The model ACL was loaded only in the first 25% of the landing phase as the knee flexed from 33° to 48°. ACL force decreased to zero shortly after initial impact, then increased quickly to reach a maximum of 253 N (∼ 0.4 BW) at 40 ms (Fig. 7).
The patellar tendon applied an anterior shear force to the lower leg throughout the simulated landing. Peak patellar-tendon shear force was around 600 N (∼ 0.9 BW) and occurred shortly after initial impact (Fig. 8, PT). The gastrocnemius also applied an anterior shear force to the lower leg because this muscle contacts the posterior tibial condyles and therefore tends to push the lower leg anteriorly as it contracts and develops force. However, this effect was small in the model, as gastrocnemius applied a relatively small anterior shear to the lower leg.
Hamstrings applied a posterior shear force to the lower leg throughout the landing phase. This force increased significantly with time, reaching a peak of around 700 N (∼ 1.0 BW) near the end of the landing phase (Fig. 8, Hamstrings). The tibiofemoral contact force (a result of the contact forces acting in the medial and lateral knee compartments) applied an anterior shear force to the lower leg. Peak tibiofemoral shear force was 550 N (∼ 0.8 BW) and occurred at 40 ms after initial impact (Fig. 8, TF Contact).
The ground reaction applied a significant posterior shear force to the lower leg during landing. Peak shear force induced by the ground reaction was 1214 N (∼ 1.8 BW) and occurred almost immediately after initial impact. The ground reaction also gave rise to a second, smaller peak shear force of 778 N (1.1 BW) at 50 ms after impact (Fig. 8, GRF).
The total shear force applied to the lower leg was directed anteriorly in the first 70 ms of the landing phase, except for the period shortly after initial impact when the ground reaction applied a large posterior shear force to the lower leg (Fig. 8, Total). Peak total anterior shear force was 220 N (∼ 0.3 BW) and occurred at precisely the same instant (40 ms) as the maximum force transmitted to the ACL.
The purpose of this study was to calculate and explain the pattern of force transmitted to the ACL during a soft-style drop-landing motion. A specific aim was to describe and explain the interaction between muscle, joint contact, and ground reaction forces in relation to ACL loading on impact. Before interpreting the results, it is important to consider the limitations of the analysis undertaken here.
First, and perhaps most significantly, the analysis was performed on a single male subject. It is important to note, however, that the joint angles and ground reaction forces measured for this subject are within 1 SD of landing data obtained from other studies in which large numbers of subjects were used (9,18). This suggests that the results of our analysis are likely to apply more widely than to the single subject studied here.
Second, optimization theory was not used to predict muscle coordination during the simulated drop-landing maneuver. The landing movement was simulated using a 3D model of the body that has been validated previously for vertical jumping (2) and walking (3,4). In each of these studies, a dynamic optimization problem was formulated to determine the muscle excitations needed to produce an optimal performance in accordance with a meaningful cost function (e.g., minimizing metabolic energy consumption in normal gait (3)). In the present study, rather than calculating the muscle excitations according to an assumed cost function, the input excitation patterns were modified until the joint angles and ground forces calculated in the model agreed with the measurements of the same variables obtained from experiment. While the fidelity of the simulation might be improved by solving an optimization problem to predict the optimal pattern of muscle excitations, the results of Figures 3 and 4 show, at the very least, that the model simulation replicates the salient features of a soft-style drop-landing maneuver. The calculated and measured joint angles of the hip, knee, and ankle (Fig. 3) and the time histories of the vertical and fore-aft components of the ground reaction force (Fig. 4) were all within 1 SD of landing data obtained from other studies in which large numbers of subjects were used (9,18).
