Rightward shift of optimal fascicle length with decreasing voluntary activity level in the soleus and lateral gastrocnemius muscles

Across the animal kingdom, a large variety of locomotive strategies are observed, despite similar design and function of muscle (Dickinson et al., 2000). The mechanics of muscle–tendon units (MTUs) can be precisely tuned by altering activation dynamics to create favorable conditions to maximize force, positive work or negative work (Dickinson et al., 2000; Roberts and Azizi, 2011; Sawicki et al., 2015). Indeed, tendon compliance (Zajac, 1989) and muscle activity are typically tuned towards maintaining fascicle operating lengths that are at or near the plateau of their force–length relationships (Holt and Williams, 2018; Ichinose et al., 1997; MacIntosh, 2017; Rubenson et al., 2012), at least when demand is greatest, as observed in frog jumping (Holt and Azizi, 2016).

One critical aspect of such muscle tuning includes the magnitude of muscle activity; the force–length relationship of contracting muscle varies with muscle activity level (Holt and Azizi, 2014; Holt and Williams, 2018; Mayfield et al., 2016b). This activation dependence of the force–length relationship is often described in ex vivo muscle preparations; optimum length is longer at lower, compared with higher, muscle activations (Balnave and Allen, 1996; Hessel et al., 2019; Holt and Williams, 2018; Rack and Westbury, 1974; Stephenson and Wendt, 1984). However, for voluntary in vivo contractions, the relationship between muscle activity and the MTU force–length curve is less explored, with conflicting results from different collection methods. For example, it has been reported that the vastus lateralis force–fascicle length curve shifts to progressively longer optimal fascicle lengths with decreasing force levels relative to maximum force, but optimal fascicle length does not change with decreasing activity levels relative to maximum muscle activity (de Brito Fontana and Herzog, 2016).

A better understanding of lower limb MTU mechanics during submaximal activity levels would benefit our understanding of human locomotion. For example, during human walking, the soleus, medial gastrocnemius (MG) and lateral gastrocnemius (LG) are remarkably adaptable to changes in terrain (Lay et al., 2006; Lewis et al., 2015; MacLellan and Patla, 2006; Vlutters et al., 2018) thanks in part to the regulation of MTU force production through the modulation of muscle activity levels (e.g. Brennan et al., 2017; Clark, 2015). Indeed, even small modulations to muscle activity, as can occur after a stroke or with the use of assistive lower limb exoskeletons, leads to systematic changes to overall contractile or activity dynamics in the affected muscles, and to unaffected muscles that nevertheless serve a compensatory function (Nuckols et al., 2020; Tan et al., 2018). Although the characterization of human movement is highly explored, less resources have been invested to define activity-dependent changes of the triceps surae fascicle length operating ranges for submaximal, voluntary contractions. Therefore, an analysis of voluntary, in vivo submaximal ankle torque– and force–fascicle length properties of triceps surae muscles can be immediately informative to an analysis or re-analysis of human movement such as walking.

The aim of this study was to evaluate the triceps surae torque– and force–fascicle length relationships at different submaximal activity levels. We investigated three different levels to verify whether changes in activity level could lead to a shift in optimal fascicle length. We studied the soleus and LG muscles during fixed-end voluntary contractions at maximal effort and two submaximal voluntary activity levels. We hypothesized that a slight decrease in activity level would shift the optimal ankle angle and optimal soleus and LG fascicle lengths to more dorsiflexed angles and longer lengths, respectively. Strikingly, our results demonstrate that even a small reduction in muscle activity level can affect torque– and force–fascicle length relationships and should be considered when evaluating in vivo MTU performance.

Twelve healthy male and female participants (8 males and 4 females, age 25.5±2.4 years, mass 77.9±11.2 kg, height 177.4±5.6 m) were recruited from Ruhr University Bochum. Participants were free of neuromuscular disorders or injuries to their lower limbs and had no documented gait abnormalities. All protocols describe here were approved by the Human Ethics Committee of Ruhr University Bochum.

