A time-dependent mechano-bioenergetics model of muscle contraction

Predictions of skeletal muscle energy consumption under a diverse range of muscle contractile conditions are critical for improving our understanding of locomotion. Existing mathematical models, while capturing the mechanical dependence of energy consuming processes, neglect the time-dependent behaviour and recovery costs associated with regenerating ATP. This time-dependence is important for predicting the energetic response of muscles during repetitive or cyclical tasks like locomotion, where muscle undergoes many contraction cycles. This study presents a novel model to predict energetic rates based on physiological processes: Ca2+ transport costs, cross-bridge cycling costs, and ATP regeneration. Previous mathematical models include the dependence on Ca2+ transport and cross-bridge cycling, but neglect the time-dependent response and the subsequent recovery of ATP following the contraction. Model parameters were obtained from existing data on isolated muscle preparations, and predicted energetic rates were validated on separate datasets across a range of contractile conditions including dynamic, sub-maximal, and twitch contractions. The time-dependent model was able to capture the influence of contraction frequency on peak energetic rates and the time-course of energetic recovery observed experimentally. The model captures key physiological processes while maintaining a minimal number of free parameters and low computational cost. This enables generalisability across muscles and species, and implementation into larger scale musculoskeletal models.