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TECHNICAL PAPERS

Dynamic Optimization of Human Walking

[+] Author and Article Information
Frank C. Anderson, Marcus G. Pandy

Department of Biomedical Engineering, and Department of Kinesiology, ENS 610, The University of Texas at Austin, Austin, TX 78712-D3700

J Biomech Eng 123(5), 381-390 (May 16, 2001) (10 pages) doi:10.1115/1.1392310 History: Received October 21, 1999; Revised May 16, 2001
Copyright © 2001 by ASME
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Figures

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Sagittal- and frontal-plane views of the model skeleton. The inertial reference frame was fixed to the ground at the level of the floor. The axes of the inertial frame formed a right-handed coordinate system: The X axis was directed forward, the Y axis was directed upward, and the Z axis was directed laterally. There were a total of 23 generalized coordinates in the model. Wherever possible, each generalized coordinate is labeled as a number. Generalized coordinates q1–q3 specified the translation of the pelvis with respect to the origin of the inertial frame, and q4–q6 were X-Y-Z body-fixed, Euler angles which specified the orientation of the pelvis with respect to the inertial frame. The relative orientations of the HAT, right thigh, and left thigh with respect to the pelvis were specified using Z-X-Y body-fixed Euler angles at the back (q7–q9), right hip (q10–q12), and left hip (q17–q19), respectively. Generalized coordinate q9 (rotation of the HAT in the transverse plane) is not shown because it lies inside the HAT segment.
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Schematic showing some of the muscles in the model. A total of 54 musculotendinous actuators controlled the model. Abbreviations used for the muscles are as follows: ERCSPN, erector spinae; EXTOBL, external abdominal obliques; INTOBL, internal abdominal obliques; ILPSO, iliopsoas; ADLB, adductor longus brevis; ADM, adductor magnus; GMEDA, anterior gluteus medius and anterior gluteus minimus; GMEDP, posterior gluteus medius and posterior gluteus minimus; GMAXM, medial gluteus maximus; GMAXL, lateral gluteus maximus; TFL, tensor fasciae latae; SAR, sartorius; GRA, gracilis; HAMS, semimembranosus, semitendinosus, and biceps femoris long head; RF, rectus femoris; VAS, vastus medialis, vastus intermedius, and vastus lateralis; BFSH, biceps femoris short head; GAS, gastrocnemius; SOL, soleus; PFEV, peroneus brevis and peroneus longus; DFEV, peroneus tertius and extensor digitorum; DFIN, tibialis anterior and extensor hallucis longus; PFIN, tibialis posterior, flexor digitorum longus, and flexor hallucis longus. Muscles included in the model but not shown in the diagram are: PIRI, piriformis; PECT, pectinius; FDH, flexor digitorum longus/brevis and flexor hallucis longus/brevis; and EDH, extensor digitorum longus/brevis and extensor hallucis longus/brevis.
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Metabolic energy expenditure plotted as a function of walking speed. The rate of metabolic energy expenditure increases parabolically as walking speed increases (solid line) 16. When the rate of metabolic energy consumption is normalized by the distance traveled, an optimal walking speed is predicted at 80 m/min (dashed line) 16.
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Orientation of the pelvis in the model (black lines) and in the subjects (gray lines). The gray vertical lines represent one standard deviation above and below the mean for the subjects. 0 and 100 percent indicate heel strike of the same leg (one gait cycle) for the model and the subjects. The orientation of the pelvis is described by the body-fixed X-Y-Z Euler angles (see Fig. 1). Pelvic list (top) occurs about the X axis of the pelvis, with listing to the right being positive. Transverse rotation (middle) occurs about the Y axis of the pelvis, with rotation to the left being positive. Pelvic tilt (bottom) occurs about the Z axis of the pelvis, with posterior tilt being positive. OTO denotes opposite toe-off, OHS opposite heel-strike, TO toe-off, and HS heel strike.
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Angular displacement of the back in the model (black lines) and in the subjects (gray lines). The gray vertical lines represent one standard deviation above and below the mean for the subjects. The back angles define the orientation of the HAT segment relative to the pelvis and are described by body-fixed Z-X-Y Euler angles (Fig. 1). Flexion-Extension (top) occurs about the Z axis of the HAT, with extension being positive. Lateral Bending (middle) occurs about the X axis of the HAT, with bending to the right being positive. Axial Rotation (bottom) occurs about the Y axis of the HAT, with rotation to the left being positive.
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Angular displacement of the hip in the model (black lines) and in the subjects (gray lines). The gray vertical lines represent one standard deviation above and below the mean for the subjects. The hip angles define the orientation of the thigh relative to the pelvis and are described by body-fixed Z-X-Y Euler angles (Fig. 1). Flexion-extension (top) occurs about the Z axis of the thigh, with flexion being positive. Abduction-adduction (middle) occurs about the X axis of the thigh, with adduction being positive. Internal-external rotation (bottom) occurs about the Y axis of the thigh, with internal rotation being positive.
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Angular displacements of the knee, ankle, and subtalar joints in the model (black lines) and in the subjects (gray lines). The gray vertical lines represent one standard deviation above and below the mean for the subjects. Knee extension, ankle dorsiflexion, and subtalar inversion are all positive.
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Vertical, fore-aft, and transverse components of the ground-reaction force generated by the model (black lines) and the subjects (gray lines) during walking. For the model, the resultant force in each direction was found by summing the forces developed by the ground springs located under the sole of each foot. Spikes in the model ground forces are due to oscillations in the ground springs.
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Comparison of EMG data recorded for one subject (gray wavy lines) with muscle excitation histories predicted by the model (black lines) for walking. Subject EMG data were normalized by dividing by the maximum electrode voltage recorded during a maximal voluntary contraction for each muscle. The vertical axes for the model excitations and subject EMG records therefore range from 0 to 1. The horizontal gray bars shown above many of the records indicate the periods of EMG activity recorded by other researchers 2829. 0 and 100 percent indicate heel strike of the same leg (one gait cycle) for the model and the subjects. Abbreviations used for the muscles are given in Fig. 2.

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