During running the muscles of the lower extremity are alternately stretching and shortening using the elastic potential of the muscles and tendons (4). This phenomenon refers to the well-documented muscle function, called stretch-shortening cycle (SSC) (20). The advantage of this spring-like behavior of muscles in natural locomotion has been known since the end of the 19th century and has been intensively studied by several researchers during the last decades (3,4,20). The mechanics of muscle function have often been described by the property of the system to resist the applied stretch. This so-called stiffness (k) is calculated by dividing the change in force by the change in length (ΔF/Δ1) (15). Different methods have been used to study the stiffness of the lower leg, including different spring-mass models (24,25). The stiffness calculations have also been extended to single joints (2,13,30) or even to single muscles (e.g., 32).
In some studies, the stiffness of the leg (the force acting on the leg spring divided by the change in leg length) has been reported to remain quite constant during running at different speeds both in animals and in humans (6,12). It has also been shown that it is possible in humans to adjust the leg stiffness to meet changes in demands of the task (7,8). Contradictory to the previous studies (6,12), leg stiffness has been reported to increase in running when the speed increased (2,24). These differences in leg stiffness patterns can be partly explained by different calculation methods (2). Torsional stiffness of the ankle joint was found to be higher in sprinting compared with running (30). However, in the study of Arampatzis et al. (2), the authors observed larger changes in the stiffness of the knee joint than in the ankle joint with increasing running speed.
The advantage of the spring-mass model is its simplicity in studying the mechanical behavior of the musculoskeletal system by using just one spring. However, it ignores the mechanisms of this multi-spring system with different elastic and viscous properties. The regulation of this complex system is thought to be controlled by central nervous system (CNS) through the feedback information from the periphery via proprioceptors. This servo-regulation hypothesis (16) suggests that the motor servo regulates and maintains the ratio of force change to length change (stiffness) of the muscle rather than controlling either of them separately. The situation is somewhat different around the joint where several muscles and other passive structures are influencing the behavior of the joint. The stiffness of a single joint depends on several variables, including muscle activation level (33), joint angle (11), range of motion, and angular velocity (19). However, the mechanisms controlling joint stiffness are not very well understood especially during multi-joint movements. Perhaps the most frequently used mechanism of stiffness control of joint is co-contraction of agonist and antagonist muscles (14,27). The function of multi-joint muscles have also been speculated to play a role in stabilizing the leg (27) as well as contributing to the work of muscles to optimize the velocity of center of mass (31). Farley and Morgenroth (8) have suggested that during hopping leg stiffness is adjusted primarily by modulating ankle joint stiffness because the moment arm of the ground reaction force is largest in the ankle. The results of Arampatzis et al. (2) suggest that in running the knee joint stiffness plays more important role (compared with the ankle joint stiffness) in controlling the leg stiffness. The purpose of this study is to investigate the stiffness regulation in the ankle and knee joint in sprinters at high running speeds.
Ten male sprinters (age 23 ± 4 yr, height 1.76 ± 0.04 m, weight 71.8 ± 4.6 kg, and 100-m record 10.91 ± 0.39 s; mean ± SD) participated in this study. Written informed consent was given by the all subjects. The study was conducted according to the declaration of Helsinki and was approved by the ethical committee of the University of Jyväskylä. After the warm-up, the subjects performed a sprint run with maximal effort. This was followed by submaximal speeds of 70%, 80%, and 90% of maximum run performed in a randomized order. The corresponding absolute running speeds were 7.00 (ranged from 6.66 to 7.31), 7.83 (7.40–8.22), 8.84 (8.33–9.36), and 9.73 (9.23–10.26) m·s−1. The subjects accelerated their preferred distance, and they were asked to maintain constant running speed between two photocells set 10 m apart. Only those trials that were within ± 2% of the target speed were accepted. The contact and flight times as well as stride frequency were determined from the ground reaction force (GRF) records. The average stride length was calculated by dividing the running speed by stride frequency.
