Muscular strength, the maximum voluntary torque (MVT) a muscle group can produce, influences the performance of athletic events (1 2 3 4,5 6–8
Theoretically, physiological cross-sectional area (PCSA) most accurately reflects the number of sarcomeres/myosin-actin cross-bridges arranged in parallel and thus able to generate tension between the tendons (9 7,10 MAX [7 muscle volume (VOL [11 11 MAX and VOL can be accurately assessed with T1-weighted magnetic resonance imaging (MRI), considered the gold standard technique (12 L F ) and further corrected for the loss of force transmission to the aponeurosis/tendon in pennate muscle (i.e., pennation angle, θ P ), sometimes referred to as effective PCSA (EFF PCSA). Therefore, PCSA relies on both the determination of VOL (via MRI) and the precise measurements of muscle architecture (L F and θ P , via ultrasound).
Previous studies comparing associations between strength and different muscle size indices (i.e., ACSAMAX vs PCSA vs VOL) have used the following muscle architecture (L F and θ P ) approximations for the calculation of PCSA: estimation from cadaveric data (7 11 11 13,14 L F has commonly been assessed, and hence, PCSA calculated, with relatively short ultrasound arrays that visualize ~30%–50% of L F (40 mm array [15,16 17 18 L F . This limitation can be minimized by use of a longer ultrasound array, thereby reducing the proportion of overall fascicle length that is extrapolated. Moreover, these issues in the assessment of L F and θ P may provide a methodological explanation for the variable findings as to the best muscle size index of strength. It is conceivable that more careful architecture, and thus also PCSA, measurements could result in PCSA being the superior determinant of muscle strength and demonstrate the utility of incorporating muscle architecture measurements within the assessment of human muscle size. Finally, muscle thickness assessed with ultrasound imaging is often considered a convenient but somewhat crude index of muscle size. Perhaps surprisingly, the relationship between muscle thickness and strength has not been compared with that of MRI-derived measures of muscle size (ACSA, PCSA, and VOL) and strength.
The theoretical basis for a close association of cross-sectional area measurements (ACSA and PCSA) and muscular strength, as opposed to VOL, is based on the assumption of longitudinal transmission of force along the muscle from the cross section of greatest area and thus the largest amount of contractile material aligned in parallel. However, lateral force transmission may provide an alternative means of transferring force from intermediate points along muscle fibers (19 20 21
The assumption of predominantly longitudinal force transmission also underpins the notion that the best measure of ACSA in relation to strength is the cross section with the greatest amount of contractile material in parallel (i.e., ACSAMAX , usually calculated as the sum of maximum ACSA from each constituent muscle, typically occurring at different points along the limb [7,22,23 quadriceps femoris (QF) muscle group, relatively proximal ACSA may be more strongly associated with strength (24 25 MAX .
The association between muscle size variables (i.e., EFF PCSA, ACSAMAX , and VOL) and joint-level function (i.e., strength/MVT) may be somewhat diluted/confounded by joint neuromechanical factors such as the leverage (moment arm) of the agonist muscles, as well as coactivation and thus opposing torque from the antagonist muscles. It is possible that muscle size variables could be very highly correlated with muscle force, as is the case for isolated animal muscles (r = 0.99 [8
Therefore, the aim of this study was to determine the effect of incorporating muscle architecture measurements, calculating muscle force, and ACSA measurement location on the human muscle size–strength relationship. Specifically by comparing (i) the relationships of four distinct QF muscle size measures (ACSAMAX and VOL from MRI, EFF PCSA from the combination of MRI with ultrasound measurements of architecture, and muscle thickness from ultrasound) with knee extensor strength in a large cohort of healthy young men; (ii) the association of these muscle size measures with muscle force as opposed to joint-level MVT; and (iii) the relationship of strength to ACSA, according to the site of ACSA measurements along the femur. We hypothesized that rigorous muscle architecture measurements (L F and/or θ P ) at eight sites throughout the QF, in combination with high-resolution MRI, would facilitate EFF PCSA rather than ACSAMAX or VOL, being the most powerful determinant of knee extension MVT; that higher associations would be found between muscle size indices with muscle force than with MVT, once joint-level confounders were accounted for; and that the MVT–ACSA relationship would be influenced by the location of the ACSA measurement along the femur length.
