BIOMECHANICS IN SPORT

PERFORMANCE ENHANCEMENT AND INJURY PREVENTION

VOLUME IX OF THE ENCYCLOPAEDIA OF SPORTS MEDICINE

AN IOC MEDICAL COMMISSION PUBLICATION

IN COLLABORATION WITH THE

INTERNATIONAL FEDERATION OF SPORTS MEDICINE

EDITED BY VLADIMIR M. ZATSIORSKY Chapter 7

Factors Affecting Preferred Rates of Movement in Cyclic Activities

P.E. MARTIN, D.J. SANDERSON AND B.R. UMBERGER

Introduction While much information has been gained about the neurophysiology of rhythmic movements, Many human movements are characterized by the especially in lower vertebrates and invertebrates, continual repetition of a fundamental pattern of relatively little attention has been directed to under- motion (e.g. walking, running, hopping, cycling, standing how cycle distance and cadence are deter- swimming, rowing). For cyclic activities, the aver- mined and controlled by the neuromusculoskeletal age speed of progression is defined by the product system in humans. Nevertheless, it is useful to gain of the average distance travelled per cycle of motion some understanding of how cycle distance and (e.g. running stride length) and the average rate cadence are related, even though available evidence or cadence at which the cycle of motion is being applies primarily to walking. Laurent and Pailhous repeated (e.g. running stride rate or cadence). In (1986) had subjects walk overground while impos- normal human movements, these speed, distance ing only stride rate or stride length by means of and cadence factors are usually freely determined auditory or visual cues and allowing all other gait or self-selected by the performer and are rarely fixed parameters to vary freely. Results revealed that or pre-established. In addition, humans have an when one parameter (e.g. stride rate) was steadily incredible ability to intentionally alter speed, dis- increased the other parameter (i.e. stride length) tance and cadence to meet the demands of the envi- remained almost constant despite the lack of con- ronment. As an example, Nilsson and Thorstensson straint imposed on all other parameters. Moreover, (1987) observed that over a normal range of walking Laurent and Pailhous found that stride rate and speeds (1.0–3.0 m · s–1), subjects were able to walk length were each strongly correlated with speed, with a lowest possible stride rate of 25 strides · but were relatively independent of each other. The min–1 at the lowest speed and a highest possible rate authors proposed that speed, not rate or length, is of 143 strides · min–1 at all speeds. Within a range of the critical parameter around which locomotion is running speeds (1.5–8 m · s–1), subjects could run organized. Indeed, Diedrich and Warren (1995) with rates as low as 33 strides · min–1 to as high as found that subjects make the transition from a walk 214 strides · min–1. Given this ability to alter cycle to a run at a critical speed (2.2 m · s–1), rather than at cadence and distance factors, how is the preferred a critical stride rate or length, when rate and length cadence chosen, and how does it relate to different are experimentally manipulated. Even if speed is optimality criteria? The mechanisms that underlie the parameter around which locomotion is ultim- the selection process leading to a particular cadence- ately organized, the flexibility with which stride rate distance combination chosen by a performer for and length can be altered implies that the central a given activity at a given speed are not clear, nervous system (CNS) must have mechanisms for although numerous factors have been considered. actively controlling these variables.

143 144 locomotion

Because of the lack of dependence between stride preferred cadence (e.g. energy cost or economy of rate and length, it has been suggested that rate and movement, mechanical work or power, muscular length are modulated by two distinct neural control efficiency, muscle stress, inertial characteristics schemes, frequency modulation for rate and ampli- of swinging limbs, movement pattern variability, tude modulation for length (Zijlstra et al. 1995). neuromuscular fatigue, lower extremity stiffness) Bonnard and Pailhous (1993) also proposed that have been examined over the course of many dec- stride rate and length are controlled differently by ades of research in movement science. In addition, the nervous system. Changes in stride rate are asso- research has focused on an equally wide variety of ciated with changes in the global stiffness of the movements or activities. While the majority of stud- lower limb during the swing phase, but not during ies have investigated walking, running and cycling, the stance phase, suggesting that rate is altered there is a more limited number of investigations on by changing the tonic activity of the lower limb other cyclic activities such as hopping, stair climb- muscles during swing. Changing the tonic activity ing, rowing, swimming and wheelchair propulsion of most or all of the muscles of the limb will alter that can offer additional insights into cadence deter- the resonant frequency of that limb as it swings mination. Our purpose is to broadly review the about the hip joint. Bonnard and Pailhous further existing research literature to consider those factors suggested that transient changes in stride length that may play an important role in establishing are linked to phasic activation of appropriate leg preferred cadences and to determine whether muscles. Patla et al. (1989) have shown that transi- selected factors appear to be especially important ent increases in stride length are indeed produced in influencing fundamental preferred cadences of by phasic increases in the activity of some muscles, numerous cyclic activities. and by decreases in the activity of others. While stride rate and length may follow fairly Minimization of movement energy cost fixed patterns during unrestrained walking and running, the CNS has the ability to dissociate rate It is intuitively appealing to speculate that submax- and length if required or desired. Hogan (1984) pro- imal, steady-state cyclic movements are organized posed a physiological mechanism that would allow such that body mass-specific rate of energy con- such a dissociation. When antagonistic muscles are sumption (e.g. J · kg–1 ·s–1) or aerobic demand (e.g. simultaneously active about a joint, the net joint ml·kg–1 · min–1) is minimized for a given task. moment is related to the difference between anta- Applying this argument specifically to cadence, gonistic muscle forces and joint stiffness is associ- energy cost for a given activity would be minimized ated with the sum of muscle forces. If the CNS when self-selected or preferred cadences are used. actively modulates the coactivation of antagonistic Data for both walking and running lend support muscles, stride rate and length can be varied inde- to this supposition. Numerous investigators (e.g. pendently within limits. As coactivation is meta- Högberg 1952; Zarrugh et al. 1974; Cavanagh & bolically costly, one might hypothesize that the Williams 1982; Powers et al. 1982; Heinert et al. preferred movement patterns require the least co- 1988; Holt et al. 1991, 1995; Hreljac & Martin 1993) activation. This leads to the possibility that cyclic have measured energy cost as stride rate, and thus activities are organized to minimize demands placed stride length, were manipulated systematically dur- on the neuromusculoskeletal system (e.g. minimiz- ing constant-speed treadmill walking or running. ing energy cost, muscle activation, or muscle stress; Results have shown consistently that energy cost or maximizing mechanical efficiency). reflects a U-shaped relationship with cadence such This review focuses specifically on the rate or that as cadence is manipulated both above and cadence at which cyclic movements are produced below an individual’s self-selected or preferred and potential factors that influence preferred or cadence, energy cost rises (Fig. 7.1). As an example, self-selected cadences. A wide variety of factors a 5% increase or decrease in stride rate of walking that may be associated with or that directly affect resulted in an 8–10% increase (1–2 ml · kg–1 · min–1) preferred rates in cyclic activities 145

