Muscular synergism, I:​ on criteria for load sharing between synergistic muscles

Dul, J.; Townsend, M. A.; Shiavi, R.; Johnson, G. E.

Affiliations

¹Department of Biomedical Engineering, Vanderbilt University, Nashville, TN 37235, U.S.A.

²Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22901, U.S.A.

³Department of Mechanical and Materials Engineering, Vanderbilt University, Nashville, TN 37235, U.S.A.

Abstract

The use of optimization techniques to predict individual muscle forces in redundant biomechanical systems implies the formulation of a criterion for load sharing between the muscles. In part I of this paper, the characteristics and performance of several linear and non-linear criteria reported in the literature have been compared for static-isometric knee flexion. The results show that linear criteria inherently predict discrete muscle action (orderly recruitment of muscles) whereas non-linear criteria can predict synergistic action. All criteria predict that relatively more force is allocated to muscles with large moment arms. When muscle stresses (or ratios of muscle force to maximum muscle force) are used as the decision variables in the objective function, then relatively more force is allocated to muscles with large maximum possible force as well. Future formulations of the optimization should consider the differences in fiber type composition among the muscles. Such an approach is presented in part II of the paper.

Links

DOI: 10.1016/0021-9290(84)90120-9

PubMed: 6501326

WoS: A1984TQ30600003

History

Received: 1983-03

Revised: 1984-04

Cited Works (12)

Year	Entry
1978	Hardt DE. Determining muscle forces in the leg during normal human walking: an application and evaluation of optimization methods. J Biomech Eng. May 1978;100(2):72-78.
1974	Penrod DD, Davy DT, Singh DP. An optimization approach to tendon force analysis. J Biomech. March 1974;7(2):123-129.
1978	Crowninshield RD. Use of optimization techniques to predict muscle forces. J Biomech Eng. May 1978;100(2):88-92.
1973	Seireg A, Arvikar RJ. A mathematical model for evaluation of forces in lower extremeties of the musculo-skeletal system. J Biomech. May 1973;6(3):313-326.
1981	Crowninshield RD, Brand RA. A physiologically based criterion of muscle force prediction in locomotion. J Biomech. 1981;14(11):793-801.
1984	Dul J, Johnson GE, Shiavi R, Townsend MA. Muscular synergism, II: a minimum-fatigue criterion for load sharing between synergistic muscles. J Biomech. 1984;17(9):675-684.
1976	Yeo BP. Investigations concerning the principle of minimal total muscular force. J Biomech. 1976;9(6):413-416.
1978	Crowninshield RD, Johnston RC, Andrews JG, Brand RA. A biomechanical investigation of the human hip. J Biomech. 1978;11(1-2):75-85.
1978	Chao EY, An KN. Graphical interpretation of the solution to the redundant problem in biomechanics. J Biomech. August 1978;11(3):159-167.
1975	Seireg A, Arvikar RJ. The prediction of muscular load sharing and joint forces in the lower extremities during walking. J Biomech. March 1975;8(2):89-102.
1978	Pedotti A, Krishnan VV, Stark L. Optimization of muscle-force sequencing in human locomotion. Math Biosci. 1978;38(1-2):57-76.
1981	Patriarco AG, Mann RW, Simon SR, Mansour JM. An evaluation of the approaches of optimization models in the prediction of muscle forces during human gait. J Biomech. 1981;14(8):513-525.

Cited By (29)

