An optimization approach to tendon force analysis

Penrod, D. D.; Davy, D. T.; Singh, D. P.

Affiliations

¹Department of Mcchanlcs and Hydraulics and Department of Orthopedic Surgery, University of Iowa, Iowa City, Iowa 32210. U.S.A.

Abstract

The problem of distribution of forces among synergistic muscles at a joint is examined. In order to arrive at a unique solution for the redundant system it is assumed that the solution represents an optimal response in terms of total muscle effort. The minimum muscle effort can be related to the concent of reciprocal inhibition. The nature of the resulting mathematical formulation is illustrated by a simple two tendon model. The formulation for a general multiaxial joint is then given, along with a general principle concerning the nature of resulting solutions. Results for two examples based upon a simplified biaxial model of the wrist are presented. Finally, the nature of several implicit assumptions in the analysis are reviewed and their consequences discussed.

Links

DOI: 10.1016/0021-9290(74)90050-5

PubMed: 4837546

WoS: A1974T316900002

History

Received: 1973-09-25

Cited Works (3)

Year	Entry
1965	Sorbie C, Zalter R. Bio-engineering studies of the forces transmitted by joints, I: the phasic relationship of the hip muscles in walking. In: Kenedi RM, ed. Biomechanics and Related Bio-Engineering Topics: Proceedings of a Symposium Held in Glasgow, September 1964. Oxford, UK: Pergamon Press; 1965:359-367.
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.
1965	Paul JP. Bio-engineering studies of the forces transmitted by joints, II: engineering analysis. In: Kenedi RM, ed. Biomechanics and Related Bio-Engineering Topics: Proceedings of a Symposium Held in Glasgow, September 1964. Oxford, UK: Pergamon Press; 1965:369-380.

Cited By (40)

Year	Entry
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.
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.
1976	Chao EY, Opgrande JD, Axmear FE. Three-dimensional force analysis of finger joints in selected isometric hand functions. J Biomech. 1976;9(6):387-396.
1978	Crowninshield RD, Johnston RC, Andrews JG, Brand RA. A biomechanical investigation of the human hip. J Biomech. 1978;11(1-2):75-85.
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.
1981	Crowninshield RD, Brand RA. A physiologically based criterion of muscle force prediction in locomotion. J Biomech. 1981;14(11):793-801.
1984	Röhrle H, Scholten R, Sigolotto C, Sollbach W, Kellner H. Joint forces in the human pelvis-leg skeleton during walking. J Biomech. 1984;17(6):409-424.
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.
1986	Brand RA, Pedersen DR, Friederich JA. The sensitivity of muscle force predictions to changes in physiologic cross-sectional area. J Biomech. 1986;19(8):589-596.
1987	Davy DT, Audu ML. A dynamic optimization technique for predicting muscle forces in the swing phase of gait. J Biomech. 1987;20(2):187-201.
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.
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.
1978	Crowninshield RD. Use of optimization techniques to predict muscle forces. J Biomech Eng. May 1978;100(2):88-92.
1985	Audu ML, Davy DT. The influence of muscle model complexity in musculoskeletal motion modeling. J Biomech Eng. May 1985;107(2):147-157.
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.
1985	Audu ML. Optimal Control Modeling of Lower Extremity Musculoskeletal Motion [PhD thesis]. Cleveland, OH: Case Western Reserve University; January 1985.
2008	Pal S. Explicit Finite Element Modeling of Joint Mechanics [PhD thesis]. University of Denver; August 2008.
1978	Hardt DE. A Minimum Energy Solution for Muscle Force Control During Walking [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; September 1978.
2001	Reffeor WS. Three Dimensional Dynamic Analysis of the Human Hand for Predicting Tendon, Ligament and Nerve Wear in the Carpal Tunnel During Typing [PhD thesis]. East Lansing, MI: Michigan State University; 2001.
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.
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.
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.
1979	Burdett RG. Biomechanical Model of the Ankle Joint [PhD thesis]. State College, PA: Pennsylvania State University; August 1979.
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.
2004	Kaya M. Coordination of Cat Hindlimb Muscles During Voluntary Movements [PhD thesis]. Calgary, AB: University of Calgary; February 2004.
2004	Scovil CY. The Viability of a 3D Forward Dynamic Model of Walking as a Research Tool to Enhance Clinical Understanding of Gait Abnormalities [PhD thesis]. Calgary, AB: University of Calgary; March 2004.
2009	Hettinga BA. Development of a Forward Simulation Model of the Speed Skating Push-Off for the Optimization of Subject Specific Klapskate Design [PhD thesis]. Calgary, AB: University of Calgary; September 2009.
2020	Han S-w. Changes in Patellofemoral Joint Mechanics in the Presence of Quadriceps Muscle Imbalance [PhD thesis]. Calgary, AB: University of Calgary; August 2020.
1990	Hawkins DA. A Cellular-Based Muscle Model: Formulation and Application for Studying Muscle Mechanics [PhD thesis]. Davis, University of California; 1990.
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.
1980	Vaughan CL. An Optimization Approach to Closed Loop Problems in Biomechanics [PhD thesis]. University of Iowa; August 1980.
1985	Herzog W. Individual Muscle Force Prediction in Athletic Movements [PhD thesis]. University of Iowa; May 1985.
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.
1999	Anderson FC III. A Dynamic Optimization Solution for a Complete Cycle of Normal Gait [PhD thesis]. University of Texas at Austin; December 1999.
2007	Seth A. A Neuromusculoskeletal Tracking Method for Estimating Muscle Forces in Human Gait from Experimental Movement Data [PhD thesis]. University of Texas at Austin; May 2007.