Hill's Muscle Model - Equation To Tetanized Muscle

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.

The muscle tension decreases as the shortening velocity increases. This feature has been attributed to two main causes. The major appears to be the loss in tension as the cross bridges in the contractile element and then reform in a shortened condition. The second cause appears to be the fluid viscosity in both the contractile element and the connective tissue. Whichever the cause of loss of tension, it is a viscous friction and can therefore be modeled as a fluid damper .