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Hill's model

Hill's model refers to either Hill's equation for tetanized muscle, or to the 3-element model.

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Hill's equation

Derived by a famous physiologist named Archibald Vivian Hill, this is a popular state equation applicable to skeletal muscle that has been stimulated to show tetanus. It relates tension to velocity. The equation is

$\left(v+b\right)(P+a) = b(P_0+a)$

where

P is the load or tension in the muscle
v is the velocity of contraction
P₀ is the maximum load or tension generated in the muscle
a and b are constants

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 P 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.