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Keywords:

  • fibre angle;
  • fibre length;
  • pennation;
  • rectus;
  • skeletal muscle;
  • thigh;
  • vastus

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. References
  9. Appendix

Despite the functional importance of the human quadriceps femoris in movements such as running, jumping, lifting and climbing, and the known effects of muscle architecture on muscle function, no research has fully described the complex architecture of this muscle group. We used ultrasound imaging techniques to measure muscle thickness, fascicle angle and fascicle length at multiple regions of the four quadriceps muscles in vivo in 31 recreationally active, but non-strength-trained adult men and women. Our analyses revealed a reasonable similarity in the superficial quadriceps muscles, which is suggestive of functional similarity (at least during the uni-joint knee extension task) given that they act via a common tendon. The deep vastus intermedius (VI) is architecturally dissimilar and therefore probably serves a different function(s). Architecture varies significantly along the length of the superficial muscles, which has implications for the accuracy of models that assume a constant intramuscular architecture. It might also have consequences for the efficiency of intra- and intermuscular force transmission. Our results provide some evidence that subjects with a given architecture of one superficial muscle, relative to the rest of the subject sample, also have a similar architecture in other superficial muscles. However, this is not necessarily true for vastus lateralis (VL), and was not the case for VI. Therefore, the relative architecture of one muscle cannot confidently be used to estimate the relative architecture of another. To confirm this, we calculated a value of whole quadriceps architecture by four different methods. Regardless of the method used, we found that the absolute or relative architecture of one muscle could not be used as an indicator of whole quadriceps architecture, although vastus medialis, possibly in concert with VL and the anterior portion of VI, could be used to provide a useful snapshot. Importantly, our estimates of whole quadriceps architecture show a gender difference in whole quadriceps muscle thickness, and that muscle thickness is positively correlated with fascicle angle whereas fascicle length is negatively, although weakly, correlated with fascicle angle. These results are supportive of the validity of estimates of whole quadriceps architecture. These data are interpreted with respect to their implications for neural control strategies, region-specific adaptations in muscle size in response to training, and gender-dependent differences in the response to exercise training.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. References
  9. Appendix

Gross muscle architecture, encompassing a muscle's size and the lengths and angles of its fibres, is a strong determinant of force production and movement performance. Most notably, larger muscles typically have a large quantity of force-producing contractile material and are therefore able to develop high forces. However, the expression of this force is modulated by both fibre angle and fibre length (Woittiez et al. 1984; Lieber & Fridén, 2000). Muscles with fibres attaching at large angles to the tendon or aponeurosis have a large physiological cross-section for their volume, and therefore produce high relative forces (Powell et al. 1984). Because fibres of pennate muscles rotate as they shorten (Muhl, 1982), and consequently their fibre shortening distance is less than that of the tendon, fibres in pennate muscles are also able to work at lower shortening speeds and have a greater opportunity to work near their optimum length. Muscles with long fibres, however, are capable of contracting with high shortening speeds and produce forces over longer length ranges, as both of these characteristics are proportional to the number of serially arranged sarcomeres in the fibres. Also, because sarcomeres of longer fibres shorten less for a given absolute fibre shortening, their ability to produce force at high muscle shortening speeds is greater than that of short fibres. Given the significant effects of muscle architecture on force-generating ability, it makes sense for muscle architecture to vary across muscles and muscle groups according to the muscles’ functional roles (Lieber et al. 1992; Zajac, 1992).

Although it would be ideal for a muscle, or muscle group, to have an architecture that is suited specifically to the force requirements of the joint (or joints) it serves, some joints perform numerous functions. At the wrist, for example, there is a requirement for high force (torque) generation when it is used during heavy lifting, levering and pushing/pulling tasks, but it also functions through a large flexion–extension range of motion, or at higher velocities in other tasks. This creates a difficulty in that an ideal wrist extensor would contain fibres that are long, but attach at relatively large angles. The evolutionary solution to this problem is to have several muscles of varying architecture working in synergy so that muscles with a smaller volume can meet the force requirements (e.g. Jacobson et al. 1992; Lieber et al. 1992, 1997).

The human quadriceps function primarily as knee extensors, providing large forces during pushing/pulling movements, and assisting in leg extension during running and jumping. In comparison with other primates, humans walk (and run) with the knee joint relatively extended (Winter et al. 1974; D’Août et al. 2002; Schmitt, 2003), although during squatting and lifting the knee joint can become flexed acutely. Therefore, the quadriceps must produce forces over large length ranges. Moreover, during jumping, the knee extensor muscle stress reaches approximately 280 kN m−2 (Thorpe et al. 1998; bilateral countermovement jump) as the knee extensor moment reaches approximately 280 Nm (Bobbert et al. 1986). Therefore, human knee extensors must also be capable of producing relatively large muscle forces, often at high shortening speeds. Additionally, the variability in human physical activity patterns might also require different patterns of force generation, and thus different force-generating capacities in these muscles.

This creates a problem with respect to optimum muscle group design. Like the wrist muscle complex, the human quadriceps femoris comprises several muscles (including the mono-articular vastii and bi-articular rectus femoris). Variability in architecture between these muscles would ensure that a range of force requirements could be met. However, a comprehensive examination of quadriceps femoris architecture has not been performed, so a detailed picture does not exist. Examination of the intermuscular variability in architecture would allow a greater understanding of how synergists cooperate during force development. This is important for the construction of appropriate models of human movement, and for the design of mechanized locomotor systems including prosthetic and robotic limbs. Despite the importance of the human quadriceps in lifting and locomotion, no research to our knowledge has comprehensively described both its intra- and intermuscular architecture. It is also not known whether quadriceps architecture is uniform, or highly variable, between muscles or individuals. Because muscle architecture changes in response to physical loading (Kawakami et al. 1995; Blazevich et al. 2003), differences in activity patterns between individuals should increase architectural heterogeneity.

By way of comparison with a ‘theoretically optimum’ muscle group, the present research investigated several hypotheses: (1) the architecture of each muscle within quadriceps femoris should be different, as members of a synergistic group should have different force-production capabilities; (2) each muscle's architecture should be relatively homogeneous along its length so that each muscle is optimally designed to fulfil its role; (3) the relative (i.e. ranked against others within the subject sample) architecture of one muscle should be similar to the relative architecture of another muscle, as humans have different genetic and physical activity profiles and each subject's architecture should reflect that; and (4) given hypothesis 3, the relative (i.e. ranked) architecture of individual muscles should be indicative of whole quadriceps architecture, i.e. the measurement of one or more identified representative regions on the muscles should allow estimation of a subject's whole quadriceps architecture. In order partially to validate the estimation of whole quadriceps architecture, we compared men and women, and examined relationships between muscle thickness, fascicle angle and fascicle length. Based on the published data, we expected men to have a greater quadriceps muscle thickness than women (Abe et al. 1998; Chow et al. 2000; Kubo et al. 2003), for there to be a positive correlation between muscle thickness and fascicle angle (Abe et al. 1998; Brechue & Abe, 2002; Kanehisa et al. 2003), and for there to be a weaker negative correlation between fascicle angle and fascicle length (Calow & Alexander, 1983; Kumagai et al. 2000; Kanehisa et al. 2003). We compared four methods of estimating whole quadriceps architecture to determine whether a ‘best method’ could be derived, with the methods differing in the proportional contribution each muscle made to the whole quadriceps estimate.

Materials and methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. References
  9. Appendix

Subjects

Sixteen women [age (mean ± SD) = 19.9 ± 3.1 years, height = 170.0 ± 0.04 m, mass = 64.6 ± 7.9 kg] and 15 men (age = 20.6 ± 2.6 years, height = 1.80 ± 0.09 m, mass = 76.0 ± 13.0 kg) volunteered for the study. None of the subjects had neuromuscular or inflammatory diseases, nor had performed weight training in the 3 years prior to the study or performed intense physical exercise more than three times a week. The subjects refrained from intense physical exertion for at least 48 h prior to examination.

