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Critical Power: Implications for Determination

of V

˙O

2max

and Exercise Tolerance

ANDREW M. JONES

1

, ANNI VANHATALO

1

, MARK BURNLEY

2

, R. HUGH MORTON

3

, and DAVID C. POOLE

4

1

School of Sport and Health Sciences, St. Luke’s Campus, University of Exeter, Exeter, Devon, England,

UNITED KINGDOM;

2

Department of Sport and Exercise Sciences, Aberystwyth University, Aberystwyth, Ceredigion,

Wales, UNITED KINGDOM;

3

Institute of Food Nutrition and Human Health, Massey University, Palmerston North,

NEW ZEALAND; and

4

Departments of Kinesiology, Anatomy and Physiology, Kansas State University, Manhattan, KS

ABSTRACT

JONES, A. M., A. VANHATALO, M. BURNLEY, R. H. MORTON, and D. C. POOLE. Critical Power: Implications for Deter-

mination of V

˙O

2max

and Exercise Tolerance. Med. Sci. Sports Exerc., Vol. 42, No. 10, pp. 00–00, 2010. For high-intensity muscular

exercise, the time-to-exhaustion (t) increases as a predictable and hyperbolic function of decreasing power (P) or velocity (V). This

relationship is highly conserved across diverse species and different modes of exercise and is well described by two parameters: the

‘‘critical power’’ (CP or CV), which is the asymptote for power or velocity, and the curvature constant (W¶) of the relationship such that

t=W¶/(PjCP). CP represents the highest rate of energy transduction (oxidative ATP production, V

˙O

2

) that can be sustained without

continuously drawing on the energy store W¶(composed in part of anaerobic energy sources and expressed in kilojoules). The limit of

tolerance (time t) occurs when W¶is depleted. The CP concept constitutes a practical framework in which to explore mechanisms of

fatigue and help resolve crucial questions regarding the plasticity of exercise performance and muscular systems physiology. This

brief review presents the practical and theoretical foundations for the CP concept, explores rigorous alternative mathematical approaches,

and highlights exciting new evidence regarding its mechanistic bases and its broad applicability to human athletic performance.

Key Words: FATIGUE, EXERCISE INTENSITY DOMAINS, V

˙O

2

KINETICS, ANAEROBIC CAPACITY, ATHLETIC PERFOR-

MANCE, MAGNETIC RESONANCE SPECTROSCOPY

It is a common experience that running, cycling, or

swimming at a relatively fast yet comfortable pace can

be continued for a considerable period without undue

fatigue. However, even slightly increasing the pace sub-

stantially increases the perceived effort and dramatically

reduces the tolerable duration of exercise. It is perhaps less

well appreciated that these experiences have solid mathe-

matical and physiological bases, which are enshrined in the

critical power (CP) concept. The CP thus represents an im-

portant parameter of aerobic function (in addition to gas

exchange threshold (GET), maximal O

2

uptake (V

˙O

2max

),

and exercise efficiency) and one that provides an invaluable

framework in which to study and understand more fully the

mechanisms of fatigue and exercise intolerance. It is only

relatively recently that some of the key features of the con-

cept have come to light, although the concept has been

studied, in one form or another, since the scientific investi-

gation of exercise began.

This review builds on the historical foundations of the

CP concept (Historical bases for the critical power concept

section) to provide essential perspectives for the reader to

appreciate the importance of contemporary discoveries and

relevance to human (and animal) muscular performance.

Two key problems that have hampered a broader imple-

mentation and interpretation of the CP concept have been

overcome in very recent investigations and are the focus

of the sections on Mechanistic bases of the critical power

concept and Application of the critical power concept to

all-out exercise. Specifically, lack of knowledge regarding

specific intramyocyte fatigue mechanisms operant during

high-intensity (severe) exercise above the CP (Mechanistic

bases of the critical power concept section) and the cum-

bersome nature of the multiple fatiguing tests thought to

be requisite for defining the power–time-to-exhaustion

(i.e., P–t) relation and extracting the parameters CP and W¶

(Application of the critical power concept to all-out exercise

section). The Mathematical features of the critical power

concept section places the two-parameter P–tmodel in its

mathematical perspective and addresses whether a more

complex three-parameter model is justifiable theoretically

and practically. Crucially, this section investigates optimal

race strategies from a mathematical orientation, which leads

Address for correspondence: Andrew M. Jones, Ph.D., School of Sport and

Health Sciences, University of Exeter, Heavitree Road, Exeter, EX1 2LU,

United Kingdom; E-mail: a.m.jones@exeter.ac.uk.

Submitted for publication November 2009.

Accepted for publication February 2010.

0195-9131/10/4210-0000/0

MEDICINE & SCIENCE IN SPORTS & EXERCISE

Ò

Copyright Ó2010 by the American College of Sports Medicine

DOI: 10.1249/MSS.0b013e3181d9cf7f

1

Copyeditor: Jamaica Polintan

Copyright @ 2010 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.

appropriately into the final section where practical applica-

tions of the CP concept are explored more fully (Practical

applications of the critical power concept section).

HISTORICAL BASES FOR THE CRITICAL

POWER CONCEPT

It can be no overstatement that the history of human

physical endeavor has been shaped and constrained by the

P–trelationship (Fig.

F1 1). Across millennia, the performance

of soldiers, laborers, and elite athletes locomoting over land,

in water, and, more recently, in flight has been bounded by

the CP and W¶parameters. For example, the Roman military

genius Vegetius, writing more than two millennia ago,

presents evidence that legionaries were required to march for

several hours at the military step (2.85 mph, 4.6 kmIh

j1

)

carrying 43.25 lb (19.6 kg) (51,81). Whipp et al. (80,81)

have estimated that this required sustaining a metabolic rate

somewhere between 1.4 and 1.7 L of O

2

Imin

j1

. As the

penalty for failure to reach this objective was death, the

military step had to be set below the CP (or CV) of most

legionaries to avoid crippling the ranks and eroding morale.

That the Roman military was arguably the finest mobile

fighting force in the world for several centuries implies that

the military step was not positioned too far below CP (CV).

In more contemporary times, the English physiologist

A. V. Hill conflated his observations in contracting isolated

frog muscles with those of exercising humans in an attempt

to understand the physiological determinants of extraordi-

nary physical performance and muscle fatigue. This led to

his construction of velocity–time curves, similar to that

schematized in Figure 1, from world records for runners,

swimmers, rowers, and cyclists (29) (see also Hill [30]). It is

pertinent that current (2009) world records also fit velocity–

time curves similar to those of Hill (29). Central to Hill

(and Otto Meyerhoff ), winning the 1922 Nobel prize was

his demonstration that both aerobic and anaerobic energy

sources were recruited to power high-intensity muscle con-

tractions (see Bassett [3] for review). It is fitting, therefore,

that our present understanding of the P–trelationship is

founded on the compartmentalization and coordinated func-

tion of these two energy sources.

In 1965, Monod and Scherrer (54) defined the CP of a

muscle (or muscular group) as ‘‘the maximum rate (of work)

that it can keep up for a very long time without fatigue.’’

They considered both dynamic work and isometric exercise

and extracted the two parameters, CP and a finite amount of

work performable above CP (‘‘energy store’’ component,

later termed W¶), by plotting total work done (abscissa)

against time-to-exhaustion (ordinate) for multiple fatiguing

exercise bouts. Linear regression for the points yielded an

intercept that corresponded to W¶, and CP was given by

the slope of the parallel line displaced downward to project

from the origin. By studying continuous and intermittent

isometric contractions and noting the improved performance

on the latter, Monod and Scherrer (54) considered CP to be

dependent, in part, on muscle blood flow and hence O

2

de-

livery. Subsequent experiments (see below) have demon-

strated unequivocally that CP is determined by oxidative

function and that W¶can be manipulated independently, for

example, by altering muscle phosphocreatine (PCr) stores,

consistent with its dependence on finite anaerobic energy

sources (52,53,65,74).

