Hill's model 1578822 219344384 2008-06-14T19:57:41Z 217.132.65.145 '''Hill's model''' refers to either Hill's equation for [[tetanized muscle]], or to the 3-element model. ==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 :<math>\left(v+b\right)(P+a) = b(P_0+a)</math> where * ''P'' is the load or tension in the muscle * ''v'' is the velocity of contraction * ''P<sub>0</sub>'' 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. ==References== <div class="references-small"> * [[Yuan-Cheng Fung|Fung YC]]. ''[[Biomechanics]]'', 2nd ed. Springer-Verlag, New York (1993). ISBN 0-387-97947-6 </div> [[Category:Equations]] [[Category:Biomechanics]] {{Mathapplied-stub}}