An improved Peronnet-Thibault mathematical model of human running performance - Alvarez-Ramirez, J. (European Journal of Applied Physiology, 2002)
Using an improved Peronnet-Thibault model to analyse the maximal power available during exercise, it was found that a 3rd-order relaxation process for the decreasing dynamics of aerobic power can describe accurately the data available for world track records and aerobic-to-total energy ratio (ATER). It was estimated that the time-scales for the decreasing dynamics are around 25 s for anaerobic power output and that they range from 2.12 h to 7.8 days for aerobic power output. In agreement with experimental evidence, the ATER showed a rapid increase during the first 300 s of exercise duration, to achieve an asymptote close to 100% after 1,000 s. In addition, the transition time when the ATER rose above 50% was found to be at a race duration of about 100 s, which would correspond to race distances of about 800 m. The results suggest that the aerobic power output achieves its maximal value at 300-400 s, and reaches a plateau at 26-28 W·kg-1 that lasts about 5,000 s. After this period, the aerobic power output decreases slowly due to the contribution of long time-scale metabolic processes having smaller energy contributions (about 30% to 40% of the total aerobic power output).