Because of the functional significance of CP, its position

relative to other signatory parameters of aerobic function—

the so-called ‘‘anaerobic threshold’’ (now more appropriately

termed the GET or lactate threshold (LT) and V

˙O

2max

—is

of great importance. In the early 1980s, two contrasting

viewpoints held that CP was placed at apparently widely

divergent locations. Specifically, the brilliant physiologist

Douglas R. Wilkie (83), whose interests included the feasi-

bility of man-powered flight (eventually realized by Bryan

L. Allen’s epic crossing of the English Channel in the

Gossamer Albatross in 1979), formulated an equation that

situated CP at a power output somewhere above V

˙O

2max

.

In marked contrast, Moritani et al. (55) placed CP at a

much lower V

˙O

2

not different from that at the ‘‘anaerobic

threshold’’ (considered by those authors to be synonymous

with LT or GET). Obviously, these two notions are mutu-

ally exclusive, and resolution of this crucial issue rests on

a combination of theoretical modeling and experimental

FIGURE 1—Top panel: Schematic showing the power–time (P–t) rela-

tionship for high-intensity exercise. Notice that although it has become

customary to illustrate the nonlinear model using reversed axes,

tremains the dependent variable. Bottom panel: Determination of

parameters CP and W¶from the linear Pj1/ttransform.

http://www.acsm-msse.org2Official Journal of the American College of Sports Medicine

Copyright @ 2010 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.

physiological approaches that characterized gas exchange

and metabolic behaviors near CP as detailed below.

Wilkie’s formulation was a valiant attempt to bring to-

gether mechanical and physiological determinants of high-

intensity exercise tolerance:

P¼EþA=tETð1expt=TÞt½1:1

where Pis a constant-power output that designates CP, Eis

the power at V

˙O

2max

,Ais work available from anaerobic

energy sources (notionally synonymous with W¶), tis

elapsed time, and Tis a V

˙O

2

time constant of 10 s (13,83).

Despite ostensibly providing a close fit to some data sets,

this equation errs dramatically: it places CP at a power out-

put above V

˙O

2max

and presumes the same very rapid Tfor

all work rates and individuals. The disparity between the T

of 10 s selected by Wilkie and the 25–40 s measured in

young healthy subjects was attributed to time delays in-

curred between V

˙O

2

in the muscle and its (then) site of

measurement via pulmonary gas exchange (83). It is now

known that TV

˙O

2

approaches 10 s only in a select few

cases; certain elite athletes such as Paula Radcliffe, the

women’s marathon world record holder (44), some cyclists

(47), and horses (49). However, in most individuals, it is

far slower and, when the transit time between muscle and

mouth is accounted for (È10–20 s), Tat the mouth faith-

fully represents that at the exercising muscle, is far longer

than 10 s, and is quite variable among individuals (26,48).

Moreover, it has been well established that constant-power

outputs that engender V

˙O

2max

are sustainable only for a

relatively short period (35,64).

At the other end of the spectrum, the conclusion of

Moritani et al. (55) that the CP is located at a V

˙O

2

that

is correlated with, and not different from, the V

˙O

2

at the

‘‘anaerobic threshold,’’ LT, or GET must be challenged on

the basis of more recent evidence. Specifically, although

CP is correlated with the LT or GET, it is clear that the CP

occurs at a substantially higher metabolic rate (and thus,

power output) at least in non–highly trained individuals

(64,65). However, it is pertinent that the metabolic rate

(i.e., V

˙O

2

) difference between GET/LT and CP becomes

compressed in very fit individuals (44) such that, in these

individuals, GET/LT and CP lie in closer proximity, but with

CP always at the higher V

˙O

2

. In summary, refinements in

data collection and modeling have demonstrated beyond

any reasonable doubt that the CP is a distinct and meaningful

parameter, not simply an alternative to maximal oxygen up-

take or the GET/LT. Its determination, however, remains a

challenge to the experimental physiologist (see Application

of the critical power concept to all-out exercise section).

In 1982, Whipp et al. (78) used a simple two-parameter

hyperbolic fit to the power–time relation:

ðPCPÞt¼W¶½1:2

which may be transformed into its linear formulation

P¼ðW¶=tÞþCP ½1:3

The power–time (P–t) curves were constructed using data

obtained from four or more independent high-intensity

constant-power exercise bouts for which the tolerable dura-

tion was 2–15 min (64). Higher-power outputs that were

predicted to induce exhaustion in G2 min were expressly

avoided because of concerns that constraints related to me-

chanical power generation might become apparent. Simi-

larly, far lower power outputs, where the subject would not

fatigue until 915–20 min and which would likely entail a

greater motivational component, were not used to determine

CP and W¶.

Poole et al. (64) used this hyperbolic analysis to charac-

terize empirically the physiological response to exercise

performed near CP in a cohort of healthy, physically active,

but not highly trained, young men. The CP was found to

occur at È80% V

˙O

2max

, approximately midway between

GET and V

˙O

2max

(Fig. F22). Accepting a margin of determi-

nation imprecision, this represented the highest power out-

put (or, more correctly, metabolic rate) (2) at which V

˙O

2

and blood [lactate] could be stabilized. Specifically, at

CP, the profile of V

˙O

2

demonstrated a pronounced slow-

component rise that was superimposed on the rapid initial

‘‘fundamental’’ increase (Fig. F33). However, after several

minutes or more at CP, the V

˙O

2

leveled off as did blood

[lactate] that increased from resting values (È1 mM) to

stabilize at 5–6 mM on average. In marked contrast, exer-

cise at a power output just 5% above CP induced a com-

pletely different metabolic response: V

˙O

2

rose inexorably

to V

˙O

2max

and blood [lactate] increased systematically

until the subject was unable to continue the exercise task

(Fig. 3). F4Figure 4 demonstrates that, for just an increment-

ally small increase in power output above CP, V

˙O

2

may

increase (via the V

˙O

2

slow component) by a liter or more

(22,64). The CP therefore presents the upper boundary of

the heavy exercise intensity domain and the lower boundary

of the severe-intensity exercise domain in which all power

outputs lead to V

˙O

2max

, and the tolerable duration of work

FIGURE 2—Schematic of the power–time (P–t) relationship for high-

intensity exercise illustrating the location of the LT (synonymous with

the GET) relative to CP for healthy, physically active young men.

CRITICAL POWER AND EXERCISE TOLERANCE Medicine & Science in Sports & Exercise

d

3

is highly predictable from the P–trelationship (Figs. 1 and 2).

In deference to Wilkie, note from Figure 4 that, whereas CP

cannot be above the power output corresponding to V

˙O

2max

,

when the slow-component increase in V

˙O

2

is allowed to run

its course and elevate V

˙O

2

to V

˙O

2max

, work rates only in-

crementally above CP result in the achievement of V

˙O

2max

.

To date, the essential characteristics of the P–trelation-

ship (and its parameters CP and W¶) describe exercise toler-

ance for locomotory activity across many species including

salamander (20), mouse (5), and horse (50), as well as for

different muscle contraction protocols (e.g., isometric [54]

and isotonic [42]) and exercise modes (running [19,37], cy-

cling

AQ2 [28,31,32,63–66,68,70,82], swimming [77], and rowing

[33]) in humans. Thus, as will be demonstrated more fully

below, the highly conserved hyperbolic P–trelationship, its

mechanistic underpinnings, and tight coherence with systemic

responses (V

˙O

2

and blood [lactate]) and muscle metabolism

support its key role in defining muscular performance in its

broadest context.

