cm-92!30/92
J.Biomechanics Vol.25,No.11,pp,1329-1335. 1992 Printed inGreat Britain
ss.m+.Jo
0 1992Pergamon PnssLtd
FORCE-LENGTH PROPERTIES AND FUNCTIONAL DEMANDS OF CAT GASTROCNEMIUS, SOLEUS AND PLANTARIS MUSCLES W. HERZOG,*~ T. R. LEONARD,* J. M. RENAUD,~ J. WALLACE,* G. CHAKI* and S. BORNEMISZA* Faculties of *Physical Education and $.Biological Sciences, The University of Calgary, Calgary,
Alberta TZN lN4, Canada Abstract-The purpose of this study was to measure isometric force-length properties of cat soleus, gastrocnemius and plantaris muscle-tendon units, and to relate these properties to the functional demands of these muscles during everyday locomotor activities. Isometric force-length properties were determined using an in situ preparation, where forces were measured using buckle-type tendon transducers, and muscle-tendon unit lengths were quantified through ankle and knee joint configurations. Functional demands of the muscles were assessed using direct muscle force measurements in freely moving animals. Force-length properties and functional demands were determined for soleus, gastrocnemius and plantaris muscles simultaneously in each animal. The results suggest that isometric force-length properties of cat soleus, gastrocnemius and plantaris muscles, as well as the region of the forcelength relation that is used during everyday locomotor tasks, match the functional demands.
INTRODUCTION It is known that instantaneous
contractile
conditions,
such as length and velocity, are major determinants of the forces a maximally stimulated muscle can exert. Forcelength properties of skeletal muscles were first mentioned by Blix (1894), and isometric force-length data on isolated fibers of frog skeletal muscle (Gordon et al., 1966) helped support the cross-bridge theory as the principal mode1 for muscular force production. Force-velocity properties of frog striated muscle were described by Hill (1938) and still serve to describe the hyperbolic relation between maximal force and velocity of shortening skeletal muscles. Isometric force-length properties have been determined at the fiber, muscle, or muscle-tendon unit level. According to the cross-bridge theory, and assuming uniform sarcomere lengths, force-length properties of isolated muscle fibers are uniquely determined by the lengths of thick and thin myofilaments. On the muscle level, additional structural factors such as the fiber length relative to the total muscle length and the arrangement of fibers within the muscle must be considered (Woittiez et al., 1984). On the muscle-tendon unit level, force-length properties are further influenced by the ratio of fiber length to series elastic element length, and the force elongation properties of series elastic elements (Zajac, 1989). A knowledge of isometric force-length properties of muscle-tendon units is considered essential when estimating force sharing among synergistic muscles (Herzog, 1987; Pedotti et al., 1978). The importance of the force-length property (as well as other muscular Received in final form 4 February 1992. TAuthor to whom correspondence should be addressed. BM25:11-F
properties such as size, fiber type distribution, force-velocity relation, etc.) in the area of muscle force predictions is associated with the assumption that muscular and neuromuscular properties may reflect the functional requirements of muscles during everyday tasks. This assumption has received support in a most recent study, where force-length properties of intact human rectus femoris muscles were found to differ systematically between elite athletes in different sports, and these differences appeared to be. associated with the functional requirements imposed chronically onto the rectus femoris muscle in the different sport activities (Herzog et al., 1991). Further support of this assumption was provided by Goslow and van de Graaff (1982), who determined isometric force-length properties of skunk triceps surae and plantaris muscles and found that they were similar in shape but not in magnitude. Since these muscles are part of a functional group, it is reasonable to assume, but not necessarily correct, that each muscle satisfies similar functional demands during skunk locomotion and that these functional demands are reflected in the particular isometric force-length properties of these muscles. In order to test the speculation that isometric force-length properties of muscles are associated with the functional demands of muscles, it is necessary to measure these quantities independently. Therefore, the purpose of this study was to measure isometric force-length properties of cat soleus (S), gastrocnemius (G), and plantaris (P) muscle-tendon units, and compare these properties with the corresponding in vim ‘force-length measurements’ obtained during everyday locomotor activities. Forcelength properties in this context refer to the relation between maximal, isometric forces and the corresponding muscular lengths, whereas in vivo
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W. HERZOCet al.
force-length measurements refer to the relation between instantaneous force and length of the muscles during locomotion (i.e. dynamic contractions and variable submaximal stimulations).
METHODS
Determination
of isometric force-length
relations
Isometric force-length relations of in situ S, G, and P muscles were determined from four male adult cats, and additionally from four male adult cats for G alone. The animals were anesthetized initially using a mask and a 5% halothane gas mixture, then they were intubated and maintained using l.O-1.5% halothane. The left leg was shaved from the hip to the proximal phalanges. A heating pad was placed underneath the animals to maintain a constant body temperature. The hind limbs of the animals were clamped using an external fixation device. This fixation device contained three U-shaped stainless steel elements, one each for the thigh, shank, and foot. Each of these elements contained four bone screws, two on either side, for rigid fixation of the device to the hind limb bones. The individual elements dfthe fixation device were connected through stainless steel rods on the one side and a 5 mm rigid metal plate on the other side. The entire device was fixed to a metal ground plate that was rigidly attached to an experimental table. This setup prevented movement of the hind limbs during the experimental contractions. Force measurements. Soleus, gastrocnemius, and plantaris tendons were exposed with a cut on the posterior aspect of the shank and were separated from one another by opening the connective tissue sheaths surrounding the entire achilles tendon. E-shaped tendon force transducers, similar to those described by Walmsley et al. (1978), were placed on the tendons of S, G, and P. These transducers are deformed when forces are transmitted by the tendons. The deformation is measured as a change in voltage by a pair of strain gauges, and these voltage signals are related to the tendon forces through an appropriate calibration procedure. Calibrations were performed in a terminal experiment by detaching the tendons of S, G, and P from the calcaneus with a bone chip and hanging known weights from the tendon. All calibration curves obtained in this way were linear within the range of forces observed (r2 > 0.990), showed no measurable hysteresis, and yielded no measurable differences in results for repeated measures. Measurements of forces from the entire gastrocnemius muscle rather than individual measures of the lateral and medial heads of G were performed since the primary interest was to determine the forces exerted by the gastrocnemius muscle on the ankle joint system. Since the medial and lateral heads of G are not strictly in parallel, independent force measurements of the two heads may not have provided the desired result.