Vertical (Fz) and horizontal (Fy) GRFs were measured with a totally 10-m-long series of force platforms (Raute Precision Oy [Lahti, Finland], natural frequencies 180 ± 10 Hz for Fz and 130 ± 10 Hz for Fy). Electromyographic activity was recorded telemetrically (Glonner Biomes 2000 [Munich, Germany], cut-off frequency 360 Hz/3 dB). The bipolar Beckman-type surface electrodes (interelectrode distance 20 mm) were placed on the gluteus maximus (GLUT), biceps femoris (BF), rectus femoris (RF), vastus medialis (VM), gastrocnemius medialis (GA), soleus (SOL), and tibialis anterior (TA) muscles. GRFs and EMGs were collected with a sampling frequency of 833 Hz, and trials were also videotaped at 200 frames·s−1 from the right side of the body. Joint markers were placed on the distal head of the fifth metatarsal bone, heel, lateral malleolus, lateral epicondyle of the femur, greater trochanter, and shoulder. Before measurements, calibration was done by a cube (length 5 m, height 2 m, and width 1 m) placed in the middle of the force plates. One contact of the right leg from the middle of the force plates was taken to the analysis. Kinetic and kinematic data were synchronized using a circuit to introduce a trigger signal to the computer.
The body segment coordinates were digitized (Motus workplace, Peak Performance Technologies, Inc., Denver, CO), filtered (Butterworth filter, cut-off frequency 20 Hz), and transferred to the computer system (SGI O2 R5000, Silicon Graphics, Inc., Mountain View, CA) for further analysis. Fy signal was filtered with least-squares method by polynomials of the second power. The scaled coordinates and GRFs were synchronized, and joint moments were calculated at 200 Hz. Anthropometric data provided by the standards of Demster (5) were used to determine inertia and mass of the segments. The average joint stiffness was calculated as a change in the joint moment (ΔM) divided by the change in joint angle (Δθ) in the braking phase. The directions for the positive joint moments and the joint angles have been defined in Figure 1. The vertical stiffness was calculated from the ratio of the peak vertical GRF to the vertical displacement of the center of the mass (COM).
EMG signals from two or three right leg contacts on the force plates were high-pass filtered (cut-off frequency 20 Hz), rectified, and averaged within every trial. EMG analysis included a time period extending from a 100-ms precontact phase (preactivation) to the end of the ground contact phase. Seven subjects could be used reliably in EMG analysis. Other three subjects had noisy EMG signals, and their EMG data could not be utilized. In the statistical analysis, means and standard deviations were calculated. Nonparametric Kendall’s W-test was used to test the effects of running speed on selected variables.
The running speed was increased almost entirely by increasing the stride frequency (from 3.30 to 4.50 Hz, P < 0.001) with only minor change in stride length (from 2.12 to 2.16 m) from 70% to the maximum running speed. The contact times decreased from 0.131 to 0.094 s (P < 0.001) and flight times from 0.172 to 0.129 s (P < 0.001), respectively. The peak Fz was constant but the peak Fy increased both in braking (P < 0.001) and in propulsion phase (P < 0.01) with increasing speed (Fig. 2).
The peak joint moments remained constant in the ankle joint, decreased 21.8% (from 275 to 215 N·m, P < 0.05) in the knee joint and increased 44.1% (from 145 to 209 N·m, P < 0.05) in the hip joint when the speed increased (Fig. 2). Correspondingly, the angular displacements decreased during the braking phase both in the ankle (31° at the 70% running speed vs 27° at the 100% running speed, NS) and in the knee joint (19° vs 13°, P < 0.05). At the beginning of the contact the hip angle was more extended at lower speeds (144° vs 138°, P < 0.01). The vertical downward displacement of center of mass (COM) during the ground contact decreased from 0.029 to 0.018 m (P < 0.01) when the running speed was increased from 70% to 100%.
The joint moment angle curves demonstrate that stretch-shortening cycle occurs both in the plantarflexor muscles (Fig. 3) and in the knee extensor muscles (Fig. 4).
The average ankle joint stiffness (see Figs. 3 and 5) was constant, and average knee joint stiffness increased from 17 to 24 N·m·deg−1 (P < 0.01) with increasing speed (Fig. 5). The vertical stiffness increased from 103 to 171 kN·m−1 (P < 0.01) with increasing speed (Fig. 5).
Average EMG of SOL muscle increased both in preactivation (P < 0.01) and during the contact phase (P < 0.05) with increasing speed (Fig. 2). The peak activation of SOL occurs about 50 ms after the beginning of contact. In GA muscle, EMG activation was maintained high throughout the preactivation phase and first half of the contact phase. Thereafter, it declined steeply toward the end of contact (Fig. 2). EMG of TA shows two activation peaks, one in the preactivation phase and other during the contact (Fig. 2). EMG activity of the VM and RF muscles increased with increasing speed (P < 0.01) in preactivation phase and the peak activity also occurred earlier at higher speeds in VM (Fig. 2). BF muscle showed highest activity in the preactivation phase, and it decreased toward the end of the contact phase (Fig. 2). The activation of BF increased also with running speed, but the increase was statistically significant only in the contact phase (P < 0.05). The preactivation of GM muscle increased with running speed (P < 0.05) and then decreased during the first half of the contact (Fig. 2).
