A method for improving the accuracy of stereotaxic procedures in monkeys using implanted fiducial markers in CT scans that also serve as anchor points in a stereotaxic frame.

We developed a relatively inexpensive method for stereotaxic placement of electrodes or needles in the brains of monkeys. Steel balls were affixed to the skulls of monkeys. These balls served as fiducial markers and were also used as points at which the monkey's skull was held in a modified stereotaxic apparatus. Computed tomography (CT) was used to establish the location of an injection target with respect to the fiducial markers. A computer program related the CT coordinates to stereotaxic coordinates. These were used to direct an electrode marker toward a target in the hypothalamus. With the marker left in place, the monkey was removed from the stereotaxic frame and a second CT scan was performed. Corrections for errors in marker placement were made and retrograde tracers were injected. This procedure was found to be more accurate and reliable than conventional stereotaxic procedures. The accuracy and repeatability of the technique were also established using a phantom model of a monkey's skull. Two important advantages of this method are that animals can be repeatedly placed into the stereotaxic frame in precisely the same position and that there are many opportunities during the procedure to check for and correct errors.

Estimating net joint torques from kinesiological data using optimal linear system theory.

Net joint torques (NJT) are frequently computed to provide insights into the motor control of dynamic biomechanical systems. An inverse dynamics approach is almost always used, whereby the NJT are computed from 1) kinematic measurements (e.g., position of the segments), 2) kinetic measurements (e.g., ground reaction forces) that are, in effect, constraints defining unmeasured kinematic quantities based on a dynamic segmental model, and 3) numerical differentiation of the measured kinematics to estimate velocities and accelerations that are, in effect, additional constraints. Due to errors in the measurements, the segmental model, and the differentiation process, estimated NJT rarely produce the observed movement in a forward simulation when the dynamics of the segmental system are inherently unstable (e.g., human walking). Forward dynamic simulations are, however, essential to studies of muscle coordination. We have developed an alternative approach, using the linear quadratic follower (LQF) algorithm, which computes the NJT such that a stable simulation of the observed movement is produced and the measurements are replicated as well as possible. The LQF algorithm does not employ constraints depending on explicit differentiation of the kinematic 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 estimate NJT exerted by standing humans perturbed by support-surface movements. We show that unless the number of kinematic and force variables recorded is sufficiently high, the confidence that can be placed in the estimates of the NJT, obtained by any method (e.g., LQF, or the inverse dynamics approach), may be unsatisfactorily low.

The use of inverse dynamics solutions in direct dynamics simulations.

Previous attempts to use inverse dynamics solutions in direct dynamics simulations have failed to replicate the input data of the inverse dynamics problem. Measurement and derivative estimation error, different inverse dynamics and direct dynamics models, and numerical integration error have all been suggested as possible causes of inverse dynamics simulation failure. However, using a biomechanical model of the type typically used in gait analysis applications for inverse dynamics calculations of joint moments, we produce a direct dynamics simulation that exactly matches the measured movement pattern used as input to the inverse dynamic problem. This example of successful inverse dynamics simulation demonstrates that although different inverse dynamics and direct dynamics models may lead to inverse dynamics simulation failure, measurement and derivative estimation error do not. In addition, inverse dynamics simulation failure due to numerical integration errors can be avoided. Further, we demonstrate that insufficient control signal dimensionality (i.e., freedom of the control signals to take on different "shapes"), a previously unrecognized cause of inverse dynamics simulation failure, will cause inverse dynamics simulation failure even with a perfect model and perfect data, regardless of sampling frequency.