Hill's muscle model

In biomechanics, Hill's muscle model refers to either Hill's equations for tetanized muscle contraction or to the 3-element model. They were derived by the famous physiologist Archibald Vivian Hill.

Equation to tetanized muscle

This is a popular state equation applicable to skeletal muscle that has been stimulated to show Tetanic contraction. It relates tension to velocity with regard to the internal thermodynamics. The equation is

where

is the tension (or load) in the muscle

is the velocity of contraction

is the maximum isometric tension (or load) generated in the muscle

coefficient of shortening heat

is the maximum velocity, when

Although Hill's equation looks very much like the van der Waals equation, the former has units of energy dissipation, while the latter has units of energy. Hill's equation demonstrates that the relationship between F and v is hyperbolic. Therefore, the higher the load applied to the muscle, the lower the contraction velocity. Similarly, the higher the contraction velocity, the lower the tension in the muscle. This hyperbolic form has been found to fit the empirical constant only during isotonic contractions near resting length.