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Many human movements are characterized by the continual repetition of a fundamental pattern of motion (e.g. walking, running, hopping, cycling,.
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Introduction
Many human movements are characterized by the continual repetition of a fundamental pattern of motion (e.g. walking, running, hopping, cycling, swimming, rowing). For cyclic activities, the aver- age speed of progression is defined by the product of the average distance travelled per cycle of motion (e.g. running stride length) and the average rate or cadence at which the cycle of motion is being repeated (e.g. running stride rate or cadence). In normal human movements, these speed, distance and cadence factors are usually freely determined or self-selected by the performer and are rarely fixed or pre-established. In addition, humans have an incredible ability to intentionally alter speed, dis- tance and cadence to meet the demands of the envi- ronment. As an example, Nilsson and Thorstensson (1987) observed that over a normal range of walking speeds (1.0–3.0 m · s–1^ ), subjects were able to walk with a lowest possible stride rate of 25 strides · min–1^ at the lowest speed and a highest possible rate of 143 strides · min–1^ at all speeds. Within a range of running speeds (1.5–8 m · s–1^ ), subjects could run with rates as low as 33 strides · min–1^ to as high as 214 strides · min–1. Given this ability to alter cycle cadence and distance factors, how is the preferred cadence chosen, and how does it relate to different optimality criteria? The mechanisms that underlie the selection process leading to a particular cadence- distance combination chosen by a performer for a given activity at a given speed are not clear, although numerous factors have been considered.
While much information has been gained about the neurophysiology of rhythmic movements, especially in lower vertebrates and invertebrates, relatively little attention has been directed to under- standing how cycle distance and cadence are deter- mined and controlled by the neuromusculoskeletal system in humans. Nevertheless, it is useful to gain some understanding of how cycle distance and cadence are related, even though available evidence applies primarily to walking. Laurent and Pailhous (1986) had subjects walk overground while impos- ing only stride rate or stride length by means of auditory or visual cues and allowing all other gait parameters to vary freely. Results revealed that when one parameter (e.g. stride rate) was steadily increased the other parameter (i.e. stride length) remained almost constant despite the lack of con- straint imposed on all other parameters. Moreover, Laurent and Pailhous found that stride rate and length were each strongly correlated with speed, but were relatively independent of each other. The authors proposed that speed, not rate or length, is the critical parameter around which locomotion is organized. Indeed, Diedrich and Warren (1995) found that subjects make the transition from a walk to a run at a critical speed (2.2 m · s–1), rather than at a critical stride rate or length, when rate and length are experimentally manipulated. Even if speed is the parameter around which locomotion is ultim- ately organized, the flexibility with which stride rate and length can be altered implies that the central nervous system (CNS) must have mechanisms for actively controlling these variables.
143
Chapter 7
Factors Affecting Preferred Rates of Movement
in Cyclic Activities
in aerobic demand (Holt et al. 1991, 1995; Hreljac & Martin 1993). Self-selected cadence and stride length for most individuals usually do not deviate substantially from those that minimize energy cost at a given speed of walking or running. Morgan et al. (1994) found that only 20% of a pool of 45 recreational runners reflected a stride length that deviated by more than a few centimetres (5% of leg length) from the most economical stride length and showed a difference in aerobic demand be- tween preferred and most economical conditions that was greater than 0.5 ml · kg–1^ · min –1. These results provide convincing evidence that most individuals self-optimize walking and running cadences, and suggest that minimizing energy cost may be an important factor contributing to cadence determination. Similar responses of energy cost or aerobic demand to cadence changes have been shown for
other activities as well. Seven competitive racewalk- ers were most economical at their preferred stride rate/stride length combinations and displayed progressively higher energy costs as cadence was either increased or decreased from the preferred rate (Morgan & Martin 1986). In addition, van der Woude et al. (1989) studied the effect of cadences ranging from 60 to 140% of preferred cadence on several cardiorespiratory measures during hand- rim wheelchair propulsion on a motor-driven tread- mill. Aerobic demand at the preferred cadence was approximately 10% lower than that for cadences either 60% or 140% of the preferred value. U-shaped relationships between aerobic demand and cadence were observed for both experienced and inex- perienced wheelchair users at several speeds of progression, although the response of the inex- perienced users was less uniform and consistent across speeds. Despite the fact that the preferred cadence of experienced wheelchair users increased systematically by more than 50% (from 0.67 to 1.03 Hz) as speed of progression was increased from 0.55 to 1.39 m · s–1^ , the preferred cadence at each speed remained the most economical cadence. Considering all of the energy cost or economy research considered thus far, preferred and most economical cadences appear to match well for mul- tiple forms of gait and wheelchair propulsion. A common feature of both types of activities is the presence of distinct propulsion and swing phases, even though magnitudes of muscular and con- tact forces are substantially different for gait and wheelchair propulsion. Unfortunately, minimization of energy cost is not generalizable to all cyclic activities. Cycling and arm cranking appear to be two tasks for which prefer- red and most economical cadences are different. Numerous investigators (e.g. Seabury et al. 1977; Jordan & Merrill 1979; Hagberg et al. 1981; Böning et al. 1984; Coast & Welch 1985; Marsh & Martin 1993,
preferred rates in cyclic activities 145
Aerobic demand (ml·kg
·min
–1 )
12
Stride rate (∆% PSR)
–10% +10%
22
–5% PSR +5%
14
16
18
20
MEC
Fig. 7.1 Most economical (MEC) and preferred cadences or stride rates (PSR) are usually closely matched for walking and running at a given speed. Energy cost or aerobic demand tends to be minimized at preferred cadences and increases as stride rate is either increased or decreased from the preferred rate. (Adapted from Hreljac & Martin 1993; Fig. 1.)