The major finding of the present study was that the ankle joint stiffness remained the same, whereas the knee joint stiffness increased with the running speed. Stefanyshyn and Nigg (30) reported ankle joint stiffness values of 5.68 N·m·deg−1 in running (4 m·s−1) and 7.38 N·m·deg−1 in sprinting (7.1–8.4 m·s−1), respectively. The present ankle joint stiffness values are very much in line with the results of sprinters in the study of Stefanyshyn and Nigg. However, in that study the sprinters were still accelerating their speed during the measurements, whereas the runners maintained constant speed. The mechanics of running during acceleration is different from the constant speed phase (18), but the actual influence of acceleration on the ankle joint stiffness is unknown. In the present study the knee joint stiffness increased from 17 to 24 N·m·deg−1, and this increase was most marked from 90% to maximal speed. This change was accompanied by decreased flexion of the knee joint (19° at 70% vs 13° at maximum running speed, NS). The joint stiffness patterns of this study (constant ankle joint stiffness and increase in knee joint stiffness with increasing running speed) followed well the tendency observed by Arampatzis et al. (2) at low running velocities. As the purpose of the study was to examine the joint stiffness regulation (via neural control of muscles), the relative running speeds (same effort/input levels) were chosen instead of absolute running speeds (same output level) because the neuromuscular requirements of each individual to reach or to maintain certain absolute running speed are closely related to effort level which can be totally different between the subjects.
Contradictory to the previous studies (2), the knee joint moment decreased with increasing running speed. This might be explained by the changes in running mechanics. At low running speeds, runners hit the ground very often with the heel (heel strikers), whereas at higher running speeds (sprinting), the foot strike is usually performed with the forefoot. As has been presented by Krabbe and Baumann (22), the heel strikers showed higher knee joint moments compared with the forefoot strikers (at 5 m·s−1 running speed). However, no real “heel strike” running patterns were observed in the present study at lower running velocities. It must be noted that the subjects of the present study were very homogenous, and the speeds used were all above those applied by, e.g., Arampatzis et al. (2). Thus, it is very difficult to generalize the speed dependence of the knee joint moment on the basis of the previous or present results.
Alexander (1) proposed that in muscles with long tendon and relatively short muscle fibers in series, the stiffness of the muscle-tendon unit is determined mainly by the stiffness of the tendon, which is known to be constant above ‘toe’ region throughout the range of force levels (29). It has also been shown that increased muscle activation would lead to increased stiffness of muscle fibers, which could be higher than the stiffness of the tendon (9,26). This means that the rate-limiting factor in the triceps surae muscle-tendon stiffness could be the stiffness of the tendon, not the dynamics of muscle activation (35). Thus, it could also be one possible theory in explaining the unchanged ankle joint stiffness observed in the present study.
The anatomical structure of the quadriceps femoris muscle group is clearly different from the triceps surae muscle group with shorter tendinous part and larger amount of muscle tissue (e.g., 34). These anatomical differences make the quadriceps muscle group able to control the musculotendinous stiffness better via the muscular activation. Large standard deviations in the knee joint stiffness reveal the large interindividual variation that is most remarkable at higher speeds. In fact, in some subjects the stiffness of the knee joint was almost constant throughout increasing speeds. Whether this is because of real individual differences in joint stiffness patterns/regulation or just intra-individual variation between contacts remains to be explored further.
In the present study, the vertical stiffness increased linearly with the running speed. It is consistent with the previous results in slow running (2,12). Increase in the vertical stiffness was accompanied by decreased vertical displacement of the COM during the eccentric phase (−37.9%, P < 0.01). The absolute values of the present study for vertical stiffness as well as for vertical displacement of the COM shows a linear continuum to the results of Arampatzis et al. (2) measured at lower running speeds (ranged from 2.5 to 6.5 m·s−1).
Farley and Gonzáles (7) found that it is possible for humans to increase the leg stiffness by increasing the stride frequency. The increase in stride frequency leads to decreased vertical displacement of the spring-mass system during the ground contact phase, and it enables the system to bounce off the ground in less time. Our data demonstrated a similar phenomena in the ankle joint where the joint stiffness showed negative correlation (r = 0.81–0.92, P < 0.01–0.001) with the contact time at all running speeds (Fig. 6). In other words, the subjects who had the highest stiffness in the ankle joint had also the shortest contact times. However, the ankle joint stiffness did not change with increasing running speed although the contact time decreased 28.2% when the speed changed from 70% to 100%. Different patterns (increasing/decreasing ankle joint stiffness) were also detected by some subjects. Probably the stiffness of the ankle joint in sprint running is determined by inherent mechanical properties of muscle-tendon units and neural activation patterns of each individual rather than by the task itself.
