The obliqueness of the fibres of a muscle in relation to the force-generating axis of the muscle-tendon complex is known as the pennation angle and its magnitude is an important determinant of the muscle's functional characteristics (Gans & Bock, 1965; Gans, 1982; Otten, 1988; Fukunaga et al. 1997). For a given muscle anatomical cross-sectional area and volume, an increased pennation angle results in a reduced muscle fibre length, compromising shortening velocity and excursion range, but also allows more contractile material to be placed in parallel, increasing maximum force generation (Alexander & Vernon, 1975; Gans, 1982; Muhl, 1982). Therefore, the maximum force produced at a given muscle fibre length in the direction of the fibres in a pennate muscle is higher than the maximum force produced in the direction of the fibres of a parallel-fibre muscle of the same anatomical cross-sectional area and volume. However, pennation angle itself also results in a tendon force loss proportional to 1 - cosine of the pennation angle. Thus, an increasing pennation angle only up to 45 deg could theoretically result in an increase both in force produced in the direction of muscle fibres and in its effective component transmitted to the tendon (Alexander & Vernon, 1975; Rutherford & Jones, 1992).
Accurate information with respect to pennation angle is important in two types of analysis: first, when the joint moment that a muscle can exert is calculated from the force that a muscle is predicted to produce in the direction of its fibres (e.g. Woittiez et al. 1983; Zajac, 1989), and secondly and inversely, when force production in the direction of a muscle's fibres is calculated from the moment-generating capacity of the muscle (e.g. Narici et al. 1992; Kawakami et al. 1994). The pennation angle of a muscle can be, and often has been, obtained by direct anatomical inspections on cadaveric specimens (Alexander & Vernon, 1975; Wickiewicz et al. 1983; Woittiez et al. 1983; Frendrich & Brand, 1990; Spoor et al. 1991). However, values taken from embalmed muscles do not represent in vivo dimensions (Yamaguchi et al. 1990) and are unlikely to reflect accurately architectural changes experimentally observed under in vivo or in situ conditions. Furthermore, pennation angle changes inversely as a function of muscle fibre length (Muhl, 1982; Huijing & Woittiez, 1984; Ichinose et al. 1995; Narici et al. 1996), and proportionally as a function of isometric force generated by the muscle (Herbert & Gandevia, 1995; Ichinose et al. 1995; Narici et al. 1996) so that the muscle's fibre volume is kept constant at different lengths and contracted stages (Baskin & Paolini, 1967). Differences have been reported for human muscle pennation angle values of up to 120–170 % between rest and maximum isometric contractions at a given joint angle (Herbert & Gandevia, 1995; Narici et al. 1996). Clearly, failure to consider this contraction effect on pennation angle may be a source of serious error in any calculations of muscle force and joint moment.
In an attempt to improve our understanding of in vivo changes of muscle architecture, modern imaging techniques have been used (Henriksson-Larsen et al. 1992; Narici et al. 1992, 1996, 1998; Kawakami et al. 1993; Herbert & Gandevia, 1995; Ichinose et al. 1995; Fukunaga et al. 1997). Real-time ultrasonography enables in vivo muscle scanning and offers promise for a realistic determination of changes in muscle architecture (Rutherford & Jones, 1992; Kawakami et al. 1993; Narici et al. 1996). Real-time ultrasonic measurements were taken in the present study in the triceps surae muscle in man. The purpose of our research work was to (1) determine in vivo changes in pennation angle and fibre length in each muscle of the triceps surae complex (gastrocnemius medialis (GM), gastrocnemius lateralis (GL) and soleus (SOL)) as a function of ankle joint angle and moment produced voluntarily during an isometric ankle plantarflexion and (2) evaluate the accuracy of estimating changes in muscle architecture in the transition from rest to a given isometric plantarflexion moment using a planimetric model assuming constant thickness and straight fibres (Huijing & Woittiez, 1984). Morphometric analysis of in vivo muscle scans would enhance our understanding of the mechanical behaviour of living muscles and enable evaluation of the applicability of simple planimetric models in estimating loads in the musculoskeletal system.