about 55–65 r.p.m. (Fig. 7.2). Although preferred cadences have been reported in only a few studies (Hagberg et al. 1981; Marsh & Martin 1993, 1997), preferred cadences are normally much higher than the most economical cadences. For example, Marsh and Martin (1997) reported most economical cadences ranging from 53 to 60 r.p.m. for each of three subject groups (highly fit cyclists, highly fit runners, and recreationally active non-cyclists) tested at power outputs ranging from 75 to 250 W. Preferred cadences were approximately 90– r.p.m. for the fit cyclists and fit runners and between 80 (at 75 W) and 65 r.p.m. (at 175 W) for a less-fit group of non-cyclists. Similarly, Böning et al. (1984) reported most economical cadences ranging from 52 to 67 r.p.m. for a group of fit, amateur road-racing cyclists for power outputs of 50–200 W, respect- ively. Finally, Seabury et al. (1977) found most eco- nomical cadences of 44, 54 and 58 r.p.m. for power outputs of 80, 163 and 196 W for two trained dis- tance runners and one recreational cyclist. Only two of the cycling studies cited above report most economical cadences exceeding 70 r.p.m. Coast and
Welch (1985) found that the most economical cadence steadily increases from approximately 50 r.p.m. at 100 W to 78 r.p.m. at 300 W for five trained cyclists, suggesting that exercise intensity may significantly impact the most economical cadence. Although pre- ferred cadences were not measured, they were still likely to be well above most economical cadences for all but the highest power outputs. Only results from Hagberg et al. (1981), who studied seven road- racing cyclists at power outputs of about 330 W, have shown a match between the most economical and preferred cadences (91 r.p.m.). Arm cranking appears to reflect an economy response similar to that observed for cycling, although the phenomenon for arm cranking has received substantially less attention. Powers et al. (1984) tested recreational runners at three arm- cranking cadences (50, 70 and 90 r.p.m.) under four power outputs (15, 30, 45 and 60 W). Aerobic demand was lowest at 50 r.p.m. for each power output condition and increased systematically as cadence increased. Unfortunately, Powers et al. did not report preferred cadences for their subjects, but other investigators have. Pelayo et al. (1997) reported an average preferred cadence of 91 r.p.m. for a group of 20 sedentary subjects exercising at 80% of their maximal arm-cranking aerobic demand, and Weissland et al. (1997) found preferred cadence increased from 74 to 81 r.p.m. as exercise intensity increased from 65 to 100% of maximal capacity. Thus, preferred cadences appear to be comparable with, or perhaps slightly lower than, those reported for cycling. Weissland et al. also investigated submaximal aerobic demand under three subject-specific cadence conditions: prefer- red cadence and cadences either 10% greater or 10% lower than preferred. Aerobic demand was significantly higher (approximately 8–13%) under the highest cadence condition relative to prefer- red cadences. Although aerobic demand differences between the preferred and –10% cadence conditions were not statistically significant, aerobic demand tended to be lower under the preferred cadence con- dition. Both Weissland et al. (1997) and Pelayo et al. (1997) observed systematic increases in heart rate as cadence increased. Considering all three arm- cranking studies cited here, the evidence suggests
146 locomotion
Aerobic demand (l·min
–1 )
Cadence (r.p.m.)
