20 healthy, recreationally active participants (17 males, 3 females, 24 ± 3 years, 75 ± 11 kg, 177 ± 7 cm) completed the experimental protocol. The participants were recreationally-trained runners. The inclusion criteria were that the participants were between 18 and 50 years old, could achieve a steady-state in oxygen uptake (V̇O₂) during a 10-min run at the required speed of 2.5 m · s⁻¹, and had no lower leg injuries within the last 6 months. We aimed to recruit a diverse group of participants to have a wide range of both E_run and AT_MA. The participants gave their informed written consent to participate in the experimental protocol which was approved by the Mount Royal University Human Research Ethics Board (HREB ID #102674).

The participants visited the lab on a single occasion. Each participant’s AT_MA was estimated using the tendon excursion method, accounting for passive forces (44). The participants laid prone on a dynamometer (Biodex Medical Systems Inc., Shirley, NY, USA) with their right knee fully extended. The shank and unshod right foot were affixed to the dynamometer using Velcro straps, with the ankle at 90°. Ankle angle was defined as the angle of the foot relative to the long axis of the shank. Briefly, the ankle was passively rotated at 0.1745 rad · s⁻¹ through the participant’s voluntary range of motion. A 12.5 MHz linear array B-mode ultrasound probe (65 mm, LV8-4L65S-3, MicrUS EXT-1H, Telemed, Vilnius, Lithuania) was used to visualize the medial gastrocnemius (MG) myotendinous junction (MTJ). Ultrasound images were recorded at 39 Hz. The displacement of the MTJ was tracked from 85° to 95°, using ImageJ (v.2.3.0/1.53s, NIH, Baltimore MD USA). AT moment arm was calculated as the ratio of MTJ displacement (in mm) to ankle joint rotation (in radians). The bias and limits of agreement compared to the caliper method for the tendon travel method, previously reported by Fletcher and MacIntosh (44) are 0.1 and 1.5 mm, respectively. The intraclass correlation coefficient for test-retest reliability has previously been reported to be r = 0.88 (44).

Since the inter-individual variation in body height was large, and a significant relationship was seen between AT_MA and body height (see results), AT_MA was normalized to body height as described previously by Scholz et al. (14) and we present both absolute and height-normalized AT_MA where appropriate.

Following this, participants ran at a speed of 2.5 m · s⁻¹ on a motorized treadmill (Woodway Pro, Woodway USA, Waukeshka, WA) for 10 min. During the run, expired V̇O₂ and V̇CO₂ were measured to quantify E_run using a metabolic cart (Quark CPET, Cosmed, Rome, Italy) according to Fletcher et al. (45) and expressed an energy cost (J · kg⁻¹ · m⁻¹) as it is a more sensitive and reliable assessment of running economy compared to the measurement of steady-state V̇O₂ alone (46–48). Prior to each testing session, the metabolic cart was calibrated using room air and a gas mixture of known composition (5% CO₂% and 16% O₂). The flow sensor was calibrated manually with a 3l syringe. Muscle-fascicle dynamics were calculated from ultrasonography and inverse dynamics during the last minute of the 10-min run, and the middle 10 consecutive steps were identified and used for further analyses. Expired gases were collected for the entire duration of the run. All participants achieved a steady-state V̇O₂ (defined as a change of <200 ml/min for any 15s period during the last 2 min of the run. The average V̇O₂ and V̇CO₂ over the last 3 min were used to calculate E_run.

E_run (J · kg⁻¹ · m⁻¹) was calculated from the average V̇O₂ and V̇CO₂ over the final 3 min of the run from the metabolic equation presented by Peronnet and Massicotte (49), which expresses the rate of energy expenditure in kJ · s⁻¹. We then expressed this rate of energy expenditure as a relative energy cost per unit distance (J · kg⁻¹ · m⁻¹):Erun(J⋅kg−1⋅m−1)=16.89V˙O2+4.84V˙CO2xBM−1xs−1×1000where V˙O₂ and V˙CO₂ is in L · s⁻¹, BM is body mass (in kg), s is speed (in m · s⁻¹) and 1,000 J · kJ⁻¹

The MG muscle fascicle of the right leg was imaged using a second 12.5 MHz linear array B-mode ultrasound probe (60 mm, LV8-5N60-A2, ArtUs EXT-1H, Telemed, Vilnius, Lithuania) at a sampling frequency of 70 Hz. The MG muscle was chosen over other triceps surae muscles because Lai et al. (37) showed that MG muscle fascicle length changes during the stance phase of running were the largest of the triceps surae muscles.