Muscle thickness and fascicle angle

In vivo muscle architecture was examined using two-dimensional (2-D), B-mode ultrasonography (Acuson Sequoia, Acuson Corporation, CA, USA) with a 3.8-cm linear array probe (7.5 MHz). 2-D ultrasound is commonly used for this purpose (e.g. Kawakami et al. 1995; Aagaard et al. 2001; Blazevich et al. 2003; Kanehisa et al. 2003; Kubo et al. 2003) and involves direct measurement of muscle thickness, fascicle angles and fascicle lengths from sonographs. The echoes reflected from the superficial and deep aponeuroses and the interspaces among the fascicles clearly delineate these structures and allows architectural measurements to be made. Measures of fascicle angle (≤ 1.5°; Kawakami et al. 1993; Narici et al. 1996; Chleboun et al. 2001) and fascicle length (≤ 1.5 mm; Kawakami et al. 1993) have been shown to be similar to those measured directly in cadavers, and are similar to those measured using 3-D ultrasound unless the transducer is not orientated in the plane of the fascicles (error range 2.4–14.0%; Kurihara et al. 2005). Muscle thickness has also been validated against magnetic resonance imaging scans in various human muscles (< 2 mm; Juul-Kristensen et al. 2000; Dupont et al. 2001).

To obtain the sonographs, subjects lay supine with their knees flexed to 45° with their legs supported and muscles relaxed. The knee bend was used to reduce fascicle curvature and improve measurement reliability, while still allowing significant interindividual variability to be seen. A water-soluble gel was applied to the probe to aid acoustic contact and remove the need to contact the skin, thus eliminating the deformation of muscle that might occur if pressure was applied. Sonographic scans were performed on the right leg with the probe orientated parallel to the muscle fascicles and perpendicular to the skin. The angle of the probe relative to the longitudinal axis of the thigh therefore varied between subjects, although approximate orientations are shown in Fig. 1. Appropriate probe alignment was achieved when several fascicles could be traced without interruption across the image (i.e. they did not run out of the plane of the sonogram). Sonographs were obtained at proximal, middle and distal sites on vastus lateralis (VL), vastus medialis (VM), vastus intermedius (VI) and rectus femoris (RF). VI was scanned simultaneously with both VL and RF to obtain sonographs of both anterior (VIant) and lateral (VIlat) portions. Scans were taken at 15 muscle sites across the quadriceps femoris at proximal, middle and distal sites as described in Fig. 1. An example sonograph is shown in Fig. 2.

image

Figure 1. Quadriceps femoris scanning sites. Sonographs were obtained at lengths equivalent to 5–73% of thigh length measured from the superior border of the patella to the anterior superior iliac spine. Muscles were scanned at three sites as indicated in the diagram above. The anterior portion of vastus intermedius (VIant, not shown) was scanned at the same sites as RF, while the lateral portion (VIlat) was scanned as per VL; thus, direct comparison can be made between sites 1 and 2 of the anterior portion with sites 2 and 3 on the lateral portion. VL: vastus lateralis, VM: vastus medialis, RF: rectus femoris, VIant: vastus intermedius (anterior portion), VIlat: vastus intermedius (lateral portion). Solid bars show the approximate transducer angles used to obtain images parallel to the fascicles on VL, VM and RF (VI not shown).

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image

Figure 2. Sagittal plane ultrasound scan of vastus lateralis (VL) and the lateral portion of vastus intermedius (VIlat). Landmarks corresponding to aponeuroses (points 1–4) and fascicles (points 5–6) were digitized (see Methods), as in the image above. Muscle thickness was calculated as the mean of the vertical distances between points 1–3 and 2–4. Fascicle angle, measured from 3 to 4 mm above the deep aponeurosis (dashed line) to mid-muscle was calculated as the angle between points 2–4 and 5–6. Aponeurosis angle was calculated as the positive angle between points 3–4 and 1–2.

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The sonographs were imported into image digitizing software (Peak Motus, Peak Technologies, CO, USA) and landmarks corresponding to the muscle fascicles and aponeuroses were digitized as shown in Fig. 3. Two points on each selected fascicle were digitized, one approximately 3–4 mm from the deep aponeurosis and a second at 50% of the distance from the deep to superficial aponeurosis. Although there was little fascicle curvature at most sites, there was a tendency for fascicles to curve slightly close to their insertion with the deep aponeurosis, as predicted by Van Leeuwen & Spoor (1992). Therefore, measuring from approximately 3–4 mm above the aponeurosis allowed accurate delineation of the fascicles. Muscle thickness was calculated as the mean of the distances between superficial and deep aponeuroses measured at the ends of each 3.8-cm-wide sonograph. Each sonograph was digitized twice on separate occasions and the mean values recorded. Sonograph pairs were re-digitized separately when muscle thickness differed by more than 2 mm or fascicle angle differed by more than 1°.

image

Figure 3. Intramuscular architecture of the quadriceps femoris. Fascicle angles [measured between the aponeurosis (a) and the fascicle (f)] vary considerably along the lengths of VL, VM and RF, but are relatively constant in VI; the magnitude of fascicle angle is represented as depth of colour and gradient of the representative fascicle (dotted line). Example sonographs are shown immediately below each muscle. Muscle thickness is also relatively variable in VL, VM and RF, but not in VI; muscle thickness is drawn to scale. Distal VM thickness was not measured in the present study so an estimate has been used to aid readability. RF is shown as a shorter muscle than the vastii muscles; however, muscle lengths are not drawn to scale.

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Fascicle length

At most sites tested, the fascicles were too long to be measured from origin to insertion. Hence, fascicle length was estimated using Eq. (1):

  • Fascicle length = sin(γ + 90°) × MT/ sin(180°− (γ + 180° − θ)),(1)

where MT is the muscle thickness, θ is the fascicle angle and γ is the angle between the superficial and deep aponeuroses. Fascicle length was only estimated at the mid-section of each muscle as: (1) such estimates assume that no fascicle or aponeurosis curvature exists, which appeared to be true only at the mid-point of the muscles, and (2) it is also assumed that muscle architecture is relatively isotropic, which is not true toward the end of a muscle where it generally changes shape in response to space constraints. Owing to significant fascicle curvature in some subjects, the reliability of fascicle length estimates for VM was unacceptably low, so they are not presented. Errors of approximately 2–7% (Finni et al. 2001, 2003b) have been reported previously with similar methods of estimating fascicle length when the entire fascicle cannot be visualized.

Reliability of measures

Digitizing reliability was determined by calculation of the intraclass correlation coefficient (ICC) and typical errors based on the double digitization of 50 randomly selected images from each muscle site. ICCs were very high for muscle thickness and fascicle angle (0.948–1.000), with little variation between muscles and muscle sites. Typical errors between repeated measurements for muscle thickness and fascicle angle ranged from 0.08 to 0.63 mm and 0.27 to 0.63°, respectively.

Reliability of the complete procedure, including the location of imaging sites, acquisition and digitization of images, and calculations of architectural parameters, was determined at each muscle's midpoint. The procedure for measuring muscle thickness and fascicle angle was also very reliable with ICCs of 0.882–0.970 and 0.899–0.991 (typical errors of 0.74–0.97 mm and 0.24–1.22°), respectively. The reliability of fascicle length estimates was slightly less reliable with ICCs of 0.758–0.863 with typical errors of 10.2–19.4 mm. The slightly lower reliability is due to the small errors in the measurements of muscle thickness, fascicle angle and aponeurosis angle being multiplied during fascicle length estimation.

Data analysis

The intramuscular homogeneity of muscle architecture was examined in two ways. First, differences in the absolute values of muscle thickness, fascicle angle and fascicle length were compared between sites within each muscle using paired t-tests with Bonferroni adjustment (α = 0.0167 for comparisons between three sites within each muscle); a reduction in type 1 error was considered more important than a reduction in type 2 error. Second, relative variation at different muscle sites within each muscle was examined using Pearson product moment correlations to determine whether there were relationships between the muscle sites irrespective of their absolute values (significant correlation = P < 0.05).