40 120
60 80 100
2
MEC
200W
100W
PC
Fig. 7.2 Preferred cadences (PC, shaded region) for cycling at a given power output tend to be substantially higher than most economical cadences (MEC), although some investigators have shown that MEC increases as power output increases. (Adapted from Böning et al. 1984.)
power. The relationships of these variables with respect to cadence or stride rate are strikingly simi- lar in shape (see Figs 7.3 & 7.4) and interpretation. Both approaches predict an optimal rate of move- ment. Curiously, Cavagna and Franzetti (1986) reported that their calculated mechanically optimal cadence for walking was 20–30% less than self- selected cadences, while Redfield and Hull (1986a) predicted a mechanically optimal cadence approxi- mately 10% higher than typical preferred cycling cadences. Thus, there appear to be other factors not accounted for in these models that influence the determination of self-selected cadences. Gaesser and Brooks (1975) examined the effect of pedalling cadence and power output on multiple expressions of efficiency. Twelve subjects rode a stationary ergometer at cadences of 40, 60, 80 and 100 r.p.m. at power outputs of 0, 200, 400, 600 and 800 kg m · min–1^. The results demonstrated that efficiency tended to increase as power output increased, although the responses varied depend- ing on the efficiency definition that was used. More
importantly, increases in cadence resulted in a decrease in efficiency, regardless of the efficiency expression. Gaesser and Brooks argued that delta efficiency, which is defined as the ratio of a change in power output and the associated change in energy cost, provides the best indicator of true mus- cular efficiency. Results from Sidossis et al. (1992) tend to contradict those of Gaesser and Brooks. In an assessment of the effects of power output (50, 60, 70, 80 and 90% of maximal aerobic capacity) and cadence (60, 80 and 100 r.p.m.) on gross and delta efficiency, Sidossis and colleagues observed that cadence had little effect on gross efficiency. Delta efficiency, however, increased significantly from 20.6 to 23.8% as cadence was increased from 60 to 100 r.p.m. Sidossis et al. speculated that the improved delta efficiency reflects an increase in muscular efficiency under higher cadence condi- tions. Citing fundamental muscle research that demonstrates peak muscular efficiency is achieved
148 locomotion
Fig. 7.3 External mechanical power (that associated with motion of the body’s centre of gravity) decreases and internal power (that associated with motion of body segments relative to the centre of gravity) increases as cadence increases. Total power, which represents the sum of internal and external components, reflects a minimum at intermediate stride rates. (Adapted from Cavagna & Franzetti 1986.)
Power (W·kg
–1 )
30 70
40 50 60
External
Internal
Total
Mechanical optimum
Cadence
Quasi-static
Moment Kinematic
Total
Optimal cadence
Fig. 7.4 Simulation results from Redfield and Hull (1986a) demonstrated that joint moment contributions associated with acceleration of the limbs (i.e. kinematic component) increase with cadence, and contributions associated with pedal forces acting on the foot (i.e. quasi-static component) decrease with cadence. The sum of these two components (total) reflects a minimum at intermediate cadences (approximately 90–110 r.p.m.). (Reprinted from Redfield & Hull (1986a), pp. 317–329, with permission from Elsevier Science.)
when fibre shortening velocity reaches one-third of the maximum velocity of shortening (e.g. Koushmerik & Davies 1969), they speculated that ‘by increasing the cadence, the active muscle fibres of the cyclists in the present experiment contracted at velocities closer to the velocity of peak muscular efficiency’ (p. 410). Widrick et al. (1992) argued that accelerations of the limbs, particularly at high cadences, contribute significantly to the muscular effort required to maintain a given cadence and power output. Further, they suggested that exclusion of internal mechanical power (that associated with limb accel- erations) from a total power expression ‘may con- found subsequent conclusions regarding optimal rates of limb movement’ (p. 376). Subjects pedalled at 40, 60, 80 and 100 r.p.m. under three external power output conditions (49, 98 and 147 W) established using a Monark bicycle ergometer. Their results demonstrated that internal mech- anical power increased systematically as cadence increased for each nominal external power output condition. Thus, total mechanical power (external power plus internal power) also increased as cadence increased. Using energy expenditure estimates computed from aerobic demands for each cycling condition and total mechanical power results, Widrick and colleagues computed mechan- ical efficiency. Optimal pedalling cadences, defined as the cadence at which mechanical efficiency was maximized, ranged from 82 r.p.m. at 49 W to 101 r.p.m. at 147 W, values that are clearly quite comparable with preferred cycling cadences. As one final example of the potential relationship between preferred and most efficient rates of move- ment, Corlett and Mahadeva (1970) developed an instrument to quantify mechanical power during a manual tyre-pumping task. Combining this assess- ment with measures of oxygen consumption, they were able to quantify the energy expenditure per stroke for different pumping rates. Interestingly, the energy cost per stroke declined as rate of pumping increased from slow (~10 strokes · min–1) to inter- mediate rates (30–40 strokes · min–1). Energy cost per stroke did not change with further increases in rate (up to 60 strokes · min–1). Further, preferred rates of movement coincided with the minimum
stroke rate at which the energy cost per stroke reached a plateau. Although efficiency was not quantified in this study, this minimum stroke rate corresponds to a rate at which efficiency would be greatest. From this brief review of mechanical power and efficiency, it can be seen that preferred cadences in several cyclic activities may correspond well with cadences at which efficiency is maximized. Unfor- tunately, the existing research literature related to human movement efficiency is difficult to interpret because of inconsistencies in the definitions of both mechanical power and energy expenditure expres- sions used in efficiency ratio calculations. Addition- ally, mechanical power and energy expenditure can be difficult to quantify and/or control experiment- ally for many activities. In part because of these difficulties, the number of different activities inves- tigated in efficiency studies is limited.