Third, knee-ligament forces were calculated by assuming that the lower leg remained in static equilibrium at each instant during the landing motion, which meant that the effects of centrifugal (velocity-dependent) and inertial forces were neglected in the analysis. Neglecting the inertial contribution of the lower leg affects the contribution made by the ground reaction force to the shear force applied at the knee. More specifically, assuming that all of the ground reaction force was transmitted to the knee meant that a much larger posterior shear force was applied to the lower leg immediately after impact (Fig. 8, GRF at 10 ms). Post hoc analysis of the landing simulation showed that the first peaks in the horizontal and vertical ground reaction force were largely due to the inertia of the lower leg; that is, the appearance of these peaks were the result of the mass of the lower leg impacting the ground. To evaluate the effect of this inertial force on the estimates obtained for knee-ligament loading, ACL force was recalculated in the model assuming no ground reaction force was transmitted to the knee 10 ms after initial impact This analysis showed that ACL force was only 149 N at that instant, indicating that the ACL is not heavily loaded when the foot first impacts the ground. The results of Figure 7 should therefore be viewed as a lower bound for ACL forces in landing.
Fourth, the calculation of ligament loading neglected axial rotation of the bones at the knee. As the living knee flexes, the tibia rotates internally relative to the femur; this phenomenon is known to increase the force transmitted to the ACL (29). Because the static equilibrium simulations were performed with the knee held in neutral axial rotation, the calculated values of ACL force may be underestimated in the model. More reliable measurements of the axial rotations of the femur and tibia in the first 50 ms of landing may help to determine the contribution of internal and external segment rotations to the pattern of force incurred by the ACL during this motion.
Fifth, the first peak in the horizontal ground reaction force did not match the result obtained from the experiment, and the precise reason for this is as yet unknown. Several factors that may have accounted for this discrepancy were investigated by the authors, including a mismatch in forward velocity of the center of mass between model and experiment before landing. Further analyses of the experimental data showed that the hip marker placed on the subject had a forward velocity of less than 0.5 m·s−1 before ground contact. A series of post hoc computer simulations aimed at investigating the influence of a 0.5 m·s−1 forward velocity on the horizontal component of the ground reaction force generated during landing produced little change from the results shown in Figure 4. Even though we have not been able to determine the cause of the disagreement between model and experiment with respect to the first peak in the horizontal ground force, this particular limitation does not affect the findings obtained from the analysis reported here. The reason is that the first peak in the horizontal ground force produces a posterior shear force at the knee, which acts to unload the ACL. If the first peak in the horizontal ground force were increased to match that generated by the subject, the posterior shear force at the knee would increase as well, and the force transmitted to the ACL would be even less. In terms of ACL loading during landing, it is the second peak in the horizontal ground reaction force that is critical. This peak produced an anterior shear force at the knee, which increased the force transmitted to the ACL during landing. Fortunately, the model was able to reproduce with reasonable accuracy the measurements obtained for both the magnitude and timing of the second peak in the horizontal ground force during landing.
Knee-ligament loading in landing is determined by the balance of muscle forces, ground reaction forces, and joint-contact forces applied to the lower leg. The pattern of force transmitted to the ACL is explained by sum of the components of each of these forces acting perpendicular to the long axis of the tibia (i.e., the total shear force; compare ACL force in Fig. 7 with Total in Fig. 8).
The analysis presented here indicates that three factors contribute most significantly to the total shear force applied to the lower leg during landing: 1) the anterior shear force supplied by the patellar tendon; 2) the anterior shear force induced by the compressive force acting at the tibiofemoral joint; and 3) the posterior shear force applied by the ground reaction. Immediately after initial impact, ACL force dropped to zero for a very short period of time. Even though the anterior shear force supplied by the patellar tendon was maximum at this time, ACL force decreased to zero because of the much larger increase in the posterior shear force applied by the ground reaction (compare PT and GRF at 10 ms in Fig. 8). The posterior shear force induced by the ground reaction was large shortly after impact because of the direction of the resultant ground reaction vector. The resultant ground reaction passed far behind the knee because the fore-aft component of the ground reaction pointed posteriorly at this time (F1h in Fig. 4B). The anterior shear force supplied by the patellar tendon peaked immediately after initial impact, even though quadriceps force did not peak until much later in the landing movement. The peak in patellar tendon shear force at this time was caused by the relatively large angle between the patellar tendon and the long axis of the tibia, which in turn was due to the posterior shift of the tibia relative to the femur brought about by the large posterior shear force applied by the ground reaction.