Absolute differences between sites of different muscles were not assessed because the positions at which the sonographs were taken from each muscle were not identical. However, comparisons between muscles were made in two ways. First, a dimensionless difference index (δ2−1) was calculated using a variation of the method proposed by Lieber et al. (1992):

  • image(2)

where MT is the muscle thickness, θ is the fascicle angle and FL is the fascicle length measured at mid-muscle, each representing muscles 1 and 2. MT and θ values were estimated as the mean of measures taken at each of the three sites (i.e. the value for each site was taken as representative of one-third of the muscle). For VM, muscle thickness was taken as the mean of proximal and middle sites as it was not measured distally. However, the index was also computed assuming a thickness of 30 mm at the distal site; there were no significant differences in the values regardless of which method was used. Fascicle length values were taken as the fascicle length measured at mid-muscle. The difference index was determined for each muscle pair, with values of δ2−1 < 0.3 representing architectural similarity, 0.3 < δ2−1 < 0.8 representing moderate similarity and δ2−1 > 0.8 representing architectural dissimilarity. The index allows absolute comparisons of muscle architecture, i.e. intermuscular similarity.

Second, an overall relative value for each architectural parameter was calculated for each muscle, and these values were compared. To calculate an overall value, measurements at each muscle site were converted to z-scores [(value – mean)/SD] and the values at each of the three sites averaged, i.e. subjects were ranked based on their magnitudes of muscle thickness, fascicle angle and fascicle length. Each muscle therefore had an overall value expressed as a mean z-score. Correlations between the z-scores of the muscles were computed to determine whether subjects’ scores for one muscle were similar to their scores for another muscle. Thus, from these analyses we could determine whether, compared with other subjects, a subject's rank by magnitude for an architectural parameter in one muscle was the same as their rank for the parameter in another. In addition, subjects with above-median scores for an architectural parameter for one muscle were compared against those with below-median architecture for their architecture in other muscles using a multivariate analysis of variance (manova) with repeated measures (α = 0.05). This test determined whether those that were ‘above median’ for a parameter in one muscle were also above median in others, i.e. whether relative architecture was similar across muscles.

Finally, the mean z-score for each parameter for the whole quadriceps femoris was calculated using the z-scores for each muscle. In order to examine relationships between the architecture of each muscle with the whole quadriceps femoris, we computed correlation statistics, and used step-wise linear regression (inclusion criterion P < 0.05; exclusion criterion P > 0.10) to predict whole quadriceps femoris architecture from that of individual muscles. This procedure assumes that each muscle's architecture contributes equally to the whole quadriceps femoris, which we have called the ‘equal ratio’ method.

However, each muscle's contribution to force production is probably not the same, so we also ran the analyses in three other ways. First, we apportioned each muscle's contribution according to its relative muscle volume (i.e. ‘volume’ method). Using MRI (3.0 T Magnetom, Siemens AG, Berlin, Germany), muscle volume was measured in a separate group of 11 women and 10 men whose physical characteristics matched as closely as possible the subjects used for the architecture analysis. Subjects lay supine with their legs straight while T2-weighted axial scans using a standard body coil were taken of the thigh from the inferior portion of the greater trochanter to the superior border of the patella (TR: 4260 ms, TE: 95 ms, averages: 3, FoV: 200 × 200, slice thickness: 4 mm, slice separation: 14 mm, centre-to-centre slice distance: 16 mm). Muscle cross-sectional area was measured for each slice using Scion Image for Windows (free to download at http://www.scioncorp.com/frames/fr_download_now.htm) and muscle volume was calculated by summing the product of cross-sectional area and slice thickness. The sum of the z-scores for each muscle was taken as the whole quadriceps z-score after the values were multiplied by their proportion of the muscle volume (i.e. 100% of the volume = 1). The proportional contributions of each muscle to the whole quadriceps architecture are reported in Table 1.

Table 1.  Muscle proportions used for estimation of whole muscle architecture
MuscleEstimation method
Equal ratio*VolumePCSAEstimated contribution§
  • *

    Whole muscle architecture estimated by assigning equal weighting to each muscle.

  • Muscle contribution apportioned by their contribution to whole quadriceps volume, which was determined by MRI imaging; data collected on 21 subjects of similar age and physical stature.

  • Muscle contribution apportioned by their relative physiological cross-sectional areas (PCSA); data from Narici et al. (1992).

  • §

    Muscle contribution apportioned by their estimated contribution to total joint moment assessed by electrophysiological techniques; data from Zhang et al. (2003).

vastus lateralis0.2500.3520.2210.242
vastus medialis0.2500.2180.2430.122
rectus femoris0.2500.1360.2360.251
vastus intermedius0.2500.2940.3000.396

In a second analysis, we apportioned each muscle's contribution according to previously published estimates of physiological cross-section (Narici et al. 1992), before summing z-scores to find an overall z-score (i.e. ‘PCSA’ method).

In a third analysis, we apportioned contributions according to the estimated contribution to knee extensor moment (i.e. ‘estimated contribution’ method) assessed electrophysiologically by Zhang et al. (2003). In their study, electrical stimulation was used to activate each quadriceps muscle independently while both the resultant force and EMG [indwelling (vastus intermedius) or surface electrodes (vastii muscles)] were measured to determine the activation–moment relationship. They then used the EMG collected during voluntary isometric knee extensions to estimate the relative contributions of each muscle.

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. References
  9. Appendix

Homogeneity of within-muscle architecture (absolute differences)

Muscle thickness and fascicle angle data are presented in Table 2, and representations of these are shown in Fig. 3. With respect to muscle thickness, VL and RF decreased proximo-distally along the thigh, whereas VM increased. Variations in VI thickness were different depending on the direction of sonograph acquisition (i.e. anterior vs. lateral portions); the anterior portion was relatively uniform, whereas the lateral portion was smaller at mid-thigh compared with proximal and distal regions. Fascicle angulation followed a slightly different pattern; whereas the fascicle angles of muscles generally decreased in the order VM > VIlat > VL > RF > VIant, the fascicle angulation usually decreased proximo-distally in VL and RF, increased proximo-distally in VM, and remained relatively constant in VI (anterior and lateral portions). Thus, muscle thickness and fascicle angle varied considerably along the lengths of some of the muscles (particularly VM, VL and RF) but not others (particularly VI), so architectural measurements taken at one part of the muscle seem not to be indicative of those taken at other sites.

Table 2.  Muscle thickness and fascicle angle measured in different muscles (means ± SD). For each muscle, data from proximal (first number), middle (second number) and distal (third number) sites are presented in order of top to bottom
MuscleMuscle thickness(mm)Fascicleangle (°)
  1. Significantly different from aproximal site and bmiddle site.

Vastus lateralis21.5 ± 3.3 9.7 ± 3.9
22.8 ± 3.213.2 ± 3.2a
16.4 ± 4.3a,b11.7 ± 3.8
Vastus medialis20.9 ± 4.510.2 ± 3.1
26.8 ± 6.3a14.0 ± 3.9a
Not measured distally28.5 ± 5.7a,b
Rectus femoris26.9 ± 5.014.0 ± 4.3
24.0 ± 4.8a13.4 ± 3.6
20.1 ± 4.9a,b10.1 ± 3.4a,b
Vastus intermedius (anterior portion)19.3 ± 4.6 6.0 ± 3.3
17.6 ± 4.1 7.1 ± 2.9
17.0 ± 4.3a 6.4 ± 2.7
Vastus intermedius (lateral portion) 6.8 ± 3.114.6 ± 2.2
 5.5 ± 2.415.9 ± 2.3
 7.2 ± 3.214.7 ± 3.3

Homogeneity of within-muscle architecture (relative differences)

Proximal VL fascicle angle was significantly correlated with the fascicle angles at middle (r = 0.48, P < 0.01) and distal (r = 0.48, P < 0.01) sites, indicating that subjects with larger fascicle angles at the proximal site also had large angles at the other sites. The correlation between the middle and distal sites, however, did not reach significance (r = 0.24, P = 0.13). Muscle thickness at each site was also correlated with the other sites (r > 0.5, P < 0.01), indicating a consistency in VL size. A similar trend was noticed for VM and RF. In VM, there was a significant correlation between proximal fascicle angle and that at the distal site (r = 0.41, P < 0.05), although correlations with the middle site did not reach significance. In addition, muscle thickness at proximal and middle sites was significantly correlated (r = 0.57, P < 0.01); muscle thickness was not measured at the distal site. In RF, there was a significant correlation between the fascicle angle at middle and distal sites (r = 0.38, P < 0.05), although correlations did not reach significance for the proximal site, whereas there were significant correlations for muscle thickness at each of the three sites (0.56 < r < 0.74, P = 0.000–0.002). Therefore, for VL, VM and RF, subjects tended to have a similar relative architecture along the length of the muscles. These trends were similar when men and women were analysed separately, although some of the correlations of similar magnitude did not reach statistical significance because of the smaller sample size.

