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Force±length characteristics of in vivo human skeletal muscle C. N. MAGANARIS Department of Life Sciences, University of Tokyo, Meguro, Tokyo, Japan ABSTRACT In the present study, the in vivo force±length relations of the human soleus (SOL) and tibialis anterior (TA) muscles were estimated. Measurements were taken in six men at ankle angles from 30° of dorsi¯exion to 45° of plantar¯exion in steps of 15°, and involved dynamometry, electrical stimulation, ultrasonography and magnetic resonance imaging (MRI). For each muscle and ankle angle studied the following three measurements were carried out: (1) dynamometry-based measurement of maximal voltage tetanic moment, (2) ultrasound-based measurement of pennation angle and ®bre length and (3) MRI-based measurement of tendon moment arm length. Tendon forces were calculated dividing moments by moment arm lengths, and muscle forces were calculated dividing tendon forces by the cosine of pennation angles. In the transition from 30° of dorsi¯exion to 45° of plantar¯exion the SOL muscle ®bre length decreased from 3.8 to 2.4 cm and its force decreased from 3330 to 290 N. Over the same range of ankle angles the TA muscle ®bre length increased from 3.7 to 6 cm and its force increased from 157 to 644 N. Over the longest muscle ®bre lengths reached the force of both muscles remained approximately constant. These results indicate that the intact human SOL and TA muscles operate in the ascending limb and plateau region of the force±length relationship. Similar conclusions were reached when calculating the theoretical operating range of the two muscle sarcomeres in the study. Keywords electrical stimulation, magnetic resonance imaging, sarcomere, soleus, tibialis anterior, ultrasonography. Received 5 June 2000, accepted 22 November 2000
One of the most important functional characteristics of skeletal muscle is the length-dependence of its force generating potential. This property was ®rst described a century ago by Blix (1894). In his experiments the isometric force of isolated frog skeletal muscles increased as a function of muscle length, levelled off, and then decreased. Similar results were obtained from single muscle ®bre experiments by Gordon et al. (1966). Their studies indicated that the length-dependence of muscle force is related to the extent of overlap between the myosin and actin ®laments in the sarcomere, providing support to the cross-bridge theory of contraction suggested by Huxley (1957). Little information is available regarding the in vivo force±length characteristics of human individual skeletal muscles. Most of the studies have examined moment±angle relations around joints, the so-called `strength curves' (for review see Kulig et al. 1984). Assuming that strength curves are representative of the force±length relations of the muscles studied could
result in erroneous conclusions because (a) the moment at a given joint angle represents the net resultant mechanical output of all synergists and antagonists crossing the joint and (b) the muscle ®bre and tendon moment arm lengths are non-linear functions of joint angle (Kawakami et al. 1998, Maganaris et al. 1998a, b, 1999, Maganaris & Baltzopoulos 1999). A procedure for in vivo joint moment measurement of individual multi-articular muscles having uni-articular synergists has been described by Herzog & ter Keurs (1988a). Application of this methodology indicated that intact human muscles may operate in a part only of the force± length relationship that the muscle would yield theoretically under in vitro conditions (Herzog & ter Keurs 1988b, Herzog et al. 1991a, b). Moreover, different results were obtained between muscles (Herzog & ter Keurs 1988b, Herzog et al. 1991b) and subject groups (Herzog et al. 1991a), possibly because of musclespeci®city in the anatomical constrains of the skeleton and/or intermuscle functional differences.
