Muscle structure governs joint function: linking natural variation in medial gastrocnemius structure with isokinetic plantar flexor function

ABSTRACT Despite the robust findings linking plantar flexor muscle structure to gross function within athletes, the elderly and patients following Achilles tendon ruptures, the link between natural variation in plantar flexor structure and function in healthy adults is unclear. In this study, we determined the relationship between medial gastrocnemius structure and peak torque and total work about the ankle during maximal effort contractions. We measured resting fascicle length and pennation angle using ultrasound in healthy adults (N=12). Subjects performed maximal effort isometric and isokinetic contractions on a dynamometer. We found that longer fascicles were positively correlated with higher peak torque and total work (R2>0.41, P<0.013) across all isokinetic velocities, ranging from slow (30°/s) to fast (210°/s) contractions. Higher pennation angles were negatively correlated with peak torque and total work (R2>0.296, P<0.067). These correlations were not significant in isometric conditions. We further explored this relationship using a simple computational model to simulate isokinetic contractions. These simulations confirmed that longer fascicle lengths generate more joint torque and work throughout a greater range of motion. This study provides evidence that ankle function is strongly influenced by muscle structure in healthy adults.


INTRODUCTION
Plantar flexor function is a critical parameter for human movement in athletes, aging and patient populations. The triceps surae muscles, comprised of the soleus, lateral gastrocnemius and medial gastrocnemius, support and accelerate the body during ambulation. Although these plantar flexors appear small relative to knee and hip musculature, plantar flexor function is critical during walking (Graf et al., 2005;JudgeRoy et al., 1996), stair climbing (Suzuki et al., 2001), running (Ellis et al., 2014;Nesser et al., 1996), and jumping (Bobbert et al., 1986). Conversely, limited plantar flexor function is associated with decreased walking speed and mobility among elderly populations (Stenroth and Sipila, 2016;Stenroth et al., 2015) and functional deficits in healthy young adults who suffer Achilles tendon injuries (Brorsson et al., 2018). Muscle wasting caused by aging negatively affects the plantar flexors, however this can be mitigated with resistance training . This highlights the importance of maintaining muscle structure throughout the lifespan. Of these muscles, the gastrocnemius muscles are particularly important in generating plantar flexor power, due in part to the longer and less pennate muscle fascicles (Lieber and Fridén, 2000).
Gastrocnemius fascicle structure has been linked with plantar flexor function in athletic and patient populations. Trained sprinters have longer gastrocnemius fascicles than non-sprinters and untrained adults , leading to decreased muscle shortening velocities during a simulated push off of a sprint start (Lee and Piazza, 2009). Even among sprinters, longer and less pennate gastrocnemius fascicles are linked with faster sprint times (Abe et al., 2001;Kumagai et al., 2000). These links between gastrocnemius structure and plantar flexor function translate to patient populations as well. For example, the magnitude of plantar flexor power deficits in patients recovering from Achilles tendon ruptures is strongly correlated with the magnitude of remodeling of the medial gastrocnemius muscle, characterized by shorter resting fascicles in the injured limb (Hullfish et al., 2019b). The importance of fascicle geometry on plantar flexor function has also been demonstrated in silico. Longer and less pennate gastrocnemius muscles increase the functional range of ankle motion during simulated muscle contractions by reducing muscle shortening velocity and operating for a longer amount of time in the optimal range of fascicle length (Baxter et al., 2018).
Although the effect of pathological changes in plantar flexor structure due to injury or aging has been demonstrated to affect function, the effects of natural variation in medial gastrocnemius structure on plantar flexor function in healthy adults remains poorly understood. If two healthy muscles undergo the same joint rotation at a specific angular velocity, the muscle with longer, less pennate fascicles theoretically shortens at a slower rate (Lieber and Fridén, 2000). While longer medial gastrocnemius fascicles are correlated with increased muscle shortening speed (Hauraix et al., 2015;Thom et al., 2007), these findings have not been translated to voluntary plantar flexor kinetics measured in vivo using isokinetic dynamometry. Given that variation in gastrocnemius muscle structure is well documented (Kawakami et al., 2000) and is modified by injury, (Hullfish et al., 2019b), training (Salzano et al., 2018), and aging (Morse et al., 2005); determining if natural variations in fascicle length and pennation angle impacts voluntary function has important implications.
