Variable gearing in pennate muscles

Abstract

Muscle fiber architecture, i.e., the physical arrangement of fibers within a muscle, is an important determinant of a muscle's mechanical function. In pennate muscles, fibers are oriented at an angle to the muscle's line of action and rotate as they shorten, becoming more oblique such that the fraction of force directed along the muscle's line of action decreases throughout a contraction. Fiber rotation decreases a muscle's output force but increases output velocity by allowing the muscle to function at a higher gear ratio (muscle velocity/fiber velocity). The magnitude of fiber rotation, and therefore gear ratio, depends on how the muscle changes shape in the dimensions orthogonal to the muscle's line of action. Here, we show that gear ratio is not fixed for a given muscle but decreases significantly with the force of contraction (P < 0.0001). We find that dynamic muscle-shape changes promote fiber rotation at low forces and resist fiber rotation at high forces. As a result, gearing varies automatically with the load, to favor velocity output during low-load contractions and force output for contractions against high loads. Therefore, muscle-shape changes act as an automatic transmission system allowing a pennate muscle to shift from a high gear during rapid contractions to low gear during forceful contractions. These results suggest that variable gearing in pennate muscles provides a mechanism to modulate muscle performance during mechanically diverse functions.

Fig. 1.

A 17th century geometric examination of muscle architecture (5). (A) The adductor muscle in the claw of a lobster exemplifies bipennate architecture. (B) A geometric model of a unipennate muscle highlighting the orientation of fibers at rest (BC and DF) and contracted (HC and ID). This classic model predicts a change in pennation angle (i.e., fiber rotation) during contraction and assumes that muscle thickness (FK) remains constant. Arrow indicates the direction of the muscles' lines of action. Modified from reference .

Fig. 2.

Simulations of an isovolumetric, three-dimensional unipennate muscle. (A) Virtual pennate muscle shown at rest in side and top view. The muscle belly is shown in red, and the aponeuroses are shown in white. Muscle thickness (t) and muscle width (w) define the two directions orthogonal to the line of action. (B) A simulation in which muscle thickness increases as fibers shorten by 13% of resting length. An increase in muscle thickness results in substantial fiber rotation and a large amount of muscle shortening (yellow arrow). This simulated shape change results in a relatively high gear ratio that would favor the velocity output of a muscle. (C) A simulation in which muscle thickness decreases as the fibers shorten by 13% of resting length. A decrease in muscle thickness counteracts fiber rotation and results in relatively little muscle shortening (compare yellow arrows in B and C). This simulated shape change results in a relatively low gear ratio and less fiber rotation that would favor muscle force production. These simulations represent extremes along a continuum of potential shape changes and highlight how dynamic shape changes during a contraction can significantly alter the force and velocity output of a pennate muscle.

Fig. 3.

Representative isotonic contractions in the lateral gastrocnemius of the wild turkey. The muscle was maximally stimulated in a branch of the sciatic nerve. Time-series plots from two sample contractions are shown. Muscle force was allowed to increase to a preset level (15% of maximum isometric force (P_o) in A–D and 80% P_o in E–H) and was kept constant as the muscle fiber (red) and the muscle–tendon unit (black) shortened at a constant velocity. All measurements were taken during a period of constant force (gray bars) and at a similar initial pennation angle. Similar contractions were performed at varying levels of force for each muscle.

Fig. 4.

Change in muscle thickness, fiber rotation, and architectural gear ratio (AGR) during a series of isotonic contractions at different force levels (P, expressed as a fraction of maximum isometric force, P_o). (A) The change in muscle thickness per millimeter of fiber shortening decreased as we increased the force level of the isotonic contractions (least-squares regression; P < 0.0001). During low-force, high-velocity contractions, muscle thickness increases (positive values), whereas at high forces, muscle thickness decreases (negative values). (B) The magnitude of fiber rotation per millimeter of fiber shortening decreases as contractions become more forceful (least-squares regression; P < 0.0001). (C) Architectural gear ratio (muscle velocity/fiber velocity) is lower for contractions at higher force levels (least-squares regression; P < 0.0001). The muscle operates with a gear ratio that favors velocity during low-force, high-velocity contractions and shifts to a gear ratio that favors force during slow, forceful contractions. Values are mean ± SE; n = 4 individuals.

Fig. 5.

Architectural gear ratio (AGR) plotted against muscle force for a series of isovelocity contractions. Data are shown for contractions performed at the same shortening velocity (23.7 mm/s) but after trains of contractions of different durations. The longer the duration of the preceding train, the more fatigued the muscle and the lower its force output. These results show that, despite a constant shortening velocity, AGR decreased significantly with increasing force (least-squares regression P < 0.0001). The pattern observed is similar to that shown for isotonic contractions. Data from two birds are shown as different symbols.

Fig. 6.

The effect of variable gearing on the functional range of a pennate muscle. The force–velocity properties of a fiber are used to predict the output force and output velocity of a muscle with a fixed gear (A) and a variable gear (B). The output force and velocity of the whole muscle are expressed in the units of V/V_max and P/P_o of the fiber. Muscle power is assumed to be conserved such that the power profiles of all curves are identical. (A) In the fixed-gear condition, the muscle is set to operate with a constant gear ratio of 1.2. (B) In the variable-gearing condition, the empirical relationship between gear ratio and force (Fig. 4C) is used to calculate the whole muscle's force–velocity curve. Variable gearing provides higher whole-muscle force during slow forceful contractions and higher velocity during fast contractions.