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Medicine & Science in Sports & Exercise:
Applied Sciences: Biodynamics

Model Prediction of Anterior Cruciate Ligament Force during Drop-Landings

PFLUM, MARY A.1,2; SHELBURNE, KEVIN B.2; TORRY, MICHAEL R.2; DECKER, MICHAEL J.1,2; PANDY, MARCUS G.3

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Author Information

1Department of Kinesiology, University of Texas at Austin, Austin, TX; 2Steadman♢Hawkins Sports Medicine Foundation, Biomechanics Research Laboratory, Vail, CO; 3Department of Biomedical Engineering, University of Texas at Austin, Austin, TX

Address for Correspondence: Kevin Shelburne, Ph.D., Steadman♢Hawkins Sports Medicine Foundation, Vail, Colorado 81657; Email: kevin.shelburne@shsmf.org.

Submitted for publication December 2003.

Accepted for publication July 2004.

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Abstract

Purpose: The aim of this study was to calculate and explain the pattern of force transmitted to the anterior cruciate ligament during soft-style drop-landings. We hypothesized that peak ACL loading is due to the anterior pull of the quadriceps on the tibia, as these muscles develop large eccentric forces upon impact.

Methods: A three-dimensional model of the body was used to simulate drop-landing. The simulation was performed by entering into the model muscle excitation patterns based on experimental EMG. The input excitation patterns were modified to create a performance response of the model that matched experimental data. Joint angles, ground reaction forces, and muscle forces obtained from the landing simulation were then applied to a model of the lower limb that incorporated a three-dimensional model of the knee.

Results: The model ACL was loaded only in the first 25% of the landing phase. Peak ACL force (∼ 0.4 BW) 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. The patellar tendon force and tibiofemoral contact force both applied significant anterior shear forces to the shank throughout the landing phase. These effects were modulated by another significant posterior shear force applied by the ground reaction, which served to limit the maximum force transmitted to the ACL.

Conclusion: The pattern of ACL force in drop-landing cannot be explained by the anterior pull of the quadriceps force alone.

Landing from a jump is often reported to be the cause of noncontact anterior cruciate ligament (ACL) injuries in competitive athletics (32). Contemporary in vivo landing studies have provided considerable insight into joint kinematics (7,13,20), kinetics (7,9,13,20), muscle activation patterns (20), landing style (13), and energy absorption strategies (9,13) used during the landing motion. While many of these studies suggest that the impact upon landing may predispose athletes to knee injuries, a detailed analysis of the internal forces acting at the knee has yet to be undertaken.

Difficulties associated with the measurement and calculation of muscle and knee-ligament forces in vivo have hindered progress in evaluating the internal state of the joint during high-impact, functional activities. In many dynamic activities, knee-ligament and joint loading are largely determined by muscle forces (5,23). Unfortunately, direct measurement of muscle forces in vivo is currently not feasible and electromyography (EMG) provides only a qualitative description of the relative effort that muscles produce during movement. Alternatively, musculoskeletal modeling and computer simulation techniques allow estimates of muscle and ligament forces to be obtained noninvasively (1,25,31,34). Detailed multisegment, multi-degree-of-freedom musculoskeletal models have been used to determine muscle, ligament, and joint-contact loading in a range of activities, from rising from a squatting position (27) to normal walking on the level (28).

The overall goal of this study was to calculate and explain the pattern of force transmitted to the ACL during a soft-style drop-landing. A specific aim was to study the interaction between muscle, joint contact, and ground reaction forces in relation to ACL loading on impact. Based on anecdotal evidence described in the literature in relation to landing (8,9,24), as well as our own findings related to isometric extension (22,25), squatting (26), and walking (28), we hypothesized that peak ACL loading in landing is due to the anterior pull of the quadriceps on the tibia, as these muscles develop large eccentric forces on impact (8,12).

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METHODS

A three-dimensional (3D) model of the body was used to simulate a drop-landing maneuver. The time histories of the joint angles and ground reaction forces measured for a single subject during landing were reproduced as closely as possible in a simulation of the model. Joint angles, ground reaction forces, and muscle forces obtained from the landing simulation were then applied to a model of the lower limb that incorporated a 3D model of the knee. The relative positions of the femur, tibia, and patella and the forces induced in the knee ligaments were found by solving a static equilibrium problem at each instant during the simulated landing motion.

Kinematic, ground reaction force, and muscle EMG data were recorded simultaneously for eight consecutive landing trials performed by one subject. The subject, a male athlete 28 yr of age, 180 cm in height, and 82 kg in weight, was similar in build and stature to the computer model. The subject routinely engaged in sporting activities such as basketball and volleyball, in which jumping and landing are commonplace. The subject had no history of orthopedic injury to the lower-extremity joints, and signed an informed consent approved by the Vail Valley Medical Center's Institutional Review Board.