The purpose of this study was to determine the relationship between medial gastrocnemius muscle structure and plantar flexor function measured on an isokinetic dynamometer in healthy young adults. Given that longer and less pennate fascicles increase the potential for total muscle shortening velocity, we hypothesized longer fascicles correlate with increased plantar flexor torque and work and that increased pennation would correlate with decreased plantar flexor torque and work during voluntary isokinetic contractions. To test this hypothesis, we quantified medial gastrocnemius fascicle length and pennation angle using ultrasound imaging and measured plantar flexion torque and work in maximal isometric and isokinetic conditions at three rates of ankle rotation on an isokinetic dynamometer. Based on our previous computational modeling , we hypothesized that fascicle length would be a stronger correlate of plantar flexor torque and work than pennation angle and muscle thickness. After we correlated medial gastrocnemius structure with plantar flexor isokinetic function, we used a musculoskeletal model to confirm the effects of varying optimal fascicle length and pennation angle on muscle kinetics and shortening velocity.
Muscle thickness was moderately and significantly correlated with fascicle length (R 2 =0.536, P<0.001) but not correlated with pennation angle (R 2 =0.064, P=0.084). Despite the positive correlation between resting muscle thickness and fascicle length, resting muscle thickness was not significantly correlated with function at any isokinetic testing condition (Table 2). Muscle thickness was positively and weakly correlated with peak torque at isometric max (R 2 =0.161). However, this correlation did not reach statistical significance (P=0.197).
Muscle structure was weakly correlated with subject stature (Table 3). Fascicle length was weakly correlated with leg length  (R 2 =0.084, P=0.046) and body mass (R 2 =0.132, P=0.011). Pennation angle was weakly correlated with body mass (R 2 =0.098, P=0.030) but not leg length. Muscle thickness was not correlated with either leg length or body mass.
Longer muscle fascicles had a greater effect on simulated plantar flexor function compared to similar decreases in pennation angle ( Fig. 3B,C). The effects of small increases in fascicle length increased with greater rates of ankle rotation during these simulated isokinetic plantar flexion contractions. A 1% increase in the gastrocnemius fascicle length led to a 0.3% increase in peak plantar flexor torque at 30°/s and 0.8% increase in peak plantar flexor torque at 210°/s (Fig. 3B). These small increases in gastrocnemius fascicle length had a greater effect on simulated plantar flexor work done by the ankle joint (Fig. 3C). Increasing the gastrocnemius fascicle length by 1% increased joint work by 0.6% during 30°/s contractions and 1.0% during 210°/s contractions.
These increases in plantar flexor kinetics caused by longer gastrocnemius muscle fascicles were explained by two factors (Fig. 4). First, the longer muscle fascicles generated greater force at each joint angle. Second, the longer muscle fascicles continued to generate muscle force in deeper plantar flexion while the shorter muscle fascicles stopped producing force starting at 40°of plantar flexion. However, similar changes in pennation angle had weaker effects on plantar flexor kinetics ( Fig. 3B,C).

DISCUSSION
In this study, we demonstrated the relationship between plantar flexor structure and function in a cohort of healthy young adults. Our findings support our hypothesis that resting fascicle length is positively correlated with peak plantar flexor torque and work while pennation angle has a smaller, negative correlation with peak plantar flexor torque and work. To determine if plantar flexor function was simply explained by muscle thickness, we regressed muscle thickness with plantar flexor kinetics and found no effect on plantar flexor torque or work in any condition. Although fascicle length has been positively correlated with muscle force in isolated muscle experiments (Lieber, 1997); to our knowledge, this is the first study to link natural variation in gastrocnemius fascicle length with plantar flexor torque and work in healthy adults (Ema et al., 2016).

