Residual force enhancement is affected more by quadriceps muscle length than stretch amplitude

Abstract

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 (rFE_TQ) and a new, non-invasive shear-wave tensiometry technique (rFE_WS). 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 rFE_TQ at long (7±5%) and very long (12±8%), but not short (2±5%) muscle lengths, whereas rFE_WS 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 rFE_TQ (r=0.63, p=0.001) and rFE_WS (r=0.52, p=0.017), but relationships were not significant between VL fascicle stretch amplitude and rFE_TQ (r=0.33, p=0.126) or rFE_WS (r=0.29, p=0.201). Squared PT shear-wave-speed-angle relationships did not agree with estimated PT 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.

Keywords: eccentric; force-length relation; human; knee extensors; muscle history dependence; physics of living systems; shear-wave tensiometry.

Figure 1.. Individual and mean residual force enhancement (rFE) magnitudes (n=11) based on corrected torque (A) and squared patellar tendon (PT) shear-wave-speed recordings (B) at the short (dots), long (triangles), and very long (squares) muscle lengths.

Individual and mean vastus lateralis (VL) muscle fascicle stretch amplitudes are shown in C (n=11). Unfilled symbols represent the individual values and horizontal bars indicate the group mean for each condition. Outliers that were excluded from analysis are indicated with a X in B (n=2). Grey lines and black numbers distinguish between participants. *Indicates a significant difference between muscle length conditions (p<0.05). ^#Indicates significant rFE based on corrected knee extension torque (A) and shear-wave-speed (B) measurements (p<0.05).

Figure 2.. Repeated-measures linear relationships between rFE_TQ and vastus lateralis (VL) fascicle stretch amplitude (A: r=0.33, 95% CI: –0.12 to 0.67, p=0.126), rFE_TQ and VL fascicle length (B: r=0.63, 95% CI: 0.27–0.83, p=0.001), rFE_WS and fascicle stretch amplitude (C: r=0.29, 95% CI: –0.19 to 0.66, p=0.201), and rFE_WS and VL fascicle length (D: r=0.52, 95% CI: 0.08–0.79, p=0.017).

Pearson correlations neglect the substantial within-subject variability and therefore were not performed (Bakdash and Marusich, 2017).

Figure 3.. Individual normalised relationships between estimated patellar tendon (PT) force (PT_F) and knee flexion angle and between squared PT shear-wave speed (PT_WS) and knee flexion angle determined from the fixed-end reference contractions at the short, long, and very long muscle lengths from part 2 of the experiment.

The average agreement across muscle lengths (100 – (PT_WS – PT_F)/(PT_WS +PT_F)×100) between normalised PT forces and squared PT shear-wave speeds is indicated as a percentage for every participant, where red font has been used to highlight instances of less than 90% agreement. The bottom right panel shows the mean normalised relationship between estimated PT force and knee flexion angle and between squared PT shear-wave speed and knee flexion angle across all participants. The angle-specific agreement across participants was 86%, 91%, and 62% at the short, long, and very long muscle lengths, respectively.

Figure 3—figure supplement 1.. Individual normalised relationships between estimated patellar tendon (PT) force (PT_F) and knee flexion angle and between squared PT shear-wave speed (PT_WS) and knee flexion angle determined from the fixed-end reference ramp contractions at the short, long, and very long muscle lengths from part 1 of the experiment.

The average agreement across muscle lengths (100 – (PT_WS – PT_F)/(PT_WS + PT_F)×100) between normalised PT forces and squared PT shear-wave speeds is indicated as a percentage for every participant, where red font has been used to highlight instances of less than 90% agreement. P2 had to be excluded from this analysis due to missing marker data. The bottom right panel shows the mean normalised relationship between estimated PT force and knee flexion angle and between squared PT shear-wave speed and knee flexion angle across all participants. The angle-specific agreement across participants was 49%, 100%, and 42% at the short, long, and very long muscle lengths, respectively.