MECHANISTIC BASES OF THE CRITICAL

POWER CONCEPT

As developed above, the P–trelationship is defined by

two constants: the power-asymptote known as the CP and

the curvature constant W¶. The W¶(J) indicates the maxi-

mum amount of work that can be performed 9CP so that

the magnitude of this work capacity remains the same re-

gardless of the chosen work rate 9CP (Fig. 1, top panel).

The CP has been defined as the highest sustainable rate

of aerobic metabolism (31,54,55) that occurs at a similar

work rate to the so-called maximal lactate steady state (66).

According to the classic interpretation, the W¶(sometimes

inaccurately called the ‘‘anaerobic work capacity’’) com-

prises the energy derived through substrate-level phos-

phorylation using PCr and glycogen, with an additional

small aerobic contribution from myoglobin- and (venous)

hemoglobin-bound O

2

stores (15,52–55). However, the

precise physiological underpinnings of the P–trelationship

are challenging to address experimentally and have been

the subject of some controversy.

FIGURE 3—Group mean oxygen uptake (V

˙O

2

)(top panel) and blood

[lactate] (bottom panel) responses (n= 8) to constant-power exercise at

CP (solid symbols) and 5% above CP (open symbols). Arrows denote

point of fatigue for CP + 5% bout; note achievement of V

˙O

2max

. For

exercise at CP, V

˙O

2

and blood lactate both stabilized, and the bout was

stopped at 24 min without fatigue. SE bars were omitted for clarity. See

text for more details. Used with permission from Poole et al. (64).

FIGURE 4—Top panel: Oxygen uptake (V

˙O

2

)/work rate relationship

for incremental exercise (solid symbols), where work rate is increased

by 25 WImin

j1

to fatigue and V

˙O

2

was achieved during constant-

power exercise (open symbols) for one healthy subject. The leftmost

open symbol is at critical power (CP), which denotes the highest power

output at which V

˙O

2

can be stabilized (see Fig. 3). All other five open

symbols denote that V

˙O

2max

is achieved in response to constant-power

exercise even when the power output is far below the maximum achieved

on the incremental test (i.e., CP + 5%). Bottom panel:Schematicillus-

trating the extraordinary size of the V

˙O

2

slow component necessary to

achieve V

˙O

2max

at a power output just above CP (i.e., at the lower end

of the severe-intensity exercise domain). On the basis of data from

Poole et al. (64).

AQ1

AQ1

http://www.acsm-msse.org4Official Journal of the American College of Sports Medicine

It is pertinent to note that the P–tparameters differ

from any physiological index of fitness in that they are

based on the measurement of performance as t(i.e., time-

to-exhaustion) and on the externally measured mechanical

work done (per unit time) rather than the behavior of any

single physiological variable, such as blood lactate concen-

tration or pulmonary V

˙O

2

. In other words, given the mul-

tifaceted nature of fatigue during high-intensity exercise

(1,18), any one solitary physiological index is unlikely to

entirely account for the W¶or the CP. The complex mecha-

nistic bases of the P–trelationship have been elucidated by

various interventions used to manipulate individually the

CP and W¶. Specifically, it has been established that the

CP increases after short-term continuous endurance training

(38) and after high-intensity interval training (23,65,72)

and may be reduced when exercise is performed in hyp-

oxia (55). The W¶is reduced after previous high-intensity

(9CP) exercise (17,28,74) and by glycogen depletion (53)

and can be increased by short-term sprint-interval training

(39). In addition, there is some evidence that the W¶may

be enhanced by dietary creatine loading (52,69) (see also

Eckerson et al. [16] and Vanhatalo and Jones [75]) and by

previous heavy-intensity exercise (41). W¶also tends to de-

crease after training interventions that increase the CP

(38,72). Interpretation of these results is challenging because

of the complex and interrelated physiological nature of CP

and W¶; thus, an intervention aimed specifically at manipu-

lating the CP might also affect the W¶and vice versa.Con-

sidering that some of the metabolites associated with

‘‘anaerobic’’ energy transfer (which have been thought to be

related to the W¶) act as signaling mechanisms to stimulate

mitochondrial respiration (which defines the CP), it is clear

that the classic interpretation of CP and W¶as distinct aerobic

and anaerobic parameters, respectively, is overly simplistic.

The severe-intensity exercise domain, which defines the

applicable range of the P–trelationship, is characterized by

two unique predictable features: at exhaustion, the V

˙O

2

will

equal V

˙O

2max

and the amount of external work done in ex-

cess of CP will equal W¶(35,64,82). The characterization of

W¶as a fixed anaerobic energy reserve (54,55), which is

primarily determined by the available intramuscular PCr and

glycogen stores (e.g., Ferguson et al. [17] and Jones et al.

[42]), is now gradually becoming redefined. It is acknowl-

edged that the magnitude of the W¶might also be attributed

to the accumulation of fatigue-related metabolites, such as

H

+

and P

i

and extracellular K

+

(18), which occurs in concert

with the depletion of intramuscular PCr and glycogen. It

has been postulated further that the W¶is intrinsically related

to the development of the V

˙O

2

slow component, which is

truncated ultimately at V

˙O

2max

(10,17,41). That the intra-

muscular [PCr] follows similar kinetics to pulmonary O

2

during exercise (67), thereby exhibiting an intensity domain–

specific behavior (42), suggests that the P–trelationship may

be intrinsically linked to muscle metabolic and respiratory

control processes within the severe-intensity exercise domain.

Below, we discuss two recent studies that were the first to

investigate the muscle metabolic underpinnings of the P–t

relationship.

The Historical bases for the critical power concept section

described the landmark study by Poole et al. (64), which

established the CP as the demarcation between the heavy-

and severe-intensity exercise domains, with distinct pulmo-

nary gas exchange and blood acid–base profiles above and

below CP (Fig. 3). Whether a metabolic steady state is at-

tained or not has important implications for the development

of muscular fatigue and exercise intolerance. However, the

mechanistic bases of the CP boundary at the level of the

contracting muscle were only recently addressed systemati-

cally. The contention that the P–trelation was defined by

muscle energetics seemed reasonable given that the two-

parameter CP model had originally been established for

small muscle group exercise (54). Jones et al. (42) examined

this contention using

31

P magnetic resonance spectroscopy

(

31

P MRS). The hypothesis that the intramuscular [PCr] and

associated phosphate-linked regulators of oxidative metab-

olism would exhibit the same intensity domain-specific be-

havior near the CP as the established systemic responses was

tested (64). During separate knee extension exercise trials

performed 10% below (20 min in duration) and 10% above

(to exhaustion) CP, the intramuscular [PCr], [P

i

], and pH

were monitored using

31

P MRS. All subjects completed

20 min of heavy exercise at 10% below CP without undue

exertion, and steady-state responses in [PCr] (È68% of

baseline), pH (È7.01), and [P

i

](È314% of baseline) were

attained within 1–3 min at levels, indicating only moderate

metabolic perturbation (Fig. F55). In contrast, when exercise

was performed 10% above CP, within the severe-intensity

exercise domain, the limit of tolerance was reached after

14.7 T7.1 min. The [PCr] and pH fell progressively with

time reaching È26% of resting values and È6.87, respec-

tively, at exhaustion, and the [P

i

] increased to È564% above

baseline (Fig. 5). These findings established the CP as a

boundary above which intramuscular [PCr], [P

i

], and pH

cannot be stabilized. The distinct responses recorded above

and below CP within a very narrow range of work rates

(CP T2 W) demonstrate the existence of a critical threshold

at CP for muscle metabolic control beyond (i.e., above)

which a physiological steady state is unattainable.

