Landing techniques are essential aspects of many athletic events, including gymnastics, basketball, soccer, football, volleyball, and parachuting. Although many investigators have analyzed the performance of the jumping phase of these sports, the analysis of the landing has been limited (2,3,6,11–17). There is a danger of injury during landing activities, and the kinematics and forces involved in different landing strategies may be closely related to the occurrence of trauma.
To develop computer models and human analogs to further study drop landings, it is necessary to quantify the forces and Achilles tendon stiffnesses present during an impact landing. This can be accomplished using force plate measurements, accelerometer readings, kinematic analyses, and inverse dynamics calculations. Different landing strategies should be studied to elucidate the muscle stiffness for different landing techniques. To isolate the role of the ankle during a drop, subjects can be instructed to perform landings with their knees stiff. Other researchers (2,13) have investigated stiff and soft landings to determine the power and work performed during each landing type but did not do Achilles tendon force or stiffness calculations.
The primary motivation behind this study was to provide inputs into a cadaver model to investigate ankle injuries (20). To replicate a human drop landing, it was necessary to create an analog Achilles tendon/triceps surae complex. This required values for initial ankle angle at impact, the Achilles tendon forces during a drop, and the Achilles tendon stiffness during the landing. These human volunteer data were required to set up the cadaver drops, which involved in situ traumatic inversion sprains to the cadaver specimens.
The goals of the testing were a) to determine the maximum vertical forces and maximum tibial accelerations, b) to calculate the Achilles tendon force and the initial Achilles tendon stiffness, and c) to determine the kinematics and kinetics of the ankle for four different landing strategies.
Four landing conditions from a 30.48-cm (12-inch) height were tested. Before each condition, the subjects were handed an instruction sheet describing the type of landing to perform, which minimized any changes in drop performance due to investigator bias during the description of the drop procedure. The instructions are provided below:
Choose whatever landing technique you would utilize in an actual sporting event, but remember to keep your arms above your head the entire test.
Stick the landing.
Now perform the same type of drop but with minimal knee flexion (do not lock your knees, but keep them as straight as you can). Remember to keep your arms above your head.
Stick the landing and flex your calf muscles.
Perform the same type of drop as in test 2, but this time try to make the landing soft as possible by absorbing the impact through your toes and by flexing your calf muscles. Remember to keep your knees as straight as possible and your arms above your head.
Stick the landing but land more flat-footed.
Perform the same type of drop as in test 3, but do not maximally flex the calf muscles. Remember to keep your knees straight as possible and keep your arms above your head.
Five trials were collected for each drop condition. The order of the trials was not randomized, because the instructions given in the final two conditions may have affected the way the self-selected stiff-kneed tests were performed. The four drops described above will be referred to as BN (knees Bent, Natural landing), SN (knees Stiff, Natural landing), SP (knees Stiff, absorb through Plantar flexors), and SH (knees Stiff, landing on Heels).
Subjects were male recreational athletes between the ages of 23 and 40 with a mean age of 29.0 ± 4.7 yr. The subjects were 175.5 ± 5.5 cm tall and weighed 723.0 ± 93.5 N. The local institutional review board approved the experimental protocol, written informed consent was obtained from each subject, and a full explanation of the test procedures provided. A single-axis accelerometer (ADXL-50, Analog Devices, Norwood, MA; ±50 g) was placed on the shank approximately 15 cm distal to the knee and aligned along the long axis of the bone. The transducer was attached to shaved skin with double-sided tape, and then a strap was tightened around the accelerometer and leg. This procedure is similar to the methods used by other investigators (6,11,14). Kinematic markers were placed on the head of the fifth metatarsal, the lateral malleolus, just below the lateral epicondyle of the knee (to approximate the knee joint center), and the anterior superior iliac spine of each patient.
An overhead drop bar was constructed to constrain the drop velocity to the vertical direction. The height of the drop was set by placing a 12-inch rod under the calcaneus as the subject hung from the bar. The adjustable bar could be raised to accommodate each subject in the study. The drop bar was positioned over an OR6–5-1000 force plate (Advanced Mechanical Technology, Inc., Watertown, MA), which was covered by a 3/4-inch pad. This pad consisted of 1/2-inch medium grade neoprene sponge and 1/4-inch 40 durometer tan gum latex adhered to the top of the sponge. Previous research at Aberdeen Proving Grounds has shown that the drop pad reasonably approximates the landing characteristics of the ground. The drop setup and the subject joint angle definitions are shown in Figure 1.
