Evidence of a tunable biological spring: elastic energy storage in aponeuroses varies with transverse strain in vivo

Abstract

Tendinous structures are generally thought of as biological springs that operate with a fixed stiffness, yet recent observations on the mechanical behaviour of aponeuroses (broad, sheet-like tendons) have challenged this general assumption. During in situ contractions, aponeuroses undergo changes in both length and width and changes in aponeuroses width can drive changes in longitudinal stiffness. Here, we explore if changes in aponeuroses width can modulate elastic energy (EE) storage in the longitudinal direction. We tested this idea in vivo by quantifying muscle and aponeuroses mechanical behaviour in the turkey lateral gastrocnemius during landing and jumping, activities that require rapid rates of energy dissipation and generation, respectively. We discovered that when aponeurosis width increased (as opposed to decreased), apparent longitudinal stiffness was 34% higher and the capacity of aponeuroses to store EE when stretched in the longitudinal direction was 15% lower. These data reveal that biaxial loading of aponeuroses allows for variation in tendon stiffness and energy storage for different locomotor behaviours.

1. Introduction

With their capacity to store elastic energy (EE), springs have long served as the classic model for tendon mechanical function in living organisms. Embedded in this thinking is the assumption that any tendinous structure can be characterized as a spring that operates with a single force–length behaviour, determined by its geometric and material properties [1]. Recent experiments have called this assumption into question for aponeuroses, the elastic-sheet-like tendons that cover the surface of muscle bellies, which can be clearly distinguished from the extramuscular ‘free’ tendon. Variations in aponeuroses stiffness have been observed with dynamic changes in muscle shape that occur during a contraction [2], and it has been shown that changes in muscle fibre length can drive changes in aponeurosis stiffness during a muscle contraction [3–5]. Here, we test the idea that such changes in stiffness could alter EE storage in aponeuroses. We studied the behaviour of the lateral gastrocnemius muscle in wild turkeys (Meleagris gallopavo). This muscle is a major ankle extensor and has been a useful model for studies on muscle mechanics because its calcified tendon allows for direct measurements of muscle force [6,7]. We studied landing and jumping because these activities require rapid rates of mechanical energy dissipation and energy generation, respectively. Therefore, it was anticipated that these distinct behaviours should elicit distinct changes in muscle length and aponeurosis mechanical behaviour.

We used Hooke's Law to formulate some simple predictions about the mechanical behaviour of aponeuroses. Hooke's Law states that the force (F) required to stretch a linear spring depends on its stiffness (F = kx); where k and x denote stiffness and the amount of stretch, respectively. It follows that the work required to stretch a spring is equal to the amount of EE stored in the spring, expressed as $\mathrm{EE}=(1/2)k{x}^2$. A substitution of x = F/k yields $\mathrm{EE}=(1/2)(F^2/k)$ and thus, for a given level of force, the amount of EE stored in the spring will be inversely proportional to its stiffness:

$$\mathrm{EE}\propto \frac{1}{k}.$$ 1.1

This proportionality tells us that when the same force is applied, a spring with a higher stiffness will store less EE. During in situ contractions, aponeuroses have been shown to be stiffer in the longitudinal direction (along the muscle's line of action) when undergoing increases in width [2,3]. Thus, we hypothesized that aponeuroses in vivo would store less energy in contractions that involved increases in width, and more energy in contractions that involved decreases in width. To test this hypothesis, we used biplanar high-speed fluoroscopy to track changes in muscle fibre length, aponeurosis length and width, and combined this with strain gauge measurements of muscle-tendon force and fine-wire electromyographic (EMG) measurements of muscle activity.

2. Material and methods

(a). Animals, training and instrumentation

Adult wild turkeys (n = 4, body mass = 3.97 ± 0.47 kg, mean ± s.d.) were purchased from a licensed breeder and housed in the Animal Care Facilities at Brown University. The data collection procedures for this study combined protocols described in [3] and [8] and are briefly described here.

All birds were trained to land and jump over the course of 5–10 days. For landing trials, birds were supported vertically (ranging in height from 0.5 m to 1.75 m) using a webbing harness attached to a pulley-rope system, allowing us to elicit a controlled free fall (see Fig. S1 in [8]). For jumping trials, birds were encouraged to jump using verbal cues and clapping.

