The synthesis of shoulder kinematics, either for simulation in a model or imitation in a robot, is a challenging task because of the contact between shoulder blade and ribcage. As the shoulder moves, the shoulder blade glides over the ribcage. In kinematic models used to predict musculoskeletal kinetics, the contact is included using equality constraints, creating interdependencies between the kinematic coordinates. Such interdependencies make motion planning complex. Robotic mechanisms often imitate the shoulder's end-effector kinematics but not the gliding shoulder blade architecture It is only recently that a gliding shoulder blade architecture has been mechanically achieved. The goal of this paper is to propose a novel kinematic parallel model of the shoulder that includes the contact without using constraints. Mechanically, the gliding architecture is replaced with a parallel architecture. A shoulder model with constraints is used to build the parallel model. It is shown that replacing the contact constraints with kinematically equivalent kinematic chains, leads to a 2-3 parallel platform model of the shoulder. The scaffold model and parallel model parameterisations of the shoulder's kinematics are analysed in terms of the forward kinematic map. The coordinate spaces of the kinematic maps are analysed, resulting in three minimal parameterisations. Each minimal parameterisation uses a set of coordinates equal to the number of degrees of freedom. The minimal coordinates are independent and considerably simplify motion planning.
The estimation of muscle forces in musculoskeletal shoulder models is still controversial. Two different methods are widely used to solve the indeterminacy of the system: electromyography (EMG)-based methods and stress-based methods. The goal of this work was to evaluate the influence of these two methods on the prediction of muscle forces, glenohumeral load and joint stability after total shoulder arthroplasty. An EMG-based and a stress-based method were implemented into the same musculoskeletal shoulder model. The model replicated the glenohumeral joint after total shoulder arthroplasty. It contained the scapula, the humerus, the joint prosthesis, the rotator cuff muscles supraspinatus, subscapularis and infraspinatus and the middle, anterior and posterior deltoid muscles. A movement of abduction was simulated in the plane of the scapula. The EMG-based method replicated muscular activity of experimentally measured EMG. The stress-based method minimised a cost function based on muscle stresses. We compared muscle forces, joint reaction force, articular contact pressure and translation of the humeral head. The stress-based method predicted a lower force of the rotator cuff muscles. This was partly counter-balanced by a higher force of the middle part of the deltoid muscle. As a consequence, the stress-based method predicted a lower joint load (16% reduced) and a higher superior -inferior translation of the humeral head (increased by 1.2 mm). The EMG-based method has the advantage of replicating the observed cocontraction of stabilising muscles of the rotator cuff. This method is, however, limited to available EMG measurements. The stress-based method has thus an advantage of flexibility, but may overestimate glenohumeral subluxation.
A clear and rigorous definition of muscle moment-arms in the context of musculoskeletal systems modelling is presented, using classical mechanics and screw theory. The definition provides an alternative to the tendon excursion method, which can lead to incorrect moment-arms if used inappropriately due to its dependency on the choice of joint coordinates. The definition of moment-arms, and the presented construction method, apply to musculoskeletal models in which the bones are modelled as rigid bodies, the joints are modelled as ideal mechanical joints and the muscles are modelled as massless, frictionless cables wrapping over the bony protrusions, approximated using geometric surfaces. In this context, the definition is independent of any coordinate choice. It is then used to solve a muscle-force estimation problem for a simple 2D conceptual model and compared with an incorrect application of the tendon excursion method. The relative errors between the two solutions vary between 0% and 100%.
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