MATERIALS AND METHODS
Participants
Fifty-two young, healthy men (age, 25 ± 2 yr; height, 1.76 ± 0.07 m; body mass, 72 ± 9 kg) free from musculoskeletal injury provided written informed consent before participation in this study, which was approved by the Loughborough University Ethical Advisory Committee. All participants were recreationally active (2200 ± 1355 MET·min·wk−1 ; assessed with the short format International Physical Activity Questionnaire [26 in vivo [27,28 in vitro (i.e., single muscle fiber–specific tension) [29
Overview
Participants completed a familiarization session and two neuromuscular function measurement sessions of their dominant leg, 7–10 d apart at a consistent time of day (starting between 1200 and 1900 h), and an imaging session (within ±7 d of the second function measurement session). Familiarization involved participants completing knee extension and flexion maximum voluntary contractions (MVC) to become accustomed to these assessments. Function measurement sessions involved assessment of unilateral isometric knee extension strength (i.e., MVT) and antagonist coactivation (hamstrings EMG), as well as knee flexion MVC for EMG normalization. Musculoskeletal imaging of the dominant limb involved acquisition of magnetic resonance T1-weighted axial plane images (1.5 T) of the QF to assess the following: ACSA along the length of each constituent muscle, VOL, and in combination with ultrasound-derived muscle architecture measurements, EFF PCSA. Ultrasonographic images were recorded at two locations along the length of each constituent muscle of the QF to assess L F , θ P , and muscle thickness using a 92-mm-wide transducer that was typically able to visualize ~80%–90% of total L F (Fig. 1 A). Sagittal plane MRI scans of the knee were also acquired and analyzed to determine patellar tendon moment arm (PTMA ), which was used (along with antagonist EMG during knee extension) to calculate muscle force.
FIGURE 1: Representative: (A) ultrasound images of vastus lateralis (VL; 50% of femur length), vastus intermedius (VI; 50% of femur length), rectus femoris (75% of femur length), and vastus medialis (VM; 40% of femur length; 0% is knee joint space); (B) axial magnetic resonance image of the thigh; and (C) sagittal magnetic resonance image of the knee joint. TFCP, tibiofemoral contact point.
Torque Recording
Knee extension and flexion torque was recorded while participants were seated on a rigid custom-made isometric dynamometer (see Fig. 6B of Ref. [30 31 30
EMG Recording
Surface EMG was recorded from the medial and lateral hamstring muscles using a wireless EMG system (Trigno; Delsys Inc., Boston, MA). Hamstring EMG measurements were performed to allow for the estimation of muscle force during knee extension MVT (see the “Moment arm and calculation of muscle force” section of Materials and Methods hereinafter). Before sensor placement skin preparation (shaving, abrading, and cleansing with 70% ethanol) was conducted. Single differential Trigno Standard EMG sensors (Delsys Inc., Boston, MA; fixed 1-cm interelectrode distance) were then positioned on the medial (semitendinosus and semimembranosus) and lateral (biceps femoris long head) hamstring muscles using adhesive interfaces at 45% of thigh length (above the popliteal fossa). The location of the sensors was determined by palpating the borders of the biceps femoris long head and the medial hamstrings (semitendinosus and semimembranosus), respectively. Each sensor was then placed at 50% of the mediolateral muscle width and parallel to the presumed orientation of the underlying fibers. The isometric dynamometer had a section of the seat removed to accommodate the placement of Hamstring EMG sensors on the skin without compression. EMG signals were amplified at source (×300; 20- to 450-Hz bandwidth) before further amplification (overall effective gain, ×909) and sampled at 2000 Hz via the same analog-to-digital converter and computer software as the force signal, to enable data synchronization. In offline analysis, EMG signals were corrected for the 48-ms delay inherent to the Trigno EMG system.
Knee Extension MVC
After a brief warm-up of the dominant-leg knee extensors (3-s contractions at 50% (×3), 75% (×3), and 90% (×1) of perceived maximum), participants performed 3–4 MVC with the instruction to “push as hard as possible” for 3–5 s. The MVC was separated by ≥30 s of rest. Biofeedback was provided by placing a horizontal cursor on the torque–time curve, with a horizontal cursor indicating the greatest torque obtained within that session, and verbal encouragement was provided during all MVC. Knee extensor MVT was defined as the greatest instantaneous torque achieved during any MVC during that measurement session. RMS EMG from each of the hamstring sites during knee extension MVT (i.e., over a 500-ms time period, 250 ms either side of instantaneous knee extension MVT) was normalized to that measured during knee flexion MVT (knee flexion EMGMAX ; see hereinafter) and then averaged across the two hamstring sites (normalized antagonist HEMG). Knee extension MVT had a between-session within-participant coefficient of variation (calculated as: [SD/mean] × 100) value of 3.0%.