With his arms folded across his chest, the subject performed a drop-landing maneuver by stepping off a 60-cm-high platform onto a force plate. The subject was instructed to step off the platform, not jump off, and to land as naturally as possible with both feet planted firmly on the ground. The foot of the dominant limb landed directly onto a six-component, strain-gauged force plate (Bertec Corp., Columbus, OH) fixed to the laboratory floor. Anterior-posterior, vertical, and medial-lateral ground reaction forces were sampled at 1200 Hz. Center of pressure was calculated from the sampled ground reaction forces.

Subject kinematics were recorded using a 3D passive-marker motion analysis system (Motion Analysis Corporation, Santa Rosa, CA). Thirteen retroreflective spherical markers (diameter = 25 mm) were used to define a four-segment, rigid-link model of the lower limb (16). Five synchronized infrared cameras captured the motion at a frequency of 120 Hz. The cameras were calibrated with mean residual errors in the range of 1.85−2.95 mm over a volume of 1.50 × 1.10 × 1.50 m.

The coordinate data for each marker trajectory were smoothed using a fourth-order Butterworth filter with a 10-Hz cutoff frequency (7,9). Joint angular displacements, velocities, and accelerations were calculated from the filtered marker positions.

Pairs of preamplified, pregelled, silver–silver-chloride, bipolar EMG surface electrodes (Biomed Inc., Salt Lake City, UT) were attached to the right lower limb of the subject to record activity in seven muscles: lateral gastrocnemius, tibialis anterior, vastus lateralis and medialis, rectus femoris, medial hamstrings, and the biceps femoris. The electrodes were placed along the lines of action of the muscle fibers with a center-to-center distance of approximately 25 mm. Electrode placements were confirmed via manual muscle testing. A single ground electrode was placed over the anterior tibial spine. The EMG data were collected at 1200 Hz with a TeleMyo telemetric system (Noraxon USA, Scottsdale, AZ) and postprocessed with custom software using a 50-ms root-mean square (RMS) window algorithm (11,30). The EMG data were then scaled to a maximal value calculated for each muscle using the average of five maximal voluntary contractions performed by the subject. Maximum voluntary contractions (MVC) were collected using methods described previously by Lange et al. (17). For the quadriceps muscle group, the subject performed maximal concentric contraction while seated on the edge of a chair, with the knee flexed to 90° and the foot flat on the floor. The subject contracted the quadriceps maximally for 5 s against an immovable torque bar with a tibial pad attached; EMG data were recorded for five separate trials. Isometric hamstrings were measured in the same position, except the subject contracted his hamstrings in an attempt to flex his knee against the immovable torque bar. For the gastrocnemius muscle, the subject stood erect with hips and knees fully extended and, upon command, attempted to plantarflex the ankle against immovable shoulder pads located above each acromion. To ensure true MVC records, the subject practiced leg-muscle contractions several times before testing. Visual biofeedback was used to help the subject isolate a specific muscle group during the practice session.

A 3D model of the body was used to calculate leg-muscle forces in landing (Fig. 1). Details of this model are given by Anderson and Pandy (2,3); only a brief description is provided here. The skeleton was modeled as a 10-segment, 23-degree-of-freedom (dof) articulated chain. The pelvis, which had 6 dof, could translate and rotate freely in space. A 3-dof ball-and-socket joint was placed at the level of the 3rd lumbar vertebra to model relative movements of the upper body and pelvis. Each hip was modeled as a 3-dof ball-and-socket joint, each knee as a 1-dof hinge, and each ankle as a 2-dof universal joint. Two segments, a hindfoot and a toes segment, were used to model each foot. For the toes segment, the five metatarsals were consolidated and represented as a single rigid body. The toes segment articulated with the hindfoot segment via a 1-dof metatarsal joint. Five damped springs were placed under the sole of each foot to simulate interaction with the ground; each spring applied forces in all three coordinate directions simultaneously.

FIGURE 1Computer-gen...
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FIGURE 2Schematic di...
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The inertial properties of all segments were based on anthropometric measures obtained from five healthy adult males (age 26 ± 3 yr, height 177 ± 3 cm, and mass 70.1 ± 7.8 kg). All data were recorded according to the methods described by McConville et al. (19). The mass, position of the center of mass, and principal moments of inertia for each segment in the model were calculated by averaging the anthropometric data for the subjects.

