Frequency domain-based models of skeletal muscle

Abstract

Models of skeletal muscle based on its response to sinusoidal stimulation have been in use since the late 1960s. In these methods, cyclic excitation at varying frequencies is used to determine force or muscle length amplitude and phase as functions of excitation frequency. These functions can then be approximated by models consisting of combinations of poles and zeros and pure time delays without the need to combine force–length or force–velocity relationships. The major findings of a series of frequency response studies undertaken in our laboratory revealed that: • The frequency response models for isometric force including orderly recruitment of motor units were relatively invariant of the particular strategy or oscillation level employed. A critically damped second order model with corner frequency near 2 Hz and a pure time delay best described the relationship between input stimulation and output isometric force. • The frequency response models for load-moving muscles consisted of an overall gain which is a function of mass, dependent mostly on the width of the length–force relation at a given load (force), and a frequency-dependent gain component independent of load mass. The phase lag between input and output was also independent of load. • Muscle function and architecture are the primary determinants of its isometric force frequency response. • Tendon viscoelasticity (excluding the aponeurosis) has no significant effect on isometric force dynamic response, but does have a minor effect on load-moving dynamic response. The effect of tendon in reducing or augmenting the load-moving muscle response bandwidth is muscle-dependent. • The joint produces decreased high frequency gain and uniformly increased phase lags between input excitation and output force in isometric conditions. The joint acts as a lag network in load-moving conditions, increasing the phase lag without significant effect on the gain. Despite its inherent non-linear properties, the joint does not significantly deteriorate output signal quality in either isometric or load-moving conditions. • Co-contraction strategy has a significant effect on the dynamic response of the joint. These frequency-based models have shown to be robust as long as the excitation type and mechanical conditions under which they are obtained are not varied. They are particularly useful for the design of neuroprostheses, where a dynamic description of muscle output as a function of stimulus input under given conditions is desirable.