Kinematic Data Consistency in the Inverse Dynamic Analysis of Biomechanical Systems

Abstract

Inverse dynamic analysis is used in the study ofhuman gait to evaluate the reaction forces transmittedbetween adjacent anatomical segments and to calculate thenet moments-of-force that result from the muscle activityabout each biomechanical joint. The quality of theresults, in terms of reaction and muscle forces, is greatlyaffected not only by the choice of biomechanical model butalso by the kinematic data provided as input. This three-dimensional data is obtained through the reconstruction ofthe measured human motion. A biomechanical model isdeveloped representing human body components with acollection of rigid bodies interconnected by kinematicjoints. The data processing, leading to the spatialreconstruction of the anatomical point coordinates, usesfiltering techniques to eliminate the high frequencycomponents arising from the digitization process. Thetrajectory curves, describing the positions of theanatomical points are obtained using a form of polynomialinterpolation, generally cubic splines. The velocities andaccelerations are then the polynomial derivatives. Thisprocedure alone does not ensure that the kinematic data isconsistent with the biomechanical model adopted, becausethe underlying kinematic constraint equations are notnecessarily satisfied. In the present work, thereconstructed spatial positions of the anatomical pointsare corrected by ensuring that the kinematic constraints ofthe biomechanical model are not violated. The velocity andacceleration equations of the biomechanical model are thencalculated as the first and second time derivatives of theconstraint equations. The solution to these equationsprovides the model with kinematically consistent velocitiesand accelerations. The procedures are demonstrated throughthe application to a normal cadence stride period and theresults discussed with respect to the underlying principlesof the techniques used.