Muscle length measurements. Muscle-tendon unit lengths were measured using a pair of calipers and were related to the ankle and/or knee joint angles, which were measured using a goniometer. Ankle and knee joint angles were defined as the included angles between foot and shank, and shank and thigh, respectively. Knee joint angles were kept constant at a nominal joint configuration of 90”, and length changes of the muscles were produced by altering the ankle joint angle exclusively. Muscular stimulation. Stimulations were performed using a nerve cuff electrode that was placed around the tibia1 nerve, distal to the tibial/sciatic junction. The sciatic nerve was ligated and cut proximal to the tibial/sciatic junction to avoid contraction of muscles not of interest in this study. Gauze that was periodically soaked in a warm saline solution was placed around the nerve and the exposed parts of the hind limb to prevent tissues from drying. In order to produce maximal tetanic contractions, the nerve was stimulated supramaximally using square-wave pulses. For the different animals, stimulation voltages ranged from 1.0 to 2.5 V for 1.0-2.5 s. Pulse durations were chosen between 0.1 and 0.2 ms, and the stimulation frequencies ranged from 80 to 100 Hz for S and 100 to 120 Hz for G and P. The actual stimulation parameters were determined individually for each animal and muscle to assure maximal force response. Protocol. Maximal total forces were measured for six to twelve different muscle lengths using supramaximal stimulation of the tibia1 nerve. The corresponding passive forces were obtained for zero stimulation of the nerve. At each length, muscle forces were measured two or three times at intervals of 2 min. Measurements at different muscle lengths were separated by an interval of 5 min. The rectal and muscle temperatures were obtained before each series of contractions at a given length and were kept within 35-38°C and 32-35°C respectively. Repeat force measurements were obtained for selected muscle lengths to observe possible deteriorations of the preparation. Such deteriorations did not occur. Data analysis. Total and passive forces were averaged for the repeat trials and plotted as a function of ankle joint angle. For the one joint soleus muscle, muscle-tendon unit lengths are uniquely determined by the ankle joint angle; for gastrocnemius and plantaris, muscle-tendon unit lengths were related to the ankle joint angle using a constant knee joint angle of 90”. All total force values were normalized relative to the muscle volumes, that were determined in a terminal experiment using an immersion technique. These normalized force data were plotted against ankle joint angles, and were approximated using best-fitting polynomial regression lines. Force values were also normalized relative to physiological cross-sectional area (PCSA), using estimates of mean fiber lengths and angles of pinnation obtained from the literature (Sacks and Roy, 1982).
Properties and demands of cat muscles
Determination offunctional
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requiremenrs
Functional requirements for a variety of locomotor conditions were determined from direct muscle force measurements of S, G, and P in eight cats, using chronically implanted tendon force transducers and digitization of the hind limb kinematics from video records. The tendon force transducers were similar but considerably smaller than those used in the previous part of the study, and they were surgically implanted onto the tendons of S, G, and P of the left hind limb. Video records were obtained from a sagittal plane view of the left side of the animals from a camera running at a nominal rate of 30 Hz. The knee and ankle joint angles were defined as above and were determined from five digitized landmarks; two points from the sole of the foot, the lateral malleolus, and the estimated knee and hip joint centers. After complete recovery from surgery, the animals were placed on a treadmill and tendon forces and hind limb kinematics were measured for walking (0.4-1.2 m s- ‘) and trotting (1.8-2.4 m s- ‘). The animals used in this part of the study were different from those used for the determination of force-length properties. This had to be done since the small tendon force transducers required in the functional experiments were not strong enough to withstand the maximal forces of the muscles produced during the isometric force-length experiments. However, the animals selected for the two experiments were age, sex, and weight matched. Furthermore, isometric force-length properties and in uiuo force-length measurements during locomotion were similar among all animals and all muscles, thus justifying this approach. For representation of gastrocnemius and plantaris forces as a function of ankle joint angles during locomotion, it was necessary to account for length changes of these muscles at the knee joint, and relate these length changes to a knee joint angle of 90”. The resulting ankle joint angles are hereafter referred to as adjusted ankle joint angles. The procedures used to calculate adjusted ankle joint angles were identical to those reported by Stephens et al. (1975). Expressing isometric force-length properties and functional requirements of the muscles in terms of joint angles rather than muscle-tendon unit, muscle, or fiber lengths has the advantage that the results from different animals can be compared directly.
RESULTS
Total forces increase steadily for soleus muscle for decreasing ankle joint angles (i.e. increasing muscle length) [Fig. l(a)]. The same is true for gastrocnemius and plantaris muscles up to ankle joint angles of about 80”; for longer muscle lengths, maxima1 isometric forces tend to decrease [Fig. l(b) and (c), respectively]. Passive forces appear to be slightly higher in G compared to S, and in S compared to P (note that the open triangle at an ankle joint angle of 50” and force of
Fig. 1. Force-length relations of cat soleus (a), gastrocnemius (b), and plantaris muscles (c). Total forces and passive forces are shown with corresponding symbols for the same animals. Knee joint angles were fixed at 90” for all experiments. Forces in S increase continuously for decreasing joint angles (i.e. increasing muscle length) whereas forces for G and P appear to peak at joint angles of about 80”.
20 N for P is a total, not a passive, force value). Furthermore, passive forces start to come into play at somewhat larger ankle joint angles for S and G compared to P. Total forces are largest for G and, on an average, smallest for S which corresponds to the size of these muscles. The variations of total force for a
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W. HERZOGet al.
given muscle may be explained partly through vari-
ations of muscle size among animals. The volumes for all four soleus muscles studied were within 1 cm3 and peak isometric forces do not appear to be strongly related to muscle volume (Table 1). For gastrocnemius and plantaris muscles, the volumes ranged from 17 to 33.5cm3 and from 7 to 12cm3, respectively. The corresponding peak forces appear to increase with increasing muscle size. Therefore, normalization of force-length relations with respect to muscle volumes resulted in a decrease in the variation of force magnitudes between force-length properties from different animals for G and P, but not for S [Fig. 2(a-c)]. Peak forces normalized with respect to muscle volume ranged from about 7.5 to 10 Ncmm3 for all three muscles. However, when normalizing peak forces relative to physiological cross-sectional areas, muscle S is considerably stronger on an average (32.8 Ncm-‘) than muscles G (19.1 Ncm-‘) and P (16.9 Ncm-‘). The vertical lines at ankle joint angles of 60 and 140 approximate the range of motion observed during cat walking, trotting, and galloping [Fig. 2(ac)]. This range of motion, expressed in terms of ankle joint angles, contains an adjustment factor for length changes of G and P associated with knee joint motion. Length changes of P associated with deviations of the metatarsophalangeal joint from its nominal value of 180” were not accounted for since the partial, in-series arrangement of P with the flexor digitorum brevis (Abraham and Loeb, 1985) makes quantification of such changes virtually impossible. Within the functional range of motion, maximal isometric forces of S, G, and P tend to increase as muscle length increases. Forces of the soleus muscle remain similar for different speeds of walking/trotting, whereas gastrocnemius and plantaris forces tend to increase with increasing speeds of locomotion [Fig. 3(a-c)]. Peak forces for walking at 0.4 m s- 1 occur at adjusted ankle joint angles of 95-100” for all three muscles. Peak forces for walking at 1.2 ms-’ and trotting at 2.4 m s-l occur at adjusted ankle joint angles of
Table 1. Muscle volumes and the corresponding peak isometric forces for cat gastrocnemius, soleus, and plantaris muscles Gastrocnemius
Cat 1 2 3 4 5 6 7 8
Soleus
Plantaris
Volume (cm3)
Peak force (N
Volume
Peak force
Volume
Peak force
(cm3)
(N)
(cm?
