Excessive knee loading during jump landing is an important injury mechanism, particularly for the anterior cruciate ligament.1 Sagittal plane postures of the lower extremities and torso can modulate the force vector through the knee joint.2 A dynamical modelling method has been advocated where the simplest model (least number of variables and parameters) that exhibit specific behavior is used to understand control strategies.3 The goal of this study was to develop a planar, reduced-order, multi-body, dynamical model of the human lower extremity and torso. The model was then used to find optimal postures that minimize knee loading during landing from a jump.
The model included a mass and three segments (torso, upper leg, lower leg) with quadriceps activation by a passive spring/dashpot force system Quad(t) at the knee (Fig 1A). The mass, length, muscle stiffness and damping parameters of the model were based on previous human-scale characteristics from bipedal gait simulations.4 The torso angle Ψ was fixed relative to the vertical axis during the simulation, while the ankle angle θ(t) was initially set at t=0, but varied by the dynamical control during the landing. All simulations had the same initial center of mass height set to 2 m (constant energy). The relative stiffness and damping ratio were changed and the effect of these parameters on the induced forces were studied. We calculated the shear and whole resultant forces on the knee and reported maximums during the simulations.
The results of this undamped model (Fig 1B) predict minimum forces in the knee (BW) of FShear=4.0 and FResultant=58 at torso and ankle angles each approximately 70-85°. The damped model (Fig 1C) had slightly different optimal solutions of approximately FShear=4.2 and FResultant=36 for shear force at Ψ=70° and θ0=65° and resultant force at Ψ=60° and θ0=70°.
This study demonstrates two strategies for controlling landing forces in the lower extremity; the posture of the torso and lower extremity can be positioned during the flight phase in preparation for initial ground contact, while the stiffness and damping ratio could be varied through neuromuscular control during the stance phase. The optimal postures were highlighted in the results, but the contour plots also predict other posture forces that might occur during specific real world landing measurements and situations that could lead to injury. Damping creates a narrower range of optimal postures and the possibility to control either shear or resultant force in the knee.
 Boden et al., J Am Acad Orthop Surg, 2010.  Shimokochi et al., J Ath Train, 2016.  Full and Koditschek, J Exp Bio, 1999.  Merker et al., Bioinsp Biomim, 2011.