Application of optimization principles in determining the applied moments in human leg joints during gait

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Chao, Edmund Yee-Su¹; Rim, Kwan¹

Application of optimization principles in determining the applied moments in human leg joints during gait

J Biomech. September 1973;6(5):497-510

Affiliations

¹University of Iowa, Iowa City, Iowa 5240, U.S.A.
Abstract

In certain dynamic linkage problems, the moments applied at the joints are not known and must be determined from the measured displacement history. This class of problems is defined as the Inverse Dynamics Problems, which are of great importance in the field of biomechanics. The determination of applied moments at the human lower extremity joints during gait is a perfect example of this type of problem.

The most commonly used method of solving these problems is to numerically differentiate the measured displacement data and calculate the moments and the forces using Newton's laws of motion. This method is questionably satisfactory and the results obtained may be improved further. This paper presents a new systematic method based on the mathematical theory of optimization to determine the applied moments at the leg joints during gait. The convergence characteristic of this method has been well demonstrated and the results obtained are less sensitive to the inherent errors in the displacement measurements.
Links

DOI: 10.1016/0021-9290(73)90008-0

PubMed: 4748498

WoS: A1973Q698200008
History

Received: 1972-11-14

Cited Works (2)

Year	Entry
1972	Kinzel GL, Hall AS Jr, Hillberry BM. Measurement of the total motion between two body segments, I: analytical development. J Biomech. January 1972;5(1):93-105.
1971	Chao EY-S. Determination of Applied Forces in Linkage Systems With Known Displacements: With Special Application to Biomechanics [PhD thesis]. University of Iowa; May 1971.

Cited By (24)

Year	Entry
1990	Ong HD, Hemami H, Simon S. Simulation studies of musculo-skeletal dynamics in cycling and sitting on a chair. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:518-533.
1991	Winter DA. The Biomechanics and Motor Control of Human Gait: Normal, Elderly and Pathological. 2nd ed. Waterloo, ON: University of Waterloo Press; 1991.
2009	Winter DA. Biomechanics and Motor Control of Human Movement. 4th ed. Hoboken, NJ: Inc, John Wiley & Sons; 2009.
1984	Nissan M, Gilad I. The cervical and lumbar vertebrae: an anthropometric model. Eng Med. July 1984;13(3):111-114.
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.
1980	Onyshko S, Winter DA. A mathematical model for the dynamics of human locomotion. J Biomech. 1980;13(4):361-368.
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.
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.
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.
1985	Audu ML, Davy DT. The influence of muscle model complexity in musculoskeletal motion modeling. J Biomech Eng. May 1985;107(2):147-157.
1998	Kuo AD. A least-squares estimation approach to improving the precision of inverse dynamics computations. J Biomech Eng. February 1998;120(1):148-159.
1985	Audu ML. Optimal Control Modeling of Lower Extremity Musculoskeletal Motion [PhD thesis]. Cleveland, OH: Case Western Reserve University; January 1985.
2014	Vlietstra N. Comparing Methods for Full Body Inverse Dynamics Analysis of a Standing Long Jump [Master's thesis]. Allendale, MI: Grand Valley State University; April 2014.
1978	Hardt DE. A Minimum Energy Solution for Muscle Force Control During Walking [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; September 1978.
1988	Verstraete MC. A Method for Computing the Three-Dimensional Forces and Moments in the Lower Limb During Locomotion [PhD thesis]. East Lansing, MI: Michigan State University; 1988.
1991	Meglan DA. Enhanced Analysis of Human Locomotion [PhD thesis]. The Ohio State University; 1991.
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.
1997	Runge CF. Joint Torque Analyses of Early Postural Responses to Fast Platform Translations: Implications for the Sensorimotor Control of Balance [PhD thesis]. Stanford University; February 1997.
1992	Kautz SA. Biomechanics of Pedalling With Non-Circular Chainrings in Cycling [PhD thesis]. Davis, University of California; 1992.
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.
1982	Balakrishnan S. The Interpretation of Medio-Lateral Reaction Forces in Human Locomotion Using Body Coordinate Systems [PhD thesis]. Winnipeg, MB: University of Manitoba; March 1982.
1991	Luchies CW. Fall Arrest Biomechanics: Sway and Stepping Responses in Healthy Young and Old Adults [PhD thesis]. University of Michigan; 1991.