CYCLIC ANALOG TO FORCE?
The cycling data, previously presented, demonstrate that power is a function of cyclic velocity. When considering various aspects of muscular performance, it is often useful to know force and power. What might be the cyclic analog to the traditional force-velocity relation? To address this question, consider that power is the product of force and velocity. Consequently, traditional force-velocity relations can be determined from power-velocity data simply by dividing power by velocity. Dividing power (Nm·s−1) by cyclic velocity (Hz × m·s−1) produces a value in units of N × s, which is mechanical impulse. Impulse represents the integral of force over time and thus accounts for force and the period over which that force acts. Therefore, impulse may be an appropriate term for describing neuromuscular function during time-dependent actions. Impulse-velocity relations during maximal cycling are shown in Figure 9.
Impulse decreased with pedaling frequency (Fig. 9A), and the relations were separated such that cyclists produced greater impulses on shorter cranks for any specific pedaling frequency. The overall decreasing relations reflect the effects of pedaling frequency, which determines excitation-relaxation for all crank lengths, velocity for each length, and the time over which force was produced. The separation of those relations reflects differences due to force-velocity effects. Impulse also decreased with pedal speed (Fig. 9B), and relations were separated such that impulse was greater with longer cranks for any specific pedal speed. That separation was likely because of excitation-relaxation kinetics associated with pedaling frequency. Impulse for all the crank lengths tended to converge to one curve when plotted against cyclic velocity (Fig. 9C), with the exception that the relation for the shortest length (120 mm) differed significantly from the others. Even with that difference, data for all five crank lengths were well represented by a single Hill-type equation (r2 > 0.997) for each individual. The convergence of these relations suggests that "cyclic velocity" accounts for muscle shortening velocity and excitation-relaxation kinetics and thus constrains power and impulse for a broad spectrum of conditions. These data provide compelling evidence that impulse and power are governed by the interaction of cycle frequency and shortening velocity. However, one could argue that they might represent some nuance of voluntary motor control or biomechanics during cycling rather than intrinsic neuromuscular function.
To determine if our cycling results were truly representative of intrinsic neuromuscular function, we (12) made use of work-loop data published by Swoap et al. (18). Specifically, we calculated impulse, power, shortening velocity, and cyclic velocity from the data they reported (Fig. 10). Similar to our cycling data, impulse calculated from their work-loop data decreased with increasing cycle frequency but was separated such that impulse was greater for smaller excursions (Fig. 10A). Impulse also decreased with increasing shortening velocity but was separated such that impulse for any specific velocity was greater for longer excursions (Fig. 10B). Finally, impulse for all the excursion lengths, except the smallest, decreased similarly with increasing cyclic velocity (Fig. 10C). Data from the smallest excursion length were clearly different from all the other data (similar to our human cycling data), possibly because of reduced history-dependent effects or tendon compliance (8). Data for all excursion lengths except the smallest were well represented by a single Hill-type equation (r2 > 0.987). These relations from isolated muscle demonstrate that similar relations produced during maximal cycling are representative of basic neuromuscular function and are not an artifact of coordination or biomechanical constraints.
EXCEPTIONS TO THE RULE
Impulse-cyclic velocity relations from work loops and maximal cycling exhibited similar convergence and a similar exception to that convergence. For both models, the shortest excursion (1-mm excursion for the work loops and the 120-mm cranks for cycling) deviated from the other data. The reason for those exceptions remains unknown; however, two explanations seem plausible. First, the small excursions may have been too small to activate history-dependent effects that are known to increase excitation and relaxation rates (3). In that case, cycle frequency would reduce force to a greater extent at these small excursions. Alternatively, impulse and power during the smallest excursions may be greatly influenced by tendon compliance. Specifically, muscles may initially shorten faster than the muscle-tendon unit until the passive force in the tendon reaches equilibrium with the active muscle force. During small excursions, this equilibration process may occupy most or all of the shortening phase. Consequently, muscle force may be reduced because of increased shortening velocity of the muscle fibers relative to the velocity of the muscle-tendon unit.
The relations between power, impulse, and cyclic velocity may be useful in a number of applications. First, these data suggest that maximal power occurs at a unique cyclic velocity but not at a unique shortening velocity. For cycling, the optimal cyclic velocity for all crank lengths was 3.8 ± 0.1 H × m·s−1 (15). When attempting to maximize power, cycle frequency and shortening velocity must always be considered interactively rather than individually, and the optimal frequency or velocity for a novel crank length can be easily calculated. Furthermore, the relations of impulse and power with cyclic velocity for one excursion length can be used to predict performance for other excursion lengths. This predictive capacity can reduce the need for testing numerous excursion lengths and therefore simplify experimental designs.