For VIant, there was a correlation between fascicle angle at middle and distal sites (r = 0.47, P < 0.05), although there was no correlation with the proximal site. Proximal muscle thickness was correlated with both the middle (r = 0.52, P < 0.01) and the distal sites (r = 0.38, P < 0.05), although the correlation between middle and distal sites did not reach significance (r = 0.30, P = 0.10). Therefore, subjects who had larger fascicle angles at mid-muscle also had a larger fascicle angle distally, but not proximally, whereas subjects who had thicker muscles proximally were also thicker in other regions. For VIlat, whereas there was a correlation between fascicle angle at proximal and middle sites (r = 0.71, P < 0.001), there was no correlation with the distal site. There were no significant correlations for muscle thickness between any of the sites, suggesting that subjects with thicker muscles at one site did not necessarily have thicker muscles at another site. Therefore, the consistency of muscle architecture in VI varied between anterior and lateral portions; subjects who had a specific muscle thickness and/or fascicle angle at one site also had a similar relative architecture at other sites in the anterior portion, but this was not the case for the lateral portion of the muscle.

Intermuscular variation in architecture (absolute differences)

The difference index (δ2−1) calculated between muscles allowed comparisons of overall muscle architecture between muscles. As detailed in Table 3, the index was generally low for comparisons between the superficial quadriceps muscles (δ2−1 < 0.36) but higher between superficial and deep muscles (i.e. VI, δ2−1 = 0.46–0.77). Thus, there was reasonable architectural similarity between the superficial quadriceps only. Furthermore, the anterior and lateral portions of the VI were highly dissimilar in their architecture (δ2−1 = 1.97). So even within the same muscle, architectural dissimilarity was significant.

Table 3.  Difference Index (δ2−1) quantifying the architectural difference between the quadriceps muscles
 VMRFVIantVIlat
  1. δ2−1 < 0.3 represents architectural similarity, 0.3 < δ2−1 < 0.8 represents moderate similarity, and δ2−1 > 0.8 represents architectural dissimilarity. The three superficial quadriceps muscles were more similar to each other (δ2−1 < 0.36) than the deeper vastus intermedius.

VL0.360.200.660.76
VM0.080.460.55
RF 0.700.77
VIant  1.97
VIlat   

z-scores were also calculated for each architectural parameter at each muscle site and an average z-score was computed to provide a global parameter for the whole muscle; results of RM manova and correlation analyses are presented in Table 4. For VL, subjects with a greater-than-median whole muscle fascicle angle or fascicle length (fascicle length at mid-muscle was taken as representative of the whole muscle) did not have statistically different fascicle angles or lengths in any other muscle. Also, those with greater muscle thickness had a greater muscle thickness in VIlat (P < 0.05) but not in any other muscle. These results were consistent with the correlation analysis, which showed no relationship between the architecture of VL and other muscles, with the single exception of VL thickness being correlated with VIlat thickness (r = 0.41, P < 0.05). Therefore, subjects with a given magnitude of architecture in VL relative to the other subjects did not have the same relative magnitude of architecture in the other muscles in the quadriceps femoris.

Table 4.  Relative relationships between muscle architectural variables for different muscles within the quadriceps femoris
± medianVLVMRFVIantVIlat
FATHFLFATHFATHFLFATHFLFATHFL
  1. After z-scores were computed for each variable for each subject, subjects with greater-than- or less-than-median scores were compared (left column) and correlations among the variables were computed. For each relationship, the top number indicates the F-ratio and the bottom number the correlation (r). Asterisks indicate levels of significance: *P < 0.05, **P < 0.01, ***P < 0.001. FA: fascicle angle, TH: muscle thickness, FL: fascicle length.

VLFAF = 52.8***4.3*5.4*NS NS  NS  NS  
r = 10.55**−0.48**NS NS  NS  NS  
TH8.5**34.8***NS NS NS  NS  6.3* 
0.55**1NS NS NS  NS  0.41* 
FLNSNS12.3**    NS  NS  NS
−0.48**NS1    NS  NS  NS
VMFA5.6*  20.9***NS25.8***  NS  NS  
   10.48**NS  0.38*  NS  
TH   NS24.8*** NS  NS  NS 
   0.48**1 NS  0.46*  NS 
RFFA6.6*  20.6*** 27.8***NSNSNS  NS  
0.37*  0.93*** 1NSNSNS  NS  
TH NS  NSNS54.4***NS NS  NS 
 NS  NSNS10.44* NS  NS 
FL  NS  NS6.8*17.6***  NS  NS
  NS  NS0.44*1  NS  NS
VlantFANS  NS NS  43.9***5.5*NSNS  
NS  0.38* NS  10.51**−0.40*NS  
TH NS  NS NS 4.9*43.9***NS NS 
 NS  0.46* NS 0.51*1NS NS 
FL  NS    NSNSNS17.0***  NS
  NS    NS−0.40*NS1  NS
VlantFANS  NS NS  NS  25.8***NSNS
NS  NS NS  NS  10.63***NS
TH 10.3**  NS NS  NS NS14.7**NS
 0.41*  NS NS  NS 0.63***10.44*
FL  NS    NS  NSNSNS69.2***
  NS    NS  NSNS0.44*1

Nonetheless, subjects with larger VM fascicle angles also had larger VL and RF fascicle angles (and there was a trend toward larger angles in VIant, P = 0.09). There was a strong relationship between VM and RF fascicle angles (r = 0.93, P < 0.001), suggesting that fascicle angle in one muscle was highly predictive of the other. Despite this, subjects with greater muscle thickness or fascicle length in VM did not have greater magnitudes in other muscles. These results were mirrored to some extent in RF, where subjects with larger RF fascicle angles also had larger VL and VM fascicle angles but subjects with greater muscle thickness or fascicle lengths did not have greater magnitudes in other muscles. Thus, although there was a strong correlation between VM and RF fascicle angle, there was no significant correlation with VL.

In VI, subjects with greater thickness of VIlat also had a thicker VL (P < 0.01), but there were no other significant differences in either portion of VI. These results were consistent with correlation statistics, which did not support a relationship between relative VI architecture and that in other muscles. Therefore, although there was some constancy of fascicle angle between VM, VL and RF, subjects with a certain relative magnitude of muscle thickness or fascicle length of one quadriceps muscle seemed not to have a similar relative magnitude of other muscles.

Contribution of individual muscle architectures to whole quadriceps architecture

Whole quadriceps architecture was estimated by four methods (see Methods): (1) equal ratio, (2) volume, (3) PCSA and (4) estimated contribution. Although there was a strong intercorrelation between the methods for calculating whole quadriceps thickness (R2 > 0.95), fascicle angle (R2 > 0.96) and fascicle length (R2 > 0.92), the contributions of individual muscles toward the score for whole quadriceps architecture varied (see Table 5). In particular, apportioning muscle contribution relative to each muscle's volume was different to the other methods. For example, thickness of VL was more highly correlated with whole quadriceps thickness (r = 0.71, P < 0.001) when whole quadriceps thickness was estimated using the volume method than when muscle contributions were apportioned using equal ratio (r = 0.63), PCSA (r = 0.58) or estimated contribution (r = 0.59), as was VL fascicle length (r = 0.81, P < 0.001) when compared with the equal ratio, PCSA and estimated contribution methods (r = 0.70, 0.64 and 0.61, respectively). Differences between the methods were also highlighted by the fact that statistically significant gender differences in whole quadriceps thickness were detected when the equal ratio (P = 0.02), PCSA (P = 0.03) and estimated contribution (P = 0.01) methods were used, but not when contributions were apportioned by muscle volume (P = 0.10). These data show that gender-related size differences were most clearly seen when quadriceps thickness was estimated by the estimated contribution method, although they could not be detected using the volume method.

