Timing matters: tuning the mechanics of a muscle–tendon unit by adjusting stimulation phase during cyclic contractions

During locomotion, skeletal muscles are recruited to generate force and perform a diverse set of mechanical actions (Dickinson et al., 2000). Muscle performance is strongly influenced by its mechanical state and neural activation (Hill, 1925,, 1938; Gordon et al., 1966; Josephson, 1999). The timing and magnitude of activation dictates the context in which muscle forces will generate or absorb mechanical energy (Josephson, 1993, 1999; Ahn and Full, 2002). When activated during a period of shortening, skeletal muscle functions as a motor by performing positive work (Josephson, 1985, 1999; Dickinson et al., 2000). When active during lengthening, however, muscle functions as a brake by performing negative work and dissipating mechanical energy (Josephson, 1985, 1999; Dickinson et al., 2000). Finally, within a relatively compliant muscle–tendon unit (MTU), the muscle can be active and isometric (i.e. at constant length), generating high forces to act as a strut while energy is cycled in series elastic elements (Ettema, 1996a,, 2001; Roberts et al., 1997; Dickinson et al., 2000).

The neuromechanical factors that ultimately determine the amount of force or work produced by active skeletal muscle are its force–length (F–L) and force–velocity (F–V) properties (Hill, 1925,, 1938; Gordon et al., 1966), the magnitude and timing of muscle activation (Josephson, 1985; Stevens, 1996; Dickinson et al., 2000) and environmental factors, such as externally applied loads or strain patterns (Josephson, 1985). Sinusoidal length changes similar to those observed during steady locomotion (e.g. walking, running, swimming, flying) provide a useful paradigm for probing how the mechanical state of active muscle ultimately governs cyclic force and power production in a functional task. This sort of ‘work loop’ experiment allows for exploration and understanding of how activation kinetics, as well as F–L and F–V dynamics, govern the mode of operation (motor, brake or strut) of a muscle depending on when it is stimulated along its length trajectory (Josephson, 1985, 1999; Ahn, 2012). One limitation of the ‘work loop’ paradigm is the potential inaccuracy when extrapolating from isolated muscles to isolated MTUs. Changes in length applied directly to a MTU may not reflect the length and/or velocity of the underlying muscle fascicles (contractile elements or CEs), especially if there is considerable series compliance from elastic tissues (series elastic elements or SEEs). This decoupling can make it difficult to resolve the relative contribution of the CEs and SEEs to the mechanical behavior of the MTU.

Recent muscle-level studies of terrestrial gait have observed that in the distal, more compliant MTUs of many species, including humans, CEs (i.e. active muscle) are in fact used as a strut to allow the SEEs (i.e. tendon, aponeurosis) within MTUs to stretch and recoil during cyclic limb motions (Roberts et al., 1997; Biewener et al., 1998; Fukunaga et al., 2001; Ishikawa et al., 2005; Takeshita et al., 2006; Dean and Kuo, 2011; Farris and Sawicki, 2012; Farris et al., 2013). In other words, CE length changes are decoupled from MTU trajectories via SEE compliance, and CE–SEE interaction is ‘tuned’ to cycle large amounts of energy in tendons and aponeuroses while the CE itself remains relatively isometric (Robertson and Sawicki, 2014). This ‘tuned’ pattern facilitates length change dynamics suitable for high CE force production, which, in turn, require relatively smaller active volumes of muscle to generate force during each stride (Roberts et al., 1997; Gabaldon et al., 2008).

Our understanding of the patterns of neural control necessary to tune CE and SEE interactions to allow for effective force production is limited. Multiple in vitro work loop studies exploring the role that tendon compliance plays in gait have relied on mathematical models of the SEE in order to decouple CE and MTU trajectories in the absence of direct muscle level measurements (Ettema et al., 1990; Ettema, 1996a,, 2001; Lou et al., 1999; Barclay and Lichtwark, 2007; Lichtwark and Barclay, 2010, 2012). For example, Ettema (1996a) integrated a mathematical model with experimental data to conclude that effective elastic energy storage and release in an SEE is strongly dependent on the timing of muscle stimulation during a MTU stretch–shorten cycle, and that SEE compliance can significantly affect muscle-level energetics without having a dramatic effect on MTU force production. While there is no doubt that mathematical models of MTUs provide a useful avenue for examining the interaction between CE and SEE, they do have limited ability to capture some aspects of the dynamics of force generation in both muscle and tendon. In fact, multiple studies have shown that model-based predictions of muscle force production are flawed for active contractions during non-isokinetic (i.e. variable length/velocity) conditions (Caiozzo and Baldwin, 1997; Sandercock and Heckman, 1997; Lou et al., 1998; Lichtwark and Wilson, 2005). This is further complicated by incomplete models of biological tendons, which do not capture their tendency to dissipate energy over a stretch–shorten cycle (Bennet et al., 1986; Lieber et al., 1991; Maganaris and Paul, 2000).

