{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T08:29:33Z","timestamp":1785400173401,"version":"3.56.0"},"reference-count":18,"publisher":"The Company of Biologists","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006,2,15]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>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-1m-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.<\/jats:p>","DOI":"10.1242\/jeb.02010","type":"journal-article","created":{"date-parts":[[2006,1,31]],"date-time":"2006-01-31T21:12:40Z","timestamp":1138741960000},"page":"622-632","source":"Crossref","is-referenced-by-count":29,"title":["Constrained optimization in human running"],"prefix":"10.1242","volume":"209","author":[{"given":"Anne K.","family":"Gutmann","sequence":"first","affiliation":[{"name":"Department of Theoretical and Applied Mechanics, Cornell University,Ithaca, NY 12853, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Brian","family":"Jacobi","sequence":"additional","affiliation":[{"name":"Department of Biological Sciences, Florida State University, Tallahassee,FL 32306, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael T.","family":"Butcher","sequence":"additional","affiliation":[{"name":"Department of Biological Sciences, University of Calgary"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John E. A.","family":"Bertram","sequence":"additional","affiliation":[{"name":"Department of Cell Biology and Anatomy, Faculty of Medicine, University of Calgary, Calgary, AB T2N 4N1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"237","reference":[{"key":"2021042509560305800_REF1","unstructured":"Alexander, R. McN. (2000). Energetics and optimization of human walking and running: The 2000 Raymond Pearl Memorial Lecture. Am. J. Human Biol.14,641-648."},{"key":"2021042509560305800_REF2","doi-asserted-by":"crossref","unstructured":"Alexander, R. McN. (2001). Design by numbers. Nature412,591.","DOI":"10.1038\/35088155"},{"key":"2021042509560305800_REF3","doi-asserted-by":"crossref","unstructured":"Bertram, J. E. A. (2005). Constrained optimization in human walking: cost minimization and gait plasticity. J. Exp. Biol.208,979-991.","DOI":"10.1242\/jeb.01498"},{"key":"2021042509560305800_REF4","doi-asserted-by":"crossref","unstructured":"Bertram, J. E. A. and Ruina, A. (2001). Multiple walking speed-frequency relations are predicted by constrained optimization. J. Theor. Biol.209, 1-9.","DOI":"10.1006\/jtbi.2001.2279"},{"key":"2021042509560305800_REF5","doi-asserted-by":"crossref","unstructured":"Cavagna, G. A., Heglund, N. C. and Taylor, C. R.(1977). Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure. Am. J. Physiol.233,R243-R261.","DOI":"10.1152\/ajpregu.1977.233.5.R243"},{"key":"2021042509560305800_REF6","doi-asserted-by":"crossref","unstructured":"Cavanagh, P. R. and Williams, K. R. (1982). The effect of stride length variation on oxygen uptake during distance running. Med. Sci. Sports Exerc.14, 30-35.","DOI":"10.1249\/00005768-198201000-00006"},{"key":"2021042509560305800_","doi-asserted-by":"crossref","unstructured":"Diedrich, F. J. and Warren, W. H., Jr (1995a). Why change gaits? Dynamics of the walk-run transition. J. Exp. Psychol. Hum. Percept. 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Sport1,27-35."},{"key":"2021042509560305800_REF12","doi-asserted-by":"crossref","unstructured":"Knuttgen, H. G. (1961). Oxygen uptake and pulse rate while running with undetermined and determined stride lengths at different speeds. Acta Physiol. Scand.52,366-371.","DOI":"10.1111\/j.1748-1716.1961.tb02232.x"},{"key":"2021042509560305800_REF13","doi-asserted-by":"crossref","unstructured":"Kram, R. and Taylor, C. R. (1990). Energetics of running: A new perspective. Nature346,265-267.","DOI":"10.1038\/346265a0"},{"key":"2021042509560305800_REF14","doi-asserted-by":"crossref","unstructured":"Liefeldt, G., Noakes, T. D. and Dennis, S. C.(1992). Oxygen delivery does not limit peak running speed during incremental downhill running to exhaustion. Eur. J. Appl. Physiol.64,493-496.","DOI":"10.1007\/BF00843756"},{"key":"2021042509560305800_REF15","doi-asserted-by":"crossref","unstructured":"Marsh, A. P. and Martin, P. E. (1997). Effect of cycling experience, aerobic power, and power output on preferred and most economical cycling cadences. Med. Sci. Sports Exerc.29,1225-1232.","DOI":"10.1097\/00005768-199709000-00016"},{"key":"2021042509560305800_","doi-asserted-by":"crossref","unstructured":"Minetti, A. E. (1998). A model equation for the prediction of mechanical internal work of terrestrial locomotion. J. Biomech.31,463-468.","DOI":"10.1016\/S0021-9290(98)00038-4"},{"key":"2021042509560305800_REF17","unstructured":"Rouviere, C. (2002). Dynamics of gait transition. Undergraduate honors thesis, Florida State University,Tallahassee, FL, USA."},{"key":"2021042509560305800_REF18","unstructured":"Saibene, F. (1990). The mechanisms for minimizing energy expenditure in human locomotion. Eur. J. Clin. 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