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Cocontraction of pairs of antagonistic muscles: Analytical solution for planar static nonlinear optimization approaches. (English) Zbl 0784.92003
Summary: It has been stated in the literature that static, nonlinear optimization approaches cannot predict coactivation of pairs of antagonistic muscles; however, numerical solutions of such approaches have predicted coactivation of pairs of one-joint and multijoint antagonists. Analytical support for either finding is not available in the literature for systems containing more than one degree of freedom.
The purpose of this study was to investigate analytically the possibility of cocontraction of pairs of antagonistic muscles using a static nonlinear optimization approach for a multidegree-of-freedom two- dimensional system. Analytical solutions were found using the Karush- Kuhn-Tucker conditions, which were necessary and sufficient for optimality in this problem. The results show that cocontraction of pairs of one-joint antagonistic muscles is not possible, whereas cocontraction of pairs of multijoint antagonists is. These findings suggest that cocontraction of pairs of antagonistic muscles may be an “efficient” way to accomplish many movement tasks.

92C10 Biomechanics
49N70 Differential games and control
49N75 Pursuit and evasion games
Full Text: DOI
[1] Andrews, J.G.; Hay, J.G., Biomechanical considerations in the modeling of muscle function, Acta morphol. neerl.-scand., 21, 199-223, (1983)
[2] Avriel, M., Nonlinear programming, (1976), Prentice-Hall Englewood Cliffs, N.J
[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] Crowninshield, R.D.; Brand, R.D., The prediction of forces in joint structures: distribution of intersegmental resultants, Exercise sport sci. rev., 9, 159-181, (1981)
[6] Davy, D.T.; Audu, M.L., A dynamic optimization technique for predicting muscle forces in the swing phase of gait, J. biomech., 20, 187-201, (1987)
[7] 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)
[8] Dul, J.; Townsend, M.A.; Shiavi, R.; Johnson, G.E., Muscular synergism. I. on criteria for load sharing between synergistic muscles, J. biomech., 17, 663-673, (1984)
[9] Herzog, W., Individual muscle force estimations using a nonlinear optimal design, J. neurosci. methods, 21, 167-179, (1987)
[10] Herzog, W.; Binding, P., Predictions of antagonistic muscular activity using nonlinear optimization, Math. biosci., 111, 217-229, (1992) · Zbl 0781.92007
[11] Herzog, W.; Leonard, T.R., Validation of optimization models that estimate the forces exerted by synergistic muscles, J. biomech., 24, S1, 31-39, (1991)
[12] Hughes, R.E.; Chaffin, D.B., Conditions under which optimization models will not predict coactivation of antagonist muscles, Proc. am. soc. biomech., 12, 69-70, (1988)
[13] Luenberger, D.G., Linear and nonlinear programming, (1984), Addison-Wesley Reading, Mass · Zbl 0241.90052
[14] Minoux, M., Mathematical programming: theory and algorithms, (1986), Wiley New York · Zbl 0602.90090
[15] 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)
[16] Pedotti, A.; Krishnan, V.V.; Stark, L., Optimization of muscle force sequencing in human locomotion, Math. biosci., 38, 57-76, (1978)
[17] Rockafellar, R.T., Convex analysis, (1970), Princeton Univ. Press Princeton, N.J · Zbl 0202.14303
[18] Zajac, F.E.; Gordon, M.E., Determining Muscle’s force and action in multi-articular movement, Exercise sports sci. rev., 17, 187-230, (1989)
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