A metabolic energy expenditure model with a continuous first derivative and its application to predictive simulations of gait

Whether humans minimize metabolic energy in gait is unknown. Gradient-based optimization could be used to predict gait without using walking data but requires a twice differentiable metabolic energy model. Therefore, the metabolic energy model of Umberger et al. (2003 Umberger BR, Gerritsen KG, Martin PE. 2003. A model of human muscle energy expenditure. Comput Methods Biomech Biomed Eng. 6(2):99–111.Taylor & Francis Online , Google Scholar) was adapted to be twice differentiable. Predictive simulations of a reaching task and gait were solved using this continuous model and by minimizing effort. The reaching task simulation showed that energy minimization predicts unrealistic movements when compared to effort minimization. The predictive gait simulations showed that objectives other than metabolic energy are also important in gait.