The purpose of the present study was to use a novel, in vitro muscle–tendon work loop approach to probe how the temporal aspects of neural control influence muscle–tendon interaction within a relatively compliant MTU. We extended the work loop approach by including independent measurements of both CE and MTU length in order to make observations that did not rely on model estimates for CE or SEE force production. Using direct measurements of CE length from sonomicrometry in conjunction with externally applied cyclic length changes via a servo-controlled ergometer, we examined how the onset timing of muscle stimulation within an MTU length change cycle (i.e. muscle stimulation phase, φ_stim) relates to the ‘tuned’ muscle–tendon interaction observed within compliant MTUs during steady speed terrestrial gait (Fig. 1). We expected that the relationship between overall MTU net work and muscle stimulation phase, φ_stim, would follow the same trends previously observed in work loop experiments using direct measurements from CE only (Josephson, 1999) and a combination of empirical measures and model-based estimates from whole MTUs (Ettema, 1996a). First, we hypothesized that there would be a φ_stim that would generate net zero work over a MTU length change cycle. We refer to the stimulation phase leading to net zero work as (φ_stim=φ_net zero). Second, we expected that muscle stimulation with onset that occurred earlier in the MTU length change cycle (φ_stim<φ_net zero) would generate net negative work while muscle stimulation onset that occurred later in the cycle (φ_stim>φ_{net zero}) would generate net positive work. Finally, we expected that the muscle stimulation phase resulting in net zero work for the MTU over a length change cycle (φ_stim=φ_{net zero}) would be ‘tuned’, allowing the CE to operate isometrically with all positive and negative work resulting from cycling of elastic energy in the SEE.

All results reported here are taken from trials where cyclic length changes were applied to the MTU with a cycle frequency (ω_cycle) of 2 Hz (i.e. cycle period=500 ms) and an amplitude (A_cycle) of 4 mm with an initial (minimum) MTU length corresponding to a CE length of 1.2L₀ (Figs 1 and 3). Key metrics characterizing the muscle–tendon architecture of preparations used in this study can be found in Table 1. 

For all experimental conditions explored, peak force was recorded for each cycle of strain/stimulation (Figs 2 and 3) and was averaged within (N=4 cycles) and between (N=6 subjects) preparations to determine an average peak force (Fig. 4A). The highest peak force was observed at 12.5% muscle stimulation phase (Fig. 2 and Fig. 4A), and minimum values were recorded for stimulation phase of −37.5% (Fig. 4A). Peak forces were significantly different from the 25% phase (Tukey's; P<0.05) at −50%, −37.5%, −25% and 50%, and in no-stimulation conditions (Fig. 4A).

All conditions showed significant decoupling of the change in length of the CE from that of the MTU (Figs 2 and 3). Decoupling was particularly obvious immediately following stimulation; when the rapid rise in force resulted in SEE stretch and significant shortening of the CE, regardless of the direction of length change of the MTU. CE shortening following stimulation onset was observed for all conditions (Figs 2 and 3) and was minimal at 25% muscle stimulation phase (Fig. 3D and Fig. 4B).

Length change dynamics observed immediately following onset of muscle stimulation were of particular interest in this study because it is during this period that active force production tends to decouple MTU trajectory from CE and SEE strain (Fig. 3). All conditions, except for 12.5% stimulation phase had CE shortening excursions significantly greater than those in the 25% stimulation phase (Tukey's; P<0.05) (Fig. 4B). The greatest MTU force output and largest SEE stretch during the period of active CE shortening was observed at 12.5% stimulation phase (Fig. 4B). SEE strains were significantly less at 37.5% and 50% compared with 25% stimulation phase (Tukey's; P<0.05).