22 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 20

) either increased or decreased from the preferred –1 rate (Morgan & Martin 1986). In addition, van der

·min Woude et al. (1989) studied the effect of cadences –1 18 ranging from 60 to 140% of preferred cadence on several cardiorespiratory measures during hand- rim wheelchair propulsion on a motor-driven tread- 16 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

Aerobic demand (ml·kg relationships between aerobic demand and cadence 14 MEC were observed for both experienced and inex- perienced wheelchair users at several speeds of progression, although the response of the inex- 12 –10% –5% PSR +5% +10% perienced users was less uniform and consistent Stride rate (∆% PSR) across speeds. Despite the fact that the preferred cadence of experienced wheelchair users increased Fig. 7.1 Most economical (MEC) and preferred cadences systematically by more than 50% (from 0.67 to or stride rates (PSR) are usually closely matched for walking and running at a given speed. Energy cost or 1.03 Hz) as speed of progression was increased aerobic demand tends to be minimized at preferred from 0.55 to 1.39 m · s–1, the preferred cadence at cadences and increases as stride rate is either increased or each speed remained the most economical cadence. decreased from the preferred rate. (Adapted from Hreljac Considering all of the energy cost or economy & Martin 1993; Fig. 1.) research considered thus far, preferred and most economical cadences appear to match well for mul- tiple forms of gait and wheelchair propulsion. A in aerobic demand (Holt et al. 1991, 1995; Hreljac common feature of both types of activities is the & Martin 1993). Self-selected cadence and stride presence of distinct propulsion and swing phases, length for most individuals usually do not deviate even though magnitudes of muscular and con- substantially from those that minimize energy cost tact forces are substantially different for gait and at a given speed of walking or running. Morgan wheelchair propulsion. et al. (1994) found that only 20% of a pool of 45 Unfortunately, minimization of energy cost is not recreational runners reflected a stride length that generalizable to all cyclic activities. Cycling and arm deviated by more than a few centimetres (5% of cranking appear to be two tasks for which prefer- leg length) from the most economical stride length red and most economical cadences are different. and showed a difference in aerobic demand be- Numerous investigators (e.g. Seabury et al. 1977; tween preferred and most economical conditions Jordan & Merrill 1979; Hagberg et al. 1981; Böning et that was greater than 0.5 ml · kg–1 · min–1. These al. 1984; Coast & Welch 1985; Marsh & Martin 1993, results provide convincing evidence that most 1997) have examined the effect of pedalling cadence individuals self-optimize walking and running on aerobic demand or energy cost under a variety cadences, and suggest that minimizing energy cost of power outputs and for subject groups differing may be an important factor contributing to cadence in terms of fitness status and experience with the determination. locomotion activity. In general, aerobic demand or Similar responses of energy cost or aerobic energy cost reflects a curvilinear relationship with demand to cadence changes have been shown for cadence such that minimum demand occurs at 146 locomotion

3.2 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,

2.8 200W suggesting that exercise intensity may significantly impact the most economical cadence. Although pre- )

–1 ferred cadences were not measured, they were still

2.4 likely to be well above most economical cadences PC for all but the highest power outputs. Only results from Hagberg et al. (1981), who studied seven road- MEC 2 racing cyclists at power outputs of about 330 W, have shown a match between the most economical

Aerobic demand (l·min 100W and preferred cadences (91 r.p.m.). 1.6 Arm cranking appears to reflect an economy response similar to that observed for cycling, although the phenomenon for arm cranking has 1.2 received substantially less attention. Powers et al. 40 60 80 100 120 (1984) tested recreational runners at three arm- Cadence (r.p.m.) cranking cadences (50, 70 and 90 r.p.m.) under four Fig. 7.2 Preferred cadences (PC, shaded region) for power outputs (15, 30, 45 and 60 W). Aerobic cycling at a given power output tend to be substantially demand was lowest at 50 r.p.m. for each power higher than most economical cadences (MEC), although output condition and increased systematically as some investigators have shown that MEC increases as cadence increased. Unfortunately, Powers et al. did power output increases. (Adapted from Böning et al. 1984.) not report preferred cadences for their subjects, but other investigators have. Pelayo et al. (1997) about 55–65 r.p.m. (Fig. 7.2). Although preferred reported an average preferred cadence of 91 r.p.m. cadences have been reported in only a few studies for a group of 20 sedentary subjects exercising (Hagberg et al. 1981; Marsh & Martin 1993, 1997), at 80% of their maximal arm-cranking aerobic preferred cadences are normally much higher demand, and Weissland et al. (1997) found preferred than the most economical cadences. For example, cadence increased from 74 to 81 r.p.m. as exercise Marsh and Martin (1997) reported most economical intensity increased from 65 to 100% of maximal cadences ranging from 53 to 60 r.p.m. for each of capacity. Thus, preferred cadences appear to be three subject groups (highly fit cyclists, highly fit comparable with, or perhaps slightly lower than, runners, and recreationally active non-cyclists) those reported for cycling. Weissland et al. also tested at power outputs ranging from 75 to 250 W. investigated submaximal aerobic demand under Preferred