Eur J Appl Physiol (1992) 65:438-444

Applied Physiology Joumal of

and Occupational Physiology © Springer-Verlag1992

Assessment of human knee extensor muscles stress from in vivo physiological cross-sectional area and strength measurements M. V. Narici t, L. Landoni 2, and A. E. Minetti 1 1 Reparto Fisiologia Lavoro Muscolare, Istituto di Tecnologie Biomediche Avanzate, Consiglio Nazionale delle Ricerche, Via Ampbre 56, 1-20131 Milan, Italy 2 Centro S. Pio X, Servizio di Risonanza Magnetica, Via Nava 31, 1-20159 Milan, Italy Accepted July 2, 1992

Summary. The physiological cross-sectional areas (CSAp) of the vastus lateralis (VL), vastus intermedius (VI), vastus medialis (VM) and rectus femoris (RF) were obtained, in vivo, from the reconstructed muscle volumes, angles of pennation and distance between tendons of six healthy male volunteers by nuclear magnetic resonance imaging (MRI). In all subjects, the isometric maximum voluntary contraction strength (MVC) was measured at the optimum angle at which peak force occurred. The MVC developed at the ankle was 746.0 (SD 141.8) N and its tendon component (Ft), given by a mechanical advantage of 0.117 (SD 0.010), was 6.367 (SD 1.113) kN. To calculate the force acting along the fibres (F 0 of each muscle, Ft was divided by the cosine of the angle of pennation and multiplied for (CSAp.ECSAp-1), where ECSAp was the sum of CSAp of the four muscles. The resulting Ff values of VL, VI, VM and RF were: 1.452 (SD 0.531) kN, 1.997 (SD 0.187) kN, 1.914 (SD 0.827) kN, and 1.601 (SD 0.306) kN, respectively. The stress of each muscle was obtained by dividing these forces for the respective CSAp which was: 6 . 2 4 x 10 -3 (SD 2.54× 10 -3) m 2 for VL, 8.35 X 10-3 (SD 1.17 x 10-3) m 2 for VI, 6.80 x 10 -3 (SD 2 . 6 6 x 1 0 -3) m 2 for VM and 6 . 6 2 x 1 0 -3 (SD 1.21 x 10-3) m 2 for RF. The mean value of stress of VL, VI, VM and RF was 250 (SD 19)kN m - 2 ; this value is in good agreement with data on animal muscle and those on human parallel-fibred muscle. Key words: Force/CSA - Muscle stress - Specific tension - Skeletal muscle strength - MRI

Introduction The absolute force of a muscle is known to be directly proportional to its cross-sectional area (Weber 1846). Animal and human muscle may, however, be either parallel-fibred, if fibres lie parallel to its length, or penCorrespondence to: M. V. Narici

nate, if they lie at an angle with respect to the axis of traction of the muscle. Because of this different architecture, the anatomical cross-sectional area (CSA) of a parallel-fibred muscle will cut all the fibres at right angles and will thus correspond to the physiological CSA (CSAp). In the case of a pennate muscle, the anatomical CSA will only cut a limited number of fibres and will not correspond to the physiological CSA. Furthermore, whereas the overall force exerted by the fibres of a parallel-fibred muscle is the same as that measured along the tendon, the force exerted by the fibres of a pennate muscle is the tendon component divided by the cosine of the angle of pennation of the fibres. It follows that, in order to calculate the stress of a muscle correctly, care must be taken to relate the force developed along the fibres to that cross-sectional area that will cut all the fibres at right angles, that is to say, the physiological CSA. Nevertheless, the stress values of human skeletal muscle that appear in the literature vary largely, ranging from about 200 kN m -2 to 1000 kN m -a (Narici et al. 1988), and in most cases depart from the values for animal muscle, typically comprised between 150 kN m - 2 and 300 kN m - 2 (Close 1972). Those few reports on human muscle that agree with the data on animals either refer to CSAp measured on cadavers (Haxton 1944; Alexander and Vernon 1975) or to parallel-fibred muscle where CSA equals CSAp (Ralston et al. 1949; Nygaard et al. 1983). So far, while the in vivo measurement of the CSAp of human parallel-fibred muscle has been straightforward, that of pennate muscles could not be obtained. In a recent pilot study, however, we were able to estimate in vivo the CSAp of each of the four muscles constituting the human quadriceps from muscle volume, pennation angle and distance between the tendons obtained from nuclear magnetic resonance imaging (MRI) scans (Giannini et al. 1990). As the calculated stress values were in quite good agreement with the data on animal muscle and on human parallel-fibred muscle, in order to validate the study further, the authors decided to extend these measurements to a larger population.