Table 5.  Correlations between individual muscle architecture scores and whole quadriceps femoris architecture estimated by four methods (see Methods)
ParameterEqual ratioVolumePCSAEstimated contribution
FATHFLFATHFLFATHFLFATHFL
  1. Generally, architecture in VIlat was poorly correlated with whole quadriceps femoris architecture. Asterisks indicate levels of significance: *P < 0.05, **P < 0.01, ***P < 0.001. FA: fascicle angle, TH: muscle thickness, FL: fascicle length.

VLFA0.61***  0.73***  0.59**  0.63***  
TH 0.63***  0.71***  0.58**  0.59** 
FL  0.70***  0.81***  0.64***  0.61***
VMFA0.91***  0.83***  0.91***  0.85***  
TH 0.75***  0.75***  0.76***  0.61** 
RFFA0.91***  0.55**  0.90***  0.84***  
TH 0.50**  0.40*  0.48**  0.58** 
FL  0.59**  NS  0.55**  0.49**
VIantFA0.58**  0.64***  0.62***  0.70***  
TH 0.60**  0.60**  0.66***  0.71*** 
FL  0.60**  0.65***  0.69***  0.76***
VIantFANS  NS  NS  NS  
TH 0.37*  0.37*  NS  0.39* 
FL  NS  NS  NS  NS

Prediction of whole quadriceps architecture from individual muscle architecture

Regression equations showing the prediction of whole quadriceps architecture from individual muscles are presented in Table 6. Variables were added step-wise by greatest contribution to explained variance; equations are presented in order of entry. For muscle thickness, VM was the best indicator of whole quadriceps thickness, although, depending on the method of estimating whole quadriceps thickness, VL, RF and VIlat were also reasonable indicators. VM fascicle angle was also the best predictor of whole quadriceps fascicle angle, except when the estimated contribution method was used to estimate whole quadriceps fascicle angle; VL and VIant were also useful predictors. VL and VIant were the best indicators of whole quadriceps fascicle length, although VM fascicle length was not used in this analysis (see Methods). Therefore, VM fascicle angle and muscle thickness scores seemed to be the best predictors of quadriceps femoris estimates, while VL and VIant scores were reasonable predictors of all architectural parameters. VIlat, however, was not a useful predictor of quadriceps thickness, fascicle angle or fascicle length.

Table 6.  Regression equations to predict whole muscle architecture estimated by each of the four methods (see Methods)
MethodParameterEquation
  1. Variables were added step-wise by greatest contribution to explained variance; equations are presented in order of entry. Equation constants were less than 0.00008 in all cases and are therefore not presented. Adjusted R2 = 1.000 and standard error of the estimate < 0.0004 for all equations. aVM fascicle length was included in these analyses (see Methods). FA: fascicle angle, TH: muscle thickness, FL: fascicle length.

Equal ratioFAVM × 0.347 + VL × 0.283 + VIant × 0.238 + RF × 0.407
THVM × 0.528 + RF × 0.351 + VL × 0.379 + VIant × 0.312
FLaVL × 0.557 + RF × 0.513 + VIant × 0.513
VolumeFAVM × 0.335 + VL × 0.441 + VIant × 0.310 + RF × 0.246
THVM × 0.454 + VL × 0.527 + VIant × 0.362 + RF × 0.189
FLaVL × 0.699 + VIant × 0.538 + RF × 0.249
PCSAFAVM × 0.344 + VIant × 0.292 + VL × 0.255 + RF × 0.392
THVM × 0.517 + RF × 0.334 + VIant × 0.378 + VL × 0.338
FLaVIant × 0.612 + VL × 0.489 + RF × 0.481
EstimatedFARF × 0.439 + VIant × 0.406 + VL × 0.295 + VM × 0.182
contributionTHVIant × 0.532 + VL × 0.396 + RF × 0.380 + VM × 0.278
FLaVIant × 0.680 + VL × 0.451 + RF × 0.431

Validity of whole quadriceps estimates: interaction between muscle thickness, fascicle angle and fascicle length

In the whole quadriceps, muscle thickness was positively correlated with fascicle angle, regardless of whether the equal ratio (r = 0.67), PCSA (r = 0.68), volume (r = 0.71) or estimated contribution (r = 0.65) methods were used (P < 0.001). In addition, fascicle angle and fascicle length were negatively correlated (r = –0.45, −0.48, −0.54 and −0.53 for the equal ratio, PCSA, volume and estimated contribution methods, respectively; P < 0.05). Thus, when architecture at all muscles sites was combined to give an average muscle architecture for the quadriceps femoris, those muscles with greater thickness tended to have larger fascicle angles, whereas those with longer fascicles had lesser fascicle angles.

Significant correlations between muscle thickness and fascicle angle were also seen for VL, VM, VIlat and VIant individually, but not RF (see Table 7a–e). However, fascicle angle was only negatively correlated with fascicle length for VL and VIant (fascicle length not measured in VM). Thus, although there was a strong indication that subjects with large quadriceps fascicle angles to have longer fibres, this was true only for the VL and VIlat when muscles were analysed separately.

Table 7.  Correlations between muscle thickness, fascicle angle and fascicle length based on z-scores (see Methods) for each muscle (a–e)
 FATHFL
  1. Asterisks indicate levels of significance: *P < 0.05, **P < 0.01, ***P < 0.001. FA: fascicle angle, TH: muscle thickness, FL: fascicle length.

(a) vastus lateralis
 FA10.55**−0.48**
 TH 1NS
 FL  1
(b) vastus medialis
 FA10.48** 
 TH 1 
 FL   
(c) rectus femoris
 FA1NSNS
 TH 10.44*
 FL  1
(d) vastus intermedius (anterior)
 FA10.51**−0.40*
 TH 1NS
 FL  1
(e) vastus intermedius (lateral)
 FA10.63***NS
 TH 10.44*
 FL  1

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. References
  9. Appendix

Intermuscular variation in quadriceps architecture (absolute differences)

In order to produce forces with broad magnitude, range and velocity characteristics, it has been suggested that muscles within synergistic groups tend to vary in their architecture (Lieber & Fridén, 2000). Our examination suggests that this is only partly true for the human quadriceps muscles. The difference index calculated to provide quantitative assessment of intermuscular variability revealed a close similarity between the mean architecture of the three superficial quadriceps muscles (i.e. VL, VM and RF; δ2−1 < 0.36), despite RF being bi-articular and VL and VM being mono-articular. Given that muscles within the human quadriceps femoris act via a common (patellar) tendon, this similarity in mean architecture is indicative of a similarity in their force-generating potential during uni-joint knee extension (where RF functions as a mono-articular knee extensor), although their angle of attachment to the tendon would also influence their contribution to knee function. Nonetheless, the deeper VI is architecturally dissimilar to the superficial muscles, indicating that it has a different force-generating potential, and possibly a different role during knee extension. A clear picture of its role is difficult to ascribe because its architecture varies significantly. The anterior portion is characterized by long fibres attaching at small angles to the aponeurosis, whereas the lateral portion has shorter fibres attaching at larger angles (δ2−1 = 1.97); the medial portion was not examined.

This intermuscular variation suggests that the superficial and deep quadriceps muscles have different roles, and could be recruited uniquely based on their force-generation properties. Such recruitment variability has been previously shown. In the quadriceps femoris, Zhang et al. (2003) found that the relative contribution of each muscle to the total isometric knee extensor moment changed as contraction force increased, such that the contribution of VI decreased whereas the contribution of VL, VM and RF increased (the increase in RF approached statistical significance, P = 0.06). Similar findings have been reported for the biceps brachii, which also consists of multiple muscles attaching via a common tendon (Brown et al. 1993). Nonetheless, other studies employing surface EMG analyses have also shown muscle-specific changes in quadriceps muscle activation as force levels are varied (Ebersole et al. 1999; Pincivero & Coelho, 2000; Rabita et al. 2000; Pincivero et al. 2002, 2004b; Cramer et al. 2004), knee joint angle, and therefore whole quadriceps femoris muscle length, is changed (Ebersole et al. 1999; Signorile et al. 1995), velocity is increased (Cramer et al. 2004) or contraction mode is changed from concentric or isometric to eccentric (Narici et al. 1996; Pincivero et al. 2006). These findings are not predicted by a model that assumes a similarity in architecture of the superficial quadriceps muscles. However, these variations might be explained by differences in intramuscular architecture, as discussed below (‘Homogeneity of within-muscle architecture’). Movement-specific muscle activation strategies will have to be examined further as a relationship between muscle architecture and recruitment has yet to be demonstrated. Notwithstanding, there is some support for hypothesis 1, that the architecture of each muscle within the quadriceps should be different, for the superficial vs. deep quadriceps muscles; however, there seems to be some uniformity among the superficial muscles.