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The major findings of the present study were that (1) the architecture of the triceps surae complex was homogeneous at the studied sites of the muscle complex, (2) the muscle thickness increased as a function of contraction intensity in GL and SOL but it did not change in GM, and (3) a planimetric model assuming constant thickness and straight fibres did not estimate accurately in vivo changes in muscle architecture occurring in the transition from rest to a given isometric contraction intensity.
The similarity in pennation angle, fibre length and thickness values along and across the studied sites over each muscle's belly at a given state of contraction indicated that muscle architecture was consistent over the studied regions and sections in each muscle. As mentioned in Methods, measurements that were taken from the central region over the mid-sagittal axis of each muscle's belly were used as input to the muscle model. It is important to realize that the representativeness of the values that were incorporated in the planimetric model with respect to the architecture of the whole muscle would not affect the validity of the results of our comparisons between actual and modelled muscle architecture, since these were made with respect to a given area of the muscle. Nevertheless, it should be remembered that architectural measurements were taken over a limited area of each muscle and consequently conclusions should not be drawn about the homogeneity in the architecture of the studied muscles over their whole volume. From data concerning the resting length of the human lower limb muscles obtained either from cadavers (Wickiewicz et al. 1983; Friendrich & Brand, 1990) or by in vivo measurements (Fukunaga et al. 1992) and by taking into account the dimensions of the acquired sonographs (9 cm × 3.7 cm), it is estimated that ∼47, 51 and 30 % of the length of GM, GL and SOL, respectively, was scanned at rest. During isometric plantarflexion Achilles' tendon stretches and since the musculotendon length does not change as force develops, all three muscles shorten, and therefore the relative scanned length over each individual muscle belly during contraction should have been increased compared with the resting state.
In the present study GM pennation angle mean values at the neutral ankle position were larger (by ∼5 deg at rest and 7 deg during MVC) and fibre length mean values smaller (by about 5 mm at rest and 10 mm during MVC) than the corresponding values reported by Narici et al. (1996). These discrepancies are likely to be due to the difference in the GM length between the two studies; in the present study the knee was flexed at 90 deg, while in that of Narici et al. (1996) the knee was fully extended. Since gastrocnemius is a bi-articular muscle crossing both ankle and knee joints, GM and GL would be slacker at any given ankle position at the knee angle of 90 deg than at the knee extension position and this in turn would clearly affect both pennation angle and fibre length. However, an alteration in the knee joint angle at a given ankle angle and state of contraction would not have any effect in SOL architecture since this muscle crosses only the ankle joint.
Differences in the architecture of GM between rest and MVC at any given ankle position were in line with those previously reported by Narici et al. (1996). A constancy in GM thickness was visualized whether comparing the resting state with MVC or comparing the different contraction intensities during graded static plantarflexion at the neutral ankle position. However, in both GL and SOL, thickness increased as a function of contraction intensity while in these muscles the model underestimated changes occurring from rest to MVC in both pennation angle and fibre length at any given ankle angle. Therefore, it is reasonable to suggest that changes in GL and SOL thicknesses as a function of contraction intensity may account for the observed differences in these muscles between actual architectural changes and those estimated by the model. A substantial difference between actual and modelled pennation values implies consequences for the validity of calculated individual muscle forces from an analysis incorporating resting pennation values. The force produced by an individual muscle of a group of muscles ending in a common tendon is given by the equation:
