Eur J Appl Physiol (1990) 60:395-401
.uo.e,°A p p l i e d Physiology Journal o f
and Occupational Physiology @ Springer-Verlag 1990
Eccentric and concentric torque-velocity relationships during arm flexion and extension Influence of strength level T i b o r H o r t o b ~ g y i and F r a n k I. K a t c h
University of Massachusetts, Department of Exercise Science, Amherst, MA 01003, USA Accepted January 17, 1990 Summary. Forty men were tested with a computerized dynamometer for concentric and eccentric torques during arm flexion and extension at 0.52, 1.57, and 2.09 rad.s-1. Based on the summed concentric and eccentric torque scores, subjects were placed into a high strength (HS) or low strength (LS) group. The eccentric and concentric segments of the torque-velocity curves (TVCs) were generated using peak torque and constantangle torque (CAT) at 1.57 and 2.36 rad. Angle of peak torque was also recorded. Compared to LS, HS had significantly greater estimated lean body mass (+ 10.2 kg) and approximately 25% greater average torque output. Reliability of the peak torque scores on 2 days in 20 subjects was r_0.85. The difference between observed torques and the mathematically computed criterion torque scores averaged 1% for three validation loads that ranged from 11.4 to 90.4 kg. Statistical analysis revealed that torque output in LS plateaued at low concentric velocities and was also flattened with increasing eccentric velocities. Conversely, torque ouptput for HS increased with decreasing concentric velocities and increased with increasing eccentric velocities. The method of plotting the TVCs for peak or CAT did not influence the pattern of TVC. Eccentric flexion peak torque occurred at a significantly shorter muscle length (1.88 rad) than concentric torque (2.12 tad). This difference was also present for extension; it was 1.88 rad for eccentric and 2.03 rad for concentric torque. These findings are discussed in terms of study design, neural inhibition, activation history, muscle-tendon elasticity, muscle fiber types, muscle architecture, and methodological considerations. The present results illustrate the importance of strength level to explain individual differences in TVC. Key words: Muscle strength - Torque-velocity curve M u s c l e elasticity - Neural factors - Dynamometry
Introduction
An understanding of human skeletal muscle function Offprint requests to: F. I. Katch
relies on findings from denervated and isolated preparations (Rack and Westbury 1969; Hill 1970). Accumulating evidence suggests that mechanical properties of intact human muscles in most but not all aspects resemble those of animal preparations (e.g. Wilkie 1950). One disputed feature is the shape of the force- (or in humans) torque-velocity curve (TVC), particularly at the low velocity end. In animal models, muscular forces were found to increase with decreasing contraction velocity. Many researchers have successfully reproduced this hyperbolic TVC in various human muscles (Wilkie 1950; Thorstensson et al. 1976; Lesmes et al. 1978; Coyle et al. 1981; Ivy et al. 1981; Tihanyi et al. 1982; Griffin 1987). However, other investigators report a plateauing of torques at low velocities (Rodgers and Berger 1974; Perrine and Edgerton 1978; Gregor et al. 1979; Caiozzo et al. 1981). These differences in the TVC appear to be related to two factors; tension-restricting neural inhibition of the human subjects or the method of assessing TVC. There are several problems with these two factors to explain the discrepant data on the TVC pattern. First, direct neurophysiolog~cal evidence has yet to be presented to pinpoint the source of the tension-limiting mechanism. Perhaps neural inhibition is a ubiquitous feature of untrained subjects in the studies that observed flattened TVC and used constant-angle torque (CAT) to generate the TVC. Second, studies reporting TVC with a plateau used only CAT to plot TVC, but did not report TVC wkh peak torque (e.g. Perrine and Edgerton 1978). Thus, it is impossible to tell whether the differences in the shape of the TVC would have been present. Indeed, there are only two studies that directly compared the TVCs generated by peak torque and CAT. Yates and Kamon (1983) explored the influence of muscle fiber composition on the TVCs plotted with peak and CAT. These authors concluded that the method of plotting the TVC and fiber typing had little influence on the TVC pattern. In contrast, Osternig et al. (1983) examined the TVC at six CATs and with peak torque in ten males. The differences in the TVCs were substantial; with CAT, the TVCs were flattend across
the entire velocity spectrum, whereas with peak torque, TVC was hyperbolic. The results from these studies are incongruous. It is still unclear whether the plateauing is the result of some neural inhibition, or an intrinsic property of the human skeletal muscle assessed in vivo. Finally, the shape of the eccentric segment of the TVC has not been compared using peak torque and CAT in various subject populations. One outcome could be that the tension-limiting mechanism is absent in individuals with higher absolute strength. Thus, the eccentric and concentric TVC would be different in subjects with lower strength. Such an approach may help to clarify whether the flattened TVC is influenced by strength level. Indeed, one study has suggested that strength level may be a more important classification variable than body size or fiber-type composition (Kroll et al. 1980). The purpose of the present study was threefold: (1) to compare the pattern of the eccentric and concentric TVC in high strength (HS) and low strength (LS) subjects, (2) to assess the influence of peak torque and CAT on the shape of the TVC, and (3) to compare the angle of peak torque in HS and LS individuals during concentric and eccentric contractions. Methods Subjects. Forty men participated as subjects and signed an informed consent before testing. Their physical characteristics appear in Table 1. Subjects were classified as HS or LS according to strength level. Subjects were placed into HS and LS groups based on the cumulative torque scores obtained during concentric and eccentric actions at 0.52, 1.57, and 2.09 rad.s-'. Twelve HS subjects were university college athletes in football, baseball, or rugby, and had participated in systematic strength training at least three times a week for 6 years or more. The remaining eight HS subjects were recreational weight lifters who had trained approximately three times a week for less than 2 years. In the LS group, six subjects were non-competitive runners, and 14 pursued recreational activities other than weight lifting.
