To properly compare explosive torque production in dynamic conditions the muscle’s contractile capability should be the same/similar. To do that, each subject was positioned in order to express the same F–L potential (i.e., fraction of the maximum force in accordance with the F–L curve of fascicles) during each explosive-dynamic contraction (see Table 1). The F–L potential expresses the operating length of the muscle fascicles with respect to the F–L curve and can be calculated based on the fascicle operating range throughout the F–L curve during contraction (see Nikolaidou et al., 2017; Bohm et al., 2019; Monte et al., 2020).

Explosive contractions are typically investigated in the first 150 ms after contraction onset, due to the importance of this time window in athletic events (e.g., ground contact in sprint running) and daily life activities (balance recovery). For each participant, the range of motion (ROM) during EDC contractions was set as to present the optimal fascicle length “in the middle” of the 150 ms time window (Table 1): these contractions were, thus, set to start 75 ms before reaching the target length (i.e., the optimal length obtained from the F–L relationship using the fixed-end contractions at different joint angles), independently from the values of angular acceleration (see Figure 1). Therefore, each participant had his own dynamometric configuration. In order to reach this goal two issues were taken into account: (i) with increasing angular acceleration the time necessary to reach the target length decreases; therefore the ROM had to be determined experimentally during pilot testing and each EDC contraction started from a different knee angle (see Table 1); (ii) to avoid that the dynamometer stops accelerating as soon as the set velocity is reached, the dynamometer peak angular velocity was set to 660°.s^–1 (see Hahn et al., 2017 for further details).

Several pilot tests were performed to establish and check the experimental procedures for the explosive contractions. Even though ROM and torque onset were different among contractions, the target length of each participants (optimal length, that corresponds at an optimal angle of ∼65°) during EDC contractions was reached 75 ms after torque onset in all acceleration conditions (see Table 1). The primary aim of this standardisation was to allow the muscles to work within a similar force–length potential in all contractions (see Table 1). The differences in fascicle length during the first 150 ms of contraction are, thus, not expected to have a significant effect on mechanical output; the observed differences could be essentially attributed to the differences in contraction velocity imposed by the different angular acceleration.

The procedures to determine the force–length, force–velocity, and power–velocity relationships are similar to those reported in previous studies (Tillin et al., 2012b, 2018; Nikolaidou et al., 2017; Monte et al., 2020), which involved: (1) the assessment of the torque–angle and torque–angular velocity by means of the dynamometer; (2) the conversion of torque into force values using patellar tendon moment arm; and (3) the combination of these force values with ultrasound data, to obtain the force–length, force–velocity, and power–velocity relationships of the fascicles and of the muscle belly.

Briefly, the participants were secured on a dynamometer (Biodex System 4 Pro, United States) by means of a trunk and pelvic strap, the arms crossed in front of the chest. Due to the knee joint rotation that occurs during knee extension contractions from rest to MVC (Tsaopoulos et al., 2006), the knee and the dynamometer axis of rotation were aligned at 65° of knee flexion during MVC (Bakenecker et al., 2019). Therefore, the alignment was performed at higher torque values than during the dynamic explosive contractions. This implies that the soft tissues displacement was different in the two cases (maximum vs. explosive contraction). However, during pilot tests, we checked for different configurations (i.e., different alignment during sub-maximal contraction) and no significant differences in offset were observed (i.e., differences in the alignment between centers of rotation could not affected our results). Furthermore, to avoid possible inaccuracies in knee angle measurements due to soft tissue deformation we used 2D video analysis to calculate the actual knee joint angle during all contractions on the basis of the following markers: iliac spine, greater trochanter of the opposite side, lower portion of the patella (patellar tendon origin), upper anterior surface of the tibia (patellar tendon insertion), and knee centre of rotation. The marker positions were recorded by means of a Casio Exilim Camera (200 fps, Casio Computer Co., Ltd., Tokyo, Japan) and analysed with a video processing software (Tracker v4.0). The camera was positioned on the left side of the subject, perpendicular to the thigh longitudinal axis. To eliminate any radial distortion, a rectilinear filter was applied during marker tracking on the video frames. The resultant marker trajectories were smoothed using a forward and reverse second order low pass Butterworth filter (cut-off: 15 Hz). Based on these kinematic data, the patellar tendon moment arm could be calculated [as proposed by Bakenecker et al. (2019)].