Drops were performed with only one leg landing on the force plate. A pad was placed on the floor beside the force plate to provide a continuous surface for the landings. Three warm-up drops were performed to familiarize the subject with the protocol, then testing began. The subjects were filmed using a 60-Hz camera (Panasonic WV-D5000, Secaucus, NJ), and kinematic analysis was performed with a commercial motion analysis system (Peak Performance Technologies, Inc., Englewood, CO). The force and accelerometer data were collected at 1800 Hz and were synchronized to the kinematic data.
The kinematic data were processed using Woltring’s Fortran package (21). The position and angular data were interpolated using a quintic spline fit, then differentiated to obtain velocities and accelerations. A generalized cross-validation method was utilized to determine appropriate smoothing parameters, after which it was decided to use a smoothing parameter corresponding to a cut-off frequency of 20 Hz.
Inverse dynamics were performed to determine the Achilles tendon force acting on the foot during each landing type. A free-body diagram of the foot is shown in Figure 2. If moments are summed about the ankle joint center (point O), the governing equation is:MATH
where σMo is the sum of all external moments about point O, I is the mass moment of inertia (which is a scalar in a two-dimensional analysis), α is the angular acceleration, m is the mass of the foot, a is the acceleration (measured by videography) of the center of mass of the foot, and d is the vector from point O to the center of mass of the foot. Substituting in force values from the free-body diagram, the equation becomes:MATH
where Mint is the internal moment at the ankle, F and Mz are the ground reaction loads measured by the force plate, r is the vector from point O to the center of the force plate, W is the weight of the foot, and d is the vector from point O to the center of mass of the foot.
The center of mass of the foot was estimated as being at the midpoint of the ankle marker and the head of the fifth metatarsal. The angular acceleration of the foot was determined by differentiating the foot position using Woltring’s package. The mass and moment of inertia for the foot were determined from regression equations based on height and weight of each subject using the Generator of Body Data (GEBOD) computer program (7). The mean foot mass for the subjects was 0.769 ± 0.079 kg, and the mean mass moment of inertia about the transverse (medial-lateral) axis of the center of mass of the foot was 0.00335 ± 0.00053 kg·m−2.
The internal moment at the ankle joint is influenced by a number of forces, including muscle activity, moments acting due to the bony interfaces within the joint, and ligamentous and soft tissue structures. For the current analysis, it was assumed that the action of the Achilles tendon was the dominant force, neglecting all other structures inducing an internal moment. To calculate the Achilles tendon force, a moment arm must be determined. A study by Rugg et al. (18) calculated the moment arm of the Achilles tendon as a function of ankle flexion angle θa using magnetic resonance imaging (MRI). A cubic polynomial was fit to data obtained from this study, and the moment arm Marm determined from the equation:MATH
The calculated internal moment was divided by the moment arm to calculate the Achilles tendon force.
After the Achilles tendon forces were determined, the stiffness of the plantar flexors was calculated. The change in length of the gastrocnemius as a function of knee and ankle angle has been determined using cadavers (5). Cubic equations involving the knee and ankle angles were calculated as:MATH
where %δL is the percent change in gastrocnemius length and φa and φk are the ankle and knee angles, respectively. The φa and φk angles used by Grieve et al. (5) are the supplement angles of the angle definitions used in the current study (θa and θk). The original length L of the gastrocnemius muscle was estimated as the distance between the ankle marker and the knee marker, and the overall change in length δL calculated as the product of L and %δL. The Achilles tendon force was plotted as a function of δL, and a linear regression performed on the curve between the beginning of impact (F y > 10 N) and the point of maximum Achilles tendon force. By using this technique, an estimation of the muscular stiffness during the primary impact phase of the landing can be obtained.