439 Ft

1 u -1

m. 9 .t

-1

Fig. 1. Scheme of a pennate muscle showing: the pennation angle (0), the distance (t) between the tendons (thick parallel lines), the cross-sectional area of each fibre (a), the CSAp of the muscle (m'p -1 "t-1)'sin0; dashed line), the tendon area (m.p-~.t -1) and the forces acting along the tendon (Ft) and along the fibres (F0

Methods

Subjects. Six healthy male volunteers [age 34.0 (SD 4.7) years; mass 74.1 (SD 8.2) kg; height 1.74 (SD 0.04) m] took part in this study, after giving informed consent. All subjects were fully motivated and well-accustomed to the development of maximum voluntary force.

Physiological CSA determination. Physiological CSA of the four muscles constituting the quadriceps: vastus lateralis (VL), vastus intermedius (VI), vastus medialis (VM) and rectus femoris (RF) was calculated from the equation: CSAp = (m .p - 1. t - 1). sin 0,

(1)

Where: m = muscle mass (kg), p = muscle density (kg m -3), t = distance between the tendons (m) and 0= angle of pennation (rad); these are shown in the scheme of a pennate muscle in Fig. 1. This equation is essentially based on that of Alexander and Vernon (1975), as in their paper the non-"reduced physiological cross-sectional area", represented by the total cross-sectional area of all muscle fibres n' a (number n fibres each of cross-sectional area a), is equal to (m.p -1 .t-1).sin0. As m ' p - 1 equals the volume, Eq. 1 simplifies to: CSAp = (V. t - 1). sin 0

(2)

The muscles of the dominant thigh were reconstructed from 12 MRI axial images (Figs. 2, 3) carried out with a 1.5-T magnet (Gyroscan S 15, Philips, Eindhoven, The Netherlands) with a magnetic field resonance frequency for the protons of 63.8664 MHz. Spinecho, Tl-weighted, multislice sequences with a slice thickness of 0.01 m (axial scans), 0.006 m (coronal scans) and 0.007 m (sagittal scans) were utilized. Each slice, interspaced by a distance of 1/12 femur length was digitized with a graphic tablet for successive data processing. Purposely created software running on a computer (Olivetti PE28) performed a B-SPLINE interpolation to add slices between those originally acquired. Muscle volumes were obtained with standard computer-aided design programming techniques consisting of a double integration of the spatial coordinates, from a reference plane. The validity of this volume-estimation technique was initially tested against the volume of an irregularly shaped water-filled dummy and also against an isolated bovine calf muscle. A mean distance between the tendons was obtained from ten measurements interspaced by 1/10 muscle length carried out on sagittal planes for the three vasti (Fig. 4) and on coronal planes for the rectus femoris. As this muscle is bipennate, its CSAp was calculated by treating the muscle as two separate halves, each with a tendon thickness t, and by dividing the volume by 2. Its total CSAp was then obtained by multipling the CSAp of each half by 2. For each muscle, a mean angle of pennation was obtained from the angle of muscle fibre fasciculi that could be measured, with a conventional goniometer, on coronal (for RF and VL) and sagittal (for VI and VM) MRI pictures (Fig. 5). The orientation of these planes was chosen out of several trials carried out for VL, VI and