Transducers and radiopaque markers were implanted on the lateral gastrocnemius muscle-tendon unit (MTU) under sterile surgical procedures. The lateral gastrocnemius is unipennate and all muscle fibres span from the proximal to distal portion of the aponeurosis that lies on the muscle belly (see Fig. S7 in [9]). While each bird was under anaesthesia, small (0.8–1.0 mm diameter) radiopaque tantalum markers were surgically implanted along a proximal muscle fibre and also onto the aponeurosis surface (figure 1) to measure length and width changes [3,8]. Two foil strain gauges were glued onto the deep and superficial aspects of the bony tendon to measure muscle force, and fine-wire bipolar electrodes were implanted near the fascicle bead-pair to measure EMG signals [10]. After surgery, birds were given Carprofen as an analgesic and allowed to recover for 24–36 h prior to the landing and jumping experiments.

Figure 1.

Experimental data collection. (a) Two high-speed biplanar X-ray cameras captured the positions of radiopaque markers surgically implanted (b) along the muscle fibre (red markers) and aponeurosis surface (blue markers). The illustration shows a coronal plane view of the lateral gastrocnemius muscle-tendon unit [3]. (c–f) Representative data illustrate changes in muscle force, fibre length, and aponeurosis shape during two landing and two jumping trials in a single bird, highlighting the variable shape changes in the aponeurosis during in vivo muscle contractions. For instance, aponeurosis length increased in all trials while aponeurosis width either increased or decreased. Note that landing height in (c) and (d) are 1.0 m and 1.5 m, respectively. (Online version in colour.)

(b). Biplanar high-speed fluoroscopy

In vivo measurements of muscle-tendon force and EMG activity were combined with high-speed biplanar fluoroscopy [3,8] to capture changes in muscle and aponeurosis shape during landing and jumping (figure 1). The positions of two markers located along a fascicle at the proximal end of the muscle were used to track muscle fascicle length. Aponeurosis length was calculated from the distance between the midpoint of a line defined by two markers at the proximal end of the aponeurosis (figure 1b) and a single marker on the distal aponeurosis. The location of four radiopaque beads located on the medial and lateral aspects of the aponeurosis were used to calculate aponeurosis width. A midpoint between markers on each side of the aponeurosis was calculated, and the distance between these midpoints was used to calculate aponeurosis width.

Following the in vivo trials, we used established in situ measurements [3] to quantify muscle force during isometric ‘fixed-end’ contractions using a servomotor (Model 310-BLR, Aurora Scientific). These values were used to calibrate strain gauge measurements recorded during the in vivo trials [6,8]. In total, we captured 17 jumps and 47 landings across the four birds and successfully analysed 14 jumping and 14 landing trials (see the electronic supplementary material), which were free from marker drop out, strain gauge malfunction and poor task performance.

(c). Data analysis and statistics

Radiopaque marker positions for each trial were tracked using XMALab [11]. The three-dimensional marker coordinates, expressed relative to the global coordinate system, were imported into IGOR Pro and combined with EMG and muscle force data. Muscle fibre length, aponeurosis length and aponeurosis width were measured as inter-marker distances first and then filtered using a smoothing spline algorithm [3]. Reference values for fibre length, aponeurosis length and width were measured when the bird was in the air prior to landing on the ground. This allowed us to capture marker positions during a 0.05 second time period when the muscle was in a relaxed state, defined by a MTU force that ranged between 5 and 10 N (approx. 2–4% of maximum isometric tetanic force [3]) and by an EMG signal that was visually inspected to be nil.

To measure apparent longitudinal stiffness and EE storage in the aponeurosis, we plotted MTU force as a function of aponeurosis length during the period of force rise from 30 N to 130 N, a range that was consistent across all trials. Apparent longitudinal stiffness was measured by calculating the linear slope while EE storage was measured using trapezoidal integration. It should be noted that our measure of apparent longitudinal stiffness is challenged by the complex structure of the muscle-aponeurosis interface. While we use the force at the distal tendon to calculate stiffness, the close association of the aponeurosis with the muscle belly means that forces on any given portion of the aponeurosis may vary and therefore, local aponeurosis strains may also vary [12,13]. The ability to directly measure the force acting on the aponeurosis remains elusive, and therefore, our measure of force is a necessary simplification. Despite this, we have no reason to expect that the relationship between forces experienced by the aponeurosis and the force measured at the distal tendon changes between different contractions. In addition, it is probable that as aponeurosis width increases during an active muscle contraction, EE is stored with changes in transverse strains and loads; however, we do not attempt to quantify energy storage that is directly associated with transverse strains.