Knee Flexion MVC
Knee flexion MVC was then performed in the same manner as knee extension MVC after prior warm-up contractions. Knee flexion MVT was defined as the greatest instantaneous torque achieved during any MVC during that measurement session. RMS hamstring EMG for a 500-ms epoch at knee flexion MVT (250 ms either side) was analyzed for each site (knee flexion EMGMAX ); this approach was intended to capture muscle activity measures during the 500-ms period with the highest mean torque during the plateau phase of the 3–5 s MVC where torque is relatively stable.
Fascicle Length, Pennation Angle, and Muscle Thickness
L F, θ P , and muscle thickness of the constituent QF muscles (vastus lateralis (VL), vastus intermedius (VI), vastus medialis (VM), and rectus femoris (RF)) were measured using a B-mode ultrasonography machine (EUB-8500; Hitachi Medical Systems UK Ltd, Northamptonshire, United Kingdom) and a 92-mm, 5- to 10-MHz linear-array transducer (EUP-L53L) coated with water-soluble transmission gel. To match the knee joint angle during MVC, these images were collected while participants sat at rest in the same isometric dynamometer and joint configuration used for maximum strength testing. Images were captured at rest at two sites along the length of each constituent muscle of the QF. Specifically, ultrasound images were recorded at 50% of superficial mediolateral muscle width at the following locations along the length of the femur from the knee joint space: 30% and 50% of femur length (VI), 50% and 70% of femur length (VL), 20% and 40% of femur length (VM), and 55% and 75% of femur length (RF). The locations of these ultrasound recordings were largely adopted from prior research incorporating multiple ultrasound measurements along the length of each constituent muscle of the QF (32
θ P at each individual recording site was measured as the angle of insertion of the muscle fascicles into the deep aponeurosis (Fig. 1 A), except for the VI where θ P was measured as the angle between the proximal end of each fascicle and the femur. L F was measured as the length of the fascicular path between the insertions into the superficial and deep aponeurosis (Fig. 1 A). When the fascicular path extended beyond the acquired image, the missing portion of the fascicle was estimated by extrapolating linearly the fascicular path and the aponeurosis (18,33 L F and θ P at each measurement site were taken as the mean of three individual fascicles. L F and θ P of each constituent muscle were averaged across the two measurement sites of that muscle. Overall QF L F and θ P were calculated as the mean of the four constituent muscles. Muscle thickness at each measurement site (i.e., two per muscle) was quantified as the mean of the distance between the deep and superficial aponeurosis at each end, and the middle of the image before being averaged across sites within each muscle (Fig. 1 A). Finally, the muscle thickness for each constituent muscle was summed to quantify overall QF muscle thickness.
MRI Scan and Analysis Procedures for Muscle Size and PTMA
Muscle size variables
Participants reported for their MRI scan (1.5 T Signa HDxt, GE) having not completed any strenuous physical activity in ≥36 h and had received prior instruction to arrive in a relaxed state having eaten and drunk normally. Upon arrival, participants sat quietly for 15 min before their MRI scan. Participants lay resting supine at a knee joint angle of 163° (180° = full extension) while MR imaging was conducted. A receiver eight-channel whole-body coil allowed axial T1-weighted images (time of repetition/time to echo, 550/14 ms; image matrix, 512 × 512; field of view, 260 × 260 mm; pixel size, 0.508 × 0.508 mm; slice thickness, 5 mm; interslice gap, 0 mm) of the dominant leg to be acquired from the anterior superior iliac spine to the knee joint space in two overlapping blocks. Oil‐filled capsules placed on the lateral side of the thigh allowed for the alignment of the blocks during analysis (OsiriX software, Version 6.0; Pixmeo, Geneva, Switzerland). The constituent muscles (VM, VL, VI, and RF) were manually segmented in every third image (i.e., every 15 mm; Fig. 1 B) starting from the most proximal image in which the muscle appeared. The number of images (slices) manually segmented along the length of each constituent muscle was as follows (mean ± SD): VL, 24 ± 2 (range, 21–28); VI, 24 ± 1 (range, 21–28); VM, 23 ± 2 (range, 20–26); and RF, 22 ± 1 (range, 20–25).