Correspondence: C. N. Maganaris, Manchester Metropolitan University, Active Life Span Research, Alsager ST7 2HL, UK. Ó 2001 Scandinavian Physiological Society
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In the present study, a combination of dynamometry, electrical stimulation, ultrasonography and magnetic resonance imaging (MRI) has been used to estimate the in vivo force±length characteristics of the human soleus (SOL) and tibialis anterior (TA) muscles. Application of these techniques may allow estimation of force±length relations in several intact human muscles, eliminating the previous studies' major limitations. M A T E R I A L S AN D M E T H O D S Subjects Six healthy males (age: 24±32 years, height: 167± 183 cm, body mass: 70±82 kg) from whom informed consent had previously been obtained volunteered to participate in this study. All were physically active and none had any orthopaedic abnormality in the lower extremities. The study was approved by the local ethics committee. Experimental protocol Measurements were taken in the leg preferred for kicking (right in all subjects) at ankle angles of )30° (dorsi¯exion direction), ±15°, 0° (neutral anatomical position: the foot at right angles to the shank), +15° (plantar¯exion direction), +30° and +45°. All six subjects could rotate passively the foot over the range from ±15 to +30°, but a slight force was applied externally to bring the foot at the end-range positions examined. At each one of the above six ankle angles the following three measurements were taken: (1) measurement of ankle moment, (2) measurement of tendon moment arm length and (3) measurement of pennation angle and ®bre length. Moment measurements. Subjects were placed in the prone position on the bench of an isokinetic dynamometer (Lido Active, Loredan Biomedical, Davis, USA), having the knee of the tested leg ¯exed at 60° (180°: the knee fully extended). The pivot point of the lever arm of the dynamometer was visually aligned with the rotation axis of the ankle joint. Velcro straps around the foot, the heel and the dynamometer footplate, and a mechanical stop below the knee prevented any observable movement of the lower extremity during contractions. Maximal isometric ankle plantar¯exion and dorsi¯exion moments were elicited by means of percutaneous electrical stimulation, after compensating for gravitational and passive ankle moments. Maximal tetanic contractions of the SOL and TA muscles were produced by 2 s of stimulation at 100 Hz using 100 ls bi-polar wave pulses. The maximal stimulating voltage used was 150±175 V for the SOL muscle and 280
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125±150 V for the TA muscle. The criterion for the de®nition of maximal voltage was that no further increase in moment could be achieved with an increasing voltage of 25 V, plateau values to agree within 5%. The electrodes consisted of two aluminium foil pads, 8 ´ 10 cm for the SOL muscle and 4 ´ 4 cm for the TA muscle, covered in tissue which was soaked in water. The electrodes were placed within the muscle borders with guidance from axial-plane muscle sonographs. For the SOL muscle the electrodes were bandaged over the proximal region of the gastrocnemius muscle and distal region of the SOL muscle. For the TA muscle the electrodes were bandaged in the motor point area over the muscle proximal region, and in the muscle distal region. Stimuli were delivered by a custom-built, high-voltage stimulator and controlled by a purpose-developed computer software. Moments were measured twice, 2 min apart, and average values were used for further analysis. Surface EMG signals from the nearby SOL and peroneus tertius muscles during the TA muscle stimulation, and from the TA and peroneus tertius muscles during the SOL muscle stimulation showed no evidence of current leakage. Several experiments have shown that the bi-articular gastrocnemius muscle is slack below knee ¯exion of 90°, transmitting thus negligible force through the Achilles tendon during plantar¯exion contraction (Hof & van der Berg 1977, Gravel et al. 1987, Herzog et al. 1991b). Additional support for this was taken in pilot experiments of the present study: stimulation of the triceps surae muscle with the foot ®xed at maximum dorsi¯exion yielded a gradual decrease in the measured plantar¯exion moment in the transition from full knee extension to 65° of knee ¯exion, but no further moment reduction was obtained in the transition from 65° of knee ¯exion to maximum knee ¯exion (45°). Therefore, the moments recorded in this study were considered to have negligible contributions from muscles other than the SOL and TA muscles. Moment measurements were taken 3±4 days after a familiarization trial and repeated on a second occasion 3±4 days later. No difference (P < 0.05, Student's t-test) was found in the measurements taken between the two tests. Tendon moment arm length measurements. The lengths of tendon moment arms around the tibio-talar joint were measured from in vivo MRIs. Details of the methodology followed have been described elsewhere (Maganaris et al. 1998a, 1999). Sagittal-plane MRIs at the level of the ankle were taken using a 1.5 T/64 Hz scanner (G.E. Signa Advantage, Milwaukee, USA) and a fastGRASS sequence at a ¯ip angle of 90° with 15 ms repetition time, 6.7 ms echo time, 24 cm ®eld of view, 1 excitation, 256 ´ 128 matrix, 5 mm slice thickness Ó 2001 Scandinavian Physiological Society
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and 2 s scanning time. Scanning was performed while the subject was performing isometric plantar¯exion and dorsi¯exion maximum voluntary contractions (MVCs) against mechanical stops, having the knee and ankle joints secured at the positions examined in the study. In the images taken the perpendicular distances from the talar bone centre to the Achilles and TA tendon action lines were digitized and considered as the SOL and TA tendons moments arms, respectively.
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lation was calculated dividing the moment measured by the tendon moment arm length (Fig. 1). To estimate muscle force, a muscle model with no angulation between tendons and aponeuroses was employed. The contractile force acting along the muscle ®bres was calculated dividing the estimated tendon force by the cosine of pennation angle (Fig. 2).