Comparison with other measurements of muscle structure and function
Our measurements of medial gastrocnemius structure and isokinetic plantar flexor torque and work compare favorably with previous reports in the literature. We decided to measure resting muscle structure at 16°plantar flexion to approximate the ankle angle at which medial gastrocnemius muscle-tendon slack occurs (Zellers et al., 2018). Other measurements of gastrocnemius structure were acquired with the ankle either under load or neutrally aligned which may explain slightly longer (4-9 mm) and less pennate (6-11°) muscle fascicles (Baxter and Piazza, 2014;Kubo et al., 2003;Thom et al., 2007) than those we measured in this current study. Similarly, our measurements of pennation at slack are comparable to earlier measurements in the medial gastrocnemius at the same position (Hoang et al., 2007). Our measurements of plantar flexion torque and work capacity compares well with the literature. Our values for torque and work done at 30 and 120°/s compares well with previously reported values (Randhawa and Wakeling, 2013;Woodson et al., 1995) and our values for maximal isometric torque compares well with studies with similar subject positioning (Arampatzis et al., 2006). A previous study reported higher values for torque generation, however in this case, the subjects were all male and were seated rather than positioned in prone (Baxter and Piazza, 2014).
Interpreting results within the force-velocity model of muscle Our results suggest that fascicle length and pennation angle, which govern absolute muscle shortening velocity (Lieber and Ward, 2011), have greater effects on isokinetic plantar flexor function than muscle thickness. Neither fascicle length nor pennation angle were significantly correlated with peak isometric torque. Our results are consistent with the force-length and force-velocity properties of muscle. While fascicles of different lengths undergo the same absolute contractile velocity during a given isokinetic contraction, longer fascicles have additional sarcomeres in series which extend the functional operating length of the muscle while reducing relative shortening velocity. This enables longer fascicles to operate at slower velocities on the force-velocity curve, increasing force production at all isokinetic speeds (Fig. 5A) (Lieber and Fridén, 2000). Similarly, the force-velocity effects are also affected by variation in pennation angle. Greater muscle pennation increases the fascicle shortening demands for a given muscle shortening contraction. Thus, more pennate muscles generate less force and do less work in isokinetic conditions (Fig. 5B). Our experimental  findings that fascicle length explained more variation in plantar flexor kinetics than pennation angle agrees with the theoretical framework of the force-velocity properties of muscle and our recent computational model  as well as the computational results described in this paper (Figs 3 and 4).
Our results highlight the effects of natural variability in muscle fascicle lengths on plantar flexor function. Force-length characteristics have been demonstrated in humans in vivo (Maganaris, 2001), however, these results were only reported in isometric contractions. Despite evidence of variations in muscle structure between different populations of human subjects Hullfish et al., 2019a;Kearns et al., 2000;Kubo et al., 2003;Lee and Piazza, 2009), there are few studies reporting the relationship between variations in resting fascicle length or pennation angle and dynamic muscle function in humans (Ema et al., 2016). Outside of the plantar flexors, one study found that elbow extensor velocity under no load was positively correlated with muscle volume and pennation angle but not muscle length (Wakahara et al., 2013). However, this previous study did not directly measurement fascicle length, instead they used muscle length as a surrogate for fascicle length. Differences in fascicle length explains almost 50% of reduced fascicle shortening velocity between young and old men . Our previous work did not find a relationship between fascicle length and peak torque during isokinetic contractions at 30, 120 and 210°/s. However, these previous studies measured fascicle length at neutral, which is a less reliable position to measure fascicle length given the sensitive relationship between passive fascicle load and length (Aeles et al., 2017).