specific regression equation (Wilmore and Behnke 1969) shown in the footnote of Table 1. Equipment and procedures. Subjects were tested for arm flexion and extension strength using the Biodex dynamometer (Shirley, NY). The 550 W DC servomotor is interfaced with four strain gauges located at the output shafts of the powerhead. Three A/D channels provide simultaneous conversion of real-time data signals for torque, velocity, and position. The three parallel A/D input channels have the capacity of 10-bit A/D conversion in 35 ps. After signal conditioning and data transfer to a microcomputer, the data were stored on floppy disks for subsequent analysis. Subjects were seated, and straps were secured around the upper arm, waist, and shoulders to provide a stable position. The dominant upper arm was positioned on a padded support. The axis of the elbow joint was aligned with the axis of the measuring shaft, and the seat and lever arm settings were set to conform to the individuals' body size. During the arm flexion and extension movements, subjects grasped a plastic handle on the lever arm in a neutral anatomical position (Fig. 1). A balanced order test protocol was used to assess isokinetic concentric and eccentric torque for arm flexion and extension. During concentric actions, subjects performed maximum arm flexion and extension at a preset velocity. For eccentric actions, the lever arm moved at the preset velocity when an initial resistance was applied to the exercise bar. For example, eccentric tests of the biceps started in a fully flexed arm position. The motor driven lever arm was cued by the subject to begin flexion against the resistance of the volitionally contracting but lengthening biceps. Before testing, subjects warmed-up for each testing mode with two submaximal and one maximal contraction. The tests included two maximal flexion/extension cycles at each testing velocity of 0.52, 1.57, and 2.09 rad.s-' (or 30, 90, and 120"s -I). There was a 3-s pause between flexion and extension and 1-min rest between speed conditions. The criterion score was peak torque corrected for gravity. Torque-velocity curves. The TVC was plotted using three different measures of torque. Each individual torque-position curve was digitized for (1) peak torque, (2) CAT at 1.57 rad, and (3) CAT at 2.36 rad. Thus, TVCs were established using peak torque, CAT 1.57 rad, and CAT 2.36 rad for concentric and eccentric flexion and extension at 0.52, 1.57, and 2.09 rad.s-'. The angles of 1.57 and 2.36 rad were selected to plot TVC at CAT because eccentric, isometric, and concentric peak torques occurred approximately midway between these two angles. In addition to peak torque, the corresponding angle of peak torque was also recorded (3.14 rad = arm straight).
Anthropometry. Body mass was measured to an accuracy of +25 g on a beam balance, and stature was measured on a portable stadiometer to f 0.01 m. Lean body mass was estimated from an age-
Table 1. Physical characteristics of subjects High strength (n = 20)
Low strength (n = 20)
Variable
Mean
SE
Mean
SE
Age (years) Body mass (kg) Stature (m) LBM (kg)" Fat (%)
23.1 90.9 1.78 75.7 16.7
3.28 16.73 0.07 11.42 4.65
22.6 76.6 1.78 65.6 14.5
5.01 11.50* 0.09 8.71* 5.02
" L e a n body mass calculated from the equation, LBM = 44.636 + 1.08717 x body mass - 0.7396 x abdomen girth (Wilmore and Behnke 1969) * Significant difference between groups (p 0.05). I n contrast, c o n c e n t r i c t o r q u e s at 2.09 r a d . s - 1 were s i g n i f i c a n t l y (p < 0.05) l o w e r t h a n t o r q u e s at 0.52 r a d . s -1 d u r i n g f l e x i o n ( - 1 1 . 9 N m ) a n d e x t e n s i o n ( - 6 N m) in H S b u t n o t in LS ( - 2 . 2 N m for f l e x i o n a n d - 5 N m f o r e x t e n s i o n , p > 0.05). T h e 10.1 N m d i f f e r e n c e b e t w e e n s p e e d s 0.52 r a d . s -1 a n d 1.57 r a d - s - 1 was also s i g n i f i c a n t d u r i n g e x t e n s i o n in H S (p < 0.05). Figure 2 illustrates the second relevant three-way i n t e r a c t i o n , i.e. m e t h o d x c o n t r a c t i o n t y p e x s p e e d . D a t a in Fig. 2 are t h e m e a n s p o o l e d a c r o s s g r o u p s . P o s t - h o c analysis showed that TVC with peak torques and CAT
398 Flexion
Table 3. C o m p a r i s o n o f angle o f peak eccentric and concentric torques at three velocities during arm extension and flexion in high strength (n = 20) and low strength (n = 20) groups. Values are in radians (3.14 r a d = a r m straight)
100
= Z
Velocity (rad. s- 1)
80
60 ¢.
[
40
-2.4
-1.6
1
I
-0.8
0.0
I
I
f
0.8
1.6
2.4
Extension 110
_= Z
"~
9O
70
50 -2.4
I
t
I
[
I
-1.6
-0.8
0.0
0.8
1.6
r 2.4
Flexion Eccentric" 0.52 1.57 2.09 Concentric 0.52 1.57 2.09 Extension Eccentric b 0.52 1.57 2.09 Concentric 0.52 1.57 2.09
High strength
Low strength
Mean
+ SE
Mean
4- SE
1.85 1.84 1.87
0.043 0.032 0.034
1.83 1.94 1.96
0.044 0.042 0.051
2.11 2.04 2.14
0.044 0.039 0.047
2.14 2.17 2.12
0.057 0.053 0.047
1.91 1.85 1.79
0.088 0.053 0.066
1.99 1.89 1.86
0.070 0.051 0.043
1.94 2.02 2.10
0.054 0.050 0.057
1.97 2.09 2.04
0.077 0.073 0.084
a Angle of eccentric peak flexion torque significantly less than concentric (p < 0.05) but not different between groups and speeds (p>0.05) u Angle of eccentric peak extension torque significant greater than concentric (p < 0.05) but not different between groups and speeds (p > 0.05)
Velocity, r a d . s -1 Fig. 2. C o m p a r i s o n o f torque-velocity curves o b t a i n e d for a r m flexion a n d extension using peak t o r q u e a n d c o n s t a n t angle torq u e (CAT) at 1.57 rad a n d 2.36 rad. N o t e : M e a n s ± S E p o o l e d across groups. - - © - - = Peak t o r q u e ; - - • - - = C A T 90 ° ; - - 0 - = C A T 135 °
at 1.57 or 2.36 r a d . s -1 were significantly different at every speed (p 0.05), but the type of contraction main effect was significant (p < 0.05); eccentric p e a k flexion torque occurred at a significantly (p < 0.05) shorter muscle length (1.88 rad) than concentric p e a k flexion torque (2.12 rad). For extension, there was no significant three-way interaction (t7>0.05), but the type of contraction x speed interaction was significant (p < 0.05); p e a k extension eccentric torque at 2.09 rad. s - 1 occurred at a
Torque-velocity relationship In the present study, we found that: (1) the pattern of the TVC differs by strength level (HS vs LS); (2) the pattern of the TVC is independent of the method of using p e a k torque versus CAT, and (3) there are differences in the angle of p e a k torque between contraction types (eccentric vs concentric). M a n y prior studies have shown that, unlike the force-velocity curve in isolated frog sartorius muscle (Hill 1970), the TVC plateaus at low concentric velocities when secured on an isokinetic d y n a m o m e t e r (Per-