Figure 3—figure supplement 2.. Individual squared patellar tendon (PT) shear-wave-speed-time (green), knee extension torque-time (blue), and summed quadriceps’ muscle activity level-time traces (grey) during maximum voluntary fixed-end reference contractions at a 70° crank-arm angle from part 1 of the experiment.

Knee extension torques and the summed quadriceps muscle activities (shown on the right y-axis) were normalised to the maximum knee extension torque and maximum summed quadriceps’ muscle activity level, respectively. P2 was excluded due to missing marker data.

Figure 4.. Exemplar (n=1) squared patellar tendon (PT) shear-wave-speed-time (A, B, C), corrected knee extension torque-time (D, E, F), and normalised quadriceps muscle activity level-time traces (G, H, I) for the stretch-hold (blue) and fixed-end reference (green) contractions at the short (A, D, G), long (B, E, H), and very long (C, F, I) muscle lengths.

The vertical grey shaded areas show the time intervals where mean squared PT shear-wave speeds and corrected torques were analysed to evaluate rFE_WS and rFE_TQ.

Figure 5.. Solid lines indicate the mean normalised fitted relationship between patellar tendon (PT) shear-wave speed and knee flexion angle (Panel A) and mean fitted relationship between quadriceps’ muscle activity level and knee flexion angle (Panel B) across all participants (N=11) with lower and upper 95% confidence intervals (dashed lines).

Two different knee joint angles (i.e. the short and long muscle lengths), with a matched PT shear-wave-speed capacity (85% of maximum PT shear-wave speed), were selected as the target knee joint angles for the stretch–hold and fixed-end reference contractions. A third target knee joint angle, referred to as the ‘very long muscle length’, was defined as a crank-arm angle 15° more flexed than the crank-arm angle at the long muscle length.

Figure 6.. Exemplar (n=1) summed superficial quadriceps’ muscle activity level-time (A), knee flexion angle-time (B), and crank-arm angle-time traces during stretch-hold (blue line) and fixed-end reference (green line) contractions at the long muscle length.

For each muscle length condition, participants were instructed to match their quadriceps’ muscle activity level (calculated as a 250 ms centred root-mean-square amplitude) between two predefined traces 5% apart that ramped up to 50% of their angle-specific maximum over 3 s during both stretch-hold and fixed-end reference contractions. Outcome measures were analysed in the time interval from 2.5 to 3 s after stretch (vertical dotted lines), which corresponded to ~6 s after contraction onset in the stretch-hold and fixed-end reference contractions.

Figure 7.. Corrected torque was calculated by multiplying the force acting at the shank (FShank) by the external moment arm to the knee (rKnee).

${\displaystyle {\mathrm{F}}_{Shank}}$ acted at the midpoint of the pad attached to the shank and $r_{Knee}$ was the perpendicular distance from the line of action of ${\displaystyle {\mathrm{F}}_{Shank}}$ to the knee joint centre (KJC). ${\displaystyle {\mathrm{F}}_{Shank}}$ was calculated by dividing the calculated dynamometer force (${\displaystyle {\mathrm{F}}_{Dyna}}$) by the cosine of the angle between the two force vectors, ${\displaystyle {\mathrm{F}}_{Shank}}$ and ${\displaystyle {\mathrm{F}}_{Dyna}}$, whose respective directions were defined by the normal vectors of the planes formed by Shank Marker 1 (S1), S2, and S3, and Dynamometer Marker 1 (D1), D2, and the dynamometer’s axis of rotation (AoR). ${\displaystyle {\mathrm{F}}_{Dyna}}$ was calculated by dividing the measured torque at the dynamometer AoR by the external moment arm of the dynamometer (${\displaystyle {\mathrm{r}}_{Dyna}}$). ${\displaystyle {\mathrm{r}}_{Dyna}}$ was calculated as the distance between P and AoR. P was defined as the shortest distance between the projection of AoR onto the vector formed by S3 and the midpoint of the pad attached to the shank (SF). Transparent colored markers indicate captured markers, whereas solid marker KJC was calculated as the midpoint between the lateral and medial epicondyles of the femur (LEF and MEF, respectively), and solid marker SF was calculated as the midpoint between S1 and S2.