Fig. 2. Magnetic resonance imaging (MRI) coronal plane images of the thighs, showing the levels, interspaced by 1/12 femur length, at which the axial scans were carried out. In this coronal picture 61 mm---480 mm (in this case the MRI software does not enable the standard to be printed)

VM on coronal and sagittal planes, but only on coronal planes for RF, to give the highest pennation angles. For VL and VM, however, the mean angles measured on coronal planes did not significantly differ from those evaluated on sagittal planes. The accuracy of the measurement of the angle of pennation was tested on a boving triceps brachii muscle first by the MRI technique and then by direct measurement on the dissected muscle. The error of the MRI technique was estimated to be +0.035 rad. The slice thickness, repetition time and echo time were respectively 0.01 m, 0.496 s (fast-feed echo) and 0.008 s for the axial scans, 0.007 m, 0.262 s, 0.015 s for the coronal scans and 0.007 m, 0.360 s and 0.015 s for the sagittal scans.

Force measurements. Subjects were asked to sit in an adjustable, straight-backed chair with the pelvis and trunk tightly secured by two velcro straps. A load cell mounted on the chair frame was connected to a padded metal strap placed around the subject's ankle via a steel cable (30 mm in diameter), which could always be maintained at a tangent to the ankle by means of an adjustable pulley system (Fig. 6). Isometric maximal voluntary contraction (MVC) of both quadriceps was measured at 0.0872-tad intervals from 1.571 rad to 2.094 rad of knee extension (full knee extension being 3.142 rad) and only the MVC of the dominant limb was used for data analysis. This range of angles was chosen to find the optimum angle at which the quadriceps force was at its highest, as in a previous paper it was shown that this occurs at around 1.920 rad of knee extension (Narici et al. 1988). In all subjects, the moment arm for the external force (Ra) was obtained from the sum

440

Fig. 3. The 12 MRI axial images of the thighs from 0/12 femur length (upper left) to 11/12 femur length (lower right)

of the distance from the knee-space to the point of application of the external force, measured by anthropometry, plus 2.0ram, which corresponded to the approximate distance (assessed by MRI on one subject at 1.832 tad of knee extension) from the centre of rotation of the femoral condyle to the knee-space. For each individual, the moment arm for the patellar ligament (Rpt) was obtained at the angle corresponding to the highest MVC from the data of Smidt (1973).

where ZCSAp = sum of the CSAp of VL, VI, VM and RF). Finally, the stress of each muscle was calculated by dividing Ff (Eq. 3) by its CSAp.

Stress calculation. To calculate the stress of each muscle, the force

M e a n values o f muscle v o l u m e s (V), distance b e t w e e n the t e n d o n s (t), angles o f p e n n a t i o n (0) a n d the p h y s i o l ogical cross-sectional areas ( C S A p ) c o m p u t e d f r o m these d a t a are r e p o r t e d in T a b l e 1. F i g u r e 7 shows a typical i m a g e o f the q u a d r i c e p s muscles (of the left thigh) o b t a i n e d f r o m the r e c o n s t r u c t i o n o f the M R I axial images, using c o m p u t e r - a i d e d design techniques. The rec o n s t r u c t e d v o l u m e was f o u n d to u n d e r e s t i m a t e t h a t o f the water-filled d u m m y b y 6 . 5 % a n d t h a t o f the b o v i n e

measured at the ankle (Fa) had first to be converted to its tendon component by dividing by the mechanical advantage given by Rp~/ Ref. To estimate the force acting along the fibres (Ff) of each of the four muscles composing the quadriceps, the force along the tendon (Ft), acting at an angle 0 with respect to the fibres (Fig. 1), was divided by cos0 and then multiplied by the proportionate fraction of the total CSAp occupied by each muscle. It was assumed therefore that each muscle would exert a force equal to: (CSAp" ECSAp - ~)'Ft •cos - 10