(N)
21.0 27.5 24.0 33.5 21.5 17.0 28.5 17.5
193.5 242.0 193.0 290.0 139.5 160.0 221.2 154.1
6.0 5.0 5.0 5.5 -
48.5 36.0 48.0 36.0 -
1.0 8.0 9.0 12.0 -
56.4 74.0 90.0 106.0 -
I 180
(4
1M)
140
120
100
80
Bo
40
ANKLE ANGLE (“,
Fig. 2. Force-length relations of cat soleus (a), gastrocnemius (b), and plantaris muscles (c). Forces were normalized with respect to muscle volume. Data of all animals combined were approximated using a best-fitting polynomial. Approximate limits of ankle joint motion (including considerations of muscular length changes associated with knee joint motion) during free walking and trotting are indicated by the intermittent vertical lines at 60 and 140”. Force-length properties of S, G, and P are similar and may be associated primarily with the ascending limb of the force-length relation.
approximately 80” for all muscles and both speeds. At all speeds and for each muscle, peak forces appear to occur after nearly isometric or slightly eccentric contractions of the muscl+tendon unit. Peak force production is followed by a decrease in force and a generally large concentric contraction of all muscles at each speed.
1333
Properties and demands of cat muscles DISCUSSION
SOLEUS FORCE (Nl a-
IM
135
90
105
120
75
sn ANKLE ANGLE ,‘:
(4
(4 PUNTARIS
FORCE IN) IS
1w
110
120
ICQ
40 @I 50 ANKLE ANGLE (“) ADJUSTED TO 90 *KNEE JOINT ANGLE
w
Fig. 3. Representative force requirements of soleus (a), gastrocnemius (b), and plantarjs muscles (c) during a step cycle for nominal speeds of locomotion of 0.4, 1.2, and 2.4 m s-l. Arrows indicate the instant of first paw contact with the ground. Ankle joint angles are adjusted in such a way that length changes of gastrocnemius and plantaris muscle-tendon units associated with knee joint configurations other than 90” are compensated for. Peak forces tend to
occur at smaller ankle joint angles (i.e.longer muscle-tendon unit lengths) for fast walking (1.2 ms-‘) and trotting (2.4 m s - ’ ) compared to slow walking (0.4 m s - ’ ). Furthermore, peak forces of S are similar for all speeds of locomotion, whereas the corresponding forces increase with increasing locomotor speeds for G and P.
The shapes of the isometric forc&ength relations of cat S, G, and P are similar, and correspond to those for the same muscles in the striped skunk (Goslow and van de Graaff, 1982). This similarity implies that the force potential of the entire functional group (i.e. the force that is transmitted by the achilles tendon) is also similar to that of the individual muscles that make up the group. Therefore, maximal isometric forces of the entire achilles tendon are relatively small at extended ankle joint angles and become increasingly larger with flexion of the ankle joint up to an optimal angle of about 80” (for a corresponding knee joint angle of 90”). Through trigonometric relations, it can be ascertained that at extended ankle joint angles, the moment arm of the achilles tendon about a transverse axis through the ankle joint is relatively small. Therefore, peak moments that may be produced by the triceps surae/plantaris group about the ankle joint are small for extended ankle joint angles compared to ankle joint angles of around 80”. Theoretically, it would be simple to design the cat ankle joint in such a way that force and moment potentials were nearly constant throughout the functional range by choosing appropriate force-length properties of the individual muscles. However, in such a design the absolute peak force/moment potential would be significantly reduced compared to nature’s design of the actual cat ankle joint. Within the functional range of motion (about 60-140” in the ankle joint) isometric forces of cat S, G, and P tend to increase for increasing muscle-tendon unit lengths, maybe with the exception of the extreme lengths in G and P [Fig. 2(a+)]. This result contradicts the ‘textbook notion’ that optimal length of muscles is somewhere near the middle of the anatomical range of motion; and it is contrary to results reported for frog semitendinosus muscle, which has a decreasing isometric force potential for increasing muscle length within its normal range of motion (Mai and Lieber, 1990). Furthermore, human lower limb muscles have been found to operate on different parts of the force-length relation (ascending limb, near optimal length, or descending limb) for joint excursions experienced during everyday movements, such as locomotion (Cutts, 1988). The question, thus, arises if and how the part of the force-length relation that a muscle occupies for movements within the normal range of joint motion may relate to its functional demands. Muscles that tend to operate on the ascending part of the force-length relation (such as cat S, G, and P) have an increased isometric force potential for increasing muscle lengths, and a decreased isometric force potential for decreasing muscle lengths. Theoretically, therefore, it appears to be of advantage if a muscle operating on the ascending part of the force-length relation increases its force during a functional task while elongating and decreases its force while shorten-
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W. HERZOG et al.
ing, and vice versa for a muscle working predominantly on the descending limb. Cat soleus, gastrocnemius, and plantaris muscles appear to adhere to the above theoretical considerations. They tend to work on the ascending part of the force-length relation [at the muscle-tendon unit level, Figs l(ac) and 2(ac)] and they increase force primarily while elongating and decrease force while shortening for walking and trotting movements [Fig. 3(a-c)]. In contrast to cat S, G, and P, frog semitendinosus muscle occupies primarily the descending part of the isometric force-length relation and, in accordance with our theoretical considerations, is thought to approach peak forces during jumping while shortening (Mai and Lieber, 1990). Furthermore, human rectus femoris muscles were found to operate on the ascending part of the isometric force-length relation for high-performance runners and on the descending part for high-performance cyclists (Herzog et al., 1991). Since rectus femoris muscles are believed to increase force while lengthening during running and while shortening during cycling, these results further support the above idea of interrelation between isometric force potential and functional demands. However, despite the conceptual agreement of the results obtained on frog semitendinosus and human rectus femoris muscles with our results on cat triceps surae and plantaris muscles, these findings must be considered with caution for a variety of reasons. Most importantly, Mai and Lieber (1990) did not directly measure semitendinosus forces in frogs, but calculated these forces from estimates of the contractile conditions of the muscle for jumping movements; and Herzog et al. (1991) determined isometric force-length relations of human rectus femoris muscles using maximal voluntary contractions rather than supramaxima1 activation of the muscle; thus, their results may be related to neuromuscular mechanisms of activation rather than adaptations of the isometric force-length relation. Peak forces for cat soleus muscle occurred at ankle joint angles of about 95-100” for walking at a speed of 0.4 ms-‘. For the two higher speeds (i.e. 1.2 ms-’ walking; 2.4 m s- ’ trotting) peak forces occurred towards ankle joint angles of 80”, which corresponds closely to the optimal length of the soleus muscle tendon unit. For all three speeds of locomotion studied, soleus forces remained nearly constant [Fig. 3(a)]; therefore, it is safe to assume that the average fiber and sarcomere lengths were longer at the instant of peak force demands for the 1.2 and 2.4 m s- ’ speeds compared to the corresponding values at 0.4 m s-r. According to the isometric force-length relations found in this study for soleus [Figs l(a) and 2(a)], the potential of S to produce force is higher at muscle lengths encountered for the two high speeds of locomotion compared to the low speed. Furthermore, for all three speeds of locomotion peak soleus forces occur after phases of predominant eccentric contractions. Since these eccentric contractions tend to be faster for