After a warm-up based on sub-maximal fixed-end and iso-velocity contractions, the torque–angle relationship was obtained based on eight maximum fixed-end contractions (MVCs) at different joint angles (from 90° to 20° where 0° = knee fully extended) with 10° intervals, while the torque–angular velocity relationship was obtained based on values of maximum torque recorded during the iso-velocity phase at the angular velocities of 60, 90, 180, 280, and 360°.s^–1.

During the MVCs and the iso-velocity tests, the subjects were instructed to push “as hard as possible” for 4–5 s (for the MVCs) or over the entire ROM (for the iso-velocity trials). Two maximal fixed-end contractions were performed for each joint angle, with 2 min of recovery in between, whereas for the iso-velocity trials three consecutive contractions (with 30 s of recovery in between) were performed at each velocity with 2 min of recovery between velocities. For each iso-velocity trial, participants were instructed to extend their knee as hard as possible from ∼0.5 s before the start of the set to the end of the set. This protocol pre-loaded the muscles facilitating maximal voluntary neuromuscular activation, and therefore maximum torque, throughout the entire ROM (Tillin et al., 2012a, 2018).

During all contractions, fascicle length changes were recorded by means of an ultrafast ultrasound apparatus with a 5.5 cm linear array probe operating at 1000 fps (Supersonic, Aixplorer, France). The probe was fixed to the skin by means of a plastic strap approximately at 50% of the femoral length, aligned on the muscle belly and corrected with respect to the superficial and deep aponeurosis, in order to have a clear image of the perimysial connective intramuscular tissue, that it is indicative of the muscle fascicle structure. The probe was never removed during the entire experimental session and a marker on the skin was drawn to reposition the probe in the same position during the second experimental session (48 h later).

Finally, the EMG activity of the VL and BF were recorded during each contraction by means of two bipolar Ag-AgCl electrodes. The electrodes were attached over the muscle belly according to the SENIAM recommendations (Hermens et al., 2000). The raw EMG data were recorded at 1000 Hz with a PowerLab System (PowerLab, ADInstruments, Dunedin, New Zealand).

All devices were synchronised with an external manual trigger (5 V) and all data were collected at 1000 Hz.

During the explosive dynamic concentric contractions the participants were instructed to extend their knee “as fast and as hard” as possible with an emphasis on “fast” (Sahaly et al., 2001) in four separate conditions: 1000 (EDC₁₀₀₀), 2000 (EDC₂₀₀₀), 3000 (EDC₃₀₀₀), and 4000°.s^–2 (EDC₄₀₀₀). For each condition, the lever arm angular acceleration was preprogrammed using a real-time control custom program (LabView v.10) to increase the Biodex capability, as proposed by Van Roie et al. (2020). At least 15 contractions were recorded for each condition; 1 min of recovery was imposed after each contraction and their order was randomised.

As previously suggested by Tillin et al. (2018), in concentric conditions the dynamometric arm moved slowly (10°.s^–1) from the maximum knee joint flexion angle to the angular position at which the acceleration phase starts (which was different for each acceleration condition, see knee angle at voluntary torque onset in Table 1). In all concentric contractions, the starting angle for each participant was selected in order to have 75 ms of contraction before and after the target joint angle: the angle at which his optimal fascicle length was observed (about 65°, see knee angle at 75 ms from torque onset in Table 1 and Figure 1).

During each dynamic explosive concentric contraction, participants were instructed to avoid any countermovement (negative/flexor torque). For all concentric conditions, the real-time knee angle signal (Biodex output) was displayed on a computer monitor in front of the participants. In this way, the subject could control the start of the acceleration phase (Tillin et al., 2018).