The dependent variables analyzed were the maximum vertical ground reaction force, the maximum tibial acceleration, and the calculated Achilles tendon force. By using SPSS (SPSS, Inc., Chicago, IL), a reliability analysis was performed on each of the dependent variables to ensure that there was no training or sequence dependence for the five trials of a single drop condition. An average score for the five trials of each drop type was calculated and used for further statistical analyses. Three different one-way analyses of variance (ANOVA) with repeated measures were performed using SigmaStat (Jandel Scientific, San Rafael, CA) to determine differences between landing techniques, and post hoc analysis was performed using Student-Newman-Keuls method.
Representative accelerometer, vertical force, and Achilles tendon force data are shown in Figures 3, 4, and 5, respectively. Subjects performed the requested skills with reasonable consistency. Kinematic angles found during the testing are shown in Table 1. The average minimum knee angles for drop type BN (with knee bend) were nearly 20° less than the three stiff-legged drops, indicating greater knee flexion for the BN drops. The tibia-to-vertical angles at impact were consistent for the three stiff-kneed drop types. The ankle angles at impact were also recorded. The SP drop plantar flexion angle was 10° larger than the other drop types.
Reliability analyses were performed on the five trials of each drop type for each dependent variable (4 types × 6 dependent variables = 24 reliability analyses). The analyses were performed to determine whether there were any training, fatigue, or other systematic difference in the different trials and whether it was appropriate to take an average score across the five trials. A Cronbach’s alpha and an analysis of variance comparing the five trials were determined for each reliability analysis. The reliability analyses demonstrated that the data did not show significant dependence on trials. In the cases where the ANOVA comparing the different trials showed any significant differences, the Cronbach’s alpha was over 0.90. Because there was only one score below 0.70 in the 24 different reliability analyses, it was determined that the tests provided reliable results. An average score was therefore calculated for each individual for each of the four drop types.
There were significant differences in peak forces (P < 0.00001), peak tibial accelerations (P = 0.0057), and peak calculated Achilles tendon forces (P = 0.0239). The average peak vertical forces, peak accelerations, and peak calculated Achilles tendon forces are shown in Table 2. There were significant differences between all variables across the different drop types. The lowest vertical forces were achieved for drops BN and SP, which were significantly lower than SN and SH but not significantly different from one another. The forces obtained for the SH drops were significantly higher than all other drop types. The peak accelerations for the SH drops were also significantly higher than all other drop types. BN, SN, and SP accelerations were not significantly different from one another, although the SP drops did have the smallest peak accelerations.
The maximum Achilles tendon force was highest for drop type SP. It was significantly greater than drop type SH, which generated the lowest forces, but not from the other two drop types.
In general, the Achilles force increased linearly with gastrocnemius length in the interval between the onset of impact and the point of maximum Achilles tendon force. A representative graph for each drop type is shown in Figure 6. If the correlation coefficient r2 was less than 0.7, the stiffness value for the trial was eliminated from the average calculation. Furthermore, upon visual examination of the plots, curves that were outliers were eliminated. The resulting trial values were averaged for each subject, and the resulting scores used to determine means and standard deviations for each drop type. The stiffness and r2 value for each drop type are shown in Table 3. The overall average stiffness for all drop types was 166,345 N·m−1.
The angular data in Table 1 demonstrate that the subjects were able to perform the required tasks with little difficulty. The ankle angles at impact compare favorably to values found by Gross and Nelson (6) for landings with heel contact (126.8 ± 3.3°) and for landings without heel contact (130.1 ± 3.6°). The minimum knee bend angle highlighted the differences between the BN drops and the stiff-legged drops: the subjects flexed their knees 30° more during the BN drops than during the stiff-kneed drops. The tibia-to-vertical angles upon impact and the knee angles at impact were remarkably similar for all four drop types (refer to Table 1).