Mechanical optimization of muscular effort One approach in the search for an explanation for preferred rates of movement is to use optimization or modelling strategies. These strategies use modifi- able characteristics, such as cadence, and kinematic constraints to define muscle action. Such strategies have been used to predict optimal cycling cadence (Redfield & Hull 1986a, 1986b; Hull & Gonzalez 1988; Hull et al. 1988; Kautz & Hull 1993). In cycling, there is an important link between pedalling cadence and performance. Cyclists use the gears of the bicycle to select a particular cadence suited to the riding demands. The traditional approach has been to col- lect empirical data whereby metabolic cost (e.g. aer- obic demand) of riding at particular combinations of cadence and power output have been determined (e.g. Dickinson 1929; Garry & Wishart 1931; Gaesser & Brooks 1975; Seabury et al. 1977; Jordan & Merrill 1979; Hagberg et al. 1981; Böning et al. 1984; Coast & Welch 1985; Marsh & Martin 1993, 1997). Hull and colleagues have taken a different approach to identifying essential factors that deter- mine optimal pedalling cadence. They argued that physiological cost, which is of considerable import- ance with respect to overall performance, is directly
preferred rates in cyclic activities 149
crank velocity was not acceptable. Thus, use of this assumption may compromise the validity of model predictions. In a separate presentation, MacLean and Lafortune (1991b) compared optimal cadence determined using five net joint moment-based cost functions with the cadence at which group mechanical efficiency was maximized, the latter being assumed to reflect the optimal cadence criterion. Using a group of 10 experienced cyclists riding at 200 W over five cadences from 60 to 120 r.p.m. (in incre- ments of 15 r.p.m.), they found that only one of their five moment-based cost functions (one based solely on the net moment about the knee) yielded an optimal cadence matching that at which gross mechanical efficiency was maximized (80.4 and 81.3 r.p.m., respectively). The remaining moment- based cost functions yielded optimal cadences that were substantially higher, on average about 100 r.p.m., and much nearer to values reported by Hull and colleagues (Redfield & Hull 1986a; Hull et al. 1988). MacLean and Lafortune suggested that it is not surprising that minimizing the net knee moment will minimize physiological cost and max- imize gross mechanical efficiency because of the many muscles acting about the knee in cycling. Other issues surrounding optimization of cycling cadence, including seat height, foot position, etc., have been explored and are reviewed by Gregor et al. (1991). There remains conjecture regarding the relationships between muscle characteristics and selection of optimal rate (Chapman & Sanderson 1990), and these have yet to be resolved. Currently, there are few or no published empirical data that substantiate the supposed relationship between muscle moments, muscle stress and cadence selec- tion. Clearly, this needs to be a focus of ongoing research.