For each condition, 15 “good” contractions were selected. The quality of the contraction was controlled in real-time by an operator using the LabChart software, based on the EMG and the torque signals. Exclusion criteria were similar to those reported by Tillin et al. (2018) and Tillin et al. (2012a). Therefore, the EDC contractions were excluded if: (1) baseline torque exceeded ± 2 Nm in the 2 s preceding active-torque onset; (2) baseline torque in the 100 ms preceding active torque changed by more than 2.5 Nm; (3) torque onset occurred earlier than 20 ms (all conditions) or later than 30 ms into the acceleration phase. Torque onset in all conditions was defined as the point at which the first derivative of the active torque–time curve crossed zero for the last time (Tillin et al., 2012a). During these procedures, the total torque generated by the knee extensors was corrected for the gravitational torque effects (determined during a passive joint rotation driven by the dynamometer).

As in the case of the MVCs and iso-velocity tests, ultrasound data, EMG activity, and kinematic data were recorded at 1000 Hz. The location of the electrodes, as well as the location of the ultrasound probe, was the same used for the MVCs and iso-velocity trials.

The total torque generated by the knee extensors was corrected for the gravitational torque effects (determined during a passive joint rotation driven by the dynamometer) and for the EMG–torque relationships of the antagonist muscles (BF) (see Kellis and Baltzopoulos, 1996, 1998). The dynamometer torque output was also corrected for inertia and passive torque. The moment of inertia (i.e., shank, foot, and dynamometric arm) was estimated as proposed by Farcy et al. (2014) and Hauraix et al. (2017) and the passive torque was calculated and subtracted to the measured values as proposed by Tillin et al. (2012a, b). Finally, the torque generated by the knee extensors was converted into force by knowing the patellar tendon moment arm [as proposed by Bakenecker et al. (2019)].

For the ultrasound measurements, a validated semi-automatic tracking algorithm was used to quantify the muscle fascicle length and pennation angle frame by frame (Gillett et al., 2013). The length of muscle fascicles was defined as the distance along the fascicles between the deep and superficial aponeuroses, whereas the pennation angle (α) was defined as the angle between the collagenous tissue and the deep aponeurosis (Franchi et al., 2018; Monte and Zamparo, 2019). Since VL fascicles could be longer than the field of view of the ultrasound probe, the automatic software performed a linear extrapolation of the fascicle length, as reported by others (Randhawa et al., 2013; Hahn et al., 2017; Nikolaidou et al., 2017; Monte et al., 2020). As discussed by Franchi et al. (2020), this extrapolation method may be suitable for estimating fascicle length in muscles that present a relatively linear fascicle arrangement, or a consistent fascicle curvature, as in the case of the middle region of VL. Furthermore, at the end of the auto-tracking, every frame of the tracked fascicle lengths and pennation angles was visually examined to check the algorithm accuracy. Whenever the fascicle length or pennation angle was deemed inaccurate, the two points defining the muscle fascicles were manually repositioned.

The EMG signal was always analysed starting from force onset; in the fixed-end and iso-velocity contractions the EMG signal was smoothed to match the root mean square (RMS) epochs used for the explosive voluntary contractions (Tillin et al., 2012a, 2018). The EMG data at maximum voluntary force (MVF) was then calculated from the average RMS amplitude over a 10 ms epoch either at MVF for each fixed-end knee angle, or at any given knee angle for the best MVC at each velocity (Tillin et al., 2012a,b, 2018).

To reconstruct the force–angle relationship, the highest value of force recorded at each knee angle was taken as the MVF for that angle (see Figure 2, upper panel). Furthermore, the fascicle length obtained at MVF was measured and used to reconstruct the F–L relationships (see Figure 2, middle panel). Therefore, based on MVF data and muscle fascicle length collected at each joint angle, the F–L relationship was also determined for each subject (Monte et al., 2020). The maximum isometric voluntary force (F_max) was calculated as the peak of the F–L relationships, while the optimal fascicle length (L₀) as the VL fascicle length at which F_max occurs (see Figure 2, middle panel).

To reconstruct the fascicles and muscle F–V relationships the ultrasound data collected during the iso-velocity trials were used. For these procedures, fascicle velocity was obtained as the first derivative of the fascicle length changes, whereas the belly velocity as the first derivative of the belly length changes (obtained as: Fascicle length. cos α, where α is the pennation angle). As calculated, belly length does not represent the entire length of the VL muscle belly but only the projection of the VL fascicle length to the plane of the MTU; this method to estimate muscle belly velocity (Vb), is utilised when the myotendinous junctions is not tracked with a second ultrasound probe, as in our case (Wakeling et al., 2011; Randhawa et al., 2013; Hauraix et al., 2015; Bohm et al., 2019). Therefore, the F–V relationship was determined twice, based on the force–fascicle velocity and force–belly velocity values during the iso-velocity test (see Figure 2, bottom panel). Note that, as proposed by Holt et al. (2016), force values refer to the force of the whole muscles only, whereas muscle and fascicles velocities are measured independently.