We decided to measure the structure of the medial gastrocnemius due to previous observations linking structural changes in that muscle following Achilles tendon rupture to functional deficits (Baxter et al., 2018;Hullfish et al., 2019b) coupled with similar observations with other studies (Peng et al., 2017(Peng et al., , 2019. Prior studies have linked plantar flexor torque measurements with medial gastrocnemius structure without accounting for the other two triceps surae muscles (Hauraix et al., 2015;Thom et al., 2007). These studies approximated the torque generated by the gastrocnemius by multiplying total plantar flexor torque values by constant value ranging from 0.159 (Fukunaga et al., 1996) to 0.218 (Morse et al., 2005). As these are constant values, this adjustment would not affect the correlations we have found in this study. In addition, we performed an analysis on the publically available data set (Crouzier et al., 2018) and determined that fascicle length and pennation angles of the medial gastrocnemius correlate with both the lateral gastrocnemius and soleus muscles (R 2 >0.413, P<0.023).

Limitations
This study was affected by several limitations. Despite having a relatively small sample size (N=12), our in vivo findings agree with both basic principles of skeletal muscle mechanics (Lieber and Fridén, 2000) and our computational model. We did not confirm maximal effort during contractions across the triceps surae using electromyography. Instead, we provided subjects verbal encouragement and real-time visual feedback (Drazan et al., 2019) and had each subject repeat each maximal contraction condition until their peak torques were consistent between consecutive trials (McNair et al., 1996). We used muscle thickness as a proxy for muscle volume, which is positively correlated with measurements of muscle volume acquired with magnetic resonance imaging (R 2 =0.527, P<0.001) (Crouzier et al., 2018) and cadaveric measurements (R 2 =0.497, P=0.017) (Bandholm et al., 2007). We did not find a statistically significant correlation between medial gastrocnemius thickness and isometric torque. This can be potentially explained by the important role of the soleus, which we did not characterize in this study, in isometric plantar flexor Fig. 3. Longer muscle fascicles generate greater plantar flexor torque and work during simulated isokinetic contractions. We simulated the effects of varying fascicle length (x-axis) and pennation angle ( y-axis) using a simplified musculoskeletal model of the lower leg (A). After each model permutation was initialized by solving for tendon slack lengths to reach static equilibrium at 16°plantar flexion, we simulated maximal isokinetic plantar flexion contractions at 30, 120 and 210°/s. Small increases in fascicle length had a greater effect on peak torque (B) than similarly small decreases in pennation angle. Similar to peak joint torque, longer fascicles also increased the amount of work done by the muscle during maximal contractions at each on speed (C). We tested a wide range (±50%) of fascicle lengths and pennation angles centered at the average measurements made in the in vivo experiment. Peak torque was calculated as the product of the active contributions of the gastrocnemius muscle and the muscle moment arm (Nm). Joint work was calculated as the integral of the torque-angle curve.
function. We did not quantify plantar flexor moment arm, which may affect muscle shortening dynamics and plantar flexor kinetics (Baxter and Piazza, 2014;Nagano and Komura, 2003).
We used medial gastrocnemius structure as a surrogate measure of the triceps surae muscle structure, rather than characterizing all three muscles of the triceps surae. Our secondary analyses of published data found that the medical gastrocnemius structure is correlated with the structure of the other two muscles (Crouzier et al., 2018). While variations in lateral gastrocnemius and soleus structure might strengthen the correlation between plantar flexor structure and function, it will not decrease our observed correlations. As the soleus plays a large role in isometric strength in plantar flexion, this may explain the lack of correlation between medial gastrocnemius thickness and isometric strength. We did not evaluate the possibility of muscle gearing contributing to our observed effects, nor did the computational muscle model consider this phenomenon (Millard et al., 2013). Although muscle gearing has profound effects on shortening kinetics in isolated muscle preparations (Azizi et al., 2008), the effects measured in vivo in humans are smaller (Randhawa and Wakeling, 2013). We did not alter tendon compliance in our computational simulation. However, our previous simulations of a heel raise found a very small effect of altered tendon compliance on kinetic output .
In conclusion, our study demonstrates the link between resting structure of the medial gastrocnemius with isokinetic plantar flexion function. These findings may have important implications on plantar flexor function following muscle remodeling elicited through injury, training and aging. However, the link between isokinetic plantar flexor function and ambulatory function requires further investigation, and future work should directly test the link between muscle structure and movement biomechanics.