The MG fascicle lengths and MTJ shortening/elongation were measured manually using ImageJ from the respective ultrasound images during the stance phase. Fascicle and AT length change, velocity, work and power were calculated at each 5% of stance for the entire stance phase and averaged over 10 consecutive stance phases. To correct for AT shortening and lengthening as a result of changes in ankle joint angle, ankle angle was measured using a high-speed video camera (Ziqian, N5 1080p Webcam, 50 Hz). Ankle angle was measured at each instance during stance using Tracker (v. 6.0.8, Open Source Physics, Compadre.org/osp). AT length change due to ankle joint rotation (in mm) during the stance phase was calculated from the ankle joint change (in radians) and the measured AT moment arm length (in mm), a derivation of the equation to calculate AT moment arm from the tendon excursion method (44, 50). Instantaneous tendon length was estimated by subtracting the measured MG fascicle length, taking the effect of muscle pennation angle into account (51).

Vertical ground reaction forces of the right foot were measured using a commercially available instrumented insole (Loadsol, Novel.de, St Paul MN USA), collected at 100 Hz during the last minute of the run. These insoles have been shown to be reliable and valid compared to inverse dynamics, at a significantly reduced cost. Specifically, Hullfish and Baxter (40) showed peak plantarflexion moment to be on average 5.4% higher using the insoles compared to inverse dynamics using marker-based motion capture and a force-measuring treadmill; however, the 95% CI for the difference between the two measurements included 0% difference. Data were saved to a smart device (iPad mini-4, Apple Inc. Cupertino CA) for subsequently analyzed according to Hullfish and Baxter (40).

Plantarflexion moment during the stance phase was calculated according to Hullfish and Baxter (40). The force insole has three force sensing zones, which we treated as discrete one-dimensional force plates, assuming the measured ground reaction forces were orthogonally directed and in the middle of each force-sensing zone. The geometric centres of pressure of each force-sensing zone were measured using digital calipers (Mastercraft Tool Co, Earth City, MO) to the nearest 0.02 mm. the reported accuracy of the calipers. The moment arms of each zones were then calculated by subtracting the distance between the posterior sensor and the ankle joint. We then calculated sagittal plane plantar flexion moment as the sum of the products of each zone moment arm and the applied load (40). AT force was calculated from the calculated plantarflexion moment divided by the measured AT_MA. MG force was estimated based on the relative physiological cross-sectional area of all ankle plantarflexors (0.1746, 52) divided by the cosine of the measured pennation angle of the MG muscle fascicle. The foot lever ratio was determined as the length of the forefoot, divided by the AT_MA length (31). Mechanical work performed by the MG and AT, respectively, was calculated as the integral of fascicle (or tendon) force and length change over the entire stance phase. Positive fascicle work was considered fascicle shortening. AT positive work, a measure of AT strain energy storage, was calculated by integrating the AT force over the measured AT elongation, omitting elongations below the length at heelstrike, in order to quantify AT energy storage/return during the stance phase alone (39).

Three wireless electromyography (EMG) sensors (Delsys Trigno, Natick Massachusetts, USA) were placed on the participants’ right lower leg, using double-sided stickers, along the presumed fascicle angle according to SENIAM guidelines (53). The sensors have four 1 mm x 5 mm parallel bars (contacts), of 99.9% silver with a fixed inter-electrode distance of 10 mm. These sensors were located on the lateral gastrocnemius (LG), soleus (SOL), and tibialis anterior (TA). EMG signals were collected at 2,048 Hz during the last 2 min of each trial. To reduce noise and signal artifact, the signal was filtered through a 5th order Butterworth filter (high and low pass filter of 20 and 500 Hz, respectively). EMG amplitude was calculated as the root mean square (RMS) of the raw, filtered EMG signal. This RMS was interpreted as the level of muscle activation during stance: a combination of motor unit recruitment and rate coding.

In order to compare the metabolic energy cost required to store elastic strain energy within the AT, the MG energy cost was calculated over the entire stance phase according to Fletcher and MacIntosh (20), which has been described in detail elsewhere (20, 54, 55). In brief, the metabolic cost of the MG during the stance phase was determined from the estimated number of in-parallel crossbridges that were needed to generate the measured MG force, the amount of crossbridge cycles to accommodate MG fascicle shortening and the amount of half-sarcomeres in series from the measured MG fascicle length. The estimated number of in-parallel crossbridges was derived from the MG force divided by the estimated force per crossbridge. The force per crossbridge decreases with increasing shortening velocity from a crossbridge force of 3 pN under near-isometric conditions (53) to 0 pN at maximal shortening velocity based on the linear sarcomere force-velocity relationship (57). Sarcomere shortening velocity (V) was calculated from the instantaneously measured fascicle shortening velocity throughout the stance phase and scaled to maximal shortening velocity (V_max). We assumed a maximal fascicle shortening velocity of 10.6 fascicle lengths · s⁻¹ which was calculated from the assumed maximal shortening velocities of Type I and Type II fibers of 4.4 fascicle lengths · s⁻¹and 16.8 fascicle lengths · s⁻¹ at physiological temperatures (38) and assuming the MG consisted of 50% Type I fibres (58). We expressed total muscle energy cost across the entire stance phase relative to body mass since E_run is determined primarily by the energy needed for muscle contraction of sufficient average force to support body weight for the full stride duration (7). Therefore, average muscle force and thus muscle energy cost is related to the average vertical force (Fz) during stance, as dictated by body mass and running speed and the Fz moment arm and the moment arm of the Achilles tendon (59, 60).

