Enthalpy efficiency of the soleus muscle explains improvements in running economy

During human running, the soleus, as the main plantar flexor muscle, generates the majority of the mechanical work through active shortening. The fraction of chemical energy that is converted into muscular work (i.e. the enthalpy efficiency) depends on the muscle shortening velocity. Here, we investigated the soleus muscle fascicle behavior during running with respect to the enthalpy efficiency as a mechanism that could explain previously reported improvements in running economy after exercise-induced increases of plantar flexor strength and Achilles tendon stiffness. Healthy amateur runners were randomly assigned to a control (n=10) or intervention group (n=13), which performed a specific 14-week muscle-tendon training. Significant increases in plantar flexor maximum strength (10%) and Achilles tendon stiffness (31%) yet reduced metabolic cost of running (4%) was found only in the intervention group (p<0.05). Following training, the soleus fascicle velocity profile throughout stance was altered, with the fascicles operating at a higher enthalpy efficiency during the phase of muscle-tendon unit lengthening (15%) and in average over stance (7%, p<0.05). These findings show that the improvements in energetic cost following increases in plantar flexor strength and Achilles tendon stiffness can be attributed to increased enthalpy efficiency of the operating soleus. This provides the first experimental evidence that the soleus enthalpy efficiency is a determinant of human running economy. Furthermore, the current results imply that the soleus energy production in the first part of the stance phase were the muscle-tendon unit is lengthening is crucial for the overall metabolic energy cost of running.


30
Habitual bipedalism has been recognized as a defining feature of humans [1] and an exceptional endurance running ability has been linked to the evolution of the human lineage [2][3][4]. Economy, which is the mass-specific rate of oxygen uptake or metabolic energy consumption at a given speed [5,6], plays a crucial role for endurance running performance [7]. The cost of generating force and work through muscles to support and accelerate the body mass is the main source of metabolic energy 35 expenditure during locomotion [8,9]. The force-length-velocity potential of muscles, defined as the fraction of maximum force according to the force-length [10] and force-velocity relationships [11], at which muscles operate during running [12,13] largely dictates the required active muscle volume and consequently the energetic cost of contraction [5,12,14].
In human running, the triceps surae is the major contributor to propulsion and the main plantar flexor muscle group that transmits force through the Achilles tendon (AT) [15,16], consuming a significant amount of metabolic energy [17]. In earlier studies, we provided evidence that both the contractile capacities of the triceps surae and the mechanical properties of the AT, i.e. its stiffness, influence running economy [18,19]. We found that the most economical runners feature a combination of higher 5 plantar flexor muscle strength and AT stiffness [18] and that a specific training of muscle strength and AT stiffness can in fact improve running economy [19]. Although the association of the AT stiffness and energetic cost of running has been confirmed by other research groups [20,21], the underlying physiological mechanisms are yet unclear.
The soleus is the greatest muscle of the triceps surae [22] and generates the majority of work/energy to 10 lift and accelerate the body [15] by actively shortening throughout the entire stance phase of running [12,23]. In the first part of the stance, the fascicle shortening is paralleled by a lengthening of the muscletendon unit (MTU) [12], indicating that a part of the body's mechanical energy is stored as strain energy in the AT, but also that the fascicles generate work and save this work as strain energy in the AT. In the second part of the stance phase, where the MTU shortens (propulsion phase), the tendon strain energy 15 is returned to the body and contributes to the ongoing work generation by active fascicle shortening [12].
The metabolic cost of generating work by active shortening of muscles depends on the velocity of the shortening [24]. The enthalpy efficiency (or mechanical efficiency) quantifies the fraction of chemical energy from ATP hydrolysis that is converted into mechanical muscular work [25]. The relation of enthalpy efficiency and shortening velocity shows a steep increase at low velocities with the peak at 20 around 20% of the maximum shortening velocity [25,26]. During submaximal running, the soleus operates below the optimal velocity for maximal efficiency [12], suggesting that small changes in the shortening velocity may substantially influence the enthalpy efficiency of the soleus muscular work production.
The mechanical interaction of the soleus muscle with the series AT regulates the fascicle shortening 25 dynamics. The AT takes over a great part of the length changes of the entire soleus MTU, thereby decoupling the muscle fascicle and MTU behavior and, besides the storage and release of strain energy, allowing the fascicles to operate at velocities favorable for economical force generation [12,23]. The mechanical properties of the tendon in combination with the strength capacity of the muscle may determine the amount of fascicle decoupling during the stance phase of running. However, similar to an 30 increase in muscle strength [27], tendons can adapt to periods of higher mechanical loading by increasing stiffness [28,29]. Our earlier findings of improved energetic cost after an exercise-induced increase in AT stiffness and muscle strength evidenced a direct association between a balanced adaptation of tendon and muscle and improvements in running economy [19]. Considering a given work produced by the soleus muscle during the stance phase of running, the energetic cost depends on the 35 enthalpy efficiency under which this muscular work is generated. Assuming that a combination of increased plantar flexor strength and AT stiffness may influence the soleus fascicle shortening pattern during the stance phase of running, the overall enthalpy efficiency might improve. This would provide an explaining mechanism to the previously reported improvements in running economy following an effective muscle-tendon training [19]. To the best of our knowledge, no study experimentally examined the operating soleus muscle fascicles with respect to the enthalpy efficiency and its association to the energetic cost of running.
Here, we investigated the effect of a specific muscle-tendon training, which has been shown to increase muscle strength of the plantar flexors as well as AT stiffness [19], on the enthalpy efficiency of the operating soleus fascicles during running. Based on our earlier study [19], we expected an improvement 5 in running economy after 14 weeks of training. We hypothesized that the training-induced increase in muscle strength and AT stiffness modulates the soleus fascicle velocity pattern throughout the stance phase towards velocities associated with a higher enthalpy efficiency of the operating soleus muscle, thereby reducing the energetic cost of running.

