High-frequency oscillations as a consequence of neglected serial damping in Hill-type muscle models.
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.
Günther
Michael
M
Institut für Astronomie und Astrophysik, Abteilung Theoretische Astrophysik, Biomechanik-Gruppe, Eberhard-Karls-Universität, Auf der Morgenstelle 10 C, 72076, Tübingen, Germany. guenther@tat.physik.uni-tuebingen.de
Schmitt
Syn
S
Wank
Veit
V
D000818:Animals; D004558:Electric Stimulation / Q000379:methods; D006612:High-Frequency Ventilation; D008124:Locomotion / Q000502:physiology*; D008954:Models, Biological; D008959:Models, Neurological; D009119:Muscle Contraction / Q000502:physiology*; D018482:Muscle, Skeletal / Q000502:physiology*; D013314:Stress, Mechanical; D013552:Swine; D013710:Tendons / Q000502:physiology; D016474:Weight-Bearing