399 rine and Edgerton 1978; Osternig et al. 1983). Some researchers asserted that neural inhibition prevented the subjects from exerting maximum knee extension torque during low-velocity concentric actions. However, direct neurophysiological evidence has not yet been presented to relate the flattened shape of the TVC to neural inhibition. Further, the results for the use of CAT versus peak torque as an alternative to derive the TVC are also in conflict (see below). Thus, the issue of neural inhibition remains unresolved. The conflict is underscored by the numerous studies that confirm the resemblance of TVC between isolated preparations and intact human muscle (e.g. Tihanyi et al. 1982). Inadequate study design may be one reason for the conflicting data from previous investigations. For example, the pattern of the TVC has been scrutinized only for a single group of healthy untrained subjects (Perrine and Edgerton 1978), for moderately trained subjects (Westing et al. 1988), or for groups with a predominance of slow-twitch or fast-twitch muscle fibers whose training status was not evaluated (Gregor et al. 1979; Yates and Kamon 1983). Subjects with a preponderance of fast-twitch fibers had larger differences in torque at high but not at low velocity (Gregor et al. 1979; Coyle et al. 1981). Thus, plateauing of torques at low velocities may be independent of fiber type. The low correlations between muscular strength and/or unloaded movement velocity and percentage of fasttwitch fibers in previous (Thorstensson et al. 1976; r=0.50) and recent studies (Houston et al. 1988; r = 0.31), as well as theoretical interpretations (Kroll et al. 1980), allude to the possibility that strength level per se may be more important than fiber typing for explaining individual differences in TVC. Indeed, it is counterintuitive that musle fiber-type composition alone would correlate highly with muscular strength (r>0.71, 50% common variance), unless one ignores other sources of variation that contribute to torque output, such as muscle lever arm alignment (An et al. 1981), architectural features (Wickiewicz et al. 1984), and neural regulation of muscle force (Sale 1988). Based on the above reasoning, we have re-examined concentric-eccentric segments of TVC using subjects' strength level as the independent variable. Our results show that torque output of LS individuals plateaued at low concentric velocities and the torques did not increase with increasing velocities during eccentric actions. To the contrary, TVC for the approximate 25% stronger individuals did not plateau during low-velocity concentric testing, and the eccentric torques increased with increasing velocity. These observations suggest that the TVC is sensitive to individual differences in muscular strength. We hypothesized that the shape of the TVC may be different for subjects with different strength levels and the plateauing may not be present for HS because the purported neural inhibition would be absent. However, the absence of the "tension-limiting inhibition" in HS could be substantiated only if the correlations were similar and low in HS and LS between torque output and (1) muscle architecture, (2) fiber type, or (3) muscle size. Unfortunately, data are un-
available for HS and LS to assess the influence of muscle architecture on the TVC. Other data point to the importance of strength level in lieu of fiber typing (Kroll et al. 1980). To address the third potential factor, the muscle size-torque relationship, we have regressed isometric, concentric, and eccentric torques on estimated physiological muscle cross-sectional area, muscle volume, and muscle mass in HS (n=20) and LS (n = 20) (Hortobfigyi et al. 1988). These physical dimensions explained only 20%-30% of the variance in torque output, and the correlations and regression slope coefficients were not different between HS and LS (p > 0.05). Therefore, muscle fiber type and muscle size together explain only a small proportion of variance in torque output. Thus, the flattened TVC in LS may be due to some neural inhibition, whereas the rising-patterned TVC in HS may be the result of the absence of this inhibition. What "neural factors" could be responsible for the observed patterning of the TVC in HS and LS? Is it the same mechanism that operates for the concentric and eccentric TVC segments? The answers are not known to these questions. It could be that the propinquity of concentric torques at the low velocities in LS may be associated with the inability to fully activate all motor units available due to fatigue and discomfort-related reflex inhibition (Woods et al. 1987). Perhaps an augmented inhibition from the Golgi-tendon organs may be operative. If so, it would be a different mechanism from the inability of healthy individuals to fully activate the available motor units because of inexperience with maximum effort contractions (Perrine and Edgerton 1978). Healthy individuals are capable of fully activating all muscle fibers of small and large muscle groups (Sale 1988), although Belanger and McComas (1981) reported that motor unit activation varies between muscle groups and may be incomplete. Furthermore, Wickiewicz et al. (1984) rebutted the notion that the plateauing phenomenon would be related to "activation history" and emphasized the significance of architectural features of the contributing muscles. Based on these observations, the plateauing phenomenon cannot be fully subsumed under the rubric of inhibitory neural mechanisms. To assess the role of "activation" versus "inhibition," one possible consideration for future studies could be to compare the torque outputs with and without superimposed electrical stimulation during concentric contractions in subjects with different strength level or fiber composition. In addition to the dubious role of neural inhibition in HS subjects during concentric torque production, it is possible that the greater eccentric torques with increasing velocity were due to an enhanced muscle extensibility in HS compared to LS. Although the twitchto-tetanus ratio was not measured in the present study, several investigators reported a significant decrease in this ratio following strength training that was interpreted as increased muscle extensibility (Edgerton et al. 1975). Increased muscle extensibility allows for a more efficient transfer of muscle tension to the connective tissue-tendon complex (Less et al. 1977). If so, then the
400 greater muscle extensibility coupled with a depressed inhibition from the Golgi-tendon organs may produce an increased muscle stiffness (Nichols and Houk 1976) and larger torque production. The enhancement of eccentric torques with increasing velocity for the elbow flexors and extensors of the present study agrees with prior findings for the arm flexors (Rodgers and Berger 1974) and wrist extensors (Walmsley 1986). On the other hand, our findings are at variance with those of Griffin (1987) and Asmussen et al. (1965) for the arm flexors, and Westing et al. (1988) for the knee extensors. Differences in muscle groups, methods, equipment, and subject material may explain part but not all the discrepant data.
TVC with peak versus CA T The second aspect of the present paper is the comparison of the TVCs generated with peak versus CAT. Based on the premise that the use of peak torque may confound the TVC due to incomplete tension build-up at the different velocities and muscle lengths, and oscillatory characteristics of the dynamometer, several authors used CAT versus peak torque to generate the TVC. Except for the studies by Yates and Kamon (1983), Osternig et al. (1983), and Westing et al. (1988), no previous study has explored TVCs with both peak torque and CAT. In prior studies that reported a plateaued TVC using CAT only, a hyperbolic TVC might have been obtained had the authors also used peak torque. In addition to the data displayed in Fig. 2, the findings of Yates and Kamon (1983) and Westing et al. (1988) convincingly show the differences between TVC for peak torque and CAT without a significant interaction. A priori, we assumed that strength level might help to explain the peculiar patterning of the TVC. However, there was no significant strength level x method of generating the TVC (CAT versus peak torque) interaction. Thus, the method of generating the TVC has little influence on the patterning of the TVC; the plateauing phenomenon is more likely to be associated with methodological problems than with biophysical muscle properties (Ivy et al. 1983).