Participants and experimental design
A statistical power analysis was performed a priori to calculate the required sample size by means of the software G*Power (version 3.1.9.6, HHU Düsseldorf, Germany) [30]. For this purpose, we used the effect size of the rate of oxygen consumption from our previous intervention study with the same training 15 regimen (d = 1.04) [19]. Since the main outcome of interest was the effect of training, the power analysis was conducted for the post-hoc time point comparison for the intervention group considering a Bonferroni correction of the p-values (α = 0.025 (adjusted), power 0.8, two-tailed paired t-test). The analysis revealed a required sample size of n = 12 for the intervention group. Under consideration of potential dropouts, we recruited 36 participants and randomly assigned them to either an intervention (n 20 = 19) or control group (n = 17). Inclusion criteria were age 20 to 40 years, at least three times per week running training and no severe muscular-tendinous injuries in the previous year. Only habitual rearfootstriking runners were considered. To quantify the foot strike pattern, we assessed the strike index [31], a measure of the position of the center of pressure with respect to the heel relative to foot length at touchdown, during a pretest session. A strike index of 0 indicates extreme rearfoot striking and of 1 25 extreme forefoot striking, while <0.3 was set as the threshold for the study inclusion. Due to injuries (not related to the intervention) and time required for the assessment and/or training, 13 participants canceled their commitment. Twenty-three participants completed the intervention, 13 in the intervention group (age: 29 ± 5 years, height: 178 ± 8 cm, mass: 73 ± 8 kg, 4 female) and 10 in the control group (age: 31 ± 3 years, height: 175 ± 10 cm, mass: 70 ± 11 kg, 7 female). For the intervention group, the 30 same 14-week muscle-tendon training was added to the regular ongoing training habits as in our earlier study [19]. Before and after the intervention period, the maximal plantar flexion moment and AT stiffness as well as energetic cost of running at 2.5 m/s were assessed in both groups. In order to explain the expected improvements in running economy (i.e. energetic cost) following the muscle-tendon training, we experimentally determined a) the foot strike pattern and temporal gait parameters as well as b) the 35 soleus MTU and fascicle behavior in addition to the soleus electromyographic (EMG) activity during running. We further determined c) the soleus force-fascicle length relationship and force-fascicle velocity relationship in order to calculate the force-length and force-velocity potential of the fascicles during running (i.e. fraction of maximum force according to the force-length and force-velocity curve [12,13,32]) and assessed d) the efficiency-fascicle velocity relationship to calculate the efficiency of the soleus 40 during running. Because changes in running economy were not expected without any intervention [19], the assessment of the soleus fascicle behavior was not conducted in the control group. The ethics committee of the Humboldt-Universität zu Berlin approved the study and the participants gave written informed consent in accordance with the Declaration of Helsinki.