cadences were approximately 90–95 three subject-specific cadence conditions: prefer- r.p.m. for the fit cyclists and fit runners and between red cadence and cadences either 10% greater or 80 (at 75 W) and 65 r.p.m. (at 175 W) for a less-fit 10% lower than preferred. Aerobic demand was group of non-cyclists. Similarly, Böning et al. (1984) significantly higher (approximately 8–13%) under reported most economical cadences ranging from 52 the highest cadence condition relative to prefer- to 67 r.p.m. for a group of fit, amateur road-racing red cadences. Although aerobic demand differences cyclists for power outputs of 50–200 W, respect- between the preferred and –10% cadence conditions ively. Finally, Seabury et al. (1977) found most eco- were not statistically significant, aerobic demand nomical cadences of 44, 54 and 58 r.p.m. for power tended to be lower under the preferred cadence con- outputs of 80, 163 and 196 W for two trained dis- dition. Both Weissland et al. (1997) and Pelayo et al. tance runners and one recreational cyclist. Only (1997) observed systematic increases in heart rate two of the cycling studies cited above report most as cadence increased. Considering all three arm- economical cadences exceeding 70 r.p.m. Coast and cranking studies cited here, the evidence suggests preferred rates in cyclic activities 147 that the most economical cadences for arm cranking shape of the observed muscle efficiency function, are lower than the preferred cadences and that the Hill also noted that high rates of movement of short economy response for arm cranking is similar to duration are likely to result in a substantial loss of that observed in cycling. Nevertheless, much more efficiency, whereas movement cycles of longer dura- evidence is needed before any definitive conclu- tion suffer from only a small decline in efficiency. sions can be drawn. This suggests that high cadences may have a more deleterious effect on performance than low rates. Maximizing mechanical efficiency Cavagna and Franzetti (1986) examined the effect of cadence on mechanical power required to sustain Mechanical efficiency, which has been defined in constant-speed walking. They noted that maintain- several ways (e.g. gross efficiency, net efficiency, ing walking speed with long stride lengths and a work efficiency, delta efficiency; Gaesser & Brooks low cadence increases the magnitude of ground 1975), has also been proposed as a key element in contact forces, whereas use of short stride lengths in the processes underlying the selection of preferred combination with a high cadence requires that the rates of movement. Even from the early 1920s it has limbs be accelerated more frequently. They further been known that there is a rate of movement that is suggested that an optimum condition might exist at most efficient for a given power output (e.g. Hill intermediate cadences that would reduce inefficien- 1922; Dickinson 1929). An examination of the notion cies created by either extreme, and used a mech- of maximizing efficiency of human movement is anical power assessment to test this notion. Two not independent of the principle of minimization of components of mechanical power were quantified the energy cost since an expression of energy cost as cadence was varied under controlled walking forms the denominator of an efficiency ratio. speeds: external power required to lift and acceler- More specifically, changes in gross efficiency (total ate the centre of mass of the body and internal mechanical power output divided by gross rate of power used to accelerate the limbs relative to the energy expenditure) as cadence is manipulated centre of mass. As predicted, external power under controlled power conditions are necessarily declined and internal power increased as stride inversely related to changes in energy cost (e.g. as rate increased (Fig. 7.3). The sum of these two energy cost rises, gross efficiency falls). Movement power components, which provided an expres- efficiency has been investigated in numerous cyclic sion of total mechanical power required to sustain tasks including running (e.g. Kaneko et al. 1987), walking speed, exhibited a minimum at inter- walking (Zarrugh et al. 1974), manual working tasks mediate cadences of approximately 34, 43 and 52 (Corlett & Mahadeva 1970), and cycling (Coast et al. strides · min–1 for walking speeds of 4.6, 5.5 and 1986). 6.6 km · h–1, respectively. Assuming that mech- Hill (1922), using an elbow flexion task, observed anical power is somewhat reflective of demands that the efficiency of muscular contractions in- placed on the musculature, overall muscular effort creased rapidly to a maximum of approximately would be minimized at these minima. 26% and then fell more slowly as the duration of As will be discussed below, Hull and colleagues contractions increased. Peak efficiency occurred (Hull & Jorge 1985; Redfield & Hull 1986a) applied for contraction durations of approximately 1 s. a similar concept when using a joint moment cost Hill subsequently cited cycling as an activity con- function to examine the relative demands of gener- sistent with this 1 s optimum contraction duration. ating pedal forces and accelerating the limbs under Benedict and Cathcart (1913) had previously re- different cycling cadences. Their quasi-static moment ported a most efficient cadence of 70 r.p.m. for component was a function of external forces applied cycling. The significance of Hill’s observation, how- to the foot via the pedal, and is analogous to ever, is muted when one recognizes that contrac- Cavagna and Franzetti’s external power expression. tions of individual muscles during pedalling rarely Their kinematic moment component was related last for more than half a pedal cycle. Because of the to limb accelerations, which is analogous to internal 148 locomotion