higher speeds of locomotion, one would associate again (as for the force-length properties) a larger force potential for soleus muscle with the high speeds of locomotion compared to the low speed. Thus, from the point of view of the mechanical properties of S, and for relatively constant stimulation of the muscle, one would expect peak forces of S to increase with increasing speeds of locomotion, similar to what is observed for gastrocnemius and plantaris muscles. Since soleus forces remain virtually constant for a large range of locomotor speeds [Fig. 3(a); Gregor et al., 1988; Herzog and Leonard, 1991; Walmsley et al., 19781, it appears that stimulation of the soleus muscle is either inhibited or does not have the same effect at high speeds of locomotion compared to low speeds. Hodgson (1983) argued that the steady force levels in cat soleus muscles at different speeds of locomotion may be associated with an inhibition of S for increasing locomotor speeds through rubrospinal and cutaneous pathways. However, such inhibition has not been verified in studies using electromyographic measurements on S. Walmsley et al. (1978) reported slight increases in peak-integrated EMG activities for cat soleus muscles with increasing speeds of locomotion, and Gregor et al. (1988) found constant mean EMG activity during the stance phase of locomotion for speeds ranging from 0.8 to 2.2 ms-‘. However, since the relations between central stimulation and measured activation (EMG), as well as between measured activation and muscular forces are not clearly established, inferences from EMG measurements on muscular force and stimulation may be misleading. It may be argued that forces of cat soleus muscle remain about constant for different locomotor speeds despite similar stimulation (as quantified through EMG), and more favorable mechanical conditions (muscle length and speed of elongation) that exist at high compared to low speeds because of the differences in the active state. For example, for slow walking (0.8 m s- ‘) the time period from the onset of EMG to peak force production in S is clearly over 100 ms (Walmsley et al., 1978; Fig. 2), whereas the corresponding time period is only about 80ms for running at 3.0 ms-’ (Walmsley et al., 1978; Fig. 3). Similarly, Gregor et al. (1988) show slightly decreasing EMG burst durations prior to paw contact for increasing speeds of locomotion in cat soleus muscles. It appears, therefore, that the active state in cat S during locomotion may not be as fully developed at the end of the eccentric contraction (i.e. when peak forces tend to occur) for high compared to low speeds of locomotion. Forces in cat gastrocnemius and plantaris muscles increase with increasing speeds of locomotion. This result is consistent with the previous findings for these muscles (Herzog and Leonard, 1991) and is also consistent with the results obtained from the medial head of the gastrocnemius muscle (e.g. Walmsley et al., 1978; Hodgson, 1983). When relating mechanical properties of muscles to functional demands, it is important to realize that the
Properties and demands of cat muscles two are not directly comparable. For example, in this particular study, isometric force-length properties were obtained for supramaximally stimulated muscles under isometric conditions. The force-angle relations during locomotion were obtained under conditions of variable, submaximal stimulation, and dynamic behavior of the muscles. Nevertheless, such comparisons suggest that the force-length properties of cat S, G, and P correspond in a meaningful way to the functional demands of these muscles during everyday motor tasks. Similar findings were reported for frog semitendinosus (Mai and Lieber, 1990) and human rectus femoris muscles (Herzog et al., 1991). Future studies may focus on generalizing these isolated results, and on investigating the mechanisms of possible adaptations of force-length properties to changing functional requirements. Acknowledgements-This study was supported by a grant and a student scholarship from NSERC of Canada. We thank Dr Merle Olson for providing technical help and laboratory space. REFERENCES Abraham, L. D. and Loeb, G. E. (1985) The distal hindlimb musculature of the cat (patterns of normal use). Exp. Brain Res. 58, 580-593.
Blix, M. (1894) Die Laenge und die Spannung des Muskels. Skand Arch. Physiol. 5, 149-206. Cutts, A. (1988) The range of sarcomere lengths in the muscles of the human lower limb. 1. Anat. 160, 79-88. Gordon, A. M., Huxley, A. F. and Julian, F. J. (1966) The variation in isometric tension with sarcomere length in vertebrate muscle fibers. J. Physiol. (Land.) 184, 170-192. Goslow, G. E. Jr and van de Graaff, K. M. (1982) Hindlimb joint angle changes and action of the primary ankle extensor muscles during posture and locomotion in the striped skunk (Mephitis mephitis). J. Zoo!. (Land.) 197, 405-419. Gregor, R. J.. Roy, R. R., Whiting, W. C., Lovely, R. G., Hodgson, J. A. and Edgerton, V. R. (1988) Mechanical
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output of the cat soleus during treadmill locomotion: in viuo vs in situ characteristics. J. Biomechanics 21, 721-732. Herzog, W. (1987) Individual muscle force estimations using a non-linear optimal design. J. Neurosci. Methods 21, 167-179. Herzog, W., Guimaraes, A. C., Anton, M. G. and CarterErdman, K. A. (1991) Moment-length relations of rectus femoris muscles of speed skaters/cyclists and runners. Med. Sci. Sports Exert. 23, 1289-1296. Herzog, W. and Leonard, T. R. (1991) Validation ofoptimization models that estimate the forces exerted by synergistic muscles. J. Biomechanics 24, 31-39. Hill, A. V. (1938) The heat of shortening and the dynamic constants of muscle. Proc. R. Sot. Land. 126, 136-195. Hodgson. J. A. (1983) The relationship between soleus and gastrocnemius muscle activity in conscious cats-a mode1 for motor unit recruitment. J. Physiol. 337, 553-562. Mai, M. T. and Lieber, R. L. (1990) A mode1 of semitendinosus muscle sarcomere length, knee and hip joint interaction in the frog hindlimb. J. Biomechanics 23, 271-279. Pedotti. A., Krishnan, V. V. and Stark, L. (1978) Optimization of muscle force sequencing in human locomotion. Math. Biosci. 38, 57-76. Rack, P. M. H. and Westbury, D. R. (1969) The effects of length and stimulus rate on tension in the isometric cat soleus muscle. J. Physiol. 204,443-460. Sacks, R. D. and Roy, R. R. (1982) Architecture of the hind limb muscles of cats: functional significance. J. Morphol. 173, 185-195. Stephens, J. A., Reinking, R. M. and Stuart, D. G. (1975) The motor units of cat medial gastrocnemius: electrical and mechanical properties as a function of muscle length. J. Morphol. 146,495512. Walmsley, B.. Hodgson, J. A. and Burke, R. E. (1978) Forces produced by medial gastrocnemius and soleus muscles during locomotion in freely moving cats. J. Neurophysiol. 41, 1203-1216. Woittiez, R. D., Huijing, P. A., Boom, H. B. K. and Rozendal, R. H. (1984) A three-dimensional muscle model: a quantified relation between form and function ofskeletal muscles, J. Morphol. 182,95-113. Zajac, F. E. (1989) Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. In CRC Critical Reviews in Biomedical Engineering (Edited by Bourne, J. R.). Vol. 17, No. 4, pp. 359-411. CRC
Press, Boca Raton.