In every dynamic condition, onset of muscle stimulation was followed by rapid force development, shortening and positive power production by the CE, regardless of whether the MTU was shortening or lengthening. During MTU lengthening, positive power production by the CE was associated with negative power (energy storage) from the SEE. Energy stored in the SEE has two possible fates. It can be returned externally to the motor, as positive MTU power, or it can do work on the CE to lengthen active muscle fibers. The extent to which work done by the CE on the SEE could be returned externally varied, depending on the phase of stimulation (Fig. 5). Under some conditions (e.g. 0% phase), all of the energy stored in the SEE was released to do work on the CE, rather than contributing to MTU power.

The r values computed based on CE versus MTU velocities were between 0 and 1 (i.e. positively correlated) for all conditions examined (Fig. 6). A minimum mean r value of 0.09 was observed for the 25% stimulation phase condition (Fig. 6B), which was significantly lower than all other stimulation phase conditions except for 12.5% (Tukey's P<0.05) (Fig. 6D).

The MTU produced approximately zero net work with onset of muscle stimulation at 25% of the MTU length change cycle (i.e. φ_stim=φ_{net zero}=25%) (Fig. 3F, Fig. 5H and Fig. 7A). Because net work over the course of an entire MTU length change cycle must be due to the CE, net work in the CE and MTU were nearly identical in all muscle stimulation phase conditions (Fig. 7A). Even in the condition with nearly zero net work (i.e. φ_stim=φ_{net zero}=25%), we did not observe ‘tuned’, strut-like isometric behavior of the CE. Instead, at 25% stimulation phase, the CE underwent an appreciable change in length following stimulation (Fig. 3D and Fig. 4B) and thus generated and absorbed substantial but equal amounts of mechanical energy (Fig. 5H and Fig. 7B,C).

When muscle stimulation onset occurred earlier in the MTU length change cycle than for conditions of net zero work (φ_stim<φ_net zero=25%), the MTU and CE generated net negative work (Fig. 3C, Fig. 5G and Fig. 7A). Maximal energy absorption by the MTU and CE occurred for 0% stimulation phase. Muscle stimulation phases ranging from −12.5% to +12.5% of the MTU length change cycle generated significantly more net negative CE and MTU work than at 25% stimulation phase (Tukey's; P<0.05) (Fig. 7A). We note that, as expected, SEE net work was small and ∼zero or negative for all conditions studied here because passive tissues can only store and return mechanical energy with small losses (Fig. 7A).

For muscle stimulation onset that occurred later in the MTU length change cycle than net zero work conditions (φ_stim>φ_{net zero}=25%), the MTU and CE generated net positive work (Fig. 3I, Fig. 5I and Fig. 7A). Maximal net positive MTU and CE work per cycle was observed at 50% muscle stimulation phase; however, none of the conditions generated net positive work that was significantly different from the 25% stimulation condition (Tukey's; P≥0.05) (Fig. 7A).

While the mechanical roles of elastic elements during terrestrial gaits are well understood, the role that neural control plays in governing them is not. Therefore, we used a novel in vitro MTU work loop approach to determine how MTU, CE and SEE mechanics are modulated by the timing of muscle stimulation within a cyclical MTU strain trajectory (i.e. muscle stimulation phase). We specifically focused on elucidating the role of neural control in shaping muscle–tendon interaction dynamics which produced zero net MTU work, conditions akin to steady-speed terrestrial locomotion.

We hypothesized that: (1) there would be an onset timing of muscle stimulation relative to the MTU length change cycle that resulted in net zero MTU work over a stretch–shorten cycle (φ_stim=φ_net zero); and that (2) muscle stimulation timed earlier (φ_stim<φ_net zero) would result in net negative MTU work, while muscle stimulation timed later (φ_stim>φ_net zero) would result in net positive MTU work. Our data supported these hypotheses (Fig. 7A). We note that, despite significant decoupling of CE and whole MTU dynamics observed here (Fig. 6), φ_net zero for a compliant MTU occurred at a similar muscle stimulation phase as has been previously observed for isolated muscles without significant series elastic tissues (Josephson, 1985, 1999).

