Analytical study of the effects of soft tissue artefacts on functional techniques to define axes of rotation.

The accurate location of the main axes of rotation (AoR) is a crucial step in many applications of human movement analysis. There are different formal methods to determine the direction and position of the AoR, whose performance varies across studies, depending on the pose and the source of errors. Most methods are based on minimizing squared differences between observed and modelled marker positions or rigid motion parameters, implicitly assuming independent and uncorrelated errors, but the largest error usually results from soft tissue artefacts (STA), which do not have such statistical properties and are not effectively cancelled out by such methods. However, with adequate methods it is possible to assume that STA only account for a small fraction of the observed motion and to obtain explicit formulas through differential analysis that relate STA components to the resulting errors in AoR parameters. In this paper such formulas are derived for three different functional calibration techniques (Geometric Fitting, mean Finite Helical Axis, and SARA), to explain why each technique behaves differently from the others, and to propose strategies to compensate for those errors. These techniques were tested with published data from a sit-to-stand activity, where the true axis was defined using bi-planar fluoroscopy. All the methods were able to estimate the direction of the AoR with an error of less than 5°, whereas there were errors in the location of the axis of 30-40mm. Such location errors could be reduced to less than 17mm by the methods based on equations that use rigid motion parameters (mean Finite Helical Axis, SARA) when the translation component was calculated using the three markers nearest to the axis.

Dynamic Parameter Identification of Subject-Specific Body Segment Parameters Using Robotics Formalism: Case Study Head Complex.

Accurate knowledge of body segment inertia parameters (BSIP) improves the assessment of dynamic analysis based on biomechanical models, which is of paramount importance in fields such as sport activities or impact crash test. Early approaches for BSIP identification rely on the experiments conducted on cadavers or through imaging techniques conducted on living subjects. Recent approaches for BSIP identification rely on inverse dynamic modeling. However, most of the approaches are focused on the entire body, and verification of BSIP for dynamic analysis for distal segment or chain of segments, which has proven to be of significant importance in impact test studies, is rarely established. Previous studies have suggested that BSIP should be obtained by using subject-specific identification techniques. To this end, our paper develops a novel approach for estimating subject-specific BSIP based on static and dynamics identification models (SIM, DIM). We test the validity of SIM and DIM by comparing the results using parameters obtained from a regression model proposed by De Leva (1996, "Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters," J. Biomech., 29(9), pp. 1223-1230). Both SIM and DIM are developed considering robotics formalism. First, the static model allows the mass and center of gravity (COG) to be estimated. Second, the results from the static model are included in the dynamics equation allowing us to estimate the moment of inertia (MOI). As a case study, we applied the approach to evaluate the dynamics modeling of the head complex. Findings provide some insight into the validity not only of the proposed method but also of the application proposed by De Leva (1996, "Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters," J. Biomech., 29(9), pp. 1223-1230) for dynamic modeling of body segments.

Model of soft tissue artifact propagation to joint angles in human movement analysis.

This work describes the kinematic laws that govern the transmission of soft tissue artifact errors to kinematic variables in the analysis of human movements. Artifacts are described as relative translations and rotations of the marker cluster over the bone, and a set of explicit expressions is defined to account for the effect of that relative motion on different representations of rotations: the rotation around the screw axis, or rotation vector, and three Euler angle sequences (XY'Z, YX'Y″, ZX'Y″). Although the error transmission is nonlinear in all cases, the effect of artifacts is greater on Euler sequences than on the rotation vector. Specifically, there are crosstalk effects in Euler sequences that amplify the errors near singular configurations. This fact is an additional source of variability in studies that describe artifacts by comparing the Euler angles obtained from skin markers, with the angles of an artifact-free gold standard. The transmission of errors to rotation vector coordinates is less variable or dependent on the type of motion. This model has been tested in an experiment with a deformable mechanical model with a spherical joint.

Propagation of soft tissue artifacts to the center of rotation: a model for the correction of functional calibration techniques.

This paper presents a mathematical model for the propagation of errors in body segment kinematics to the location of the center of rotation. Three functional calibration techniques, usually employed for the gleno-humeral joint, are studied: the methods based on the pivot of the instantaneous helical axis (PIHA) or the finite helical axis (PFHA), and the "symmetrical center of rotation estimation" (SCoRE). A procedure for correcting the effect of soft tissue artifacts is also proposed, based on the equations of those techniques and a model of the artifact, like the one that can be obtained by double calibration. An experiment with a mechanical analog was performed to validate the procedure and compare the performance of each technique. The raw error (between 57 and 68mm) was reduced by a proportion of between 1:6 and less than 1:15, depending on the artifact model and the mathematical method. The best corrections were obtained by the SCoRE method. Some recommendations about the experimental setup for functional calibration techniques and the choice of a mathematical method are derived from theoretical considerations about the formulas and the results of the experiment.

Kinematic description of soft tissue artifacts: quantifying rigid versus deformation components and their relation with bone motion.

This paper proposes a kinematic approach for describing soft tissue artifacts (STA) in human movement analysis. Artifacts are represented as the field of relative displacements of markers with respect to the bone. This field has two components: deformation component (symmetric field) and rigid motion (skew-symmetric field). Only the skew-symmetric component propagates as an error to the joint variables, whereas the deformation component is filtered in the kinematic analysis process. Finally, a simple technique is proposed for analyzing the sources of variability to determine which part of the artifact may be modeled as an effect of the motion, and which part is due to other sources. This method has been applied to the analysis of the shank movement induced by vertical vibration in 10 subjects. The results show that the cluster deformation is very small with respect to the rigid component. Moreover, both components show a strong relationship with the movement of the tibia. These results suggest that artifacts can be modeled effectively as a systematic relative rigid movement of the marker cluster with respect to the underlying bone. This may be useful for assessing the potential effectiveness of the usual strategies for compensating for STA.