Determination of joint functional axes from noisy marker data using the finite helical axis

When video-based motion analysis systems are used to measure segmental kinematics, the finite helical displacement computed between two adjacent body segments in two successive positions i, i + 1 is often used to approximate the instantaneous joint movement. The measured trajectories of the external markers glued on the skin are very perturbed compared to the real displacement of the bony structure, and the inaccuracy in the measurement leads to stochastic errors in the position and direction of the finite helical axis of motion (FHA). As the errors associated with the FHA estimates are inversely proportional to the rotaion magnitude (Woltring, H.J., Huiskes, R., de Lange, A., 1983. Measurement error influence on helical axis accuracy in the description of 3D finite joint movement in biomechanics. In: Woo, S.L., Mates, R.E. (Eds.), Biomechanics symposium AMD 56 (FED 1), New York ASME, pp. 19-22), it is illusive to expect to assess the helical displacement between two neighbouring positions, and so to describe the joint evolution using FHA theory in such a context. A quantification of the errors on the FHA parameters computed between two successive positions i, i + 1 is proposed in this paper, using a numerical simulation of the knee joint evolution during gait. This case has been chosen because previous studies (Cappozzo, A., Catani, F., Leardini, A., 1993. Skin movement artifacts in human movement photogrammetry. Proceedings of the 14th Congress of the International Society of Biomechanics. Paris, France, pp. 238-239) have experimentally described skin and soft tissues perturbations. The results obtained from this simulation lead to two conclusions: first, they confirm the relative FHA cannot be used to represent accurately the joint kinematics during a given movement and second, they allow a prediction of the minimum joint displacement required in order to have a reliable determination of the helical axis. The aim of this paper is not to present a new calculation method for the FI-IA, but to propose an alternative use of the FHA. It is generally assumed to describe a joint displacement using a sequence of-rotations about three successive axes. In this case, thr difficulty for clinical applications is to correctly locate these axes, in order that case, coincide with the functional axes of the considered joint. If the FHA theory is used to determine the location and orientation of these functional axes from corresponding pure movement recording, then the results can be very accurate provided that the measured displacement between the two finite positions i and j be sufficient with respect to the perturbing noise. One consequence of this remark is that the rotation axis of the considered. joint may remain stable in the ranee of morion between these positions. An example of this alternative use of the FHA is displayed in this paper which concerns the determination of the flexion/extension axis of the elbow joint. The elbow joint has been chosen for two reasons: first, it deals with a stable joint rotation asis and second. experimental data were available on a fleshless upper-limb on which the flexion/extension axis of the elbow was as marked by an anatomy specialist. (C) 1998 Elsevier Science B.V.