Our final hypothesis was that (3) the muscle stimulation phase resulting in net zero work (φ_stim=φ_{net zero}) would be ‘tuned’ so that all positive and negative work produced by the MTU would be the result of elastic energy storage and return in the SEE, with little to no positive/negative mechanical work output from active muscle (CE). This hypothesis was not supported because the CE produced non-negligible amounts of both positive and negative work over a stretch–shorten cycle for the φ_stim=φ_net zero≈25% condition (Fig. 7B).

During steady-speed terrestrial locomotion, compliant MTUs at distal joints (e.g. the ankle) cyclically lengthen and shorten from step to step. This creates an opportunity for optimally coordinating muscle activation timing and amplitude to ‘tune’ muscle–tendon interaction for maximal performance. For example, if muscles are activated with timing and amplitude that supplies a rigid force producing strut (i.e. ‘tuned’ to be nearly isometric), they can allow elastic tissues to stretch and recoil during limb segment lengthening and shortening in order to cycle the energy required for steady gait. Because of the intrinsic force–length and force–velocity relationships, strut-like muscle-level dynamics are particularly well suited for high force production, reducing the volume of active muscle required to meet force demands and ultimately increasing the economy of locomotion (Roberts et al., 1997; Gabaldon et al., 2008).

Our results suggest that, even in the presence of highly compliant elastic tissues in series with muscle fascicles, tuning the CE for strut-like force production (i.e. near isometry) during cyclic contractions is challenging. Contrary to our third hypothesis, the net zero work condition (φ_{net zero}=25%) resulted in significant length changes of the CE. That is, the net zero work condition was accomplished not by isometric force production by the CE, but by significant and approximately equal amounts of positive and negative work (Fig. 7B,C). Shortening work occurred early in the period of force production, as the CE shortened against the SEE and lengthening work occurred when the SEE recoiled against the CE. Although this pattern represented the most decoupled CE/MTU behavior (Fig. 6), it was far from the ‘ideal’ of an isometric CE strut supporting the cyclic stretch and recoil of tendon.

Why is isometric muscle behavior difficult to achieve under the conditions of our experiment? One likely issue is the combination of asymmetric muscle activation/deactivation dynamics (Zajac, 1989) and a symmetric/sinusoidal strain pattern. In general, muscle force onset occurs more rapidly than offset (Fig. 2). When symmetric patterns of MTU strain are applied to a muscle with asymmetric force onset/offset, some muscle shortening and lengthening is going to be required to match passive forces in SEEs. One possible approach to addressing this asymmetric force output is to apply an asymmetric strain pattern. Marsh and co-workers have demonstrated that when asymmetric strains are applied, it is possible to maximize power output from muscle alone (Askew and Marsh, 1997; Girgenrath and Marsh, 1999). With this in mind, we attempted to design an ergometer controller that would apply the required MTU strain pattern to keep CE length constant during muscle activation/deactivation using real-time sonomicrometry measurements as feedback (Sawicki and Roberts, 2009). The resulting MTU strain pattern was highly asymmetric and the length of the CE remained more isometric than shown in the current study. However, it was still not possible to achieve ‘perfect’ isometry as we could not avoid internal CE shortening against the SEE early in the supramaximal contractions of the compliant MTU. We note that animals probably use dynamically changing moment arms (Carrier et al., 1994) and pennation angles (Azizi et al., 2008), combined with differential sub-maximal motor-unit recruitment patterns (Holt et al., 2014) that can be modulated by reflex feedback (Maas and Lichtwark, 2009) to help ‘dial in’ nearly perfect strut-like muscle action during real-world locomotion.