2.5 Mechanical optimum

Total 2.0

Optimal cadence Total )

–1 1.5 External

Kinematic Moment 1.0 Power (W·kg

0.5

Internal Quasi-static 0.0 30 40 50 60 70 Cadence

Fig. 7.3 External mechanical power (that associated with Fig. 7.4 Simulation results from Redfield and Hull (1986a) motion of the body’s centre of gravity) decreases and demonstrated that joint moment contributions associated internal power (that associated with motion of body with acceleration of the limbs (i.e. kinematic component) segments relative to the centre of gravity) increases as increase with cadence, and contributions associated cadence increases. Total power, which represents the sum with pedal forces acting on the foot (i.e. quasi-static of internal and external components, reflects a minimum component) decrease with cadence. The sum of these two at intermediate stride rates. (Adapted from Cavagna & components (total) reflects a minimum at intermediate Franzetti 1986.) cadences (approximately 90–110 r.p.m.). (Reprinted from Redfield & Hull (1986a), pp. 317–329, with permission power. The relationships of these variables with from Elsevier Science.) respect to cadence or stride rate are strikingly simi- lar in shape (see Figs 7.3 & 7.4) and interpretation. importantly, increases in cadence resulted in a Both approaches predict an optimal rate of move- decrease in efficiency, regardless of the efficiency ment. Curiously, Cavagna and Franzetti (1986) expression. Gaesser and Brooks argued that delta reported that their calculated mechanically optimal efficiency, which is defined as the ratio of a change cadence for walking was 20–30% less than self- in power output and the associated change in selected cadences, while Redfield and Hull (1986a) energy cost, provides the best indicator of true mus- predicted a mechanically optimal cadence approxi- cular efficiency. Results from Sidossis et al. (1992) mately 10% higher than typical preferred cycling tend to contradict those of Gaesser and Brooks. In cadences. Thus, there appear to be other factors not an assessment of the effects of power output (50, accounted for in these models that influence the 60, 70, 80 and 90% of maximal aerobic capacity) determination of self-selected cadences. and cadence (60, 80 and 100 r.p.m.) on gross and Gaesser and Brooks (1975) examined the effect of delta efficiency, Sidossis and colleagues observed pedalling cadence and power output on multiple that cadence had little effect on gross efficiency. expressions of efficiency. Twelve subjects rode a Delta efficiency, however, increased significantly stationary ergometer at cadences of 40, 60, 80 and from 20.6 to 23.8% as cadence was increased from 100 r.p.m. at power outputs of 0, 200, 400, 600 and 60 to 100 r.p.m. Sidossis et al. speculated that the 800 kg m · min–1. The results demonstrated that improved delta efficiency reflects an increase in efficiency tended to increase as power output muscular efficiency under higher cadence condi- increased, although the responses varied depend- tions. Citing fundamental muscle research that ing on the efficiency definition that was used. More demonstrates peak muscular efficiency is achieved preferred rates in cyclic activities 149 when fibre shortening velocity reaches one-third stroke rate at which the energy cost per stroke of the maximum velocity of shortening (e.g. reached a plateau. Although efficiency was not Koushmerik & Davies 1969), they speculated that quantified in this study, this minimum stroke rate ‘by increasing the cadence, the active muscle fibres corresponds to a rate at which efficiency would be of the cyclists in the present experiment contracted greatest. at velocities closer to the velocity of peak muscular From this brief review of mechanical power and efficiency’ (p. 410). efficiency, it can be seen that preferred cadences in Widrick et al. (1992) argued that accelerations of several cyclic activities may correspond well with the limbs, particularly at high cadences, contribute cadences at which efficiency is maximized. Unfor- significantly to the muscular effort required to tunately, the existing research literature related to maintain a given cadence and power output. human movement efficiency is difficult to interpret Further, they suggested that exclusion of internal because of inconsistencies in the definitions of both mechanical power (that associated with limb accel- mechanical power and energy expenditure expres- erations) from a total power expression ‘may con- sions used in efficiency ratio calculations. Addition- found subsequent conclusions regarding optimal ally, mechanical power and energy expenditure can rates of limb movement’ (p. 376). Subjects pedalled be difficult to quantify and/or control experiment- at 40, 60, 80 and 100 r.p.m. under three external ally for many activities. In part because of these power output conditions (49, 98 and 147 W) difficulties, the number of different activities inves- established using a Monark bicycle ergometer. tigated in efficiency studies is limited. Their results demonstrated that internal mech- anical power increased systematically as cadence Mechanical optimization of increased for each nominal external power output muscular effort condition. Thus, total mechanical power (external power plus internal power) also increased as One approach in the search for an explanation for cadence increased. Using energy expenditure preferred rates of movement is to use optimization estimates computed from aerobic demands for or modelling strategies. These strategies use modifi- each cycling condition and total mechanical power able characteristics, such as cadence, and kinematic results, Widrick and colleagues computed mechan- constraints to define muscle action. Such strategies ical efficiency. Optimal pedalling cadences, defined have been used to predict optimal cycling cadence as the cadence at which mechanical efficiency (Redfield & Hull 1986a, 1986b; Hull & Gonzalez was maximized, ranged from 82 r.p.m. at 49 W to 1988; Hull et al. 1988; Kautz & Hull 1993). In cycling, 101 r.p.m. at 147 W, values that are clearly quite there is an important link between pedalling cadence comparable with preferred cycling cadences. and performance. Cyclists use the gears of the bicycle As one final example of the potential relationship to select a particular cadence suited to the riding between preferred and most efficient rates of move- demands. The traditional approach has been to col- ment, Corlett and Mahadeva (1970) developed an lect empirical data whereby metabolic cost (e.g. aer- instrument to quantify mechanical power during a obic demand) of riding at particular combinations manual tyre-pumping task. Combining this assess- of cadence and power output have been determined ment with measures of oxygen consumption, they (e.g. Dickinson 1929; Garry & Wishart 1931; Gaesser were able to quantify the energy expenditure per & Brooks 1975; Seabury et al. 1977; Jordan & Merrill stroke for different pumping rates. Interestingly, the 1979; Hagberg et al. 1981; Böning et al. 1984; Coast & energy cost per stroke declined as rate of pumping Welch 1985; Marsh & Martin 1993, 1997). increased from slow (~10 strokes · min–1) to inter- Hull and colleagues have taken a different mediate rates (30–40 strokes · min–1). Energy cost approach to identifying essential factors that deter- per stroke did not change with further increases in mine optimal pedalling cadence. They argued that rate (up to 60 strokes · min–1). Further, preferred physiological cost, which is of considerable import- rates of movement coincided with the minimum ance with respect to overall performance, is directly 150 locomotion associated with muscular effort and that mechanical r.p.m. appear to agree well with preferred cadences markers (e.g. net joint moments) can provide a reas- of experienced cyclists, rather than with the most onable representation of lower-extremity muscular economical or efficient cadences (30–60 r.p.m.) effort (Redfield & Hull 1986a,b). In their earlier reported in the research literature (e.g. Hill 1922; efforts, Hull and colleagues (Hull & Jorge 1985; Dickinson 1929; Garry & Wishart 1931; Gaesser & Redfield & Hull 1986a) developed a five-bar linked- Brooks 1975). Second, predicted optimal cadence segment model that could be used to simulate net rises with increasing power output, and third, op- joint moment profiles under many different ped- timal cadence appears to be relatively insensitive alling conditions (e.g. different cadences, power to pedalling style. outputs, crank-arm lengths). Inputs for their model Redfield and Hull (1986b) refined and extended included scaled pedal-force profiles, measured crank their simulations of optimal cycling cadence by positions, lower-extremity kinematic data