The model was actuated by 54 musculotendinous units. Six abdominal and back muscles controlled the relative movements of the pelvis and upper body, and 24 muscles actuated each leg. Each musculotendon actuator was represented as a three-element Hill-type muscle in series with tendon (33). Parameters defining the force-producing properties of each actuator are given by Anderson and Pandy (2). The input to each muscle in the model consisted of a time-dependent pattern of muscle excitation, which represented the net neural drive from the central nervous system to the muscle (33). Muscle excitation-contraction dynamics (i.e., the relation between muscle excitation and muscle activation) was modeled as a first-order process (33). Thus, given the pattern of excitation for each muscle, the model of muscle excitation-contraction dynamics was used to calculate the corresponding pattern of muscle activations. These results, together with the time histories of muscle length and muscle contraction velocity, were then input into the Hill-type model of contraction dynamics to calculate the corresponding values of muscle force.

The landing simulation was constrained to be bilaterally symmetric. At time t = 0, the model feet were placed 60 cm above the ground, and the hip, knee, and ankle angles were assigned to the values measured for the subject.

A forward simulation was performed by entering into the model the time histories of the incoming muscle excitation signals. The muscle excitation patterns were initially based on experimental EMG data; however, because EMG data were acquired from only seven leg muscles for the subject studied here, these data were supplemented with measurements reported by McNitt-Gray et al. (20) of EMG activity in other leg muscles recorded for landing. However, experimental EMG activity still could not be obtained for all the muscles represented in the model, particularly those which are deep lying, such as iliopsoas. In these instances the initial input muscle excitations were merely guessed. The input muscle excitations for all the muscles were manually adjusted until the performance of the model matched the in vivo data (i.e., the time histories of the joint angles and ground reaction forces in the model were required to be qualitatively similar to the experimental data recorded in this study and within 1 SD of data reported previously by others (9,18)). Forward integration of the landing simulation required approximately 2 min using an 800-MHz Pentium® IV workstation.

Knee-ligament forces were calculated using another model of the lower limb that incorporated a 3D model of the knee. Five segments were used to represent the lower limb in this model: thigh, shank, patella, hindfoot, and toes. These segments were connected by five joints: hip, tibiofemoral joint, patellofemoral joint, ankle, and metatarsal joint (Fig. 2). The pelvis was treated as the base segment, and remained fixed to the ground. The hip, ankle, and metatarsal joints were represented in exactly the same way as in the model used to simulate landing. Relative movements of the bones at the knee were represented by 12 dof: six generalized coordinates were used to describe the position and orientation of the tibia relative to the femur, and another six coordinates described the position and orientation of the patella relative to the femur.

The geometry of the distal femur, proximal tibia, and patella was based on parasagittal sections of the bones obtained from 23 cadaveric knees (14). The shapes of the medial and lateral tibial plateau, the medial and lateral femoral condyles, the medial and lateral patellar surfaces of the femur, and the medial and lateral patellar facets were reproduced by fitting polynomials to the digitized cadaver data. The contacting surfaces of the femur and tibia were modeled as deformable, with cartilage represented as a thin, homogeneous, linearly elastic material. The model of patellofemoral mechanics was based on the assumptions that the patellar tendon was inextensible and that interpenetration between the facets of the patella and the patellar surfaces of the femur can be neglected. Details of the knee model are given by Pandy et al. (21).

The geometry of the cruciate and collateral ligaments, the posterior capsule, and the anterolateral structures of the knee were modeled using 13 elastic elements (Fig. 2B). The ACL and PCL were each represented by an anterior and a posterior bundle. The MCL was represented by two layers: a superficial layer comprised of three bundles, and a deep layer comprised of two bundles. The LCL and the anterolateral structures (ALS) were each represented by one bundle, while the posterior capsule was represented by two: a medial and a lateral bundle. Each ligament bundle was assumed to be elastic, and its properties were described by a nonlinear force–strain curve (6). The origin and insertion sites of the ligament bundles were based on data reported by Garg and Walker (14). Stiffness and reference strain values assumed for each ligament bundle were adjusted until the response of the model in anterior-posterior drawer and axial rotation matched in vitro data reported in the literature (28). The parameters assumed for the model ligaments are given by Shelburne et al. (28). The behavior of the meniscus was approximated by applying a posterior shear force to constrain anterior movement of the shank relative to the thigh (28).

Thirteen muscles were represented in the lower-limb model (Fig. 2A). The paths of all muscles except vasti, hamstrings, and gastrocnemius were identical with those incorporated in the model used to simulate landing. Whereas vasti, hamstrings, and gastrocnemius were each represented as one muscle in the landing model, the separate portions of each of these muscles were included in the lower-limb model. Forces in the separate portions of these muscles were estimated from the relative cross-sectional area of each muscle. For example, vastus medialis force was found by multiplying vasti force obtained from the landing simulation by the cross-sectional area of vastus medialis and then dividing by the total cross-sectional area of vasti.