Net ankle joint torque and ankle joint angle were measured from the right leg of participants using an isokinetic dynamometer (Fig. 1; IsoMed2000, D&R Ferstl, Hermau, Germany). Participants laid prone on the bench of the dynamometer with their knee slightly bent (∼5 deg flexion from straight leg) and their foot tightly strapped to a foot plate to minimize heel lift during contractions. Knee and ankle angle were initially measured using a handheld goniometer. Accessory movements of the participants were minimized during experiments by securing straps around the waist and when needed, additional straps around the thigh. The participant's right ankle was positioned to neutral (i.e. sole of the foot perpendicular to shank), which we defined as 0 deg, with plantar flexed (PF) positions defined as negative angles, and dorsiflexed (DF) positions defined as positive angles (Fig. 1). The lateral malleolus, which was assumed to approximate the ankle joint axis of rotation in the sagittal plane, was aligned with the dynamometer axis during contraction under maximal voluntary activation to ensure that the ankle joint and dynamometer axes were aligned when torque was analysed.

Net ankle joint torque and ankle joint angle were sampled at 1000 Hz using an AD converter [Power1401, Cambridge Electronic Design (CED), Cambridge, UK] and Spike2 data collection software (CED). Torque and angle data were filtered using a low-pass fourth-order 20 Hz Butterworth filter. Ankle joint torques caused by gravity acting on the foot were considered negligible because of the foot segment's relatively low mass (<1.8% body mass) and most of that mass being distributed close to the axis of rotation (Dempster and Gaughran, 1967; Winter, 2009).

Electromyography (EMG) was used to measure the muscle activity of the right leg's soleus, LG and MG (AnEMG12 amplifier; OT Bioelettronica, Torino, Italy). EMG signals were band-pass analog filtered between 10 and 500 Hz and recorded using two electrodes (8 mm recording diameter, Ag–AgCl; Covidien, Mansfield, MA, USA) placed in a bipolar configuration on each muscle, according to international guidelines (Hermens et al., 2000). Data were sampled at 5 kHz using a Power 1401-3 data acquisition system and Spike2 data collection software (CED). The anterior tibialis was assumed to have a negligible contribution to the net ankle joint torque during these experiments, as shown by Raiteri et al. (2015).

A 128-element, flat, linear ultrasound transducer [60 Hz sampling rate, 60×50 mm (width×depth) field of view; LS128 CEXT-1Z, Telemed, Vilnius, Lithuania] was used to image soleus and LG fascicles simultaneously throughout all experiments. Each muscle's fascicle lengths were measured at rest and during the plateau of torque production across contraction conditions from a representative fascicle using already-described tracking software and procedures (Farris and Lichtwark, 2016; Gillett et al., 2013). Absolute fascicle length data are available in Fig. S1.

We decided to test three activity levels in this study. These included a maximal activity level and two submaximal activity levels [30 and 22% maximal voluntary contraction (MVC)]. These submaximal activity levels differed by only 8% of maximum activity as measured at a neutral ankle joint angle (sole of the foot perpendicular to the shank) so that we could assess if relatively minor activity level changes, as would be expected with slight changes in movement speeds like walking, could shift the resulting optimal fascicle lengths of the soleus and LG muscles.

Participants received real-time biofeedback of their soleus muscle activity level [moving 0.25 s root mean square (RMS) amplitude] via a computer monitor so that they could match 22 and 30% MVC activity levels at various ankle joint angles to within ±5% of a pre-defined EMG RMS amplitude (Fig. 2), similar to experiments on the tibialis anterior (Raiteri and Hahn, 2019). The activity levels were normalized relative to the maximum soleus EMG amplitude measured at a neutral ankle angle during 100% MVC (see below). After a familiarization session, participants became consistent at matching their soleus muscle activity to within ±5% of the desired levels.