The study by Jones et al. (42) demonstrated that the in-

tramuscular [PCr] and pH continued to decrease until the

limit of tolerance when exercise was performed at a work

rate slightly above CP. It had been speculated that the pre-

dictable exercise tolerance above CP may reflect the rate of

decrease in some intramuscular fatigue–inducing factor or

factors toward some ‘‘low, limiting value’’ and that these

factors may include [PCr] and/or pH (64). However, Jones

et al. (42) did not resolve whether these variables would reach

the same low values at exhaustion at different work rates

within the severe-intensity exercise domain. Such behavior,

if present, would resemble the consistent attainment of pul-

monary V

˙O

2max

at fatigue in the severe-intensity exercise

domain irrespective of the work rate (35,64). Inspiration of

CRITICAL POWER AND EXERCISE TOLERANCE Medicine & Science in Sports & Exercise

d

5

hyperoxic gas during exercise is associated with a reduced

[PCr] slow component and improved high-intensity exercise

tolerance (27). Surprisingly, only one study has addressed the

consequences of manipulating the inspired O

2

fraction on the

P–trelationship: in a limited sample of two subjects, hyp-

oxia was shown to reduce the CP with no consistent effect on

the W¶(55). In a recent study, Vanhatalo et al. (73) therefore

tested the hypotheses that hyperoxia would increase the

‘‘aerobic’’ CP parameter without changing the W¶and that

intramuscular [PCr] and pH would reach the same low, pos-

sibly limiting, values at exhaustion during exercise at differ-

ent work rates within the severe-intensity exercise domain.

Using exhaustive single-leg knee extension bouts at four

different exercise intensities above CP, the P–trelation

was determined in normoxia (i.e., 0.21 O

2

AQ3 ) and hyperoxia

(0.70 O

2

, balance N

2

) (73). Using

31

P MRS, [PCr] (È5%–

10% of resting baseline) and pH (È6.65) values measured

at the limit of tolerance were not significantly different ei-

ther among the different work rates or with different in-

spired O

2

fractions. Rather, consistent with CP being a

parameter of oxidative function, hyperoxia increased CP

(normoxia = 16.1 T2.6, hyperoxia = 18.0 T2.3 W, PG0.05),

thereby extending the time-to-exhaustion (in trials lasting

longer than È4 min) and reducing the rate at which [PCr] and

pH decreased with time. Surprisingly, however, hyperoxia

served to reduce W¶(1.92 T0.70 vs 1.48 T0.31 kJ, PG0.05)

such that there was an inverse correlation between changes

in CP and W¶(r=j0.88)—a finding that contradicts the

classic definition of the W¶parameter as a fixed anaerobic

energy reserve (73). Exercise training is also associated with

a similar mutual interdependency between CP and W¶(72),

which may be attributed to the relative changes induced by

a given intervention on the CP (the lower boundary of the

severe-intensity exercise domain) and the V

˙O

2max

,resulting

in a change in the range of work rates that encompass the

severe-intensity exercise domain (10). These recent findings

indicate that the W¶may not represent a fixed ‘‘anaerobic’’

substrate store, per se, but rather a mechanical work capacity

that can be used while [PCr] and pH project toward a nadir

value, which occurs near V

˙O

2max

and ultimately exhaustion

(35,64). It is important to note that the limit of tolerance in

severe exercise might occur when a particular intramuscular

environment is achieved (36), of which the [PCr] and pH

measured in this study should be regarded as only two of

many possible indicators.

Collectively, these recent MRS investigations have ex-

tended our knowledge of the mechanistic bases of the P–t

relationship. Specifically, it is now known that CP repre-

sents a critical threshold for intramuscular metabolic control,

above which exhaustive exercise results in the attainment of

consistently low end-exercise pH and [PCr] values irre-

spective of the chosen work rate within the severe-intensity

exercise domain. This P–trelationship therefore encom-

passes a specific range of high-intensity work rates where

exercise induces a predictable and inexorable progression of

increasing intramuscular metabolic perturbation, which ul-

timately limits exercise tolerance. The P–trelationship may

therefore be regarded as an inherent characteristic of muscle

bioenergetics.

APPLICATION OF THE CRITICAL POWER

CONCEPT TO ALL-OUT EXERCISE

Despite the physiological significance of the CP concept

and its broad applicability across exercise modes and species

(see Historical bases for the critical power concept section

for references), estimation of its parameters is not routine

during either physiological research or diagnostic exercise

testing. We believe that the primary reason for this is that

the cumbersome nature of the repeated fatiguing exercise

bouts required for CP and W¶resolution has limited its

wider application. In contrast, the incremental exercise test

that permits extraction of several key aerobic parameters

FIGURE 5—Muscle [PCr] (A), pH (B), and [P

i

] (C) responses to GCP

(solid circle) and 9CP (open circle) knee extension exercise in a repre-

sentative subject. [PCr] and [P

i

] data are expressed as percentage

change from resting baseline. Redrawn from Jones et al. (42).

http://www.acsm-msse.org6Official Journal of the American College of Sports Medicine

(i.e., GET/LT, V

˙O

2max

, efficiency) in a single procedure has

become almost ubiquitous in exercise testing facilities. To

address this problem, recent investigations have explored

the potential of using prolonged all-out exercise to deter-

mine CP and W¶in a single test.

All-out cycle exercise bouts of 30 s (Wingate test) and up

to 90 s (12,25) have been used to measure maximal power

output and to estimate the so-called ‘‘anaerobic capacity’’

and accumulated O

2

deficit. During these all-out tests, power

output typically falls to less than 50% of its initial/peak

value, which is well below the power output at V

˙O

2max

measured during fast-ramp incremental exercise protocols

(12,14). Although these tests were too short to determine

CP (7), a potential link between all-out exercise and CP

was suggested (7,14). However, these investigations begged

two crucial questions: 1) If all-out exercise continued be-

yond 90 s, would power output eventually stabilize? 2) As

the theoretical precepts of the CP concept mandate, once

W¶is expended, would this stable power output be CP?

Our pilot experiments established that the stabilization of

power output required approximately 3 min of all-out cy-

cling against a fixed resistance using a Lode Excalibur Sport

ergometer (11). Crucial aspects of this test protocol include

thefollowing:1)Subjectsneedtobehighlymotivatedand

fully familiarized with the test protocol before data collection.

2) During the test, pacing is prevented by absence of any

time-based feedback, and the subject is strongly encouraged

to maximize cadence, and therefore power output, at all

times. 3) A valid test is characterized by a V

˙O

2

response that

depicts no decremental trend at any point during the test and

attains 995% of ramp test–determined V

˙O

2max

. In our ex-

perience, having carried out eight experimental studies in

two laboratories using the 3-min test, healthy untrained sub-

jects are capable of reaching V

˙O

2max

within the first 60 s

and sustaining this for the remainder of the test.

When these conditions are met, a distinct plateau in power

output is present within 3 min. The end-test power output, as

calculated from the mean power output during the final 30 s

of the test, occurs at a power output significantly above the

GET but significantly below the power output recorded at

the end of a ramp test (i.e., at approximately one-third of

peak power; Fig.

F6 6A) (11). One remarkable feature of this

response is that V

˙O

2max

is not only achieved extremely rap-

idly but also sustained, confirming that all-out exercise can

provide a maximal challenge to the aerobic system (24,84)

despite the relatively modest end-test power output.

Practically, these experiments demonstrated that end-

test power in the 3-min all-out test was near CP. This is in

agreement with CP theory, in that once the W¶has been used,

the highest power output that can be attained is CP because

(as defined in equation 1.3) P=(W¶/t) + CP, and therefore,

when W¶= 0, this equation reduces to P=CP(11,70).