Participant demographics and experimental set up
We quantified medial gastrocnemius structure and plantar flexor function in 12 healthy young adults (six male, six female, age: 25±4.54, BMI: 23.1±4.48)who provided written informed consent in this study, which was approved by the University of Pennsylvania IRB (#828374). Subjects were recreationally active and had no reported history of Achilles tendon injury or recent muscle injury in either leg. We acquired measurements of medial gastrocnemius structure and function of the right leg with subjects positioned prone on an isokinetic dynamometer (System 4, Biodex, Shirley, NY, USA). Each subject was positioned prone on a treatment table that was rigidly secured to the dynamometer while wearing standardized lab shoes. After their foot was secured to the foot plate with the medial malleolus aligned with the spindle of the dynamometer, each subject selected their ankle range of motion by fully dorsi-flexing and plantar flexing their ankle. Once the subject specific range of motion was set, the investigator set the ankle neutral position, which was recorded for post-processing. To ensure consistency between subjects, all experimental procedures were performed by a single investigator

Muscle structure measurement
To quantify medial gastrocnemius structure, we acquired ultrasound images of the medial gastrocnemius throughout the entire passive range of motion of each subject. We positioned the 7.5 MHz, 6 cm probe (LV7.5/60/128Z-2, SmartUs, TELEMED) over the mid-substance of the muscle belly and secured it to the leg using a custom-made cast and strap system. Ultrasound images were acquired between 30 and 60 Hz while each subject's ankle was moved through its passive range of motion moving from plantar flexion to dorsiflexion at a rate of 10°/s. We quantified resting fascicle length, pennation angle, and muscle thickness with the ankle at the resting angle rather than at neutral to avoid stretching the fascicles (Aeles et al., 2017). Fig. 4. Longer muscle fascicles lead to increased plantar flexor torque throughout the ankle range of motion during simulated isokinetic contractions. Longer gastrocnemius fascicles (more red) generated greater amounts of plantar flexor torque throughout the entire range of motion compared to shorter fascicles (more blue). These effects were similar at slow (A), medium (B) and fast (C) simulated isokinetic contraction speeds. Fig. 5. Longer and less pennate muscle fascicles reduce the shortening speed demands during a given isokinetic contraction. (A) Longer and (B) less pennate fascicles decrease relative shortening velocity during a given joint rotation, which results in increased fascicle force. The forcevelocity properties of skeletal muscle are more sensitive to changes in fascicle length than pennation angle, which agrees with our experimental findings that ankle torque is more strongly correlated with fascicle length than pennation angle.
This resting angle was set to 16°plantar flexion for all subjects based on values of average resting ankle position across 42 patients reported in the literature (Zellers et al., 2018). We manually identified the superficial and deep aponeuroses and a muscle fascicle by selecting two points on each structure to form a line (Fig. 6). This manual approach of fascicle measurement has been demonstrated to be repeatable within the same observer (Drazan et al., 2019). We calculated fascicle length as the distance between the superficial and deep attachments of the fascicle and pennation angle as the angle between the fascicle and the deep aponeurosis. Muscle thickness was calculated as the fascicle length multiplied by the sine of the pennation angle. We measured fascicles that were in the middle of the imaging frame for all subjects. In case that the entire fascicle was not in frame, linear extrapolation was used to calculate fascicle length. We averaged each measurement of structure across three passive range of motion trials to determine the measures of resting muscle structure we used in our analyses.

Muscle function measurement
To determine plantar flexor work and peak torque, subjects performed maximal voluntary plantar flexor contractions on an isokinetic dynamometer. Subjects performed maximal isometric contractions at neutral ankle angle and isokinetic contractions at three rotational velocities across their range of motion. The subject's right foot was secured to a foot plate with the medial malleolus of the ankle aligned with the dynamometer's spindle. First, we measured peak isometric plantar flexor torque with the ankle at neutral with subjects in prone position. Next, peak isokinetic plantar flexion contractions were performed throughout a subject's entire range of motion at three speeds: slow (30°/s), medium (120°/s), and fast (210°/s). At the start of each of these trials, we confirmed that the subject positioned their ankle in their peak dorsi-flexion angle. We provided verbal encouragement (McNair et al., 1996) as well as visual feedback to ensure that subjects maximally contract their plantar flexors during each condition. Contractions were not ramped or pre-activated, instead subjects were instructed to immediately 'push as hard and as fast as they could' by the examiner. Subjects continued to perform maximal plantar flexion contractions for each test condition until the peak torque was consistent for two consecutive trials.