Participants performed preconditioning contractions before experimental testing by completing at least ten 3–5 s contractions that gradually increased in effort from ∼50 to 100% of their maximum perceived effort. Participants performed at least two 100% MVCs of plantar flexion for 6 s each at a neutral ankle angle of 0 deg to determine the maximum soleus EMG RMS amplitude at this ankle joint angle. Subjects were given verbal motivation by the investigator and additional trials were performed until there was no more than a 5% difference in peak torque between 100% MVCs. Three minutes of rest were provided between contractions, and the soleus EMG RMS amplitude from the 100% MVC that met the above criterion with the highest ankle joint torque was used to determine the maximal activity level (100% MVC) and the two target soleus muscle activity levels (22 and 30% MVC). In total, participants completed experiments at all three activity levels, but the maximal activity level was not controlled across ankle joint angles, whereas the submaximal activity levels were. Data were also collected when subjects were instructed to relax, which will be referred to as 0% MVC. We measured the net ankle joint torque produced at each activity level at ankle angles of −10 (PF), 0, 5, 10, 15, 20, 25, 30 and 35 deg (DF). Ankle dorsiflexion angles >25 deg were not achievable by all participants without substantial discomfort. Therefore, the more extreme dorsiflexion angles were only tested in a subset of participants (N=11 at 30 deg, N=10 at 35 deg). Passive (0% MVC activity level) ankle joint torque data were also captured by moving the ankle between −10 and 35 deg at 1 deg s⁻¹ for five full cycles, and torque data from the last two rotations were averaged. Passive levels were confirmed by visual inspection of EMG traces during rotations.

Participants performed contractions from the lowest to highest activity levels (22, 30 and 100% MVC) and the order of joint angles within each activity level was randomized. This procedure was selected to minimize the effects of fatigue from the 100% MVCs. Contractions lasted 6 to 10 s for 100% MVCs and submaximal contractions, respectively. Participants received at least 3 min of rest between 100% MVCs, at least 30 s of rest between submaximal contractions, and 5 min of rest between the activity level conditions. More time was given if requested by the participant. To monitor fatigue, periodic 100% MVCs at a 0 deg ankle angle were measured and testing was concluded if torque was <90% of the initial 100% MVC. All torque data were normalized to 100% MVC at peak angle torque. Each condition was repeated twice and averaged, unless the two torque values were >5% different (with successful EMG matching), which resulted in a third measurement and an average being taken.

Active torque– and force–ankle angle, and active torque– and force–fascicle length relationships (for soleus and LG) were created from each participant's dataset at each activity level. Each data point during contraction was the average of the last 3 s of the steady-state torque phase. During the 22 and 30% MVC activity levels, subjects produced a steady-state torque and activity level after ∼5 s from the start of the contraction. At 100% MVC, participants reached a steady-state torque within ∼1 s.

The calculation of active ankle joint torque from net ankle joint torque was done by considering changes in passive joint torque caused by fascicle shortening during activation (Figs S2–S4). The assumption is often made that the active torque produced during a fixed-end contraction is correctly measured if the peak-to-peak amplitude is calculated (i.e. the change in passive torque at the tested joint angle to the maximum torque obtained during contraction), but this method will underestimate active torque production when the muscle of interest generates passive force at the tested joint angle. This is because the peak-to-peak calculation does not account for shortening of the parallel elastic component during contraction, as already described eloquently by others (Hoffman et al., 2012; Hoffman et al., 2014; MacIntosh, 2017; MacIntosh and MacNaughton, 2005; Rode et al., 2009; Siebert et al., 2008). Briefly, while fixed-end contractions induce some measurable MTU shortening owing to joint rotation, even if this shortening is accounted for muscle fascicles still considerably shorten while the in-series elastic tissues lengthen during muscle activation. The correct passive torque to subtract from the maximum measured torque during contraction should thus be measured at the same fascicle length as that achieved during contraction (MacIntosh and MacNaughton, 2005). Because triceps surae muscle fascicles shorten during plantar flexor activation, when passive torque is present it will be less during activation compared with the passive torque at the same MTU length (MacIntosh and MacNaughton, 2005). Therefore, using the traditional method of calculating active torque (i.e. total torque–passive torque at a specific joint angle) will underestimate active torque, and this underestimation may increase when higher passive torques are present at rest or when muscle fascicles shorten more due to increases in muscle activity at the same joint angle. To achieve accurate active torque estimates that account for shortening of the parallel elastic component during contraction, we calculated active torque as the difference between the total torque during the contraction (i.e. peak torque at a given ankle joint angle) and the passive torque measured at the same fascicle length as that achieved during contraction at peak torque (Fig. S2). This approach has been used previously to construct in vivo active force–length curves of the human MG following supramaximal single electrical percutaneous stimulations of the tibial nerve (Hoffman et al., 2012; Hoffman et al., 2016). We provide examples of how much relationships can change between methods in Figs S3 and S4, which show the torque–ankle angle and torque–fascicle length relationships constructed using both the traditional and corrected methods of calculating active ankle joint torque. The approach is reliable and consistent across experimental sessions (Hoffman et al., 2012). Outside of human muscle, others (MacIntosh and MacNaughton, 2005; Rode et al., 2009; Siebert et al., 2008) have found that this corrected method used to construct torque–fascicle length curves more appropriately describes the force–length relationships of animal muscles (rats and cats) with high in-series compliance.

