An analytical model to quantify the impact of the propagation of uncertainty in knee joint angle computation

Abstract

ABSTRACTJoint kinematics are typically described using Cardan angles or the attitude vector and its projection on the joint axes. Whichever the notation used, the uncertainties present in gait measurements affect the computed kinematics, especially for the knee joint. One notation – the attitude vector – enables the derivation of an analytical model of the propagation of uncertainty. Thus, the objective of this study was to derive this analytical model and assess the propagation of uncertainty in knee joint angle computation. Multi-session gait data acquired from one asymptomatic adult participant was used as reference data (experimental mean curve and standard deviations). Findings showed that an input uncertainty of 5° in the attitude vector and joint axes parameters matched experimental standard deviations. Taking each uncertainty independently, the cross-talk effect could result from uncertainty in the orientation of either the attitude vector (intrinsic variability) or the first joint axis (extrinsic variability). We concluded that the model successfully estimated the propagation of input uncertainties on joint angles and enabled an investigation of how that propagation occurred. The analytical model could be used to a priori estimate the standard deviations of experimental kinematics curves based on expected intrinsic and extrinsic uncertainties.

Keywords

• Joint coordinate system
• attitude vector
• Euler and cardan angles
• knee kinematics
• cross-talk
• reproducibility