Gait on level ground at constant speed requires no net mechanical work, but most terrestrial animals experience terrain that imposes varying mechanical demands (e.g. slowing down, speeding up, going up- or downhill). The decoupling of MTU and CE by SEEs may afford considerable advantages during unsteady locomotion, including: (1) limiting negative work absorbed by CE when active during MTU lengthening (Roberts and Azizi, 2010); (2) amplifying positive work by allowing muscle to operate at velocities for optimal power output during MTU shortening (Lichtwark and Barclay, 2010); and (3) providing a rapid means of mechanical feedback (i.e. ‘preflex’) following environmental perturbation (Daley and Biewener, 2006; Biewener and Daley, 2007). Our results support previous research suggesting that locomotion tasks involving net generation or absorption of mechanical energy may be accessible by adjusting timing of muscle stimulation relative to the pattern of MTU strain (Ettema, 1996a, 2001; Lichtwark and Wilson, 2005; Lichtwark and Barclay, 2010, 2012). We observed that slight changes in muscle stimulation onset phase from the φ_{net zero} (i.e. 25%±12.5%) resulted in near maximal values of net positive or negative work, respectively (Fig. 7A). Our data are consistent with previous studies by Ettema (1996a) and Lichtwark and Barclay (2010), which varied frequency, phase and stimulation duty in a compliant MTU. Both of these studies emphasized the importance of proper muscle stimulation timing to either effectively store and return energy in series tendon (Ettema, 1996a) or maximize efficiency in shortening for performing positive work (Lichtwark and Barclay, 2010). Shifting muscle activation phase could provide a potentially simple neural mechanism for altering compliant MTU function to produce net negative (braking or moving downhill), net zero (constant speed) or net positive (acceleration or moving uphill) mechanical work output.

The most novel aspect of this study was the use of implantable sonomicrometry for direct measurement of muscle-level mechanics during dynamic work loop experiments. Previous work loop studies of MTU mechanics have relied on model-based approximations of SEE force–length behavior to dissect CE from SEE length changes. Ettema left the biological SEE intact, approximated SEE stiffness under high force conditions, and assumed perfect elasticity (i.e. all energy stored in SEE must be returned) to calculate the contribution of the SEE (Ettema et al., 1990; Ettema, 1996a,b). Multiple studies, however have demonstrated that biological tendons exhibit non-linear force–length behavior at low strains (Lichtwark and Wilson, 2007), and that volumetric changes in active muscle can change elastic properties of aponeurosis/SEE (Azizi and Roberts, 2009). Tendons will also dissipate some energy over a stretch–shorten cycle (Fig. 7A) (Bennet et al., 1986; Lieber et al., 1991; Maganaris and Paul, 2000). Lichtwark and Barclay avoided many of these pitfalls by removing the tendon altogether and replacing it with elastic strips of latex with well-defined linear stiffness (Lichtwark and Barclay, 2010, 2012). While this is an excellent approach to studying the effect of series compliance on muscle level function, it lacks many of the aforementioned mechanical features of biological tendons that might have a subtle but significant impact on CE mechanics. Despite this, findings presented here confirm the previous experimental observations of Lichtwark and colleagues (Lichtwark and Wilson, 2007; Lichtwark and Barclay, 2010, 2012) without the need for any sort of model-based approximation and further highlight that SEE compliance can have a profound impact on CE contractile dynamics.

While work loops have proved to be an effective means of exploring how strain trajectories and neural activation influence muscle-level mechanics and energetics (Ahn, 2012), they depart from muscle function during ‘real-world’ locomotion in significant ways (Marsh, 1999). During locomotion, muscle strain trajectories are not a pre-existing phenomenon to which neural activation patterns can be applied. Rather, they are an emergent behavior resulting from active muscle force, transmitted through mechanical lever systems (i.e. biological moment arms) and interaction with an inertial-gravitational load (Marsh, 1999; Richards and Clemente, 2012; Robertson and Sawicki, 2014). To understand the dynamic interplay of all of these factors, and the role that they play in generating stable/efficient MTU mechanics observed in gait, trajectory must not be imposed (Robertson and Sawicki, 2014).

During locomotion in the ‘real-world’, the dynamic interactions between MTUs of the limb and the load of the body serve to couple muscle stimulation frequency and phase. Thus, future work should focus on simulating a dynamic inertial environment (i.e. mechanical advantage, gravitational load) that can freely interact with a biological MTU undergoing cyclic stimulation (Sheppard et al., 2009; Farahat and Herr, 2010; Robertson and Sawicki, 2014). With direct, real-time measurements of both fascicle-level dynamics via sonomicrometry and muscle force from the ergometer as we have done in the current study, we could simulate spindle organ (i.e. length/velocity) and/or Golgi tendon (i.e. force) afferent feedback. By varying muscle stimulation intensity (via rate-coding) as a function of simulated feedback within and between muscle stimulation pulses, it may be possible to begin systematically exploring how environment dynamics, as well as feed-forward and feed-back neural control processes (e.g. reflexes) govern the influence of muscle activation on the mechanics and energetics of muscle–tendon interaction (Stevens, 1996; Farahat and Herr, 2010; Richards and Clemente, 2012).