where FM is the force produced in the muscle, PCSA/ΣPCSA is the relative physiological cross-sectional area (rPCSA) of the muscle, FT is the tendon force and a the pennation angle of the muscle (Narici et al. 1992). To quantify the extent of an erroneously calculated FM during MVC using either cadaveric (Alexander & Vernon, 1975; Wickiewicz et al. 1983; Woittiez et al. 1983; Friendrich & Brand, 1990; Spoor et al. 1991) or modelled MVC pennation data (mean values), we assumed representative values for FT and rPCSA for each individual muscle and we compared the forces calculated with those derived from incorporating pennation data (mean values) collected in the present study during an ankle plantarflexor MVC. The results presented were derived by incorporating experimentally obtained and modelled pennation data at an ankle angle of −15 deg (the angle at which peak plantarflexor MVC was achieved by all subjects). Incorporation of cadaveric data resulted in an underestimation of ∼16, 15 and 10 % in forces produced in GM, GL and SOL, respectively, compared with the corresponding calculations derived using experimentally observed pennation values during a plantarflexor MVC. An incorporation of modelled pennation values resulted in underestimated forces in GM, GL and SOL by ∼1, 10 and 9 %, respectively, compared with the corresponding calculations incorporating in vivo collected pennation data. Inversely, in an analysis estimating each individual muscle's moment-generating capacity at an ankle angle of −15 deg, use of cadaveric pennation data resulted in overestimated moments by ∼20, 17 and 10 % in GM, GL and SOL, respectively, compared with the corresponding moments calculated using experimentally collected pennation data. Use of modelled pennation values resulted in overestimated moments in GM, GL and SOL by ∼1, 11 and 10 %, respectively, compared with the corresponding moments calculated using experimentally collected pennation data. Assuming a ratio between PCSAs in GM:GL:SOL of 2:1:6 (Wickiewicz et al. 1983; Woittiez et al. 1983; Friendrich & Brand, 1990; Fukunaga et al. 1992), common moment arms (Achilles tendon moment arm), and specific tensions for all three muscles (Woittiez et al. 1983), it can be calculated that the above differences would result in an overestimated triceps surae moment-generating capacity of ∼14 % and 10 % using cadaveric and modelled pennation data, respectively, compared with the corresponding moment calculated by incorporating experimentally collected pennation data. At submaximal contraction intensities corresponding to 20, 40, 60 and 80 % of MVC at the neutral ankle position, incorporation of cadaveric and modelled pennation data resulted in an overestimation of generated moments of 2–18 % (from a moment corresponding to 20 % of MVC to a moment corresponding to 80 % of MVC) and 4–17 % in GL and 1–10 % and 3–12 % in SOL compared with calculations incorporating the corresponding actual pennation data. In GM, incorporation of cadaveric and modelled pennation data resulted in an overestimation in generated moments at submaximal contraction intensities of 5–20 % and in an underestimation of 1–5 % (from a moment corresponding to 20 % of MVC to a moment corresponding to 80 % of MVC) compared with calculations incorporating the corresponding actual pennation data. Triceps surae moments at intensities corresponding to 20, 40, 60 and 80 % of MVC were overestimated by ∼4, 8, 12 and 16 % using cadaveric pennation data and by 2, 5, 6 and 8 % using modelled pennation data, compared with moments calculated by incorporating the corresponding experimentally collected pennation data. The above analysis suggests that musculoskeletal models estimating the mechanical output of the triceps surae muscle using either cadaveric (Woittiez et al. 1983) or modelled pennation data (Zajac, 1989) may result in unrealistic calculations not only when maximum isometric force is generated, but also in dynamic conditions, when compared with calculations incorporating experimentally collected, force-specific pennation data. Use of the regression model presented in the Appendix would result in an incorporation of force-specific pennation data in all three muscles of the triceps surae complex and a realistic analysis of loads in the lower extremity.
The present study showed that changes in human muscle thickness were not always predictable, but instead appeared to be muscle specific. The thickness of GM did not change in response to contraction intensity but the thicknesses of GL and SOL changed. Our findings concerning a constant thickness in the human GM at different muscle lengths and between different contracting stages are in line with in vivo observations of Narici et al. (1996) using ultrasonography on the same human muscle. Herbert & Gandevia (1995), using ultrasonography, observed large increases in the human brachialis muscle thickness, when the elbow flexor group produced isometrically a moment equal to 100 % of MVC, compared with rest at a given elbow joint angle. Ichinose et al. (1995) using ultrasonography found an insignificant but systematic decrease in the resting human vastus lateralis muscle thickness, when a static force equal to 10 % of MVC was produced by the knee extensors compared with rest in a series of knee joint angles. However, the decrease became significant when the knee joint was positioned at 80 and 100 deg. Furthermore, Zuurbier & Huijing (1993), by studying in situ changes in the rat GM geometry during maximal isometric contractions at different lengths, demonstrated that the assumption of a constant two-dimensional area (derived from the two major assumptions of the model mentioned above), when the muscle is planimetrically modelled as a parallelogram did not hold true. All above observations raise doubts about the applicability of simple planimetric models for describing changes in muscle architecture.
