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Muscular forces from static optimization
KTH, School of Engineering Sciences (SCI), Mechanics.
2006 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

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. Load-sharing 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.

Place, publisher, year, edition, pages
Stockholm: KTH , 2006. , x, 38 p.
Trita-MEK, ISSN 0348-467X ; 2006:09
Keyword [en]
movement analysis; muscle forces; static optimization
National Category
Other Materials Engineering
URN: urn:nbn:se:kth:diva-3943OAI: diva2:10125
2006-05-19, Seminarierummet, Teknikringen 8, KTH, Stockholm, 11:30
QC 20101116Available from: 2006-05-10 Created: 2006-05-10 Last updated: 2010-11-16Bibliographically approved
List of papers
1. Evaluation of load-sharing and load capacity in force-limited muscle systems
Open this publication in new window or tab >>Evaluation of load-sharing and load capacity in force-limited muscle systems
2006 (English)In: Computer Methods in Biomechanics and Biomedical Engineering, ISSN 1025-5842Article in journal (Other academic) Submitted
Abstract [en]

This study had the objective to develop an algorithm for accurate force decomposition in a redundant musculoskeletal system. The hypothesis was that the calculated load-sharing is dependent on the optimality criterion adopted, but also on the magnitude of carried load. The developed algorithm emphasizes that several established optimization techniques can be unified, by identifying and separating the underlying optimization functions and the numerical methods to solve the resulting system. A numerically efficient and easily adaptable solution method is thereby created. In addition, individual capacity values are introduced for the muscles, allowing the evaluation of a magnitude-dependent load-sharing, and a load carrying capacity of the whole system. By modularizing the optimization method, the algorithm can be used as part of larger simulation systems. To illustrate the possibilities of the algorithm, a model of the upper limb is used in a set of demonstrative examples. The results from the examples show how the interactions between synergistic muscles is predicted in different configurations, and at different load levels.

National Category
Other Materials Engineering
urn:nbn:se:kth:diva-5679 (URN)
QS 20120316Available from: 2006-05-10 Created: 2006-05-10 Last updated: 2012-03-16Bibliographically approved
2. Static optimization of muscle forces during gait in comparison to EMG-to-force processing approach
Open this publication in new window or tab >>Static optimization of muscle forces during gait in comparison to EMG-to-force processing approach
2007 (English)In: Gait & Posture, ISSN 0966-6362, E-ISSN 1879-2219, Vol. 26, no 2, 279-288 p.Article in journal (Refereed) Published
Abstract [en]

Individual muscle forces evaluated from experimental motion analysis may be useful in mathematical simulation, but require additional musculoskeletal and mathematical modelling. A numerical method of static optimization was used in this study to evaluate muscular forces during gait. The numerical algorithm used was built on the basis of traditional optimization techniques, i.e., constrained minimization technique using the Lagrange multiplier method to solve for constraints. Measuring exact muscle forces during gait analysis is not currently possible. The developed optimization method calculates optimal forces during gait, given a specific performance criterion, using kinematics and kinetics from gait analysis together with muscle architectural data. Experimental methods to validate mathematical methods to calculate forces are limited. Electromyography (EMG) is frequently used as a tool to determine muscle activation in experimental studies on human motion. A method of estimating force from the EMG signal, the EMG-to-force approach, was recently developed by Bogey et al. [Bogey RA, Perry J, Gitter AJ. An EMG-to-force processing approach for determining ankle muscle forcs during normal human gait. IEEE Trans Neural Syst Rehabil Eng 2005;13:302-10] and is based on normalization of activation during a maximum voluntary contraction to documented maximal muscle strength. This method was adapted in this study as a tool with which to compare static optimization during a gait cycle. Muscle forces from static optimization and from EMG-to-force muscle forces show reasonably good correlation in the plantarflexor and dorsiflexor muscles, but less correlation in the knee flexor and extensor muscles. Additional comparison of the mathematical muscle forces from static optimization to documented averaged EMG data reveals good overall correlation to patterns of evaluated muscular activation. This indicates that on an individual level, muscular force patterns from mathematical models can arguably be more accurate than from those obtained from surface EMG during gait, though magnitude must still be validated.

Load sharing, Movement analysis, Simulation of gait, Static optimization
National Category
Other Materials Engineering
urn:nbn:se:kth:diva-5680 (URN)10.1016/j.gaitpost.2006.09.074 (DOI)000247978300018 ()17071088 (PubMedID)2-s2.0-34249945682 (ScopusID)
QC 20101116. Uppdaterad från Submitted till Published (20101116).Available from: 2006-05-10 Created: 2006-05-10 Last updated: 2010-11-16Bibliographically approved

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