Muscle Torque Generator Model For A Two Degree-of-Freedom Shoulder Joint

Abstract

Muscle Torque Generators (MTGs) have been developed as an alternative to muscle-force models, reducing the complexity of muscle-force models to a single torque at the joint. Previous studies have been conducted to determine functions to scale joint torque based on position and velocity-dependent properties. However, current MTGs can only be applied to single Degree of Freedom (DOF) joints, leading to complications in modeling joints such as the shoulder, which has 3 DOF. Therefore, this project aimed to develop, for the first time, an MTG model that accounts for the coupling between 2 DOF at the shoulder joint, with shoulder plane of elevation and shoulder elevation being the DOF of interest. The 2 DOF MTG form was based on previous research for a single DOF MTG. Three different 2 DOF MTG equations were developed to evaluate the effect of the degree of coupling between DOF. Polynomial torque-angle scaling, torque-velocity scaling, and passive functions were defined for the different coupling equations, as well as the activation function. The Biodex System 4 Pro™ was used to determine the net joint torques at the shoulder for 20 participants in isometric, isokinetic, and passive tests. Data was processed and normalized to compare the relative shoulder strength of individuals. MATLAB’s Curve Fitting Toolbox™ was used to find the curves or surfaces that best fit the experimental data for the MTG functions with different degrees of coupling. A completely general model, a female general model, a male general model, and 13 subject-specific models were fit for the three coupling methods. It was found that subject-specific models tended to fit higher-order curves and surfaces compared to the general models that contained averaged data. The models were validated against experimental isokinetic torque data. It was determined that the male general model with position coupling resulted in the lowest error (6.4%), with the position coupling for the completely general model resulting in the next lowest error (8.0%). The female general model resulted in higher errors (average error of 19.9% ± 7.1%), with limited coupling showing the best results with an error of 11.6%. For subject-specific models, it was determined that the average error was the lowest for position and velocity coupling with an error of 22.8% and increasing with decreased coupling. The subject-specific models predicted the general torque trend well for most participants; however, the subject-specific models were highly dependent on the participant’s consistent effort during data collection. The work demonstrated that subject-specific, completely general, female general, and male general MTG models can predict torque results that are dependent on multiple DOF of the shoulder. Future work should include the addition of a fatigue model and the bi-articular nature of the biceps brachii.