From each passive trial, the calculated active torques and fascicle lengths produced at −10 (PF), −5, 0, 5, 10, 15, 20, 25, 30 and 35 deg (DF) were recorded from passive ankle angle rotations from −35 to 35 deg, to establish the passive torque–fascicle length relationship. Next, the net ankle joint torque and fascicle lengths were measured during contraction at the desired muscle activity levels. For each trial and joint angle, soleus fascicle length at peak ankle joint torque during contraction was compared with the same fascicle length during the passive rotation. The passive ankle joint torque at this matched fascicle length was then subtracted from the peak ankle joint torque during contraction to give the corrected active torque.

We next used the torque and ankle angle data to estimate (plantar flexor) force–angle, and force–fascicle length relationships. It is important to consider that converting ankle joint torque into plantar flexor force requires several participant-specific parameters to estimate the moment arm at each ankle angle and contraction intensity (Holzer et al., 2020; Maganaris, 2004). We were not able to collect angle-specific moment arms from each participant, and therefore pulled averaged parameter data from the literature. Because relatively different moment arm–ankle angle relationships have been reported and vary widely (Holzer et al., 2020), we present plantar flexor force estimates using three possible relationships: two separate relationships reported by Rubenson et al. (2012) (referred to as force estimates 1 and 2), and one relationship reported by Maganaris (2004) (referred to as force estimate 3). Extrapolation of these papers’ moment arm functions was necessary because moment arms are not available at all of the ankle angles we studied.

Finally, active torque– and force–ankle angle, and active torque– and force–fascicle length relationships were normalized to the maximum torque produced across all ankle angles at 100% MVC and plotted for all participants, and then a second-order polynomial equation was fitted for each activity level (Hessel et al., 2019). We used these equations to estimate optimal ankle angle and optimal soleus and LG fascicle lengths for producing maximum plantar flexion torque and force.

To compare torque, force and EMG at different activity levels and angles, for each muscle, we designed a full-factorial, two-way ANOVA with fixed effects for activity level (100, 30 and 22%) and ankle angle (−10, 0, 5, 10, 15, 20, 25, 30 and 35 deg), and a random effect for each individual. Response parameters included torque and soleus/LG/MG activity levels. To compare the interaction between ankle angle, muscle activity level and fascicle length on plantar flexor torque and force, we added a fascicle length covariate to our ANOVA model above, with a response parameter of ankle torque/force. Alpha values were set at 0.05 and assumptions of normality and homogeneity of variance were evaluated using the Shapiro–Wilk test of normality and Levene's test for equality of variances. A best Box–Cox transformation was used for all data sets to meet assumptions, when necessary. When model effects were significant, a post hoc Tukey’s honestly significant difference (HSD) all-pairwise comparison analysis was used to test for differences among group means. Data are presented as means±s.e.m. All fitted lines on graphs show 95% confidence intervals of the fit. Statistical analysis was conducted using JMP (JMP Pro 12.2, SAS Institute, Cary, NC, USA).

