×

zbMATH — the first resource for mathematics

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.

MSC:
92C10 Biomechanics
49N90 Applications of optimal control and differential games
PDF BibTeX XML Cite
Full Text: DOI
References:
[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)
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.