A muscle's force depends on the recruitment patterns of its fibers

Abstract

Biomechanical models of whole muscles commonly used in simulations of musculoskeletal function and movement typically assume that the muscle generates force as a scaled-up muscle fiber. However, muscles are comprised of motor units that have different intrinsic properties and that can be activated at different times. This study tested whether a muscle model comprised of motor units that could be independently activated resulted in more accurate predictions of force than traditional Hill-type models. Forces predicted by the models were evaluated by direct comparison with the muscle forces measured in situ from the gastrocnemii in goats. The muscle was stimulated tetanically at a range of frequencies, muscle fiber strains were measured using sonomicrometry, and the activation patterns of the different types of motor unit were calculated from electromyographic recordings. Activation patterns were input into five different muscle models. Four models were traditional Hill-type models with different intrinsic speeds and fiber-type properties. The fifth model incorporated differential groups of fast and slow motor units. For all goats, muscles and stimulation frequencies the differential model resulted in the best predictions of muscle force. The in situ muscle output was shown to depend on the recruitment of different motor units within the muscle.

FIGURE 1

Composite traces of muscle force for a series of contractions in the medial gastrocnemius at a range of stimulation frequencies. Measured forces are shown in gray, and predicted forces are shown in black. The forces were modeled using differential model E, with v₀ estimated at 5 and 10 s⁻¹ (a) or 2.74 and 3.59 s⁻¹ (b) for the slow and fast-fibers, respectively, and with fast fibers comprising 75% of the muscle.

FIGURE 2

Forces for a 5 Hz train of twitches in the medial gastrocnemius, calculated using different muscle models. Models A–E are shown in panel a. For comparison, a homogeneous model in which a single-step first-order ordinary differential equation was used to calculate the activation is shown in panel b. Measured tendon forces are shown in gray, and predicted forces are shown in black. Vertical lines show the times of each stimulus. The forces were modeled with v₀ estimated at 5 and 10 s⁻¹ for the slow and fast-fibers, respectively, and with fast fibers comprising 75% of the muscle. The coefficient of determination, r², is shown for each model with respect to the measured force.

FIGURE 3

The performance of the different muscle models across a range of stimulation frequencies for the lateral gastrocnemius. Measured tendon forces are shown in gray, and predicted forces are shown in black. The forces were modeled with v₀ estimated at 5 and 10 s⁻¹ for the slow and fast-fibers, respectively, and with fast fibers comprising 75% of the muscle.

FIGURE 4

The performance of the different muscle models for the different stimulation frequencies and muscles. Bars show the mean + SEM values (N = 20) pooled from the different goats, fiber-type proportions and choices of v₀.

FIGURE 5

The main effects of model parameters and experimental factors on the coefficient of determination. Points show the main effects (least-squares adjusted means) from the ANOVA. Where a factor had a significant effect on the coefficient of determination, the points are shown by filled circles; open circles denote no significant effect. Post hoc Tukey tests identified specific differences within each category, and they are denoted by the horizontal bars.

FIGURE 6

EMG and activation states for the medial gastrocnemius during a tetanic contraction stimulated at 20 Hz. Raw EMG is shown in panel a. EMG intensity is shown for the high (240.5–422.9 Hz) and low (82.4–247.0 Hz) frequency bands (b), corresponding to the fast- and slow-motor unit activity, respectively. The intensities were normalized to their maximum values during these supramaximal stimuli. The activation profiles are shown for the fast- and slow-motor units, and a general activation for the whole muscle (c).