A point cluster method for in vivo motion analysis: applied to a study of knee kinematics

A new method for deriving limb segment motion from markers placed on the skin is described. The method provides a basis for determining the artifact associated with nonrigid body movement of points placed on the skin. The method is based on a cluster of points uniformly distributed on the limb segment. Each point is assigned an arbitrary mass. The center of mass and the inertia tensor of this cluster of points are calculated. The eigenvalues and eigenvectors of the inertia tensor are used to define a coordinate system in the cluster as well as to provide a basis for evaluating non-rigid body movement. The eigenvalues of the inertia tensor remain invariant if the segment is behaving as a rigid body, thereby providing a basis for determining variations for nonrigid body movement. The method was tested in a simulation model where systematic and random errors were introduced into a fixed cluster of points. The simulation demonstrated that the error due to nonrigid body movement could be substantially reduced. The method was also evaluated in a group of ten normal subjects during walking. The results for knee rotation and translation obtained from the point cluster method compared favorably to results previously obtained from normal subjects with intra-cortical pins placed into the femur and tibia. The resulting methodology described in this paper provides a unique approach to the measurement of in vivo motion using skin-based marker systems.