Exercise protocol 5
The supervised resistance training program was performed for 14 weeks and was charactarized by five sets per session of four repetitive isometric ankle plantarflexion contractions (3 s loading, 3 s relaxation) at 90% of the maximum voluntary contraction (MVC) strength (adjusted every two weeks), three to four times a week. The ankle joint was set to 5° dorsiflexion and the knee joint was fully extended. This loading regimen has been shown to provide a sufficient magnitude and duration of strain to promote AT 10 adaptation in addition to increases in muscle strength of the plantar flexors [19,29,33]. Online biofeedback of the strength effort was displayed to control the desired loading.

Strength of the plantar flexors and Achilles tendon stiffness
The strength of the plantar flexors of the right leg was measured before and after the 14 weeks in a 15 The resultant ankle joint moment was calculated using an established inverse dynamics approach to 20 account for misalignments between dynamometer and joint axis as well as passive and gravitational moments [34,35]. Furthermore, the contribution of the antagonistic muscles to the ankle joint moment was considered by means of an EMG-based method [36].
For the determination of AT stiffness, five ramp-MVCs with steadily increasing effort from rest to maximum under the same considerations (i.e. accounting for axis misalignment, passive and 25 gravitational moments and co-activation) were conducted at 0° ankle angle. The force applied to the AT was calculated as quotient of the joint moment and the individual tendon lever arm, which was determined using the tendon-excursion method [37,38] and corrected for tendon alignment during the contraction [39]. The corresponding AT elongation during the ramp MVCs was analyzed based on the displacement of the gastrocnemius medialis-myotendinous junction (MTJ) visualized by B-mode 30 ultrasonography captures (My Lab 60, Esaote, Genova, Italy, 25 Hz). The MTJ displacement artefacts due to an unavoidable change in the ankle joint angle during the MVCs was corrected [40] and the five contractions were averaged to give a reliable measure of the elongation [41]. The AT stiffness was calculated between 50% and 100% of the maximum tendon force using linear regression [29]. In order to calculate AT strain, the rest length was measured from the tuberositas calcanei to the MTJ at an ankle 35 angle of 110° (plantar flexed) and extended knee (i.e. a position that provides AT slackness [42]).

Energetic cost of running
During a 10-minute running trial on a treadmill (h/p cosmos mercury, Isny, Germany) at 2.5 m/s, a breathby-breath cardio pulmonary exercise testing system (MetaLyzer 3B-R2, CORTEX Biophysik GmbH, 40 Leipzig, Germany) recorded the percentage of concentration of oxygen and carbon dioxide expired.
Rate of oxygen consumption (V O2) and carbon dioxide production (V CO2) was calculated as average of the last three minutes [43]. Running economy was expressed in units of energy by: where the energetic cost is presented in [W/kg] and V O2 and V CO2 in [ml/s/kg] [6,44]. To reduce testretest variability [45], the shoes, time of testing and training activity during the previous 72 hours were 5 the same for the pre and post measurements. No food intake was allowed during the last 3 hours before testing.

