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To understand the organization and efficiency of biological movement, it is important to evaluate the energy requirements on the level of individual muscles. To this end, predicting energy expenditure with musculoskeletal models in forward-dynamic computer simulations is currently the most promising approach. However, it is challenging to validate muscle models  in-vivo  in humans, because access to the energy expenditure of single muscles is difficult. Previous approaches focused on whole body energy expenditure, e.g., oxygen consumption (VO2), or on thermal measurements of individual muscles by tracking blood flow and heat release (through measurements of the skin temperature). This study proposes to validate models of muscular energy expenditure by using functional phosphorus magnetic resonance spectroscopy ( 31 P-MRS).  31 P-MRS allows to measure phosphocreatine (PCr) concentration which changes in relation to energy expenditure. In the first 25 s of an exercise, PCr breakdown rate reflects ATP hydrolysis, and is therefore a direct measure of muscular enthalpy rate. This method was applied to the gastrocnemius medialis muscle of one healthy subject during repetitive dynamic plantarflexion movements at submaximal contraction, i.e., 20% of the maximum plantarflexion force using a MR compatible ergometer. Furthermore, muscle activity was measured by surface electromyography (EMG). A model (provided as open source) that combines previous models for muscle contraction dynamics and energy expenditure was used to reproduce the experiment in simulation. All parameters (e.g., muscle length and volume, pennation angle) in the model were determined from magnetic resonance imaging or literature (e.g., fiber composition), leaving no free parameters to fit the experimental data. Model prediction and experimental data on the energy supply rates are in good agreement with the validation phase (<25 s) of the dynamic movements. After 25 s, the experimental data differs from the model prediction as the change in PCr does not reflect all metabolic contributions to the energy expenditure anymore and therefore underestimates the energy consumption. This shows that this new approach allows to validate models of muscular energy expenditure in dynamic movements  in vivo .

Energy Expenditure of Dynamic Submaximal Human Plantarflexion Movements: Model Prediction and Validation by in-vivo Magnetic Resonance Spectroscopy