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Skeletal muscle is the body's mechanical actuator: it converts chemical energy (ATP) into force and work. Hill's model (1938) is the fundamental mathematical description of the force-velocity relationship: (F+a)(v+b) = constant, with hyperbolic form. At zero force (zero load), the speed is maximum (v_max); at zero speed (isometric contraction), the force is maximum (F). Maximum power occurs at v v_max/3.

The length-tension relationship of the sarcomere explains the cardiac Frank-Starling mechanism: at optimal length (2.02.2 m), the actin-myosin overlap is maximum and the force is maximum. Above (excessive elongation) or below (extreme contraction), the force decreases because the number of active cross-bridges is reduced. This relationship determines the optimal working range of the muscle in vivo.

Muscle fatigue is the decrease in maximum strength available during sustained activity. The first-order model captures the dynamics: fatigue accumulates (k_f) upon activation and recovers (k_r) at rest, with k_r << k_f (fatigue accumulates faster than it recovers). Peripheral (accumulation of Pi, H, ADP; glycogen depletion) and central (reduction of corticomotor drive) mechanisms contribute.

The summation of contractions over time (temporal summation) allows the muscle to generate forces much greater than a single twitch: at frequencies above the fusion frequency (~50 Hz in fast muscle, ~20 Hz in slow), the twitches fuse in a sustained tetanic contraction. In EMG, force is approximately linear with the RMS of the electrical signal in the range 2080% of MVC (Maximal Voluntary Contraction), allowing EMG to be used to estimate force in vivo.

The mechanical efficiency of muscle ( 2030%) means that ~7080% of chemical energy is dissipated as heat. This has important thermoregulatory consequences: during intense exercise, heat production can exceed 1 kW in an athlete, requiring active dissipation (sweating, peripheral vasodilation). Muscle heat also contributes to maintaining body temperature in the cold (shivering).

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