For our statistical approach, we implemented general linear model (ANOVA) designs in SYSTAT 11 to examine the influence of aponeurosis width (increase or decrease) on apparent longitudinal stiffness and EE storage. The designs treated aponeurosis width (increase or decrease) as a ‘between-subjects’ fixed factor to compare the values of apparent longitudinal stiffness and EE storage, which were treated as dependent variables. The designs also treated ‘individual’, ‘task’ and ‘height’ as independent variables and used interaction terms and nested designs as needed [14]. The models were simplified when independent variable(s) and/or their interaction terms were statistically insignificant. Similar to our previous approach [3], the final model treated ‘individual’ as a random factor and the interaction term (individual × task × height) as covariates to account for variation among the trials that consisted of either jumping or landing and trials that consisted of different landing heights, which ranged from 0.5 m to 1.75 m. Statistical significance for all tests was set at 0.05.

3. Results

Both landing and jumping involved a rapid rise in muscle force, during which the aponeurosis stretched in the longitudinal direction. We designed the experiment with the idea that landing would involve muscle fibre lengthening whereas jumping would involve muscle fibre shortening. While this distinct pattern was observed in some cases (figure 1c,e), there was considerable variation in muscle length and aponeurosis width behaviour from bird to bird and trial to trial (figure 1d,f), presumably because aponeurosis width behaviour is governed by an interaction between muscle force and fascicle length change [3]. Moreover, in the initial phase of landing, where we quantified strains, muscle fascicles have been observed to lengthen, shorten or remain isometric [8], paralleling the behaviour observed here. In order to focus on understanding the effect of aponeurosis width on EE storage, we decided to compare trials where aponeurosis width either increased or decreased, irrespective of whether the bird jumped or landed. When partitioning the data in this manner, we ended with four jumping and 11 landing trials in the ‘aponeurosis width increase’ category and three jumping and 10 landing trials in the ‘aponeurosis width decrease’ category.

(a). Influence of aponeurosis width strain on apparent longitudinal stiffness and elastic energy storage

As expected, changes in aponeurosis width influenced apparent stiffness (ANOVA: F_2,17 = 10.92; p = 0.006) and the amount of EE storage (ANOVA: F_2,14 = 13.9; p = 0.001) in the longitudinal direction. In trials where aponeurosis width decreased (−2.38 ± 0.22%) during force rise, apparent longitudinal stiffness was 147.25 ± 13.45 N mm⁻¹, and the amount of EE stored was 55.27 ± 5.92 mJ (figure 2). On the other hand, when aponeurosis width increased (1.34 ± 0.35%) during force rise, apparent longitudinal stiffness increased to 197.27 ± 20.72 N mm⁻¹ and the amount of EE stored decreased to 46.86 ± 5.62 mJ.

Figure 2.

Aponeuroses elastic mechanical behaviour. (a) Apparent longitudinal stiffness and elastic energy storage were quantified from the force–length behaviour for each trial. The force–length behaviour of the aponeurosis, taken from two different trials, illustrates two distinct patterns. When aponeurosis width increased during an in vivo contraction (light grey line), muscle force coincided with less aponeurosis stretch in the longitudinal direction. When aponeurosis width decreased (dark grey line), muscle force coincided with more aponeurosis stretch in the longitudinal direction. During the period of force rise analysed (30 N–130 N), (b) increases in aponeurosis width strains were (c) accompanied by smaller increases in aponeurosis length strains. Thus, the aponeurosis was stiffer (d) and thus, stored less energy (e) in the longitudinal direction.

4. Discussion

Our findings support our hypothesis that aponeuroses in vivo behave as variable stiffness springs and vary in their capacity to store energy. We found that during landing and jumping, the aponeurosis of the lateral gastrocnemius muscle in turkeys underwent dynamic changes in length and width. This shape-changing behaviour effectively modulates aponeurosis stiffness and its capacity to store EE in the longitudinal direction. For instance, when the gastrocnemius aponeurosis underwent an increase in width (as opposed to a decrease), its apparent longitudinal stiffness was 34% higher, and EE storage calculated from longitudinal strain was 15% lower. The increase in aponeurosis width is associated with changes in muscle shape and forces that load the aponeurosis in the transverse direction [2,3,9]. As a consequence, aponeuroses longitudinal stiffness and their capacity to store EE is not fixed, but will vary depending on how the muscle and aponeurosis change shape during an active in vivo contraction.

