Linking in vivo muscle dynamics to force–length and force–velocity properties reveals that guinea fowl lateral gastrocnemius operates at shorter than optimal lengths Free

The isometric force–length (F–L) and isotonic force–velocity (F–V) relationships are two widely used empirical measures of muscle contractile properties that characterize mechanical output under controlled conditions (Blix, 1894; Hill, 1938; Gordon et al., 1966; Huxley, 1957; Caiozzo, 2002; Nelson et al., 2004; Alcazar et al., 2019; Sugi and Ohno, 2019). The most common purpose of F–L and F–V experiments is to systematically characterize muscle contractile properties under consistent conditions that can be compared across fiber types, muscles, species and experimental treatment groups (e.g. changes with training, unloading, age, drug treatment, etc.) (Always, 1995; Rassier et al., 1999; Jones, 2010; Raj et al., 2010). The F–L relationship identifies the fascicle length associated with maximum isometric force (L₀), and the F–V relationship demonstrates the force–velocity trade-off that results in an optimal velocity for maximum power output (V_opt) (e.g. Fenn and Marsh, 1935; Gordon et al., 1966; James et al., 1998; Zajac, 1989; Askew and Marsh, 1998). These characteristics are often used to interpret in vivo muscle fascicle lengths, velocities and forces. These properties are also widely used to specify Hill-type muscle actuator properties in musculoskeletal and neuromechanical simulations of movement, in software such as OpenSim and AnyBody (e.g. Delp et al., 2007; Biewener et al., 2014; Seth et al., 2018; Cox et al., 2019). However, the tightly controlled experimental conditions resulting in the F–L and F–V relationships do not represent typical in vivo conditions, which are submaximal and include dynamic, time-varying activation, force, length and velocity. Some previous studies have compared in vivo operating lengths with the F–L curve, but most of these studies focused on in vivo strain ranges, without direct measures of muscle force (e.g. Gregor et al., 1988; Holt and Azizi, 2014; Ahn et al., 2018). Considering the wide-spread use of F–L and F–V properties to characterize muscle contractile performance, it is important to understand how these properties relate to in vivo muscle fascicle operating ranges and force and power output.

With in vivo muscle fascicle strain and muscle–tendon force data, work loops can characterize muscle mechanical function under dynamic in vivo conditions (Josephson, 1985; Prilutsky et al., 1996; Roberts et al., 1997; Biewener et al., 1998a,b; Roberts, 2001; Ahn, 2012; Sawicki et al., 2015; Sponberg et al., 2023). By plotting force against length over a full cycle, the area enclosed by the force–length loop corresponds to the total work output of the muscle and is therefore called a ‘work loop’. In vivo work loops can characterize the complexity and variation in function of muscles in natural movements, with time-varying activation, strain and force. These work loops can have complex shapes, due to less constrained length and activation trajectories compared with the sinusoidal trajectories typically used for ex vivo or in situ work loops (Tu and Dickinson, 1994; Luiker and Stevens, 1994; Stevens, 1996; Rome and Lindstedt, 1997; Askew and Marsh, 1997). For example, in vivo work loops in turkeys and wallabies have revealed that some distal muscles with long in-series tendons contract isometrically during force development in steady locomotion, resulting in an L-shaped work loop representing a ‘strut-like’ function, which enables tendinous structures to cycle elastic energy (Roberts et al., 1997; Biewener et al., 1998b; Griffiths, 1989). In vivo studies have also revealed that work loop shape is sensitive to the load applied during early muscle activation, as well as the phase of activation relative to the applied load (Daley and Biewener, 2003; Daley et al., 2009; Daley and Biewener, 2011; Gordon et al., 2020; Schwaner et al., 2023). For example, during strenuous locomotor tasks, such as incline running or obstacle navigation, the LG shows a more open work loop compared with steady, level locomotion, as a result of earlier force onset at longer muscle fascicle lengths (Roberts et al., 1997; Daley and Biewener, 2003, 2011; Daley et al., 2009; Gordon et al., 2020; Schwaner et al., 2023). While these in vivo studies provide insight into the functional range of muscle and the dynamic interactions between strain, activation and force, it can be difficult to interpret underlying mechanisms because of the complexity and variability of in vivo data. Consequently, it is important to connect contractile mechanisms measured through controlled benchtop experiments (ex vivo, in situ), to the more realistic and complex conditions of in vivo natural movements (Sponberg et al., 2023).

The experimental conditions for the F–L and F–V curves differ from in vivo contraction conditions because they are tightly controlled to keep length and tension constant, respectively. In vivo muscle fascicle length trajectories are dynamic, and force output varies depending on both activation and strain history (Josephson, 1999; Edman et al., 1982; Gregor et al., 1988; Herzog et al., 1992). Additionally, while passive forces are approximated as exponential in the F–L curve, in reality, passive forces are also time and history dependent, and will therefore vary under dynamic conditions (Joumaa et al., 2008; Herzog, 2019). Furthermore, both the F–L and F–V relationships are typically collected under maximal stimulation, which rarely occurs in vivo (Strojnik, 1995). Under submaximal conditions, the plateau of the F–L curve shifts to longer lengths with decreasing activation level, and the F–V curve shifts to lower forces for a given shortening velocity (de Haan, 1988; Chow and Darling, 1999; Holt and Azizi, 2014, 2016; Holt et al., 2014). These differences have important implications for interpreting in vivo operating ranges relative to inferred maximal capacities for force, power and shortening velocity. For example, during maximum jumping tasks, cane toads and frogs shorten their muscle fascicles across the F–L plateau, operating their muscle fascicles around L₀ and V_opt (i.e. Holt and Azizi, 2016). However, for lower jump distances, with lower activation, in vivo operating ranges are poorly aligned with optimal lengths and velocities predicted by the maximal tetantic F–L and F–V curves (Holt and Azizi, 2016). Previous studies have focused on quantifying muscle operating length for near-maximum ballistic behaviors (Azizi and Roberts, 2010), and fewer have analyzed muscle force and operating lengths during submaximal cyclical tasks (Gregor et al., 1988; Rubenson et al., 2012; Bohm et al., 2019). Therefore, it is still largely unknown how F–L and F–V muscle properties relate to in vivo muscle fascicle operating ranges during submaximal locomotion.