Intramuscular pressure increases as muscle contracts and under isometric conditions there is a positive relationship between contraction intensity and intramuscular pressure (Sejersted et al. 1984; Aratow et al. 1993). Associated with an increasing intramuscular pressure is an increasing curvature of some of the muscle fibres (e.g. Otten, 1988; Van Leeuwen & Spoor, 1992). When pennation angle from the central mid-sagittal region of each muscle was calculated from the formula sina= thickness/fibre length (Kawakami et al. 1995), a difference was found compared with the value obtained by digitizing. Pennation values from the sine formula for a given image, set of architectural characteristics and contraction intensity at the neutral ankle position were higher than the respective values derived from digitizing measurements on the superficial aponeurosis of each muscle (angle a in Fig. 2). However, when pennation angles were derived from digitizing measurements on the deep aponeurosis of each muscle (angle b in Fig. 2), the sine formula gave lower pennation values. For a given muscle, the absolute value of the difference between pennation values obtained by digitizing and with the sine formula was of a similar level between aponeuroses. The difference between pennation values obtained from the two different approaches indicated a curving fibre shape in each muscle. The similarity between the latter percentage difference between the pennation values-contraction intensity curve (Fig. 7) and the intramuscular pressure-contraction intensity curve (Sejersted et al. 1984; Aratow et al. 1993) supports in an indirect but correlational way an association between intramuscular pressure and fibre curvature. The similarity of the absolute value of the above difference between the superficial and deep aponeuroses of the same muscle indicated a homogeneous curvature at the respective insertion points, implying no alteration in the loss of force transmitted to the tendon during contraction calculated according to the sine formula. When a muscle is planimetrically represented as a parallelogram the fibres are modelled as straight lines between aponeuroses. The measurement of fibre length along a straight line in the present study was to enable the application of such a model. The morphometric analysis performed indicated, however, that fascicles curved as a function of contraction intensity. Changes in fibre curvature are not taken into account when using simple planimetric models. However, more complex muscle models allow incorporation of the curving fibre shape and aponeuroses orientation during muscle contraction (Van Leeuwen & Spoor, 1992).
Figure 7. Percentage difference between pennation angle values obtained by digitizing and from the sine formula as a function of contraction intensity at the neutral ankle position
Notice the similarity between the change in fibre curvature (percentage difference between pennation values) as a function of isometric contraction intensity in each muscle in the subjects of the present study (n= 6) and the change in intramuscular pressure as a function of isometric contraction intensity in studies by Sejersted et al. (1984) and Aratow et al. (1993).
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As intramuscular pressure builds up during contraction, the muscle becomes less compliant in the direction of its thickness. The line of action of the effective muscle fibre force transmitted to the tendon lies on the longitudinal axis of the tendon. The point at which the muscle's distal tendon is attached remains constant during contraction. However, the spatial orientation of the longitudinal axis of the tendon may change when contraction results in an increased muscle thickness in a muscle adjoining bones and other rigid tissue, such as in co-activated synergist, stabilizer and antagonist muscles. Thus, an increased muscle thickness as a result of a high contraction intensity may have implications for the magnitude of the musculotendon moment arm involved and calculation of the respective developed moment. In the case of GM, GL and SOL whose distal tendons join to form the Achilles tendon, a high contraction isometric plantarflexion may result in a displacement of the Achilles tendon relative to its resting position due to an increased thickness in GL and SOL during contraction compared with rest.
In conclusion, this study showed that both pennation angle and fibre length of all three muscles of the triceps surae complex are consistent over a major part of the muscle and change both in response to changes in ankle angle at rest and during isometric contractions at intensities up to 100 % of plantarflexor MVC. Changes in individual muscle architecture in transition from rest to a given contraction intensity were not always predictable by a model representing the muscle planimetrically as a parallelogram. Changes in a muscle's pennation angle should be taken into account and modelled accordingly when either individual muscle forces or generated moments are to be estimated.