Muscular Forces from Static Optimization

At every joint there is a redundant set of muscle activated during movement or loading of the system. Optimization techniques are needed to evaluate individual forces in every muscle. The objective in this thesis was to use static optimization techniques to calculate individual muscle forces in the human extremities. A cost function based on a performance criterion of the involved muscular forces was set to be minimized together with constraints on the muscle forces, restraining negative and excessive values. Load-sharing, load capacity and optimal forces of a system can be evaluated, based on a description of the muscle architectural properties, such as moment arm, physiological cross-sectional area, and peak isometric force. The upper and lower extremities were modelled in two separate studies. The upper extremity was modelled as a two link-segment with fixed configurations. Loadsharing properties in a simplified model were analyzed. In a more complex model of the elbow and shoulder joint system of muscular forces, the overall total loading capacity was evaluated. A lower limb model was then used and optimal forces during gait were evaluated. Gait analysis was performed with simultaneous electromyography (EMG). Gait kinematics and kinetics were used in the static optimization to evaluate of optimal individual muscle forces. EMG recordings measure muscle activation. The raw EMG data was processed and a linear envelope of the signal was used to view the activation profile. A method described as the EMG-to-force method which scales and transforms subject specific EMG data is used to compare the evaluated optimal forces. Reasonably good correlation between calculated muscle forces from static optimization and EMG profiles was shown. Also, the possibility to view load-sharing properties of a musculoskeletal system demonstrate a promising complement to traditional motion analysis techniques. However, validation of the accurate muscular forces are needed but not possible. Future work is focused on adding more accurate settings in the muscle architectural properties such as moment arms and physiological cross-sectional areas. Further perspectives with this mathematic modelling technique include analyzing pathological movement, such as cerebral palsy and rheumatoid arthritis where muscular weakness, pain and joint deformities are common. In these, better understanding of muscular action and function are needed for better treatment.