Soleus EMG amplitudes for the 22% and 30% conditions were successfully matched by all participants (Fig. 2A, Table 1). At all angles, 95% confidence intervals of the mean covered the target value and the s.e.m. at each angle was <1% EMG amplitude. MG and LG (Fig. 2A) activity followed soleus activity closely at the 22 and 30% activity levels. For all three muscles, the mean activity was significantly different between the 22 and 30% activity levels (Tukey’s HSD test, P<0.05), but not among ankle angles (angle × activity level interaction, P<0.05; followed by Tukey’s HSD analysis). At each ankle angle, soleus, MG and LG muscles during the 100% activity condition (i.e. 100% MVC) produced significantly more variation in muscle activities than their corresponding 30 or 22% conditions. Notably, the largest group level variation in EMG amplitude was produced at −10 deg by MG and LG (as indicated by Levene's test, P<0.01; followed by post hoc Tukey’s HSD test, P<0.05 on s.d.). Most subjects reported that the 100% MVC contraction at −10 deg was uncomfortable because they felt as if their triceps surae muscles would cramp, so it is possible that this played a role. Furthermore, because of increased tendon compliance and increase fascicle shortening at this plantar flexed angle (Hug et al., 2013), the relationship between the position of the surface EMG electrodes and muscle could have substantially changed, contributing to the greater EMG amplitude variability.

Soleus and LG fascicle lengths (Fig. 2B; Table 2) showed similar trends, with increasing lengths as the ankle moved towards more dorsiflexed positions, and decreasing lengths as triceps surae muscle activity levels increased. During fixed-end contractions, soleus fascicles shortened on average 20.6, 25.7 and 34.0% of their passive length for the 22, 30 and 100% activity levels, respectively. LG fascicles shortened on average 21.6, 23.5 and 28.6% of their passive length for the 22, 30 and 100% activity levels, respectively. For both muscles, 100 and 0% activity levels produced the shortest and longest fascicles, respectively (Tukey’s HSD test, P<0.05). Despite a consistent decrease in LG fascicle lengths from the 22 to 30% activity level at all ankle angles, only soleus fascicle lengths significantly decreased from 22 to 30% activity (Tukey’s HSD test, P<0.05). Absolute soleus and LG fascicle lengths are shown in Fig. S1.

The 100% MVC activity level produced a typical torque–angle relationship, with a long ascending limb and peak active torque being produced at an estimated optimal ankle angle of ∼25 deg (vertical line in Fig. 3). Net ankle joint torque decreased with decreasing muscle activity levels at all ankle angles (Tukey’s HSD test, P<0.05; Fig. 3; Table 2). At peak torque across ankle angles from the submaximal activity levels, 22 and 30% MVC produced ∼48 and ∼56% of the 100% MVC torque, respectively. Also, the torque produced at 22 or 30% MVC muscle activity levels was a larger proportion of the joint angle specific torque at 100% MVC as the ankle became more plantar flexed (Tukey’s HSD test, P<0.05; Fig. 3; Table 2).

The statistical analysis indicated that torque values between ankle angles of 20 and 30 deg were not different (note: individual variation taken into account, see the Materials and Methods), indicating a 10 deg-wide plateau region at 100% MVC and a short descending limb. For the 22 and 30% MVC activity levels, there was no statistical difference between 25 and 35 deg, indicating a ∼10 deg-wide plateau region of the torque–angle relationship and no descending limb. Although it is clear that decreasing activity levels shifted the optimal ankle angle to more dorsiflexed positions via qualitative evaluation of the data, because no statistically significant descending limb of the torque–ankle angle relationship was found for the 22 and 30% activity levels, the exact locations of the optimal ankle angles could not be determined for the submaximal activity levels.

Similar to the torque–ankle angle curves, the 100% MVC activity level produced a torque–fascicle length relationship with a long ascending limb, plateau region, and short descending limb. For both soleus and LG (Fig. 3), decreasing their activity level increased their fascicle lengths at a specific ankle angle (Tukey’s HSD test, P<0.05; Fig. 3, Table 3, Fig. S5). In general, the shape of the torque–fascicle length relationship covered a smaller fascicle length range for the LG than for the soleus, but the trends observed for decreasing activity levels were similar. In contrast to the 100% MVC condition, the submaximal activity levels displayed only an ascending limb and a plateau region, but no descending limb of the torque–fascicle length relationships was observed (i.e. no statistical drop in torque with increasing fascicle length). Thus, for both soleus and LG, we could not generate a condition that resulted in measurements on the descending limb at either submaximal activity level. Qualitatively, based on the shape of the torque–length curves (Fig. 3), there was a rightwards shift of optimal soleus and LG fascicle lengths, but it is quantitatively unclear how big this shift was.