Joint kinematics and foot strike pattern
During running, kinematics of the right leg were captured by a Vicon motion capture system (250 Hz) 10 using anatomical-referenced reflective markers (greater trochanter, lateral femoral epicondyle and malleolus, fifth metatarsal and calcaneus). The touchdown of the foot and the toe-off was determined from the kinematic data as consecutive minimum in knee joint angle over time [46].
The foot strike pattern was analyzed by means of the strike index [31] determined during the ten-minute running trial. A self-developed algorithm [47] was used to calculate the strike index from the plantar 15 pressure distribution (120 Hz) captured by the integrated pressure plate (FDM-THM-S, Zebris Medical GmbH, Isny, Germany).

Soleus muscle-tendon unit length changes, fascicle behavior and electromyographic activity during running 20
During an additional 3-minute running trial at the same speed, kinematics of the ankle joint served to calculate the length change of the soleus MTU as the product of ankle angle changes and the previously assessed individual AT lever arm [48]. The initial soleus MTU length was determined at neutral ankle joint angle based on the regression equation provided by Hawkins & Hull [49]. Ultrasonic images of the soleus muscle fascicles were obtained synchronously to the kinematic data at 146 Hz (Aloka Prosound  25 Alpha 7, Hitachi, Tokyo, Japan). The ultrasound probe (6 cm linear array, UST-5713T, 13.3 MHz) was mounted on the shank over the medial aspect of the soleus muscle belly using a custom antiskid neoprene-plastic cast. The fascicle length was post-processed from the ultrasound images using a selfdeveloped semi-automatic tracking algorithm [50] and corrections were made if necessary during visual inspection of each image. At least nine steps were analyzed for each participant and averaged [13,51]. 30 The velocities of MTU and fascicles were calculated as the first derivative of the lengths over the time.
Synchronized surface EMG of soleus was measured (1000 Hz) by means of a wireless EMG system (Myon m320RX, Myon AG, Baar, Switzerland). The EMG data are presented as normalized to the maximum EMG value observed from the individual MVCs [12].

Soleus force-length, force velocity and efficiency-velocity relationship
To determine the soleus force-fascicle length relationship (for details see [12]), the participants were placed in prone position on the bench of the dynamometer with the knee fixed in flexed position ( fig. 1) to restrict the contribution of the bi-articular muscle gastrocnemius to the plantar flexion moment (~120°) [52]. MVCs were performed with the right leg in eight different joint angles, equally distributed between 10° plantar flexion to the individual maximum dorsiflexion and executed in a randomized order. The joint moments were calculated using the approach described above. The force acting on the AT was calculated by dividing the joint moment by the previously determined AT lever arm. The corresponding soleus fascicle behavior during the MVCs was captured synchronously at 30 Hz by ultrasonography and fascicle length was measured as described above ( fig. 1). The ultrasound probe remained attached 5 between the running trial and MVCs. An individual force-fascicle length relationship was calculated by means of a second-order polynomial fit ( fig. 1), giving the individual maximum force and optimal fascicle length for force generation (L0).
The force-velocity relationship of the soleus was assessed using the classical Hill equation [11] and the muscle-specific maximum fascicle shortening velocity (Vmax) and constants of arel and brel. For Vmax we 10 took values of human soleus type 1 and 2 fibers measured in vitro at 15°C reported by Luden et al. [53].
The values were then adjusted for physiological temperature conditions (37 °C) using the temperature coefficients provided by Ranatunga [54]. An average fiber type distribution (type 1 fibers: 81%, type 2: 19%) of the human soleus muscle reported in literature [53,[55][56][57] was then the basis to calculate a representative value of Vmax of the soleus in vivo as 6.77 L0/s [12], were L0 refers to the individual 15 measured optimal fascicle length. arel was calculated as 0.1 + 0.4FT, where FT is the fast twitch fiber type percentage (see above), which then equals to 0.175 [58,59]. The product of arel and Vmax gives brel as 1.182 [60]. Based on the assessed force-length and force-velocity relationship, it was possible to calculate the individual force-length and force-velocity potential of the soleus muscle as a function of the fascicle operating length ( fig. 1) and velocity during running (i.e. force-length and force-velocity potential 20 as fraction of maximum force according to the force-length and force-velocity curve [12,13,32]).
Furthermore, we determined the enthalpy efficiency-shortening velocity relationship for the soleus muscle fascicles to calculate the enthalpy efficiency of the soleus muscle as a function of the fascicle operating velocity during running. For this purpose, we referred to the experimental efficiency values provided by the paper of Hill 1964 in table 1 [24]. The original values were presented as a function of 25 relative load (relative to maximum tension) which we then transposed to the shortening velocity (normalized to maximum shortening velocity) on the basis of the classical Hill equation [11]. The corresponding values of enthalpy efficiency and shortening velocity were then fitted using a cubic spline, giving the right-skewed parabolic-shaped curve with a peak efficiency of 0.45 at a velocity of 0.18 Vmax.
The resulting function was then used to calculate the efficiency of soleus during running. 30

