions and related architectural changes to joint positions so as to discuss their functional implications.

The pennation angle has been defined as the angle made by fascicles and the line of action (pull) of muscle (12, 21, 28). According to this definition, the present fascicle angles are not equal to pennation angles because, in the present study, the angles of aponeuroses with respect to the line of action of muscle were not considered. Some studies, however, have reported that the influence of aponeurosis angulation on force transmission from fascicles to tendon is negligible and that the angle of fascicles arising from the aponeuroses can be used as the pennation angle (8, 29). In addition, from our observation, the aponeuroses in intact muscles were not so slanted as they are in the removed preparations (12) because of the existence of adjacent muscles and bones. Thus we consider that the present fascicle angles can be substitutable for pennation angles, at least for the triceps surae muscles.

The LG had the longest fascicle lengths in the triceps surae muscles. This means that the number of sarcomeres in series is the largest for this muscle, which illustrates eminent velocity potential of LG, as suggested previously (11, 12, 32). On the other hand, MG was characterized by shorter fascicle lengths and larger fascicle angles. The MG can thus pack more fibers within a certain volume and hence would have greater force potential. These results are in accordance with the previous report that the physiological cross-sectional area of MG is 2.5 times greater than that of LG, whereas the muscle volume difference between them is only 1.7 times (7). The maximal shortening velocity of a muscle is also influenced by fiber type composition (28). However, because fiber type composition of MG and LG is similar (13), maximal shortening velocity and maximal force would be principally determined by their architectural properties.

As the ankle was plantar flexed, changes in fascicle lengths became smaller in MG and LG both in passive and active conditions. This result appears contradictory because the moment arm length of the Achilles tendon increases as a result of plantar flexion (22), and excursion of the muscles connected to the Achilles tendon for a certain displacement of ankle joint angles should increase in a more plantar flexed position. Smaller fascicle length changes could then be due to 1) increase in fascicle angles that augments tendon excursion relative to fascicle length change (8), 2) slackness of fascicles at the plantar flexed position, and 3) decreased tendon elongation due to decreased muscle force. In MG, fascicle angle increased greatly, and at shorter lengths the difference between passive and active conditions became smaller, resulting in smaller l_mus. These results would suggest that all of the above possibilities are influential. When the knee joint angle was 90°, the fascicle length of MG in the active condition did not change irrespective of ankle positions. In this position, fascicle angles of MG were ~60°. The force of muscle fibers is transmitted to the tendon by a factor of the cosine of the pennation angle (7, 8, 14). In this position, the factor for MG is ~0.5; i.e., only one-half of the force exerted by fibers is effectively transmitted to the tendon. Therefore, in this position the contribution of MG to Achilles tendon force would be considerably smaller. No difference in torque with the knee positioned at 45 and 90° might reflect an insignificant contribution of MG.

Figure 4 shows the relationships between fascicle length in the passive condition and l_mus for MG, LG, and Sol. The l_mus corresponds to the tendinous movement of each muscle, which would result from elongation of the tendinous tissues (tendons and aponeuroses) during isometric contraction (5). The tendon elongation is a function of the linear force at the tendon (30). Considering also that the averaged l_mus of the three muscles was correlated with plantar flexion torque, the larger l_mus would result from greater muscle force. Because l_mus was larger when the fascicle lengths were longer, it is suggested that the force exerted by the muscle is greater with longer fascicle lengths. It thus follows that Fig. 4 might roughly represent the length-force relationships of the three muscles. Of course, it is impossible to quantitatively assess muscle force from l_mus because l_mus would depend on the compliance of tendons, the total lengths of which are unknown from the present data. One should also be mindful that the length-force characteristics of the tendon is nonlinear, with greater tendon length change at lower force (30). However, the tendency of l_mus to increase as the fascicle length increases would indicate that the muscle force is greater when the fascicle length is longer. Further dorsiflexion beyond the present setting (knee 0° with 15° dorsiflexion) caused discomfort or localized pain in the gastrocnemius muscles in the subjects, which prevented active force production. The fascicle lengths at this position therefore appear to be their maxima in the physiological range. The data therefore suggest that each muscle uses only a part of the length-force relationship. This speculation is in line with a previous report (3) on human cadavers that showed that the lower limb muscles use approximately the ascending limb and plateau region of the length-force relationship. However, the present data cannot give precise information on which part of the relationship is used in vivo because muscle forces and sarcomere lengths are unknown. Furthermore, due to the fascicle angles, the component of the force exerted by fascicles in the direction of the tendon is smaller when fascicle lengths are shorter. Thus the relationship between fascicle lengths and l_mus might be modified by this angulation effect, especially at shorter fascicle lengths.