Six adult bullfrogs (Lithobates catesbeianus Shaw 1802) with body masses ranging from 214 to 373 g, were purchased from a licensed vendor and housed in the Brown University Animal Care facility in a large tank of shallow water with free access to a terrestrial platform. Subjects were fed large, vitamin-enriched crickets ad libitum twice weekly. Before use in experimental procedures, animals were given a minimum acclimation period of 1 week. Prior to their use in any experimental preparation, frogs were anesthetized and euthanized by double pithing. All animal procedures were approved by Brown University Institutional Animal Care and Use Committee.

A single limb from each subject was removed just below the hip, the skin was removed and the limb was placed in a bath of oxygenated amphibian Ringer's solution (100 mmol l⁻¹ NaCl, 2.5 mmol l⁻¹ KCl, 2.5 mmol l⁻¹ NaHCO₃, 1.6 mmol l⁻¹ CaCl₂, 10.5 mmol l⁻¹ dextrose) and kept at room temperature (∼22°C) during dissection. All muscles were completely removed except the plantaris longus (PL) MTU, which serves as the primary ankle extensor, and is known to be both compliant (i.e. high ‘fixed-end’ compliance and SEE/MTU length ratio), and a major source of power output during jumping. Caution was taken during removal of proximal muscles to ensure the sciatic nerve remained intact. The PL muscle was left intact at its proximal insertion point (the knee joint), and freed from the ankle and tibia/fibula, with great care taken to preserve series aponeurosis and free tendon up to its distal insertion point at the toes.

Following dissection, a bipolar electrode cuff constructed from two silver wires and plastic tubing (7 mm length, 1.5 mm inner diameter) was carefully placed over the free (but intact) sciatic nerve just proximal to the PL insertion point at the knee and connected to a Grass S48 stimulator (Grass Technologies, West Warwick, RI, USA). Sonomicrometry transducers (1 mm diameter, Sonometrics Inc., London, Ontario, CA, USA) were implanted along a superficial, proximal muscle fascicle of the PL muscle and sutured in place to provide direct measurement of fascicle (CE) length change (i.e. decoupled from whole MTU length change) (Fig. 1).

Intact sections of femur and tibia were securely mounted on acrylic bolted at the bottom of a chamber with continuously circulating oxygenated Ringer's solution maintained at room temperature (22°C). The distal end of the free tendon was placed in a custom friction clamp attached to a servomotor (310 B-LR, Aurora Scientific Inc., Cambridge, MA, USA) via a rigid stainless steel cable (stiffness≈94.1 N mm⁻¹) (Fig. 1).

MTU force and length were recorded from the servomotor and CE length was recorded using sonomicrometry (Fig. 1) and a 16-bit A/D converter (National Instruments USB-6251, Austin, TX, USA) sampling at 1000 Hz. Data were processed and analyzed using custom MATLAB software (MathWorks Inc., Natick, MA, USA). Raw data (MTU force, MTU length, CE length) were smoothed using a 4th order Butterworth, zero-lag filter with low pass cut-off frequency of 25 Hz. In all trials, we subtracted the length change of the stainless steel cable connecting the ergometer and the MTU, by subtracting 1/94.1 mm N⁻¹ of force to get the true length change of the MTU.

