The relationship between two different mechanical cost functions and muscle oxygen consumption

Inverse-dynamic models often use cost functions to solve the load-sharing problem. Although it is often assumed that energy is minimised, most cost functions are based on mechanically related measures like muscle force or stress. The aim of this study was to analyse the relationships of two cost functions with experimentally determined data on muscle energy consumption. Four subjects performed isometric contractions generating combinations of elbow flexion/extension and pro/supination moments. Muscle oxygen consumption (VO2) of the m. biceps breve, m. biceps longum, m. brachioradialis and m. triceps laterale was measured with near infrared spectroscopy. Both cost functions were implemented into an existing inverse-dynamic shoulder and elbow model and the individual cost values per muscle were calculated, normalised and subsequently compared to experimental VO2 values. The minimum stress cost function led to a good correspondence between VO2 and cost for the m. triceps laterale but for the flexor muscles cost was significantly lower. A newly proposed energy-related cost function showed, however, a far better correspondence. The inclusion of a linear term and muscle mass in the new criterion led model results to correspond better to experimental results. The energy-related cost function appeared to be a better measure for muscle energy consumption than the stress cost function and led to more realistic predictions of muscle activation.