Biaxial strain and variable stiffness in aponeuroses

Abstract

The elastic structures of many muscles include both an extramuscular free tendon as well as a sheet-like aponeurosis. An important distinguishing feature of aponeuroses is that these tendinous structures function as the attachment and insertion surfaces of muscle fascicles and therefore surround a substantial portion of the muscle belly. As a result, aponeuroses must expand both parallel (longitudinal) and perpendicular (transverse) to a muscle's line of action when contracting muscles bulge to maintain a constant volume. In this study, we use biplanar high-speed fluoroscopy to track the strain patterns of the turkey lateral gastrocnemius aponeurosis during active and passive force production in situ. We find that the behaviour of the aponeurosis during passive force production is consistent with uniaxial loading, as aponeuroses stretch only in the longitudinal direction. By contrast, our results show that aponeuroses are stretched in both longitudinal and transverse directions during active force production and that transverse strains are on average 4 times greater than longitudinal strains. Biaxial loading of aponeuroses appears to effectively modulate longitudinal stiffness, as we find the measured stiffness in the longitudinal direction varies in proportion to transverse strain. We conclude that biaxial strain during active force production distinguishes aponeuroses from free tendons and may function to dynamically modulate stiffness along the axis of muscle force production. It is likely that consideration of strains measured only in the longitudinal direction result in an underestimation of aponeurosis stiffness as well as its capacity for elastic energy storage.

Figure 1. Methodological description of the in situ preparation used to quantify strain patterns in the lateral gastrocnemius aponeurosis of wild turkeys

A, schematic diagram of the muscle preparation showing the location of the sonomicrometry crystals along a proximal muscle fascicle as well as the approximate position of the radio-opaque markers on the surface of the aponeurosis. The distal end of the tendon was attached to an ergometer, which controlled and measured muscle force and muscle–tendon length. B and C, single frames from videos captured using two high-speed fluoroscopes. The 3D positions of the surface markers were used to calculate the strain patterns in the aponeurosis during passive and active force production.

Figure 2. Time series data from a representative active isotonic contraction

Force measured by the ergometer (A) is allowed to rise to preset level and is kept constant for most the contraction. During force production longitudinal (B) and transverse (C) aponeurosis strains are determined from marker positions, and muscle fascicle lengths (D, black line) and muscle–tendon lengths (D, grey line) are measured from sonomicrometry and the ergometer, respectively. Fascicle shortening in the early part of the contraction, before muscle–tendon movement, is associated with the stretch of aponeurosis in both the longitudinal and transverse directions. Positive strain values represent tissue extension. Note that longitudinal aponeurosis strain follows the force pattern. Also note that once aponeurosis length is constant the MTU shortens at a faster rate than the fascicle due to the architectural gearing (Azizi et al. 2008) present in this pinnate muscle.

Figure 3. The relationship between active muscle force and peak aponeurosis strain during a muscle contraction

Aponeurosis strain along the muscle's line of action (longitudinal) increases linearly with muscle force (P < 0.001). The data are fitted with a linear least-squares regression described by the equation y= 1.9x+ 0.17. Aponeurosis strain orthogonal to the muscle's line of action (transverse) increases with force across contractions at relatively low forces but reaches a plateau across the higher range of forces. Note that transverse strain is on average about four times greater than longitudinal. Data shown are pooled from four individuals. Error bars represent the standard error of the mean. Positive strain values represent tissue extension. Muscle force is plotted as the proportion of the maximum isometric force (P_o).

Figure 4. Representative time series data from sinusoidal length changes applied to the passive, unstimulated muscle–tendon

During sinusoidal loading, increases in force (A) coincide with muscle fascicle (D, black lines) and muscle–tendon (D, grey lines) lengthening. Aponeurosis strain in the longitudinal direction (B) is in phase with force and muscle–tendon length; the aponeurosis lengthens as force and muscle–tendon length increase. Transverse aponeurosis strains (C) are out of phase, tending to decrease (shorten) as force and muscle–tendon length increases. Positive strain values represent lengthening and negative strain values represent shortening.

Figure 5. A comparison of measured longitudinal stiffness during passive and active force production

A, data pooled for four individuals show longitudinal stiffness increases curvilinearly with increasing stretch of the aponeurosis in the transverse direction. Each data point represents a single contraction. The data are fitted with a second order polynomial (R²= 0.62). This pattern suggests that the biaxial loading of the aponeurosis during active contractions increases longitudinal stiffness. B, a comparison of average longitudinal stiffness during passive and active force production. The comparison shown is limited to active contractions occurring at forces comparable to passive tests (<50 N) in order to limit the confounding effect of large force variation. Stiffness differs significantly between passive and active conditions (P= 0.004). Error bars are the standard error of the mean.