Peak torque-length relationship Our results confirm the prediction that angle of peak flexion and extension torque are the same for HS and LS, and vary minimally (approx. 0.09 rad) with velocity of contraction. This was not surprising because during isokinetic actions, the angular velocity of the limb is controlled by the dynamometer. Thus, the optimal muscle length for exerting peak torque is expected to be independent of strength level or muscle fiber-composition (Ivy et al. 1981; Yates and Kamon 1983). It was somewhat unexpected that concentric and eccentric peak torque would occur at significantly different angles during flexion and extension. For flexion, for example, peak eccentric torque occurred at shorter
muscle length (1.88 rad) than concentric torque (2.12 tad). Maximum isometric flexion torque was obtained at 1.83 rad for both groups (Table 2). This pattern is similar to that reported by Singh and Karpovich (1966) who recorded peak isometric and eccentric torques at 1.75 rad (100 °) and concentric torques at 2.09 rad (120°), but offered no explanation for the difference. It is known that the muscle length-torque relationship is influenced by the muscle's lever arms (An et al. 1981) and intrinsic length-tension properties (Rack and Westbury 1969). One attractive explanation could be that while the lever arms would vary in a similar manner during concentric and eccentric motions, the intrinsic properties would change according to the nature of the contraction. Consequently, attainment for peak torque during isokinetic concentric flexion should be require longer time to achieve maximal motor unit activation. This is exactly what happened. The range of motion was 1.02 tad at similar averaged velocities during concentric actions. This was computed as follows: 3.14 rad (starting position for concentric flexion) minus 2.12 rad (angle of peak torque)--1.02 rad. Conversely, during arm flexion with eccentric resistance, the flexor muscles become stretched upon movement initiation and full activation may be achieved earlier (Hill 1970) with the facilitatory effects of short-range stiffness (Rack and Westbury 1969). Thus, the necessary change in muscle length to achieve peak torque may be less compared to concentric actions. The current results are consistent with this assumption because the required change was 0.83 rad. This was calculated as 1.88 rad (angle of peak torque) minus 1.05 rad (starting position for eccentric arm flexion) equals 0.83 rad. Thus, it is possible that peak isometric and eccentric torques occur at the optimal sarcomere overlap. In contrast, concentric torques, owing to differences in activation history and stiffness, may deve!op at a shorter muscle length (Pollack 1983). An alternative to the above scenario could be a differential role played by the antagonist muscles as predicted by the equilibrium-point theorem (Bizzi and Abend 1983). Implicit in one version of this principle is that the nervous system varies the necessary activities of the agonists and antagonists to achieve a dynamic equilibrium at a given muscle-length and lever-arm combination under zero load condition of an arm movement. However, Hasan and Enoka (1985) have recently impugned this theorem for conditions with resistance. For arm motions against resistance, they suggested that the stretch reflex could compensate for disadvantageous moment arms. In the present study, this may be true for peak eccentric torques that occurred at a shorter muscle length compared to isometric and concentric peak torques. In summary, the pattern of the TVC differed according to strength level; it plateaued for the eccentric and concentric segments for LS but not for HS subjects. It appears that the method of plotting the TVC (peak torque versus CAT) has no effect on the patterning of the TVC. It is possible that intrinsic muscle properties and neural factors both contribute to the differences in
401
angle of peak concentric and eccentric torque during arm flexion and extension. The current results illustrate the importance of strength level to explain individual differences in TVC. Acknowledgement. Supported in part by a grant from Hydra-Fitness Industries, Belton, Texas, USA.
References An KN, Morrey BF, Linscheid RL, Chao EY (1981) Muscle across the elbow joint. J Biochem 14:659-669 Asmussen E, Hansen D, Lammert O (1965) The relation between isometric and dynamic muscle strength in man. No 20 Belanger AY, McComas AJ (1981) Extent of motor unit activation during effort. J Appl Physiol 51:1131-1135 Bizzi E, Abend W (1983) Posture control and trajectory formation in single- and multi-joint arm movements. In: Desmedt JE (ed) Motor control mechanisms in health and disease. Raven Press, New York (Advances in neuroloy, vol 39, pp 31-45) Caiozzo VJ, Perrine JJ, Edgerton VR (1981) Training-induced alterations of the in vivo force-velocity relationship of human muscle. J Appl Physiol 51:750-754 Coyle EF, Feiring DC, Rotkis TC, Cote III RW, Roby FB, Lee W, Wilmore JH (1981) Specificity of power improvements through slow and fast isokinetic training. J Appl Physiol 51 : 1437-1442 Edgerton VR, Barnard RJ, Peter J, Meier A (1975) Properties of immobilized hind-limb muscles of Galago senegalensis. Exp Neurol 46:115-131 Gregor RJ, Edgerton VR, Perrine J J, Campion DS, DeBus C (1979) Torque-velocity relationship and muscle fiber composition in elite female athletes. J Appl Physiol 47:388-392 Griffin JW (1987) Differences in elbow flexion torque measured concentrically, eccentrically, and isometrically. Phys Ther 67:1205-1208 Hasan Z, Enoka RM (1985) Isometric torque-angle relationship and movement-related activity of human elbow flexors: implications for the equilibrium-point hypothesis. Exp Brain Res 49:441-450 Hill AV (1970) First and last experiments in muscle mechanics. University Press, Cambridge Hortobfigyi T, Katch FI (1988) Relation between arm muscle and physiological cross-sectional area and measures of arm muscular strength. Med Sci Sports Exerc 20:$80 Houston ME, Norman RW, Froese EA (1988) Mechanical measures during maximal velocity knee extension exercise and their relation to fiber compo'sition of the human vastus lateralis. Eur J Appl Physiol 58:1-7 Ivy JL, Withers RT, Brose G, Maxwell BD, Costill DL (1981) Isokinetic contractile properties of the quadriceps with relation to fiber type. Eur J Appl Physiol 47:247-255 Kirk RE (1982) Experimental design: procedures for the behavioral sciences. Brooks/Cole, Belmont Kroll W, Clarkson PM, Kamen G, Lambert J (1980) Muscle fiber