Statistics
An analysis of variance for repeated measures was performed for the plantar flexion moment (normalized to body mass) and AT stiffness (normalized to resting length) as well as metabolic energy cost, foot strike index and temporal gait characteristics during running with the time point as the within-35 subjects factor (pre vs. post) and the group as a between-subjects factor (intervention vs control). The post-hoc analysis was conducted separately for each group considering a Benjamini-Hochberg correction (adjusted p-values reported). Normality of the standardized residuals was controlled using the Kolmogorov-Smirnov test with Lilliefors correction.
Anthropometric group differences as well as baseline differences of the plantar flexion moment, AT 40 stiffness and energetic cost were tested using a t-test for independent samples. A paired t-test was used to analyze the training effects on the assessed gait characteristics, kinematics and MTU and fascicle parameters. If normality tested by the Kolmogorov-Smirnov test was not given, the Wilcoxon signed rank test was applied. The level of significance was set to α = 0.05 and the statistical analyses were performed using SPSS (IBM Corp., version 22, NY, USA). Effect sizes (Hedges' g) in absolute values were calculated to assess the strength of the intervention effects, were 0.2 ≤ g < 0.5 indicate small, 0.5 5 ≤ g < 0.8 indicate medium, and g ≥ 0.8 indicate large effects [61].

Results
There were no significant differences in age (p = 0.421), body height (p = 0.361) and mass (p = 0.382) between intervention and control group. No baseline differences between groups were observed for the Following the training, the soleus force-velocity potential was significantly lower in the phase of MTU 40 lengthening (p = 0.030, g = 0.64) and significantly higher when the MTU shortened (p = 0.045, g = 0.58) with no significant difference over the entire stance (p = 0.249, g = 0.31, fig. 4). This was the consequence of a tendency towards higher fascicle shortening velocity during MTU lenthgening (pre 0.088 ± 0.054 Vmax, post 0.129 ± 0.061 Vmax, p = 0.073, g = 0.51) and a significantly lower velocity during MTU shortening after training (pre 0.174 ± 0.057 Vmax, post 0.127 ± 0.008 Vmax, p = 0.007, g = 0.83. Furthermore, the averaged EMG activation over the phase of MTU shortening (p = 0.028, g = 0.67) and 5 the entire stance phase of running was significantly reduced following the intervention (p = 0.017, g = 0.60, fig. 3 & fig. 4). Compared to pre-intervention running, the fascicle velocity in the phase of MTU lengthening was closer to the velocity for optimal enthalpy efficiency after the training (fig. 5).
Consequently, the fascicles operated at a significantly higher enthalpy efficiency in the phase of MTU lengthening after the training (p = 0.006, g = 0.85, fig. 5 & fig. 6), while there was no significant pre-post 10 difference in the phase of MTU shortening (p = 0.640, g = 0.12, fig. 6). Over the entire stance phase of running the enthalpy efficiency of the fascicle shortening was also significantly increased following the training (p = 0.025, g = 0.66, fig. 6).

