A theory of physiological similarity in muscle-driven motion

Muscle contraction is the primary source of all animal movement. I show that the mechanical output of such contractions is constrained by a characteristic dimensionless number, the “effective inertia”, Γ. Contractions with equal Γ may be considered physiologically similar, in the sense that they involve equal fractions of the muscle’s maximum strain rate, strain capacity, work and power density; there exists a unique musculoskeletal geometry which enables a unit volume of muscle to deliver maximum work and power simultaneously, corresponding to Γ close to unity. External forces truncate the accessible mechanical performance space by introducing parasitic losses, and fundamentally alter how musculoskeletal anatomy modulates muscle performance, challenging canonical notions of skeletal force-velocity trade-offs. Γ varies systematically under isometric transformations of musculoskeletal systems, with profound consequences for our understanding of muscle mechanics and animal locomotion.