Download Linear weight sum method to estimate muscle force based on

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]