Minimization of neuromuscular fatigue
Recently, a number of investigators have explored the role of muscle fatigue in determining the op- timal cadence for cycling during both steady-state and exhaustive exercise. Sargeant (1994) has defined muscle fatigue as ‘the failure to generate or maintain the required or expected force or power output,
resulting from muscle activity, and reversible by rest’ (p. 116). In a series of papers, Takaishi, Moritani and colleagues (Takaishi et al. 1994, 1996, 1998) have estimated neuromuscular fatigue, using charac- teristics of the electromyograph (EMG) signal, to help explain differences between preferred and most energetically optimal cadences in cyclists and non-cyclists. Takaishi et al. (1994) had eight non- cyclists pedal at rates ranging from 40 to 80 r.p.m., at 75% of maximal aerobic power. Not surpris- ingly, metabolic cost was minimized at the lower cadences, and increased significantly as cadence approached 80 r.p.m. In contrast, the slope of the integrated EMG curve (iEMG) over the course of an exercise bout at a given cadence was significantly lower for the higher cadences. Over time, an increase in the slope of the iEMG is thought to reflect the recruitment of additional motor units, and/or an increase in the firing frequency of previously recruited motor units. As such, the slope of the iEMG is directly related to the intensity of the act- ivity (Takaishi et al. 1994). Takaishi et al. (1996) also found that the slope of the iEMG was lower at higher cadences (80– r.p.m.) in six trained cyclists, whereas metabolic cost was minimized at 60–70 r.p.m. In both cases, the cadences at which the slope of iEMG was found to be lowest were similar to the preferred cadences of the subjects (Takaishi et al. 1994, 1996). As the slope of iEMG was lower at higher cadences, Takaishi et al. (1994, 1996) concluded that the higher cadences chosen by competitive cyclists are selected to help minimize peripheral neuromuscular fatigue. They further noted that the lower iEMG slopes at the higher cadences suggests that fewer type II muscle fibres would be needed to meet the demands of the cycling task. In support of this contention, Ahlquist et al. (1992) found that glycogen depletion was much greater in type II muscle fibres after cycling at 50 r.p.m. than at 100 r.p.m. at a power output equivalent to 85% of maximal aerobic power. Glycogen depletion was not different in type I fibres between the two cadence conditions. The lower pedal forces required at a higher cadence for a fixed power output (Patterson & Moreno 1990) would require lower muscle forces, and not require the recruitment of as
preferred rates in cyclic activities 151
many type II fibres (Ahlquist et al. 1992). Patterson and Moreno (1990) noted that the resultant pedal forces were minimized at 90 r.p.m. (at 100 W) and 100 r.p.m. (at 200 W) in a group of 11 recreational cyclists. These values were also very close to the preferred cadences at both power outputs. During steady-state cycling, greater recruitment of type II fibres at lower cadences would presumably lead to more rapid fatigue. At higher cadences, the greater reliance on type I fibres would help prevent the onset of fatigue. Nevertheless, metabolic energy cost will still be higher under high cadence condi- tions due to the greater number of repetitions per- formed per unit of time (Takaishi et al. 1994, 1996). Takaishi et al. (1996) also noted that non-cyclists showed large increases in the iEMG of the vasti muscles at higher pedalling rates, whereas the trained cyclists did not demonstrate such an increase. The authors suggested that the lack of increase in iEMG for trained cyclists at higher cadences was related to pedalling skill developed by the trained cyclists. In subsequent research, Takaishi et al. (1998) demonstrated that while the vasti iEMG did not increase substantially for trained cyclists ( N = 7) as cadence increased, biceps femoris iEMG did increase dramatically. Trained non- cyclists ( N = 7) demonstrated a general increase in the iEMG of the vasti muscles as cadence increased, with no increase in biceps femoris activity. In addition, normal pedal forces decreased for both trained cyclists and trained non-cyclists as cadence increased; however, the normal pedal forces were lower for trained cyclists than trained non-cyclists at all but the lowest cadence (45 r.p.m.). The invest- igators suggested that the trained cyclists had developed a pedalling technique that involved pull- ing up the leg, via knee flexion, during the recovery portion of the pedal cycle at higher cadences. The speculated technique would allow for the lower pedal force seen in the cyclists, and presumably result in lower muscle stress in the vasti group, and a lower dependence on type II muscle fibres (Takaishi et al. 1998). Some papers in the literature would seem to con- tradict the findings of the above mentioned studies. Carnevale and Gaesser (1991) found that time to exhaustion was greater at 60 r.p.m. than 100 r.p.m.
in a group of seven untrained subjects at multiple power levels. Similarly, McNaughton and Thomas (1996) reported time to exhaustion was greater at 50 r.p.m. than at 90 or 110 r.p.m. for untrained subjects. These results are consistent with the general finding that metabolic cost is minimized around 50– r.p.m. (Seabury et al. 1977; Carnevale & Gaesser 1991; Marsh & Martin 1993, 1997; McNaughton & Thomas 1996). While the work of Carnevale and Gaesser, and of McNaughton and Thomas is cer- tainly relevant, it cannot be directly compared with the studies by Takaishi et al. (1994, 1996, 1998). The former investigations used power outputs designed to bring about volitional exhaustion in a 1- to 10-min range, while Takaishi et al. (1994, 1996, 1998) used power output levels that were designed to allow subjects to cycle for at least 15 min without suffer- ing undue fatigue. Carnevale and Gaesser (1991) and McNaughton and Thomas (1996) also used untrained subjects, while Takaishi et al. (1996, 1998) used a combination of untrained non-cyclists, trained non-cyclists, and trained cyclists. A final point not directly addressed by Carnevale and Gaesser (1991) was that while time to exhaustion was substantially greater for 60 r.p.m. vs. 100 r.p.m. at the lowest power output, the time to exhaustion difference between 60 and 100 r.p.m. all but disap- peared as power output was increased. With regard to this, Hill et al. (1995) suggested that the advantage of decreased metabolic cost at lower cadences may be offset as power output increases, due to the increased muscle force requirements per cycle. While the data relating to the role of muscle fatigue in setting preferred rate of movement dur- ing different modes of cycling are as yet equivocal, the theoretical work of Sargeant (1994) may provide some additional insight. In a muscle of mixed fibre type, the optimal rate of shortening will be a com- promise between the power–velocity relationships of type I and type II fibres. During real-world cycling, maximal power output is achieved at ap- proximately 120 r.p.m. (Sargeant 1994). Based on the combined power–velocity relationship of a theor- etical whole muscle, and the ability of the CNS to selectively recruit motor units, Sargeant argued that at 80% of maximal power output, pedalling at 120 r.p.m. would result in a reserve of 20% available
152 locomotion
walking stride rate in able-bodied (Royer et al. 1997) and unilateral below-knee amputees (Mattes et al. 2000). Thus, while the FDHO model and pendular mechanics are theoretically sound and appear to apply well to cyclic activities in which the extre- mities are being oscillated, the magnitude of the effect on cadence is not well substantiated.