Pennation angle and ®bre length measurements. Pennation angles and ®bre lengths were measured from in vivo muscle sonographs taken during maximal voltage moment generation (see above) at the knee and ankle joint angles studied. Details of the methodology followed have been described elsewhere (Maganaris et al. 1998b, Maganaris & Baltzopoulos 1999). A 7.5-MHz linear-array, B-mode probe (Esaote Biomedica AU3 Partner, Florence, Italy; width and depth resolutions: 10.62 mm, respectively) was secured with adhesive over the muscle mid-sagittal axis, between the two stimulating electrodes. In the scans recorded the echoes re¯ected from muscle fascicles and interfascicular tissue were identi®ed. Fascicular length was considered to represent ®bre length and it was digitized taking into account any curvature along the fascicle path between origin and insertion. Pennation angle measurements were taken at the fascicular insertions into the tendon aponeurosis. The two uni-pennate halves of the TA muscle were scanned separately and average values of ®bre length and pennation angle were used for further analysis (Fig. 1). All MRI and ultrasound scan morphometrics were performed three times and mean values were used for further analysis. Inter- and intra-observer variations of the scanning procedures and image analyses involved have been con®rmed to be less than 9% (Maganaris & Baltzopoulos 1999, Maganaris et al. 1998a, b, 1999). At each one of the six ankle angles studied the force transmitted through the tendon during muscle stimu-
Figure 1 Muscle sonographs at 15° of dorsi¯exion. Top: SOL
sonograph. Middle: TA sonograph with the scanning probe aligned in the plane of the super®cial uni-pennate half of the muscle. Bottom: TA sonograph with the scanning probe aligned in the plane of the deep uni-pennate half of the muscle. SF, subcutaneous fat; LG, lateral gastrocnemius; SOL, soleus; FHL, ¯exor hallucis longus; TA1, super®cial uni-pennate half of TA; TA2, deep uni-pennate half of TA; TP, tibialis posterior. In each scan the white stripes are echoes generated by collagen rich tissue surrounding the echo-absorptive fascicles. The oblique stripes are interfascicular tissue echoes, and the horizontal stripes pointed by the white arrows are aponeurotic echoes. The line drawn along the fascicular path from origin to insertion was considered as the ®bre length. The insertion angle a of the fascicle in the aponeurosis was considered as the muscle pennation angle. Ó 2001 Scandinavian Physiological Society
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Figure 2 Geometric models for
estimating forces. Top: The lower extremity musculoskeletal model used to calculate the force Ft transmitted through the tendon from the joint moment M and the tendon moment arm length d. According to the moment equilibrium equation, Ft Md)1. Bottom: The muscle model used to calculate the force Fm acting along the ®bres from the tendon force Ft. The model shown represents the SOL muscle and the deep uni-pennate half of the TA muscle during maximal isometric contraction (see also Fig. 1). According to the vectorial analysis of forces, Fm Ft cos±1 a.
neutral anatomical positions (for discussion see Marsh et al. 1981). From Figure 3 it is obvious that different force changes were obtained in the two muscles in the transition from minimal to maximal ®bre lengths. In the SOL muscle the difference between the shortest and longest ®bre lengths was 1.4 cm and that between minimal and maximal muscle forces 3080 N. The respective difference values in the TA muscle were 2.3 cm and 487 N. However, the normalized force± length curves yielded similar results in the two muscles (Fig. 4). This indicates that intermuscle differences in physiological cross-sectional area (Fukunaga et al.
R E S U L T S A N D D IS C U S S I O N In Table 1 are shown the measured or calculated values of the parameters examined in the TA and SOL muscles over the range of ankle angles from ±30 to 45°. Based on these data two observations can be made: (a) the two muscles exhibited inverse patterns of changes in any given parameter as a function of ankle angle. This is not surprising given that the TA and SOL muscles function reciprocally around the ankle joint. (b) Neither muscle exerted its maximal force at the neutral ankle position. This is in contrast with the general notion that skeletal muscles generate maximal forces at
Table 1 The parameters examined as a function of ankle angle in the SOL and TA muscles
Ankle angle (°) )30
)15
0
+15
SOL muscle Moment (N m) 144 7 Tendon moment arm length (cm) 5.1 0.3 Pennation angle (°) 32 3 Fibre length (cm) 3.8 0.2 Tendon force (N) 2825 181 Muscle force (N) 3330 203
149 5.4 35 3.5 2760 3370
7 0.4 3 0.2 170 209
107 6 40 3 1782 2330
7 0.3 3 0.2 112 147
TA muscle Moment (N m) 10 2 Tendon moment arm length (cm) 7 0.4 Pennation angle (°) 24 3 Fibre length (cm) 3.7 0.3 Tendon force (N) 143 16 Muscle force (N) 157 19
15 6 22 4 250 270
2 0.4 3 0.4 29 32
22 4.9 20 4.5 449 478
2 0.4 2 0.4 42 45
+30
+45
5 0.4 3 0.2 90 126
32 3 7 0.4 50 4 2.6 0.2 457 44 711 69
12 2 7.2 0.4 55 4 2.4 0.2 167 16 290 27
24 3 4.2 0.4 17 2 5 0.4 571 63 597 66
26 3 4 0.4 15 2 5.6 0.4 650 87 673 90
25 3 4 0.3 14 2 6 0.4 625 80 644 88
68 6.6 45 2.8 1032 1460
Values are mean SD (n = 6).
