Muscle Contraction - Force-length and Force-velocity Relationships

Force-length and Force-velocity Relationships

For more details on this topic, see Hill's muscle model.

Unlike mechanical systems such as motors, the force a muscle can generate depends upon both the length and shortening velocity of the muscle.

Force-length relationship, also called the length-tension curve, relates the strength of an isometric contraction to the length of the muscle at which the contraction occurs. Muscles operate with greatest active force when close to an ideal length (often their resting length). When stretched or shortened beyond this (whether due to the action of the muscle itself or by an outside force), the maximum active force generated decreases. This decrease is minimal for small deviations, but the force drops off rapidly as the length deviates further from the ideal. As a result, in most biological systems, the range of muscle contraction will remain on the peak of the length-tension curve, in order to maximize contraction force (a notable exception is cardiac muscle which functions on ascending limb so it can increase force when stretched by an increase in preload-Starling's law). Due to the presence of elastic proteins within a muscle (such as titin), as the muscle is stretched beyond a given length, there is an entirely passive force, which opposes lengthening. Combined together, we see a strong resistance to lengthening an active muscle far beyond the peak of active force.

Force–velocity relationship: The speed at which a muscle changes length (usually regulated by external forces, such as load or other muscles) also affects the force it can generate. Force declines in a hyperbolic fashion relative to the isometric force as the shortening velocity increases, eventually reaching zero at some maximum velocity. The reverse holds true for when the muscle is stretched – force increases above isometric maximum, until finally reaching an absolute maximum. This has strong implications for the rate at which muscles can perform mechanical work (power). Since power is equal to force times velocity, the muscle generates no power at either isometric force (due to zero velocity) or maximal velocity (due to zero force). Instead, the optimal shortening velocity for power generation is approximately one-third of maximum shortening velocity.

These two fundamental properties of muscle have numerous biomechanical consequences, including limiting running speed, strength, and jumping distance and height.