The observed co-contraction between the plantarflexor and dorsiflexor muscles, as well as between the knee extensors and knee flexor muscles, will stiffen the joints and the whole leg for the forthcoming impact to the ground (14). Muscle activation of plantarflexors and knee extensors increased during the preactivation phase (Fig. 2) as speed increases. The preactivation of these muscles will increase the stiffness of those muscle-tendon units to tolerate and absorb high impact loads at the beginning of the ground contact (10,23). Additionally, the preactivation of the triceps surae muscle together with stretch reflex activity will ensure the high muscular (and ankle joint) stiffness to support and push the body off the ground as has been pointed out by Komi and Gollhofer (21). This enhanced activation by the stretch reflex is also evident in the present study in the SOL muscle where the activation peaks at 50 ms after the beginning of the contact phase (Fig. 2). Taking into account the electromechanical delay of 13–15 ms reported by Nicol and Komi (28), the mechanical response of stretch reflex would then occur about 60–70 ms after the beginning of the contact. The average contact times in our study were 130 ms at 70% and 94 ms at maximal running speed. Hence, the mechanical effect of stretch reflex response appears at the end of the braking phase or early push-off phase of sprint running.
According to the results of the present study, it seems that in sprint running the spring-like behavior of the leg is adjusted by changing the knee joint stiffness while the stiffness of the ankle joint remains constant. This theory is further reinforced by the joint moment-angle relationships presented in Figures 3 and 4. The ankle joint moments were lower in the concentric phase, which implies that the subjects were not able to tolerate the applied load and utilize the stored elastic energy as efficiently as in the knee joint where the joint moment-angle curves followed the same path in the eccentric and concentric phases. However, we have to be cautious in concluding the role of the knee joint stiffness in sprint running because of the large variation in knee joint stiffness values especially at higher running speeds (Fig. 5).
In the present study, both the ankle joint stiffness and joint moment were constant at different running speeds. Arampatzis et al. (2) reported an increase in the ankle joint moment while the stiffness of the ankle joint showed a curvilinear pattern (without any significant difference) with the increasing running speed from 2.5 to 6.5 m·s−1. In the studies of Stefanyshyn and Nigg (30) and Farley and Morgenroth (8), the ankle joint stiffness increased with the running speed and hopping height. However, contrary to the present study, the ankle joint moment was also increased correspondingly. It is possible that the different results are simply due to task differences. The submaximal levels of tasks in the other studies were probably not high enough to fully load the triceps surae muscle-tendon unit, as subjects were still able to increase their ankle joint stiffness. Furthermore, the different nature of the tasks will make the comparison difficult between sprinting and hopping in place (8) as well as between constant speed sprinting and acceleration (30). However, we believe that the constant ankle joint stiffness observed in this study might be due to dominating role of the (constant) tendon stiffness already discussed earlier.
In the whole subject group, the ankle joint stiffness showed higher values with shorter contact times at all measured relative running speeds (Fig. 6). Unfortunately, no correlation was found between ankle or knee joint stiffness and running speed. It could be explained by increased output of hip extensor muscles because the increase in running speed is achieved by increasing the work and power produced by the hip extensors (23). Still one would assume that stiffer ankle and knee joint will transmit the work done by hip extensors better and thus propelling the body forward more effectively as in world-class level sprinters (17). According to the results of this study, it seems that ankle or knee joint stiffness may not be a limiting factor in increasing the running speed. However, high ankle joint stiffness may shorten the ground contact time and thus enhance the mechanical efficiency of locomotion.
The authors would like to acknowledge the assistance of Mr. Markku Ruuskanen and Ms. Sirpa Roivas (technical preparations) as well as Ms. Pirkko Puttonen and Ms. Marja-Liisa Romppanen (data analysis). This study was supported in part by a grant (119/722/99) from the Ministry of Education (Finland).
Address for correspondence: Sami Kuitunen, Neuromuscular Research Center, Department of Biology of Physical Activity, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland; E-mail: firstname.lastname@example.org.
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Keywords:© 2002 Lippincott Williams & Wilkins, Inc.
JOINT MOMENT; STIFFNESS; RUNNING; REGULATION MECHANISMS; EMG