, Volume 97, Issue 1, pp 63-79

High-frequency oscillations as a consequence of neglected serial damping in Hill-type muscle models

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Abstract

High-frequency vibrations e.g., induced by legs impacting with the ground during terrestrial locomotion can provoke damage within tendons even leading to ruptures. So far, macroscopic Hill-type muscle models do not account for the observed high-frequency damping at low-amplitudes. Therefore, former studies proposed that protective damping might be explained by modelling the contractile machinery of the muscles in more detail, i.e., taking the microscopic processes of the actin–myosin coupling into account. In contrast, this study formulates an alternative hypothesis: low but significant damping of the passive material in series to the contractile machinery—e.g., tendons, aponeuroses, titin—may well suffice to damp these hazardous vibrations. Thereto, we measured the contraction dynamics of a piglet muscle–tendon complex (MTC) in three contraction modes at varying loads and muscle–tendon lengths. We simulated all three respective load situations on a computer: a Hill-type muscle model including a contractile element (CE) and each an elastic element in parallel (PEE) and in series (SEE) to the CE pulled on a loading mass. By comparing the model to the measured output of the MTC, we extracted a consistent set of muscle parameters. We varied the model by introducing either linear damping in parallel or in series to the CE leading to accordant re-formulations of the contraction dynamics of the CE. The comparison of the three cases (no additional damping, parallel damping, serial damping) revealed that serial damping at a physiological magnitude suffices to explain damping of high-frequency vibrations of low amplitudes. The simulation demonstrates that any undamped serial structure within the MTC enforces SEE-load eigenoscillations. Consequently, damping must be spread all over the MTC, i.e., rather has to be de-localised than localised within just the active muscle material. Additionally, due to suppressed eigenoscillations Hill-type muscle models taking into account serial damping are numerically more efficient when used in macroscopic biomechanical neuro-musculo-skeletal models.