A novel procedure for knee flexion angle estimation based on functionally defined coordinate systems and independent of the marker landmarks

Abstract

Knee angles are kinematic quantities that are commonly presented in gait analysis reports. They are typically calculated as the relative angles between the anatomical coordinate systems rigidly attached to the femur and the tibia. To give these angles a biomechanical meaning, the coordinate systems must be defined with respect to some anatomical landmarks. For example, if one axis of the joint coordinate systems is directed along the knee flexion/extension axis, then the relative angle assumes the meaning of flexion/extension angle. Defining accurate anatomical coordinate systems is not an easy task, because it requires skills in marker placement, landmark identification and definition of a biomechanical model. In this paper, we present a novel method to (i) functionally define two coordinate systems attached to femur and tibia and (ii) functionally calculate the knee angle based on the relative differential kinematics between the previously defined coordinate systems. As the main limitation, this method is unable to provide an absolute measurement of the knee flexion/extension angle; however, it is able to accurately capture and display the relative angular motion of the knee. We show that our method produced consistent results even when the measured coordinate systems were randomly modified, removing any anatomical referencing. The proposed method has the advantage of being independent/invariant of the choice of the original coordinate systems of the femur and tibia, removing the need for accurate marker placement. Some major consequences are that (i) the markers may be placed on optimal landmarks, for example, minimizing the soft tissue artifacts or improving the subject's comfort, and (ii) there is no need for anatomical calibration when technical marker clusters/triads are used.