(3)

Results

441

Fig. 4. The MRI sagittal image of the vastus medialis muscle (ar-

row) in which the distance between the tendons was measured

Fig. 5. An MRI sagittal image of the vastus medialis muscle in which the pennation of the muscle fibre fasciculi is visible

e

Fig. 7. A frontal view of the quadriceps muscles obtained by computer-aided design reconstruction of the MRI axial images: the vastus lateralis (/), the rectus femoris (r), the vastus medialis (m) and the vastus intermedius (0 and the femur bone (f; data on its volume not presented)

Fig. 6. The apparatus used to test the quadriceps strength. The subject is secured to the experimental chair at the pelvis (at) and at the trunk (e). The force produced is measured by a load cell (a) connected to the subject's ankle via a steel cable (b), which by passing through the pulley (c) can always be maintained at a tangent to the ankle. The position of a and c can be modified both horizontally and vertically

calf muscle b y 2 . 8 % (its v o l u m e assessed b y d i v i d i n g its m a s s b y 1056 kg m - 3 , the d e n s i t y o f muscle). T h e m e c h a n i c a l a d v a n t a g e o f the q u a d r i c e p s muscle, used to calculate the f o r c e in its t e n d o n , was f o u n d to be 0.117 (SD 0.010). T h e e v a l u a t e d stress o f VL, VI, V M , a n d R F r a n g e d f r o m 237 k N m - 2 to 279 k N m - 2 (Table 1); this gave a m e a n stress f o r the q u a d r i c e p s g r o u p o f 250 (SD 19) k N m - 2

442 Table 1. Muscle volumes, distance between tendons (t), physiological cross-sectional area (CSAp), the fraction of each muscle's CSAp over the sum of the four muscles' CSAp (CSAp/ECSAp), the quadriceps force developed at the ankle (Fa), its tendon com-

ponent (Ft) and the force exerted by the fibres (Ff) for the vastus lateralis (VL), vastus intermedius (VI), vastus medialis (VM) and rectus femoris (RF). Values are given as means (SD)

Muscle

Volume (m3) x 10 -4

t (m) x 10-2

0 (tad)

CSAp (m2) x 10 -a

CSAp" ECSAp -1

VL

5.857 (1.590) 5.740 (0.937)

2.8 (0.3) 2.2 (0.1)

0.2984 (0.0733) 0.3316 (0.105)

6.24 (2.54) 8.35 (1.17)

0.2126 (0.044) 0.3014 (0.0359)

VI

Fa (N)

746.0 (141.8) VM RF

4.245 (0.996) 2.387 (0.901)

3.5 (0.5) 2.2 (0.3)

0.5602 (0.0873) 0.3630 (0.0925)

6.80 (2.66) 6.62 (1.21)

Discussion This study has shown that human skeletal muscle physiological CSA may be determined in vivo and non-invasively, by MRI. To our knowledge, this report and a previous one by the same investigators (Giannini et al. 1990) are the only studies whereby measurement of CSAp has been carried out in vivo. There are several reports on the CSAp measured in cadavers (Haxton 1944; Alexander and Vernon 1975; Wickiewicz et al. 1983; Friederich and Brand 1990). Muscles of embalmed cadavers, however, have often been reported to shrink after the fixation process, and their CSAp may thus appear smaller than those of living subjects. Nevertheless, our mean values of CSAp of VL, VI, VM and RF are remarkably similar to those reported for cadaver S1 by Friederich and Brand (1990). The pennation angles measured by MRI generally fall within the range of angles measured in cadavers and reported in the literature (see Yamaguchi et al. 1990). It was noted that the pennation angle of VM dramatically increased proximally to distally, towards the knee. Its proximal fibres presented an angle of 0.122 rad while its more distal fibres close to the knee had an angle of 1.204 rad. This observation is in line with that of Lieb and Perry (1968), who reported a fibre angle range of 0.262 rad to 0.314 tad in the upper fibres and 0.873 tad to 0.960 tad in the distal fibres in cadavers. In our study, pennation angles were measured with the subjects lying supine with the quadriceps relaxed and leg fully extended. For VL, the angle measured with this method was of 0.297 rad and appears fairly comparable to the angle of 0.263 rad, quadriceps relaxed, obtained in vivo with ultrasound by Henriksson-Lars6n et al. (1992). Our pennation data and those of the above-mentioned authors are apparently higher than the angle found by Rutherford and Jones (1992) also obtained in vivo with ultrasound; they reported angles for VL and VI respectively of: 0.1326 rad and 0.1431 tad, quadriceps relaxed, knee at right-angle; 0.105 tad and 0.122 rad, quadriceps passively stretched by full knee flexion.