Moreover, the work performed in the 3-min test above CP

(termed ‘‘WEP’’) should equal W¶. This logic led us to test

the hypothesis that the CP and W¶parameters could be

established using a single 3-min all-out test. To demonstrate

FIGURE 6—(A) Power profile during a 3-min all-out test in a well-

trained cyclist. Dashed lines represent the power output achieved at the

end of a 30 WImin

j1

ramp test (upper) and the power output associated

with the GET (lower). Note the similarity of the end-test power (316 W)

with the independently determined critical power (317 W, dotted line).

(B) Correlation between the critical power and the end-test power dur-

ing the 3-min all-out test from the study of Vanhatalo et al. (70). Dashed

line, line of identity; solid line, best-fit least-squares linear regression.

(C) Knee extensor torque during 60 intermittent MVC performed in a

5-min period in a single subject (data reproduced from Burnley [9]).

Dashed line represents the independently determined critical torque.

As with the responses to cycle exercise, the ‘‘end-test torque’’ (74.3 NIm)

coincides closely with the critical torque (74.2 NIm).

CRITICAL POWER AND EXERCISE TOLERANCE Medicine & Science in Sports & Exercise

d

7

that the CP and the end-test power were synonymous, it

was necessary to measure CP independently, in the same

subjects, using established methods (i.e., five tests to fatigue

performed on separate days). When this was done, the end-

test power in the 3-min all-out test closely matched CP

(Fig. 6B) (70). Indeed, in 8 of 10 cases, the end-test power

was within 5 W of CP. Moreover, the WEP was not different

from W¶, although the results were considerably more vari-

able for this parameter (70).

An important feature of the CP concept is that it conflates

mechanical (i.e., power) and metabolic (V

˙O

2

and lactate)

response profiles according to the established behavior

characteristic of the heavy- and severe-intensity exercise

domains (Historical bases for the critical power concept and

Mechanistic bases of the critical power concept sections)

(11,64). Thus, when constant-load exercise was performed

15 W below the end-test power, 9 of 11 subjects completed

30 min of exercise and 7 did so, achieving our criteria for

the attainment of a steady state (G1 mM increase in blood

[lactate] from 10 to 30 min). In contrast, none of the subjects

completed 30 min of exercise above the end-test power,

with exhaustion occurring within 13 min, on average. Dur-

ing exercise above the end-test power, V

˙O

2

rose to reach

V

˙O

2max

at exhaustion, and blood [lactate] continued to in-

crease. These data provide further support that the 3-min

end-test power occurs near the heavy/severe–intensity ex-

ercise domain boundary (i.e., CP) and also the maximal

steady state for V

˙O

2

and [lactate].

The correspondence between the parameters of the 3-min

all-out test (end-test power and WEP) and those of the P–t

relationship (CP and W¶) was further investigated using in-

terval training (72) and previous exercise (74). Specifically,

4 wk of high-intensity interval training increased the con-

ventionally established CP and the 3-min test end-test power

by È25 W, with no difference between CP estimates derived

from different protocols either before or after training (72).

Previous high-intensity or sprint exercise, followed by limited

or no recovery time to restore intramuscular W¶-associated

energy stores (19,54,58,64), has been shown to reduce the

W¶(17,28). Similarly, a 30-s all-out sprint performed 2 min

(but not 15 min) before a 3-min all-out test reduced WEP

but not the end-test power (74). These investigations have

demonstrated that the end-test power and WEP are sensitive

to interventions expected to influence CP and/or W¶.Other

interventions that have been used to manipulate the 3-min all-

out test performance include protocol manipulation (71) and

dietary supplementation (75,76). Both the end-test power and

the WEP were shown to be unaffected by short-term dietary

creatine loading (75), short-term bicarbonate ingestion (76),

and pacing during the first 30 s of the all-out test (71).

Collectively, the evidence summarized above supports

that 3-min end-test power and WEP represent faithful esti-

mates of CP and W¶, respectively. However, the possibility

that the agreement between parameters is coincidental rather

than mechanistic must be considered: perhaps because of the

arbitrary selection of a fixed resistance on the one hand (71)

and of the limits placed on power output consequent to the

attainment of V

˙O

2max

on the other (11,72). In contrast, if

the power profile of all-out cycle exercise has a fundamental

physiological basis, then the performance of a completely

different exercise mode should produce similar agreement

between end-test muscle performance and the exercise mode

equivalent to CP. To test this supposition, Burnley (9) in-

vestigated the agreement between the ‘‘end-test torque’’

measured during a series of intermittent isometric maximal

voluntary contractions (MVC) of the quadriceps and the

‘‘critical torque’’ estimated from five separate tests involving

submaximal intermittent contractions of the quadriceps con-

tinued until task failure (at È35%–60% MVC). A 5-min pe-

riod of maximal contractions (3-s contraction and 2-s rest)

was required to achieve a plateau in torque at È29% MVC,

and this plateau corresponded to the critical torque (Fig. 6C).

In other words, the results of these experiments were strictly

analogous to the cycling experiments detailed above and

supported the contention that all-out exercise results in the

eventual attainment of CP (or torque) irrespective of the mode

of exercise.

MATHEMATICAL FEATURES OF THE

CRITICAL POWER CONCEPT

The two-parameter CP model. The CP concept de-

fines a two-component bioenergetic supply-and-demand

system, which lends itself ideally to mathematical modeling.

Both supply components are endogenous, but demand is de-

termined exogenously. As originally defined, the assumptions

canbeformulatedasfollows:

1) There is an ‘‘aerobic’’ energy supply component that is

rate- but not capacity-limited. This rate limit is denoted as

the CP.

2) There is an ‘‘anaerobic’’ energy supply component that is

capacity- but not rate-limited. This capacity limit is

denoted as W¶.

3) Exercise can continue at any power output as long as

supply is adequate to meet demand.

Thus, we can deduce that if an individual exercises con-

tinuously at a constant power Pless than or equal to CP,

exercise duration is ‘‘infinite’’ because the entire demand

can be met aerobically, and the limit of tolerance cannot be

predicted using the power–duration relationship. On the

other hand, if P9CP, then the aerobic supply alone is in-

sufficient, and the excess power requirement above CP must

be met by using the W¶component. The length of time until

exhaustion, t, that this excess requirement can be sustained

can be deduced by dividing the available capacity, W¶,by

the rate at which it is required (PjCP), yielding:

t¼W0

=ðPCPÞ½4:1a

Because this equation defines a rectangular hyperbola, asymp-

totic to the horizontal axis at t= 0 and to the vertical axis at

http://www.acsm-msse.org8Official Journal of the American College of Sports Medicine

P= CP, it is usually called the hyperbolic form of the CP

model. Because the total amount of work, W, accomplished

during the interval 0 to t, is given by W=Pt (Fig. 1), five

other algebraically equivalent equations can be deduced:

P¼W0

=tþCP ½4:1b

W¼W0þCPt ½4:1c

t¼ðWW0Þ=CP ½4:1d

W¼W0P=ðPCPÞ½4:1e

P¼CPW=ðWW0Þ½4:1f

Equations 4.1c and 4.1d are linear forms, the former well

known and due originally to Monod and Scherrer (54). All

the other equations are hyperbolae, although equation 4.1b

is usually linearized by substituting x=1/t. It is important

to realize that, although mathematically equivalent, these

equations are not statistically equivalent when it comes

to estimating the parameters from collected data (21,34).

Equation 4.1a with tas dependent variable and Pas inde-

pendent is the most natural to use, although equations 4.1c

and 4.1d are almost as natural, and 4.1b using x=1/tis often

used. Given the capabilities of modern computing equip-

ment, there is no reason to prefer a linear to a hyperbolic

equation. Application of the model is unlimited by exercise

modality as long as any two of the three variables t,P,orW

(or their analogs, velocity and distance, in other exercise

modalities) can be measured.

