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First published online January 31, 2006
Journal of Experimental Biology 209, 622-632 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02010

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Constrained optimization in human running

Anne K. Gutmann¹, Brian Jacobi², Michael T. Butcher³ and John E. A. Bertram^4,*

¹ Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 12853, USA
² Department of Biological Sciences, Florida State University, Tallahassee, FL 32306, USA
³ Department of Biological Sciences, University of Calgary
⁴ Department of Cell Biology and Anatomy, Faculty of Medicine, University of Calgary, Calgary, AB T2N 4N1, Canada

^* Author for correspondence (e-mail: jbertram{at}ucalgary.ca)

Accepted 21 November 2005

Walking humans spontaneously select different speed, frequency and step length combinations, depending on which of these three parameters is specified. This behavior can be explained by constrained optimization of cost of transport (metabolic cost/distance) where cost of transport is seen as the main component of an underlying objective function that is minimized within the limitations of specified constraints. It is then of interest to ask whether or not such results are specific to walking only, or indicate a more general feature of locomotion control. The current study examines running gait selection within the framework of constrained optimization by comparing self-selected running gaits to the gaits predicted by constrained optimization of a cost surface constructed from cost data available in the literature. Normalizing speed and frequency values in the behavioral data by preferred speed and frequency reduced inter-subject variability and made group behavioral trends more visible. Although actual behavior did not coincide exactly with running cost optimization, self-selected gait and predictions from the general human cost surface did agree to within the 95% confidence interval and the region of minimal cost+0.005 ml O₂ kg^-1 m^-1. This was similar to the level of agreement between actual and predicted behavior observed in walking. Thus, there seems to be substantial evidence to suggest that (i) selection of gait parameters in running can largely be predicted using constrained optimization, and (ii) general cost surfaces can be constructed using metabolic data from one group that will largely predict the behavior of other groups.

Key words: gait, locomotion, cost, control, human

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