J.Biomechanics Vol.25,No.11,pp,1329-1335. 1992 Printed inGreat Britain
ss.m+.Jo
0 1992Pergamon PnssLtd
FORCE-LENGTH PROPERTIES AND FUNCTIONAL DEMANDS OF CAT GASTROCNEMIUS, SOLEUS AND PLANTARIS MUSCLES W. HERZOG,*~ T. R. LEONARD,* J. M. RENAUD,~ J. WALLACE,* G. CHAKI* and S. BORNEMISZA* Faculties of *Physical Education and $.Biological Sciences, The University of Calgary, Calgary,
Alberta TZN lN4, Canada Abstract-The purpose of this study was to measure isometric force-length properties of cat soleus, gastrocnemius and plantaris muscle-tendon units, and to relate these properties to the functional demands of these muscles during everyday locomotor activities. Isometric force-length properties were determined using an in situ preparation, where forces were measured using buckle-type tendon transducers, and muscle-tendon unit lengths were quantified through ankle and knee joint configurations. Functional demands of the muscles were assessed using direct muscle force measurements in freely moving animals. Force-length properties and functional demands were determined for soleus, gastrocnemius and plantaris muscles simultaneously in each animal. The results suggest that isometric force-length properties of cat soleus, gastrocnemius and plantaris muscles, as well as the region of the forcelength relation that is used during everyday locomotor tasks, match the functional demands.
INTRODUCTION It is known that instantaneous
contractile
conditions,
such as length and velocity, are major determinants of the forces a maximally stimulated muscle can exert. Forcelength properties of skeletal muscles were first mentioned by Blix (1894), and isometric force-length data on isolated fibers of frog skeletal muscle (Gordon et al., 1966) helped support the cross-bridge theory as the principal mode1 for muscular force production. Force-velocity properties of frog striated muscle were described by Hill (1938) and still serve to describe the hyperbolic relation between maximal force and velocity of shortening skeletal muscles. Isometric force-length properties have been determined at the fiber, muscle, or muscle-tendon unit level. According to the cross-bridge theory, and assuming uniform sarcomere lengths, force-length properties of isolated muscle fibers are uniquely determined by the lengths of thick and thin myofilaments. On the muscle level, additional structural factors such as the fiber length relative to the total muscle length and the arrangement of fibers within the muscle must be considered (Woittiez et al., 1984). On the muscle-tendon unit level, force-length properties are further influenced by the ratio of fiber length to series elastic element length, and the force elongation properties of series elastic elements (Zajac, 1989). A knowledge of isometric force-length properties of muscle-tendon units is considered essential when estimating force sharing among synergistic muscles (Herzog, 1987; Pedotti et al., 1978). The importance of the force-length property (as well as other muscular Received in final form 4 February 1992. TAuthor to whom correspondence should be addressed. BM25:11-F
properties such as size, fiber type distribution, force-velocity relation, etc.) in the area of muscle force predictions is associated with the assumption that muscular and neuromuscular properties may reflect the functional requirements of muscles during everyday tasks. This assumption has received support in a most recent study, where force-length properties of intact human rectus femoris muscles were found to differ systematically between elite athletes in different sports, and these differences appeared to be. associated with the functional requirements imposed chronically onto the rectus femoris muscle in the different sport activities (Herzog et al., 1991). Further support of this assumption was provided by Goslow and van de Graaff (1982), who determined isometric force-length properties of skunk triceps surae and plantaris muscles and found that they were similar in shape but not in magnitude. Since these muscles are part of a functional group, it is reasonable to assume, but not necessarily correct, that each muscle satisfies similar functional demands during skunk locomotion and that these functional demands are reflected in the particular isometric force-length properties of these muscles. In order to test the speculation that isometric force-length properties of muscles are associated with the functional demands of muscles, it is necessary to measure these quantities independently. Therefore, the purpose of this study was to measure isometric force-length properties of cat soleus (S), gastrocnemius (G), and plantaris (P) muscle-tendon units, and compare these properties with the corresponding in vim ‘force-length measurements’ obtained during everyday locomotor activities. Forcelength properties in this context refer to the relation between maximal, isometric forces and the corresponding muscular lengths, whereas in vivo
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W. HERZOCet al.
force-length measurements refer to the relation between instantaneous force and length of the muscles during locomotion (i.e. dynamic contractions and variable submaximal stimulations).
METHODS
Determination
of isometric force-length
relations
Isometric force-length relations of in situ S, G, and P muscles were determined from four male adult cats, and additionally from four male adult cats for G alone. The animals were anesthetized initially using a mask and a 5% halothane gas mixture, then they were intubated and maintained using l.O-1.5% halothane. The left leg was shaved from the hip to the proximal phalanges. A heating pad was placed underneath the animals to maintain a constant body temperature. The hind limbs of the animals were clamped using an external fixation device. This fixation device contained three U-shaped stainless steel elements, one each for the thigh, shank, and foot. Each of these elements contained four bone screws, two on either side, for rigid fixation of the device to the hind limb bones. The individual elements dfthe fixation device were connected through stainless steel rods on the one side and a 5 mm rigid metal plate on the other side. The entire device was fixed to a metal ground plate that was rigidly attached to an experimental table. This setup prevented movement of the hind limbs during the experimental contractions. Force measurements. Soleus, gastrocnemius, and plantaris tendons were exposed with a cut on the posterior aspect of the shank and were separated from one another by opening the connective tissue sheaths surrounding the entire achilles tendon. E-shaped tendon force transducers, similar to those described by Walmsley et al. (1978), were placed on the tendons of S, G, and P. These transducers are deformed when forces are transmitted by the tendons. The deformation is measured as a change in voltage by a pair of strain gauges, and these voltage signals are related to the tendon forces through an appropriate calibration procedure. Calibrations were performed in a terminal experiment by detaching the tendons of S, G, and P from the calcaneus with a bone chip and hanging known weights from the tendon. All calibration curves obtained in this way were linear within the range of forces observed (r2 > 0.990), showed no measurable hysteresis, and yielded no measurable differences in results for repeated measures. Measurements of forces from the entire gastrocnemius muscle rather than individual measures of the lateral and medial heads of G were performed since the primary interest was to determine the forces exerted by the gastrocnemius muscle on the ankle joint system. Since the medial and lateral heads of G are not strictly in parallel, independent force measurements of the two heads may not have provided the desired result.