Here, we investigated the correspondence between muscle F–L and F–V relationships and the in vivo muscle dynamics and operating ranges in the guinea fowl lateral gastrocnemius (LG) muscle during walking and running. We compared LG F–L and F–V characteristics across individuals, and directly related an individual's in vivo work loop during walking and running to their respective F–L and F–V characteristics, to evaluate muscle contraction dynamics over complete stride cycles. Long-standing arguments suggest that muscle fascicles operate near optimal conditions for force and power during in vivo tasks (Rome, 1998; Burkholder and Lieber, 2001; Lieber and Ward, 2011). Here, we tested the hypothesis that muscle fascicles operate on the F–L plateau, near L₀ to optimize economy of force development, and at velocities near V_opt to optimize power production during walking and running. Previous work revealed that the LG produces work while rapidly shortening under low forces around the swing–stance transition, and then rapidly transitions to near-isometric contraction just after the time of foot contact (T_c), acting as a strut as forces reach a peak around mid-stance (Daley and Biewener, 2003, 2011; Gordon et al., 2020; Schwaner et al., 2023). Therefore, we expected LG to operate near V_opt while producing work during the swing–stance transition, and to operate near zero velocity and L₀ at the time of peak force for economy of force development. Additionally, we aimed to fully characterize LG operating range during walking and running and evaluate dynamic relationships between strain and force observed in vivo. We tested for a correlation between in situ connective tissue compliance and work loop shape, to determine whether individuals with higher compliance exhibit higher in vivo muscle work output during walking and running. Data relating in situ and in vivo muscle properties are essential to understand contributors to in vivo force development beyond the F–L and F–V properties, and to inform future benchtop experiments that characterize muscle under controlled yet dynamic conditions that more accurately reflect natural movements.

We used 11 adult guinea fowl, Numida meleagris (Linnaeus 1758), for this study. We divided animals into two cohorts: combined in vivo and in situ (n=6) and in situ only (n=5). The combined in vivo and in situ birds were habituated to handling and trained on the treadmill before treadmill data collection sessions. These birds first underwent surgical procedures for in vivo transducer implantation, and in vivo data collection while walking and running on the treadmill, before collection of in situ data. The details of the procedures are described below. The in situ only cohort was used as a quality control to ensure that in situ data collected following in vivo experiments were similar to data collected without a prior in vivo procedure. All procedures were licensed and approved by the University of California Institutional Animal Care and Use Committee (IACUC) (AUP 20-048). Animals were euthanized at the end of the experiments by injection of Euthasol (pentobarbital sodium) while under deep isoflurane anesthesia (5%) delivered by mask.

Sonomicrometry, electromyography (EMG) and force transducers were implanted into the LG muscle and its associated distal tendon while the animals were under surgical anesthesia (isoflurane 1.5–3%, mask delivery), following procedures similar to Daley and Biewener (2003, 2011). Feathers were removed from the left leg, and the surgical field was cleaned 3 times with antiseptic solution (povidone iodine) and alcohol wipes. Transducer leads were tunneled under the skin from a ∼20 mm incision over the synsacrum to a ∼50 mm incision over the lateral shank. Sonomicrometry crystals (1.0 mm; Sonometrics Inc., London, ON, Canada) were implanted within the LG muscle belly in the middle third of the muscle, aligned along muscle fascicles. The alignment of crystals was checked post-mortem to ensure that fascicle lengths were measured accurately. Transducer signals from a sonometrics DS3 digital sonomicrometer (Sonometrics Inc.) were checked via SonoLab software (Sonometrics Inc.). Transducers were secured and the muscle was closed using 5-0 silk suture (Silk, Ethicon, Somerville, NJ, USA). Two bipolar EMG electrodes (AS 632 Teflon-coated stainless steel wire, Cooner Wire Co., Chatsworth, CA, USA) were implanted in the middle third of the muscle belly. A custom-designed E-type stainless steel tendon buckle force transducer was placed around the common gastrocnemius tendon and secured with 5-0 silk ties. EMG and buckle transducers were connected through a 9-way micro-connector plug (580-M09, NorComp Inc., Charlotte, NC, USA). Sonomicrometry leads were connected through an 18-way connector [ST60-18P(30), Hirose Electric Co. Ltd, Downers Grove, IL, USA]. Both connectors were secured using 4-0 silk suture to the skin on the bird's dorsal synsacrum. Skin was closed using 4-0 silk suture (Silk, Ethicon). At the end of the surgery, joint centers of rotation were marked using a combination of permanent markers (black medium sharpie, Newell-Rubbermaid Office, Oak Brook, IL, USA) and non-toxic paint (Painters, Elmer's Products Inc., Westerville, OH, USA).