The muscle fascicle operating range on the force-velocity relationship (61), scaled to activation (8), was estimated from the measured fascicle shortening velocity (v) relative to maximal shortening velocity (V_max of 10.6 Lf · s⁻¹). The measured muscle fascicle force (P) was scaled to the maximal isometric force (P_o), the latter of which was measured during a maximal isometric voluntary contraction at 90° ankle angle, which is considered the short-side of the plateau region of the MG’s force-length relationship (62). The operating range of the muscle fascicles on the force-length relationship was assessed from the calculated fascicle force relative to maximum (P/P_o) and the estimated sarcomere length during stance. Estimated sarcomere length was calculated assuming a sarcomere length of 2.6 µm at the short side of the plateau region of the sarcomere force-length relationship (63). Sarcomere lengths during stance (L) were then estimated from the measured fascicle length change relative to the fascicle length measured during the maximal isometric contraction. This fascicle length was considered maximal optimal length (L_o) of 2.6 µm. Thus, sarcomere lengths during stance (L) could be calculated as the relative change in fascicle length at L_o to the measured fascicle length during stance since length change must be accommodated from changes in sarcomere lengths.

The number of half-sarcomeres in series was determined as the ratio of the measured fascicle length (in µm) to sarcomere length, assuming an optimal sarcomere length at maximal activation of 2.6 µm (63). Thus, this method allowed us to convert the measured fascicle lengths (in mm) to estimated sarcomere lengths (in µm). The number of crossbridge cycles during stance was determined from the measured MG fascicle length change during stance. We assumed that for each crossbridge cycle the filaments move 10 nm (64). We worked under the assumption that for each crossbridge cycle, one adenosine triphosphate (ATP) was consumed (65), and for each mol of ATP, 48 kJ of energy was released per mol ATP consumed (66).

Values are presented as mean ± standard deviation unless otherwise indicated. We classified individuals having “SHORT” (n = 11, 29.5 ± 1.9 mm) or “LONG” (n = 9, 36.6 ± 2.5 mm) AT_MA based on a bimodal distribution of AT_MA. Statistical analysis was performed using JASP (Version 0.16.2.0). Shapiro-Wilk tests were performed to test for normality and Levene’s tested for equality of variance of all dependent variables. Student Independent samples t-tests were utilized to determine differences between AT_MA, E_run, stance time and foot lever ratio between groups. Two-way repeated measures analysis of variance (ANOVA) for unequal sample sizes between groups (with Type III sum of squares to adjust for unequal sample sizes) was used to test effects of group on the dependent variables. A two-way repeated-measures ANOVA was used to test for differences in MG muscle energy cost at every 5% interval across the stance phase, with %stance as the repeated measures factor and group as the between subject factor. Similarly, three-way repeated measures ANOVAs for unequal sample sizes between groups (with adjusted Type III sum of squares) were also performed to test for differences in force-length (force × length × group) and force-velocity (force × velocity × group) relations between groups. Tukey’s post-hoc tests were used to detect significant differences between groups during stance based on dependent variables when there was no significant interaction but a significant simple main effect of group. The effect sizes were determined using Cohen’s d, with small, medium, and large sizes being d ≥ 0.2, d ≥ 0.5, d ≥ 0.8, respectively. The a priori level of significance was set at p < 0.05.

Our study is not without several limitations. We acknowledge that our results may only apply to recreationally-trained runners at one (relatively slow) running speed of 2.5 m · s⁻¹. Fletcher and MacIntosh (20) show that both muscle energy cost and AT strain energy return increase with speed, and we cannot discount that the relative contribution of AT strain energy may be more important at higher running speeds than the 2.5 m · s⁻¹ tested here (16); however, muscle energy cost also increases with running speed (20), since higher forces need to be generated at a faster rate, elevating the muscle and whole-body metabolic costs (7). Kovács et al. (27) also found that the relationship between AT_MA and E_run got stronger (longer AT_MA result in lower E_run) with an increase in running speed, so while we cannot speculate on the impact of faster or slower running speeds on the reported AT_MA vs. E_run, we would anticipate our results to be similar at faster running speeds: (1) that mechanical strain energy storage and return is lower than the muscle metabolic cost required to store that strain energy and (2) AT_MA is but one factor influencing the E_run (favorably or unfavorably).