The two-parameter CP model has been adapted for ramp

exercise (56), where the ramp rate (or slope) variable, s,is

used in place of P. In this instance, assuming that P=0at

t= 0, whence W= 1/2st

2

, there are similarly six algebraically

equivalent equations. As sis the only logical independent

variable, the most natural and mathematically simplest equa-

tion is as follows:

t¼CP=sþﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ð2W0

=sÞ

p½4:2a

although

W¼W0þCP2

=sþﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ð2W0CP2

=sÞ

q½4:2e

could be used if work is to be measured as the dependent

variable. Early evidence (61) suggests that parameter esti-

mates obtained for the same subjects from ramp and constant-

power protocols are equivalent.

The two-parameter CP model has also been adopted for

intermittent exercise (60). In this application, nis the num-

ber of completed work and rest cycles; t

w

and t

r

are the

durations, and P

w

and P

r

are the power outputs of the

corresponding work and rest periods, respectively. nis ob-

served as exercise proceeds, but t

w

,t

r

,P

w

, and P

r

are set

before exercise commences. Subject to certain constraints on

feasible combinations of these last four variables, total en-

durance time is given by the following equation:

t¼nðtwþtrÞþ½W0nfðPwCPÞtwðCP PrÞtrg=ðPwCPÞ½4:3a

No other equivalent forms of this equation have been pub-

lished, although they could theoretically be derived. Instead

of equation 4.3a, equation 4.1c has been used (4,45) to es-

timate CP and W¶by cumulating both Wand tover all the

repeated work and rest cycles, whether complete or not.

Although unpublished, this can be shown algebraically and

numerically to provide the same estimates of CP and W¶as

equation 4.3a, and experimental observations have con-

firmed their equivalence (8).

The three assumptions above are sufficient to derive all

the mathematical equations presented so far, but it is im-

portant to realize that, in theory, implicitly embedded in

these assumptions are several others, specifically:

4) Aerobic power is available at its limiting rate CP the

moment exercise begins, remaining so until exercise

ceases at exhaustion.

5) The power domain over which the model applies is all

of CP GPGV.

6) The time domain over which the model applies is all of

0GtGV.

7) CP and W¶are constants, independent of Pand/or t.

8) The efficiency of transformation of metabolic energy to

mechanical energy is constant across the whole power

(and time) domain(s).

All of these assumptions have been questioned previ-

ously (58), and it should be noted that when prediction trials

are limited to the severe-intensity exercise domain, where

2 min GtG15 min (Historical bases for the critical power

concept section) (64), data conform well to the original two-

parameter model. The fine-tuning of the mathematical

model, as discussed below, may allow the extension of this

applicable range at the extremes of the power (and time)

continuum or improved fit when using different exercise

modalities.

To deal with assumption 4), Wilkie (83) introduced a

correction factor for oxygen uptake kinetics on the basis of

a single exponential with time constant Tand without delay.

Replacing the Edesignating power at V

˙O

2max

in Wilkie’s

original suggestion with CP (equation 1.1), equation 4.1c

now becomes:

W¼W0þCPtCPTð1et=TÞ½4:1g

If Tis known and times to exhaustion no less than about 3T

are used in the estimation of W¶and CP, then the exponential

term may be regarded as negligible, and a revised and larger

estimate of W¶can be obtained by adding CPTto the original

W¶estimate. However, if Tis unknown, it may be estimable

usingequation4.1gifsufficientshort-duration(i.e.,tG3T)

trial data are collected. No correction factor has been pub-

lished or derived for any of the other forms of equations 4.1,

AQ4

CRITICAL POWER AND EXERCISE TOLERANCE Medicine & Science in Sports & Exercise

d

9

4.2, or 4.3, although the unnecessarily complex mathematics

could be done if required.

The three-parameter CP model. The three-parameter

CP model (57) has been developed to deal with assumptions

5), 6), and 7) simultaneously, although assumptions 4) and 8)

remain in force. The key difference between the two- and

three-parameter models from a mathematical standpoint is

simply that the horizontal asymptote of the rectangular hy-

perbola (where Pis plotted as the independent and tis plot-

ted as the dependent variable) is no longer constrained to

t= 0 but rather regarded as a real third parameter that can be

estimated from the data at t=k,wherekis the temporal

asymptote. Equation 4.1a is therefore reformulated with the

third parameter as:

t¼W0

=ðPCPÞk½4:4a

From a physiological standpoint, the three-parameter model

conjectures a dynamic feedback that limits maximal available

power output between a finite amount (P

max

)andCP,ac-

cording to the existing anaerobic energy supply at any instant,

where P

max

can be interpreted as a maximum ‘‘instantaneous

power.’’ Graphically, it is because kG0, P

max

is the finite

point where the hyperbola crosses the horizontal axis at t=0.

In practical terms what this means is that when a subject is

fully rested, P

max

could be developed as a maximal effort, but

when the anaerobic store is fully depleted, only CP could be

developed. Between these extremes, maximal power declines

proportionally. This manifests, for example, by observing

that a maximal finishing sprint at the end of, say, a 1500-m

race is not as fast it would be if the athlete was fully rested.

As previously, there are six algebraically equivalent equa-

tions. Equation 4.4a is the most natural, but:

W¼W0t=ðtþkÞþCPt½4:4c

or

t¼½WþCPkW0þﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

fðWþCPkW0Þ24CPkW g=2CP

q½4:4d

could both be contemplated. The temporal asymptote kG0

is unhelpful from a physiological standpoint because neg-

ative endurance times are meaningless. More relevant physi-

ologically is P

max

,sokcan be replaced if preferred by the

reparameterization W¶/(P

max

jCP). Equation 4.4c is an up-

ward-sloping concave curved line, starting at 0 and tending

toward the straight line (equation 4.1c) from below for large t.

Indeed, data ‘‘dropping below’’ the straight line in this way

(see Bishop et al. [6], their Fig. 2, p.127) (54) are frequently

observed phenomena when tdurations span a wider range.

Note that letting k= 0 in any of equations 4.4 reduces them

to the corresponding versions of equations 4.1. If kis repa-

rameterized, letting P

max

YVachieves the same result. Note

also that like the two-parameter model, the three-parameter

model is unlimited by exercise modality, as long as any two

of the three variables t,P,orW(or their analogs, velocity and

distance, in other forms of exercise) can be measured.

There are no published equations or applications, as yet,

of the three-parameter model to ramp exercise. The mathe-

matics can easily be done, yielding as the most natural

equation:

t¼CP=sþkþﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðk2þ2W0=sÞ

p½4:5a

and it will be again noted that, when k= 0 (or letting

P

max

YVin the reparameterization), this equation reverts

to the two-parameter equation 4.2a. Further mathemati-

cally equivalent equations could be algebraically derived if

desired. No three-parameter equations for intermittent ex-

ercise have yet been developed, although it may be spec-

ulated that using the cumulative procedure described above

ought to work with equation 4.4c.

The feedback system of the three-parameter model per-

mits the investigation of another exercise modality, all-out

effort, not possible with the two-parameter model where Pis

unbounded. Morton (59) has shown that the time course of

power output during all-out effort declines exponentially

from P

max

at t= 0, asymptotically to CP as tYVaccording

to the following equation:

P¼CP þðPmax CPÞet=k½4:6b

In practice, there is usually a short-lived period of buildup

of Pobserved, due, for example, to inertial or acceleration

considerations (11,59), rather than observing a genuine P

max

start at t= 0 (Fig. 6A). By integrating equation 4.6b assum-

ing a zero start, work performed, W, follows an exponential

rise toward linearity with time according to the equation:

W¼W0ð1et=kÞþCPt½4:6e

In some applications, W(or more usually, its analog distance)

may be given, and tis the dependent variable. Reversing the

variables in equation 4.6e is not possible because equation

4.6e is a transcendental equation in t, and an iterative solu-

tion to equation 4.6e is the only feasible expedient. In respect

to assumption 4), Wilkie’s correction applied to the three-

parameter model has not been published for any of the three-

parameter equations given, although again the mathematics

could be done if required.