type composition and knee extension isometric strength fatigue patterns in power- and endurance-trained males. Res Q Exerc Sports 51:323-333 Lesmes GR, Costill DL, Coyle EF, Fink WJ (1978) Muscle strength and power changes during maximal isokinetic training. Med Sci Sports 10:266-269 Less M, Krewer SE, Eickelberg WW (1977) Exercise effects on strength and range of motion of hand intrinsic muscles and joints. Arch Phys Med Rehabil 58:370-374 Nichols TR, Houk JC (1976) Improvement in linearity and regulation of stiffness that results from actions of stretch reflex. J Neurophysiol 39:119-142 Osternig L, Hamill J, Sawhill JA, Bates BT (1983) Influence of torque and limb speed on power production in isokinetic exercise. Arch Phys Med Rehabil 62:163-171 Perrine J, Edgerton VR (1978) Muscle force-velocity and powervelocity relationships under isokinetic loading. Med Sci Sports 10:159-166 Pollack GH (1983) The cross-bridge theory. Physiol Rev 63:10491113 Rack PMH, Westbury DR (1969) The effects of length and stimulation rate on tension in the isometric cat soleus muscle. J Physiol (Lond) 204:443-460 Rodgers KL, Berger RA (1974) Motor-unit involvement and tension during maximum, voluntary concentric, eccentric, and isometric contractions of the elbow flexors. Med Sci Sports 6:253-259 Sale DG (1988) Neural adaptation to resistance training. Med Sci Sports Exerc 20:S135-S145 Singh M, Karpovich PV (1966) Isotonic and isometric forces of forearm flexors and extensors. J Appl Physiol 21:1435-1437 Thorstensson A, Grimby G, Karlsson J (1976) Force-velocity relations and fiber composition in human knee extensor muscles. J Appl Physiol 40; 12-16 Tihanyi J, Apor P, Fekete Gy (1982) Force-velocity-power characteristics and fiber composition in human knee extensor muscles. Eur J Appl Physiol 48:331-343 Walmsley RP (1986) Eccentric wrist contractions and the force velocity relationship in muscle. J Orthop Sports Phys Ther 8:288-293 Westing SH, Seger JY, Karlson E, Ekblom B (1988) Eccentric and concentric torque-velocity characteristics of the quadriceps femoris in man. Eur J Appl Physiol 58:100-104 Wickiewicz TL, Roy RR, Powell PL, Perrine JJ, Edgerton VR (1984) Muscle architecture and force-velocity relationships in humans. J Appl Physiol 57:435-443 Wilkie DR (1950) The relation between force and velocity in human muscle. J Physiol (Lond) 110:249-280 Wilmore J, Behnke AR (1969) Anthropometric estimation of body density and lean body weight in young males. J Appl Physiol 27:25-31 Woods JJ, Furbush F, Bigland-Ritchie B (1978) Evidence for a fatigue-induced reflex inhibition of motoneuron firing rates. J Neurophysiol 58:125-137 Yates JW, Kamon E (1983) A comparison of peak and constant angle torque-velocity curves in fast and slow-twitch populations. Eur J Appl Physiol 51:67-74
.uo.e,°A p p l i e d Physiology Journal o f
and Occupational Physiology @ Springer-Verlag 1990
Eccentric and concentric torque-velocity relationships during arm flexion and extension Influence of strength level T i b o r H o r t o b ~ g y i and F r a n k I. K a t c h
University of Massachusetts, Department of Exercise Science, Amherst, MA 01003, USA Accepted January 17, 1990 Summary. Forty men were tested with a computerized dynamometer for concentric and eccentric torques during arm flexion and extension at 0.52, 1.57, and 2.09 rad.s-1. Based on the summed concentric and eccentric torque scores, subjects were placed into a high strength (HS) or low strength (LS) group. The eccentric and concentric segments of the torque-velocity curves (TVCs) were generated using peak torque and constantangle torque (CAT) at 1.57 and 2.36 rad. Angle of peak torque was also recorded. Compared to LS, HS had significantly greater estimated lean body mass (+ 10.2 kg) and approximately 25% greater average torque output. Reliability of the peak torque scores on 2 days in 20 subjects was r_0.85. The difference between observed torques and the mathematically computed criterion torque scores averaged 1% for three validation loads that ranged from 11.4 to 90.4 kg. Statistical analysis revealed that torque output in LS plateaued at low concentric velocities and was also flattened with increasing eccentric velocities. Conversely, torque ouptput for HS increased with decreasing concentric velocities and increased with increasing eccentric velocities. The method of plotting the TVCs for peak or CAT did not influence the pattern of TVC. Eccentric flexion peak torque occurred at a significantly shorter muscle length (1.88 rad) than concentric torque (2.12 tad). This difference was also present for extension; it was 1.88 rad for eccentric and 2.03 rad for concentric torque. These findings are discussed in terms of study design, neural inhibition, activation history, muscle-tendon elasticity, muscle fiber types, muscle architecture, and methodological considerations. The present results illustrate the importance of strength level to explain individual differences in TVC. Key words: Muscle strength - Torque-velocity curve M u s c l e elasticity - Neural factors - Dynamometry
Introduction
An understanding of human skeletal muscle function Offprint requests to: F. I. Katch
relies on findings from denervated and isolated preparations (Rack and Westbury 1969; Hill 1970). Accumulating evidence suggests that mechanical properties of intact human muscles in most but not all aspects resemble those of animal preparations (e.g. Wilkie 1950). One disputed feature is the shape of the force- (or in humans) torque-velocity curve (TVC), particularly at the low velocity end. In animal models, muscular forces were found to increase with decreasing contraction velocity. Many researchers have successfully reproduced this hyperbolic TVC in various human muscles (Wilkie 1950; Thorstensson et al. 1976; Lesmes et al. 1978; Coyle et al. 1981; Ivy et al. 1981; Tihanyi et al. 1982; Griffin 1987). However, other investigators report a plateauing of torques at low velocities (Rodgers and Berger 1974; Perrine and Edgerton 1978; Gregor et al. 1979; Caiozzo et al. 1981). These differences in the TVC appear to be related to two factors; tension-restricting neural inhibition of the human subjects or the method of assessing TVC. There are several problems with these two factors to explain the discrepant data on the TVC pattern. First, direct neurophysiolog~cal evidence has yet to be presented to pinpoint the source of the tension-limiting mechanism. Perhaps neural inhibition is a ubiquitous feature of untrained subjects in the studies that observed flattened TVC and used constant-angle torque (CAT) to generate the TVC. Second, studies reporting TVC with a plateau used only CAT to plot TVC, but did not report TVC wkh peak torque (e.g. Perrine and Edgerton 1978). Thus, it is impossible to tell whether the differences in the shape of the TVC would have been present. Indeed, there are only two studies that directly compared the TVCs generated by peak torque and CAT. Yates and Kamon (1983) explored the influence of muscle fiber composition on the TVCs plotted with peak and CAT. These authors concluded that the method of plotting the TVC and fiber typing had little influence on the TVC pattern. In contrast, Osternig et al. (1983) examined the TVC at six CATs and with peak torque in ten males. The differences in the TVCs were substantial; with CAT, the TVCs were flattend across