Limb stiffness
Recently, Farley, McMahon, and co-workers (Blickhan 1989; McMahon & Cheng 1990; Farley et al. 1991; Farley et al. 1993; Farley & Gonzalez 1996; Ferris & Farley 1997) have used a simple spring- mass model of the human body to demonstrate that limb stiffness may determine rate of movement in bounding and running gaits. According to this model, the human body is represented as a massless spring (the ‘leg spring’) and a point mass. It has been shown that the stiffness of the leg spring remains nearly constant as running speed increases in humans and several other animal species (Farley et al. 1993; He et al. 1991). As running speed increases, the leg spring is swept through a larger angle, increasing the effective stiffness of the overall sys- tem, and causing the body to bounce off the ground at a faster rate. During hopping, or at a constant run- ning speed, however, the stiffness of the leg spring appears to be modulated to produce a different hopping rate. Farley et al. (1991) had four subjects hop forwards on a treadmill-mounted force platform at speeds from 0 to 3 m · s–1^ , and in place on a ground-based force platform. During both hopping conditions, and at all but the fastest treadmill speed, the mean preferred rate was 132 hops · min–1^. The body behaved as a simple spring-mass system at the pre- ferred hopping rate and at all rates above preferred. Below the preferred hopping rate, the body did not behave as a simple spring-mass system, implying that the storage and reutilization of elastic energy would be compromised at low rates. At hopping rates above preferred, the stiffness of the leg spring was increased to allow the body still to behave as a simple spring-mass system. As ground contact time decreased with increasing hopping rate, Farley et al. (1991) suggested that metabolic cost would increase
at rates above preferred, as the time to generate muscular force would be shortened. A shortened ground contact time has been suggested to require the recruitment of less-economical fast-twitch muscle fibres, and consequently increase metabolic cost (Kram & Taylor 1990). Ferris and Farley (1997) further showed that subjects increase hopping rate by increasing leg-spring stiffness, regardless of sur- face compliance. However, leg-spring stiffness was increased disproportionately more on compliant surfaces than stiff surfaces, to keep the total vertical stiffness nearly constant at a given rate. Farley and Gonzalez (1996) had four subjects run on a treadmill-mounted force platform at 2.5 m · s–1^ , and at stride rates from 26% below to 36% above preferred (preferred stride rate = 79.8 strides · min–1^ ), to see how the behaviour of the spring-mass model was altered to produce different stride rates. While the stiffness of the leg spring has been found to remain constant, and the angle through which the leg spring is swept increases as speed increases (He et al. 1991; Farley et al. 1993), Farley and Gonzalez found that different stride rates at a constant speed are produced primarily by increasing the leg-spring stiffness. The stiffness of the leg spring was in- creased over twofold from the lowest stride rate to the highest rate, while the angle swept by the leg spring only decreased slightly at the highest rate. In fact, when stride rate (Farley & Gonzalez 1996) and hopping rate (Farley et al. 1991) were each increased by 65%, leg-spring stiffness increased by approximately the same amount (twofold), demonstrating the similarities between these two forms of locomotion. Farley and Gonzalez (1996) stated that the ability to adjust the leg-spring stiffness is likely to be an important factor in adapting the locomotor system to the demands of the environment. In physiological terms, the stiffness of the leg spring can be adjusted in at least two ways. Changing the orientation of the limbs relative to the ground (McMahon et al. 1987), and changing muscle activation patterns (Farley & Gonzalez 1996) will each result in an altered leg- spring stiffness. In summary, Farley et al. (1991) sug- gested their findings help explain why metabolic cost is minimized at the preferred rate of movement in bounding or running gaits. Metabolic cost below
154 locomotion
the preferred rate will increase due to a loss of elastic strain energy from the system. Above the preferred rate, metabolic cost will increase due to a shorter ground contact time. While the spring-mass model has been valuable in distinguishing import- ant aspects of rate selection in bounding and run- ning gaits, it is not directly applicable to other activities, such as walking, where kinetic energy and gravitational potential energy are 180° out of phase, and the body does not behave as a simple spring-mass system. Interestingly, Bonnard and Pailhous (1993) found that during walking, stride rate is highly dependent on limb stiffness during the swing phase, but independent of limb stiffness dur- ing stance. The stiffness changes noted by Farley and co-workers (Blickhan 1989; McMahon & Cheng 1990; Farley et al. 1991; Farley et al. 1993; Farley & Gonzalez 1996; Ferris & Farley 1997) during run- ning and hopping relate implicitly to the stance phase.