The differences in maximum vertical force and maximum acceleration for the different drop configurations can be explained by the amount of energy absorbed by eccentric contractions of the musculature. The SP drops had slightly lower vertical forces than the BN drops. This indicates that during normal landings, the body does not maximize the energy-absorbing characteristics of the ankle plantar flexors. Because the knees may be “prepared” to bend more during the BN drops, the gastrocnemius may not be firing fully because it will not be in an optimum position once the knees bend. This is reiterated by the Achilles force data. Drop type SP resulted in the greatest amounts of Achilles tendon force, whereas the SH resulted in the smallest. Because the gastrocnemius is a two-joint muscle, it becomes more slack when the knee is bent. This may explain the lower Achilles tendon force obtained during the BN drops. During the SP drops, the subjects plantar flexed more when instructed to absorb the impact energy through their toes. The data show that this results in a softer landing, both in maximum acceleration and in peak force, than the other drop strategies (although not all comparisons were statistically significant).
These data compare favorably to values reported by other investigators. To compare the forces to other studies, it is necessary to normalize them to body weight and multiply them by two (assuming landings occur symmetrically on both feet). It is also necessary to realize that different studies utilized different landing surfaces; the current pad used a neoprene sponge/latex combination, others utilized a thin rubber pad, others used the force plate surface. The maximum vertical forces, normalized to body weight, are shown in Table 4. Panzer (17) provides a review of other ground reaction forces, including forces for running of 1–3 times body weight (× BW), for a triple jump of 7.1–12.6 × BW, and for basketball rebounds of 2.3–7.1 × BW. Nigg (15) also reviews different loads including a running takeoff before a jump (1.4–8.1 × BW) and landings on a mat after 50–150 cm drops (1.5–3.3 × BW). The results from the current study can be most directly compared to those of McNitt-Gray (12) and to those of Dufek and Bates (3). During landings from 0.32 m, gymnasts and recreational athletes averaged 3.9 and 4.2 × BW, respectively, when landing onto a thin layer of rubber. This compares to 4.29 × BW obtained for the BN drops in the current study. The Dufek and Bates study shows the change in vertical force that can be expected when the stiffness of the knees is altered.
A recent study by Zhang et al. (22) investigated the energy dissipation of lower extremity joints during drops of 32, 62, and 103 cm. The subjects were instructed to use three different self-selected landing strategies based on knee joint range of motion (soft, normal, and stiff). As height increased, the eccentric work by the ankle musculature increased. It is interesting to note that the eccentric ankle work during the stiff drop landing was not significantly different than that during the normal drop landing. This is consistent with the maximum Achilles tendon force measured in the current study, which was nearly identical for the SP and BN landings.
Hennig and Lafortune (8) have expressed concern about using skin-mounted accelerometers. They argue that movement of the skin and motion artifacts can produce accelerations up to two times greater than for bone-mounted accelerometers. Gross and Nelson (6), however, are of the opinion that skin-mounted accelerometers provide acceptable results, provided a strapping preload is applied to the transducer. In their study, subjects landed after performing a maximum jump. Peak accelerations obtained at the tibia and calcaneus were 14.3 ± 3.6 G and 20.8 ± 9.3 G, respectively. They modeled the accelerometer attachments with a spring and dashpot, and found that their predicted error at the tibia was less than 8%. Nigg (15) reports accelerations of 10–14 G for running on asphalt and 28–35 G when landing from 1.5 m onto a 7-cm mat. When the mat thickness was increased to 40 cm, the accelerations were reduced to 8 G. These values are all consistent with the maximum accelerations ranging from 9.8 to 20.7 G obtained in the current study.
The maximum Achilles tendon forces can also be compared to other studies. The highest forces were for the SP drops, followed by the SN drops. This is consistent with Devita and Skelly’s (2) conclusion that the role of the gastrocnemius and soleus muscles increases as knee stiffness increases. Burdett’s (1) joint prediction model calculated Achilles tendon forces of 5.3–10 × BW for the plantar flexion group during running. Komi et al. (10) implanted a force transducer into the Achilles tendon of a healthy volunteer and obtained maximum forces of 9 kN for running, 2.2 kN for a squat jump, 1.9 kN for a countermovement jump, and 4.0 kN for repeated hopping. Although there is some concern over the accuracy of the calibration methods, this is the best in vivo comparison available. Scott and Winter (19) also calculated forces during running, obtaining peak plantar flexion moments of 170 Nm, resulting in a plantar flexion force of 3100 N or 6.3 × BW. Finally, McNitt-Gray (12) calculated net joint moments at the ankle for drops from 0.32, 0.72, and 1.28 m. Normalizing to body mass, she obtained values of 4.28, 5.10, and 6.25 N-m/kg for the three drop heights. This can be compared to the current study, which had values of 1.246, 1.414, 1.517, 1.237 N-m·kg−1 for the BN, SN, SP, and SH drops, respectively.