Peak ACL force at 40 ms after impact was due primarily to an increase in the anterior shear force induced by tibiofemoral contact, a relatively large anterior shear force supplied by the patellar tendon, and a decrease in the posterior shear force induced by the ground reaction. Patellar tendon shear force was relatively high 40 ms after impact because vasti force was high (compare vasti in Fig. 6 with PT in Fig. 8), and also because the patellar tendon was anteriorly inclined with respect to the long axis of the tibia.
The anterior shear force induced by the tibiofemoral contact force also peaked around 40 ms after initial impact. There were two reasons for this: 1) vasti force was relatively large at this time, and this force was transmitted directly through the condyles of the knee in the model; and 2) the magnitude of the resultant ground reaction was highest at this time (F2v and F2h in Fig. 4) and its direction was more closely aligned with the long axis of the tibia (i.e., it passed closer to the knee) because the fore-aft component was directed anteriorly (F2h in Fig. 4B). (We note here that the vertical component of the ground reaction always passes behind the knee because the tibia is angled anteriorly relative to the ground). Thus the ground force contributed significantly to the tibiofemoral contact force at around 40 ms after initial impact.
Tibiofemoral contact force results in an anterior shear force at the knee because the articular surface of the model tibia is sloped an average of 8° posteriorly. This slope, coupled with a large tibiofemoral contact force, creates an anterior drawer of the tibia relative to the femur. Dejour and Bonnin (10) studied the effect of posterior tibial slope on anterior tibial translation in normal and ACL-deficient knees using a weight-bearing radiographic technique. Their results showed a 6-mm increase in anterior tibial translation for every 10° increase in posterior tibial slope, in both intact and ACL-deficient knees. The results of the present study suggest that tibial slope contributes significantly to the anterior shear force applied to the knee during landing.
The posterior shear force induced by the ground reaction decreased around 40 ms after impact. This decrease is explained mainly by the fact that the fore-aft component of the ground force pointed anteriorly at this time. The fore-aft ground force increased quickly at 40 ms to reach a peak of 1.1 BW at 40 ms (F2h in Fig. 4B). Thus the resultant ground force vector became more closely aligned with the long axis of the tibia, decreasing the shear component of the ground reaction at the knee.
Much has been written about the intrinsic and extrinsic factors responsible for noncontact ACL injuries in sports. One popular belief is that landing with an extended knee increases the anterior pull of the quadriceps, in turn straining the ACL. The reasoning is as follows: If the knee is more fully extended during ground contact, the patellar tendon will be more anteriorly inclined relative to the long axis of the tibia. This, combined with a large quadriceps force developed in eccentric contraction, causes a large anterior shear force to be applied to the lower leg. An increase in anterior shear force increases anterior translation of the tibia relative to the femur, causing an increase in ACL force (32). Thus quadriceps force is often implicated in ACL injury, as these muscles are thought to pull the tibia anteriorly with such vigor as to overstrain the ACL. The model calculations revealed that the pattern of ACL force in landing cannot be explained by the mechanism of quadriceps force alone. The maximum force transmitted to the model ACL resulted from a complex interaction between the patellar tendon force, the compressive force acting at the tibiofemoral joint, and the force applied by the ground to the lower leg. While the role of the patellar tendon was significant in determining peak ACL loading in landing, the contributions of the shear forces induced by the tibiofemoral contact force and the ground reaction force were just as important and cannot be discounted (Fig. 8). The latter two mechanisms have received less attention in the literature, and future studies ought to be directed at understanding the relationship between knee flexion angle and the anterior and posterior shear forces induced by tibiofemoral contact and the ground reaction force, respectively.
