A model predicting the metabolic energy a muscle consumes during time-varying isometric force as a sum of power-law functions of joint torque and of torque rate, with empirically fitted exponents of about 1.36 for torque and 2.5 for torque rate. It captures that reducing force costs several times more energy than increasing it, paralleling the asymmetry between negative and positive mechanical work, and shows the same exponents carry over to multi-joint, multi-muscle tasks, enabling prediction of energy-optimal movement.
Through human-subject experiments in which participants produced sinusoidal isometric forces of varying mean, amplitude, frequency, and rise/fall timing, this paper builds a model of the metabolic en…