Residual force enhancement within the human quadriceps is greatest during submaximal stretch-hold contractions at a very long muscle length

Little is known about how muscle length affects residual force enhancement (rFE) in humans. We therefore investigated rFE at short, long, and very long muscle lengths within the human quadriceps and patellar tendon (PT) using conventional dynamometry with motion capture (rFETQ) and a new, non-invasive shear-wave tensiometry technique (rFEWS). Eleven healthy male participants performed submaximal (50% max.) EMG-matched fixed-end reference and stretch-hold contractions across these muscle lengths while muscle fascicle length changes of the vastus lateralis (VL) were captured using B-mode ultrasound. We found significant rFETQ at long (7±5%) and very long (12±8%) but not short (2±5%) muscle lengths, whereas rFEWS was only significant at the very long (38±27%), but not short (8±12%) or long (6±10%) muscle lengths. We also found significant relationships between VL fascicle length and rFETQ (r=0.63, p=.001) and rFEWS (r=0.52, p=.017), but relationships were not significant between VL fascicle stretch amplitude and rFETQ (r=0.33, p=.126) or rFEWS (r=0.29, p=.201). PT shear-wave speed-angle relationships did not agree with estimated quadriceps muscle force-angle relationships, which indicates that estimating PT loads from shear-wave tensiometry might be inaccurate. We conclude that increasing muscle length rather than stretch amplitude contributes more to rFE during submaximal voluntary contractions of the human quadriceps.


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Residual force enhancement (rFE) is a unique history-dependent property of skeletal muscle 38 and is defined as the enhanced steady-state force following active muscle lengthening (i.e. 39 stretch) relative to the steady-state force obtained during a fixed-end reference contraction at 40 the same muscle length and level of activation (Edman et al. 1978;Cook and McDonagh 1995). 41 rFE has been observed across muscle structural scales ranging from single sarcomeres (Leonard 42 et al. 2010) or isolated fibres from animals (Abbott and Aubert 1952) or humans (Pinnell et al. 43 2019) to whole human muscles working in vivo (Cook and McDonagh 1995)   In vitro experiments have shown that rFE is independent of stretch velocity (Edman et al. 1978; 47 Tilp et al. 2009), but dependent on muscle length, whereby rFE is greater when the stretch ends 48 at longer muscle lengths (Bullimore et al. 2007; Hisey et al. 2009). rFE generally increases with 49 increasing stretch amplitude (Edman et al. 1978(Edman et al. , 1982 until some critical amplitude on the One potential solution to more directly quantify in vivo rFE involves using a new, non-invasive 87 technique known as shear-wave tensiometry, which was introduced by Martin et al. (2018). 88 These authors previously showed that the shear-wave propagation velocity in free tendons 89 depends primarily on axial stress under physiological loads, and that in vivo tendon shear-wave 90 speeds can be tracked by a shear-wave tensiometer, which consists of a skin-mounted tapping 91 device and miniature accelerometers. The squared tendon shear-wave speeds measured with 92 this device were shown to strongly correlate with joint torques during fixed-end knee extension 93 and plantar flexion contractions (Martin et al. 2018). Squared Achilles and patellar tendon (PT) 94 shear-wave speeds were also shown to strongly correlate with joint torques that were estimated  Therefore, the aim of this study was to examine whether rFE is muscle-length dependent within 100 the human quadriceps using conventional dynamometry and shear-wave tensiometry to 101 estimate knee joint torques and PT loads, respectively. To achieve this aim, participants (N=16) 102 performed submaximal voluntary EMG-matched (50% of the knee joint angle-specific 103 maximum superficial quadriceps muscle activity) and rotation-amplitude-matched (15° knee 104 joint rotation) stretch-hold and fixed-end reference contractions at short, long, and very long 105 muscle lengths. To ensure that rFE was not influenced by differences in the muscle's isometric 106 force capacity at short and long muscle lengths, we attempted to match PT loads at short and 107 long muscle lengths. Based on the findings from in vitro experiments and the mechanisms 108 predicted to contribute to greater rFE at longer muscle lengths, such as sarcomere length non-109 uniformities (Morgan 1990) and increased titin forces at longer muscle lengths (Flann et al. 110 2011), we hypothesised that rFE would increase with increasing muscle length rather than 111 increasing stretch amplitude, which was partly verified by imaging muscle fascicle lengths and 112 6 length changes from one muscle, the vastus lateralis (VL), using B-mode ultrasound. We also 113 expected a strong agreement (≥90%) between squared PT shear-wave speeds and the estimated  Consequently, the sample sizes for shear-wave-speed and rFEWS data for the short, long, and 125 very long muscles lengths were 11, 9, and 11, respectively.