The architectural differences between muscles would also affect the efficiency of force transfer to the tendon, given that forces are transferred laterally between muscles (e.g. Huijing, 2003; Maas & Huijing, 2005). For example, the shorter RF fascicles attaching at larger angles (12.5°, 112.3 mm length at 45° knee angle) would be expected to generate high relative peak forces over shorter length ranges, which is commensurate with reports that it works quasi-isometrically during many human movements (Gregoire et al. 1984; Ingen Schenau et al. 1987; Jacobs & Ingen Schenau, 1992). This can be compared with the immediately adjacent, architecturally dissimilar VIant (6.5°, 162.1 mm at 45° knee angle), which is suited to generating lower peak forces over greater length ranges. Even when fibre rotation is accounted for, which would allow RF fascicles to shorten less relative to the whole muscle shortening, there is still a significant force–length discrepancy between the muscles. As shown in Fig. 4, a similar relative shortening of RF and VI (anterior) fascicles would result in a different tendon or aponeurosis displacement (10.0 mm vs. 14.2 mm in the example). The discrepancy would result in a shear stress between their aponeuroses, and is likely to affect force transfer efficiency.

image

Figure 4. Effect of intermuscular fascicle length and angle differences on tendon/aponeurosis excursion. When rectus femoris (RF) fascicles shorten (from FLRF1 to FLRF2, where FL is the fascicle length) and rotate (θRF1 to θRF2, where θ is the fascicle angle) in this example, the aponeurosis or tendon displaces 10 mm. This represents a fascicle shortening of 9.7 mm, or 8.7%. If the vastus intermedius (VI; anterior region) fascicle shortens by the same proportion, 14.0 mm, or 8.7%, and rotates, the aponeurosis or tendon displaces 14.2 mm, which is a difference (Diff.) of 4.2 mm, or 42%. Thus, even when fascicle rotation is accounted for, the differing architectures of RF and VI result in differential displacement of the tendon or aponeurosis. Either RF and VI must be activated uniquely, or there will be a shear force in the tendon or aponeurosis. In this example, it was assumed that the muscle thickness would remain constant given that RF and VI apply opposing forces of similar magnitude on the tendon/aponeurosis.

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Alternatively, a lesser recruitment of VI as contraction intensity increases (see Zhang et al. 2003) would allow matching of muscle shortening. Because VIant contains longer fibres, and presumably a greater number of sarcomeres in series, a similar absolute shortening of RF and VI fascicles would result in a lesser shortening of VI sarcomeres. This would improve force production via optimization of force–length and force–velocity relationships and might allow more efficient force production. As discussed above, variations in the recruitment of individual muscles has been demonstrated previously, but the hypothesis that the strategy of unique muscle activation would improve force transfer efficiency has yet to be examined. Data from near-infrared spectroscopy experiments has shown that the increase in O2 utilization, and therefore energy consumption, by the superficial quadriceps muscles with increasing force levels is similar between muscles (de Ruiter et al. 2005). These data are consistent with the hypothesis that the unique activation of muscles optimizes efficiency under different loading conditions. Furthermore, strength training of the quadriceps has not only been shown to alter the proportional activation of the quadriceps muscles (Pincivero et al. 2004a) but has been shown to reduce the EMG measured from superficial quadriceps muscles at prescribed submaximal force levels (i.e decreased EMG–force ratio). This latter change is also indicative of a greater efficiency of force production (Narici et al. 1996; Rabita et al. 2000). The contention that unique muscle activation would be a useful optimization strategy also suggests that the EMG–force ratios of individual muscles, and their adaptation with movement training, would be specific to the person as architecture varies considerably interindividually. This contention has been given some credence by Rabita et al. (2000), who showed that alterations in the EMG–force relationship varied significantly between muscles and also between individuals. Thus, although direct evidence that humans adopt a unique activation strategy in order to minimize shear forces and improve force transfer efficiency in the human quadriceps is not available, published data are strongly supportive of the concept.

Importantly, many muscle models assume that architectural variations have little impact on the active length range of muscles working in synergistic groups (see Van den Bogert et al. 1998), largely because it is supposed that connective tissues would be overstretched/injured if significant discrepancies existed. Based on our data, this assumption might need to be revised; significant intermuscular architectural differences might explain some of the difficulties in accurately modelling complex muscle groups. Thus, the effects of architectural dissimilarity in muscles functioning as a synergistic group are complex, and more research is required to understand activation strategies used to optimize muscle function. Regardless, the quadriceps femoris probably cannot be accurately modelled as a muscle group that provides a force exactly equal to the sum of each of its constituents.

Homogeneity of within-muscle architecture (absolute differences)

Although mean architecture measures were relatively consistent between muscles, except for VI, our data also show that architecture does vary significantly within them. For example, fascicle angle increased proximo-distally in VM, decreased proximo-distally in RF and was greater centrally in VL. Furthermore, fascicle angle was significantly different in anterior and lateral regions of VI, although it changed little along the length of the muscle. These results are consistent with previous reports of intramuscular architectural variation (Scott et al. 1993; Blazevich et al. 2003) and provide little support for our second hypothesis, that the intramuscular architecture should be relatively homogeneous. They are also suggestive of the possibility that different regions of the muscles have different functional roles, and perhaps are activated uniquely during knee extension. Although there are no data describing region-specific variations in activation of the individual quadriceps muscles, different regions of other muscles such as the long head of biceps brachii are differentially activated as force patterns are altered (ter Haar Romeny et al. 1984). A similar examination of the quadriceps muscles might reveal region-specific activation patterns.

Intramuscular architectural variation is probably required in pennate muscles in order to achieve mechanical stability (Van Leeuwen & Spoor, 1992), although such variation might further influence muscle function and force transfer between muscles. For the same relative shortening of fascicles in different regions of the muscles, aponeurosis displacement will be different. Most planimetric models of muscle assume a constant fascicle angle along the length of a muscle, which might not represent the muscles appropriately. More complex muscle models that allow fascicle angle and length parameters to vary (Woittiez et al. 1984; Otten, 1988; Savelberg & Schamhardt, 1995) will probably be more accurate. To estimate the extent to which models might be affected when architecture is assumed to be constant, we constructed a planimetric model of a unipennate muscle containing three segments, or parallelepipeds (Savelberg & Schamhardt, 1995), as shown in Fig. 5. It was assumed that each segment contributed to the tendon force in proportion to its estimated physiological cross-section (muscle thickness2/fascicle length), and the total muscle force was equal to the sum of forces provided by each segment (see Appendix A). The model was run with three different inputs: (1) where each segment was identical in its architecture, with mean VL (middle) data being assumed to run throughout the muscle; (2) where each segment varied in its architecture, with mean VL proximal, middle and distal data being used as input for the three segments; and (3) where each segment varied, with VL (middle) data being used as input for the middle segment but mean − 1 SD data being used from distal and proximal VL as input for segments 1 and 3 (see Fig. 5). The results of the model show little difference in the force–length curves when the muscle is assumed to have a constant architecture compared with a varying architecture (Fig. 5A vs. Fig. 5B) when the architecture varies within the orders of magnitude reported for VL in the present study. However, when more significant architectural variation is input into the model (Fig. 5C), the force–velocity relationship changes far more dramatically. Muscles that vary considerably in their architecture, such as VM, will probably not to be accurately modelled when intramuscular architecture is assumed not to vary, so consideration must be given as to whether uniform muscle models are appropriate for use.

image

Figure 5. A planimetric muscle model was constructed, according to Appendix A. The muscle consisted of three segments which were either identical in their architecture (non-varying architecture, A), varied according to normal data for the VL collected in the present study (varying architecture, B), or varied more considerably in the proximal and distal segments than the measurements in the present study (i.e. mean minus 1 SD) (varying architecture, C). Muscle thickness (MT) and fascicle angle (θ) parameters used in the model are shown (parameters correspond to muscle optimum length). As shown in the graph of muscle force vs. muscle length (D), modelling the muscle as three distinct segments makes a relatively small difference to the output of the model when architecture varies only moderately (A vs. B). However, when the muscle's architecture varies considerably (A vs. C), the ability for a uniform muscle model to predict muscle force is significantly reduced.