predicted applying a muscle stress-based function that from crank position and anthropometric constraints, had been used previously in gait research (e.g. and pedal angles derived from a sinusoidal func- Crowninshield & Brand 1981). Their muscle stress- tion. In an effort to delineate muscle function more based cost function improved prediction of both effectively, net joint moments were subsequently propulsive and recovery phase pedal forces as well divided into a quasi-static component, which was as net joint moments, compared with their previous a function of external forces applied to the foot via moment-based modelling efforts. Hull et al. (1988) the pedal, and a kinematic moment related to limb subsequently used the muscle stress function to pre- accelerations. dict the optimal cadence for a 200 W power output Redfield and Hull (1986a) specifically explored and found a minimum in this cost function in the the relationship between net joint moments and range of 95–100 r.p.m., a value that was consistent pedalling cadence. Net joint moments were simu- with their earlier work using the moment cost func- lated for cadences of 63, 80 and 100 r.p.m. at a power tion (Redfield & Hull 1986a). Interestingly, the close output of 200 W. They found that as cadence match between the optimal cadences predicted increased, the kinematic moment increased and the from the muscle-stress and net joint moment cost quasi-static moment decreased. The increased kine- functions led Hull et al. to conclude that the matic moment was attributed to the increased accel- moment-based function offered the advantage of erations of the limbs at higher speeds, whereas the greater ease of computation without sacrificing decreased quasi-static moment was a function of accuracy in predicting optimal cadence. the inverse relationship between pedal force and A crucial feature of any simulation research is the cadence when power output is maintained. When extent to which its results can be supported by these components are added, a parabolic-like curve empirical data. A fundamental assumption made representing the total moment is derived (Fig. 7.4). by Hull et al. (1988) was that pedal forces scale in From these results, Redfield and Hull showed that inverse proportion to the scaling of crank angular the total joint moment is high at relatively low velocities as pedalling cadence changes (i.e. as crank cadences (< 80 r.p.m.) because of a high quasi-static velocity increases, pedal forces decrease). MacLean contribution. At relatively high cadences (> 120 and Lafortune (1991a) showed that while the nor- r.p.m.), the total moment is also high because of mal component of the pedal force scaled in pro- high kinematic moment contributions. Thus, total portion to crank velocity during the propulsive joint moment is minimized, suggesting that muscu- phase or downstroke, the reverse was true during lar effort is minimized, at intermediate cadences the upstroke or recovery phase (i.e. as cadence (105 r.p.m. in their analysis for a 200 W power out- increased, the normal component increased). Fur- put). Redfield and Hull concluded that their joint ther, shear forces applied to the pedals increased moment cost function provided a valid criterion for during the downstroke and became smaller in the assessing optimal cadence for several reasons. First, upstroke as cadence increased. They concluded predicted optimal cadences of the order of 90–110 that scaling of pedal forces in inverse proportion to preferred rates in cyclic activities 151 crank velocity was not acceptable. Thus, use of this resulting from muscle activity, and reversible by assumption may compromise the validity of model rest’ (p. 116). In a series of papers, Takaishi, Moritani predictions. and colleagues (Takaishi et al. 1994, 1996, 1998) have In a separate presentation, MacLean and Lafortune estimated neuromuscular fatigue, using charac- (1991b) compared optimal cadence determined teristics of the electromyograph (EMG) signal, to using five net joint moment-based cost functions help explain differences between preferred and with the cadence at which group mechanical most energetically optimal cadences in cyclists and efficiency was maximized, the latter being assumed non-cyclists. Takaishi et al. (1994) had eight non- to reflect the optimal cadence criterion. Using a cyclists pedal at rates ranging from 40 to 80 r.p.m., group of 10 experienced cyclists riding at 200 W at 75% of maximal aerobic power. Not surpris- over five cadences from 60 to 120 r.p.m. (in incre- ingly, metabolic cost was minimized at the lower ments of 15 r.p.m.), they found that only one of their cadences, and increased significantly as cadence five moment-based cost functions (one based solely approached 80 r.p.m. In contrast, the slope of the on the net moment about the knee) yielded an integrated EMG curve (iEMG) over the course of an optimal cadence matching that at which gross exercise bout at a given cadence was significantly mechanical efficiency was maximized (80.4 and lower for the higher cadences. Over time, an 81.3 r.p.m., respectively). The remaining moment- increase in the slope of the iEMG is thought to reflect based cost functions yielded optimal cadences the recruitment of additional motor units, and/or that were substantially higher, on average about an increase in the firing frequency of previously 100 r.p.m., and much nearer to values reported by recruited motor units. As such, the slope of the Hull and colleagues (Redfield & Hull 1986a; Hull iEMG is directly related to the intensity of the act- et al. 1988). MacLean and Lafortune suggested that ivity (Takaishi et al. 1994). it is not surprising that minimizing the net knee Takaishi et al. (1996) also found that the slope of moment will minimize physiological cost and max- the iEMG was lower at higher cadences (80–90 imize gross mechanical efficiency because of the r.p.m.) in six trained cyclists, whereas metabolic cost many muscles acting about the knee in cycling. was minimized at 60–70 r.p.m. In both cases, the Other issues surrounding optimization of cycling cadences at which the slope of iEMG was found to cadence, including seat height, foot position, etc., be lowest were similar to the preferred cadences of have been explored and are reviewed by Gregor et the subjects (Takaishi et al. 1994, 1996). As the slope al. (1991). There remains conjecture regarding the of iEMG was lower at higher cadences, Takaishi et relationships between muscle characteristics and al. (1994, 1996) concluded that the higher cadences selection of optimal rate (Chapman & Sanderson chosen by competitive cyclists are selected to help 1990), and these have yet to be resolved. Currently, minimize peripheral neuromuscular fatigue. They there are few or no published empirical data that further noted that the lower iEMG slopes at the substantiate the supposed relationship between higher cadences suggests that fewer type II muscle muscle moments, muscle stress and cadence selec- fibres would be needed to meet the demands of the tion. Clearly, this needs to be a focus of ongoing cycling task. research. In support of this contention, Ahlquist et al. (1992) found that glycogen depletion was much greater in Minimization of neuromuscular fatigue type II muscle fibres after cycling at 50 r.p.m. than at 100 r.p.m. at a power output equivalent to 85% Recently, a number of investigators have explored of maximal aerobic power. Glycogen depletion the role of muscle fatigue in determining the op- was not different in type I fibres between the two timal cadence for cycling during both steady-state cadence conditions. The lower pedal forces required and exhaustive exercise. Sargeant (1994) has defined at a higher cadence for a fixed power output muscle fatigue as ‘the failure to generate or maintain (Patterson & Moreno 1990) would require lower the required or expected force or power output, muscle forces, and not require the recruitment of as 152 locomotion many type II fibres (Ahlquist et al. 1992). Patterson in a group of seven untrained subjects at multiple and Moreno (1990) noted that the resultant pedal power levels. Similarly, McNaughton and Thomas forces were minimized at 90 r.p.m. (at 100 W) and (1996) reported time to exhaustion was greater at 50 100 r.p.m. (at 200 W) in a group of 11 recreational r.p.m. than at 90 or 110 r.p.m. for untrained subjects. cyclists. These values were also very close to the These results are consistent with the general finding preferred cadences at both power outputs. During that metabolic cost is minimized around 50–60 steady-state cycling, greater recruitment of type II r.p.m. (Seabury et al. 1977; Carnevale & Gaesser fibres at lower cadences would presumably lead to 1991; Marsh & Martin 1993, 1997; McNaughton & more rapid