Knee-ligament forces were calculated by assuming that the lower limb was in static equilibrium at each instant during the landing simulation; specifically, the inertial contributions of the femur, tibia, patella, hindfoot, and toes segments were neglected in these calculations. The equations of motion for the lower-limb model define a system of 18 nonlinear differential and algebraic equations in 18 unknowns (28). The muscle forces, ground reaction forces, joint angles of the hip, ankle, and metatarsal joints, and the flexion-extension and internal-external rotation angles of the knee obtained from the landing simulation were used as inputs to these equations. The 18 unknowns were the varus-valgus angle of the knee, the three translations of the tibia relative to the femur, the six generalized coordinates defining the position and orientation of the patella relative to the femur, and the eight joint torques needed to hold the lower limb static at each instant. Thus the static equilibrium problem can be stated as follows: Given the muscle forces, ground reaction forces, flexion-extension and internal-external rotation angles of the knee, and the joint angles of the hip, ankle, and metatarsal joints, find the positions of the tibia and patella relative to the femur as well as the magnitudes of the joint torques needed to equilibrate the lower limb at each instant during the landing simulation. Details of the lower-limb model used to calculate knee-ligament forces are given by Shelburne et al. (28).

A computational solution to this problem was found by integrating the equations of motion of the lower-limb model forward at each time step of the landing simulation until the accelerations and velocities of all the joints approached zero. A proportional-integral-derivative control scheme was used to drive the joint velocities and accelerations to zero. Once the values of the generalized coordinates corresponding to static equilibrium of the lower limb had been determined, the forces transmitted to the knee ligaments were found using the force–strain relationships assumed for the various ligament bundles incorporated in the model.

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RESULTS

The joint angles calculated in the model were qualitatively similar to the subject (Fig. 3). The hip and knee angles in the model and experiment were nearly the same throughout the landing phase, with correlation values of r2 = 0.995 and r2 = 0.996, respectively (Fig. 3, Hip and Knee). There was some discrepancy between model and experiment at the ankle, particularly early in the landing phase, where the amount of dorsiflexion was exaggerated in the model (Fig. 3, Ankle). Nonetheless, the correlation between model and experiment was still relatively high (r2 = 0.842) for the ankle (see Table 1), and the peak values for hip, knee, and ankle joints exhibited by the model were also within 1 SD of previously published experimental data (9,18).

Figure 3
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Table 1
Table 1
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There was also good agreement in the ground forces measured for the subject and those obtained from the model simulation. Consistent with results reported by others, two distinct peaks were visible in the measured vertical force (Fig. 4, Vertical). The first peak, F1v, measured 1.7 ± 0.1 BW and occurred at 12 ± 0.3 ms after initial impact. The second peak, F2v, measured 3.9 ± 0.4 BW and occurred at 38 ± 1.6 ms. By comparison, the model generated peak forces of 2.0 BW at 11 ms for F1v and 4.1 BW at 39 ms for F2v. The first peak (F1v) coincided with the forefoot impacting the ground, while the second peak (F2v) was caused by impact of the heel with the ground.

FIGURE 4Vertical and...
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Two distinct peaks were also seen in the measured fore-aft ground force (Fig. 4, Fore-aft). The first peak, F1h, measured 2.0 ± 0.1 BW and occurred at 12 ± 0.3 ms after initial impact. The second peak, F2h, measured 1.4 ± 0.1 BW and occurred at 39 ± 3 ms. Although the model underestimated the magnitude of each peak (model data = 1.2 BW and 1.1 BW for F1h and F2h, respectively), the timing of each peak was very consistent with the records obtained from the force plate (11 ms and 40 ms for F1h and F2h, respectively). The peaks F1h and F2h were also caused by impact of the forefoot and the heel with the ground, respectively.

The pattern of quadriceps and hamstrings activations assumed in the model was consistent with EMG activity recorded from experimental data (Fig. 5). There was some difference between the modeled and measured activation patterns for gastrocnemius; however, this muscle did not contribute much to the force borne by the ACL during landing (see below). The quadriceps muscles, specifically the vasti, were the prime movers of the lower limb in landing (Fig. 6). Vasti force increased quickly from initial ground contact, reaching a maximum of around 4500 N (6.4 BW) at 60 ms. The model hamstrings and gastrocnemius developed much less force. For example, peak force developed in gastrocnemius was roughly four times less than that calculated for vasti (compare vasti with hamstrings and gastrocnemius in Fig. 6).

FIGURE 5Comparison o...
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FIGURE 6Time histori...
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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).

FIGURE 7Time history...
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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.

FIGURE 8Shear forces...
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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.

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DISCUSSION

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.

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Keywords:

KNEE; JUMPING; LIGAMENT INJURY; QUADRICEPS; SHEAR FORCE; COMPUTER SIMULATION

©2004The American College of Sports Medicine

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