A linear muscle model predicts the hyperbolic force-velocity relationship.

A variety of different schemes have been reported in the literature for linearizing the force-velocity relationship observed in muscle, a dominant element in the muscle. This report extends assertions that a linear muscle system has force-velocity characteristics as described by Hill's hyperbolic equation, and that no linearization whatsoever is required. The muscle is modeled as a parallel combination of passive elasticity, and series elasticity connected to the parallel combination of active state tension generator, viscosity and length tension elasticity. Each of the elements are linear. Simulation solutions of this third-order system yield a hyperbolic shaped force-velocity curve using physiologically derived estimates, based on the oculomotor system, for the parameters of the muscle model.