fatigue. At higher cadences, the greater Thomas 1996). While the work of Carnevale and reliance on type I fibres would help prevent the Gaesser, and of McNaughton and Thomas is cer- onset of fatigue. Nevertheless, metabolic energy tainly relevant, it cannot be directly compared with cost will still be higher under high cadence condi- the studies by Takaishi et al. (1994, 1996, 1998). The tions due to the greater number of repetitions per- former investigations used power outputs designed formed per unit of time (Takaishi et al. 1994, 1996). to bring about volitional exhaustion in a 1- to 10-min Takaishi et al. (1996) also noted that non-cyclists range, while Takaishi et al. (1994, 1996, 1998) used showed large increases in the iEMG of the vasti power output levels that were designed to allow muscles at higher pedalling rates, whereas the subjects to cycle for at least 15 min without suffer- trained cyclists did not demonstrate such an ing undue fatigue. Carnevale and Gaesser (1991) increase. The authors suggested that the lack of and McNaughton and Thomas (1996) also used increase in iEMG for trained cyclists at higher untrained subjects, while Takaishi et al. (1996, 1998) cadences was related to pedalling skill developed used a combination of untrained non-cyclists, by the trained cyclists. In subsequent research, trained non-cyclists, and trained cyclists. A final Takaishi et al. (1998) demonstrated that while the point not directly addressed by Carnevale and vasti iEMG did not increase substantially for trained Gaesser (1991) was that while time to exhaustion cyclists (N = 7) as cadence increased, biceps femoris was substantially greater for 60 r.p.m. vs. 100 r.p.m. iEMG did increase dramatically. Trained non- at the lowest power output, the time to exhaustion cyclists (N = 7) demonstrated a general increase in difference between 60 and 100 r.p.m. all but disap- the iEMG of the vasti muscles as cadence increased, peared as power output was increased. With regard with no increase in biceps femoris activity. In to this, Hill et al. (1995) suggested that the advantage addition, normal pedal forces decreased for both of decreased metabolic cost at lower cadences may trained cyclists and trained non-cyclists as cadence be offset as power output increases, due to the increased; however, the normal pedal forces were increased muscle force requirements per cycle. lower for trained cyclists than trained non-cyclists at While the data relating to the role of muscle all but the lowest cadence (45 r.p.m.). The invest- fatigue in setting preferred rate of movement dur- igators suggested that the trained cyclists had ing different modes of cycling are as yet equivocal, developed a pedalling technique that involved pull- the theoretical work of Sargeant (1994) may provide ing up the leg, via knee flexion, during the recovery some additional insight. In a muscle of mixed fibre portion of the pedal cycle at higher cadences. The type, the optimal rate of shortening will be a com- speculated technique would allow for the lower promise between the power–velocity relationships pedal force seen in the cyclists, and presumably of type I and type II fibres. During real-world result in lower muscle stress in the vasti group, and cycling, maximal power output is achieved at ap- a lower dependence on type II muscle fibres proximately 120 r.p.m. (Sargeant 1994). Based on the (Takaishi et al. 1998). combined power–velocity relationship of a theor- Some papers in the literature would seem to con- etical whole muscle, and the ability of the CNS to tradict the findings of the above mentioned studies. selectively recruit motor units, Sargeant argued that Carnevale and Gaesser (1991) found that time to at 80% of maximal power output, pedalling at 120 exhaustion was greater at 60 r.p.m. than 100 r.p.m. r.p.m. would result in a reserve of 20% available preferred rates in cyclic activities 153 power, due to the muscle being at the shortening and that the resonant frequency of the FDHO model velocity corresponding to the peak of the power– corresponds to the preferred rate of walking. velocity curve. At 60 r.p.m. there would be no Results for 24 young adults supported their hypo- power reserve, as the muscle would be on the thesis that ‘the resonant frequency of a harmonic ascending limb of the power–velocity curve. oscillator can accurately predict that chosen by sub- Pedalling at 120 r.p.m. would also allow the small- jects when appropriate adjustments are made to est possible contribution from type II fibres to meet the formula based on an optimization criterion of the demands of the cycling task (assuming type I minimum force’ (p. 64). They concluded that the fibres were maximally activated). Sargeant addi- physical attributes of the lower extremity, more tionally contends that having the smallest theor- specifically its inertial characteristics, specify the etical contribution from type II fibres requires a most economical stride rate. In subsequent research, progressive increase in cadence as power output is Holt et al. (1991) confirmed that preferred stride rate increased. Sargeant’s model also predicts that at was not different from that predicted from their lower power outputs, the demands are best met at a FDHO model. Subjects walked under eight stride rate lower cadence. This would allow a greater reliance conditions (preferred rate, rate predicted using the on more economical type I fibres than at higher FDHO model, and rates 5, 10 and 15 strides · min–1 cadences. While the work of Sargeant (1994) is higher or lower than the FDHO rate) as aerobic mostly theoretical in nature, at the very least it demand was measured. Both preferred and FDHO suggests that the preferred or optimal rate of move- predicted stride rates resulted in minimal aerobic ment during cycling, and other cyclic activities, may demand, lending additional support to the asso- well be determined in large part by underlying ciation between preferred stride rate and gait eco- mechanical properties of the specific muscles most nomy. Although the FDHO model has not been involved in producing the movements. At present, applied to activities other than gait, recent research this notion has not been thoroughly investigated has successfully predicted preferred stride rates for experimentally. backward walking (Schot & Decker 1998) and for 3- to 12-year-old children (Jeng et al. 1997), effectively Pendular properties of swinging limbs extending the generalizability of the phenomenon. The association between the energy cost of walk- Kugler and colleagues (Kugler et al. 1980; Kugler & ing and running and the inertial characteristics of Turvey 1987) noted that limb motions in locomotion the lower extremity has been demonstrated in sev- are auto-oscillatory and possess mechanically con- eral segment loading studies in which segment iner- servative characteristics of a pendular-like mode of tia has been modified artificially (e.g. Martin 1985; organization; in other words, the limbs represent Myers & Steudel 1985; Steudel 1990). In contrasting complex pendulum systems. During cyclic activity proximal and distal applications of load, more dis- of an anatomical system (e.g. walking), a certain tally positioned load on the segment produces a amount of mechanical energy is dissipated from the larger increase in the moment of inertia of the leg system with each cycle of motion. Thus, muscular about the hip and a greater increase in the aerobic effort is required to sustain limb pendular-like demand of gait than proximal loading. Less atten- movements. It has been hypothesized that a reson- tion has been paid to the effect of load distribution ant frequency for any complex pendulum system on the temporal features of walking and running. can be predicted if the anthropometric and inertial Consistent with the pendular phenomenon, Martin characteristics of the limbs are known. Further, it (1985) reported a small (1.2%) but statistically is suggested that the resonant frequency relates significant decrease in stride rate and increase directly to the fundamental rate that minimizes the (2.0%) in swing time when 0.50 kg was added to energy cost associated with sustaining the motion. each foot during treadmill running at 3.33 m · s–1. Holt et al. (1990) proposed that walking can be mod- Recent data from our laboratory have also shown elled as a force-driven harmonic oscillator (FDHO) predictable effects of shank and foot loading on 154 locomotion walking stride rate in able-bodied (Royer et al. 1997) at rates above preferred, as the time to generate and unilateral below-knee amputees (Mattes et al. muscular force would be shortened. A shortened 2000). Thus, while the FDHO model and pendular ground contact time has been suggested to require mechanics are theoretically