The ACSA values measured along the length of each muscle were expressed relative to femur length (defined by the number of axial slices between the proximal greater trochanter (100% femur length) and the knee joint space (0% femur length)). Cubic spline interpolation (1000 point; GraphPad Prism 6; GraphPad Software) was then used to quantify ACSA for each constituent muscle at 5% intervals along the length of the femur, and overall QF ACSA at each 5% interval was calculated by summation. QF ACSAMAX was calculated as the summation of the maximal measured ACSA from each constituent muscle, and the location relative to femur length was also recorded.
The volume of each constituent QF muscle was calculated as the area under the ACSA–femur length curve after cubic spline interpolation, and the constituent muscle volumes were summed for overall QF VOL. The EFF PCSA of each individual QF muscle was calculated as follows: muscle volume (cm3 ) divided by L F multiplied by the cosine of θ P . L F and θ P were mean values from two ultrasound measurement sites along the length of each individual QF muscle. Overall QF EFF PCSA was calculated via the summation of the individual QF muscle EFF PCSAs.
Moment arm and calculation of muscle force
Immediately after thigh imaging, a lower extremity knee coil was used to acquire sagittal images (time of repetition/time to echo, 480/14 ms; image matrix, 512 × 512; field of view, 160 × 160 mm; pixel size, 0.313 × 0.313; slice thickness, 2 mm; interslice gap, 0 mm) of the knee joint. Sagittal plane images were used to determine PTMA , the perpendicular distance from the patellar tendon line of action to the tibiofemoral contact point, which was approximately the midpoint of the distance between the tibiofemoral contact points of the medial and lateral femoral condyles (Fig. 1 C). The tibiofemoral contact point was used as an approximation of the joint center of rotation (34 MA length was then corrected to that during MVC by estimating moment arm at 115° from previously published data fitted with a quadratic function (35 MA . Antagonist knee flexor torque at knee extension MVT was estimated by expressing the antagonist HEMG amplitude during knee extensor MVT relative to the knee flexor EMGMAX (normalized antagonist HEMG) and multiplying by the knee flexor MVT (assuming a linear relationship between EMG amplitude and torque).
Statistics
All statistical analyses were conducted using SPSS Version 26.0 (IBM Corp., Armonk, NY), unless stated. Significance was defined as P < 0.05. MVT (knee extension and flexion) and normalized antagonist HEMG from each of the duplicate test sessions was averaged for each participant to produce criterion values for the calculation of muscle force and statistical analysis. Knee extension MVT, muscle force, QF size (VOL, ACSAMAX , EFF PCSA, and muscle thickness), PTMA , QF L F , and QF θ P were tested for outliers using the Grubbs’ test, also referred to as the ESD method (extreme studentized deviate; https://www.graphpad.com/quickcalcs/grubbs1/ MAX , EFF PCSA, and muscle thickness). To statistically assess differences between Pearson’s product–moment bivariate correlations (e.g., MVT vs QF VOL compared with MVT vs QF ACSAMAX , MVT vs QF VOL compared with muscle force vs QF VOL, or MVT vs ACSA at 50% of femur length compared with MVT vs ACSA at 70% of femur length), an online resource (http://comparingcorrelations.org 36 37 z -test (two dependent groups (i.e., same group), overlapping (i.e., one variable in common), two-tailed test, α level = 0.05, confidence value = 0.95, null value = 0). Pearson’s product–moment bivariate correlations were also calculated between MVT and location-specific QF ACSA measurement at 5% intervals between 10% and 90% of femur length. Between-participant coefficient of variation (CVB ) for all variables was calculated as follows: [cohort SD/cohort mean] × 100. L F and θ P were compared between muscles (i.e., once mean values had been derived across two measurement sites within each muscle) using a one-way ANOVA with stepwise multiple comparison corrected least significant difference (LSD) post hoc testing.
RESULTS
Group-level muscle strength, size, and architecture
Knee extension MVT was 246 ± 42 N·m (range, 173–396 N·m; CVB 17.3%), and QF muscle force was 5874 ± 960 N (range, 3886–8681 N; CVB 16.3%), respectively. Whole QF EFF PCSA, VOL, and ACSAMAX were 167 ± 19 cm2 (range, 124–206 cm2 ; CVB 11.4%), 1838 ± 263 cm3 (range, 1254–2573 cm3 ; CVB 14.3%), and 90 ± 12 cm2 (range, 68–125 cm2 ; CVB 13.8%), respectively. QF muscle thickness was 92 ± 11 mm (range, 74–123 mm; CVB 11.5%). Constituent QF muscle size variables are reported in Table 1 .
TABLE 1 -
Muscle size of overall and constituent
quadriceps femoris (QF) muscles.