These values were fitted using the following exponential equation, which was identified to be most applicable to F–V data measured in vivo compared to the classical Hill’s equation (Thomas et al., 1987):

where v is the fascicle/belly velocity (m.s^–1), F is the force value, F_max the maximal isometric force recorded during the MVC and extrapolated by the polynomial fit and a and b are experimentally determined constants. Constants a and b were obtained from the intercept (a/b) and slope (1/b) of the linearised Hill’s plot of (P₀ − P)/V vs. P, where V is the angular velocity of shortening (Ferri et al., 2003; Monte et al., 2020). Finally, the intercept value on the abscissa was taken as the maximal fascicle shortening velocity (Vf_max) or maximum belly shortening velocity (Vb_max).

The P–V relationship was determined based on the product of force and muscle belly velocity at any given time point.

As in the case of the MVCs and iso-velocity contraction, the joint torque generated by the knee extensors was calculated by taking into account gravitational torque, inertia, passive torque, and the antagonist contribution. Of the 15 recorded contractions, 5 were selected and further analysed: those in which the angle after 75 ms from onset was closer to target (see Figure 1 and Table 1).

Torque onset was defined as the point at which the first derivative of the active torque–time curve crossed zero for the last time (Tillin et al., 2012a, 2018). All the analysed variables (ultrasound, torque, and EMG parameters) were thus averaged over the five analysed contractions in each condition. The off-line analysis was conducted using custom-developed programs in LabVIEW (LabVIEW, v.10, AD Instruments, Sydney, Australia).

The absolute values of explosive torque reported in this study are the average of the torque values in the first 150 ms of explosive contraction (during the rising torque–time curve).

The five selected explosive contractions in each condition were also analysed for EMG. The EMG signal was filtered with a band-pass fourth order Butterworth filter at 20–450 Hz, whereas the onset of muscle activity was detected using a visual, systematic inspection method as suggested by Tillin et al. (2010, 2012b). During each condition, the RMS EMG amplitude of VL was measured with a time window of 10 ms, from EMG onset up to 150 ms. The EMG signal, as determined in EDC contractions as a function of time, was normalised for the maximum EMG amplitude recorded during the F–L and F–V evaluations. Normalised EMG reported in this study are the average of the EMG values in the first 150 ms of explosive contraction (during the rising torque–time curve).

As in the case of the MVCs and iso-velocity contractions, fascicle length and pennation angle for each explosive contraction were recorded with an automatic software (see F–L and F–V analysis); examples of ultrasound images are reported in Supplementary Figure 1. A reliability and sensitivity study of the ultrafast-ultrasound-based measurement of VL fascicle behaviour during explosive contraction revealed very good reliability between single trials, with coefficient of multiple correlations (CMC) ranging from 0.92 to 0.97. Moreover, the average root mean square difference (RMSD) values were about 1.3–0.7 mm for VL fascicle lengths (see Supplementary Tables 1, 2).

Based on the ultrasound data, fascicle velocity (V_fascicle) was calculated as the first derivative of the fascicle length–time curve, whereas the muscle belly velocity (V_belly) was calculated as the first derivative of the belly length (obtained as: Fascicle length ⋅ cos α, where α is the pennation angle). To take into account the possible mismatch among fascicle and muscle belly, the belly gearing (G_b) was calculated as the ratio between belly velocity and fascicle velocity (Wakeling et al., 2011).

The F–V and the P–V potentials (i.e., fraction of the maximum force or power that a muscle could reach during a given shortening velocity) of fascicle and muscle belly were calculated for each dynamic contraction using the F–V and P–V relationships, as well as the instantaneous value of fascicles and belly shortening velocity (Bohm et al., 2019; Monte et al., 2020).