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Muscle activity levels 128 A two-way repeated-measures ANOVA on the mean time-matched steady-state summed 129 muscle activity level data from the superficial quadriceps muscles (VL, rectus femoris (RF), 130 and vastus medialis (VM)) found a significant main effect of contraction condition (F1,10 = 131 12.59, p = .005). However, mean differences between stretch-hold and fixed-end reference 132 contractions were within the allowed variation (<6% difference between the desired and 133 recorded EMG levels) and not significant according to Sidak post-hoc comparisons at the short Mean time-matched steady-state squared PT shear-wave speeds during the respective stretch-157 hold and fixed-end reference contractions were 3900 ± 2770 m 2 s -2 and 3677 ± 2703 m 2 s -2 at the 158 short muscle length, 2872 ± 1179 m 2 s -2 and 2775 ± 1215 m 2 s -2 at the long muscle length, and 159 2601 ± 1554 m 2 s -2 and 1800 ± 846 m 2 s -2 at the very long muscle length. A two-way repeated-160 measures mixed-effects analysis on shear-wave-speed data revealed significant main effects of 161 contraction condition (F1,10 = 12.11, p = .006) and muscle length (F1.35,13.52 = 5.00, p = .034), 162 and a significant interaction between contraction condition and muscle length (F1. 69 rFETQ values of 2 ± 5%, 7 ± 5% and 12 ± 8% were calculated at the short, long, and very long 176 muscle lengths, respectively. rFEWS values at the same respective lengths were 8 ± 12%, 6 ± 177 10% and 38 ± 27%. A two-way repeated-measures mixed-effects analysis on rFE data revealed   Outliers that were excluded from analysis are indicated as an X in B (n = 2). Grey lines and black numbers 192 distinguish between participants. *Indicates a significant difference between muscle length conditions (P < 0.05).   The mean target knee joint angles determined from the optical motion analysis system for the 235 fixed-end reference contractions were 28.2 ± 2.3°, 68.1 ± 10.1° and 83.6 ± 7.9° for the short, 236 long, and very long muscle lengths, respectively. For the stretch-hold contractions, the mean 237 target knee joint angles were 28.2 ± 4.3°, 68.7 ± 18.4° and 86.1 ± 19.2° for the short, long, and 238 very long muscle lengths, respectively. During the stretch-hold contractions, the measured knee 239 joint rotations during the amplitude-matched dynamometer-imposed rotations were 9.0 ± 4.3°, 240 14.7 ± 2.3° and 15.7 ± 2.8° to the short, long, and very long muscle lengths, respectively. The

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The main purpose of this study was to examine whether rFE magnitudes, which were estimated 258 from resultant knee joint torques and PT shear-wave speeds during time-and EMG-matched 259 submaximal stretch-hold and fixed-end reference contractions, are different at short, long, and 260 very long muscle lengths. To our knowledge, this is the first in vivo experiment that has 261 attempted to estimate rFE at more than two muscle lengths, and the first to use shear-wave 262 tensiometry. We found that resultant knee extension torques were significantly higher during during submaximal stretch-hold and fixed-end reference contractions, we found significant 277 rFETQ at the long and very long muscle lengths, but not at the short muscle length ( Figure 1A).

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This is in accordance to a previous study with a similar setup, where we also found significant length and therefore significant rFE based on our data (Figures 1 and 3).
In vitro findings suggest that rFE is not only muscle-length dependent, but also stretch- where rFE increased from <2% to ~2-4% to ~6-14% as the target muscle length increased from 328 3 mm shorter to 3 mm and 9 mm longer than the muscle's optimal length for isometric force 329 production (Hisey et al. 2009 Figure 1B) we calculated might therefore be erroneous, which is supported by the much lower 347 than expected normalised PT shear-wave speeds determined during the fixed-end reference 348 contractions at the very long muscle length (see Figures 3 and 4). Unsurprisingly, the average 349 agreement between normalised PT shear-wave speeds and estimated quadriceps' forces was 350 worst at this muscle length (agreement at short: 72.4%; long: 81.5%; very long: 24.3%).

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In general, obtaining plausible shear-wave speeds from the PT proved to be very difficult. In  predefined EMG/muscle activity ramps that were 5% apart. shear-wave speed) was selected as the reference knee joint angle for the fixed-end contractions 500 at short and long muscle lengths. An additional fixed-end reference contraction was performed 501 at a knee joint angle that was 15° more flexed than the joint angle at the long muscle length 502 (which is referred to as the 'very long muscle length'). Stretch-hold contractions to the short, 503 long, and very long muscle lengths were performed with a 15° crank arm rotation amplitude to 504 the predetermined knee joint angle for each muscle length condition. The hold phase of the 505 stretch-hold contractions was 6 s, which allowed rFE to be determined (Figures 4 and 6). The 506 crank arm rotation velocity was set to 60°s -1 and was triggered 1.5 s after participants reached 507 the plateau of the required muscle activity level. Similar to part 1, participants were asked to 508 ramp up their muscle activity level and hold it at 50% of their angle-specific maximum muscle 509 activity level during stretch-hold and fixed-end contractions ( Figure 6A). The two contraction  All data processing and analysis were performed using custom-written scripts in Python.

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Torque and crank arm angle data were filtered using a dual-pass fourth-order 20 Hz low-pass 604 Butterworth filter. The knee angle was determined as the dihedral angle between the planes of 605 the three markers on the shank and thigh. EMG signals from the superficial quadriceps muscles 606 (VL, RF, VM) and the biceps femoris muscle were smoothed using a centred moving root-

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where red font has been used to highlight instances of less than 90% agreement. P2 had to be excluded from this quadriceps muscle activities (shown on the right y-axis) were normalized to maximum knee extension torques and 870 maximum summed quadriceps muscle activity level, respectively. P2 was excluded due to missing marker data.