Muscle Volume , cm3
ACSAMAX , cm2
EFF PCSA, cm2
Muscle Thickness, mm
VM
441 ± 68
25 ± 4
40 ± 7
26 ± 5
VI
547 ± 104
25 ± 4
54 ± 10
20 ± 4
VL
610 ± 98
28 ± 5
52 ± 8
25 ± 3
RF
240 ± 47
13 ± 2
21 ± 3
22 ± 3
QF
1838 ± 263
90 ± 12
167 ± 19
92 ± 11
Data are mean ± SD. VM, vastus medialis; VI, vastus intermedius; VL, vastus lateralis; RF, rectus femoris.
Overall QF L F was 106.6 ± 8.9 mm (range, 87.8–125.5 mm; CVB 8.4%), and QF θ P was 15.5° ± 1.8° (range, 12.2°–19.0°; CVB 11.5%). L F (i.e., mean of two sites) differed between constituent QF muscles (ANOVA, P < 0.001). Specifically, VI L F (98.7 ± 9.7 mm) was shorter than that of the VM (105.8 ± 15.2 mm), VL (113.1 ± 11.7 mm), and RF (108.9 ± 14.7 mm; LSD, 0.001 ≤ P < 0.019), and VM L F was shorter than that of the VL (LSD, P = 0.019). L F did not differ between any other individual QF muscles (LSD, 0.211 ≤ P ≤ 0.221). θ P differed between constituent QF muscles (one-way ANOVA, P < 0.001). Post hoc testing revealed that θ P differed between all individual QF muscles (LSD (all), P < 0.001; VL 16.0° ± 3.2°; VI 13.4° ± 3.3°; VM 19.2° ± 3.9°; and RF 13.5° ± 2.6°) except between VI and RF (LSD, P = 0.814). PTMA was 4.41 ± 0.30 cm (range, 3.65–5.16 mm; CVB 6.7%).
Correlation of muscle size variables with MVT and muscle force
MVT was correlated with all four QF size variables, with the bivariate correlation between MVT and VOL producing the highest r value (r = 0.773, P < 0.001), followed by ACSAMAX (r = 0.697, P < 0.001), EFF PCSA (r = 0.685, P < 0.001), and muscle thickness (r = 0.406, P = 0.003; Figs. 2 A–D). Statistical comparisons revealed no differences between the bivariate correlation coefficients of MVT and MRI-derived measures of muscle size: MVT with VOL or ACSAMAX (z = 1.614, P = 0.107), MVT with VOL or EFF PCSA (z = 1.555, P = 0.120), and MVT with ACSAMAX or EFF PCSA (z = 0.151, P = 0.880). However, correlation coefficients between MVT with VOL (z = 3.699, P < 0.001), ACSAMAX (z = 2.417, P = 0.015), or EFF PCSA (z = 2.393, P = 0.017) were each greater than the correlation coefficient between MVT and muscle thickness.
FIGURE 2: Scatterplots showing the relationships between knee extension maximum voluntary torque (MVT) and quadriceps femoris size measures: (A) muscle volume (VOL), (B) maximum anatomical cross-sectional area (ACSAMAX ), (C) effective physiological cross-sectional area (EFF PCSA), and (D) muscle thickness. Solid lines indicate the trend of the relationship between variables.
Muscle force was correlated with, or had a tendency to be correlated with, all four QF muscle size variables but with lower correlation coefficients than for MVT (VOL r = 0.627, P < 0.001; ACSAMAX r = 0.598, P < 0.001; EFF PCSA r = 0.575, P < 0.001; and muscle thickness r = 0.269, P = 0.054; Figs. 3 A–D). The correlation coefficients produced for each muscle size variable with muscle force were lower than for with MVT: VOL with muscle force or MVT (z = 3.306, P < 0.001), ACSAMAX with muscle force or MVT (z = 2.069, P = 0.039), EFF PCSA with muscle force or MVT (z = 2.252, P = 0.024), and muscle thickness with muscle force or MVT (z = 2.275, P = 0.023). In summary, muscle size variables explained 9.2% to 20.4% more of the variance in MVT than in muscle force. For context, we also calculated the correlation between PTMA and MVT finding a weak, significant relationship (r = 0.285, P = 0.041).
FIGURE 3: Scatterplots showing the relationships between quadriceps femoris muscle force and quadriceps femoris size measures: (A) muscle volume (VOL), (B) maximum anatomical cross-sectional area (ACSAMAX ), (C) effective physiological cross-sectional area (EFF PCSA), and (D) muscle thickness. Solid lines indicate the trend of the relationship between variables.