As part of a larger study, we recorded steady-state locomotion trials that were each 30 s in duration, for a total of 4–12 trials per individual over 1–3 days of experiments (2–6 trials per day) (Schwaner et al., 2022). Birds walked and ran on a motorized treadmill (Woodway, Waukesha, WI, USA) at constant speeds of 0.67 and 1.56 m s⁻¹, respectively. We recorded in vivo EMG, muscle fascicle length changes and muscle tendon force at 5000 Hz using the USB-6363-X model National Instruments Data Acquisition board through the MATLAB data acquisition toolbox (Analog Input Recorder Application, MATLAB 2021a, MathWorks, Natick, MA, USA). We recorded video from the sagittal plane using a high-speed camera (collected at 200 Hz, Phantom VEO 410S, Wayne, NJ, USA). For each bird, we selected one trial per gait condition (i.e. walking and running) for further analysis. We selected the trial in which the bird maintained steady speed for most of the trial and we had a complete dataset for the entire trial, including video, muscle force, muscle fascicle length and EMG activity data.

The joint centers of rotation and several body points were digitized using DeepLabCut (version 2.2.1) (Mathis et al., 2018; Nath et al., 2019) (see Schwaner et al., 2022). Filtered marker locations (low-pass second-order Butterworth filter, cut-off frequency of 30 Hz) were used to determine foot contact and take-off times and ankle joint kinematics. We tracked stance, swing and stride periods based on foot contact and take-off times using the kinematics of the instrumented left leg, after Schwaner et al. (2022). Using the ankle joint kinematics, we cut strides from mid-swing to mid-swing. Unsteady strides resulting from accelerations, decelerations or unexpected animal movement were excluded from analysis. Steady strides were determined based on foot velocity during stance being within 3 s.d. of the treadmill belt speed. We further analyzed in vivo measures of muscle force, fascicle length, activation and kinematics in a custom-written MATLAB script (MATLAB, version 2021a, MathWorks). We obtained myoelectric intensities from raw EMG signals in time and frequency using wavelet decomposition, using wavelets optimized for muscle (after Von Tscharner, 2000; Wakeling et al., 2002; Daley et al., 2009; Gordon et al., 2015; Schwaner et al., 2023). We calculated an activation threshold as +3 s.d. above baseline muscle activation, and used these to determine the onset and offset timing of muscle activation (T_act, T_deact, respectively) for further analysis. To characterize in vivo fascicle length and velocity operating ranges, we identified five important time points during the stride cycle for further analysis: (1) time of LG EMG activity onset (T_act), (2) time of foot contact (T_c), (3) time of 50% force rise (T_rise), (4) time of peak force (T_peak) and (5) time of 50% force decay (T_fall).

For all individuals (n=11), we characterized the F–L and F–V relationships in situ. Birds were maintained under deep surgical anesthesia throughout the experiment (induction at 2.5–3% isoflurane, maintenance at 1.5–2%, mask delivery). A ∼25 mm incision was made posterior to the thigh muscles to access the sciatic nerve, which was isolated and instrumented with a custom-built nerve cuff (after Naples et al., 1988) and then immersed in mineral oil. For in situ only birds, the left LG muscle was instrumented with sonomicrometry transducers (1.0 mm, Sonometrics Inc.), positioned mid-belly along the fascicle, in the same position as for the in vivo birds. For the in vivo birds, we used the sonomicrometry crystals already placed in the previous surgery. The distal free tendon of the gastrocnemius muscle was connected to an ergometer (310C-LR, Aurora Scientific Inc., Aurora, ON, Canada) using a custom clamp allowing measurement of muscle force and changes in muscle length. On average, 20.8±6.6 mm free tendon (mean±s.d.) remained attached to the muscle during experiments. The clamp was placed immediately proximal to the extra cartilaginous tissue that occurs in the tendon at the crossing of the ankle joint, while avoiding the force buckle. The medial gastrocnemius (MG) was separated from the LG by making an incision along the aponeurosis connective tissue between the two muscles.

For combined in vivo and in situ birds, we calibrated the E-shaped tendon force buckles before in situ data collection by using the ergometer to induce sinusoidal length changes on the muscle while measuring length and force. We completed the calibration of the tendon buckle before starting the F–L and F–V experiments to allow the buckle to be removed for the in situ experiments. We calculated buckle calibration using a linear regression fit to the loading phase of the sinusoidal oscillations, to convert the measured strain voltage into a force in newtons. The buckle calibrations were found to be linear within the recorded range of forces (maximum 38±19 N, mean±s.d.), with a mean (±s.d.) R² of 0.95±0.06 and range between 0.85 and 0.99.

To induce muscle contractions, the sciatic nerve was stimulated using 0.2 ms square wave pulses at 100 Hz (4100 High Power Stimulator, A-M Systems, Carlsborg, WA, USA). We used twitch contractions at gradually increasing voltages to determine the optimal stimulation voltage (6.5–8.5 V). Stimulation trains with a 200 ms duration were used to construct the F–L relationship. Muscle force and muscle fascicle length were recorded at 1000 Hz using a National Instruments AD board (NI USB-6363) and Igor Pro 6.4 (Wavemetrics Inc., Lake Oswega, OR, USA). To construct the F–L curve, the LG was measured under isometric conditions at a series of lengths during fixed-end tetanic contractions (Fig. 1). For each individual, we used a 2nd degree polynomial fit to 9±1 individual contractions to obtain the F–L curve. This was determined based on the shape of the force maxima of a series of contractions: we aimed to obtain contractions that would capture the parabolic shape of the F–L curve. At each length, we first measured the passive force and length of the resting muscle, then the muscle was stimulated maximally for 200 ms (ensuring a near-maximum tetanic contraction), and the maximum active isometric force and corresponding fascicle length were measured for each contraction. We used 200 ms stimulation to minimize muscle fatigue. From the series of F–L experiments, we determined the maximum tetanic force (F_max), as well as the optimal fascicle length at which this F_max is produced (L₀). F_max was confirmed during a 400 ms contraction and was found to deviate minimally (±4% s.d.) from that measured for 200 ms stimulation.

