Optimization of muscle-force sequencing in human locomotion

Pedotti, A.; Krishnan, V. V.; Stark, L.

Affiliations

¹Centro per lo Studio delta Teoria dei Sistemi, CNR, Instituto di Eieitronica Politecnico di Milano, Italy

²Division of Engineering, San Francisco State University, San Francisco, California 94132

³Departments of Physiological Optics and Engineering Science, University of California, Berkeley, California 9472

Abstract

Human locomotion has been studied thoroughly, but sequences of muscle forces providing for coordinated gait are not well understood. We have approached this problem indirectly by computing such sequences under different optimality criteria involving minimization of muscular forces. Experimental kinematic and ground reaction measurements along with EMG data from the same subjects obtained during level walking enables us to select J=Σ(F_iF_max)² as the most feasible criterion. The results are discussed in terms of the economy and neurological control of locomotion.

Links

DOI: 10.1016/0025-5564(78)90018-4

WoS: A1978ES74600004

History

Received: 1977-07-28

Revised: 1977-09-09

Cited Works (7)

Year	Entry
1939	Elftman H. Forces and energy changes in the leg during walking. Am J Physiol. January 1939;125(2):339-356.
1975	Cappozzo A, Leo T, Pedotti A. A general computing method for the analysis of human locomotion. J Biomech. September 1975;8(5):307-320.
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.
1976	Cappozzo A, Figura F, Marchetti M, Pedotti A. The interplay of muscular and external forces in human ambulation. J Biomech. 1976;9(1):35-43.
1953	Hill AV. The mechanics of active muscle. Proc R Soc Lond B Biol Sci. March 11, 1953;141(902):104-117.
1970	Morrison JB. The mechanics of the knee joint in relation to normal walking. J Biomech. January 1970;3(1):51-61.
1969	Rack PMH, Westbury DR. The effects of length and stimulus rate on tension in the isometric cat soleus muscle. J Physiol. October 1969;204(2):443-460.

Cited By (65)