Mathematically optimal strategies. Given the rele-

vance in today’s world of competitive sports performance,

and the reward accruing to winners, it is natural to ask

whether performance time (or the amount of work accom-

plished) can be mathematically optimized. The early work of

Keller (46) gives a hint of the complexities. Nevertheless,

Fukuba and Whipp (19) have investigated the problem for

the two-parameter CP model. They demonstrate that there

is no unique optimal strategy, in that any one of an infinite

number of strategies, involving stagewise steps of periods

of constant power, produces an identical endurance time,

provided that Pnever drops below CP. In fact, any smooth

and continuous trace of P, never dropping below CP, will

also yield exactly the same endurance time because the in-

tegral of Pabove CP equals W¶. That this is so is a direct

http://www.acsm-msse.org10 Official Journal of the American College of Sports Medicine

consequence of the lack of any feedback system in the two-

parameter model.

The situation in the three-parameter model is quite dif-

ferent. It has been mathematically proven that there is a

unique optimal solution, although it may be as unacceptable

to as many sport scientists as is the above solution for

the two-parameter model, albeit for different reasons. That

unique strategy turns out to be maximal all-out effort for

the entire duration of the exercise (59), and equations

AQ5 4.6b

and 4.6e apply. As an optimal strategy, all-out effort for a

short-duration exercise is universally accepted, but for a

longer-duration exercise, it quite definitely runs counterin-

tuitively to what is generally believed and what is normally

practiced. Nevertheless, it fits well to at least 3 min of all-out

data (59), and it can quite easily be numerically demonstrated

to be optimal. Despite some empirical evidence of the supe-

riority of faster starting (e.g., Jones et al. [43]), this raises a

question mark concerning the three-parameter model.

PRACTICAL APPLICATIONS OF THE

CRITICAL POWER CONCEPT

The CP and W¶parameters that can be educed from the

P–trelationship for severe-intensity exercise domain have

a variety of applications in sport and exercise science and

medicine, although these have not been as widely appre-

ciated to date as, perhaps, they should be. These appli-

cations include the assessment of physical fitness, the

prescription of exercise training, and the prediction of per-

formance during high-intensity exercise. Although this sec-

tion will focus on competitive athletes, it should be noted

that many of these same concepts could be equally applied

to other populations including patients, physical laborers, and

those involved in recreational physical activities. However,

in athletes, an understanding of the CP concept is addition-

ally important in the design of optimal warm-up programs

and in informing pacing strategy and the tactics used during

acompetition.

As has been highlighted earlier in this review, there is

evidence that the CP represents the highest power output

that can be sustained without a progressive loss of homeo-

stasis as indicated by 1) a continuous decline in muscle

[PCr] and pH and in blood pH and [bicarbonate] and 2) a

continuous increase in blood [lactate], pulmonary V

˙O

2

, and

ventilation (42,64). These data, along with evidence that the

CP occurs at a similar exercise intensity to the so-called

‘‘maximal (lactate) steady state’’ (66), have led to the sug-

gestion that the CP represents the highest rate of oxidative

metabolism that can be sustained without a progressively

increasing contribution to energy turnover from substrate-

level phosphorylation (i.e., PCr hydrolysis and ‘‘anaerobic’’

glycolysis). In contrast, the W¶represents a fixed amount of

work (kJ) that can be completed during exercise above the

CP, which is derived principally from anaerobic processes.

Although it is becoming clear that W¶is a mechanical work

capacity that is related, at least in part, to the ‘‘distance’’

between the CP and the V

˙O

2max

rather than to an ‘‘anaerobic

capacity,’’ per se, it is notable that the CP increases because

of continuous or interval endurance training (23,38,65,72)

and that the W¶increases because of power or sprint train-

ing (39), although the effects are not mutually exclusive.

The measurement of changes in the P–trelationship after

a training intervention is likely to be functionally more

valuable than the measurements of discrete physiological

constructs such as, for example, V

˙O

2max

, GET/LT, or ‘‘an-

aerobic power.’’ However, the requirement for subjects to

complete a series of constant work rates to exhaustion both

before and after the training period has possibly precluded

widespread assessment of training-induced changes in the

P–trelationship in practice. In this regard, the advent of a

single all-out test for the estimation of CP and W¶(Appli-

cation of the critical power concept to all-out exercise sec-

tion) (11,70), which is sensitive at least to endurance

training (72), might facilitate more routine assessment of

changes in the P–trelationship after training.

Given that the time-to-exhaustion (t) at a specific constant

severe-intensity power output can be accurately estimated

using equation 4.1a, it is clear that knowledge of an indi-

vidual athlete’s CP and W¶parameters should enable exer-

cise performance capacity (i.e., the time required to cover a

given distance) to be accurately predicted. For example, if

a distance runner wishes to complete a continuous severe-

intensity training run (often termed ‘‘tempo’’ running), then

the maximum sustainable time for a given velocity will be

given by:

t¼D0

=ðVCVÞ½5:1

Also, the shortest time that the runner could complete a

given distance (D) is given by:

t¼ðDD0Þ=CV ½5:2

If the runner’s CV is 6.0 mIs

j1

and his/her D¶is 150 m,

then the endurance time at a velocity of 6.2 mIs

j1

would be

750 s (12.5 min), and the endurance time at a velocity of

6.1 mIs

j1

would be 1500 s (25 min). This information could

be used by a coach to prescribe a training session that is

challenging but manageable, resulting in physiological ad-

aptation but with the avoidance of overreaching. The CP

concept can also be applied in the design of interval training

sessions (60). With the assumption that the power output

during the work interval (P

w

) is greater than CP (but not so

great that exhaustion occurs within the first bout of work)

and that the power output during the recovery interval (P

r

)

is less than the CP, it can be calculated that the W¶during

exercise will be consumed by a function of:

ðPwCPÞtw½5:3

and that the W¶during recovery will be restored as a func-

tion of:

ðCP PrÞtr:½5:4

If the mean power output over the work/recovery cycle is

greater than the CP, then W¶will fall predictably at the end

CRITICAL POWER AND EXERCISE TOLERANCE Medicine & Science in Sports & Exercise

d

11

of each work interval, and the endurance time for any

combination of work interval power output, recovery inter-

val power output, work interval duration, and recovery in-

terval duration (i.e., the number of complete work intervals

and one partial work interval that can be accomplished be-

fore W¶is expended) can be calculated (equation 4.3a). This

assumes that the CP and W¶are essentially the same during

intermittent exercise as during continuous exercise and that

the processes that consume and restore W¶are linear, as-

sumptions that are yet to be verified (60).

Knowledge of CP and W¶will also enable an athlete and

his or her coach to make informed decisions on appropri-

ate pacing and tactical strategies to maximize competitive

performance. One important consideration, which is often

overlooked, is that the time to cover a given competitive

distance depends not only on the metabolic capability of the

athlete but also on the athlete covering the minimum possi-

ble distance for the event. For example, if we consider the

5000-m track event, an athlete will only cover 5000 m if he

or she runs close to the curb for the entire distance, some-

thing that is rare in practice. If the athlete runs wide on the

bends, the actual distance covered can be significantly in-

creased. Taking an extreme example, an athlete who ran in

the second lane for the entire 5000-m event would actually

cover approximately 5100 m (equivalent to giving a more

conservative opponent a head start of 100 m).

