A biomechanical model for size, speed and anatomical variations of the energetic costs of running mammals

Here we propose a model of energetic costs and the muscle-tendon unit function on running mammals. The main goal is to set a simple theoretical framework which gives an understanding of the biomechanical principles behind the size, speed and anatomical variations of the energetic costs of running mammals. The model is a point-like mass withstood by a two-segment leg with an extensor muscle serially attached to a tendon. We considered withstanding body weight during the stance phase as the main role of the muscle-tendon unit during fast locomotion. The ground reaction force dependence on speed and the time of stance phase as well as other biomechanical characteristics were taken from previous empirical studies of running. At the same time, the morphological variations with body mass were taken from empirically well-established allometric equations for mammals. The metabolic cost was estimated from an empirical equation relating metabolic power with muscular force and speed in shortening and stretching. Our model predicts the pattern of mass specific metabolic rate variations with both speed and body mass. It also gives an explanation of the experimentally reported linear inverse relationship between the rate of energy used for running and the time of application of force by the foot to the ground during each stride. It also suggests an explanation of the unusual energy saving adaptations of large macropodids. It provides some predictions on the relationship, between energy costs and muscle-tendon unit characteristics, testable on further experiments.