The F–V relationship was determined through a series of 8–10, 400 ms after-loaded isotonic contractions. Force was allowed to rise to a predefined level between 0.1 and 0.9 of F_max and then the muscle was allowed to shorten while maintaining constant force. Forces and corresponding velocities were measured during a 30 ms period after the force had reached a stable plateau (Fig. 2).

We fitted a second-degree polynomial curve (polynomial curve fitting tool, MATLAB 2022a, MathWorks) to the active and passive F–L curve. Based on these curves we determined the peak isometric force (F_max) and optimum length (L₀) from the fitted active F–L curve. To ascertain the activation dependence of L₀ (i.e. Holt and Azizi, 2014), in one individual we measured the F–L relationship for twitch and brief 50 ms tetanic contractions, resulting in submaximal forces between a twitch and maximally tetanic contraction. We determined the corresponding peak isometric force and optimum length under these submaximal conditions. Data were then normalized to F_max and L₀ (after Holt and Azizi, 2016).

We fitted a standard hyperbolic equation in MATLAB to determine the F–V curve, and normalized velocity to L₀ per second (L₀ s⁻¹) to allow comparison of the F–V relationship among birds. We multiplied force by velocity from the fitted F–V curve to obtain the power curve. From the power curve, we determined the peak power and the optimal shortening velocity at which peak power is produced, V_opt.

We obtained muscle fascicle lengths (L_fascicle), muscle length and thickness using calipers while the muscle was under passive tension that corresponds to an active muscle fascicle length of L₀. All measured morphological parameters are presented in Table S1. These measurements were used to calculate the fractional length correction factor (L_fascicle/L_crystals) used to convert sonomicrometry distance to the total fascicle length, assuming homogeneous strain. This assumption is unlikely to lead to substantial errors because the LG fascicles are relatively short and L_crystals was large relative to L_fascicle. Crystal alignment relative to the fascicle axis was verified post-mortem, and found to be within ±13 deg, indicating that errors due to crystal misalignment were <3%. The fractional length correction factor was also applied to in vivo data to calculate total fascicle length and strain. We calculated the physiological cross-sectional area (PCSA) from the animal's LG and combined LG and MG (total gastrocnemius) muscle mass divided by muscle density multiplied by fascicle length (L₀) (Alexander and Vernon, 1975).

After obtaining the F–L and F–V curve for each bird, we normalized muscle fascicle length, velocity and muscle–tendon force to the optima based on the contractile parameters obtained for that individual. Specifically, we normalized fascicle length by dividing instantaneous length by L₀. We calculated velocity normalized to optimal fascicle length, in units of L₀ s⁻¹. The LG maximum isometric stress was calculated by dividing LG maximum isometric force (F_max) by LG PCSA. In vivo stress was calculated by dividing in vivo measured gastrocnemius force by the combined gastrocnemius (LG and MG) PCSA, based on the simplifying assumption of uniform stress and strain between LG and MG. An estimate of total gastrocnemius F_max was calculated based on the assumption of uniform stress between LG and MG, resulting in force contributions proportional to PCSA. The total gastrocnemius PCSA was calculated to be 2.45× LG PCSA; therefore, total gastrocnemius F_max was calculated by multiplying LG F_max by 2.45. In vivo fractional force was then calculated by dividing instantaneous in vivo force by total gastrocnemius F_max (Table S1). To estimate the stiffness of the combined tendon and aponeurosis, we measured the fascicle shortening during a maximal tetanic fixed-end contraction, which is approximately equal to tendon stretch in these conditions, and then divided by the measured maximum force.

Summary values in the text are provided as means±s.d., unless otherwise specified. To test the main hypotheses of our study, we compared fascicle lengths and velocity at specific time points in the in vivo stride cycle with the in situ measured values of L₀ and V_opt. We used a paired t-test (ttest, MATLAB 2021a, MathWorks) to test the following: (1) whether muscle fascicle length at the time of peak force (F_pk) differed significantly from L₀, (2) whether muscle fascicle shortening velocity at T_c differed significantly from V_opt, and (3) whether muscle fascicle shortening velocity at F_pk differed significantly from 0. Paired t-tests are appropriate for the analysis because all statistical comparisons were made between the in vivo and in situ values measured within the same muscle and individual bird. To characterize the in vivo operating range, we measured in vivo lengths and velocities for time points spanning the active period: T_act, T_c, T_rise, T_peak, T_fall (defined above in ‘In vivo data analysis’), and calculated the mean and standard deviation across individuals.

To characterize potential dynamic strain effects observed in vivo during walking and running, we used linear mixed-effects (LME) models (fitlme, MATLAB 2021a, MathWorks) to test for relationships between strain and force and specific time points. In the first LME analysis, we tested the relationship between the in vivo observed passive force and corresponding muscle fascicle strain and velocity during passive force rise. In this statistical analysis, the peak magnitude of the in vivo passive force during early swing was the response variable (Y). We investigated fascicle strain, fascicle velocity and gait (walk, run) as predictors, with individual as a random effect. We compared multiple models. Model 1 included only the intercept and individual as a random effect: [Y∼1 + (1|individual)]; we used this as a reference model and null hypothesis. This reference model was compared to five alternative models: Model 2: [Y∼1 + strain + (1|individual)]; Model 3: [Y∼1 + velocity + (1|individual)]; Model 4: [Y∼1 + gait + (1|individual)]; Model 5: [Y∼1 + strain * velocity + (1|individual)]; and Model 6: [Y∼1 + gait + strain * velocity + (1|individual)]. We compared candidate models based on their Akaike's information criterion (AIC), total adjusted R², and log-likelihood ratio tests, which supported the selection of Model 6 across all variables tested.