sound and appear to the recruitment of less-economical fast-twitch apply well to cyclic activities in which the extre- muscle fibres, and consequently increase metabolic mities are being oscillated, the magnitude of the cost (Kram & Taylor 1990). Ferris and Farley (1997) effect on cadence is not well substantiated. further showed that subjects increase hopping rate by increasing leg-spring stiffness, regardless of sur- Limb stiffness face compliance. However, leg-spring stiffness was increased disproportionately more on compliant Recently, Farley, McMahon, and co-workers surfaces than stiff surfaces, to keep the total vertical (Blickhan 1989; McMahon & Cheng 1990; Farley stiffness nearly constant at a given rate. et al. 1991; Farley et al. 1993; Farley & Gonzalez 1996; Farley and Gonzalez (1996) had four subjects run Ferris & Farley 1997) have used a simple spring- on a treadmill-mounted force platform at 2.5 m · s–1, mass model of the human body to demonstrate that and at stride rates from 26% below to 36% above limb stiffness may determine rate of movement preferred (preferred stride rate = 79.8 strides · in bounding and running gaits. According to this min–1), to see how the behaviour of the spring-mass model, the human body is represented as a massless model was altered to produce different stride rates. spring (the ‘leg spring’) and a point mass. It has been While the stiffness of the leg spring has been found shown that the stiffness of the leg spring remains to remain constant, and the angle through which the nearly constant as running speed increases in leg spring is swept increases as speed increases (He humans and several other animal species (Farley et et al. 1991; Farley et al. 1993), Farley and Gonzalez al. 1993; He et al. 1991). As running speed increases, found that different stride rates at a constant speed the leg spring is swept through a larger angle, are produced primarily by increasing the leg-spring increasing the effective stiffness of the overall sys- stiffness. The stiffness of the leg spring was in- tem, and causing the body to bounce off the ground creased over twofold from the lowest stride rate to at a faster rate. During hopping, or at a constant run- the highest rate, while the angle swept by the leg ning speed, however, the stiffness of the leg spring spring only decreased slightly at the highest rate. appears to be modulated to produce a different In fact, when stride rate (Farley & Gonzalez 1996) hopping rate. and hopping rate (Farley et al. 1991) were each Farley et al. (1991) had four subjects hop forwards increased by 65%, leg-spring stiffness increased on a treadmill-mounted force platform at speeds by approximately the same amount (twofold), from 0 to 3 m · s–1, and in place on a ground-based demonstrating the similarities between these two force platform. During both hopping conditions, forms of locomotion. and at all but the fastest treadmill speed, the mean Farley and Gonzalez (1996) stated that the ability preferred rate was 132 hops · min–1. The body to adjust the leg-spring stiffness is likely to be an behaved as a simple spring-mass system at the pre- important factor in adapting the locomotor system ferred hopping rate and at all rates above preferred. to the demands of the environment. In physiological Below the preferred hopping rate, the body did not terms, the stiffness of the leg spring can be adjusted behave as a simple spring-mass system, implying in at least two ways. Changing the orientation of the that the storage and reutilization of elastic energy limbs relative to the ground (McMahon et al. 1987), would be compromised at low rates. At hopping and changing muscle activation patterns (Farley & rates above preferred, the stiffness of the leg spring Gonzalez 1996) will each result in an altered leg- was increased to allow the body still to behave as a spring stiffness. In summary, Farley et al. (1991) sug- simple spring-mass system. As ground contact time gested their findings help explain why metabolic decreased with increasing hopping rate, Farley et al. cost is minimized at the preferred rate of movement (1991) suggested that metabolic cost would increase in bounding or running gaits. Metabolic cost below preferred rates in cyclic activities 155 the preferred rate will increase due to a loss of ferred rate of movement. Smoll (1975), and Smoll elastic strain energy from the system. Above the and Schutz (1978) found distinct individual differ- preferred rate, metabolic cost will increase due to a ences in preferred cadences and movement vari- shorter ground contact time. While the spring-mass ability in a cyclic upper-limb task. They noted that model has been valuable in distinguishing import- movement variability is uncorrelated with pre- ant aspects of rate selection in bounding and run- ferred cadence, and is likely to be related to underly- ning gaits, it is not directly applicable to other ing biological variability. According to Smoll (1975), activities, such as walking, where kinetic energy movement variability is indicative of the status of an and gravitational potential energy are 180° out individual performance, and is an essential compon- of phase, and the body does not behave as a simple ent of a complete description of that performance. spring-mass system. Interestingly, Bonnard and Movement variability has previously been char- Pailhous (1993) found that during walking, stride acterized as stochastic in nature (Hirokawa 1989). rate is highly dependent on limb stiffness during the Recent research by Hausdorff and colleagues swing phase, but independent of limb stiffness dur- (Hausdorff et al. 1995, 1996), however, has demon- ing stance. The stiffness changes noted by Farley strated that variations in the stride interval during and co-workers (Blickhan 1989; McMahon & Cheng steady-state walking exhibit long-range correla- 1990; Farley et al. 1991; Farley et al. 1993; Farley & tions, such that the fluctuations in stride interval at Gonzalez 1996; Ferris & Farley 1997) during run- any point in time are dependent on stride inter- ning and hopping relate implicitly to the stance vals at previous times. The long-term correlations phase. extend as far back as 1000 strides (Hausdorff et al. 1996). Interestingly, when subjects walked in time Minimizing movement variability with a metronome set at their preferred stride rate, the long-range correlations disappeared, and the In addition to metabolic cost, mechanical minimiza- variations in stride interval became random in tion phenomena and limb inertial properties, move- nature (Hausdorff et al. 1996). Hausdorff et al. (1995) ment stability or variability may be another factor proposed that chaotic variability is an intrinsic that determines the preferred or optimal rate of part of the normal locomotor control system. The movement during cyclic activities. The reader researchers also suggested that supraspinal centres should note that high movement stability and low are responsible for the presence of the long-term movement variability are synonymous in the pre- correlations. From a control perspective, systems sent context. Much, if not all, of the literature relat- that possess long-range correlations are inherently ing to movement stability during cyclic activities more resistant to perturbations (Hausdorff et al. comes out of a dynamical systems approach to 1995). Movement variability/stability is clearly a movement organization. According to dynamical relevant factor for cyclic movement control, and systems theory, ‘behavioural patterns and their a possible determinant of preferred rate of dynamics are shown to arise in a purely self- movement. organized fashion from cooperative coupling among One of the most complete accounts of the relation- individual components’ (Kelso & Schöner 1988, ship between movement stability and preferred rate p. 27). A primary focus of this theory is the study of movement is provided by Holt et al. (1995). Their of stability and the loss of stability. Well-learned paper is notable because they employed stability, or preferred movement patterns are associated with metabolic, mechanical and inertial measures, allow- high stability, and a loss of stability is usually ing direct comparisons not usually possible in uni- indicative of an impending change in behaviour focal studies. They determined three measures of (such as the transition from walking to running). movement stability for eight subjects at their pre- There is also evidence from more traditional ferred speed as they walked on a treadmill at pre- motor behaviour circles that movement variability ferred stride rate, optimal stride rate predicted by a is an important and relevant issue in control of pre- force-driven harmonic oscillator model of the lower 156 locomotion