ACSA along the length of the femur
The ACSAMAX of each of the four constituent muscles occurred at 28.4% ± 3.6% (VM), 57.1% ± 5.1% (VL), 57.9% ± 4.3% (VI), and 68.2% ± 5.7% femur length (RF; Fig. 4 A). Considering location/femur length–specific ACSA of the whole QF (i.e., sum of all four constituents at each femur length), the highest ACSA occurred at 55% femur length (71 ± 10 cm2 ; Fig. 4 B). As the association between muscle force and muscle size measures was weaker than that for MVT (see previous paragraph), only bivariate correlations between location-specific ACSA measures and MVT were conducted. Significant correlations were observed between MVT and QF ACSA measurements at 25%–85% of femur length, with the highest correlation (r = 0.719, P < 0.001) occurring at 65% of femur length (i.e., more proximal than the position of highest location-specific ACSA; Fig. 4 C). In fact, ACSA measured at 65% femur length and two adjacent locations (60% and 70%) had marginally but not significantly (0.0688 ≤ z ≤ 0.4744, 0.6352 ≤ P ≤ 0.9452) higher correlation coefficients with MVT (r = 0.701–0.719) than ACSAMAX (r = 0.697). Statistical comparisons between correlation coefficients revealed that the association between MVT and ACSA at 65% of femur length was greater than the association between MVT and ACSA at 10%–45% of femur length (1.979 ≤ z ≤ 4.457, 0.001 ≤ P ≤ 0.048) and 75%–90% of femur length (2.093 ≤ z ≤ 3.493, 0.001 ≤ P ≤ 0.036); and had a tendency to be greater than 50%–55% of femur length (z = 1.711–1.843, 0.065 ≤ P ≤ 0.087). The association of MVT–ACSA at 65% of femur length did not differ compared with the that between MVT and ACSA at 60% or 70% of femur length (0.556 ≤ z ≤ 0.656, 0.512 ≤ P ≤ 0.579).
FIGURE 4: Location-specific anatomical cross-sectional area (ACSA) at 5% intervals along the length of the femur for the constituent quadriceps femoris (QF) muscles (A) and overall QF muscle group (B). C, Bivariate correlations between QF ACSA at 5% intervals along femur length and knee extension isometric maximum voluntary torque; 0% = distal, 100% = proximal. Significance of bivariate correlations are indicated as follows: *P < 0.05, **P < 0.01, ***P < 0.001. Data displayed in panels A and B are mean ± SD.
DISCUSSION
This study examined the relationship between QF size measures (VOL, EFF PCSA, ACSAMAX , and muscle thickness) and both knee extensor strength (MVT) and internal muscle force in a large cohort of healthy young men, as well as the influence of ACSA location along the femur on the relationship with strength. Our first two hypotheses were refuted as incorporating thorough muscle architecture measurements when determining EFF PCSA did not result in this index of QF size becoming the preeminent muscle size determinant of MVT, and muscle force was not more strongly associated with muscle size variables than joint-level MVT. In agreement with our final hypothesis, the MVT–ACSA relationship was influenced by ACSA measurement location with stronger correlations at specific locations of 60%–70% of femur length than for other locations.
Knowledge of the muscle size measurements underpinning strength and strength change is important in order to understand, assess/monitor, and potentially modify the most important determinants. Surprisingly, in the current study, determination of EFF PCSA involving comprehensive MRI scanning along the length of the constituent QF muscles and the incorporation of two ultrasonographic muscle architecture measurements per muscle did not result in EFF PCSA being the highest correlate of MVT. In fact, comparisons of correlation coefficients revealed no difference between the association of EFF PCSA, ACSAMAX , or VOL with MVT, although qualitatively VOL explained 59.8% of the variance in MVT, which was ~11%–13% greater than either EFF PCSA (46.9%) or ACSAMAX (48.6%). As far as we are aware, the current study involved the most thorough in vivo investigation to date with (i) a large cohort (n = 52 vs n = 19 [17 n = 26 [11 n = 39 [7 EFF PCSA measurements, we took multiple ultrasonographic measurements at two sites for each constituent muscle with a long ultrasound array to provide a rigorous assessment of muscle architecture as opposed to estimation from cadaveric data (7 11 11 13 θ P and. L F ) differed between the constituents QF muscles, indicating that all four muscles should be assessed to accurately determine EFF PCSA of each muscle and thus also of the whole muscle group. Despite these attempts to improve the EFF PCSA measurement, the current study provides robust evidence that with these techniques, EFF PCSA is not more strongly associated with strength than VOL or ACSAMAX , and qualitatively VOL actually explained ~13% more variance than EFF PCSA. Our finding that VOL was qualitatively the greatest correlate of muscular strength over cross-sectional area measurements (EFF PCSA and ACSAMAX ) was consistent with one previous report ([11 EFF PCSA ([11 MAX (7 17 EFF PCSA, ACSAMAX , VOL) in predicting strength seem relatively subtle, but with three of five data sets indicating VOL may be marginally superior.
