A multi-body optimization framework with a knee kinematic model including articular contacts and ligaments

Multi-body optimization is one of the methods proposed to reduce the errors due to soft-tissue artifact in gait analysis based on skin markers. This method uses a multi-body kinematic model driven by the marker trajectories. The kinematic models developed so far for the knee joint include a lower pair (such as a hinge or a spherical joint) or more anatomical and physiological representations including articular contacts and the main ligaments. This latter method allows a better representation of the joint constraints of a subject, potentially improving the kinematic and the subsequent static and dynamic analyses, but model definition and mathematical implementation can be more complicated. This study presents a mathematical framework to implement a kinematic model of the knee featuring articular contacts and ligaments in the multi-body optimization. Two penalty-based methods (minimized and prescribed ligament length variations) consider deformable ligaments and are compared to a further method (zero ligament length variation) featuring isometric ligaments. The multi-body optimization is performed on one gait cycle for five asymptomatic male subjects by means of a lower limb model including the foot, shank, thigh and pelvis. The mean knee kinematics, ligament lengthening and contact point positions are compared over the three methods. The results are also consistent with results from the literature obtained by bone pins or biplanar fluoroscopy. Finally, a sensitivity analysis is performed to evaluate how the joint kinematics is affected by the weights used in the penalty-based methods. The approach is purely kinematic, since the penalty-based framework does not require the solution of the joint static or dynamic analyses and makes it possible to consider ligament deformations without the definition of ligament stiffness that generally cannot be identified through in vivo measurements. Nevertheless, as far as a knee kinematic model is concerned, particularly in musculoskeletal modeling, this approach appears to be a good compromise between standard non-physiological kinematic models and complex deformable dynamic models.