In a second LME analysis on the in vivo data, we used a linear mixed-effects ANOVA to test whether the magnitude of the late-swing in vivo passive force was a significant predictor of total active force during stance. In this test, the maximum in vivo active force during stance was a response variable (Z). We compared two models. Model 1 included only the intercept and individual as a random effect [Z∼1 + (1|individual)’], which we used as a reference model and null hypothesis. This reference model was compared with the alternative model in which the peak late-swing passive force is a continuous linear predictor [Z∼1 + passive force magnitude + (1|individual)]. Based on a similar selection to that described above, Model 2 was statistically supported.

For each guinea fowl, a series of isometric contractions was used to construct the passive and active curves of the LG F–L relationship (Fig. 1A,B). Across all birds (n=11), the maximum LG force measured was 136±24 N. Stress was calculated by dividing peak force (F_max) by PCSA (Table S1), resulting in measures of maximum muscle stress with a mean of 278.9±47.2 kPa (Table 1). To compare the shape of the active and passive F–L curves across birds, we normalized the force to the maximum force (LG F_max) and the fascicle length to L₀ (L/L₀) (Fig. 1C), using the morphological measures (Table S1). The polynomial fit to the FL data had an average R² of 0.83±0.095 (Table S3). In comparing the results between the ‘combined’ and ‘in situ only’ cohorts, the maximum forces averaged 136.0±24 N for combined and 133.7±16 N for in situ only, with no significant difference between the groups (P=0.8). Across all birds, we found that active isometric force remained within 0.95 F_max over a large range of fractional fascicle lengths (0.29±0.05 L₀) (Table S2). The force plateau started at an average length of 0.85±0.02 L₀, and ended at an average length of 1.13±0.04 L₀. Passive forces remained low across the active F–L curve, but showed high variation among individuals at long fractional lengths (Fig. 1C). Although we do not have an explanation for this variation, the passive forces consistently occurred at long lengths relative to L₀ and, consequently, the variation does not substantially impact force predictions over the observed in vivo operating ranges. We found only weak correlations between the free tendon length in the in situ preparation (i.e. the length between the muscle–tendon junction and the tendon clamp) and the F–L plateau width, V_opt, F_max and total fixed end compliance measured across birds (R² of 0.01–0.13; Table S2). This may reflect that a large fraction of the tendon compliance occurs in the aponeurosis rather than the free tendon, and suggests that the variation in free tendon length was not the main source of individual variation in our dataset.

The LG F–V relationship for each individual was constructed based on a series of individual isotonic contractions at different levels of fractional force (Fig. 3). As an example, we show measurements from two trials from an individual bird, with force set at 0.3 and 0.9 F_max (Fig. 2A,B), and illustrate where these individual measurements fall on the resulting F–V curve (Fig. 2C). We multiplied force by velocity from the fitted F–V curve to obtain the power curve and the optimal shortening velocity at peak power output (V_opt). The mean normalized V_opt across all birds occurred at 2.9±0.4 L₀ s⁻¹ (Fig. 3). The mean force at V_opt was 0.41±0.04 F_max. Summary values from the F–L and F–V experiments are provided in Table 1. The average R² of the F–V curve was 0.985±0.02. Detailed fit parameters and goodness of fit results of the F–L and F–V curves can be found in Table S3.

In vivo muscle force, fascicle length and activation were used to construct muscle work loops for walking and running. A representative sequence of four strides shows typical force, length and activation patterns over time (Fig. 4). Work loop shape was relatively repeatable across strides in steady walking and running, but varied among individuals, as shown for two representative individuals in Fig. 5. These examples represent the range of variation in work loop shape across individuals in the current dataset. Some individuals exhibited near-isometric contraction, with a narrow force peak (Fig. 5A,B) and others exhibited substantial shortening throughout force development, resulting in an open work loop shape and higher work output (Fig. 5C,D). In running, total work output was higher as a result of a combination of higher peak force and greater shortening during force development compared with walking (Fig. 5).

To test the hypothesis that muscle fascicle length at time of peak force (F_pk) differed significantly from L₀, we compared in vivo values of length at F_pk for walking and running with L₀ (Fig. 6). At F_pk in running, fascicle length was 0.77±0.12 L₀, which is significantly shorter than L₀ (P=0.002). Similarly, during walking, F_pk occurred at 0.77±0.13 L₀, which is significantly shorter than L₀ (P=0.002). These data indicate that in vivo force production during walking and running mainly occurs on the ascending limb of the maximal tetanic F–L curve. We also compared the in vivo operating lengths to the F–L curve at lower activation levels that correspond more closely to submaximal in vivo activation (Fig. 6B). Lower activation levels resulted in a rightward shift of the F–L curve (towards longer lengths), which puts in vivo operating ranges even further down the ascending limb of the submaximal F–L curve (Fig. 6B).

To test the hypothesis that the LG fascicles shorten at V_opt while producing power during walking and running, we compared in vivo shortening velocities with V_opt at the time of foot contact (T_c) when force is low and power is near its in vivo peak (Fig. 7). In walking, at T_c, shortening velocity averaged 2.33±1.5 L₀ s⁻¹, and did not differ significantly from V_opt based on a paired t-test (P=0.36). In running, velocity at T_c averaged 2.69±1.1 L₀ s⁻¹ and did not differ significantly from V_opt based on a paired t-test (P=0.54). The in vivo operating values are shown graphically relative to the F–V curve in Fig. 7.