It can be shown that an athlete’s maximal mean velocity

for a given distance (and hence, the shortest time possible

for that distance) is dictated by the crossing point of his or

her individual velocity–time curve and the distance–time

curve (Fig.

F7 7). Where the athlete covers a distance that is

greater than the theoretical race distance, the point of inter-

section will move downward and to the right, thus reducing

the maximal mean velocity and increasing the time taken to

complete the distance (Fig. 7). These considerations are not

just theoretical. Jones and Whipp (40) have reported that

the athletes who ran at the highest mean velocity in both the

800- and 5000-m events at the Olympic Games in 2000 were

not the winners of those races; rather, the winners were able

to husband their metabolic resources to better effect by run-

ning closer to the actual race distance. Thus, athletes in these

and other events and sports that are performed in the severe-

intensity exercise domain should be conscious of minimizing

the distance covered in any competition because the race

outcome is not simply a function of the energetic potential of

the athlete at the outset of the competition.

Knowledge of the ratio D¶/CV (or W¶/CP) might also

prove useful to the athlete and coach in terms of the selection

of competition tactics that play to the metabolic strengths of

the athlete and/or act to expunge the metabolic advantages

of a competitor. Fukuba and Whipp (19) have demonstrated

mathematically that for severe-intensity exercise (which

spans the 800-, 1500-, 3000-m steeplechase and 5000- and

possibly 10,000-m races in track athletics), the theoretical

best time for a given distance can never be attained if any

portion of the race distance is covered at a velocity below

CV (i.e., it is not possible to ‘‘make up for lost time’’ with a

sprint finish). Moreover, the ‘‘endurance parameter ratio’’

(D¶/CV) dictates the flexibility of the race pace that can be

selected while still enabling an athlete to attain their best

mean velocity for the distance. Therefore, the best tactics for

an athlete with a high CV and a low D¶relative to the rivals

might be to operate at the highest possible mean velocity for

the distance (as dictated by their individual velocity–time

relationship). In contrast, an athlete with the opposite meta-

bolic characteristics would do better to attempt to slow the

race pace down below their main rival’s CV for some portion

of the race and to use their superior D¶in a sprint finish.

It is, of course, possible that the performance impact of

the D¶/CV ratio is intuitively known by athletes and that this

‘‘subconsciously’’ dictates their pacing strategy. However,

information on the D¶, CV, and D¶/CV ratio might still prove

invaluable in precompetition comparison of the metabolic

‘‘strengths’’ and ‘‘weaknesses’’ of individual athletes and

the creation of tactical plans designed to optimize perfor-

mance. With regard to the latter, there is increasing evidence

that a fast start (43) or even an all-out pacing strategy (59)

might optimize performance at least during exercise at the

upper end of the extreme domain (i.e., 2–3 min in duration).

A fast-start strategy results in a faster rise of V

˙O

2

toward

the maximum, thus resulting in a greater overall O

2

con-

sumption during the exercise bout (10,43). Given the same

energy yield through the complete depletion of W¶, this

would be expected to enhance exercise tolerance or per-

formance. The completion of a ‘‘priming’’ bout of exercise

has the potential to enhance performance during subse-

quent high-intensity exercise at least in part through a sim-

ilar mechanism (10,17,41). Further research is required to

FIGURE 7—Schematic illustration of the effect of race distance on the

time to complete the race. Curves a and care the distance curves to 800

and 5000 m, respectively; curves b and dare examples of distance

curves that may pertain if the athlete did not run the shortest possible

distance (e.g., by running wide on the bends in track races). Note that

because of the shape of the individual V–tcurve, a small reduction in

average velocity results in a relatively large increase in race time as race

distance increases. See text for detailed explanation. Redrawn from

Jones and Whipp (40).

http://www.acsm-msse.org12 Official Journal of the American College of Sports Medicine

ascertain the effects of different pacing strategies and pre-

vious exercise protocols on the CP and W¶and their rela-

tionships to changes in V

˙O

2

kinetics.

The relative importance of the CV and D¶to success in

different events can be illustrated about two hypothetical

elite female endurance athletes and the use of equation 5.2.

Assume that athlete A has a CV of 5.85 mIs

j1

and a D¶of

75 m, whereas athlete B has a marginally inferior CV of

5.82 mIs

j1

but a superior D¶of 95 m. In a head-to-head race

of 800 or 1500 m, it can be calculated that athlete B would

be the clear winner (by around 3 and 2 s, respectively).

However, at 3000 m, the predicted difference between the

athletes becomes negligible, and at 5000 m and beyond, it

can be calculated that athlete A would have an increasingly

significant advantage. Theoretically, this concept could be

used by handicappers in selecting the race distance at which

the metabolic capabilities of two athletes (e.g., a 1500-m

specialist and a 5000-m specialist) are precisely matched,

thus guaranteeing the closest of finishes for the benefit of

spectators!

This section has provided some of the practical applica-

tions of the CP concept to human athletic endeavor. How-

ever, it is reiterated that the concept also has important

implications for understanding exercise intolerance, de-

scribing exercise performance potential, and investigating

the efficacy of potentially ergogenic interventions in dis-

eased as well as healthy populations (62) and in the elderly

as well as the young (63). Indeed, in almost all situations, it

might be considered that the CP (and W¶) is more relevant,

from a functional perspective, than are the more commonly

measured aerobic performance parameters of LT/GET and

V

˙O

2max

. Along with others (79), we therefore urge that,

wherever possible, this is taken into account in the design

of studies that are interested in defining or enhancing ex-

ercise tolerance.

CONCLUSIONS

The hyperbolic two-parameter (i.e., CP, W¶) power–time

(P–t) relation defines exercise tolerance within the severe-

intensity exercise domain for t(time-to-exhaustion) values

between approximately 2 and 15 min. Thus, all metabolic

rates above CP (or CV, the asymptote for power or velocity)

yield an inexorable increase in both V

˙O

2

(to V

˙O

2max

) and

blood [lactate], as W¶is progressively depleted to fatigue.

Whereas the time-to-exhaustion can be manipulated by al-

tering work rate and/or O

2

supply, for example, the within-

subject fatigue process is characterized by depletion of W¶

and corresponding perturbations of intramuscular [PCr]

(close to 100% depletion), [P

i

] and [H

+

]. In marked contrast,

work rates at or below CP (i.e., in the heavy domain) facil-

itate achievement of an apparent steady state for V

˙O

2

and

blood [lactate] as well as for intramuscular [PCr], [P

i

], and

[H

+

]. Knowledge of an athlete’s CP (or CV) and W¶(or D¶)

can be used to refine and monitor training protocols and to

optimize competition pacing strategies. Hopefully, the re-

cent development of a single test to define an individual’s

CP and W¶, combined with the development of P–tmodels

that encompass exercise durations outside the 2- to 15-min

window and intermittent exercise, will help the CP concept

fulfill its considerable potential utility in exercise science

and medicine.

This work has not been supported by any funding agency.

The results presented in this review do not constitute endorse-

ment by the American College of Sports Medicine.

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15

AUTHOR QUERIES

AUTHOR PLEASE ANSWER ALL QUERIES

AQ1 0Figures 3 and 4 contain pixilated text and lines. Please confirm if okay to proceed with

the processed figures otherwise kindly send replacement figures.

AQ2 0References were renumbered to follow alphabetical listing.

AQ3 0Please supply the unit of measure of O

2

given here.

AQ4 0Please check if equation numbering is correct.

AQ5 0Only equations 4.6b and 4.6e were provided in this article. Please check if changes

made here are correct.

AQ6 0Please check if data of this reference were presented correctly. Also, please supply

publisher/symposium location and/or page information if this has been published.

END OF AUTHOR QUERIES