0.2332 (0.0442) 0.2415 (0.0560)

Ft (N)

Fe (N)

Stress (kNm -2)

1451.9 (531.8) 1997.1 (186.6)

237 (13) 241 (16)

1913.2 (826.5) 1601.3 (305.6)

279 (20) 243 (22)

6366.5 (111.5)

Their angles referring to the quadriceps contracted with the knee fully extended (0.244 rad for VL and 0.279 rad for VI) are, nevertheless, comparable to ours. Differences in leg position, however, should perhaps not be overlooked since, in a position of passive full flexion, the angles of VL and VI are smaller than those referring to the quadriceps relaxed with the knee flexed by 1.571 rad. In both these studies using ultrasound, an increase in pennation angle with muscle contraction was observed. For the VL muscle this increase seems to be of the order of 80% (74%, Henriksson-Lars6n et al. 1992; 84%, Rutherford and Jones 1992). As pointed out by Alexander and Vernon (1975), during the contraction of a muscle, the volume (the product of the area of the tendon and the distance between the tendons, t) remains constant and, as the area of the tendon should also be constant, t should not change. Thus, i f V't -1 remains constant, the CSAp should simply increase as a function of the sine of the increased angle. For VL, for instance, an increase in pennation angle of 80% will, in our case, increase its CSAp from 6.24 x 10-3 m 2 to 10.7 × 10 -3 m 2, that is to say by 71%. If one assumes that upon contraction, the ratio CSAp.ECSAp -1 remains constant, the force Ff acting along the fibres of VL, given by Eq. 3 (Methods), will change from 1.452kN (when 0=0.298 rad) to 1.163kN (when 0= 0.537 rad). Dividing this force by a theoretical CSAp of 10.7 x 10-s m 2 (contracted muscle) one would obtain a stress of 108.7 kN m-Z, about half of that of the present study. MRI has not yet enabled the measurement of pennation angles in the contracted state and therefore it is difficult to state at present if the magnitude of this increase in CSAp is correct. Nevertheless, the values of stress that were obtained in the present study, ranging from 237 k N m -2 to 279 k N m -2 are consistent with those obtained on animal muscle, which range from 154 kN m -2 to 294 kN m - 2 (Close 1972). The order of magnitude of human muscle stress thus far reported in the literature may be regarded as somewhat intriguing; this has ranged from 94.9 kN m - 2 (Winter and Maughan 1991) to 1000 kN m -2 (Fick 1910). For the human

