Muscular synergism, II: a minimum-fatigue criterion for load sharing between synergistic muscles

wbldb

Dul, J.¹; Johnson, G. E.²; Shiavi, R.¹; Townsend, M. A.²

Muscular synergism, II: a minimum-fatigue criterion for load sharing between synergistic muscles

J Biomech. 1984;17(9):675-684

©1984 Pergamon Press Ltd.

Affiliations

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

²Department of Mechanical and Materials Engineering, Vanderbilt University, Nashville. TN 37235. U.S .A
Abstract

A new physiological criterion for muscular load sharing is developed. The criterion is based on the assumption that the endurance time of muscular contractions is maximized, hence muscular fatigue is minimized. The optimization problem is cast in the form of a linearly constrained, non-linear MINIMAX optimization.

The new method predicts that: (1) there is synergistic muscle action, (2) muscle force increases non-linearly with external force (load), (3) relatively more force is allocated to muscles that have a large maximum force (large muscles), (4) relatively more force is allocated to muscles with a high percentage of slow-twitch fibers (muscles that are fatigue-resistant), (5) the load sharing does not depend on the moment arm of the muscles (although the absolute force levels do depend on this variable).

The predicted load sharing between two cat muscles during standing and walking is in good agreement with direct force measurement data from the literature.
Links

DOI: 10.1016/0021-9290(84)90121-0

PubMed: 6501327

WoS: A1984TQ30600004
History

Revised: 1984-03

Revised: 1984-04

Cited Works (5)

Year	Entry
1984	Dul J, Townsend MA, Shiavi R, Johnson GE. Muscular synergism, I: on criteria for load sharing between synergistic muscles. J Biomech. 1984;17(8):663-673.
1981	Crowninshield RD, Brand RA. A physiologically based criterion of muscle force prediction in locomotion. J Biomech. 1981;14(11):793-801.
1978	Pedotti A, Krishnan VV, Stark L. Optimization of muscle-force sequencing in human locomotion. Math Biosci. 1978;38(1-2):57-76.
1973	Johnson MA, Polgar J, Weightman D, Appleton D. Data on the distribution of fibre types in thirty-six human muscles: an autopsy study. J Neurol Sci. January 1973;18(1):111-129.
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 (38)

