Why Does Metabolic Rate Increase Curvilinearly with Running Velocity?

The ‘cost of generating force’ model proposes that a major determinant of metabolic rate during running is the rate of muscular force production. However, the amount of muscle force needed during running is affected by the effective mechanical advantage (EMA), the ratio of the ground reaction force moment arm (R) to the muscle moment arm (r), R/r. The ‘cost of generating force’ model assumed that EMA and active muscle volume remain constant across velocity. With this assumption, the cost of generating force hypothesis explains 80% of the linear increase in metabolic rate in human runners across a moderate velocity range. Additionally, many studies have demonstrated a linear relationship between metabolic rate and running velocity for a diverse assortment of species. However, in humans there is less of a consensus of how to mathematically characterize the relationship. Using 7 sub-elite male runners, I performed a more systematic analysis of EMA over 6 different velocities (8, 10, 12, 14, 16 and 18km/hr) to explain both the remaining 20% and the curvilinear increase in metabolic rate. I hypothesized that the curvilinear metabolic rate pattern observed in elite runners at fast sub-maximal velocities can be explained by a decrease in EMA at the hip, knee and ankle joints, which necessitates a greater volume of active muscle recruitment. Over the velocity range, all subjects demonstrated a curvilinear increase in metabolic rate. Ankle EMA decreased by 14.5 ± 4.1%, while hip EMA showed the largest magnitude decrease of 51.2 ± 30.2%. Accordingly, the active volume of hip extensor muscles increased 50.1% from 448 ± 245 cm3 to 898 ± 250cm3 across the velocity range. The ankle extensor active muscle volume increased by 32.8% from 713 ±145cm3 to 1061 ± 159cm3. I extended the cost of generating force model and found that in human runners, metabolic rate is proportional to the rate of force generation multiplied by the volume of muscle activated