Although these relations, demonstrated in healthy nonfatigued humans and animal preparations, are quite convergent, some conditions may arise in which relations for different excursion lengths do not converge. Any condition that alters the force-velocity relation to a greater or lesser extent than it alters excitation-relaxation kinetics could produce nonconvergent relations. If a disease, injury, or fatigue condition altered excitation-relaxation kinetics (e.g., excitation-contraction coupling or calcium ATPase function) to a greater extent than it reduced velocity-dependent force, impulse and power would be improved with greater excursion lengths. This improvement would occur because any specific cyclic velocity arises from a combination of shortening velocity and cycle frequency. Movements with greater excursion will produce a given cyclic velocity with more shortening velocity and less cycle frequency. Consequently, the effects of excitation-relaxation will be reduced. In contrast, any condition that negatively influenced force-velocity characteristics (e.g., myosin ATPase) would produce less impulse and power for any specific cyclic velocity with greater excursion lengths. In either of these cases, analyzing the degree to which power and impulse did not converge could help to explain the extent to which the excitation-relaxation kinetics differed from normal. These analyses would be more specific to a dynamic task than isometric measures such as time to peak tension or half relaxation time or traditional force-velocity relations.
MAXIMAL POWER: WORK LOOPS VERSUS CYCLING
The characteristically similar relations produced during in situ muscle work loops and voluntary maximal cycling suggest that cycling is well represented by work loops. However, the magnitude of those relations was quite different, likely reflecting differences in muscle mass, fiber type, and possibly single muscle versus multi-muscle and multi-joint activity. In an effort to determine just how similar power during cycling and work loops might be, I extracted data from a previous article in which my colleagues and I (13) reported maximal cycling power and muscle volumes determined by magnetic resonance imagery. Normalized power of the 16 subjects, who were younger than 50 yr (the range in which age did not influence normalized power), was 84 ± 3 W·L−1 or 79 ± 3 W·kg−1, assuming a density of 1.06 kg·L−1. Although we did not determine muscle fiber type distribution in those individuals, it may be reasonable to assume approximately 50% Types I and II fibers. Comparison of power output with work-loop power is problematic because most of the muscles studied using work loops were predominantly composed of a single fiber type (18). One way to form a direct comparison is to average power output from a mostly Type I and a mostly Type II muscle. Data reported by Swoap et al. (18) indicated that rat plantaris (4% Type I) and soleus (95% Type I) produced maximal power outputs of 144 W·kg−1 and 26 W·kg−1, respectively. The arithmetic average of those two values suggests that maximal power for a muscle with a fiber type distribution of 50/50 might be approximately 85 W·kg−1. However, the optimal velocities for plantaris and soleus differ, and an intermediate velocity would be required for maximal power of a mixed muscle. Data for 4-Hz cycling (the smallest used for plantaris and the greatest used for soleus) suggest that a maximal average power of 77 W·kg−1 would occur at a strain of 4 mm (shortening velocity of 32 mm·s−1 or a cyclic velocity of 128 Hz × mm·s−1). These human cycling and in situ work-loop power data, 79 and 77 W·kg−1, respectively, are remarkably similar and, although anecdotal, provide additional support for the applicability of work loops to maximal voluntary human activity.
As a final example of the similarity of maximal cycling and work loops, two groups have reported that increasing the portion of the movement cycle spent shortening increases maximal power. Askew and Marsh (2) reported that power of mouse soleus was 40% greater when the muscle shortened for 75% of the cycle time and lengthened for 25% compared with shortening and lengthening for 50% each. My colleagues and I (14) performed a similar experiment using a maximal cycling model and reported a 4% increase in average power and an 8% increase in instantaneous power when the leg extended for 58% of the cycle. Although our increases in power were smaller than those reported by Askew and Marsh (2), so was our perturbation in pedal trajectory. The perturbation we could impose in that study was limited by our ability to control chain tension on the ergometer. We have since developed techniques that allow greater perturbations in pedal trajectory and have observed that a 70% duty cycle increased power during leg extension by 44%.
Muscular power and impulse during work-producing actions are interactively constrained by cycle frequency and average muscle shortening velocity. Cycle frequency constrains muscular function via excitation-relaxation kinetics, whereas average shortening velocity represents force-velocity properties. These two factors constrain muscular impulse and power across a very wide range of frequencies and velocities, including low frequencies where excitation-relaxation might not be expected to exert a substantial effect. The interaction of shortening velocity and cycle frequency failed to account for muscular impulse and power at very small excursions, and this may be caused by a lack of history-dependent effects or tendon compliance. Finally, maximal cycling and isolated muscle work loops produce characteristically and quantitatively similar results, suggesting that cycling may serve as a window through which basic neuromuscular function can be observed.
The author thanks his coauthors on the previous manuscripts that formed the basis for this review: Clay Anderson, Nick Brown, Rodger Farrar, Scott Lamb, Waneen Spirduso, and Bruce Wagner. The author also thanks Andy Coggan, Chris Davidson, Steve Elmer, Roger Enoka, Scott Gardner, John McDaniel, Barry Shultz, and Missy Thompson for their help and feedback during the preparation of this manuscript and several others who contributed in various ways: Vince Caiozzo, Greg Clark, Walter Herzog, Rodger Kram, John Mattson, Richard Normann, Steve Swoap, and Doug Syme.
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Keywords:© 2007 American College of Sports Medicine
muscular power; force-velocity; cyclic velocity; excitation; relaxation