Optimal Control Modeling of Lower Extremity Musculoskeletal Motion

The application of optimal control theory in the study of musculoskeletal motion was investigated. The research includes a comparative study of muscle models of varying complexity. Four such models ranging in complexity from simple input-output models to very sophisticated phenomenological models were examined. A model was developed which was able to strike a compromise between model complexity and practicability in musculoskeletal motion applications.

In the solution process several optimal optimal control algorithms were compared to determine their ability to handle the large scale nonlinear constrained optimization problems typically encountered in these studies. These algorithms were used to solve four different problems of varying complexity.

The selected muscle model and optimal control algorithm were used to solve the muscle-force sharing problem of gait analysis. The objective function used is the metabolic energy consumption. This quantity was described empirically by deriving appropriate expressions for its components in terms of the state and control variables of the muscle model. The results using this dynamic optimization algorithm are compared with similar results obtained using a static optimization approach.

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.
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.
1978	Crowninshield RD. Use of optimization techniques to predict muscle forces. J Biomech Eng. May 1978;100(2):88-92.
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.
1981	Crowninshield RD, Brand RA. A physiologically based criterion of muscle force prediction in locomotion. J Biomech. 1981;14(11):793-801.
1957	Huxley AF. Muscle structure and theories of contraction. Prog Biophys Biophys Chem. 1957;7:255-318.
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.
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.
1976	Hatze H. The complete optimization of a human motion. Math Biosci. 1976;28(1-2):99-135.
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.
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.
1938	Hill AV. The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Biol Sci. October 10, 1938;126(843):136-195.
1978	Pedotti A, Krishnan VV, Stark L. Optimization of muscle-force sequencing in human locomotion. Math Biosci. 1978;38(1-2):57-76.
1973	Chao EY-S, Rim K. Application of optimization principles in determining the applied moments in human leg joints during gait. J Biomech. September 1973;6(5):497-510.

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.

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.

1978

Crowninshield RD. Use of optimization techniques to predict muscle forces. J Biomech Eng. May 1978;100(2):88-92.

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.

1981

Crowninshield RD, Brand RA. A physiologically based criterion of muscle force prediction in locomotion. J Biomech. 1981;14(11):793-801.

1957

Huxley AF. Muscle structure and theories of contraction. Prog Biophys Biophys Chem. 1957;7:255-318.

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.

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.

1976

Hatze H. The complete optimization of a human motion. Math Biosci. 1976;28(1-2):99-135.

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.

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.

1938

Hill AV. The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Biol Sci. October 10, 1938;126(843):136-195.

1978

Pedotti A, Krishnan VV, Stark L. Optimization of muscle-force sequencing in human locomotion. Math Biosci. 1978;38(1-2):57-76.

1973

Chao EY-S, Rim K. Application of optimization principles in determining the applied moments in human leg joints during gait. J Biomech. September 1973;6(5):497-510.

Year	Entry
2004	Oi N, Pandy MG, Myers BS, Nightingale RW, Chancey VC. Variation of neck muscle strength along the human cervical spine. Stapp Car Crash J. 2004;48:397-417. SAE 2004-22-0017.
1999	Anderson FC, Pandy MG. A dynamic optimization solution for vertical jumping in three dimensions. Comput Methods Biomech Biomed Eng. 1999;2(3):201-231.
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.
1985	Audu ML, Davy DT. The influence of muscle model complexity in musculoskeletal motion modeling. J Biomech Eng. May 1985;107(2):147-157.
2014	Yoder A. Low Back Biomechanics During Walking of Individuals With a Lower-Limb Amputation [Master's thesis]. Colorado School of Mines; 2014.
1991	Meglan DA. Enhanced Analysis of Human Locomotion [PhD thesis]. The Ohio State University; 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.
2011	Matrangola SL. An Experimental and Simulation Based Approach Toward Understanding the Effects of Obesity on Balance Recovery from a Postural Perturbation [PhD thesis]. Virginia Polytechnic Institute and State University; September 8, 2011.

Year

Entry

2004

Oi N, Pandy MG, Myers BS, Nightingale RW, Chancey VC. Variation of neck muscle strength along the human cervical spine. Stapp Car Crash J. 2004;48:397-417. SAE 2004-22-0017.

1999

Anderson FC, Pandy MG. A dynamic optimization solution for vertical jumping in three dimensions. Comput Methods Biomech Biomed Eng. 1999;2(3):201-231.

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.

1985

Audu ML, Davy DT. The influence of muscle model complexity in musculoskeletal motion modeling. J Biomech Eng. May 1985;107(2):147-157.

2014

Yoder A. Low Back Biomechanics During Walking of Individuals With a Lower-Limb Amputation [Master's thesis]. Colorado School of Mines; 2014.

1991

Meglan DA. Enhanced Analysis of Human Locomotion [PhD thesis]. The Ohio State University; 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.

2011

Matrangola SL. An Experimental and Simulation Based Approach Toward Understanding the Effects of Obesity on Balance Recovery from a Postural Perturbation [PhD thesis]. Virginia Polytechnic Institute and State University; September 8, 2011.