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Computational and Mathematical Methods in Medicine
Volume 2015, Article ID 407156, 6 pages
Research Article

Parametric Modeling of Human Gradient Walking for Predicting Minimum Energy Expenditure

Departament de Biologia Animal, Universitat de Barcelona, 08028 Barcelona, Spain

Received 17 December 2014; Revised 2 February 2015; Accepted 3 February 2015

Academic Editor: Zhonghua Sun

Copyright © 2015 Gerard Saborit and Adrià Casinos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A mathematical model to predict the optimum gradient for a minimum energetic cost is proposed, based on previous results that showed a minimum energetic cost when gradient is −10%. The model focuses on the variation in mechanical energy during gradient walking. It is shown that kinetic energy plays a marginal role in low speed gradient walking. Therefore, the model considers only potential energy. A mathematical parameter that depends on step length was introduced, showing that the optimal gradient is a function of that parameter. Consequently, the optimal negative gradient depends on the individual step length. The model explains why recent results do not suggest a single optimal gradient but rather a range around −10%.