Multibody biomechanical models of the upper limb

Abstract

Although the upper limb is needed nearly for all commonly performed activities it is still one of the lesser studied parts of the human musculoskeletal system. In this work three musculoskeletal models of the upper limb, based on multibody formulations, are presented. The aim of this work is to compare the performance and applicability of three biomechanical models with different levels of complexity. The models are based on data published by Garner and Pandy [1,2] and by the Delft Shoulder group [3,4]. The simpler model (Model 1) is defined by 4 rigid bodies – thorax, humerus, ulna and radius – and three anatomical articulations – glenohumeral (GH), humeroulnar (HU) and radioulnar (RU). The remaining two are more complex and include 7 rigid bodies – thorax, rib cage, clavicle, scapula, humerus, ulna and radius – constrained by the sternoclavicular, acromioclavicular, scapulothoracic, GH, HU and RU articulations. The muscular system supporting the skeletal system is different for each of the biomechanical models: Model 1 is defined by 15 muscles modeled by 24 bundles and since the thorax, clavicle and scapula are considered as one body, all muscles between these are neglected; Model 2 is an extension of Model 1. The inclusion of the shoulder girdle leads to a total of 21 muscles modeled by 37 bundles; Model 3 uses the muscle data set published by the Delft Shoulder group. All data was scaled to our skeletal system making a total of 20 muscles modeled by 127 bundles. The muscle contraction dynamics is simulated by the Hill-type muscle model. Being the activation of each muscle unknown the whole problem of force sharing is redundant. This indeterminacy is overcome by an optimization technique applied through the minimization of an objective function related with muscle metabolic energy consumption. In models 2 and 3, while looking for the optimal solution, not only the equations of motion must be satisfied but also the stability of the glenohumeral and scapulothoracic joints must be assured. The input for the model analysis comprises the data for an abduction motion, kinematically consistent with the biomechanical models developed, acquired using video imaging at the Laboratory of Biomechanics of Lisbon. Taking into account that Model 1 is only applicable in a small range of motion all three models gave results consistent with the literature.