For both soleus and LG muscles, the ascending limb extended to longer fascicle lengths during the 22% MVC compared with the 30% MVC activity level. This qualitative observation suggests a general shift of the 22% activity level curve towards longer fascicle lengths compared with the 30% MVC condition. Based on these data, decreasing activity level changes the torque–fascicle length relationship for both soleus and LG. Finally, if we consider the shift of the torque–fascicle length relationship at each ankle angle, the shift was greater at more plantar flexed angles (Fig. S5). For example, fascicle length was shifted to ∼10 and 20% longer fascicle lengths at ankle angles of 0 and −10 deg, respectively.

The 100% MVC activity level produced similar force–angle relationships from all three force estimates. Compared with torque–ankle angle relationships, force–ankle relationships are more right-shifted towards dorsiflexed angles, with no noticeable descending limb for force estimate 3, and no descending limb or plateau region for force estimates 1 and 2 (Fig. 3, Table 2). Compared with the 100% MVC force–ankle angle relationship, all submaximal force estimates had a leftward-shifted curve towards more plantar flexed angles (Fig. 3). Active force decreased with decreasing muscle activity levels at all ankle angles (Tukey’s HSD test, P<0.05; Fig. 3, Table 2). However, no statistically significant descending limb of the force–ankle angle relationship was found for the 22 and 30% activity levels (no difference between these ankle angles with Tukey’s HSD analysis). Therefore, although it is clear that decreasing activity levels shifted the optimal ankle angle to more dorsiflexed positions, as with the torque–angle relationship, the exact position of optimal length should be viewed with some restraint, and may be more dorsiflexed than suggested by the fits here.

In comparison with the torque–fascicle length curves, soleus and LG force–fascicle length relationships are rightward shifted towards longer fascicle lengths (Fig. 3). For both soleus and LG (Fig. 3), decreasing their activity level increased their fascicle lengths at a specific ankle angle (Tukey’s HSD test, P<0.05; Fig. 3, Table 3). Notably, the 22 and 30% MVC curves are separate, but their shape is similar, with neither showing a descending limb, and only force estimate 3 suggesting submaximal plateau regions (Tukey’s HSD analysis of interaction, P<0.05; Fig. 3, Table 3). As can be seen from the curves produced by the three different force estimates, the exact locations of these optimal lengths will depend on the force-dependent subject-specific moment arms (Holzer et al., 2020), and so, while the trends are clear, the exact magnitude of the shift is unclear and will need to be individually determined in the future.

The objective of this study was to evaluate the torque– and force–fascicle length relationships between 100% MVC and two slightly different submaximal activity levels in the soleus and LG during fixed-end contractions. Our results indicate that compared with 100% MVC, activity levels of 30 and 22% MVC shifts the ankle joint torque– and force–angle and torque– and force–fascicle length relationships towards more dorsiflexed ankle angles and longer fascicle lengths. Furthermore, this trend is also present during the small activity level reduction from 30 to 22% MVC.

During 100% MVC, our constructed torque–fascicle length curves show that both soleus and LG fascicles achieved an ascending limb, a plateau region with an optimal fascicle length at ∼25 deg, and a descending limb. Several previous studies have built torque–fascicle length or torque–ankle angle relationships of the plantar flexors from 100% MVC (Anderson et al., 2007, ankle angle range: 40 deg PF to 20 deg DF; Kawakami et al., 1998, range: 30 deg PF to 15 deg DF; Sale et al., 1982, range: 30 deg PF to 20 deg DF) or other maximal contraction means (Hoffman et al., 2012, supramaximal peripheral nerve twitch stimulation, range: 0 deg DF to 20 deg DF; Maganaris, 2001, percutaneous tetanic electrical stimulation, range: 45 deg PF to 30 deg DF). The observed relationships of these studies line up well when overlapped with our tested ankle angle range (10 deg PF to 35 deg DF), indicating that during relatively strong contractions, the plantar flexors reside predominantly on the ascending limb of the torque–angle and the torque–fascicle length relationships, and only achieve a plateau region and perhaps a small descending limb at the most dorsiflexed positions.

