Effects of shortening velocity on the stiffness to force ratio during isometric force redevelopment suggest mechanisms of residual force depression

Figures

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  Figure 1. Theoretical relationships between relative muscle stiffness (km) and relative isometric force (FISO). Total muscle stiffness (black) is estimated as the sum of titin stiffness (red) and cross-bridge (CB) stiffness (blue). (a) If the proportion of weakly- to strongly-bound cross bridges is independent of FISO and titin stiffness is constant, then the relationship between km and FISO will be linear. (b) If titin stiffness is constant, but the proportion of weakly- to strongly-bound cross bridges depends non-linearly on FISO, then the total stiffness will also increase non-linearly with FISO. (c) If both titin stiffness and the proportion of weakly- to strongly-bound cross bridges increase linearly with FISO, then the total stiffness should also increase linearly with FISO.

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  Figure 2. Relative isometric force and stiffness after 1000 ms of active shortening. (a) Mean relative isometric forces after active shortening were lower than pure isometric force (HSD, p < 0.05). The fastest active shortening velocity produced a larger mean relative force than the slowest active shortening velocity (HSD, p < 0.05), demonstrating less residual force depression in the fastest active shortening velocity than in the slowest active shortening velocity. (b) Mean relative muscle stiffness after active shortening did not differ significantly among shortening velocities (ANOVA, F = 0.37, p < 0.77). Bars with the same letter are not significantly different (HSD, p > 0.05).

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  Figure 3. Mean values (+ 1 S.D.) of relative force (a, b) and relative stiffness (c, d) after different pause durations (a, c) and different velocities of active shortening (b, d). Mean relative force (a) and stiffness (c) represent mean values for all conditions including no shortening, 1/8L0/s, 1/2L0/s and 2L0/s, and mean relative force (b) and stiffness (d) represent mean values for all pause durations including 10, 20, 80, and 1000 ms. Mean relative force and stiffness increased with increasing pause duration and decreasing shortening velocity. Bars with the same letter are not significantly different (HSD, p > 0.05).

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  Figure 4. Change in relative muscle force and stiffness during isometric force redevelopment following active shortening at different velocities. Data points (n = 7 muscles per group) are means across muscles with error bars representing S.D. (a) Relative force increases with increasing pause duration. The rate of increase varies with shortening velocity. (b) Relative stiffness increases with increasing pause duration and shortening velocity affects the stiffness vs. pause duration relationship. The slope of the relationship increases with increasing shortening velocity.

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  Figure 5. Relative force vs. relative stiffness at different active shortening velocities. Data points (n = 7 muscles per group) are means across muscles with error bars representing S.E. The slope and the y-intercept of the relative stiffness-force relationship differed significantly among shortening velocities, including ‘no shortening’ (ANCOVA, slope, p < 0.001; y-intercept, p < 0.001).

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  Figure 6. Muscle force (a, upper trace) and length (a, lower trace) in the active shortening group, muscle force (b, upper trace) and length (b, lower trace) in the pure isometric group and measurement of instantaneous muscle stiffness (c). (a) Protocols used to evaluate the effects of active shortening and duration of isometric force redevelopment on muscle stiffness and force. Active shortening was performed from 1.05L0 to L0 at three different velocities; 1/8 L0/s (red), ½ L0/s (green) and 2 L0/s (blue). Instantaneous muscle stiffness was measured using a quick transient with an amplitude of 0.9% L0 and a velocity of 3L0/s for four pause durations (10, 20, 80 and 1000 ms). (b) Pure isometric contraction was performed at L0. Instantaneous muscle stiffness was measured using a quick transient for four pause duration (10, 20, 80 and 1000 ms). (c) Muscle force (upper trace, blue) responded to a rapid transient (lower trace, red) at 3L0/s. The linear parts of the force–time trace (thick line, blue) and the length–time trace (thick line, red) were used to determine stiffness. The linear slope of the force–time trace was divided by the linear slope of the length–time trace, which gives the…