15
Our current study showed for the first time that a specific muscle-tendon training that increases plantar flexor muscle strength and AT stiffness facilitates the enthalpy efficiency of the operating soleus muscle during the stance phase of running. The increased enthalpy efficiency was found in the first part of the stance phase where the soleus muscle produces work by active shortening and transfers muscular work to the tendon as strain energy. Furthermore, the results provide additional evidence that a combination 20 of greater plantar flexor muscle strength and Achilles tendon stiffness decrease the energy cost of running [18,43] and strongly indicate that the soleus enthalpy efficiency is the explaining determinant.
Following the intervention, the energetic cost of running was significantly reduced by about -4%. At the same time, the soleus, which is the main muscle for work/energy production during running [15,16], operated at a significantly increased (+7%) enthalpy efficiency throughout the stance phase. The 25 enthalpy efficiency quantifies the portion of energy from ATP hydrolysis used by a muscle that is converted into mechanical muscular work [25]. Enthalpy efficiency depends on the velocity of muscle shortening with a steep increase at low velocities until the peak at around 0.18 Vmax and again decreasing at higher shortening velocities [24,25]. For the whole stance phase, fascicle shortening, the force-length potential and the force-velocity potential of the soleus muscle was not significantly different 30 before and after the intervention, indicating a similar energy production through muscular work of the soleus muscle. During the propulsion phase of running (i.e. MTU shortening), where both tendon and muscle transfer energy/work to the skeleton [62,63], the enthalpy efficiency of the operating soleus muscle was high both pre and post intervention (94% and 93% of the maximum efficiency). In contrast, during the first part of the stance phase (i.e. MTU lengthening), where energy is transferred from the 35 contractile element to the tendon, the enthalpy efficiency was lower during pre-intervention running (77% of the maximum efficiency). The relevant part of the soleus fascicle shortening occurred during this first part of stance (59% of the entire shortening range). In combination with the high muscle activation (muscle activation was higher during MTU lengthening than during MTU shortening), this indicates an important energy production through muscular work during MTU lengthening. 40 The exercise-induced increase in muscle strength and AT stiffness resulted in an alteration of the operating fascicle velocity profile that led to a significant increase of the enthalpy efficiency of the operating soleus in the phase of MTU lengthening (88% of the maximum efficiency), improving the efficiency of muscular work production. The significant increase of the enthalpy efficiency following training in the phase of MTU lengthening demontrates that a substantial part of the entire muscular work 5 was generated more economically. In the second part of the stance phase, where the MTU shortened, the high efficiency was maintained after the intervention and, further, the fascicles operated at a significantly higher force-velocity potential. This was possible due to a shift of the shortening velocity around the plateau of the efficiency-velocity curve, from the descending part of the plateau before the training to the ascending part after training ( fig. 5), without a significant decline in the enthalpy efficiency. 10 Consequently, the overall enthalpy efficiency throughout the stance phase of each step during running was increased. Furthermore, the higher force-velocity potential in the phase of MTU shortening due to training was accompanied by a reduced soleus EMG activation. The overall EMG activity during the stance phase was significantly lower as well after the intervention. This may indicate that a less active soleus muscle volume was required during running, which could -in addition to the higher operating 15 enthalpy efficiency -reduce the metabolic energy cost [5,14,64].
Previous studies provided evidence that the cost of force to support the body mass and the time course of force application to the ground are the major determinants of the energetic cost of running [8,65,66].
According to the 'cost of generating force hypothesis' [8], the rate of metabolic energy consumption is directly related to the body mass and the time available to generate force, which results in a constant 20 cost coefficient (i.e. energy required per unit force). However, modifications in the muscle effective mechanical advantage (i.e. ratio of the muscle moment arm to the moment arm of the ground reaction force [67]) within the lower extremities can influence the cost coefficient of human locomotion [68,69].