Minimizing movement variability
In addition to metabolic cost, mechanical minimiza- tion phenomena and limb inertial properties, move- ment stability or variability may be another factor that determines the preferred or optimal rate of movement during cyclic activities. The reader should note that high movement stability and low movement variability are synonymous in the pre- sent context. Much, if not all, of the literature relat- ing to movement stability during cyclic activities comes out of a dynamical systems approach to movement organization. According to dynamical systems theory, ‘behavioural patterns and their dynamics are shown to arise in a purely self- organized fashion from cooperative coupling among individual components’ (Kelso & Schöner 1988, p. 27). A primary focus of this theory is the study of stability and the loss of stability. Well-learned or preferred movement patterns are associated with high stability, and a loss of stability is usually indicative of an impending change in behaviour (such as the transition from walking to running). There is also evidence from more traditional motor behaviour circles that movement variability is an important and relevant issue in control of pre-
ferred rate of movement. Smoll (1975), and Smoll and Schutz (1978) found distinct individual differ- ences in preferred cadences and movement vari- ability in a cyclic upper-limb task. They noted that movement variability is uncorrelated with pre- ferred cadence, and is likely to be related to underly- ing biological variability. According to Smoll (1975), movement variability is indicative of the status of an individual performance, and is an essential compon- ent of a complete description of that performance. Movement variability has previously been char- acterized as stochastic in nature (Hirokawa 1989). Recent research by Hausdorff and colleagues (Hausdorff et al. 1995, 1996), however, has demon- strated that variations in the stride interval during steady-state walking exhibit long-range correla- tions, such that the fluctuations in stride interval at any point in time are dependent on stride inter- vals at previous times. The long-term correlations extend as far back as 1000 strides (Hausdorff et al. 1996). Interestingly, when subjects walked in time with a metronome set at their preferred stride rate, the long-range correlations disappeared, and the variations in stride interval became random in nature (Hausdorff et al. 1996). Hausdorff et al. (1995) proposed that chaotic variability is an intrinsic part of the normal locomotor control system. The researchers also suggested that supraspinal centres are responsible for the presence of the long-term correlations. From a control perspective, systems that possess long-range correlations are inherently more resistant to perturbations (Hausdorff et al. 1995). Movement variability/stability is clearly a relevant factor for cyclic movement control, and a possible determinant of preferred rate of movement. One of the most complete accounts of the relation- ship between movement stability and preferred rate of movement is provided by Holt et al. (1995). Their paper is notable because they employed stability, metabolic, mechanical and inertial measures, allow- ing direct comparisons not usually possible in uni- focal studies. They determined three measures of movement stability for eight subjects at their pre- ferred speed as they walked on a treadmill at pre- ferred stride rate, optimal stride rate predicted by a force-driven harmonic oscillator model of the lower
preferred rates in cyclic activities 155
(Smoll 1975; Smoll & Schutz 1978), perhaps making the finding of lower variability at all running speeds less surprising. One should keep in mind that the paper by Brisswalter and Mottet dealt with speeds near the preferred transition speed, and did not include data on preferred speed or stride rate for walking or running. In a paper dealing with the walk-to-run trans- ition, Diedrich and Warren (1998) presented an account of movement stability over a range of walk- ing and running speeds. The walking stability func- tion had a minimum at 1.66 m · s–1^ and 61.8 · strides · min–1. The data from Diedrich and Warren com- pare favourably with the results from Maruyama and Nagasaki (1992). At a speed of 1.67 m · s–1^ , Maruyama and Nagasaki reported minimum variability at 62.0 strides · min–1^ , and a preferred rate of 62.4 strides · min–1. While the stability and metabolic cost relationships were very similar in shape, the respective minima were not coincident (energetically optimal walking speed ~1.3 m · s–1^ ). Diedrich and Warren (1998) emphasized the sim- ilarities between the overall behaviour of the stabil- ity and economy functions, and suggested that any minor differences were likely to be related to the fact that global energy expenditure includes costs not associated with the locomotor task. As with research by others (Maruyama & Nagasaki 1992; Holt et al. 1995; Sekiya et al. 1997), the findings of Diedrich and Warren (1995, 1998) point to a strong, if not perfect (Brisswalter & Mottet 1996), relation- ship between movement stability and economy. Patla (1985) examined EMG variability at fast, normal and slow stride rates in seven subjects walk- ing on a treadmill at preferred speed. He used a pat- tern recognition technique to estimate variability. Surprisingly, muscle activity patterns were found to be more variable for the normal stride rate than the slow or fast rates. The author suggested that the attentional demand necessary to walk in a non-preferred manner could account for the lower variability under these conditions. The finding of increased variability for muscle activity at the pre- ferred rate is in direct contrast to the notion that kinematic variability is minimized at the preferred rate (Maruyama & Nagasaki 1992; Holt et al. 1995; Sekiya et al. 1997).