Statistical methodology and analysis
To test our hypothesis that fascicle length would be positively and strongly correlated with plantar flexor function and that pennation angle would be negatively and moderately correlated with plantar flexor function, we performed univariate linear regression to determine the relationship between measures of medial gastrocnemius structure with peak plantar flexor torque and work at each contraction condition. We opted to use univariate regression to directly test each of our two a priori hypotheses. We calculated the strength correlation for each of these regression analyses using the coefficient of determination (R 2 ), which is an index of the correlation strength ranging between 0 and 1 where values between 0 and 0.04 indicate negligible correlation, 0.04 and 0.25 indicate weak correlation, 0.25 and 0.64 indicate moderate correlation, and 0.64 and 1 indicate strong correlation (Morton et al., 2005). We set an a priori alpha level of 0.05 and performed all statistical analysis using scientific computing software (MATLAB, MathWorks, Natick, MA, USA).
Because muscle structure and anthropometry varied in our subjects, we quantified muscle thickness and lower-leg length to determine if these factors accounted for some of the variability in plantar flexor kinetics. We calculated muscle thickness as the product of the resting fascicle length and the sine of the pennation angle. We quantified lower-leg length by measuring the distance between reflective markers placed on the lateral malleolus and the proximal head of the fibula that was measured using a 12 camera motion capture system (Raptor Series, Motion Analysis Corporation, Rohnert Park, CA, USA). To evaluate the effect of patient stature on resting muscle structure, we linearly regressed fascicle length, pennation angle and muscle thickness against body mass and leg length. Additionally, muscle thickness was linearly regressed against fascicle length and pennation angle.
In silico model of the plantar flexor structure and function We simulated the three isokinetic contraction speeds to demonstrate how variations in fascicle length and pennation angle affected joint kinetics and muscle shortening velocity (Fig. 3A) using a musculoskeletal model Delp et al., 2007). Briefly, the ankle was constrained by a pin joint and actuated by a combined gastrocnemius muscle, soleus muscle, and tibialis anterior muscle. The musculoskeletal model was positioned in the prone position and resting ankle angle was set at 16°plantar flexion, which matched previous literature reports (Zellers et al., 2018) and the ankle angle at which we measured medial gastrocnemius structure in the current study. During each test speed, we changed the optimal fascicle length (which we will refer to as fascicle length for consistency with our in vivo measurements) and pennation angle of both the gastrocnemius and soleus muscles. We set the fascicle length of the gastrocnemius muscle to 64 mm and the pennation angle to 22°, which we acquired from ultrasound images of our test subjects in 16°of plantar flexion. The soleus muscle was set to the model default values of 44 mm for fascicle length and 28°of pennation. We iteratively adjusted by fascicle length and pennation angle by 10%, ranging from 50% to 150% of the model default values (Fig. 3A). During each test iteration, we used a gradient based optimization procedure to find the tendon slack lengths that placed the ankle in static equilibrium. We then simulated maximal plantar flexor contractions at 30, 120, and 210°/s and recorded the muscle force generated and shortening velocities of the gastrocnemius and soleus muscles. To test the isolated effects of muscle structure on kinetic output, we maximally excited both muscle actuators throughout the entire simulation. Additionally, we did not change tendon compliance because our previous simulations found very small effects of altered compliance on kinetic output . To test the effects of variations in gastrocnemius structure, we analyzed the contributions of gastrocnemius force towards ankle kinetics.

Data availability
Study data and simulation files are hosted online. https://doi.org/10.5281/zenodo.