In our study, the metabolic cost of running was reduced after the training without any changes in the contact time and body mass, indicating a decrease of the cost coefficient. The similar strike index and 25 lower leg kinematics before and after the intervention suggest unchanged effective mechanical advantages within the lower extremities and, therefore, this would not be the reason for the reduced cost coefficient. Instead, our findings show that an adjusted time course of the shortening velocity of the soleus muscle during the stance phase of running following the training can influence the cost coefficient as a result of increased enthalpy efficiency of the operating soleus and, thus, complement the earlier 30 studies on the mechanical advantage and cost coefficient interaction [66,67]. The observed continuous soleus fascicle shortening behavior during the stance phase of running in our study is in agreement with other in vivo experiments using the ultrasound methodology and comparable running speeds [23,[70][71][72]. The importance of the energy production by the plantar flexor muscles for the propulsion phase (i.e. shortening of the MTU) during running is well accepted [23,[73][74][75] because the mechanical power 35 produced at the ankle joint in this phase is highest and determines running performance [76][77][78]. Our current results regarding the enthalpy efficiency of muscular energy gain and running economy show for the first time that also the phase of the MTU lengthening is crucial for the overall metabolic energy consumption during running.
The findings of the current study provide further evidence [20,43] that a strength training of the plantar 40 flexors has the potential to improve running economy. We used a specific high intensity muscle-tendon training [28,29,33], targeting an adaptation of both AT stiffness and plantar flexor muscle strength [18,43], to maintain the functional integrity of the contractile and series-elastic element [79]. Strength increases without concomitant stiffening of the AT after a period of training may increase levels of operating and maximum AT strain [29,80], which have been associated with pathologies [81] but also possible functional decline [82,83]. In our study, the maximum AT strain during the MVCs was not 5 affected by the training (pre 6.2 ± 1.6%, post 6.0 ± 1.2%, p = 0.501) despite an increase in the muscle strength of the plantar flexors, indicating a balanced adaptation of muscle and tendon. Therefore, a specific muscle and tendon training [28,29,33] can be recommended to increase endurance performance and a specific diagnostic of muscle and tendon properties may allow tailoring the training to individual deficits of muscle strength or tendon stiffness [79]. 10 To assess the enthalpy efficiency-shortening velocity relationship, we used a biologically founded value of Vmax, i.e. 6.77 L0/s. However, during submaximal running, the lower activation level and selective slow fibre type recruitment may affect the actual enthalpy efficiency-shortening velocity relationship. Furthermore, differences in fibre type distribution may also affect the shape of the enthalpy efficiencyshortening velocity curve [26]. We evaluated the effect of a) decreasing and increasing Vmax by 10% 15 intervals and b) replacing the underlying enthalpy efficiency values from Hill (1964) [24] by the data presented by Barclay et al. (1993) [26] for the predominantly slow fiber type soleus mouse muscle, comparable to the human soleus muscle. The significant pre to post enthalpy efficiency increase for the MTU lengthening phase and entire stance phase persisted for values between Vmax-30% and Vmax+10% both using the data of Hill or Barclay and colleagues (p<0.05), which confirms and strengthens the 20 observed intervention effect.
In conclusion, the current study gives new insights into the soleus muscle mechanics and metabolic energetics during human running. In support of our earlier study, an exercised-induced increase of plantar flexor muscle strength and AT stiffness reduced the metabolic energy cost of running. We found 25 the reason for this improvement to be an alteration in the soleus fascicle velocity profile throughout the stance phase, which led to a significantly higher enthalpy efficiency of the operating soleus muscle. The enthalpy efficiency was particularly increased in the phase of muscle-tendon unit lengthening, where the activation is high and the soleus generates an important part of the mechanical energy required for running.

Funding
Funding for this research was supplied by the German Federal Institute of Sport Science (grant no. ZMVI14-070604/17-18).