×

zbMATH — the first resource for mathematics

Predictions of antagonistic muscular activity using nonlinear optimization. (English) Zbl 0781.92007
Summary: Optimization theory is used more often than any other method to predict individual muscle forces in human movement. One of the limitations frequently associated with optimization algorithms based on efficiency criteria is that they are thought to not provide solutions containing antagonistic muscular forces; however, it is well known that such forces exist. Since analytical solutions of nonlinear optimization algorithms involving multi-degree-of-freedom models containing multijoint muscles are not available, antagonistic behavior in such models is not well understood.
The purpose of this investigation was to study antagonistic behavior of muscles analytically, using a three-degree-of-freedom model containing six one-joint and four two-joint muscles. We found that there is a set of general solutions for a nonlinear optimal design based on a minimal cost stress function that requires antagonistic muscular force to reach the optimal solution. This result depends on a system description involving multijoint muscles and contradicts earlier claims made in the biomechanics, physiology, and motor learning literature that consider antagonistic muscular activities inefficient.

MSC:
92C10 Biomechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Andrews, J.G.; Hay, J.G., Biomechanical considerations in the modeling of muscle function, Acta morphol. neerl.-scand., 21, 199-223, (1983)
[2] Bean, J.C.; Chaffin, D.B.; Schultz, A.B., Biomechanical model calculation of muscle contraction forces: a double linear programming method, J. biomech., 21, 59-66, (1988)
[3] Crowninshield, R.D., Use of optimization techniques to predict muscle forces, J. biomech. eng., 100, 88-92, (1978)
[4] Crowninshield, R.D.; Brand, R.A., A physiologically based criterion of muscle force prediction in locomotion, J. biomech., 14, 793-802, (1981)
[5] Dul, J.; Johnson, G.E.; Shiavi, R.; Townsend, M.A., Muscular synergism. II. A minimum fatigue criterion for load sharing between synergistic muscles, J. biomech., 17, 675-684, (1984)
[6] Herzog, W., Individual muscle force estimations using a non-linear optimal design, J. neurosci. methods, 21, 167-179, (1987)
[7] Hughes, R.E.; Chaffin, D.B., Conditions under which optimization models will not predict coactivation of antagonist muscles, Proc. amer. soc. biomech., 12, 69-70, (1988)
[8] Kaufman, K.R.; An, K.N.; Litchy, W.J.; Chao, E.Y.S., Physiological prediction of muscle forces. I. theoretical formulation, Neuroscience, 40, 781-792, (1991)
[9] Kaufman, K.R.; An, K.N.; Litchy, W.J.; Chao, E.Y.S., Physiological prediction of muscle forces. II. application to isokinetic exercise, Neuroscience, 40, 793-804, (1991)
[10] Pedersen, D.R.; Brand, R.A.; Cheng, C.; Arora, J.S., Direct comparison of muscle force predictions using linear and nonlinear programming, J. biomech. eng., 109, 192-198, (1987)
[11] Pedotti, A.; Krishnan, V.V.; Stark, L., Optimization of muscle force sequencing in human locomotion, Math. biosci., 38, 57-76, (1978)
[12] Penrod, D.D.; Davy, D.T.; Singh, D.P., An optimization approach to tendon force analysis, J. biomech., 7, 123-129, (1974)
[13] Seireg, A.; Arvikar, R.J., A mathematical model for evaluation of force in lower extremities of the musculoskeletal system, J. biomech., 6, 313-326, (1973)
[14] Zajac, F.E.; Gordon, M.E., Determining Muscle’s force and action in multi-articular movement, Exercise sports sci. rev., 17, 187-230, (1989)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.