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The functional implications of intramuscular variations in architecture are unclear; however, we posit two hypotheses (additional to the requirement for mechanical stability; Van Leeuwen & Spoor, 1992). First, the muscles might be intended to have both ‘force-generating’ and ‘force-transfer’ regions. The greater fascicle angle and subsequently larger physiological cross-section in one region might perform the function of generating high muscle forces. A second, force-transfer, region might be designed to have fibres in line with the tendon to allow greater efficiency of force transfer. The use of a transfer section consisting of muscle, rather than tendon, would permit greater control over muscle–tendon stiffness, and subsequently over movement control. The second hypothesis is that fascicles within muscles tend to align with the joint's centre of rotation, which would improve the efficiency of force transfer from muscle to bone. The present data cannot confirm this hypothesis because the angle of the aponeurosis relative to the tendon was not measured, so pennation angle could not be determined. However, our findings that fascicle angle generally increased in VM proximo-distally, but not in RF and VI, and that the lateral portion of VI had greater fascicle angles, tend to support the hypothesis, whereas the finding that fascicle angle decreased from middle to distal regions in VL is not supportive.

Intramuscular architectural variation should also affect the hypertrophic response to, and therefore the function of, different regions of the muscle. The variation in fascicle angle (and length) along these muscles would probably affect fascicle strain in response to an imposed stress (Maganaris & Paul, 2000; Muramatsu et al. 2002; Finni et al. 2003a). Given the assumption that the hypertrophic response of muscle is somewhat related to fibre strain (e.g. Goldspink, 1978; Vandenburgh & Kaufman, 1979; Gregory et al. 1986; Wong & Booth, 1990; Hather et al. 1991; Goldspink et al. 1992, 1995), one would predict region-specific muscle hypertrophy in response to muscle loading. Published data are consistent with this hypothesis (Housh et al. 1992; Narici et al. 1996; Häkkinen et al. 2001). Interestingly, both Häkkinen et al. (2001) and Narici et al. (1996) reported greater proportional hypertrophy proximally in VM and distally in VL; our data show that in these regions the fibre angles of both muscles are relatively smaller. Unfortunately, there are no data showing a direct link between local muscle architecture and the hypertrophic response. A direct conclusion is also made more difficult in view of the findings of Housh et al. (1992) whose subjects increased at the mid-level of VM and VL only. Furthermore, there is a lack of agreement as to the predominant sites of hypertrophy in VI and RF. It is possible that adaptations are exercise-specific, and might also be influenced by the activity profiles of the subjects used. Thus, although the hypothesis that intramuscular architectural variation should result in region-specific hypertrophic adaptations to exercise training has some support, a direct link between hypertrophy and pre-existing architecture has not yet been made.

Homogeneity of within-muscle architecture (relative differences)

Despite architecture varying considerably along the length of three of the quadriceps quartet, there was a constant intersubject variability of regional variation in VL, VM and RF. For example, subjects who had a greater proximal fascicle angle in a given muscle, relative to the other subjects, also tended to have greater fascicle angles at middle and distal sites in that muscle. This was not necessarily the case for VI. In the anterior portion, muscle thickness between sites was highly correlated (i.e. subjects with greater or lesser thickness at one region also had greater or lesser thickness at another region), but fascicle angle was only correlated between middle and distal regions. For the lateral portion, muscle thickness between regions was not correlated, and fascicle angle was only correlated between proximal and middle regions. Thus, while intersubject differences in one region of a superficial muscle were similar to those in other regions, and therefore in broad terms relative architecture in one region is a reasonable indication of relative architecture in another, there was less evidence of this for VI. Because our second hypothesis was that muscle architecture should be uniform throughout a muscle, it stands also that we would expect a subject's relative architecture (i.e. compared to the rest of the sample of subjects) at one region of a muscle to be indicative of its relative architecture at another region in all muscles within the quadriceps femoris. Thus, our hypothesis was proved to be incorrect.

Intermuscular variation in quadriceps architecture (relative differences)

Relative intermuscular variation was considerably greater than that within a muscle. For example, subjects who had a greater mean fascicle angle of VM also tended to have greater angles in VL and RF, and this was also true for RF, where greater fascicle angles were indicative of greater angles in VL and VM. However, this was not the case for VL and VI (both anterior and lateral regions), where relative architecture was not predictive of architecture in other muscles. Thus, although there is some indication that the architecture in one superficial muscle is reflective of that in another, this is not completely true for VL and does not hold true for the deep VI. These data are not supportive of hypothesis 3, that the relative architecture of one muscle should be similar to that of another. Therefore, to gain an overall impression of whole quadriceps architecture a description of more than one muscle is required.

Contribution of individual muscle architectures to whole quadriceps architecture

We also sought a global measure of architecture for the quadriceps femoris. The low mean intermuscular architecture variability in superficial quadriceps muscles was suggestive that this might be possible, although these muscles differed in a region-specific manner. We used four methods for estimating whole quadriceps architecture, including (1) allowing the mean architecture of each muscle an equal weighting (equal ratio), (2) weighting by relative muscle volumes (volume), (3) weighting by relative muscle physiological cross-sections (PCSA) and (4) weighting by estimated contribution to knee extensor torque as reported by Zhang et al. (2003; estimated contribution). There were no significant differences in muscle thickness, fascicle angle or fascicle length values found for the whole quadriceps between the methods (R2 > 0.92), but there were some differences in the level of contribution of each of the muscles. Most notably, whereas the equal ratio, PCSA and estimated contribution methods gave statistically similar results, estimation by volume resulted in VL thickness and fascicle length being more highly correlated with whole quadriceps thickness, and RF thickness being less highly correlated with whole quadriceps thickness. Furthermore, a statistically significant gender difference in muscle thickness (men > women) was found using the equal ratio, PCSA and estimated contribution methods, but not using the volume method. Given the above, we suggest caution in weighting architectural values by volume when estimating whole quadriceps architecture.

Prediction of whole quadriceps architecture from individual muscle architecture

An important benefit of estimating whole quadriceps architecture is that it allows the identification of individual muscles whose characteristics might be representative of the muscle group. An understanding of this would preclude the necessity to measure architecture of all four muscles in order to characterize an individual's whole quadriceps architecture. Unfortunately, according to the regression analysis (Table 6), estimation of whole quadriceps architecture requires the inclusion of data of up to four muscles: VL, VM, RF and VIant. This is not supportive of hypothesis 4, that the relative architecture of individual muscles should be indicative of relative whole quadriceps architecture, i.e. compared with other subjects, a subject's rank by magnitude for an architectural parameter in one muscle was not the same as their rank for the parameter in another. Most typically, VM architecture was the best predictor of quadriceps architecture, as evidenced by its primary inclusion in the estimation of fascicle angle and muscle thickness for almost all methods of estimating whole quadriceps thickness and fascicle angle (see Table 6). Because VM fascicle length measures were unreliable owing to the excessive curvature of the fascicles in some subjects, they could not be used to predict whole quadriceps fascicle length. In this instance, both VL and VIant were the primary predictors. In general, VL and VIant were most frequent secondary predictors. VIlat was excluded in all instances and is therefore considered a poor estimate of whole quadriceps architecture. Thus, VM architecture was generally the best predictor of whole quadriceps architecture, although the inclusion of at least VL and/or VIant is needed for more accurate estimates. Although these muscles might allow a ‘representative snapshot’ of the whole quadriceps to be drawn, it is not known whether gross changes in quadriceps architecture that result from physical training or detraining can be quantified by measurement of only two of the quadriceps muscles. This needs to be determined from studies specifically examining architectural adaptation.