All of the studies reviewed so far have dealt exclusively with adults. A few papers in the literat- ure have dealt with movement variability during locomotion in children. Jeng et al. (1997) determined interlimb and intralimb stability in 45 children aged 3–12 years walking on a treadmill at their preferred stride rates and ±25% of preferred stride rate. In most cases, interlimb and intralimb stability was maximized under preferred stride rate conditions. The authors also noted that by age 7 years, children exhibit a self-optimization pattern similar to adults. Jeng et al. (1997) also observed that 5- to 6-year-olds demonstrated an ability to modulate stride rate not seen in 3- to 4-year-olds, but as a consequence the gait of the 5- to 6-year-olds became more variable. Variability subsequently decreased in the 7- to 12- year-olds. The dramatic differences between the 5- to 6- and 3- to 4-year-olds are possible due to mor- phological changes that occur between ages 3 and 6; however, they may also be indicative of a transition from a rigid form of control to a more adaptive form of control (Jeng et al. 1997). A more adaptive form of control would by its very nature require more vari- ability in the system. Clark and Phillips (1993) have also suggested that infants also go through a period of stability acquisition during the first 3 months of independent walking. Although the picture is far from complete, locomotion development in chil- dren may undergo at least two distinct phases of stability acquisition. One is associated with the ini- tial development of the walking skill, and a second is associated with an increase in the adaptability of stride rate to meet the demands of the environment. The literature on movement variability at differ- ent rates of movement in cyclic activities outside the locomotion arena is sparse. Recently, Dawson et al. (1998) reported changes in temporal variability dur- ing rowing on an ergometer and on the water in five competitive rowers, over a range of stroke rates (18–33 strokes · min–1). The authors discovered that rowers increase stroke rate primarily by decreasing the duration of the recovery phase, while the duration of the stroke phase changed very little. As stroke rate increased, variability generally decreased for both the recovery phase and the stroke phase. The decreases in variability were most dramatic for the recovery phase, which exhibited
preferred rates in cyclic activities 157
considerably higher variability than the stroke phase at the lower rates. Dawson et al. (1998) did not determine preferred stroke rate for the rowers in their study. They did note, however, that preferred stroke rate is usually in the range of 30–40 strokes · min–1^. This would suggest that movement variabil- ity is minimized at or near preferred stroke rates in competitive rowers. Based on the studies reviewed, movement stabil- ity would appear to be a contributing factor to the selection of the preferred cadences during locomo- tion. Specifically, the results of Holt et al. (1995) indic- ate that stability may cooperate with metabolic cost in setting the preferred stride rate. The findings of Dawson et al. (1998) suggest that minimizing vari- ability may be a factor in cadence selection for other activities as well. Many more studies will be needed on other cyclic activities before any far-reaching generalizations can be made regarding the role of movement stability/variability in rate of movement selection.
Summary The factors that determine the preferred and/or optimal rate of limb movement during any cyclic activity are clearly many. Metabolic cost, mechan- ical minimization phenomena, muscle mechanical properties, limb inertial parameters, movement stability and limb stiffness all appear to be asso- ciated with the preferred rate of movement for one or more activities. The tasks for the future are twofold. For the locomotion arena, well-designed multifactorial studies are needed that will allow us to determine which associated factors are causal, and which are merely related effects. Addition- ally, many studies are needed using activities other than walking, running and cycling, to determine whether the conclusions reached from the loco- motion-based studies have strong generalizability, or are activity specific. Only then will the critical factors underlying the selection of the rate of move- ment emerge.
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