The statistically equivalent but qualitatively weaker association of EFF PCSA with strength, compared with VOL, seems contrary to classic physiological theory that EFF PCSA best represents the number of actin-myosin cross-bridges in parallel and able to generate tension between tendons. There seem to be four possible explanations for this finding. First, our ability to assess complex muscle architecture and thus accurately determine EFF PCSA may be limited with the use of two-dimensional ultrasonography. Using more sophisticated three-dimensional muscle architecture imaging techniques (i.e., diffusion tensor MRI) for the determination of EFF PCSA seems a logical progression for future research. Second, it seems likely that VOL can be measured with less error than EFF PCSA, given the calculation of PCSA involves the combination of multiple variables with the potential for accumulated measurement error that might reduce the association with MVT. Third, classic physiology assumes purely longitudinal force transmission. However, evidence for the existence and importance of lateral force transmission has been documented in both amphibian myofibers (19 38,39 20,40,41 EFF PCSA is not the only geometric determinant of contractile force production. Specifically, because of lateral force transmission, the length and/or shape of a muscle/muscle group may also influence force production and explain why VOL qualitatively explained the largest amount of variance in muscular strength in the current study. Finally, although PTMA was a weaker predictor of isometric strength in this study (r = 0.285) than in some previous reports (17,24,42–44 r = 0.400–0.790), it is possible that VOL, which incorporates muscle length and cross-sectional area, may provide a (better) proxy for body size and PTMA , potentially explaining the higher correlation of VOL with MVT than cross-sectional areas.
Muscle thickness measured with ultrasound was a statistically weaker correlate of MVT (r = 0.406) than the MRI measures of muscle size (i.e., VOL, ACSAMAX , or EFF PCSA; r = 0.685–0.773). Similar (r = 0.411–0.470 [45,46 r = 0.550–0.700 [47,48 45,46,48
We had anticipated that the joint-level relationship between muscle size and strength may be limited by the influence of other neuromechanical factors (i.e., moment arm and antagonist activation/torque) that might dilute/confound this relationship, and thus, removal of these factors would lead to a stronger relationship between muscle force and size variables. However, the relationships between muscle force and muscle size variables were consistently and statistically lower than for joint-level MVT (i.e., explaining 9.2%–20.4% less variance). In essence, contrary to our hypothesis, removal of the confounding factors (moment arm and antagonist torque) weakened rather than strengthened the relationship of muscle size with force/torque. Given the convincing evidence for a very high correlation between EFF PCSA and muscle force in isolated muscles (r = 0.99; [8 49,50
It is possible that the contemporary methods that we employed are not sufficient to accurately assess antagonist torque. Although we assessed the activation of the largest of the knee flexors (medial and lateral hamstrings), only two/three of nine knee flexor muscles were measured; and antagonist torque was estimated based on an assumed linear relationship with EMG (22 51 MA measurement also used in the calculation of muscle force. Most contemporary studies, including the current investigation, typically measure PTMA in resting conditions to ensure good image quality (i.e., no movement artifact) and at a relatively extended knee joint angle due to space constraints within the bore of an MRI scanner. However, it is known that PTMA changes with contraction versus rest (52 35 MA values according to the differences in knee joint angle between the imaging and the strength measurements (50 MA may have compromised the precision of this measurement.