the entire velocity spectrum, whereas with peak torque, TVC was hyperbolic. The results from these studies are incongruous. It is still unclear whether the plateauing is the result of some neural inhibition, or an intrinsic property of the human skeletal muscle assessed in vivo. Finally, the shape of the eccentric segment of the TVC has not been compared using peak torque and CAT in various subject populations. One outcome could be that the tension-limiting mechanism is absent in individuals with higher absolute strength. Thus, the eccentric and concentric TVC would be different in subjects with lower strength. Such an approach may help to clarify whether the flattened TVC is influenced by strength level. Indeed, one study has suggested that strength level may be a more important classification variable than body size or fiber-type composition (Kroll et al. 1980). The purpose of the present study was threefold: (1) to compare the pattern of the eccentric and concentric TVC in high strength (HS) and low strength (LS) subjects, (2) to assess the influence of peak torque and CAT on the shape of the TVC, and (3) to compare the angle of peak torque in HS and LS individuals during concentric and eccentric contractions. Methods Subjects. Forty men participated as subjects and signed an informed consent before testing. Their physical characteristics appear in Table 1. Subjects were classified as HS or LS according to strength level. Subjects were placed into HS and LS groups based on the cumulative torque scores obtained during concentric and eccentric actions at 0.52, 1.57, and 2.09 rad.s-'. Twelve HS subjects were university college athletes in football, baseball, or rugby, and had participated in systematic strength training at least three times a week for 6 years or more. The remaining eight HS subjects were recreational weight lifters who had trained approximately three times a week for less than 2 years. In the LS group, six subjects were non-competitive runners, and 14 pursued recreational activities other than weight lifting.
specific regression equation (Wilmore and Behnke 1969) shown in the footnote of Table 1. Equipment and procedures. Subjects were tested for arm flexion and extension strength using the Biodex dynamometer (Shirley, NY). The 550 W DC servomotor is interfaced with four strain gauges located at the output shafts of the powerhead. Three A/D channels provide simultaneous conversion of real-time data signals for torque, velocity, and position. The three parallel A/D input channels have the capacity of 10-bit A/D conversion in 35 ps. After signal conditioning and data transfer to a microcomputer, the data were stored on floppy disks for subsequent analysis. Subjects were seated, and straps were secured around the upper arm, waist, and shoulders to provide a stable position. The dominant upper arm was positioned on a padded support. The axis of the elbow joint was aligned with the axis of the measuring shaft, and the seat and lever arm settings were set to conform to the individuals' body size. During the arm flexion and extension movements, subjects grasped a plastic handle on the lever arm in a neutral anatomical position (Fig. 1). A balanced order test protocol was used to assess isokinetic concentric and eccentric torque for arm flexion and extension. During concentric actions, subjects performed maximum arm flexion and extension at a preset velocity. For eccentric actions, the lever arm moved at the preset velocity when an initial resistance was applied to the exercise bar. For example, eccentric tests of the biceps started in a fully flexed arm position. The motor driven lever arm was cued by the subject to begin flexion against the resistance of the volitionally contracting but lengthening biceps. Before testing, subjects warmed-up for each testing mode with two submaximal and one maximal contraction. The tests included two maximal flexion/extension cycles at each testing velocity of 0.52, 1.57, and 2.09 rad.s-' (or 30, 90, and 120"s -I). There was a 3-s pause between flexion and extension and 1-min rest between speed conditions. The criterion score was peak torque corrected for gravity. Torque-velocity curves. The TVC was plotted using three different measures of torque. Each individual torque-position curve was digitized for (1) peak torque, (2) CAT at 1.57 rad, and (3) CAT at 2.36 rad. Thus, TVCs were established using peak torque, CAT 1.57 rad, and CAT 2.36 rad for concentric and eccentric flexion and extension at 0.52, 1.57, and 2.09 rad.s-'. The angles of 1.57 and 2.36 rad were selected to plot TVC at CAT because eccentric, isometric, and concentric peak torques occurred approximately midway between these two angles. In addition to peak torque, the corresponding angle of peak torque was also recorded (3.14 rad = arm straight).
Anthropometry. Body mass was measured to an accuracy of +25 g on a beam balance, and stature was measured on a portable stadiometer to f 0.01 m. Lean body mass was estimated from an age-
Table 1. Physical characteristics of subjects High strength (n = 20)
Low strength (n = 20)
Variable
Mean
SE
Mean
SE
Age (years) Body mass (kg) Stature (m) LBM (kg)" Fat (%)
23.1 90.9 1.78 75.7 16.7
3.28 16.73 0.07 11.42 4.65
22.6 76.6 1.78 65.6 14.5
5.01 11.50* 0.09 8.71* 5.02
" L e a n body mass calculated from the equation, LBM = 44.636 + 1.08717 x body mass - 0.7396 x abdomen girth (Wilmore and Behnke 1969) * Significant difference between groups (p 0.05). I n contrast, c o n c e n t r i c t o r q u e s at 2.09 r a d . s - 1 were s i g n i f i c a n t l y (p < 0.05) l o w e r t h a n t o r q u e s at 0.52 r a d . s -1 d u r i n g f l e x i o n ( - 1 1 . 9 N m ) a n d e x t e n s i o n ( - 6 N m) in H S b u t n o t in LS ( - 2 . 2 N m for f l e x i o n a n d - 5 N m f o r e x t e n s i o n , p > 0.05). T h e 10.1 N m d i f f e r e n c e b e t w e e n s p e e d s 0.52 r a d . s -1 a n d 1.57 r a d - s - 1 was also s i g n i f i c a n t d u r i n g e x t e n s i o n in H S (p < 0.05). Figure 2 illustrates the second relevant three-way i n t e r a c t i o n , i.e. m e t h o d x c o n t r a c t i o n t y p e x s p e e d . D a t a in Fig. 2 are t h e m e a n s p o o l e d a c r o s s g r o u p s . P o s t - h o c analysis showed that TVC with peak torques and CAT
398 Flexion
Table 3. C o m p a r i s o n o f angle o f peak eccentric and concentric torques at three velocities during arm extension and flexion in high strength (n = 20) and low strength (n = 20) groups. Values are in radians (3.14 r a d = a r m straight)
100
= Z
Velocity (rad. s- 1)
80
60 ¢.