443 quadriceps most authors have reported stresses of about 6 0 0 - 8 0 0 k N m -2 but figures as low as 9 4 . 9 k N m -2 have also been reported (Winter and Maughan 1991). Whereas the training status or a different muscle fibre composition of the subjects m a y contribute to this discrepancy, an incorrect use of muscle CSA and biomechanical factors represent the main reasons for these incongruities. Indeed, in those studies in which anatomical rather than physiological CSA had been used, the calculated stress values inevitably differed f r o m those of animal muscle. It is not surprising, therefore, that the only h u m a n stress data that agree with those of animal muscle either refer to parallel-fibred muscles, in which CSAa equals CSAp, as in the elbow flexors (Ralston et al. 1949; Nygaard et al. 1983; Edgerton et al. 1986), or to CSAp measured on cadavers (Haxton 1944). The use of anatomical CSA, instead of physiological CSA, in the evaluation of muscle stress also leads to another potential error arising f r o m which area is chosen to divide the force of the muscle. It has in fact been shown (Narici et al. 1989) that the anatomical CSA of the h u m a n quadriceps is at a m a x i m u m between 4/10 and 5/10 femur length and is at minimum at 2/10 and 8/10 of this length. Besides the considerable conceptual error in this approach, the mistake made in the calculation of stress will become even larger if an anatomical CSA above or below 4/10 or 5/10 femur length is chosen. Several formulae have appeared in the literature for the calculation of CSAp (Alexander and Vernon 1975; Wickiewicz et al. 1983; Rutherford 1986; Friederich and Brand 1990). The formula used in the present study corresponds to the formula for non-reduced physiological cross-sectional area of Alexander and Vernon (1975), as in their study n . a = ( m / p ' O " sin 0 (where n = number of fibres and a = cross-sectional area of each fibre) and should thus correspond to the non-reduced physiological cross-sectional area calculated by Haxton (1944). These authors multiplied this area by the cosine of the angle of pennation in order to express the force acting along the tendon and obtained what they termed the reduced physiological cross-sectional area. In our study, the inverse of this process was followed: the CSAp was not multiplied by the cosine of the angle of pennation but rather the force in the tendon was divided by the cosine of this angle so that the force acting along the fibres could be divided by the real CSAp. Failure to take into account the lever system involved in a particular joint is also a c o m m o n source of error in the calculation of muscle stress. For instance, in the knee extensor muscles, if the force developed at the ankle, rather than that acting along the tendon, is used, the resulting stress will be undestimated by more than eight times (in this case the mechanical advantage is in fact 0.117). Fibre type composition may also represent a potential cause for these differences as the stress of fast gastrocnemius muscle of the rat has been shown to be 1 7 6 k N m -2 whereas that of the slow soleus is of 224 k N m -2 (Sexton and Gersten 1967). Controversial reports exist, however, on the force per unit area of hum a n muscle fibres, while some authors report no differ-

ence between the intrinsic strength of type I and type II fibres (Maughan and N i m m o 1983; Nygaard et al. 1983) studies by Young (1984) and Grindrod (1987) seem to suggest that the force per unit area of type II fibres may be 1.8 times that of type I fibres. The muscle volumes obtained by the present computer-aided design reconstruction technique are comparable to those obtained by direct measurement. It is also noteworthy that the calculated volumes of VL, V1, VM and RF are remarkably similar to those reported by Friederich and Brand (1990) in a 37-year-old female cadaver. Of course, this similarity may be purely coincidental but the authors wish to point out that the order of magnitude of the volumes obtained with this reconstruction technique, appear reasonable when compared to cadaver data. The technique of in vivo muscle volume reconstruction has also been carried out by computed tomography (CT) for the human rectus abdomini and erector spinae muscles (Reid and Costigan 1985). However, as for this type of examination, repeated axial scans are required, the use of CT scans, which involve ionizing radiations, is not recommended. In conclusion, this study has shown the stress of human muscle may be determined in vivo f r o m force measurements and from the physiological cross-sectional area obtained by M R I techniques. The values obtained with this method demonstrate that once the physiological rather than anatomical cross-sectional area is used, the discrepancies between the stress of h u m a n and animal muscle seem no longer to exist.

