DOI: 10.5061/dryad.5hqbzkh88
title: The force response of muscles to activation and length perturbations depends on length history

description: Recent studies have demonstrated that muscle force is not determined
 solely by activation under dynamic conditions, and that length history has
 an important role in determining dynamic muscle force. Yet, the mechanisms
 for how muscle force is produced under dynamic conditions remain unclear.
 To explore how muscle force production is determined under dynamic
 conditions, we investigated the effects of muscle stiffness, activation,
 and length perturbations on muscle force. First, submaximal isometric
 contraction was established for whole soleus muscles. Next, the muscles
 were actively shortened at three velocities. During active shortening, we
 measured muscle stiffness at L0 and the force response
 to time-varying activation and length perturbations. We found that muscle
 stiffness increased with activation but decreased as shortening velocity
 increased. The slope of the relationship between maximum force
 and activation amplitude differed significantly among shortening
 velocities. Also, the intercept and slope of the relationship
 between length perturbation amplitude and maximum force decreased with
 shortening velocities. As shortening velocities were related with
 muscle stiffness, the results suggest that length history determines
 muscle stiffness and the history-dependent muscle stiffness influences the
 contribution of activation to muscle force and the contribution of length
 perturbations to muscle force. A three-parameter viscoelastic
 model that included a linear spring and linear damper in parallel with
 tunable history-dependent spring stiffness proportional to measured muscle
 stiffness predicted history-dependent muscle force with high accuracy. The
 results and simulations support the hypothesis that muscle force under
 dynamic conditions can be accurately predicted as the force response of a
 history-dependent viscoelastic material to length perturbations.
description: Protocol 1
 measured how muscles respond to time-varying activation depending on
 muscle stiffness. Muscles were stimulated isometrically at submaximal
 voltage (3.87 ± 0.88 V) and frequency (5 Hz) until they until they reached
 a steady-state force of 7.0 ± 3.0% P<sub>0</sub> in ~ 0.7s.
 Once isometric force reached steady state, active shortening was performed
 at two velocities (1.0 L<sub>0</sub>/s, 0.5
 L<sub>0</sub>/s) and under isometric conditions. At the
 midpoint of active shortening, muscle length was held constant at
 L<sub>0</sub> by changing the starting length (Fig. 1, blue).
 To evaluate how muscle force depends on the amplitude of activation, the
 amplitude of activation during active shortening was varied using an A-M
 Systems Model 4100 stimulator (A-M Systems, Sequim, Washington,
 USA).              In protocol 1, activation started
 increasing at the onset of active shortening. The amplitude of activation
 increased linearly for 100ms, and then decreased linearly for 100ms (Fig.
 1, red). Peak activation
 occurred at the midpoint of active shortening at muscle optimal length
 (L<sub>0</sub>). Six different activation amplitudes were
 used: 100%, 110%, 120%, 130%, 140% and 150% of the amplitude for the first
 submaximal isometric contraction (see above). To measure instantaneous
 muscle stiffness, quick length transients (0.9%
 L<sub>0</sub> at a speed of 3L<sub>0</sub>/s) were
 performed at L<sub>0 </sub>during active shortening.
             In protocol 2, the response of muscle force to length
 perturbations was measured for different values of muscle stiffness,
 established by varying the shortening velocity. As in protocol 1,
 isometric contraction and active shortening at 1.0 and 0.5
 L<sub>0</sub>/s were performed (Fig. 2, blue). Length
 perturbations were performed at the midpoint of active shortening where
 muscle length was L<sub>0</sub> in all trials. The shape of
 the length perturbation was varied based on a half sinusoidal curve at a
 frequency of 2.5 Hz. For the trials with no active shortening, the
 amplitudes of the sinusoidal curve were 0.2%, 0.4%, 0.6%, 0.8%, 1%, and 3%
 of L­<sub>0 </sub>(Fig. 2B, blue), and for the trials with
 active shortening, the amplitudes were 1%, 3%, 5%, 7%, 9% and 11% of
 L<sub>0</sub> (Fig. 2A, blue). Activation was constant at ~35%
 of P<sub>0 </sub>(Fig. 2A, B, red). Instantaneous muscle
 stiffness was measured at L<sub>0 </sub>using a quick length
 transient (0.9% L<sub>0</sub>, 3
 L<sub>0</sub>/s).
description: All data files are in .csv format and can be opened using a
 variety of open-source and other programs/software.