[
40
-2.4
-1.6
1
I
-0.8
0.0
I
I
f
0.8
1.6
2.4
Extension 110
_= Z
"~
9O
70
50 -2.4
I
t
I
[
I
-1.6
-0.8
0.0
0.8
1.6
r 2.4
Flexion Eccentric" 0.52 1.57 2.09 Concentric 0.52 1.57 2.09 Extension Eccentric b 0.52 1.57 2.09 Concentric 0.52 1.57 2.09
High strength
Low strength
Mean
+ SE
Mean
4- SE
1.85 1.84 1.87
0.043 0.032 0.034
1.83 1.94 1.96
0.044 0.042 0.051
2.11 2.04 2.14
0.044 0.039 0.047
2.14 2.17 2.12
0.057 0.053 0.047
1.91 1.85 1.79
0.088 0.053 0.066
1.99 1.89 1.86
0.070 0.051 0.043
1.94 2.02 2.10
0.054 0.050 0.057
1.97 2.09 2.04
0.077 0.073 0.084
a Angle of eccentric peak flexion torque significantly less than concentric (p < 0.05) but not different between groups and speeds (p>0.05) u Angle of eccentric peak extension torque significant greater than concentric (p < 0.05) but not different between groups and speeds (p > 0.05)
Velocity, r a d . s -1 Fig. 2. C o m p a r i s o n o f torque-velocity curves o b t a i n e d for a r m flexion a n d extension using peak t o r q u e a n d c o n s t a n t angle torq u e (CAT) at 1.57 rad a n d 2.36 rad. N o t e : M e a n s ± S E p o o l e d across groups. - - © - - = Peak t o r q u e ; - - • - - = C A T 90 ° ; - - 0 - = C A T 135 °
at 1.57 or 2.36 r a d . s -1 were significantly different at every speed (p 0.05), but the type of contraction main effect was significant (p < 0.05); eccentric p e a k flexion torque occurred at a significantly (p < 0.05) shorter muscle length (1.88 rad) than concentric p e a k flexion torque (2.12 rad). For extension, there was no significant three-way interaction (t7>0.05), but the type of contraction x speed interaction was significant (p < 0.05); p e a k extension eccentric torque at 2.09 rad. s - 1 occurred at a
Torque-velocity relationship In the present study, we found that: (1) the pattern of the TVC differs by strength level (HS vs LS); (2) the pattern of the TVC is independent of the method of using p e a k torque versus CAT, and (3) there are differences in the angle of p e a k torque between contraction types (eccentric vs concentric). M a n y prior studies have shown that, unlike the force-velocity curve in isolated frog sartorius muscle (Hill 1970), the TVC plateaus at low concentric velocities when secured on an isokinetic d y n a m o m e t e r (Per-
399 rine and Edgerton 1978; Osternig et al. 1983). Some researchers asserted that neural inhibition prevented the subjects from exerting maximum knee extension torque during low-velocity concentric actions. However, direct neurophysiological evidence has not yet been presented to relate the flattened shape of the TVC to neural inhibition. Further, the results for the use of CAT versus peak torque as an alternative to derive the TVC are also in conflict (see below). Thus, the issue of neural inhibition remains unresolved. The conflict is underscored by the numerous studies that confirm the resemblance of TVC between isolated preparations and intact human muscle (e.g. Tihanyi et al. 1982). Inadequate study design may be one reason for the conflicting data from previous investigations. For example, the pattern of the TVC has been scrutinized only for a single group of healthy untrained subjects (Perrine and Edgerton 1978), for moderately trained subjects (Westing et al. 1988), or for groups with a predominance of slow-twitch or fast-twitch muscle fibers whose training status was not evaluated (Gregor et al. 1979; Yates and Kamon 1983). Subjects with a preponderance of fast-twitch fibers had larger differences in torque at high but not at low velocity (Gregor et al. 1979; Coyle et al. 1981). Thus, plateauing of torques at low velocities may be independent of fiber type. The low correlations between muscular strength and/or unloaded movement velocity and percentage of fasttwitch fibers in previous (Thorstensson et al. 1976; r=0.50) and recent studies (Houston et al. 1988; r = 0.31), as well as theoretical interpretations (Kroll et al. 1980), allude to the possibility that strength level per se may be more important than fiber typing for explaining individual differences in TVC. Indeed, it is counterintuitive that musle fiber-type composition alone would correlate highly with muscular strength (r>0.71, 50% common variance), unless one ignores other sources of variation that contribute to torque output, such as muscle lever arm alignment (An et al. 1981), architectural features (Wickiewicz et al. 1984), and neural regulation of muscle force (Sale 1988). Based on the above reasoning, we have re-examined concentric-eccentric segments of TVC using subjects' strength level as the independent variable. Our results show that torque output of LS individuals plateaued at low concentric velocities and the torques did not increase with increasing velocities during eccentric actions. To the contrary, TVC for the approximate 25% stronger individuals did not plateau during low-velocity concentric testing, and the eccentric torques increased with increasing velocity. These observations suggest that the TVC is sensitive to individual differences in muscular strength. We hypothesized that the shape of the TVC may be different for subjects with different strength levels and the plateauing may not be present for HS because the purported neural inhibition would be absent. However, the absence of the "tension-limiting inhibition" in HS could be substantiated only if the correlations were similar and low in HS and LS between torque output and (1) muscle architecture, (2) fiber type, or (3) muscle size. Unfortunately, data are un-
available for HS and LS to assess the influence of muscle architecture on the TVC. Other data point to the importance of strength level in lieu of fiber typing (Kroll et al. 1980). To address the third potential factor, the muscle size-torque relationship, we have regressed isometric, concentric, and eccentric torques on estimated physiological muscle cross-sectional area, muscle volume, and muscle mass in HS (n=20) and LS (n = 20) (Hortobfigyi et al. 1988). These physical dimensions explained only 20%-30% of the variance in torque output, and the correlations and regression slope coefficients were not different between HS and LS (p > 0.05). Therefore, muscle fiber type and muscle size together explain only a small proportion of variance in torque output. Thus, the flattened TVC in LS may be due to some neural inhibition, whereas the rising-patterned TVC in HS may be the result of the absence of this inhibition. What "neural factors" could be responsible for the observed patterning of the TVC in HS and LS? Is it the same mechanism that operates for the concentric and eccentric TVC segments? The answers are not known to these questions. It could be that the propinquity of concentric torques at the low velocities in LS may be associated with the inability to fully activate all motor units available due to fatigue and discomfort-related reflex inhibition (Woods et al. 1987). Perhaps an augmented inhibition from the Golgi-tendon organs may be operative. If so, it would be a different mechanism from the inability of healthy individuals to fully activate the available motor units because of inexperience with maximum effort contractions (Perrine and Edgerton 1978). Healthy individuals are capable of fully activating all muscle fibers of small and large muscle groups (Sale 1988), although Belanger and McComas (1981) reported that motor unit activation varies between muscle groups and may be incomplete. Furthermore, Wickiewicz et al. (1984) rebutted the notion that the plateauing phenomenon would be related