View larger version (11K): [in this window] [in a new window]   Fig. 4.   Relationships between fascicle lengths in passive condition and estimated muscle length change for MG, LG, and Sol [for 3 knee positions: 0 (), 45 (), and 90° ()].

The length range of the triceps surae muscles is more limited during daily activities, such as locomotion. In the stance phase of walking (foot contact-push-off), the knee joint angle changes between 0 and 30°, and the ankle joint angle ranges between 15° dorsiflexion and 0° plantar flexion (33). From the present results, in this range fascicles of MG and LG are ~70-100% of their maximal lengths and the fascicle length of Sol ranges from 85 to 100%, where l_mus of each muscle is largest and apparently constant (Fig. 4). It appears, therefore, that the gastrocnemius and Sol muscles operate with moderate variation in length and force during locomotion (and possibly in other daily activities as well) to exert force more effectively.

The nonlinear nature of tendon elongation by applied force (less elongation as force increases) suggests relatively small l_mus at longer fascicle lengths because the passive tension of the muscle at those lengths would already have taken up the relatively large tendon compliance. However, passive plantar flexion torque ranged only up to 12 N · m (7% of the maximal torque); thus the active muscle force would have generated larger length changes, regardless of the reduced compliance. The fascicle length of MG in the active condition did not change, irrespective of ankle positions when the knee was flexed at 90°, which contrasts to the result in the passive condition. This might imply that when the knee is flexed to 90°, the MG fibers reach a length close to their active slack length, and little force is produced. The other possibility is that the very high MG fascicle angle and hence a very small muscle force component in the direction of the tendon prevented fibers from taking up the in-series compliance. On the other hand, maximal l_mus of MG was the largest among the three muscles, which would come from the prominent force potential and/or compliant tendon and aponeurosis of MG. Although MG and LG comprise one muscle unit, these two heads are thus contrasted in architectural and force-generating characteristics. It is expected from the present results that the mechanical properties of the series elastic component can be assessed with the present technique, as suggested previously (5). However, determination of the passive length-force characteristics requires the total length and cross-sectional area of the tendon as well as the force applied to it, which deserves further study.

The curvature of fascicles observed during contraction would have occurred by the intramuscular pressure and stretch of the aponeuroses (20). This observation also evidences the elongation of in-series compliance in the active condition. The results that larger fascicle curvature was observed in all muscles at shorter lengths and that MG showed the most pronounced curvature would imply that the curvature might be related to the degree of pennation. Larger pennation angles would result in greater force component perpendicular to the aponeuroses, which might cause more intramuscular pressure to develop.

In the present study, the length and angle of fascicles were determined from the midbelly of the muscles. Although it has been shown that there is marked uniformity in fiber length (4, 32) and fascicle length (4, 24) throughout a muscle, some studies have reported heterogeneity of fascicle angles (24) and even fascicle lengths (11, 21) along the length of the muscle. Thus the relationships between joint angles and fascicle arrangement might differ in the different portions of the muscle. Furthermore, the triceps surae muscles have some variations in internal fascicle arrangement. The Sol, for example, consists of two portions: portioposterior and -anterior, the latter of which (although much smaller in volume) has a bipennate architecture (27). The LG consists of three heads, and the direction of fascicles has been shown to be different among heads (26). In the present study we studied the portioposterior for Sol and the "A head" (see Ref. 26; lateral portion) for LG, which were greatest in volume. The kinetics of fascicles, which are presently being studied in our laboratory, might vary within a muscle.

Finally, it should be noted that the behavior of muscle fibers might not always be the same as that of fascicles. Although muscle fibers terminating intrafascicularly are serially connected within a fascicle to act as a functional unit, adjacent fibers do not necessarily belong to the same motor unit (31). Future studies may focus on the existence of inhomogeneous fiber lengths that might be present within a fascicle, especially during submaximal contractions.

In conclusion, from the present results it was suggested that 1) the architecture of the triceps surae muscles is considerably different, possibly reflecting their functional roles; 2) lengths and angles of fascicles change by contraction in a dissimilar manner between muscles, which might be related to the differences in force-producing capabilities of the muscle and elastic characteristics of the tendons and aponeuroses; and 3) the medial head of the gastrocnemius is in a very disadvantageous condition when the knee is flexed at 90°, irrespective of ankle positions.