ESTIMATING NET JOINT TORQUES FROM KINESIOLOGICAL DATA USING OPTIMAL LINEAR-SYSTEM THEORY

Net joint torques (NJT) are frequently computed to provide insights in to the motor control of dynamic biomechanical systems. An inverse dyna mics approach is almost always used, whereby the NJT are computed from 1) kinematic measurements (e.g., position of the segments), 2) kineti c measurements (e.g., ground reaction forces) that are, in effect, con straints defining unmeasured kinematic quantities based on a dynamic s egmental model, acid 3) numerical differentiation of the measured kine matics to estimate velocities and accelerations that are, in effect, a dditional constraints. Due to errors in the measurements, the segmenta l model, and the differentiation process, estimated NJT rarely produce the observed movement in a forward simulation when the dynamics of th e segmental system are inherently unstable (e.g., human walking). Forw ard dynamic simulations are, however, essential to studies of muscle c oordination. We have developed an alternative approach, using the line ar quadratic follower (LQF) algorithm, which computes the NJT such tha t a stable simulation of the observed movement is produced and the mea surements are replicated as well as possible. The LQF algorithm does n ot employ constraints depending on explicit differentiation of the kin ematic data, but rather employs those depending on specification of a cost function, based on quantitative assumptions about data confidence . We illustrate the usefulness of the LQF approach by using it to esti mate NJT exerted by standing humans perturbed by support-surface movem ents. We show that unless the number of kinematic and force variables recorded is sufficiently high, the confidence that can be placed in th e estimates of the NJT, obtained by any method (e.g., LQF, or the inve rse dynamics approach), may be unsatisfactorily low.