To test the hypothesis that LG operates near zero velocity (isometric contraction) while producing high forces during walking and running, we statistically compared the in vivo values of velocity at peak force during stance (F_pk) to zero velocity (Fig. 7). Muscle fascicle shortening velocity was lower at F_pk compared with T_c in both walking and running. At F_pk, velocity averaged 0.02±0.33L₀ s⁻¹ in walking which did not differ significantly from zero (P=0.89). Similarly, in running, velocity at F_pk averaged 0.03±0.3 L₀ s⁻¹ which did not differ significantly from zero (P=0.91).

We also characterized in vivo operating ranges throughout the period of muscle activity during walking and running (Fig. 6A). The differences in active muscle operating ranges between walking and running were minimal. The active fractional length range of 0.73–1.11 L₀ in running was only slightly wider that of walking (0.76–1.07 L₀). In vivo peak muscle forces were 16% higher in running versus walking, and both were far below the maximally tetanic F_max. Walking F_pk measured 0.09±0.02 F_max, while running F_pk measured 0.13±0.03 F_max, based on dividing in vivo F_pk by total gastrocnemius F_max (see Materials and Methods). In both gaits, muscles were activated at lengths close to the isometric F–L plateau. In walking, length at T_act did not differ significantly from L₀ (P=0.09), whereas in running, length at T_act was slightly longer than L₀ (P=0.01) (Table 2). Activation was followed by rapid shortening across the F–L plateau at low forces. However, significant force rise did not occur till after T_c. At T_c in walking, fascicle length averaged 0.79±0.14 L₀, significantly shorter than L₀ (P=0.002). Shortly after T_c, a sharp rise in force occurred (measured as F_rise) leading to peak force (F_pk). In running, fascicle length at T_c averaged 0.77±0.1 L₀, significantly shorter than L₀ (P=0.002). Despite slightly higher forces in running, shortening velocity was similar between gaits. Lastly, we tested for a correlation between muscle–tendon stiffness and work loop shape. We found a trend toward higher measures of in vivo net work with lower in situ muscle–tendon unit (MTU) stiffness (i.e. higher compliance), indicating more open work loops (walking R²=0.13, and running R²=0.29). While the correlation was stronger for running, it was not statistically significant for either gait because of the low sample size (n=6 for in vivo data).

Muscles exhibited a passive force rise during late swing during both gaits, indicated by an increase in force in the absence of EMG activity (Figs 4 and 5). This passive force rise occurred during rapid passive stretch (Figs 4 and 5), but at fascicle lengths near 1.0 L₀ where no significant passive force was observed for the in situ passive F–L curve (Fig. 1). The peak magnitude of the late-swing passive force correlated with passive muscle fascicle strain, strain rate and their interaction (strain: F stat=40.6, P<0.001, strain rate: F-stat=197.9, P<0.001, strain×strain rate: F-stat=352.7, P<0.001). Gait also had a significant effect on the peak passive force (gait: F-stat=85.9, P<0.001), indicating that passive force was significantly higher during running than during walking. The magnitude of the passive force during swing was also a significant positive predictor of the magnitude of the active force during the subsequent stance (F-stat=125.3, P<0.001).

In the current study, we compared dynamic, in vivo operating ranges of the LG of guinea fowl with the measured in situ isometric F–L and isotonic F–V relationships. Muscle physiological properties characterized using the F–L and F–V relationships have been used to predict and interpret dynamic in vivo muscle dynamics (i.e. Rome, 1998; Burkholder and Lieber, 2001; Lieber and Ward, 2011). Based on previous work, we hypothesized that muscles operate near optimal conditions for force during mid stance, and for power production during the swing–stance transition during walking and running. Our findings partially support the hypothesis that muscle fascicles operate near optimal conditions during walking and running – consistent with the isotonic F–V relationship, we found that the LG operated at low velocity at peak force, but at velocity near V_opt at the swing–stance transition, when the guinea fowl LG produces positive work in walking and running. Our findings are consistent with a previous study on turkey gastrocnemius and plantaris muscle, where investigators found low average shortening velocity (<0.1 V_max) at peak force (Gabaldón et al., 2008). Although not directly reported, data from Gabaldón et al. (2008) suggest that shortening velocity is also considerably higher at T_c compared with peak force (see fig. 6 in Gabaldón et al., 2008). These findings are consistent with in vivo optimization for economy of forces at higher loads and power during work production, as previously suggested for the turkey gastrocnemius (Roberts et al., 1997). However, we also found that the guinea fowl LG shortens rapidly at low forces across the F–L plateau and produces the highest in vivo forces at lengths around 0.8 L₀. This indicates that the LG mainly develops force at lengths below the optimal length predicted based on the F–L plateau. We also observed that the F–L curve shifts rightward (to longer lengths) with submaximal activation; therefore, the in vivo operating ranges correspond to lengths further down the ascending limb of the submaximal F–L curve (Fig. 6B).