The lower Achilles tendon values obtained from the current study could be due to several factors. The drop landings were from a relatively low height, resulting in landings with lower vertical forces than in other studies. In addition, the subjects’ heels contacted the landing surface, with peak forces occurring during the heel contact. Because the moment arm to the ankle is very short when this peak force occurs, the Achilles tendon is not required to exert much force to counteract the ground reaction force. In other studies, particularly when the knees are allowed to bend, more of the impact may occur on the toes. This would add substantially to the moment required by the Achilles tendon complex. Other differences may be due to greater anterior-posterior forces, which would be present in running or some of the other functional tasks. As can be seen in Figure 2, a larger anterior-posterior force can result in a larger internal moment and therefore a greater Achilles tendon force. Finally, errors may have occurred due to the low sampling rate of the video data. The inertial influence, which was very low for the current tests, may have actually been much greater. Because the mass and mass moment of inertia of the foot are so low, it is anticipated that this inertial influence would not significantly change the Achilles tendon force values.
The stiffness values obtained in the current study (144–208 N·mm−1) are about 3 times higher than those reported by Gollhofer et al. (4). In examining both countermovement jumps and squat jumps and assuming an initial triceps surae length of 40 cm, these authors obtained stiffness values of approximately 55–60 N·mm−1. Stiffnesses for drop jumps, where the athlete lands and immediately jumps (as in plyometric training), were nearly twice as high. A study by Herzog et al. (9) examined in vivo muscle stiffnesses while performing isometric strength tests. The average stiffness values ranged from 31 to 48 N·mm−1. Although the stiffness values calculated in the current study are higher than those found in other studies, differences in measurement techniques and in the functional activities investigated may account for the discrepancies. During jumping tests, the knee angle changes much more than in simple drops. This may have resulted in larger length changes in the Achilles tendon than for the drop studies, again contributing to smaller stiffness values than calculated in the current study.
There are several limitations to the current study. The knee angles were calculated using the anterior superior iliac spine as the hip marker, which may have introduced some error in these measurements. These measurements, in turn, affect the gastrocnemius length calculations. The changes in knee angle should be minimal, and all of the measurements were taken using the same marker locations. Another limitation is the fact that only one drop height was used. As discussed by Zhang et al. (22), the subjects may have totally changed their landing strategies from heights greater than 30 cm. Although drops from different heights may have provided interesting data, it was not the goal of the current study.
The lowest Achilles tendon force values were obtained during the stiff-kneed, maximum plantar flexion (SP) landings. This indicates that during normal landings, athletes may not use the full potential of the triceps surae muscles. The tibia angle at impact was remarkably similar between the bent knee and the stiff-kneed trials. The initial impact occurred with the tibia nearly vertical for all drop types. The Achilles tendon forces determined during the drop activities were larger than for other dynamic activities, and the stiffness values were also considerably higher. This may be due to greater muscle length excursions of other jumping activities that have been analyzed when compared with the landings analyzed in the present study. Data from this study will be used as inputs to a cadaveric study to analyze ankle injuries during landings on uneven surfaces and may also be useful in the development of computer models and human analogs.
Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the United States Air Force.
Work was performed at the Orthopedic Biomechanics Institute, 5848 South 300 East, Salt Lake City, UT. Dr. Self is currently an Assistant Professor in the Engineering Mechanics Department at the United States Air Force Academy.
Address for correspondence: Brian P. Self, Ph.D., HQ USAFA/DFEM, 2354 Fairchild Dr, Suite 6H2, USAF Academy, CO 80840-6240; E-mail: Brian.Self@usafa.af.mil.
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Keywords:© 2001 Lippincott Williams & Wilkins, Inc.
ACHILLES TENDON; IMPACT; STIFFNESS