Muscle length measurements. Muscle-tendon unit lengths were measured using a pair of calipers and were related to the ankle and/or knee joint angles, which were measured using a goniometer. Ankle and knee joint angles were defined as the included angles between foot and shank, and shank and thigh, respectively. Knee joint angles were kept constant at a nominal joint configuration of 90”, and length changes of the muscles were produced by altering the ankle joint angle exclusively. Muscular stimulation. Stimulations were performed using a nerve cuff electrode that was placed around the tibia1 nerve, distal to the tibial/sciatic junction. The sciatic nerve was ligated and cut proximal to the tibial/sciatic junction to avoid contraction of muscles not of interest in this study. Gauze that was periodically soaked in a warm saline solution was placed around the nerve and the exposed parts of the hind limb to prevent tissues from drying. In order to produce maximal tetanic contractions, the nerve was stimulated supramaximally using square-wave pulses. For the different animals, stimulation voltages ranged from 1.0 to 2.5 V for 1.0-2.5 s. Pulse durations were chosen between 0.1 and 0.2 ms, and the stimulation frequencies ranged from 80 to 100 Hz for S and 100 to 120 Hz for G and P. The actual stimulation parameters were determined individually for each animal and muscle to assure maximal force response. Protocol. Maximal total forces were measured for six to twelve different muscle lengths using supramaximal stimulation of the tibia1 nerve. The corresponding passive forces were obtained for zero stimulation of the nerve. At each length, muscle forces were measured two or three times at intervals of 2 min. Measurements at different muscle lengths were separated by an interval of 5 min. The rectal and muscle temperatures were obtained before each series of contractions at a given length and were kept within 35-38°C and 32-35°C respectively. Repeat force measurements were obtained for selected muscle lengths to observe possible deteriorations of the preparation. Such deteriorations did not occur. Data analysis. Total and passive forces were averaged for the repeat trials and plotted as a function of ankle joint angle. For the one joint soleus muscle, muscle-tendon unit lengths are uniquely determined by the ankle joint angle; for gastrocnemius and plantaris, muscle-tendon unit lengths were related to the ankle joint angle using a constant knee joint angle of 90”. All total force values were normalized relative to the muscle volumes, that were determined in a terminal experiment using an immersion technique. These normalized force data were plotted against ankle joint angles, and were approximated using best-fitting polynomial regression lines. Force values were also normalized relative to physiological cross-sectional area (PCSA), using estimates of mean fiber lengths and angles of pinnation obtained from the literature (Sacks and Roy, 1982).
Properties and demands of cat muscles
Determination offunctional
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requiremenrs
Functional requirements for a variety of locomotor conditions were determined from direct muscle force measurements of S, G, and P in eight cats, using chronically implanted tendon force transducers and digitization of the hind limb kinematics from video records. The tendon force transducers were similar but considerably smaller than those used in the previous part of the study, and they were surgically implanted onto the tendons of S, G, and P of the left hind limb. Video records were obtained from a sagittal plane view of the left side of the animals from a camera running at a nominal rate of 30 Hz. The knee and ankle joint angles were defined as above and were determined from five digitized landmarks; two points from the sole of the foot, the lateral malleolus, and the estimated knee and hip joint centers. After complete recovery from surgery, the animals were placed on a treadmill and tendon forces and hind limb kinematics were measured for walking (0.4-1.2 m s- ‘) and trotting (1.8-2.4 m s- ‘). The animals used in this part of the study were different from those used for the determination of force-length properties. This had to be done since the small tendon force transducers required in the functional experiments were not strong enough to withstand the maximal forces of the muscles produced during the isometric force-length experiments. However, the animals selected for the two experiments were age, sex, and weight matched. Furthermore, isometric force-length properties and in uiuo force-length measurements during locomotion were similar among all animals and all muscles, thus justifying this approach. For representation of gastrocnemius and plantaris forces as a function of ankle joint angles during locomotion, it was necessary to account for length changes of these muscles at the knee joint, and relate these length changes to a knee joint angle of 90”. The resulting ankle joint angles are hereafter referred to as adjusted ankle joint angles. The procedures used to calculate adjusted ankle joint angles were identical to those reported by Stephens et al. (1975). Expressing isometric force-length properties and functional requirements of the muscles in terms of joint angles rather than muscle-tendon unit, muscle, or fiber lengths has the advantage that the results from different animals can be compared directly.
RESULTS
Total forces increase steadily for soleus muscle for decreasing ankle joint angles (i.e. increasing muscle length) [Fig. l(a)]. The same is true for gastrocnemius and plantaris muscles up to ankle joint angles of about 80”; for longer muscle lengths, maxima1 isometric forces tend to decrease [Fig. l(b) and (c), respectively]. Passive forces appear to be slightly higher in G compared to S, and in S compared to P (note that the open triangle at an ankle joint angle of 50” and force of
Fig. 1. Force-length relations of cat soleus (a), gastrocnemius (b), and plantaris muscles (c). Total forces and passive forces are shown with corresponding symbols for the same animals. Knee joint angles were fixed at 90” for all experiments. Forces in S increase continuously for decreasing joint angles (i.e. increasing muscle length) whereas forces for G and P appear to peak at joint angles of about 80”.
20 N for P is a total, not a passive, force value). Furthermore, passive forces start to come into play at somewhat larger ankle joint angles for S and G compared to P. Total forces are largest for G and, on an average, smallest for S which corresponds to the size of these muscles. The variations of total force for a
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W. HERZOGet al.
given muscle may be explained partly through vari-
ations of muscle size among animals. The volumes for all four soleus muscles studied were within 1 cm3 and peak isometric forces do not appear to be strongly related to muscle volume (Table 1). For gastrocnemius and plantaris muscles, the volumes ranged from 17 to 33.5cm3 and from 7 to 12cm3, respectively. The corresponding peak forces appear to increase with increasing muscle size. Therefore, normalization of force-length relations with respect to muscle volumes resulted in a decrease in the variation of force magnitudes between force-length properties from different animals for G and P, but not for S [Fig. 2(a-c)]. Peak forces normalized with respect to muscle volume ranged from about 7.5 to 10 Ncmm3 for all three muscles. However, when normalizing peak forces relative to physiological cross-sectional areas, muscle S is considerably stronger on an average (32.8 Ncm-‘) than muscles G (19.1 Ncm-‘) and P (16.9 Ncm-‘). The vertical lines at ankle joint angles of 60 and 140 approximate the range of motion observed during cat walking, trotting, and galloping [Fig. 2(ac)]. This range of motion, expressed in terms of ankle joint angles, contains an adjustment factor for length changes of G and P associated with knee joint motion. Length changes of P associated with deviations of the metatarsophalangeal joint from its nominal value of 180” were not accounted for since the partial, in-series arrangement of P with the flexor digitorum brevis (Abraham and Loeb, 1985) makes quantification of such changes virtually impossible. Within the functional range of motion, maximal isometric forces of S, G, and P tend to increase as muscle length increases. Forces of the soleus muscle remain similar for different speeds of walking/trotting, whereas gastrocnemius and plantaris forces tend to increase with increasing speeds of locomotion [Fig. 3(a-c)]. Peak forces for walking at 0.4 m s- 1 occur at adjusted ankle joint angles of 95-100” for all three muscles. Peak forces for walking at 1.2 ms-’ and trotting at 2.4 m s-l occur at adjusted ankle joint angles of
Table 1. Muscle volumes and the corresponding peak isometric forces for cat gastrocnemius, soleus, and plantaris muscles Gastrocnemius
Cat 1 2 3 4 5 6 7 8
Soleus
Plantaris
Volume (cm3)
Peak force (N
Volume
Peak force
Volume
Peak force
(cm3)
(N)
(cm?