Year	Entry
1986	Denoth J. Load on the locomotor system and modeling. In: Nigg BM, ed. Biomechanics of Running Shoes. Champaign, IL: Inc., Human Kinetics Publishers; 1986:63-116.
2005	Andriacchi TP, Johnson TS, Hurwitz DE, Natarajan RN. Musculoskeletal dynamics, locomotion, and clinical applications. In: Mow VC, Huiskes R, eds. Basic Orthopaedic Biomechanics & Mechano-Biology. 3rd ed. Philadelphia, PA: Lippincott Williams & Wilkins; 2005:91-122.
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	Pedotti A, Crenna P. Individual strategies of muscle recruitment in complex natural movements. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:chap 34.
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.
1990	Yamaguchi GT. Performing whole-body simulations of gait with 3-D, dynamic musculoskeletal models. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:663-679.
1991	Winter DA. The Biomechanics and Motor Control of Human Gait: Normal, Elderly and Pathological. 2nd ed. Waterloo, ON: University of Waterloo Press; 1991.
2018	Eckersley CP, Cox CA, Ortiz-Paparoni MA, Lutz RH, Sell TC, Bass CR. A pain in the neck: a modeling analysis for design limitations of head supported mass. In: Proceedings of the 14th Ohio State University Injury Biomechanics Symposium. May 20-22, 2018; Columbus, OH.
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.
1985	Nashner LM, McCollum G. The organization of human postural movements: a formal basis and experimental synthesis. Behav Brain Sci. March 1985;8(1):135-150, 169-172.
1989	Zajac FE. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit Rev Biomed Eng. 1989;17(4):359-411.
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.
2002	Zajac FE, Neptune RR, Kautz SA. Biomechanics and muscle coordination of human walking, I: introduction to concepts, power transfer, dynamics and simulations. Gait Post. December 2002;16(3):215-232.
2003	Zajac FE, Neptune RR, Kautz SA. Biomechanics and muscle coordination of human walking, II: lessons from dynamical simulations and clinical implications. Gait Post. February 2003;17(1):1-17.
1985	Winters JM, Stark L. Analysis of fundamental human movement patterns through the use of in-depth antagonistic muscle models. IEEE Trans Biomed Eng. 1985;32(10):826-839.
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	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.
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.
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.
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.
1989	White SC, Yack HJ, Winter DA. A three-dimensional musculoskeletal model for gait analysis: anatomical variability estimates. J Biomech. 1989;22(8-9):885-893.
1995	Collins JJ. The redundant nature of locomotor optimization laws. J Biomech. March 1995;28(3):251-267.
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.
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.
2010	Ackermann M, van den Bogert AJ. Optimality principles for model-based prediction of human gait. J Biomech. April 19, 2010;43(6):1055-1060.
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.
1982	Brand RA, Crowninshield RD, Wittstock CE, Pedersen DR, Clark CR, van Krieken FM. A model of lower extremity muscular anatomy. J Biomech Eng. November 1982;104(4):304-310.
1988	Davy DT, Kotzar GM, Brown RH, Heiple KG, Goldberg VM, Heiple KG Jr, Berilla J, Burstein AH. Telemetric force measurements across the hip after total arthroplasty. J Bone Joint Surg. January 1988;70A(1):45-50.
2006	Damsgaard M, Rasmussen J, Christensen ST, Surma E, de Zee M. Analysis of musculoskeletal systems in the AnyBody modeling system. Simul Model Pract Theory. November 2006;14(8):1100-1111.
2013	Dibb AT, Cox CA, Nightingale RW, Luck JF, Cutcliffe HC, Myers BS, Arbogast KB, Seacrist T, Bass CR. Importance of muscle activations for biofidelic pediatric neck response in computational models. Traffic Inj Prev. November 22, 2013;14(suppl 1):S116-S127.
1985	Audu ML. Optimal Control Modeling of Lower Extremity Musculoskeletal Motion [PhD thesis]. Cleveland, OH: Case Western Reserve University; January 1985.
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.
2011	Dibb AT. Pediatric Head and Neck Dynamic Response: A Computational Study [PhD thesis]. Duke University; 2011.
2020	Cox CA. Computational Modeling of the Lumbar Spine: Active Musculature and Intra‐abdominal Pressure in Compressive Loading [PhD thesis]. Duke University; 2020.
2009	Carriero A. Modelling Gait Abnormalities and Bone Deformities in Children With Cerebral Palsy [PhD thesis]. Imperial College London; May 2009.
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.
2002	Henley JD. A Kinematic and Kinetic Analysis of Postural Perturbation [PhD thesis]. State College, PA: Pennsylvania State University; May 2002.
2014	Celik H. Predictive Gait Simulations for Investigation of Musculoskeletal Structure and Locomotor Function [PhD thesis]. State College, PA: Pennsylvania State University; August 2014.
1992	Li J. An Integrated Gait Analysis System (QGAIT) for Evaluation of Individual Loading Patterns At Knee Joint During Gait [PhD thesis]. Queen's University; November 1992.
1989	Yamaguchi GT. Feasibility and Conceptual Design of Functional Neuromuscular Stimulation Systems for the Restoration of Natural Gait to Paraplegics Based on Dynamic Musculoskeletal Models [PhD thesis]. Stanford University; August 1989.
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.
2002	Jinha A. Analyses of Muscle Force Predictions Based on Optimization [Master's thesis]. Calgary, AB: University of Calgary; May 2002.
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.
2012	Gopalakrishnan A. Formulating Optimization Based Musculoskeletal Simulation Approaches: Utility in Subject Assessment and Rehabilitation [PhD thesis]. University of Delaware; 2012.
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.
2023	Pariser K. Optimal Adaptive Treadmill Control to Maximize Propulsion During Gait [PhD thesis]. University of Delaware; Summer 2023.
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.
1998	Van Don BJ. Hamstring Injuries in Sprinting [PhD thesis]. University of Iowa; July 1998.
1988	Son K. Biomechanical Analyses of Weight-Moving Tasks in the Seated Position [PhD thesis]. University of Michigan; 1988.
1994	Nussbaum MA. Artificial Neural Network Models for Analysis of Lumbar Muscle Recruitment During Moderate Static Exertions [PhD thesis]. University of Michigan; 1994.
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.
2023	Kuska E. In Silico Techniques to Improve Understanding of Gait in Cerebral Palsy [PhD thesis]. University of Washington; 2023.
1996	Choi H. Muscle Forces and Spinal Loads in the Human Neck: An EMG Experiment and a Comparison of Three Modeling Methods [PhD thesis]. University of Wisconsin – Madison; 1996.
2019	Smith CR. Simulating the Effects of Anterior Cruciate Ligament Injury and Treatment on Cartilage Loading During Walking [PhD thesis]. University of Wisconsin – Madison; 2019.
1989	Crisco JJ III. The Biomechanical Stability of the Human Lumbar Spine: Experimental and Theoretical Investigations [PhD thesis]. Yale University; May 1989.