Validity of whole quadriceps estimates: interaction between muscle thickness, fascicle angle and fascicle length

On the whole, our estimates of whole quadriceps architecture appear to be a valid representation as they predict two important relationships that are normally found in individual muscles. First, a gender difference in whole quadriceps thickness was obtained for all methods except when muscles were apportioned by their relative volumes. This finding of larger muscles in men than women is consistently reported in the literature (Abe et al. 1998; Kubo et al. 2003). It is interesting to note that fascicle angles and lengths did not differ significantly between sexes. While relatively few studies have reported sex variation, Chow et al. (2000) showed differences in muscle size, fibre length and fibre angle between men and women in the gastrocnemius and soleus muscles in non-athletic, younger subjects (Chow et al. 2000). Abe et al. (1998) observed that muscle thickness and fibre angle differences in triceps brachii, vastus lateralis and gastrocnemius muscles were also different between height- and weight-matched, resistance-trained men and women. It is not clear whether differences in bodyweight (not reported by Chow et al. 2000) or fat-free body mass (men > women; Abe et al. 1998), or muscle size (Abe et al. 1998; Chow et al. 2000), might at least partly explain these differences given that greater muscle size is generally associated with either, or both, increased fascicle angles or lengths. Nonetheless, other reports suggest there is no difference between male and female trained sprinters (Abe et al. 2001), Olympic soccer, gymnastics and judo athletes (Ichinose et al. 1998). Given that there are sex-dependent differences in muscle force production and rates of injury, more effort should perhaps be directed at understanding sex-dependent architectural differences.

Our finding of a lack of sex difference in the quadriceps also implies that muscle activation strategies, and their changes with exercise training, should also be similar. This is consistent with published data showing that alterations in the EMG–force relationship of the muscles are the same in men and women as movement velocity (Cramer et al. 2004) and contraction mode (Pincivero et al. 2006) are varied. However, it is not consistent with the finding that the proportional contribution of VL increased more in men, and the contribution of VM and RF decreased in women, as knee extension contraction force increased (Pincivero et al. 2002). Because muscle architectural measurements were not performed in these studies, it is not possible to ascribe their inconsistent findings to differences in muscle architecture, although other factors such as differing exercise patterns between the men and women need also to be assessed. To our knowledge, no research has examined training-related changes in quadriceps activation between men and women. The idea that alterations in synergist activation patterns might be the same in men and women has particular implications for clinicians and therapists whose goal is to optimize movement efficiency rapidly in patients after periods of disuse.

A second indicator that our whole quadriceps architecture estimates appear to provide a valid representation of the muscle group is that the data show a significant positive correlation (r > 0.65, P < 0.001) between muscle thickness and fascicle angle regardless of the method used to estimate whole quadriceps architecture, and a weaker negative correlation between fascicle angle and fascicle length (r > 0.45, P < 0.05) (see Fig. 6), and are thus in agreement with others (Abe et al. 1998; Kumagai et al. 2000; Brechue & Abe, 2002; Kanehisa et al. 2003). In general, the highest correlations were achieved using the ‘estimated contribution’ method of estimating whole quadriceps architecture, which might give some speculative validation to the results of Zhang et al. (2003). In some respects, these whole quadriceps data should be treated with some caution because, for example, fascicle length was positively correlated with muscle thickness in RF, suggesting that important architectural characteristics of individual muscles might be missed if only whole quadriceps values are used for analysis.

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Figure 6. Relationships between whole quadriceps muscle thickness and fascicle angle (top graph: a), and fascicle angle and fascicle length (bottom graph: b). Whole quadriceps architecture in these examples was calculated by the equal ratio method (see Methods), which was associated with the lowest correlations between the variables when compared with PCSA, volume and estimated contribution methods. Muscle thickness and fascicle angle were positively correlated, while fascicle angle and fascicle length were negatively correlated. Magnitudes are presented as z-scores.

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Conclusion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. References
  9. Appendix

To our knowledge these data are the first to describe the complex architecture of the quadriceps femoris in normal humans. Although there is significant, region-specific variation in architecture of the superficial quadriceps muscles that might affect force transfer efficiency and complicate muscle models, there is some generality with respect to relative intermuscular architecture of the superficial muscles. This is not true for the deep VI. Our estimates of whole quadriceps architecture are important in that we were able to provide evidence that the architecture of single muscles cannot be used as an estimate for the whole quadriceps, but that examination of VM, along with possibly VL and VIant, can provide a snapshot. It also verified a sex-dependent size effect of muscles, and the assumed relationships between muscle thickness, fascicle angle and fascicle length that are often shown in single muscles. Assuming the architecture of individual muscles is indicative of their function, and given that the quadriceps muscles act via a common tendon during uni-joint knee extension, these data allow speculation of the functional roles of individual muscles. This is important for understanding human movement strategies, and assists in the development of muscle models and to inform the design of mechanized locomotor systems including prosthetic and robotic limbs. By examining architectural variations across the quadriceps and considering the effects of muscle architecture on function, our data lead to the assumptions that: (1) changes in the relative activation of individual muscles should change as force, velocity movement range and contraction mode are altered so that muscles with the most appropriate architectural design provide a greater contribution; (2) intramuscular activation should not be completely uniform, and should change as movement requirements change; (3) exercise training should alter the pattern of activation in order to improve force transmission between muscles with varying architecture; (4) these variations in activation with training should not induce dramatic changes in the relative energy expenditure of the muscles as the more highly active muscles should be more efficient at producing the prescribed forces; (5) exercise training should promote region-specific hypertrophic responses as strain levels should not be consistent throughout the muscle group; and (6) there should be little sex difference in these adaptations as our data do not show a sex difference in muscle architecture of the quadriceps in subjects with a common exercise background. Indeed, these hypotheses seem to be largely consistent with the published data; however, the assumption that architecture reflects function has not been empirically tested. Nor has it been determined whether the relationships reported here remain constant after periods of physical training or detraining.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. References
  9. Appendix

Appendix

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. References
  9. Appendix

Appendix A

Model specifications

The muscle was assumed to shorten 15% of its 450 mm length (i.e. 67.5 mm), with 33.75 mm of shortening being allowed between muscle optimum length and the extent of its range of motion (in lengthening and shortening). Architectural parameters at muscle optimum length were taken from the present data (measured with the muscle relaxed at a 45° knee angle). The muscle consisted of three segments, as shown in Fig. 5. Muscle fibres were assumed to possess a parabolic force–length relationship (van den Bogert et al. 1998), fibre/fascicle length and angle changed with muscle shortening, and while the fibres were at different lengths within the muscle, and at different points on their force–length curve throughout the contraction, they were assumed to reach optimum length at the same muscle length.

Equations:

  • 1. Lfasopt = MT/sin θopt

where Lfasopt is the fascicle (fibre) length at muscle optimum length, MT is the muscle thickness and θopt is the fascicle angle at optimum muscle length.

  • 2. Lfasnew = √(c − (i × 33.75)2 + MT2)

where Lfasnew is the new length of a fascicle after a proportion of muscle shortening (i), where muscle shortening has the value 1 to −1, and c = √( inline image + MT2). 33.75 refers to the possible muscle shortening distance above and below optimum (33.75 mm), as described above.

3. Ffas is the force produced by the fibre at a given fibre length, according to a parabolic force–length curve (over the contraction range, Ffas ranged from approximately 90–100% of peak force).

  • 4. θnew = sin−1(MT/Lfasnew)

where θnew is the new fascicle angle achieved after a given fibre length change.

  • 5. Fseg = cos θnew × Ffas

where Fseg is the force produced by each segment in the three-segment model.

  • 6. Ftotal = Fseg1 × a1 + Fseg2 × a2 + Fseg3 × a3

where Ftotal is the total force of all three segments at any given muscle length, Fseg1, Fseg2 and Fseg3 are the forces produced by each of the three segments, and a1, a2 and a3 are the relative contributions of each segment to the total force based on their estimated physiological cross-sections (MT2/Lfasopt).