(N)
21.0 27.5 24.0 33.5 21.5 17.0 28.5 17.5
193.5 242.0 193.0 290.0 139.5 160.0 221.2 154.1
6.0 5.0 5.0 5.5 -
48.5 36.0 48.0 36.0 -
1.0 8.0 9.0 12.0 -
56.4 74.0 90.0 106.0 -
I 180
(4
1M)
140
120
100
80
Bo
40
ANKLE ANGLE (“,
Fig. 2. Force-length relations of cat soleus (a), gastrocnemius (b), and plantaris muscles (c). Forces were normalized with respect to muscle volume. Data of all animals combined were approximated using a best-fitting polynomial. Approximate limits of ankle joint motion (including considerations of muscular length changes associated with knee joint motion) during free walking and trotting are indicated by the intermittent vertical lines at 60 and 140”. Force-length properties of S, G, and P are similar and may be associated primarily with the ascending limb of the force-length relation.
approximately 80” for all muscles and both speeds. At all speeds and for each muscle, peak forces appear to occur after nearly isometric or slightly eccentric contractions of the muscl+tendon unit. Peak force production is followed by a decrease in force and a generally large concentric contraction of all muscles at each speed.
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Properties and demands of cat muscles DISCUSSION
SOLEUS FORCE (Nl a-
IM
135
90
105
120
75
sn ANKLE ANGLE ,‘:
(4
(4 PUNTARIS
FORCE IN) IS
1w
110
120
ICQ
40 @I 50 ANKLE ANGLE (“) ADJUSTED TO 90 *KNEE JOINT ANGLE
w
Fig. 3. Representative force requirements of soleus (a), gastrocnemius (b), and plantarjs muscles (c) during a step cycle for nominal speeds of locomotion of 0.4, 1.2, and 2.4 m s-l. Arrows indicate the instant of first paw contact with the ground. Ankle joint angles are adjusted in such a way that length changes of gastrocnemius and plantaris muscle-tendon units associated with knee joint configurations other than 90” are compensated for. Peak forces tend to
occur at smaller ankle joint angles (i.e.longer muscle-tendon unit lengths) for fast walking (1.2 ms-‘) and trotting (2.4 m s - ’ ) compared to slow walking (0.4 m s - ’ ). Furthermore, peak forces of S are similar for all speeds of locomotion, whereas the corresponding forces increase with increasing locomotor speeds for G and P.
The shapes of the isometric forc&ength relations of cat S, G, and P are similar, and correspond to those for the same muscles in the striped skunk (Goslow and van de Graaff, 1982). This similarity implies that the force potential of the entire functional group (i.e. the force that is transmitted by the achilles tendon) is also similar to that of the individual muscles that make up the group. Therefore, maximal isometric forces of the entire achilles tendon are relatively small at extended ankle joint angles and become increasingly larger with flexion of the ankle joint up to an optimal angle of about 80” (for a corresponding knee joint angle of 90”). Through trigonometric relations, it can be ascertained that at extended ankle joint angles, the moment arm of the achilles tendon about a transverse axis through the ankle joint is relatively small. Therefore, peak moments that may be produced by the triceps surae/plantaris group about the ankle joint are small for extended ankle joint angles compared to ankle joint angles of around 80”. Theoretically, it would be simple to design the cat ankle joint in such a way that force and moment potentials were nearly constant throughout the functional range by choosing appropriate force-length properties of the individual muscles. However, in such a design the absolute peak force/moment potential would be significantly reduced compared to nature’s design of the actual cat ankle joint. Within the functional range of motion (about 60-140” in the ankle joint) isometric forces of cat S, G, and P tend to increase for increasing muscle-tendon unit lengths, maybe with the exception of the extreme lengths in G and P [Fig. 2(a+)]. This result contradicts the ‘textbook notion’ that optimal length of muscles is somewhere near the middle of the anatomical range of motion; and it is contrary to results reported for frog semitendinosus muscle, which has a decreasing isometric force potential for increasing muscle length within its normal range of motion (Mai and Lieber, 1990). Furthermore, human lower limb muscles have been found to operate on different parts of the force-length relation (ascending limb, near optimal length, or descending limb) for joint excursions experienced during everyday movements, such as locomotion (Cutts, 1988). The question, thus, arises if and how the part of the force-length relation that a muscle occupies for movements within the normal range of joint motion may relate to its functional demands. Muscles that tend to operate on the ascending part of the force-length relation (such as cat S, G, and P) have an increased isometric force potential for increasing muscle lengths, and a decreased isometric force potential for decreasing muscle lengths. Theoretically, therefore, it appears to be of advantage if a muscle operating on the ascending part of the force-length relation increases its force during a functional task while elongating and decreases its force while shorten-
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W. HERZOG et al.
ing, and vice versa for a muscle working predominantly on the descending limb. Cat soleus, gastrocnemius, and plantaris muscles appear to adhere to the above theoretical considerations. They tend to work on the ascending part of the force-length relation [at the muscle-tendon unit level, Figs l(ac) and 2(ac)] and they increase force primarily while elongating and decrease force while shortening for walking and trotting movements [Fig. 3(a-c)]. In contrast to cat S, G, and P, frog semitendinosus muscle occupies primarily the descending part of the isometric force-length relation and, in accordance with our theoretical considerations, is thought to approach peak forces during jumping while shortening (Mai and Lieber, 1990). Furthermore, human rectus femoris muscles were found to operate on the ascending part of the isometric force-length relation for high-performance runners and on the descending part for high-performance cyclists (Herzog et al., 1991). Since rectus femoris muscles are believed to increase force while lengthening during running and while shortening during cycling, these results further support the above idea of interrelation between isometric force potential and functional demands. However, despite the conceptual agreement of the results obtained on frog semitendinosus and human rectus femoris muscles with our results on cat triceps surae and plantaris muscles, these findings must be considered with caution for a variety of reasons. Most importantly, Mai and Lieber (1990) did not directly measure semitendinosus forces in frogs, but calculated these forces from estimates of the contractile conditions of the muscle for jumping movements; and Herzog et al. (1991) determined isometric force-length relations of human rectus femoris muscles using maximal voluntary contractions rather than supramaxima1 activation of the muscle; thus, their results may be related to neuromuscular mechanisms of activation rather than adaptations of the isometric force-length relation. Peak forces for cat soleus muscle occurred at ankle joint angles of about 95-100” for walking at a speed of 0.4 ms-‘. For the two higher speeds (i.e. 1.2 ms-’ walking; 2.4 m s- ’ trotting) peak forces occurred towards ankle joint angles of 80”, which corresponds closely to the optimal length of the soleus muscle tendon unit. For all three speeds of locomotion studied, soleus forces remained nearly constant [Fig. 3(a)]; therefore, it is safe to assume that the average fiber and sarcomere lengths were longer at the instant of peak force demands for the 1.2 and 2.4 m s- ’ speeds compared to the corresponding values at 0.4 m s-r. According to the isometric force-length relations found in this study for soleus [Figs l(a) and 2(a)], the potential of S to produce force is higher at muscle lengths encountered for the two high speeds of locomotion compared to the low speed. Furthermore, for all three speeds of locomotion peak soleus forces occur after phases of predominant eccentric contractions. Since these eccentric contractions tend to be faster for
