This study aimed to validate a simple dynamic model of single-leg drop-landing to develop a methodological foundation for investigating mechanistic causes of anterior cruciate ligament (ACL) injury and to explore mechanical associations between knee valgus torque and landing kinematics that are considered clinically as a high-risk landing posture for the injury. A triple-inverted-pendulum model in three-dimensional space, composed of rigid-links of head-arms-trunk (HAT), thigh and shank, was employed. We derived causal relationships that can predict post-impact kinetics, including impact ground reaction forces (GRFs) and corresponding knee joint torques from a given body-kinematics immediately before impact, based on an assumption of a completely inelastic collision between a landing foot (the distal end-point of the shank in the model) and the ground. The concordance correlation coefficient (CCC) analysis revealed that our model can achieve an acceptable agreement between experimentally measured and model-predicted impact GRFs and corresponding knee joint torques. The $95\%$ one-tailed lower confidence limit of CCC of vertical, mediolateral GRFs and the varus/valgus torque were $0.665>{\rho }_{c,a}=0.643,0.786>{\rho }_{c,a}=0.758$ and $0.531>{\rho }_{c,a}=0.508$, respectively, for the least acceptable values ${\rho }_{c,a}$. Using this model, effects of three types of hypothetical pre-impact kinematics with modulated (i) medial/lateral leaning HAT angle, (ii) forward/backward HAT tilt-angle, and (iii) knee flexion/extension angle on the impact GRF and corresponding knee joint torque were evaluated. We showed that the smaller knee flexion and the greater HAT leaning toward the landing-limb-side, the larger the knee valgus torque is generated, as a mechanical consequence between the specific pre-impact kinematics and the knee loading associated with the risk of ACL injury. Further exploration of hypothetical kinematics using the model in the future work might contribute to identifying the risky landing kinematics beyond experimental limitations.

这项研究旨在验证单腿下降着陆的简单动态模型，从而为研究前交叉韧带（ACL）损伤的机械原因提供方法学基础，并探讨膝外翻扭矩和着陆运动学之间的机械关联，临床上将其视为受伤的高风险着陆姿势。使用三维空间中的三重倒立摆模型，该模型由头-臂-大腿（HAT），大腿和小腿的刚性链接组成。我们推导了因果关系，可以预测撞击后的动力学，包括撞击前地面运动给定的人体运动学，包括撞击地面的反作用力（GRF）和相应的膝关节扭矩，基于着陆脚（模型中小腿的远端）与地面完全无弹性碰撞的假设。一致性相关系数（CCC）分析表明，我们的模型可以在实验测量的和模型预测的冲击GRF与相应的膝关节扭矩之间取得可接受的一致性。的$95％$ 垂直，中外侧GRF的CCC一尾下置信限和内翻/外翻扭矩为 $0.665>{\rho }_{C，\mathrm{一种}}=0.643，0.786>{\rho }_{C，\mathrm{一种}}=0.758$ 和 $0.531>{\rho }_{C，\mathrm{一种}}=0.508$分别为最小可接受值 ${\rho }_{C，\mathrm{一种}}$。使用此模型，可以对三种类型的假想碰撞前运动学进行调制（i）内侧/外侧倾斜HAT角，（ii）向前/向后HAT倾斜角和（iii）膝盖屈伸角度对冲击GRF的影响并评估相应的膝关节扭矩。我们表明，膝盖屈曲越小，HAT越靠近着陆侧，则产生的膝外翻扭矩就越大，这是特定的撞击前运动学和与ACL风险相关的膝盖负荷之间的机械结果。受伤。在将来的工作中使用该模型对假设的运动学进行进一步的探索可能有助于识别超出实验限制的危险着陆运动学。