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1992), speci®c tension (Powell et al. 1984), and optimal ®bre length (Wickiewicz et al. 1983), is the main cause of the differences in the TA and SOL muscles force± length properties. In the present experiment the maximal contractile force of either muscle increased as a function of ®bre length and remained approximately constant over the longest lengths examined (see Figs 3 and 4). This ®nding indicates that the SOL and TA muscles operate in vivo in the ascending limb and plateau region of the force±length relationship. Experimental evidence suggesting that intact muscles may function over speci®c regions of the force±length relationship has often been given. The results obtained, however, vary between studies and indicate that skeletal muscles may operate in the ascending limb (Rack & Westbury 1969, Herzog
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et al. 1991b, Leedham & Dowling 1995), plateau region (Rome et al. 1988, Lieber et al. 1992), descending limb (Herzog et al. 1991a, Lieber & Brown 1993, Lieber et al. 1994), or plateau region and part of the ascending and descending limbs of the force±length relationship (Herzog & ter Keurs 1988b, Ichinose et al. 1997). Methodological, interspecies and intermuscle differences, as well as differences in the way that long-term loading is imposed on a given muscle of the same species (see Herzog et al. 1991a) may account for the lack of consensus between studies. The optimal ankle angles for force generation in the intact TA and SOL muscles in the present experiment were the angles of +30 and ±15°, respectively. Towards the end-range positions examined the contractile force of both muscles levelled off (see Table 1). Theoretically, the sarcomere length at the optimal ankle angles would thus be 2.6 lm, i.e. the shortest length in which the human skeletal muscle sarcomere would produce maximum force according to the cross-bridge mechanism of contraction (Walker & Schrodt 1973, Lieber et al. 1994). Dividing the ®bre length of the TA and SOL muscles at +30 and ±15°, respectively, by a sarcomere length of 2.6 lm we calculated that the number of sarcomeres in series would be 21.500 in the TA muscle ®bre and 13.500 in the SOL muscle ®bre. These estimates are in general agreement with corresponding measurements in cadaveric material (Wickiewicz et al. 1983). Dividing the SOL and TA muscle ®bre lengths at the end-range positions examined by the respective number of serial sarcomeres, it was estimated that the physiological operating range of both muscle sarcomeres would be between 1.7 and 2.8 lm (Fig. 5). The longest sarcomere length estimation coincides with the theoretical length of the human
Figure 3 Force±length relationships of the SOL (top) and TA
(bottom) muscles. Values are means SD (n 6).
Figure 5 Theoretical sarcomere force±length relationship. The curve
Figure 4 Normalized force±length relationships of the SOL (squares)
and TA (circles) muscles. Average values from all six subjects are presented. Ó 2001 Scandinavian Physiological Society
shown is based on the cross-bridge mechanism of forge generation (Huxley 1957, Gordon et al. 1966). The lengths of myosin and actin ®laments were assumed to be 1.6 and 1.3 lm, respectively (Walker & Schrodt 1973, Lieber et al. 1994). The shaded line below the ascending limb and plateau region of the curve, represents the operating range of the TA and SOL muscle sarcomeres in the study, assuming that the optimal ankle angles for force generation corresponded with a sarcomere length of 2.6 lm.