higher speeds of locomotion, one would associate again (as for the force-length properties) a larger force potential for soleus muscle with the high speeds of locomotion compared to the low speed. Thus, from the point of view of the mechanical properties of S, and for relatively constant stimulation of the muscle, one would expect peak forces of S to increase with increasing speeds of locomotion, similar to what is observed for gastrocnemius and plantaris muscles. Since soleus forces remain virtually constant for a large range of locomotor speeds [Fig. 3(a); Gregor et al., 1988; Herzog and Leonard, 1991; Walmsley et al., 19781, it appears that stimulation of the soleus muscle is either inhibited or does not have the same effect at high speeds of locomotion compared to low speeds. Hodgson (1983) argued that the steady force levels in cat soleus muscles at different speeds of locomotion may be associated with an inhibition of S for increasing locomotor speeds through rubrospinal and cutaneous pathways. However, such inhibition has not been verified in studies using electromyographic measurements on S. Walmsley et al. (1978) reported slight increases in peak-integrated EMG activities for cat soleus muscles with increasing speeds of locomotion, and Gregor et al. (1988) found constant mean EMG activity during the stance phase of locomotion for speeds ranging from 0.8 to 2.2 ms-‘. However, since the relations between central stimulation and measured activation (EMG), as well as between measured activation and muscular forces are not clearly established, inferences from EMG measurements on muscular force and stimulation may be misleading. It may be argued that forces of cat soleus muscle remain about constant for different locomotor speeds despite similar stimulation (as quantified through EMG), and more favorable mechanical conditions (muscle length and speed of elongation) that exist at high compared to low speeds because of the differences in the active state. For example, for slow walking (0.8 m s- ‘) the time period from the onset of EMG to peak force production in S is clearly over 100 ms (Walmsley et al., 1978; Fig. 2), whereas the corresponding time period is only about 80ms for running at 3.0 ms-’ (Walmsley et al., 1978; Fig. 3). Similarly, Gregor et al. (1988) show slightly decreasing EMG burst durations prior to paw contact for increasing speeds of locomotion in cat soleus muscles. It appears, therefore, that the active state in cat S during locomotion may not be as fully developed at the end of the eccentric contraction (i.e. when peak forces tend to occur) for high compared to low speeds of locomotion. Forces in cat gastrocnemius and plantaris muscles increase with increasing speeds of locomotion. This result is consistent with the previous findings for these muscles (Herzog and Leonard, 1991) and is also consistent with the results obtained from the medial head of the gastrocnemius muscle (e.g. Walmsley et al., 1978; Hodgson, 1983). When relating mechanical properties of muscles to functional demands, it is important to realize that the
Properties and demands of cat muscles two are not directly comparable. For example, in this particular study, isometric force-length properties were obtained for supramaximally stimulated muscles under isometric conditions. The force-angle relations during locomotion were obtained under conditions of variable, submaximal stimulation, and dynamic behavior of the muscles. Nevertheless, such comparisons suggest that the force-length properties of cat S, G, and P correspond in a meaningful way to the functional demands of these muscles during everyday motor tasks. Similar findings were reported for frog semitendinosus (Mai and Lieber, 1990) and human rectus femoris muscles (Herzog et al., 1991). Future studies may focus on generalizing these isolated results, and on investigating the mechanisms of possible adaptations of force-length properties to changing functional requirements. Acknowledgements-This study was supported by a grant and a student scholarship from NSERC of Canada. We thank Dr Merle Olson for providing technical help and laboratory space. REFERENCES Abraham, L. D. and Loeb, G. E. (1985) The distal hindlimb musculature of the cat (patterns of normal use). Exp. Brain Res. 58, 580-593.
Blix, M. (1894) Die Laenge und die Spannung des Muskels. Skand Arch. Physiol. 5, 149-206. Cutts, A. (1988) The range of sarcomere lengths in the muscles of the human lower limb. 1. Anat. 160, 79-88. Gordon, A. M., Huxley, A. F. and Julian, F. J. (1966) The variation in isometric tension with sarcomere length in vertebrate muscle fibers. J. Physiol. (Land.) 184, 170-192. Goslow, G. E. Jr and van de Graaff, K. M. (1982) Hindlimb joint angle changes and action of the primary ankle extensor muscles during posture and locomotion in the striped skunk (Mephitis mephitis). J. Zoo!. (Land.) 197, 405-419. Gregor, R. J.. Roy, R. R., Whiting, W. C., Lovely, R. G., Hodgson, J. A. and Edgerton, V. R. (1988) Mechanical
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output of the cat soleus during treadmill locomotion: in viuo vs in situ characteristics. J. Biomechanics 21, 721-732. Herzog, W. (1987) Individual muscle force estimations using a non-linear optimal design. J. Neurosci. Methods 21, 167-179. Herzog, W., Guimaraes, A. C., Anton, M. G. and CarterErdman, K. A. (1991) Moment-length relations of rectus femoris muscles of speed skaters/cyclists and runners. Med. Sci. Sports Exert. 23, 1289-1296. Herzog, W. and Leonard, T. R. (1991) Validation ofoptimization models that estimate the forces exerted by synergistic muscles. J. Biomechanics 24, 31-39. Hill, A. V. (1938) The heat of shortening and the dynamic constants of muscle. Proc. R. Sot. Land. 126, 136-195. Hodgson. J. A. (1983) The relationship between soleus and gastrocnemius muscle activity in conscious cats-a mode1 for motor unit recruitment. J. Physiol. 337, 553-562. Mai, M. T. and Lieber, R. L. (1990) A mode1 of semitendinosus muscle sarcomere length, knee and hip joint interaction in the frog hindlimb. J. Biomechanics 23, 271-279. Pedotti. A., Krishnan, V. V. and Stark, L. (1978) Optimization of muscle force sequencing in human locomotion. Math. Biosci. 38, 57-76. Rack, P. M. H. and Westbury, D. R. (1969) The effects of length and stimulus rate on tension in the isometric cat soleus muscle. J. Physiol. 204,443-460. Sacks, R. D. and Roy, R. R. (1982) Architecture of the hind limb muscles of cats: functional significance. J. Morphol. 173, 185-195. Stephens, J. A., Reinking, R. M. and Stuart, D. G. (1975) The motor units of cat medial gastrocnemius: electrical and mechanical properties as a function of muscle length. J. Morphol. 146,495512. Walmsley, B.. Hodgson, J. A. and Burke, R. E. (1978) Forces produced by medial gastrocnemius and soleus muscles during locomotion in freely moving cats. J. Neurophysiol. 41, 1203-1216. Woittiez, R. D., Huijing, P. A., Boom, H. B. K. and Rozendal, R. H. (1984) A three-dimensional muscle model: a quantified relation between form and function ofskeletal muscles, J. Morphol. 182,95-113. Zajac, F. E. (1989) Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. In CRC Critical Reviews in Biomedical Engineering (Edited by Bourne, J. R.). Vol. 17, No. 4, pp. 359-411. CRC
Press, Boca Raton.