Our results indicate that submaximal voluntary muscle contractions produce different torque–ankle angle and torque–fascicle length curves compared with the curves obtained during 100% MVC. We found that even small differences in the voluntary submaximal muscle activity levels change the shape of the torque–ankle angle and torque–fascicle length relationships, with the curves shifting towards more dorsiflexed ankle positions and longer fascicle lengths with an 8% MVC reduction in activity level, respectively. Strikingly, at the soleus EMG-matched 22 and 30% MVC activity levels, we could not generate physiological conditions that resulted in a descending limb of the torque–fascicle length curve. In comparison, Sale et al. (1982) used electrical stimulation to elicit submaximal contractions (10 Hz stimulations, ∼34% MVC at 5 deg PF) to compare against a 100% MVC torque–ankle angle relationship. Similar to our study, they report that, while the 100% MVC relationship included an ascending limb, plateau region and descending limb, the submaximal electrical contractions produced a shift of the relationship towards more dorsiflexed angles, with only the development of the plateau region at the most dorsiflexed position of 20 deg ankle angle. Notably, Sale et al. (1982) found that the plateau regions of the 100% MVC and 10 Hz activation strategies occurred ∼10 deg more plantar flexed than in our study, the reason for which is unclear but may be related to the differences in testing apparatus or strategy. It would be informative for future experiments to compare 100% MVC matched voluntary and electrical stimulation torque–ankle angle and torque–fascicle length relationships within participants.

In comparison with torque-derived curves, estimated plantar flexor force–fascicle length curves were shifted towards more dorsiflexed ankle angles and longer fascicle lengths. Based on the fitted curves to the graphs and 95% confidence intervals of these fits, we observed that the soleus and LG exhibit activation dependence of optimal fascicle length: decreasing activity level increased soleus and LG optimal fascicle lengths. The underlying mechanism to explain this phenomenon is a current focus of research (Holt and Williams, 2018; MacIntosh, 2017). Activation dependence of optimal length, often called length-dependent activation, is an umbrella term that covers subcellular and MTU level mechanisms that are not necessarily mutually exclusive (Holt and Williams, 2018). The first mechanism is subcellular in nature and often observed in in vitro muscle preparations, where at a given level of submaximal Ca²⁺, more force is produced than expected by the myofilament overlap (Hessel et al., 2019; Stephenson and Williams, 1982; Yang et al., 1998). However, in vivo, fibers are thought, but not empirically known, to always release a supramaximal level of calcium when stimulated and thus this molecular mechanism may not be physiologically relevant (Bakker et al., 2017).

The dominant mechanism responsible for MTU length-dependent activation is associated with compliance (Holt and Williams, 2018; MacIntosh, 2017; Zajac, 1989). As activity level increases, muscle fascicles are shorter at the same joint angle (and MTU length) because of in-series compliance (Zajac, 1989). This implies that muscles with substantial in-series compliance can operate at different lengths at the same joint angles by simply changing muscle activity level. This activity-dependent change in fascicle length could potentially increase or decrease force capacity, depending on the initial position on the force–fascicle length curve (e.g. moving from the plateau to ascending limb would decrease muscle force capacity by at least 15%). The overall result for our study is that reduced activity levels lead to a shift in the optimal ankle angle and optimal fascicle length towards more dorsiflexed ankle angles (and MTU lengths) and longer fascicle lengths, respectively.

To evaluate where fascicles typically operate on the force–length curve during movement, Rubenson et al. (2012) overlaid fascicle lengths produced during walking on top of a force–length relationship built from 100% MVCs. From these data, they found that fascicle operating length is on the ascending limb or plateau region of the force–length relationship. With updated information on the shift of optimal fascicle length to longer lengths with decreasing muscle activity, we replicated this overlay with our three estimates of plantar flexor force–fascicle length curves (Fig. 3, arrows). For this, we used mean soleus fascicle length data from several literature reports of healthy, steady-state walking at or close to preferred speed (Cronin et al., 2013; Ishikawa et al., 2005; Rubenson et al., 2012). This comparison (see Fig. 3) suggests that soleus fascicles operate exclusively on the ascending limb of the force–length curve during walking.

