A linear time-varying model of force generation in skeletal muscle.

A model of isometric force production by skeletal muscle was developed in which the response to each stimulus in a train was described by a critically damped, linear second-order system. The parameters describing the system were constrained to be constant within an interstimulus interval, but were allowed to vary between interstimulus intervals. The ability of this model to match experimental data, and the time variation in the parameters (low-frequency gain and natural frequency) required to do so were examined in soleus and plantaris muscles of the cat stimulated by synchronous whole-nerve stimulation. The model produced good fits across firing rates from twitch to tetanus for slow and fast muscle, rested and fatigued muscle, and maximal submaximal stimulation. Both gain and natural frequency generally varied smoothly and predictably under all conditions. Gain increased at intermediate stimulation rates and in potentiated muscle, and decreased with fatigue and submaximal stimulation. Natural frequency was higher in fast muscle, and decreased with stimulation rate and fatigue. This modeling approach may provide a useful alternative to current models of skeletal muscle force, as its implementation is simple and it can describe force under conditions (fatigue, potentiation) where the muscle dynamics change with time.