Finally, it was surprising to find that peak ACL force for a soft-style landing is comparable to that for normal walk ing. Shelburne et al. (28) recently showed that the maximum force transmitted to the ACL in normal gait is around 0.4 BW, which is also the value estimated here for landing. In walking, the patellar tendon shear force dominates the total shear force applied to the lower leg early in stance (28). The ground reaction applies only a small posterior shear force to the lower leg early in the stance phase of walking because the angle between the resultant ground force vector and the long axis of the tibia remains small. This explains why maximum force is transmitted to the ACL in early stance. In landing, however, ACL loading is regulated to a much larger extent by the ground force generated on impact. The relatively large posterior shear force created by ground reaction limits maximum force transmitted to the ACL. The ground reaction applies a posterior shear force to the lower leg whenever the resultant ground force vector passes behind the knee. ACL force remains relatively low in a soft-style landing because the angle between the resultant ground force vector and the long axis of the tibia is kept relatively large.
This study was completed in partial fulfillment of the Master of Arts in the Department of Kinesiology at The University of Texas at Austin. Financial support was provided in part by the Steadman♦Hawkins Sports Medicine Foundation, the NFL Charities, and the Department of Biomedical Engineering at The University of Texas at Austin. The authors wish to thank Takashi Yanagawa, M.A. for his help with programming and Henry Ellis for assistance with in vivo data collection and reduction.
1. Abdel-Rahman, E. M., and M. S. Hefzy. Three-dimensional dynamic behaviour of the human knee
joint under impact loading. Med. Eng. Phys
. 20:276–290, 1998.
2. Anderson, F. C., and M. G. Pandy. A dynamic optimization solution for vertical jumping
in three dimensions. Comput. Methods Biomech. Biomed. Engin
. 2:201–231, 1999.
3. Anderson, F. C., and M. G. Pandy. Dynamic optimization of human walking. J. Biomech. Eng
. 123:381–390, 2001.
4. Anderson, F. C., and M. G. Pandy. Static and dynamic optimization solutions for gait are practically equivalent. J. Biomech
. 34:153–161, 2001.
5. Anderson, F. C., and M. G. Pandy. Individual muscle contributions to support in normal walking. Gait Posture
. 17:159–169, 2003.
6. Blankevoort, L., J. H. Kuiper, R. Huiskes, and H. J. Grootenboer. Articular contact in a three-dimensional model of the knee
. J. Biomech
. 24:1019–1031, 1991.
7. Bobbert, M. F. Drop jumping
as a training method for jumping
ability. Sports Med
. 9:7–22, 1990.
8. Boden, B. P., G. S. Dean, J. A. Feagin, Jr., and W. E. Garrett, Jr. Mechanisms of anterior cruciate ligament injury
. 23:573–578, 2000.
9. Decker, M. J., M. R. Torry, D. J. Wyland, W. I. Sterett, and J. Richard Steadman. Gender differences in lower extremity kinematics, kinetics and energy absorption during landing. Clin. Biomech
. 18:662–669, 2003.
10. Dejour, H., and M. Bonnin. Tibial translation after anterior cruciate ligament rupture. Two radiological tests compared. J. Bone Joint Surg. Br
. 76:745–749, 1994.
11. Deluca, C. J. The use of surface electromyography in biomechanics. J. Appl. Biomech
. 13:135–163, 1997.
12. DeMorat, G., P. Weinhold, T. Blackburn, S. Chudik, and W. Garrett. Aggressive quadriceps
loading can induce noncontact anterior cruciate ligament injury
. Am. J. Sports Med.
13. Devita, P., and W. A. Skelly. Effect of landing stiffness on joint kinetics and energetics in the lower extremity. Med. Sci. Sports Exerc
. 24:108–115, 1992.
14. Garg, A., and P. S. Walker. Prediction of total knee
motion using a three-dimensional computer-graphics model. J. Biomech
. 23:45–58, 1990.
15. Garner, B. A., and M. G. Pandy. The obstacle-set method for representing muscle paths in musculoskeletal models. Comput. Methods Biomech. Biomed. Engin
. 3:1–30, 2000.
16. Kadaba, M. P., H. K. Ramakrishnan, and M. E. Wootten. Measurement of lower extremity kinematics during level walking. J. Orthop. Res.