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skeletal muscle sarcomere at the right end of the plateau region of the force±length relationship (Walker & Schrodt 1973, Lieber et al. 1994). This observation provides additional support to suggest that the intact human SOL and TA muscles operate in the ascending limb and plateau region of the force±length relationship. The estimate of the sarcomere working range in the two muscles studied differs from that reported by Cutts (1988). Surprisingly, although we have examined a larger range of ankle movement the sarcomere operating range reported in the above study is almost twice as much as our estimate. The discrepancy between results may be attributed to methodological differences between studies. In the present analysis, in vivo ankle geometry and muscle architecture measurements during contraction have been incorporated, but Cutts (1988) used resting state and cadaver-based data. It must be remembered that joint geometry and muscle architecture measurements at rest or from cadaveric specimens do not re¯ect changes upon contraction (Narici et al. 1996, Kawakami et al. 1998, Maganaris et al. 1998a, b, 1999, Maganaris & Baltzopoulos 1999), and may thus result in erroneous conclusions when studying in vivo function. In vivo measurement-based estimation of the force± length characteristics of human skeletal muscle has often been attempted. Herzog et al. (1991b) and Herzog & ter Keurs 1988b) estimated the force±length properties of the gastrocnemius and rectus femoris muscles implementing a methodology for muscle moment isolation applicable to multiarticular muscles only (Herzog & ter Keurs 1988a). Leedham & Dowling (1995) estimated the force±length curve of the biceps brachii muscle applying submaximal percutaneous stimulation and using cadaver-based joint geometry data. Ichinose et al. (1997) estimated the force±length curve of the vastus lateralis muscle from cadaver-based joint geometry data and net knee extension MVC moments. Optimization methodologies have also been applied when determining the force generating potential of individual intact muscles (Herzog 1987). In the present experiment the major limitations of previous studies have been eliminated. One or more of the in vivo techniques used in this study have often been applied on several human muscles yielding reproducible results (e.g. Davies et al. 1985, Cook & McDonagh 1996 for ®rst dorsal interosseous muscle; Ismail & Ranatunga 1978, Kawakami et al. 1994, Leedham & Dowling 1995 for biceps brachii muscle; Kawakami et al. 1998, Maganaris et al. 1998a, b, Narici et al. 1996 for gastrocnemius muscle). It seems thus possible that the force±length properties of several individual intact muscles may be obtained non-invasively combining dynamometry, electrical stimulation, ultrasonography and MRI. Isolation of the target muscle 284
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mechanical action would require placement of the stimulating electrodes over the muscle motor points when accessible, or over the muscle main nerve branch when co-activation of non-tested muscles can be blocked arti®cially (e.g. Wilkie 1950). In the present experiment, some evidence of muscle isolation was obtained from EMG recordings in adjacent nonstimulated agonist and antagonist muscles. In a recent experiment involving stimulation of the TA and SOL muscles the EMG signal of non-stimulated muscles increased when moving the recording electrodes closer to the stimulating electrodes (Maganaris et al. 2000). Ultrasound scanning of electrically active regions in non-stimulated agonists and antagonists revealed, however, no fascicular shortening, thus indicating the presence of cross-talk rather than co-activation. Evidence of no current spread to non-stimulated muscles has also been given in T2-weighted MRI studies (Adams et al. 1993). For the SOL muscle, additional evidence of isolated action was obtained from results showing that knee ¯exion bellow 65° yields no detectable contribution of the gastrocnemius muscle to the triceps surae muscle moment. Thus, any contractile force transmitted from the gastrocnemius muscle to the calcaneal bone during stimulation would have only a minimal effect on the estimated force±length relation of the SOL muscle. In the present study, the TA muscle was stimulated through its motor points using maximal voltage and it is thus reasonable to assume full activation. In the SOL muscle, however, full activation cannot be assured with the present protocol. Nevertheless, assuming that a given and small portion of the SOL muscle was inactive at all ankle angles, the shape of the muscle actual force± length curve would not differ substantially from that obtained here. In conclusion, in the present study the in vivo force± length characteristics of SOL and TA muscles were estimated. The results obtained indicate that both muscles operate in the ascending limb and plateau region of the force±length curve. R E F E RE N C E S Adams, G.R., Harris, R.T., Woodard, D. & Dudley, G.A. 1993. Mapping of electrical muscle stimulation using MRI. J Appl Physiol 74, 532±537. Blix, M. 1894. Die lange und die spannung des muskels. Skand Arch Physiol 5, 149±206. Cook, C. & McDonagh, M.J.N. 1996. Measurement of muscle and tendon stiffness in man. Eur J Appl Physiol 72, 380±382. Cutts, A. 1988. The range of sarcomere lengths in the muscles of the human lower limb. J Anat 160, 79±88. Davies, C.T.M., Dooley, P., McDonagh, M.J.N. & White, M.J. 1985. Adaptation of mechanical properties of muscle to high force training in man. J Physiol 365, 277±284.
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