Our findings are at odds with our prediction that landings would exhibit fascicle lengthening, which would be associated with a decrease in aponeurosis width (negative strain by our convention), and that jumps would exhibit an increase in aponeurosis width (positive strain). Variation in the relative contribution of muscle synergists to the activity, particularly for landing and jumping tasks that require submaximal muscle activation as studied here, as well as spatial variation in proximal and distal muscle strain patterns [15–17] may have contributed to the variable behaviour in aponeuroses width that was seen between trials. It has been demonstrated that changes in aponeurosis width in situ is related to a combination of muscle force and fascicle shortening in maximally activated muscle [3], but other determinants, such as regional variation in muscle activation level and internal fluid pressures may also be important in ways that we have yet to understand.

While our measurements provide evidence of variable energy storage in aponeuroses, there are limitations of these measurements that raise the question of what these findings mean for the mechanical behaviour of other muscles. It is generally recognized that there is wide variation in muscle and tendon morphologies (e.g. [13]), and the relationship between force, fibre length change and aponeurosis deformation may vary. Therefore, the mechanical behaviour of aponeuroses in muscles with more complex architectures may differ from the relatively simple unipennate muscle studied here. While studying muscles with more complex architectures will help broaden our understanding, we must keep in mind that even our relatively simple marker set did not capture all of the complexity involved in the unipennate muscle and tendon deformations of the lateral gastrocnemius. It is well known that fascicle strain heterogeneity can occur within a muscle [16–18] and our single measure of fascicle strain could not capture this complexity. Strain heterogeneity also occurs within aponeuroses [13] and therefore, our simple marker set could not characterize the strain of the entire aponeurosis. Strains near the edges of the aponeurosis may have been higher, leading us to underestimate strain magnitudes in both length and width. While our measurements do not capture all the complexity of muscle-tendon interactions in vivo, this study along with our previous observations [2,3], suggest that aponeuroses behave as a dynamic shape-changing spring, defying the expected one-to-one relationship between muscle longitudinal force and EE storage.

It is generally assumed that the flow of energy through tendons depends only on the muscle force developed during a contraction. The observation that the energy stored in aponeuroses can vary for a given force (figure 2) demonstrates that multi-axial loading of aponeuroses structures allows for elastic behaviour that can vary dynamically between contractions and throughout a contraction. This behaviour has broad implications for understanding and modelling muscle mechanical function because the elastic behaviour of tendon will influence a muscle's length and velocity, two key variables that determine a muscle's force and power output. Not only will changes in the elastic behaviour of tendons influence muscle mechanical function, but changes in muscle mechanical function via muscle shape change will also influence the elastic behaviour of tendons, suggesting the presence of a ‘mechanical feedback loop’. Whether walking, running, or hopping, all vertebrate locomotor systems rely on the interaction between muscles and springy tendons [19] and therefore, musculoskeletal models that attempt to link muscle mechanics to energy consumption may provide better predictions when tendons are treated as variable stiffness springs.

In summary, we discovered that during landing and jumping, changes in aponeurosis width alters its stiffness and capacity to store EE in the longitudinal direction. While consideration was given to the EE stored in the longitudinal direction, it is also likely that EE is stored in the transverse direction when aponeuroses increase in width. This shape-change behaviour may allow aponeuroses to modulate EE storage because it is coupled with strain in multiple directions. While this remains to be explored, our main finding supports the idea that aponeuroses should be thought of as biological tissues that behave as variable stiffness springs, which have the capacity to modulate the amount of EE storage in vivo. Our understanding on the role of biological springs in vertebrate locomotion has expanded from a focus on free tendons to exploring the roles of springs within sarcomeres [20–22], springs within the muscle extracellular matrix [23] and springs that act along and orthogonal to the muscle's line of action [22–24]. The observation that dynamic changes in aponeuroses shape influence energy storage adds to our growing understanding of the diversity that springy mechanisms play in nature.

Ethics

The Institutional Animal Care and Use Committee approved the use of animals and the experimental protocol for this study.

Data accessibility

This article has no additional data.

Competing interests

The authors do not have any financial and personal relationships with other people or organizations that could inappropriately influence (bias) their work.

Funding

The National Institutes of Health research grant (AR055295) to T.J.R. supported this research and University of Houston CLASS Research Project to C.J.A. supported the completion of the manuscript.