We also chose to assess plantarflexion moments using a commercially-available insole, rather than the gold-standard inverse dynamics approach using marker-based motion capture while running on a force-plate embedded treadmill. These force insoles have recently been shown to be reliable and valid by our colleagues and are a fraction of the cost of inverse dynamics approaches (40). These authors have previously demonstrated that peak plantarflexion moment during running was 5.4% higher using these force insoles compared to the gold-standard; however the 95% CI for these data contained 0% error, suggesting the mean difference between methods was not significantly different (40). Together, we are confident that estimating muscle forces from joint moments using commercially-available insoles is both valid and reliable while being relatively low-cost and simple to implement in and outside of the laboratory.

Despite showing a significant group difference in the estimated muscle metabolic cost during the stance phase, we are unable to demonstrate significant group differences in whole-body E_run, although a moderate effect size (d = 0.53) was found. Based on this effect size, we would have required a post hoc sample size of n = 46 participants per group to demonstrate a statistical power >80%. We deemed this sample size too cost and time prohibitive and thus have reported the results found in 20 recreationally-trained runners (n = 9 and n = 11 per group, respectively). Perhaps with additional participants, we would be able to show a statistically significant negative relationship between AT_MA and E_run such that longer AT_MA can be associated with a lower whole-body energy cost of running. We also must acknowledge that the MG is but one of the triceps surae muscles representing a small proportion of the total triceps surae physiological cross-sectional area (∼17%, 52) so even large changes in muscle energy cost may not be reflected in whole-body metabolic cost. Future research should investigate muscle-specific energy cost of other muscles (for example those crossing the knee) in runners whose AT_MA differ in order to strengthen our understanding of how AT_MA might influence E_run directly.

Lastly, we must acknowledge that our measurement of the AT_MA was assessed using the tendon travel method, accounting for passive forces (44) at only one joint angle (i.e., at 90°). AT_MA is believed to change as function of joint angle (78–82), primarily as a result of calcaneal translation (83). However, when passive moments are correctly account for using the tendon travel method (44), or when AT_MA is determined from three-dimensional MR imaging (84), the AT_MA appears to remain constant across ankle angles. Despite these challenges, we did not see a significant group difference in ankle range of motion during the stance phase, nor differences in levels of muscle activation. If AT_MA does change with ankle angle and/or activation (84, 85), we presume these changes to be similar between groups. Importantly, previous studies examining the relationship between AT_MA and E_run, where AT_MA was also measured at a single (passive) joint angle, which was the basis for our comparison of the previously determined AT_MA vs. E_run relationships. While the tendon travel method generally underestimates AT_MA compared to sagittal plane MR imaging when passive forces are not accounted for (50), all AT_MA were measured by the same investigator, using the same tendon travel method and AT_MA was corrected for passive forces (44). The AT_MA reported here are similar to those previously reported (44, 81). We also specifically compared short AT_MA to relatively longer AT_MA across participants, and so absolute AT_MA should not have impacted our results or their interpretations.

The present study aimed to evaluate the relationship between AT_MA and E_run during submaximal running in recreationally trained runners. We have demonstrated that a longer AT_MA reduces the metabolic cost of triceps surae muscle contraction during stance. This reduction in muscle metabolic cost may translate to reductions in whole-body E_run; however, we did not show a relationship between muscle metabolic cost and whole-body E_run nor did we test whether reductions in muscle metabolic cost directly translated to a reductions in E_run on a participant-by-participant basis, the latter of which would have required systematic changes to each participant’s AT_MA, and/or foot lever ratio, which was beyond the scope of this cross-sectional investigation.

By measuring muscle and tendon dynamics and energetics during running, we were able to, quantify the magnitude of AT energy storage and return and directly compare that with the estimated muscle metabolic cost during stance. In so doing, we have strengthened the notion that a low E_run may be accomplished not from storage and return of elastic energy itself, but by keeping muscle metabolic cost low. This notion is emphasized by our present results showing longer AT_MA are associated with a reduced muscle metabolic cost without a meaningful reduction in AT energy storage and return. These results also contribute to the direct measurement of potential explanations for short (or long) AT_MA contributing to a low E_run, which until now have been largely theoretical.