References Alexander RMcN, Vernon A (1975) The dimensions of knee and ankle muscles and the forces they exert. J Hum Mov Stud 1 : 115-123 Close RI (1972) Dynamic properties of mammalian skeletal muscles. Physiol Rev 52:129-197 Edgerton VR, Roy RR, Apor P (1986) Specific tension of human elbow flexor muscles. In: Saltin B (ed) Biochemistry of exercise: VI. Int Series Sport Sci 16:487-499 Fick R (1910) Handbuch der Anatomie und Mechanik der Gelenke unter Beriicksichtigung der bewegenden Muskeln. Fischer, Jena Friederich JA, Brand RA (1990) Muscle fibre architecture in the human lower limb. J Biomech 23 : 91-95 Giannini F, Landoni L, Merella N, Minetti AE, Narici MV (1990) Estimation of specific tension of human knee extensor muscles from in vivo physiological CSA and strength measurements. J Physiol (Lond) 423 : 86P Grindrod S, Round JM, Rutherford OM (1987) Type 2 fibre composition and force per cross-sectional area in the human quadriceps. J Physiol (Lond) 390: 154P Haxton HA (1944) Absolute muscle force in the ankle flexors of man. J Physiol (Lond) 103:267-273 Henriksson-Lars6n K, Wreling ML, Lorentzon R, Oberg L (1992) Do muscle fibre size and fibre angulation correlate in pennated human muscles? Eur J Appl Physiol 64:68-72 Lieb FJ, Perry J (1968) Quadriceps function. An anatomical and mechanical study using amputated limbs. J Bone Joint Surg 50:1535-1548 Maughan RJ, Nimmo MA (1984) The influence of variations in muscle fibre composition on muscle strength and cross-sectional area in untrained males. J Physiol (Lond) 351:299-311

444 Narici MV, Roi GS, Landoni L (1988) Force of knee extensor and flexor muscles and cross-sectional area determined by nuclear magnetic resonance imaging. Eur J Appl Physiol 57:39-44 Narici MV, Roi GS, Landoni L, Minetti AE, Cerretelli P (1989) Changes in force, cross-sectional area and neural activation during strength training and detraining of the human quadriceps. Eur J Appl Physiol 59:310-319 Nygaard E, Houston M, Suzuki Y, Jorgensen K, Saltin B (1983) Morphology of the brachial biceps muscle and elbow flexion in man. Acta Physiol Scand 117 : 287-292 Ralston HJ, Polissar MG, Inman VT, Close JR, Feinstein B (1949) Dynamic features of human isolated voluntary muscle in isometric and free contractions. J Appl Physiol 1 : 526-533 Reid JG, Costigan PA (1985) Geometry of adult rectus abdominis and erector spinae muscles. J Orthop Sports Phys Ther 5 : 278280 Rutherford OM (1986) The determinants of human muscle strength and the effects of different high resistance training regimes. PhD thesis, University of London Rutherford OM, Jones DA (1992) Measurement of fibre pennation using ultrasound in the human quadriceps in vivo. Eur J Appl Physiol 65:433-437

Sexton AW, Gersten JW (1967) Isometric tension differences in fibres of red and white muscles. Science 157 : 199 Smidt GL (1973) Biomechanical analysis of knee flexion and extension. J Biomech 6: 79-92 Weber E (1846) Wagner's Handw6rterbuch der Physiologie. Vieweg, Braunschweig Wickiewicz TL, Roy RR, Powell PL, Edgerton VR (1983) Muscle fibre architecture of the human lower limb. Clin Orthop 179: 275-283 Winter EM, Maughan RJ (1991) Strength and cross-sectional area of the quadriceps in men and women. Proceedings of the Physiological Society, University College London meeting, March, 59P Yamaguchi GT, Sawa AGU, Moran DW, Fessler M J, Winters JM (1990) A survey of human muscolotendon actuator parameters. In: Winters JM, Woo SL-Y (eds) Multiple muscle systems: biomechanics and movement organization. Springer, New York Berlin Heidelberg, pp 717-773 Young A (1984) The relative strength of type I and type II muscle fibres in the human quadriceps. Clin Physiol 4:23-32