Year	Entry
1990	Seif-Naraghi AH, Winters JM. Optimized strategies for scaling goal-directed dynamic limb movements. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:312-334.
1990	Meek SG, Wood JE, Jacobsen SC. Model-based, multi-muscle EMG control of upper-extremity prostheses. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:360-376.
1990	Andersson GBJ, Winters JM. Role of muscle in postural tasks: spinal loading and postural stability. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:377-395.
1990	Hull ML, Hawkins DA. Analysis of muscular work in multisegmental movements: application to cycling. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:621-638.
2011	van Rooij L. Effect of various pre-crash braking strategies on simulated human kinematic response with varying levels of driver attention. In: Proceedings of the 22nd International Technical Conference on the Enhanced Safety of Vehicles (ESV). June 13-16, 2011; Washington, DC.
2010	Nemirovsky N, van Rooij L. A new methodology for biofidelic head-neck postural control. In: Proceedings of the 2010 International IRCOBI Conference on the Biomechanics of Impact. September 15-17, 2010; Hannover, Germany.71-84.
2013	Meijer R, Broos J, Elrofai H, de Bruijn E, Forbes P, Happee R. Modelling of bracing in a multi‐body active human model. In: Proceedings of the 2013 International IRCOBI Conference on the Biomechanics of Injury. September 11-13, 2013; Gothenburg, Sweden.576-587.
2003	Chancey VC, Nightingale RW, Van Ee CA, Knaub KE, Myers BS. Improved estimation of human neck tensile tolerance: reducing the range of reported tolerance using anthropometrically correct muscles and optimized physiologic initial conditions. Stapp Car Crash J. 2003;47:135-153. SAE 2003-22-0008.
1989	Bergmark A. Stability of the lumbar spine: a study in mechanical engineering. Acta Orthop Scand. 1989;60(suppl 230):1-54.
2007	Erdemir A, McLean S, Herzog W, van den Bogert AJ. Model-based estimation of muscle forces exerted during movements. Clin Biomech (Bristol, Avon). February 2007;22(2):131-154.
1989	Zajac FE, Gordon ME. Determining muscle's force and action in multi-articular movement. Exerc Sport Sci Rev. January 1989;17(1):187-230.
1984	Dul J, Johnson GE, Shiavi R, Townsend MA. Muscular synergism, II: a minimum-fatigue criterion for load sharing between synergistic muscles. J Biomech. 1984;17(9):675-684.
1997	Glitsch U, Baumann W. The three-dimensional determination of internal loads in the lower extremity. J Biomech. November–December 1997;30(11-12):1123-1131.
2004	Forster E, Simon U, Augat P, Claes L. Extension of a state-of-the-art optimization criterion to predict co-contraction. J Biomech. April 2004;37(4):577-581.
2011	Modenese L, Phillips ATM, Bull AMJ. An open source lower limb model: hip joint validation. J Biomech. August 11, 2011;44(12):2185-2193.
1987	Pedersen DR, Brand RA, Cheng C, Arora JS. Direct comparison of muscle force predictions using linear and nonlinear programming. J Biomech Eng. August 1987;109(3):192-199.
2010	Östh J. Active Muscle Responses in a Finite Element Human Body Model [Licentiate thesis]. Götenburg, Sweden: Chalmers University of Technology; 2010.
2016	Navacchia A. Multiscale Musculoskeletal Modeling of the Lower Limb to Perform Personalized Simulations of Movement [PhD thesis]. University of Denver; November 2016.
2005	Chancey VC. Strength of the Human Neck: Understanding the Contributions of the Ligamentous and Muscular Spine in Tension and Bending [PhD thesis]. Duke University; 2005.
2009	Carriero A. Modelling Gait Abnormalities and Bone Deformities in Children With Cerebral Palsy [PhD thesis]. Imperial College London; May 2009.
2011	Holmes MWR. A Biomechanical Evaluation of Ligament and Muscular Stiffness in the Distal Upper Extremity [PhD thesis]. Hamilton, ON: McMaster University; June 2011.
1986	Buchanan TS. A Biomechanical Analysis of the Neural Control of Muscles about the Human Elbow Joint During Isometric Tasks [PhD thesis]. Evanston, IL: Northwestern University; June 1986.
2014	El Ouaaid Z. L'effet des charges externes sur la biomécanique et la stabilité de la colonne vertébrale en posture debout [PhD thesis]. École polytechnique de Montréal; July 2014.
1995	Raasch CC. Coordination of Pedaling: Functional Muscle Groups and Locomotor Strategies [PhD thesis]. Stanford University; December 1995.
1989	Morlock M. A Generalized Three-Dimensional Six-Segment Model of the Ankle and the Foot [PhD thesis]. Calgary, AB: University of Calgary; December 1989.
1989	Read L. A Two-Dimensional Knee Joint Model Applied to Landing Movements in Alpine Skiing [Master's thesis]. Calgary, AB: University of Calgary; December 1989.
2002	Jinha A. Analyses of Muscle Force Predictions Based on Optimization [Master's thesis]. Calgary, AB: University of Calgary; May 2002.
1991	Luchies CW. Fall Arrest Biomechanics: Sway and Stepping Responses in Healthy Young and Old Adults [PhD thesis]. University of Michigan; 1991.
2019	Kingston DC. Development of a Full Flexion 3D Musculoskeletal Model of the Knee Considering Intersegmental Contact and Deep Muscle Activity During High Knee Flexion [PhD thesis]. University of Waterloo; 2019.