–1 1.6 0.09 m·s , and stride rates ranging from 30 to 80 strides · min–1. The two major findings by Maruyama and Metabolic cost Variability ) Nagasaki (1992) were that stride variability for all –1 1.4 0.08 stride phases decreased as speed increased, and variability was minimized at or near the preferred 1.2 0.07 stride rate at any given speed. In a similar study using 22 subjects walking overground, Sekiya et al. 1.0 0.06 (1997) found that spatial variability of stride length was minimized near the preferred stride rate and

0.8 0.05 Standard deviation units preferred speed. At the speed most closely appro-

Oxygen consumption (l·min ximating the commonly reported energetically optimal speed (1.38 m · s–1), temporal variability 0.6 0.04 60 80 100 120 140 was minimized at a stride rate of 58.2 strides · min–1 Per cent of predicted frequency and spatial variability was minimized at a stride rate of 60.4 strides · min–1. The preferred rates at the Fig. 7.5 Both aerobic demand and movement variability same speed were 57.1 strides · min–1 (Maruyama & reflect minima near the resonant frequency or stride rate predicted using a force-driven harmonic oscillator Nagasaki 1992) and 54.2 strides · min–1 (Sekiya et al. model. This predicted stride also corresponded well with 1997). Maruyama and Nagasaki (1992) and Sekiya preferred cadences of subjects. (Adapted from Holt et al. et al. (1997) concluded that preferred stride rate is 1995.) optimized in terms of metabolic cost and movement stability. limb, and ±15, ±25 and ±35% of predicted stride rate. Brisswalter and Mottet (1996) used variability The three stability measures were the standard and metabolic cost measures in an analysis of the deviation of the relative phase between the lower walk-to-run transition in 10 subjects walking and limb joints, the standard deviation of a normalized running on a treadmill. During the preferred trans- vector length of the phase planes for the head and ition speed trials, variability increased as walking back, and the magnitude of the spectral power speed increased in the neighbourhood of the trans- near the predicted and preferred frequencies for ition speed. After the transition, variability was the head and joints. They additionally measured much lower, consistent with the findings of others metabolic cost and mechanical energy conservation (Diedrich & Warren 1995). Brisswalter and Mottet at each stride rate. Holt and colleagues found that (1996) also expected variability to be lower for walk- movement stability was generally maximized (i.e. ing below the transition speed, and lower for run- variability was minimized) and metabolic cost ning above the transition speed; however, this was minimized at the preferred and predicted stride not the case. Variability was lower for running than rates, which were not significantly different from walking at all common speeds (±0.3 m · s–1 of trans- each other (Fig. 7.5). Holt et al. (1995) noted that the ition speed). Therefore, below the energetically op- metabolic cost curve was steeper at low stride rates timal transition speed, walking is more economical, than at high rates, but the reverse was true for the but also more variable than running. In address- stability curve. The investigators suggested that ing this paradox, the authors noted the difficulty preferred stride rate may be a compromise between in associating gross energy cost with movement metabolic cost and movement stability. efficiency, and suggested that metabolic cost alone Maruyama and Nagasaki (1992) measured the is not adequate to relate movement efficiency variability of many temporal aspects of the stride and variability. Another factor not addressed by (stride time, step time, stance time, swing time and Brisswalter and Mottet is that at the common double support time) using variable error and speeds, stride rate was higher for running than for coefficient of variation in seven subjects during walking (1–16%), and variability tended to decrease treadmill walking at speeds ranging from 0.5 to 1.7 (up to a point) with increases in rate of movement preferred rates in cyclic activities 157

(Smoll 1975; Smoll & Schutz 1978), perhaps making All of the studies reviewed so far have dealt the finding of lower variability at all running speeds exclusively with adults. A few papers in the literat- less surprising. One should keep in mind that the ure have dealt with movement variability during paper by Brisswalter and Mottet dealt with speeds locomotion in children. Jeng et al. (1997) determined near the preferred transition speed, and did not interlimb and intralimb stability in 45 children aged include data on preferred speed or stride rate for 3–12 years walking on a treadmill at their preferred walking or running. stride rates and ±25% of preferred stride rate. In In a paper dealing with the walk-to-run trans- most cases, interlimb and intralimb stability was ition, Diedrich and Warren (1998) presented an maximized under preferred stride rate conditions. account of movement stability over a range of walk- The authors also noted that by age 7 years, children ing and running speeds. The walking stability func- exhibit a self-optimization pattern similar to adults. tion had a minimum at 1.66 m · s–1 and 61.8 · strides Jeng et al. (1997) also observed that 5- to 6-year-olds · min–1. The data from Diedrich and Warren com- demonstrated an ability to modulate stride rate not pare favourably with the results from Maruyama seen in 3- to 4-year-olds, but as a consequence the and Nagasaki (1992). At a speed of 1.67 m · s–1, gait of the 5- to 6-year-olds became more variable. Maruyama and Nagasaki reported minimum Variability subsequently decreased in the 7- to 12- variability at 62.0 strides · min–1, and a preferred year-olds. The dramatic differences between the rate of 62.4 strides · min–1. While the stability and 5- to 6- and 3- to 4-year-olds are possible due to mor- metabolic cost relationships were very similar in phological changes that occur between ages 3 and 6; shape, the respective minima were not coincident however, they may also be indicative of a transition (energetically optimal walking speed ~1.3 m · s–1). from a rigid form of control to a more adaptive form Diedrich and Warren (1998) emphasized the sim- of control (Jeng et al. 1997). A more adaptive form of ilarities between the overall behaviour of the stabil- control would by its very nature require more vari- ity and economy functions, and suggested that any ability in the system. Clark and Phillips (1993) have minor differences were likely to be related to the also suggested that infants also go through a period fact that global energy expenditure includes costs of stability acquisition during the first 3 months of not associated with the locomotor task. As with independent walking. Although the picture is far research by others (Maruyama & Nagasaki 1992; from complete, locomotion development in chil- Holt et al. 1995; Sekiya et al. 1997), the findings of dren may undergo at least two distinct phases of Diedrich and Warren (1995, 1998) point to a strong, stability acquisition. One is associated with the ini- if not perfect (Brisswalter & Mottet 1996), relation- tial development of the walking skill, and a second ship between movement stability and economy. is associated with an increase in the adaptability of Patla (1985) examined EMG variability at fast, stride rate to meet the demands of the environment. normal and slow stride rates in seven subjects walk- The literature on movement variability at differ- ing on a treadmill at preferred speed. He used a pat- ent rates of movement in cyclic activities outside the tern recognition technique to estimate variability. locomotion arena is sparse. Recently, Dawson et al. Surprisingly, muscle activity patterns were found (1998) reported changes in temporal variability dur- to be more variable for the normal stride rate than ing rowing on an ergometer and on the water in five the slow or fast rates. The author suggested that competitive rowers, over a range of stroke rates the attentional demand necessary to walk in a (18–33 strokes · min–1). The authors discovered that non-preferred manner could account for the lower rowers increase stroke rate primarily by decreasing variability under these conditions. The finding of the duration of the recovery phase, while the increased variability for muscle activity at the pre- duration of the stroke phase changed very little. ferred rate is in direct contrast to the notion that As stroke rate increased, variability generally kinematic variability is minimized at the preferred decreased for both the recovery phase and the rate (Maruyama & Nagasaki 1992; Holt et al. 1995; stroke phase. The decreases in variability were most Sekiya et al. 1997). dramatic for the recovery phase, which exhibited 158 locomotion considerably higher variability than the stroke Summary phase at the lower rates. Dawson et al. (1998) did not determine preferred stroke rate for the rowers in The factors that determine the preferred and/or their study. They did note, however, that preferred optimal rate of limb movement during any cyclic stroke rate is usually in the range of 30–40 strokes · activity are clearly many. Metabolic cost, mechan- min–1. This would suggest that movement variabil- ical minimization phenomena, muscle mechanical ity is minimized at or near preferred stroke rates in properties, limb inertial parameters, movement competitive rowers. stability and limb stiffness all appear to be asso- Based on the studies reviewed, movement stabil- ciated with the preferred rate of movement for ity would appear to be a contributing factor to the one or more activities. The tasks for the future are selection of the preferred cadences during locomo- twofold. For the locomotion arena, well-designed tion. Specifically, the results of Holt et al. (1995) indic- multifactorial studies are needed that will allow us ate that stability may cooperate with metabolic cost to determine which associated factors are causal, in setting the preferred stride rate. The findings of and which are merely related effects. Addition- Dawson et al. (1998) suggest that minimizing vari- ally, many studies are needed using activities other ability may be a factor in cadence selection for other than walking, running and cycling, to determine activities as well. Many more studies will be needed whether the conclusions reached from the loco- on other cyclic activities before any far-reaching motion-based studies have strong generalizability, generalizations can be made regarding the role of or are activity specific. Only then will the critical movement stability/variability in rate of movement factors underlying the selection of the rate of move- selection. ment emerge.

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