Distal ankle extensor muscles such as the LG have a bi-articular architecture with pennate fascicles and long in-series tendons that decouple muscle fascicle and MTU dynamics (Roberts et al., 1997; Azizi and Roberts, 2014; Schwaner et al., 2021). Previous work suggests that the bi-articular LG MTU acts to control energy transfer across joints and provide ankle propulsion (i.e. Gregoire et al., 1984; Zajac et al., 2002; Lichtwark and Wilson, 2006; Schwaner et al., 2018). Under the conditions studied here, we found that guinea fowl LG work loops exhibit an L-shape (Fig. 3A), which suggests a mostly strut-like function of the muscle fascicles during stance, similar to the turkey LG (Roberts et al., 1997). At the swing–stance transition, LG muscle fascicle shortening work occurs simultaneously with energy absorption at the ankle joint (Daley and Biewener, 2003; Daley and Biewener, 2007; Daley et al., 2009), suggesting that muscle fascicles shorten against the tendon while the tendon stretches under load. For reference, individual example traces of muscle dynamics (e.g. length, activation, force) with corresponding knee and ankle angle trajectories for walking and running are provided in Figs S1 and S2. During early stance, the ankle joint absorbs energy; therefore, the positive LG work does not directly power joint work. It is interesting that the fascicles shorten near V_opt even when the muscle is not directly powering joint or limb propulsion. In late stance, positive power occurs at the ankle, yet muscle fascicles contract near isometrically, while elastic energy cycling occurs in the tendon, as observed in turkeys and wallabies (Roberts et al., 1997; Griffiths, 1989). These findings suggest that in steady gait, the guinea fowl LG mainly controls energy transfer across joints, rather than directly actuating the ankle joint. Considering that the LG mainly acts to regulate force and energy transfer during stance, it is perhaps surprising that the LG muscle fascicles do not operate on the F–L plateau for optimum economic force production. However, we note that the F–L curve suggests the active isometric force remains within 0.95 F_max of the maximum force over a large range of fractional fascicle lengths, with a strain width of 0.29±0.05 L₀. Additionally, in vivo walking and running forces are far below the tetanic F_max. Operating at shorter than optimal fractional lengths may not be ideal for force economy (Roberts et al., 1997); however, it is unlikely to limit force output because the in vivo forces in walking and running are so far below the tetanic F_max.

There may be a functional benefit to operating at lengths shorter than optimal in steady state. Obstacle perturbations sometimes require a sudden increase in muscle force development at longer fascicle lengths; for example, in uneven terrain (Daley and Biewener, 2011). Additionally, evidence shows pre-shortening of plantar flexors to function as shock absorbers (Roberts and Konow, 2013; Dick et al., 2021). In guinea fowl, the LG starts shortening near L₀ at the time of EMG onset, yet force production during the stance phase in steady gait occurs almost entirely on the ascending limb of the F–L curve (0.7–0.8 L₀). Operating at lengths on the descending limb of the F–L curve may be a strategy for avoiding the muscle damage that could arise from a rapid stretch due to an unexpected perturbation. Here, the system needs to balance what is likely a complex trade-off between economic force generation, the ability to develop force rapidly to resist a minor stretch (which increases with length), and avoidance of instabilities associated with long sarcomere lengths. Although this pattern may not be optimal for steady treadmill locomotion, the additional force potential may provide intrinsic mechanical stability in the presence of rapid unexpected perturbations. In the presence of obstacles, guinea fowl LG experiences earlier loading due to earlier foot contact, resulting in an earlier and rapid rise in force, reaching a higher peak force (Daley and Biewener, 2011; Gordon et al., 2020; Schwaner et al., 2023). The muscle fascicles continue to shorten throughout the perturbation; therefore, increased force is not directly related to fascicle stretch. However, force development occurs at longer lengths in obstacle steps. The current findings suggest some of the increase in force in obstacle steps arises from higher force potential when the fascicles operate at lengths on the F–L plateau (Fig. 8). A steady-state work loop trajectory that operates at shorter than optimal lengths provides the potential for a rapid, intrinsic increase in muscle force when the operating length of the muscle fascicles is increased by a sudden abbreviation of the swing phase, reacting more rapidly than possible through reflexive changes in activity (Loeb et al., 1999; Daley et al., 2009). Therefore, the shortening of the LG across the F–L plateau in late swing may provide a mechanical safety factor against unexpected perturbations that require rapid force development in response to varied timing of foot contact.

Shortening across the F–L plateau may occur in cyclical tasks that involve abrupt transitions in external loading with uncertain timing. Shortening across the F–L plateau is also observed in frog plantaris and semimembranosus in hopping, the rat medial gastrocnemius during trotting, and the sternohyoid muscle during swallowing (Ahn et al., 2018; Holt and Azizi, 2016). In contrast, during jumping tasks, frog plantaris muscles primarily operate on the descending limb of the F–L curve (Azizi and Roberts, 2010). These patterns may relate both to the mechanical demands of the task and to the uncertainty in externally applied loads. Ballistic movements such as jumping may involve more predictable loading patterns compared with cyclical tasks that involve abrupt load transitions in contact with the external environment.

In examining variation among individuals, we note that variation occurred in the remaining free tendon length (length from muscle–tendon junction to clamp) in our in situ preparation, which contributed to variation in the measured stiffness in the fixed-end contractions. However, we found that the variation in free-tendon length explained only a small fraction of the observed variation among individuals in the outcome measures of the F–L and F–V experiments (see Table S2). This is likely because most of the compliance in the guinea fowl LG MTU arises from within the aponeurosis, not the free tendon. We did find a trend towards greater work output, with more open work loop shape, among individuals with higher measured MTU compliance (lower stiffness) (Table S3). This suggests that some of the observed individual variation in work loop shape during walking and running arises from individual variation in the LG MTU compliance. It would be useful to investigate this further in the future through more detailed analysis of the relationships between muscle–tendon morphology, tendon material properties and 3D shape change during dynamic contractions.

Despite more than a half a century of elegant and sophisticated experiments in isolated muscle physiology, our ability to establish a framework for predicting in vivo muscle performance remains remedial. One of the remaining and unresolved challenges in relating in situ and in vivo data is our inability to accurately and confidently replicate the activation dynamics driven by the nervous system.

