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Linear weight sum method to estimate muscle force based on multiple musculoskeletal models Rencheng Zheng; Tao Liu; Yoshio Inoue; Kyoko Shibata Department of Intelligent Mechanical Systems Engineering, Kochi University of Technology, Kami, Kochi, 782-8502, Japan. Topic: Biomechanics Keyword: Linear weight sum, Redundant, Musculoskeletal model, Static optimization Abstract: Background. A human musculoskeletal system is a really complicated multi-body dynamics problem attracting interest from researchers of many fields in a long time. Since physical muscles as a motor system have an infinite number of ways to complete a motion task, optimization-based models of muscular cooperation considering physiological parameters were built to resolve the redundant problem. Static optimization, an inverse dynamics method, has been used extensively to estimate muscle force during gait on the basis of constrained nonlinear optimization technique for constraint condition. Ordinarily only one criterion is adapted as an objective function in the traditional optimization method, however, in fact muscle activation is obviously affected by many factors during gait. Method. In this paper, a constrained nonlinear optimization algorithm is proposed to estimate muscle force from joint moment based on musculoskeletal models, in which linear weight sum of muscle energy expenditure function, muscle fatigue function and muscle effort sense function are integrated into a minimum objective function. An anteroposterior human walking dynamic model of lower extremities was built, and each leg consisting three joints is controlled by nine Hill-type muscle-tendon groups. Maximal isometric muscle force was obtained by the velocity-length-force relation of muscletendon and the parameters of physiological cross-sectional area. Muscular moment arms as an experiential value were estimated from a musculoskeletal model of lower extremity. Both of them were respectively inputted into an inequality constraint equation and an equality constraint equation to express a relation between joint moment and muscle force of lower extremity during gait. Meanwhile, the joint moments of lower extremities were calculated using an inverse dynamics method in accord with the optimization algorithm. Kinematical data and ground reaction force were measured for joint moment calculation in gait laboratory. Findings. Experimental study was implemented on a volunteer healthy man who was desired to walk in a normal walking speed. Electromyography (EMG) signals were measured at the same time as a referenced volume evaluated the computational results of muscle force. Weighted coefficient to each function also can be adjusted in a real-time estimation according to a known physical performance of subject, for example, weighted coefficient to muscle energy expenditure function can be enhanced accordingly after subject ran over 1000 meters. In here, mean weight sum of three functions was applied to muscle force estimation for a standard of healthy subject walking. The study shows that linear weight sum method is a promising optimization technique to resolve the redundant problem based on optimization-based models of muscle cooperation. Interpretation. Up to now, muscle force can’t be quantitatively gained through direct measurements, and muscle contractions are generally described in “on” or “off” phase by EMG signals during gait. Optimization techniques based on musculoskeletal model as an indispensable tool can be used to estimate muscle force for deeper understanding of musculoskeletal motion mechanism. Therefore, we built the mathematical models based on the human motion mechanism and physiological parameters, and linear weight sum method as a multi-objective optimization is more reasonable than the used single objective optimization to estimate muscle force during gait. Corresponding author’s name: Rencheng Zheng Contact address: Tel.: +81-887-57-2170 Fax: +81-887-57-2170 E-mail address: [email protected]