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Antagonistic activity of one-joint muscles in three-dimensions using non-linear optimisation. (English) Zbl 1098.92004
Summary: Nonlinear optimisation, such as the type presented by R. D. Crowninshield and R. A. Brand [The prediction of forces in joint structures: Distribution of intersegmental resultants. Exercise Sports Sci. Rev. 9, 159 ff (1981)], has been frequently used to obtain a unique set of muscle forces during human or animal movements. In the past, analytical solutions of this optimisation problem have been presented for single degree-of-freedom models, and planar models with a specific number of muscles and a defined musculoskeletal geometry. Results of these studies have been generalised to three-dimensional problems and for general formulations of the musculoskeletal geometry without corresponding proofs.
We extend the general solution of the above nonlinear, constrained, planar optimisation problem to three-dimensional systems of arbitrary geometry. We show that there always exists a set of intersegmental moments for which the given static optimisation formulation will predict co-contraction of a pair of antagonistic muscles unless they are exact antagonists. Furthermore, we provide, for a given three-dimensional system consisting of single joint muscles, a method that describes all the possible joint moments that give co-contraction for a given pair of antagonistic muscles.

92C10 Biomechanics
49N90 Applications of optimal control and differential games
Full Text: DOI
[1] Crowninshield, R.D.; Brand, R.A., The prediction of forces in joint structures: distribution of intersegmental resultants, Exercise sports sci. rev., 9, 159, (1981)
[2] Crowninshield, R.D.; Brand, R.A., A physiologically based criterion of muscle force prediction in locomotion, J. biomech., 14, 11, 793, (1981)
[3] Dul, J.; Townsend, M.A.; Shiavi, R.; Johnson, G.E., Muscular synergism - II. A minimum-fatigue criterion for load sharing between synergistic muscles, J. biomech., 17, 9, 675, (1984)
[4] Seireg, A.; Arvikar, R.J., A mathematical model for evaluation of forces in lower extremities of the musculoskeletal system, J. biomech., 6, 313, (1973)
[5] MacConaill, M.A., The ergonomic aspects of articular mechanics, (1967), Springer Berlin
[6] Weber, W.; Weber, E., Mechanik der menschlichen gehwerkzeuge, (1836), W. Fischer-Verlag Göttingen
[7] Dul, J.; Townsend, M.A.; Shiavi, R.; Johnson, G.E., Muscular synergism - I. on criteria for load sharing between synergistic muscles, J. biomech., 17, 9, 663, (1984)
[8] Herzog, W.; Binding, P., Predictions of antagonistic muscular activity using non-linear optimization, Math. biosci., 111, 2, 217, (1992) · Zbl 0781.92007
[9] Herzog, W.; Binding, P., Cocontraction of pairs of antagonistic muscles: analytical solution for planar static non-linear optimization approaches, Math. biosci., 118, 1, 83, (1993) · Zbl 0784.92003
[10] Ait-Haddou, R.; Binding, P.; Herzog, W., Theoretical considerations on cocontraction of sets of agonistic and antagonistic muscles, J. biomech., 33, 1105, (2000)
[11] Binding, P.; Jinha, A.; Herzog, W., Analytical analysis of the force sharing among synergistic muscles in one and two degree-of-freedom models, J. biomech., 33, 11, 1423, (2000)
[12] Challis, J.H.; Kerwin, D.G., An analytical examination of muscle force estimations using optimization techniques, Proc. inst. mech. eng.: pt. H - J. eng. med., 207, 3, 139, (1993)
[13] Li, G.; Kaufman, K.R.; Chao, E.Y.; Rubash, H.E., Prediction of antagonistic muscle forces using inverse dynamic optimization during flexion/extension of the knee, J. biomech. eng., 121, 316, (1999)
[14] Herzog, W., Force-sharing among synergistic muscles: theoretical considerations and experimental approaches, Exercise sports sci. rev., 24, 173, (1996)
[15] Epstein, M.; Herzog, W., Theoretical models of skeletal muscle: biological and mathematical considerations, (1998), John Wiley and Sons Toronto, ON, p. 153 (Chapter: Movement Control)
[16] Lawrence, J.H.; Nichols, T.R.; English, A.W., Cat hindlimb muscles exert substantial torques outside the sagittal plane, J. neurophysiol., 69, 1, 282, (1993)
[17] Sacks, R.D.; Roy, R.R., Architecture of the hind limb muscles of cats: functional significance, J. morphol., 173, 2, 185, (1982)
[18] Leijnse, J.N., The controllability of the unloaded human finger with superficial or deep flexor, J. biomech., 30, 11-12, 1087, (1997)
[19] Tsirakos, D.; Baltzopoulos, V.; Bartlett, R., Inverse optimization: functional and physiological considerations related to the force-sharing problem, Crit. rev. biomed. eng., 25, 4-5, 371, (1997)
[20] van Bolhuis, B.M.; Gielen, C.C.A.M., A comparison of models explaining muscle activation patterns for isometric contractions, Biol. cybernet., 81, 249, (1999) · Zbl 0957.92013
[21] Silva, Miguel P.T.; Ambrosio, Jorge A.C., Solution of redundant muscle forces in human locomotion with multibody dynamics and optimization tools, Mech. based des. struct. Mach., 31, 3, 381, (2003)
[22] Dons, B.; Bollerup, K.; Bonde-Petersen, F.; Hancke, S., The effect of weight-lifting exercise related to muscle fiber composition and muscle cross-sectional area in humans, Eur. J. appl. physiol., 40, 95, (1979)
[23] Hermiston, R.T.; Bonde-Petersen, F., The influence of varying oxygen tensions in inspired gas on zenon muscle clearance and fatigue levels during sustained and dynamic contractions, J. appl. physiol., 34, 291, (1975)
[24] Bazaraa, M.S.; Sherali, H.D.; Shetty, C.M., Nonlinear programming theory and algorithms, (1993), John Wiley and Sons New York · Zbl 0774.90075
[25] Horst, R.; Pardalos, P.M.; Thoai, N.V., Introduction to global optimization, (1993), Kluwer Dordrecht, The Netherlands
[26] Wismer, D.A.; Chattergy, R., Introduction to non-linear optimization: a problem solving approach, (1979), Elsevier North Holland Inc. New York
[27] Ait-Haddou, R.; Jinha, A.; Herzog, W.; Binding, P., Analysis of the force-sharing problem using an optimization model, Math. biosci., 191, 2, 111, (2004) · Zbl 1053.92005
[28] Raikova, R.T.; Prilutsky, B.I., Sensitivity of predicted muscle forces to parameters of the optimization-based human leg model revealed by analytical and numerical analyses, J. biomech., 34, 1243, (2001)
[29] Herzog, W.; Leonard, T.R., Validation of optimization models that estimate the forces exerted by synergistic muscles, J. biomech., 24, Suppl 1, 31, (1991)
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