This study along with numerous others focused on characterizing the F–L and F–V relationships used maximal stimulation of muscle in order to create comparable contraction conditions across different muscles. However, natural movements rarely require maximum activation of muscle, complicating integrative approaches to studying muscle function (Walmsley et al., 1978; Strojnik, 1995). The potential limitation of recreating in vivo recruitment patterns is not limited to standard approaches relying on isometric and/or isotonic contraction protocols. Despite significant advances in creating more realistic contractile conditions that better reflect in vivo function, most approaches still rely on near-maximal stimulation protocols (Robertson and Sawicki, 2015; Richards and Eberhard, 2020; Mendoza et al., 2023; Rice et al., 2023). Although our ability to recreate the complexity of in vivo motor unit recruitment is limited, previous studies have shown that shifts in the F–L and F–V relationship resulting from changes in activation level change the optimal length (L₀) and velocity (V_opt). A decrease in activation level has been shown to cause a rightward shift to longer lengths and lower forces in the F–L relationship (e.g. Holt and Azizi, 2014, 2016). We found a similar shift in the F–L curve with submaximal stimulation (Fig. 6B). Similarly, optimal velocity for power production has been shown to be at a relatively slower velocity at lower activation levels (Holt et al., 2014). As the complex relationship between activation and intrinsic muscle properties remains unresolved, results relating in situ and in vivo behaviors can become difficult to interpret. For example, in vivo data from walking, a clearly submaximal locomotor behavior, have been shown to map onto the ascending limb of the maximally determined F–L relationship (current study; Rubenson et al., 2012). As such, a rightward shift in the F–L curve would suggest that muscle fascicles are at too short a length to produce force. It is clear that our ability to work across levels of biological organization to develop an integrative understanding of muscle-powered movements is limited by the lack of a protocol to better recreate natural patterns of activation in reduced complexity preparations. Future studies aimed at developing an experimental framework for recreating a dynamic activation state in isolated muscles will greatly advance our current understanding of locomotor systems.

The isometric F–L and isotonic F–V relationships allow comparison of muscle contractile properties under standard and controlled conditions, but they do not capture non-linear interactions between strain trajectory and activation dynamics that influence force and work output during dynamic tasks (Askew and Marsh, 1998; Perreault et al., 2003; McGowan et al., 2013). We found that a passive force rise (i.e. in the absence of EMG activity) occurs in early swing (Figs 3 and 4) in walking and running. This passive force rise occurs at fascicle lengths that do not result in measurable muscle passive forces in situ (Figs 1 and 5). This suggests that the passive F–L relationship under static conditions cannot capture these observed forces, which might instead relate to dynamic viscoelastic properties or history-dependent effects, such as short-range stiffness, stretch-induced residual force enhancement, and passive force enhancement (Edman et al., 1982; Edman, 2012; Herzog, 2018; Seiberl et al., 2015; Hahn and Riedel, 2018). Viscoelastic properties and history-dependent effects can provide stability in response to perturbations as active control can tune intrinsic properties (Gregor et al., 1988; Loeb et al., 1999; Lappin et al., 2006). We found that the magnitude of the active force in the stance phase has a positive correlation with the magnitude of the passive force during swing, suggesting the importance of contributions of dynamic strain and strain rate histories to passive and active force development, even during steady-state in vivo conditions. Viscoelastic elements contribute to muscle force and work during steady-state locomotion, thereby assisting in stabilizing gait (Zajac et al., 2003; Hessel et al., 2021). However, we note that the Achilles tendon is the common tendon for the LG, MG and the intermediate gastrocnemius (IG) in guinea fowl, and therefore contributions from IG or MG, via either direct or lateral transmission of force, could contribute to the apparent passive forces. Yet, no significant MG EMG activity is observed in late swing during walking and running in guinea fowl (Gordon et al., 2015), and therefore we believe agonist contributions are unlikely to explain the observed passive force.

Given our findings here, it is critical that the approaches to studying isolated muscles advance beyond the standard historical protocols. While direct measures of muscle force and length in vivo may not be practical for all systems, recent technical advances provide the potential to bridge the gaps in current understanding by using real-time feedback control to allow isolated muscles to interact dynamically with models (physical or virtual) (Robertson and Sawicki, 2015; Richards and Eberhard, 2020; Mendoza et al., 2023). Further work is needed to develop new standardized protocols to characterize muscle under dynamic but controlled conditions, including work loops with sudden perturbations in force, activation or strain trajectory (Sponberg et al., 2023). Dynamic characterization of muscle contractile function is essential for understanding how the non-linear interactions between activation and strain trajectory influence muscle force and work output during realistic locomotor conditions.

This study provides a novel comparison of in vivo muscle operating forces, fascicle lengths and velocities with optimum in situ characterized lengths and velocities. We show that the guinea fowl LG muscle fascicles shorten near optimal velocities during force development in vivo, but do not operate on the F–L plateau during force development in walking and running. We also found a rise in passive force in the LG during early swing at fascicle lengths that correspond to negligible passive forces in situ. This finding suggests that in vivo F–L dynamics are substantially influenced by dynamic strain effects such as viscoelasticity, short-range stiffness and other lengthening force enhancement. Our study provides new evidence that the static nature of the F–L properties makes intrinsic muscle properties less predictive of in vivo behavior than previously thought. Direct comparison of F–L and F–V properties with in vivo muscle F–L dynamics and operating ranges also suggests the need to further examine how dynamic interactions between strain and activation influence muscle force and work output in vivo. Complex interactions between strain and activation are especially important during unsteady locomotor tasks, where muscle–tendon force and work output may be influenced by viscoelastic and other history-dependent aspects that are not captured in isometric F–L and isotonic F–V experiments.

The authors would like to acknowledge Elizabeth Mendoza for expert advice during in situ data collection. The authors would like to thank Adrien Arias, Vivian Chong, Brooke Christensen, Catalina Dentzel, Kamila Karimjee, Zhiji Li, Elizabeth Mendoza and Daisey Vega for help with in vivo data collection, and Chris Wagner for helping with the in vivo experimental set-up. We thank the UCI University Animal Laboratory Resources team for animal husbandry and veterinary care.