Year	Entry
1990	Zajac FE, Winters JM. Modeling musculoskeletal movement systems: joint and body segmental dynamics, musculoskeletal actuation, and neuromuscular control. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:121-148.
1990	Gielen S, Schenau G-JvI, Tax T, Theeuwen M. The activation of mono- and bi-articular muscles in multi-joint movements. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:302-311.
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.
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.
2009	Chang C-Y, Rupp JD, Reed MP, Hughes RE, Schneider LW. Predicting the effects of musce activation on knee, thigh, and hip injuries in frontal crashes using a finite-element model with muscle forces from subject testing and musculoskeletal modeling. Stapp Car Crash J. 2009;53:291-328. SAE 2009-22-0011.
1989	Bergmark A. Stability of the lumbar spine: a study in mechanical engineering. Acta Orthop Scand. 1989;60(suppl 230):1-54.
2009	Andersen MS, Damsgaard M, Rasmussen J. Kinematic analysis of over-determinate biomechanical systems. Comput Methods Biomech Biomed Eng. August 2009;12(4):371-384.
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, Townsend MA, Shiavi R, Johnson GE. Muscular synergism, I: on criteria for load sharing between synergistic muscles. J Biomech. 1984;17(8):663-673.
1988	Winters JM, Stark L. Estimated mechanical properties of synergistic muscles involved in movements of a variety of human joints. J Biomech. 1988;21(12):1027-1041.
1995	Collins JJ. The redundant nature of locomotor optimization laws. J Biomech. March 1995;28(3):251-267.
2001	Anderson FC, Pandy MG. Static and dynamic optimization solutions for gait are practically equivalent. J Biomech. February 2001;34(2):153-161.
2001	Rasmussen J, Damsgaard M, Voigt M. Muscle recruitment by the min/max criterion: a comparative numerical study. J Biomech. March 2001;34(3):409-415.
2003	Thelen DG, Anderson FC, Delp SL. Generating dynamic simulations of movement using computed muscle control. J Biomech. March 2003;36(3):321-328.
2007	Sasimontonkul S, Bay BK, Pavol MJ. Bone contact forces on the distal tibia during the stance phase of running. J Biomech. 2007;40(15):3503-3509.
2010	Saraswat P, Andersen MS, MacWilliams BA. A musculoskeletal foot model for clinical gait analysis. J Biomech. 2010;43(9):1645-1652.
2023	Wakeling JM, Febrer-Nafría M, De Groote F. A review of the efforts to develop muscle and musculoskeletal models for biomechanics in the last 50 years. J Biomech. June 2023;155:111657.
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.
2018	Hume DR. Translating Data from the Laboratory Into Simulation: A Computational Framework for Subject-Specific Finite Element Musculoskeletal Simulation [PhD thesis]. University of Denver; August 2018.
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.
1997	Murray WM. The Functional Capacity of the Elbow Muscles: Anatomical Measurements, Computer Modeling, and Anthropometric Scaling [PhD thesis]. Evanston, IL: Northwestern University; June 1997.
2004	Sasimontonkul S. Do Running and Fatigued Running Relate to Tibial Stress Fractures? [PhD thesis]. Oregon State University; 2004.
2015	Shahvarpour A. Biomechanical Response of Trunk Under Perturbations and in Challenged Seated Balance [PhD thesis]. École polytechnique de Montréal; November 2015.
2017	Wen J. Identification d'une fonction coût réaliste de la distribution des forces musculaires en cours de mouvement [Master's thesis]. École polytechnique de Montréal; August 2017.
2019	Ghezelbash F. Subject-Specific Computational Musculoskeletal Modeling of Human Trunk in Lifting: Role of Age, Sex, Body Weight and Body Height [PhD thesis]. École polytechnique de Montréal; December 2019.
2022	Gaudet G. Development of a multibody model for quantification of muscle forces at upper limb as a design tool for exoskeleton synthesis [PhD thesis]. École polytechnique de Montréal; October 2022.
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.
1993	Guimaraes ACS. The EMG-Force Relation of the Cat Soleus Muscle [PhD thesis]. Calgary, AB: University of Calgary; December 1993.
2009	Raison M. On the Quantification of Joint and Muscle Efforts in the Human Body During Motion [PhD thesis]. Université catholique de Louvain; June 23, 2009.
2014	Ramsay JW. Muscle Morphological Changes, Compensatory Strategies and the Use of Predictive Simulations to Direct the Rehabilitation of Individuals Post-Stroke [PhD thesis]. University of Delaware; 2014.
1988	Son K. Biomechanical Analyses of Weight-Moving Tasks in the Seated Position [PhD thesis]. University of Michigan; 1988.
1991	Luchies CW. Fall Arrest Biomechanics: Sway and Stepping Responses in Healthy Young and Old Adults [PhD thesis]. University of Michigan; 1991.
1994	Nussbaum MA. Artificial Neural Network Models for Analysis of Lumbar Muscle Recruitment During Moderate Static Exertions [PhD thesis]. University of Michigan; 1994.
2009	Chang C-Y. Prediction of the Effects of Lower-Extremity Muscle Forces on Knee, Thigh, and Hip Injuries in Frontal Motor Vehicle Crashes [PhD thesis]. University of Michigan; 2009.
2012	Raths C. Neuromuscular Dynamics in the Context of Motor Redundancy [PhD thesis]. University of Southern California (USC); August 2012.
1999	Anderson FC III. A Dynamic Optimization Solution for a Complete Cycle of Normal Gait [PhD thesis]. University of Texas at Austin; December 1999.