title: A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.
abstract: The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.
authors: Laboratory of Biomechanical Orthopedics, Ecole Polytechnique Fédérale de Lausanne, Switzerland. alexander.terrier@epfl.ch
authors: Alexandre
authors: A
authors: Terrier
authors: Martin
authors: M
authors: Aeberhard
authors: Yvan
authors: Y
authors: Michellod
authors: Philippe
authors: P
authors: Mullhaupt
authors: Denis
authors: D
authors: Gillet
authors: Alain
authors: A
authors: Farron
authors: Dominique P
authors: DP
authors: Pioletti
mesh_terms: D001696:Biomechanical Phenomena; D005240:Feasibility Studies; D058430:Humeral Head / Q000033:anatomy & histology / Q000502:physiology; D007700:Kinetics; D008953:Models, Anatomic; D009068:Movement; D009141:Musculoskeletal System / Q000033:anatomy & histology*; D012371:Robotics; D012399:Rotation; D012782:Shoulder / Q000033:anatomy & histology* / Q000502:physiology