The relationship between MVT and ACSA in the present investigation was found to be systematically influenced by the location of the ACSA measurement relative to femur length, with r values progressively increasing from 10% up to a peak at 65% of femur length (r = 0.719) before gradually declining between 65% and 90% of femur length. Thus, the location showing the largest association between MVT and ACSA (65% of femur length) was proximal of the location with the largest location-specific ACSA of the whole quadriceps, which had a marginally lower correlation (55% of femur length, r = 0.633). The correlation coefficient between MVT and ACSA measured at 65% of femur length was found to be greater than, or have a tendency to be greater than, all other ACSA measures along the femur other than those directly adjacent (i.e., ACSA at 60% and 70% of femur length). In addition, the r value for the association between MVT and ACSA at 65% femur length was also marginally superior but statistically equivalent to that of ACSAMAX (i.e., sum of maximum ACSA from each constituent QF muscle, irrespective of location) and MVT (r = 0.697). Therefore, this rigorous MRI assessment at locations all along the femur supports the earlier suggestion based on ultrasound measurements that proximal QF ACSA may be particularly important for the strength of this muscle group (24 MAX is that a single slice image at this one location, which is a quicker, cheaper, and analytically less laborious than the imaging of the whole muscle needed to determine ACSAMAX , may be as effective at predicting function.
It was notable that the location-specific ACSA (65% of femur length) showing the highest correlation with MVT was also proximal to the ACSAMAX of all three vastii muscles (VM 28.4%; VL 57.1%; VI 57.9%) collectively comprising 87% of QF volume, with only the RF having a more proximal ACSAMAX (68.2%). We are not aware of any reason that the RF would have a disproportionate influence on knee extension strength. Alternative explanations for this observation of proximal QF ACSA being most strongly related to strength may include the differences between the imaging and strength measurements, in terms of both the state of muscle contraction (resting for MRI vs maximum contraction for MVT) and joint configurations (hip and knee close to the anatomical position for MRI scanning vs flexed hip and knee at MVT for the isometric dynamometry). For example, with the hip and knee flexed in the dynamometer, it might be expected that all four constituents of the QF would move distally compared with the anatomical position in the MRI scanner (i.e., proximal muscle locations (~65% of femur length) in the scanner may be closer to midthigh when seated on the dynamometer). On the other hand, as the muscle contracts, even during an isometric contraction, the fibers and fascicles shorten considerably. We have previously found fascicle length within the QF to shorten by 24% between rest and MVT, and as the muscle remains isovolumetric, cross-sectional area shows a corresponding increase (EFF PCSA +27% from rest to MVT [18 53 MAX . In summary, the way in which these potentially competing effects of contraction state and joint configuration combine to explain the apparent importance of proximal ACSA for isometric strength measurements is unclear.
The current study was not without its limitations, and it is important to acknowledge them. The highly specific nature of the strength assessment (isometric contraction of the knee extensors at a knee joint angle of 115°) used in the current investigation means that the results presented cannot necessarily be generalized or assumed to be the same for other muscle groups, modes of contraction (i.e., concentric or eccentric), or joint angles. Theoretically, because muscle architecture is known to change substantially with contractile force (18 EFF PCSA (18 54 55,56
In conclusion, despite incorporating comprehensive muscle architecture measurements to enhance the determination of EFF PCSA, statistical comparisons of correlation coefficients revealed no differences between the association of EFF PCSA, ACSA, or VOL with MVT, and VOL explained the highest variance in isometric knee extension MVT (~60%). This suggests that with contemporary methods of muscle architecture measurements, EFF PCSA offers no advantage over purely MRI-derived indices of muscle size, and researchers interested in understanding/explaining muscular strength may wish to use muscle volume as it does not require additional architecture measurements and seems to explain marginally more variance in strength. The location of ACSA measurements substantially affected the strength of the association with MVT, with the highest association for ACSA measured at the relatively proximal position of 65% of femur length. ACSA measured at this location was as strongly associated with MVT as ACSAMAX despite requiring only a single slice/image in contrast to scanning the whole muscle for ACSAMAX .
The authors thank the participants for their time in taking part in the study.
This study was supported financially by the Versus Arthritis Centre for Sport, Exercise, and Osteoarthritis (grant reference 20194). The authors declare no conflict of interest (financial or otherwise) and that the results of this study are presented clearly, honestly, and without fabrication, falsification, or inappropriate data manipulation. The results of this study do not constitute endorsement by the American College of Sports Medicine.
Author Contributions: T. G. B., G. J. M., T. M. M.-W., and J. P. F. contributed to the conception and design of research; T. G. B., G. J. M., and T. M. M.-W. performed experiments; T. G. B. and T. M. M.-W. analyzed data; T. G. B. and J. P. F. interpreted the results of experiments; T. G. B. prepared figures; T. G. B., and J. P. F. drafted the manuscript; T. G. B., G. J. M., T. M. M.-W., and J. P. F. edited and revised the manuscript; T. G. B., G. J. M., T. M. M.-W., and J. P. F. approved the final version of the manuscript.
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