To compute the velocity of the MTU and the CE we took the first derivative of the smoothed servomotor and sonomicrometry length change data, respectively. The length change and velocity of the SEEs was computed by simply subtracting the CE from the MTU length or velocity, respectively (e.g. Figs 2, 3 and 5). We note that this approach implies that ΔL_MTU(t)=ΔL_CE(t)+ΔL_SEE(t) and v_MTU=v_CE(t)+v_SEE(t), which assumes that CEs and SEEs reside along the same geometrical axis as the whole MTU. Finally, we computed mechanical power (mW) by multiplying instantaneous MTU force (N) and velocity (mm s⁻¹) for the MTU and each of its component parts (i.e. CE and SEE; e.g. Fig. 5). We note that, because fascicles rotate while they shorten or lengthen and we did not record fascicle pennation angle, we could not estimate length changes of the CE along the long axis of the MTU/SEE. As a result, our length change measurements using sonomicrometry crystals implanted in fascicles are likely to be an underestimate of the CE length change along the MTU/SEE long axis (Azizi et al., 2008; Azizi and Roberts, 2014). These underestimates in CE length change and velocity will lead to overestimates in calculated SEE length change and velocity and therefore tend to attribute too much MTU mechanical power to the SEE and too little to the CE.

Prior to any dynamic work loop conditions, ‘fixed-end’ contractions were performed by holding the ergometer position constant to impose an MTU length that resulted in 1 N of passive tension (CE length≈1.2L₀), and then applying four stimulation trains at a frequency (ω_stim) of 2 Hz with a duty factor (D_stim) of 10% (i.e. 50 ms). Each stimulation train consisted of pulses with a duration (t_pulse) of 0.2 ms and a pulse frequency (ω_pulse) of 100 Hz. The average peak force from the four ‘fixed-end’ contractions was recorded. Data showing a snapshot of a typical ‘fixed-end’ trial is shown in Fig. 2. The small amount of MTU shortening in these trials reflects the fact that we accounted for the ∼0.011 mm N⁻¹ of compliance of the stainless steel cable used to attach the distal tendon to the ergometer arm. We note that the amount of muscle strain against internal stretch of the series elastic tissues, or ‘fixed-end’ compliance of this preparation was ∼0.30, which is in line with the value reported for the human gastrocnemius muscles (Narici et al., 1996; Biewener and Roberts, 2000; Roberts, 2002), indicating that the bullfrog plantaris is a convenient scaled-down model for human plantarflexors.

A second set of ‘fixed-end’ contractions was performed at the conclusion of all dynamic work loop conditions. Peak force values from the second set of ‘fixed-end’ contractions were compared with those for the first to be sure that muscle fatigue or damage due to trauma or low levels of oxygenation in deep portions of the tissue did not play a significant role in observed dynamics. For the six experimental preparations reported, the final peak force was ≥80% of the initial value, so factors negatively impacting force production were considered to be a non-factor and data were used for further analysis.

Cyclic length changes were applied to the MTU with a cycle frequency (ω_cycle) of 2 Hz (i.e. cycle period=500 ms), and an amplitude (A_cycle) of 4 mm with an initial (minimum) MTU length corresponding to a CE length of 1.2L₀ (Figs 1 and 3). The MTU preparation was subjected to six cycles of shortening and lengthening, with the first and last cycle occurring in the absence of any muscle stimulation (Fig. 3). For the middle four cycles, muscle stimulation was driven via direct nerve stimulation with a specified onset timing that was different in each condition. More specifically, we defined the onset timing of muscle stimulation (i.e. muscle stimulation phase) with respect to the MTU length change cycle, with 0% referring stimulation onset at MTU minimum length (i.e. ‘bottom dead center’), and 50% referring to MTU maximum length (i.e. ‘top dead center’). We tested muscle stimulation phases ranging from −37.5% to 50% in 12.5% increments, always using a 50 ms pulse train duration (i.e. duty factor, D_stim=10%) (Fig. 1). Stimulation was delivered in a pulse train, with each individual pulse having period t_pulse=0.2 ms and pulses delivered with frequency ω_pulse=100 Hz. The order of muscle stimulation phase conditions was randomized in all in vitro preparations to minimize fatigue effects on averaged data.

To determine the influence of muscle stimulation phase on observed MTU mechanical performance, a two-factor analysis of variance (ANOVA) with subject (i.e. repeated measures) and muscle stimulation phase as the independent variables. We performed ANOVA analyses for all dependent variables of interest (Fig. 4A,B; Fig. 6D and Fig. 7A–D), with α=0.05. For dependent variables where we found a significant main effect (P<0.05), we report results from a post hoc Tukey's honestly significant difference (HSD) test, indicating which conditions were significantly different (P<0.05) from the 25% muscle stimulation phase condition. All values are reported as means±s.e.m.