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Letter to the Editor |
Cleveland, Ohio
Dear Editor:
We read with great interest the recent article by Chappell et al titled "Effect of Fatigue on Knee Kinetics and Kinematics in Stop-Jump Tasks" (July 2005, page 1022–1029). The authors concluded that "increased anterior shear force indicates a possible increased strain on the ACL and thus an increased risk for ACL injury." This interpretation of knee kinetics is, however, incorrect. During the stop jump, the body undergoes a large deceleration, and there is an external ground reaction force pushing the tibia posteriorly. The authors’ free body diagram of the lower leg (Figure 1
) correctly shows that the femur exerts an anterior shear force on the tibia, as required to balance a posterior force from the ground. However, the only anatomical structures that can pull the tibia anteriorly are the posterior cruciate ligament and, at low flexion angles, the patellar tendon. The ACL can therefore only be strained if the shear force of the patellar tendon becomes larger than the required total anterior shear force, but no attempt was made to estimate this effect. Even if such analysis were added, the fact remains that an increased posterior ground reaction force will decrease (not increase) the strain in the ACL. This is consistent with the well-known drawer test, in which an anterior, not posterior, external force is applied to strain the ACL.
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We thank Drs Ajit M. Chaudhari and Thomas P. Andriacchi, and Drs Antonie J. van den Bogert and Scott G. McLean for their comments on our recent publication entitled "Effect of Fatigue on Knee Kinetics and Kinematics in Stop-Jump Tasks" (July 2005).
Drs Chaudhari and Andriacchi expressed their concern for our definition of knee moments. We used knee-joint resultants through the entire text in this publication, which Drs Chaudhari and Andriacchi referred to as internal forces and moments. We did not change the convention from internal to external load in this publication. We did, however, find an error in our original Figure 9 after reading Drs Chaudhari and Andriacchi’s comments, which we think is the cause of the confusion in terminology. The signs for valgus and varus moments in Figure 9 should be reversed. Accordingly, the valgus and varus moments mentioned in the presentation and discussion of the results should all be reversed. We sincerely apologize for this error and the confusion due to this error, and we thank Drs Chaudhari and Andriacchi for drawing our attention to the error. The corrected Figure 9 in our original publication is shown here in Figure 1.
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The anterior-posterior component of the ground-reaction force vector acting on the foot during the stop-jump task does not have the same effects as a posterior drawer test. During the drawer test, the tester applies an anterior or posterior draw force at the proximal end of the tibia in an open kinetic chain of the lower extremity (the distal end of the kinetic chain is free). During the landing of the stop-jump task, the ground applies a ground-reaction force with a posterior component on the foot in a closed kinetic chain of the lower extremity (the distal end of the kinetic chain is fixed on the ground). The mechanical effects of the external anterior or posterior force on the ACL or PCL are not the same in these 2 situations. A posterior drawer test bears little resemblance to the situation described by Drs Chaudhari and Andriacchi and Drs van den Bogert and McLean. Clinicians can be assured that if they have a patient who is seated and whose leg is hanging from the examining table, pushing the foot posteriorly will not stretch the PCL. The posterior force on the foot makes the knee flex, not translate.
A posteriorly directed force is applied to the foot during the landing of the stop-jump task. This force would cause the knee to flex. If motor control demands required the patient or athlete to remain standing, then a quadriceps force must balance the tendency of flexion because of the posterior ground-reaction force; this would require quadriceps contraction to resist the external knee flexion moment with an internal extension moment. The quadriceps applies force on the tibia through the extensor mechanism and the patellar tendon. The quadriceps contraction can provide an anterior shear force on the tibia with the knee at a small flexion angle.
Our use of proximal tibial anterior shear force as an indicator of ACL loading in the stop-jump task is based on careful analysis of the lower biomechanics and experimental data. The ACL loading (FACL) due to sagittal plane biomechanics in the stop-jump task can be expressed as
 | (1) |
where FAP is the knee anterior draw force and 
is the ACL elevation angle1 (Figure 2). According to McLean et al,2 the knee anterior draw force can be expressed as
|
 | (2) |
where FPT, FHam, and Fk,x are the patellar tendon force, hamstring tendon force, and proximal tibial anterior shear force (knee-joint resultant force in the anterior direction), respectively, while 
and ß are the patellar tendon–tibial shaft angle and hamstring tendon–tibial shaft angle, respectively (Figure 2
). It is quite clear in the inverse dynamics of the lower extremity that Fk,x is correlated to the posterior ground-reaction force. We believe that the concern shown in our use of Fk,x as an indicator of ACL loading and the claim that the posterior ground-reaction force protects the ACL are mainly based on the role of Fk,x in Equation 2 and the obvious correlation between Fk,x and the posterior ground-reaction force.
What Drs Chaudhari and Andriacchi and Drs van den Bogert and McLean did not realize is that FPT is also correlated to the posterior ground-reaction force. The posterior ground-reaction force on the foot creates an external flexion moment relative to the knee, which needs to be balanced by an internal knee extension moment. The greater the posterior ground-reaction force is, the greater the internal knee extension moment and the greater the FPT are because the knee tension moment is created by the FPT. The effect of the posterior ground-reaction force on FPT is much greater than that on Fk,x because the moment arm of the posterior ground-reaction force relative to the knee is much greater than that of FPT. The moment arm of FPT is less than 0.05 m (according to Smidt5), whereas the vertical distance from the ground to the center of the knee joint in the stop-jump task is more than 0.4 m. This condition means that an increase of 1 N in the posterior ground-reaction force will result in an increase of more than 8 N in FPT. The effect of the external knee flexion moment on ACL loading has been acknowledged when describing the mechanism of ACL injuries while skiing in a recent letter to the editor by Drs McLean, van den Bogert, and others.3 The decreased knee flexion angle will not increase ACL loading without a large internal knee extension moment because of quadriceps muscle contraction. These considerations combined together indicate that the increasing posterior ground-reaction force will increase ACL loading and that there should be a positive correlation between Fk,x and FACL when the knee flexion angle is small.
The effect of the posterior ground-reaction force on ACL loading can be clearly demonstrated using a simplified simulation based on the real kinematic and kinetic data for a randomly selected stop-jump trial of a randomly selected female subject in our database (Table 1). To simplify the simulation, we neglected the mass and moment of inertia of the lower leg and foot. Hamstring co-contraction was not considered in this simulation. The patellar tendon moment arm, patellar tendon–tibial shaft angle, and ACL elevation angle were estimated from the knee flexion angle as 0.481 m, 19°, and 55°, respectively.1,3,4 The actually observed peak posterior and vertical ground-reaction forces during landing were 356 N and 637 N, respectively. The peak posterior ground-reaction force was increased to 656 N with a 100-N increment. The ACL loading was calculated using Equations 1 and 2.
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). Neglecting linear acceleration forces, angular acceleration moment, and gravitational forces should not have a significant effect on the results of this simulation. Adding hamstring co-contraction would only increase the ACL loading when the knee angle is small.6
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Finally, we would like to thank The American Journal of Sports Medicine for this opportunity to clarify an important issue in studies related to noncontact ACL injuries.
REFERENCES
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