A theory of physiological similarity in muscle-driven motion

Muscle contraction is the primary source of all animal movement. I show that the maximum mechanical output of such contractions is determined by a characteristic dimensionless number, the "effective inertia," Γ, defined by a small set of mechanical, physiological, and anatomical properties of the interrogated musculoskeletal complex. Different musculoskeletal systems with equal Γ may be considered physiologically similar, in the sense that maximum performance involves equal fractions of the muscle's maximum strain rate, strain capacity, work, and power density. It can be demonstrated that there exists a unique, "optimal" musculoskeletal anatomy which enables a unit volume of muscle to deliver maximum work and power simultaneously, corresponding to Γ close to unity. External forces truncate the mechanical performance space accessible to muscle by introducing parasitic losses, and subtly alter how musculoskeletal anatomy modulates muscle performance, challenging canonical notions of skeletal force-velocity trade-offs. Γ varies systematically under isogeometric transformations of musculoskeletal systems, a result which provides fundamental insights into the key determinants of animal locomotor performance across scales.