17. Lange, G. W., R. A. Hintermeister, T. Schlegel, C. J. Dillman, and J. R. Steadman. Electromyographic and kinematic analysis of graded treadmill walking and the implications for knee
rehabilitation. J. Orthop. Sports Phys. Ther
. 23:294–301, 1996.
18. Madigan, M. L., and P. E. Pidcoe. Changes in landing biomechanics during a fatiguing landing activity. J. Electromyogr. Kinesiol
. 13:491–498, 2003.
19. McConville, J., C. Clauser, T. Churchill, J. Cuzzi, and I. Kaleps. Anthropometric relationships of body and body segment moments of inertia. Technical Report AFAMRL-TR-80–119. Wright-Patterson AFB: Ohio, 1980.
20. McNitt-Gray, J. L., D. M. Hester, W. Mathiyakom, and B. A. Munkasy. Mechanical demand and multijoint control during landing depend on orientation of the body segments relative to the reaction force. J. Biomech
. 34:1471–1482, 2001.
21. Pandy, M. G., K. Sasaki, and S. Kim. A three-dimensional musculoskeletal model of the human knee
joint. Part 1: theoretical construct. Comput. Methods Biomech. Biomed. Engin
. 1:87–108, 1998.
22. Pandy, M. G., and K. B. Shelburne. Dependence of cruciate-ligament loading on muscle forces and external load. J. Biomech
. 30:1015–1024, 1997.
23. Pandy, M. G., and K. B. Shelburne. Theoretical analysis of ligament and extensor-mechanism function in the ACL-deficient knee
. Clin. Biomech
. 13:98–111, 1998.
24. Paul, J. J., K. P. Spindler, J. T. Andrish, R. D. Parker, M. Secic, and J. A. Bergfeld. Jumping
versus nonjumping anterior cruciate ligament injuries: a comparison of pathology. Clin. J. Sport Med
. 13:1–5, 2003.
25. Shelburne, K. B., and M. G. Pandy. A musculoskeletal model of the knee
for evaluating ligament forces during isometric contractions. J. Biomech
. 30:163–176, 1997.
26. Shelburne, K. B., and M. G. Pandy. Determinants of cruciate-ligament loading during rehabilitation exercise. Clin. Biomech
. 13:403–413, 1998.
27. Shelburne, K. B., and M. G. Pandy. A dynamic model of the knee
and lower limb for simulating rising movements. Comput. Methods Biomech. Biomed. Engin
. 5:149–159, 2002.
28. Shelburne, K. B., M. G. Pandy, F. C. Anderson, and M. R. Torry. Pattern of anterior cruciate ligament force in normal walking. J. Biomech
. 37:797–805, 2004.
29. Shoemaker, S. C., D. Adams, D. M. Daniel, and S. L. Woo. Quadriceps
/anterior cruciate graft interaction. An in vitro study of joint kinematics and anterior cruciate ligament graft tension. Clin. Orthop
. 294:379–390, 1993.
30. Torry, M. R., M. J. Decker, R. W. Viola, D. D. O'Connor, and J. R. Steadman. Intra-articular knee
joint effusion induces quadriceps
avoidance gait patterns. Clin. Biomech
. 15:147–159, 2000.
31. Toutoungi, D. E., T. W. Lu, A. Leardini, F. Catani, and J. J. O'Connor. Cruciate ligament forces in the human knee
during rehabilitation exercises. Clin. Biomech
. 15:176–187, 2000.
32. Yu, B., D. Kirkendall, and W. Garrett. Anterior cruciate ligament injuries in female athletes: anatomy, physiology, and motor control. Sports Med. and Arthroscopy Review
. 10:58–68, 2002.
33. Zajac, F. E. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit. Rev. Biomed. Eng
. 17:359–411, 1989.
34. Zheng, N., G. S. Fleisig, R. F. Escamilla, and S. W. Barrentine. An analytical model of the knee
for estimation of internal forces during exercise. J. Biomech
. 31:963–967, 1998.
Keywords:©2004The American College of Sports Medicine
KNEE; JUMPING; LIGAMENT INJURY; QUADRICEPS; SHEAR FORCE; COMPUTER SIMULATION