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  1. A SCAPULOTHORACIC JOINT MODEL FOR FAST AND ACCURATE SIMULATIONS OF UPPER-EXTREMITY MOTION 1Ajay Seth, 2,3Ricardo Matias, 3António Veloso, 1Scott Delp 1Stanford University, Stanford, CA, USA 2Polytechnic Institute of Setubal, Setúbal, Portugal 3Technical University of Lisbon, CIPER-FCT. Lisbon, Portugal email: aseth@stanford.edu, web: http://www.stanford.edu/group/nmbl INTRODUCTION The human shoulder is a complex mechanism that provides maneuverability and support for performing a wide range of activities [1]. When observing the behavior of the shoulder, abnormal motion of the scapula is often indicative of pathology [2]. Unfortunately, the kinematics of the scapula are difficult to measure. Computer models of the shoulder may be combined with experimental measurements of shoulder motions to better understand scapular kinematics. irregularities in scapular movement often arise from abnormal forces in muscles and surrounding tissues [3] a model of the shoulder will be more useful if it predicts changes in scapula kinematics in response to muscle forces. Here, we present a biomechanical model of the scapulothoracic joint based on a novel multibody formulation [4] to enable fast and accurate kinematic analyses and dynamic simulations of the shoulder. The purpose of this study was to: 1) test the accuracy of scapula kinematics computed with the model and 2) verify that the model reduces the effects of measurement errors when evaluating scapula kinematics from motion capture data. METHODS The scapulothoracic joint model includes coupled translation and rotation of the scapula on the surface of the thorax [5] and is parameterized by four coordinates (Fig. 1). A mobilizer formulation [4] captures the biomechanically permissible kinematics of the scapula. The scapulothoracic joint model provides the reaction loads experienced by the scapula when acted upon by forces including inertial, gravity, muscle, and scapulothoracic joint is composed of two mobilizers: an ellipsoid mobilizer and a pin mobilizer. The ellipsoid mobilizer enables the translation and rotation of the scapula on the thoracic surface and the Because Figure 1: Four coordinates of the scapulothoracic joint. Depression-elevation and adduction-abduction, specify the location of the scapula (blue) on the thoracic surface (red ellipsoid) fixed to the thorax body (green); upward- downward rotation, about the scapula axis (Z) normal to the surface, and internal rotation, about the scapula’s vertical (Y) axis, specify the orientation of the scapula withrespect to the thorax at the point of contact. Joint frame (X,Y,Z) affixed to the scapula. pin mobilizer permits internal rotation about the scapula’s Y-axis (Fig. 1). The ellipsoid surface reaction forces are not computed in order to solve the equations of motion; therefore, the low mass of the scapula does not require numerical methods for constraint stabilization during dynamical simulations. Instead the forces required to keep the scapula on the thorax (ellipsoid) surface can be obtained as joint reaction forces from a joint reactions analysis. The scapulothoracic joint was implemented and included as part of a multibody (thorax, scapula, humerus) model of the upper-extremity in OpenSim [6, 4]. We tested the ability of the model to reconstruct the kinematics of the scapula measured via bone-pins external forces. The

  2. during flexion, abduction and rotation shoulder tasks [7]. We also assessed the effects of soft-tissue errors and marker noise as measured by deviation of markers on the skin from associated landmarks on the scapula [8]. From the mean of the measured peak skin marker errors and their standard deviation, we added Gaussian noise with means and standard deviations corresponding to the average and standard deviation of the measured peak errors. We added noise with 25, 50, 75, and 100% of the mean and standard deviation of the measured errors [8] to represent a range of noise levels. Noise was added as offsets in marker locations with the direction of the offset selected at random. 50 trials of synthetic marker data were generated for each noise level. Euler sequences were computed directly from the noisy marker data and from model markers affixed to the scapula after performing an inverse kinematics analysis. We analyzed each task with added noise (50 trials) and for each of the four noise levels. RESULTS AND DISCUSSION Bone-pin markers and model markers had a root- mean-squared error (RMSE) on average below 2mm (Table 1), which is small considering that the spatial resolution of the motion-capture system is approximately 1mm [7]. Inverse kinematics analyses for 600 trials were performed in OpenSim [6] and had an average run-time faster than 120 frames/s. The Euler angles describing the spatial orientation of the scapula computed using the scapulothoracic joint showed half to a third of the variability of those angles calculated directly from noisy markers (e.g. see Fig. 2) across all trials with greater relative improvement variability) at higher noise levels. The mechanics imposed by the scapulothoracic joint reduce the effects of measurement errors and noise in marker locations compared to Euler angles evaluated directly from noisy markers (Fig. 2). Table 1: Marker errors between model kinematics and bone-pin experiments (RMSE in mm). Marker definitions are according to ISB recommendations [9]. Activity Scapula Thorax (Markers) AAAITSIJC7T8 Flexion 2.2 3.8 3.9 0.9 0.6 0.6 Abduction 3.0 2.6 3.3 0.9 0.6 0.8 Int./Ext. rot 1.8 1.7 3.2 1.6 0.9 0.7 time (s) Figure 2: Body-fixed Euler-angles for scapula spatial orientation during flexion from model-based (red) and direct marker-based evaluations (black) for the 100% noise level. Mean in bold lines and ±1SD as shaded. The scapulothoracic joint coordinates are intuitive to interpret and fully describe the kinematics of the scapula including the elevation and abduction translations of the scapula on the thorax surface. This is critical for describing pathological movements of the scapula. The application of the scapulothoracic joint also produces more reliable scapula kinematics in the presence of measurement errors and enables real-time inverse-kinematics analyses. This novel formulation of the scapulothoracic joint provides the foundation for developing fast and accurate dynamical simulations of the upper-extremity. REFERENCES 1.Veeger et al. J Biomech40, 2119-29, 2007. 2.Struyf et al. ScandJ Med Sci Sports21, 352–8, 2011. 3.Ludewig et al. J Orthop Sports Phys Ther39, 90-104, 2009a. 4.Seth et al. Nonlinear Dynamics62, 291–303, 2010. 5.van der Helm. J Biomech27, 551-69, 1994 6.Delp et al. IEEE Trans Biomed Eng37, 757-67, 2007. 7.Ludewig et al. J Bone Joint Surg91, 378-89, 2009b. 8.Matsui et al. J Orthop Sci11,180-4, 2006. 9.Wu et al. J Biomech38, 981-92, 2005. ACKNOWLEDGEMENTS We thank Paula Ludewig for the bone-pin data. Work supported by NIH grants U54 GM072970; R24 HD065690 and Portuguese STF grants FCT-PTDC/DES/ 103178/2008; PhD SFRH/BD/41846/2007. (i.e. 1/3 the Humerus ELGHEM 1.1 1.1 1.2 1.7 1.7 1.7 0.6 1.4 0.4 Mean (all) 1.7 1.8 1.4