Outside of more traditional studies, similar overlays of fascicle operating lengths have also been done when evaluating assistive lower limb devices. For example, wearing a lower limb assistive exoskeleton reduces soleus force requirements and can lower soleus muscle activity level by relatively small amounts (Collins et al., 2015). A recent study used ultrasound to measure the operating range of soleus fascicles during lower limb exoskeleton use, and found that reduced muscle activation leads to a shift of the fascicle operating range to longer operating lengths (Nuckols et al., 2020). When superimposed over the traditional 100% MVC force–length curve, it seems that the fascicles move from the ascending limb (no exoskeleton assistance) to nearly the plateau region, suggesting a maximization of force production. However, using a more appropriate and right-shifted submaximal force–fascicle length curve, the fascicle length operating range moves only slightly up the ascending limb – still an improvement in achieving maximal possible force, but not as great as previously considered. In comparison with these studies of walking versus studies using dynamometers, an important limitation should be considered: during level-ground walking, almost no fascicle shortening (but perhaps some lengthening) occurs during the stance phase where muscle activity is largest (Ishikawa et al., 2005; Rubenson et al., 2012). However, there is initial shortening during fixed-end contractions in a dynamometer that do affect force production (Mayfield et al., 2016a; Mayfield et al., 2016b) and this should be taken into account (Raiteri and Hahn, 2019). Nevertheless, these comparisons suggest that walking does not typically utilize muscle fascicles at their optimal lengths, but that optimal efficiency is still achieved through other complex neuromuscular interactions (McDonald et al., 2019) and limb design (Holowka and Lieberman, 2018).

Why would the operating fascicle lengths during walking reside on the ascending limb of the force–length relationship and thus limit force capacity? One idea comes from Holt and Azizi (2016), who provided a comparison of in vivo operating lengths and velocities to optimum lengths and velocities across activation levels, specifically during frog jumps of various distances. From this study, muscles apparently optimized for jumping do not appear to always operate optimally in vivo, and instead are tuned to maximize performance when demand is greatest, in this case, the longest jumps. This is a necessary trade-off due to the intrinsic properties of the muscle. This may also be true during human movement. For example, running EMG levels are often closer to ∼60% of soleus MVC, which shifts the force–length curve towards shorter fascicle lengths (compared with the lower muscle activity levels of walking), potentially bringing operating fascicle lengths towards the plateau of the relationship, thus maximizing fascicle force potential when need is greatest. It would be interesting to compare the walking, running and sprinting operating fascicle lengths of the lower limbs to EMG-matched force–length curves constructed from similar experimental designs as that used here, to see if the ideas of Holt and Azizi (2016) are generalizable to human locomotion.

Unlike the soleus, the LG is biarticular and so its fascicle length is affected by both ankle and knee angles. In this study, we maintained a constant knee angle. Another study that systematically changes the knee angle is needed to understand the role of knee angle on the torque–fascicle length relationships during plantar flexion. On a similar note, more muscle activity levels will be needed to determine if the shift in optimal fascicle length with changing muscle activity levels is linear throughout all possible activity levels.

We did not measure the fascicle lengths of the MG because we only had access to one ultrasound transducer. Finally, we did not separate fascicle forces of individual soleus and LG parts because of the inherent difficulties in estimating (1) force contributions from individual muscles to the net joint torque at different muscle activities and ankle angles, and (2) accurate and representative pennation angles from each muscle to estimate muscle force from tendon force, which is especially important for muscles like the soleus. This is because the soleus has a resting pennation angle of 30 deg at 20 deg plantar flexion, but this can vary by 12 deg between compartments (Bolsterlee et al., 2018).

We thank T. Weingarten for help with the experimental set-up, A. Good for the set-up cartoon in Fig. 1, and N. Tillin for fruitful discussions on earlier versions of the manuscript.