Fig. 1.
A: a common engineering approach for mechanical system identification applies a sine-wave stimulus (system input) to probe characteristics of a viscoelastic system, which acts as a filter on the stimulus to produce the measured response (system output). B: applying similar analysis to muscle fibers, the length stimulus is normalized to muscle length (ML; strain), and the measured force response from the muscle is normalized via fiber cross-sectional area (stress σ). C: these normalizations facilitate calculating the elastic moduli (Ee) and viscous (Ev), by separating the total stress response into an in-phase component that aligns temporally with the measured strain (ε) and an out-of-phase component shifted π/2 radians compared with the measured strain. The ratios of this stress-to-strain amplitude (arrows in C) represent the Ee and Ev. As frequency of the length stimulus changes, the viscoelastic muscle response changes, characterizing enzymatic behavior of actin-myosin cross bridges in activated muscle fibers. σv, Viscous stress; σe, elastic stress.