to "activation history" and emphasized the significance of architectural features of the contributing muscles. Based on these observations, the plateauing phenomenon cannot be fully subsumed under the rubric of inhibitory neural mechanisms. To assess the role of "activation" versus "inhibition," one possible consideration for future studies could be to compare the torque outputs with and without superimposed electrical stimulation during concentric contractions in subjects with different strength level or fiber composition. In addition to the dubious role of neural inhibition in HS subjects during concentric torque production, it is possible that the greater eccentric torques with increasing velocity were due to an enhanced muscle extensibility in HS compared to LS. Although the twitchto-tetanus ratio was not measured in the present study, several investigators reported a significant decrease in this ratio following strength training that was interpreted as increased muscle extensibility (Edgerton et al. 1975). Increased muscle extensibility allows for a more efficient transfer of muscle tension to the connective tissue-tendon complex (Less et al. 1977). If so, then the
400 greater muscle extensibility coupled with a depressed inhibition from the Golgi-tendon organs may produce an increased muscle stiffness (Nichols and Houk 1976) and larger torque production. The enhancement of eccentric torques with increasing velocity for the elbow flexors and extensors of the present study agrees with prior findings for the arm flexors (Rodgers and Berger 1974) and wrist extensors (Walmsley 1986). On the other hand, our findings are at variance with those of Griffin (1987) and Asmussen et al. (1965) for the arm flexors, and Westing et al. (1988) for the knee extensors. Differences in muscle groups, methods, equipment, and subject material may explain part but not all the discrepant data.
TVC with peak versus CA T The second aspect of the present paper is the comparison of the TVCs generated with peak versus CAT. Based on the premise that the use of peak torque may confound the TVC due to incomplete tension build-up at the different velocities and muscle lengths, and oscillatory characteristics of the dynamometer, several authors used CAT versus peak torque to generate the TVC. Except for the studies by Yates and Kamon (1983), Osternig et al. (1983), and Westing et al. (1988), no previous study has explored TVCs with both peak torque and CAT. In prior studies that reported a plateaued TVC using CAT only, a hyperbolic TVC might have been obtained had the authors also used peak torque. In addition to the data displayed in Fig. 2, the findings of Yates and Kamon (1983) and Westing et al. (1988) convincingly show the differences between TVC for peak torque and CAT without a significant interaction. A priori, we assumed that strength level might help to explain the peculiar patterning of the TVC. However, there was no significant strength level x method of generating the TVC (CAT versus peak torque) interaction. Thus, the method of generating the TVC has little influence on the patterning of the TVC; the plateauing phenomenon is more likely to be associated with methodological problems than with biophysical muscle properties (Ivy et al. 1983).
Peak torque-length relationship Our results confirm the prediction that angle of peak flexion and extension torque are the same for HS and LS, and vary minimally (approx. 0.09 rad) with velocity of contraction. This was not surprising because during isokinetic actions, the angular velocity of the limb is controlled by the dynamometer. Thus, the optimal muscle length for exerting peak torque is expected to be independent of strength level or muscle fiber-composition (Ivy et al. 1981; Yates and Kamon 1983). It was somewhat unexpected that concentric and eccentric peak torque would occur at significantly different angles during flexion and extension. For flexion, for example, peak eccentric torque occurred at shorter
muscle length (1.88 rad) than concentric torque (2.12 tad). Maximum isometric flexion torque was obtained at 1.83 rad for both groups (Table 2). This pattern is similar to that reported by Singh and Karpovich (1966) who recorded peak isometric and eccentric torques at 1.75 rad (100 °) and concentric torques at 2.09 rad (120°), but offered no explanation for the difference. It is known that the muscle length-torque relationship is influenced by the muscle's lever arms (An et al. 1981) and intrinsic length-tension properties (Rack and Westbury 1969). One attractive explanation could be that while the lever arms would vary in a similar manner during concentric and eccentric motions, the intrinsic properties would change according to the nature of the contraction. Consequently, attainment for peak torque during isokinetic concentric flexion should be require longer time to achieve maximal motor unit activation. This is exactly what happened. The range of motion was 1.02 tad at similar averaged velocities during concentric actions. This was computed as follows: 3.14 rad (starting position for concentric flexion) minus 2.12 rad (angle of peak torque)--1.02 rad. Conversely, during arm flexion with eccentric resistance, the flexor muscles become stretched upon movement initiation and full activation may be achieved earlier (Hill 1970) with the facilitatory effects of short-range stiffness (Rack and Westbury 1969). Thus, the necessary change in muscle length to achieve peak torque may be less compared to concentric actions. The current results are consistent with this assumption because the required change was 0.83 rad. This was calculated as 1.88 rad (angle of peak torque) minus 1.05 rad (starting position for eccentric arm flexion) equals 0.83 rad. Thus, it is possible that peak isometric and eccentric torques occur at the optimal sarcomere overlap. In contrast, concentric torques, owing to differences in activation history and stiffness, may deve!op at a shorter muscle length (Pollack 1983). An alternative to the above scenario could be a differential role played by the antagonist muscles as predicted by the equilibrium-point theorem (Bizzi and Abend 1983). Implicit in one version of this principle is that the nervous system varies the necessary activities of the agonists and antagonists to achieve a dynamic equilibrium at a given muscle-length and lever-arm combination under zero load condition of an arm movement. However, Hasan and Enoka (1985) have recently impugned this theorem for conditions with resistance. For arm motions against resistance, they suggested that the stretch reflex could compensate for disadvantageous moment arms. In the present study, this may be true for peak eccentric torques that occurred at a shorter muscle length compared to isometric and concentric peak torques. In summary, the pattern of the TVC differed according to strength level; it plateaued for the eccentric and concentric segments for LS but not for HS subjects. It appears that the method of plotting the TVC (peak torque versus CAT) has no effect on the patterning of the TVC. It is possible that intrinsic muscle properties and neural factors both contribute to the differences in
401
angle of peak concentric and eccentric torque during arm flexion and extension. The current results illustrate the importance of strength level to explain individual differences in TVC. Acknowledgement. Supported in part by a grant from Hydra-Fitness Industries, Belton, Texas, USA.
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