A T
EST FOR
D
ETERMINING
C
RITICAL
H
EART
R
ATE
U
SING THE
C
RITICAL
P
OWER
M
ODEL
M
ICHELLE
M
IELKE
,
1
T
ERRY
J.H
OUSH
,
2
C.R
USSELL
H
ENDRIX
,
2
J
ORGE
Z
UNIGA
,
2
C
LAYTON
L.C
AMIC
,
2
R
ICHARD
J. S
CHMIDT
,
2
AND
G
LEN
O. J
OHNSON
2
1
Department of Sport Sciences, University of the Paciﬁc, Stockton, California; and
2
Department of Nutrition and Health Sciences, Human Performance Laboratory, University of Nebraska—Lincoln, Lincoln, Nebraska
A
BSTRACT
Mielke, M, Housh, TJ, Hendrix, CR, Zuniga, J, Camic, CL,Schmidt, RJ, and Johnson, GO. A test for determining criticalheart rate using the critical power model.
J Strength Cond Res
25(2): 504–510, 2011–The purposes of this study were to (a)determine if the mathematical model that has previously beenusedtoestimatethecriticalpower (CP)wasapplicable toheartrate (HR) to estimate the critical heart rate (CHR), and (b)compare the CHR to the HR values at the CP (CP
HR
),ventilatory threshold (VT
HR
), and respiratory compensationpoint (RCP
HR
). Fifteen women (mean age
6
SD
= 21.7
6
2.1years)performedanincrementaltesttoexhaustiontodetermine
_
V
O
2
peak, VT
HR
, and RCP
HR
. The subjects also performed 4exhaustive workbouts at different power outputs for the determination of CP and CHR. For each power output, the totalnumber of heart beats (HB
lim
) was calculated as the product ofthe average 5second HR (bpm) and total time to exhaustion(T
lim
in minutes). The HB
lim
and total work (W
lim
in kilogramsmeters) were plotted as a function of the T
lim
at each poweroutput, and the slope coefﬁcients of the regression linesbetween HB
lim
or W
lim
and T
lim
were deﬁned as the CHRand CP, respectively. A 1way repeatedmeasures analysis ofvariance (ANOVA) indicated that CHR (172
6
11 bpm, 92.9
6
2.7%HR
max
) was similar to RCP
HR
(172
6
9 bpm, 92.9
6
2.2%HR
max
)butwashigher(
p
,
0.05)thanCP
HR
(154
6
10bpm,83.2
6
4.0%HR
max
) and VT
HR
(152
6
12 bpm, 82.1
6
4.3%HR
max
). The relationship between HR and T
lim
from theCHR test can be described by the CP model. The CHR testmay be a practical method for estimating RCP without the needto measure expired gas samples. Furthermore, like the RCP,the CHR test may be used to demarcate the heavy fromsevere exercise intensity domains, predict endurance exerciseperformance, and prescribe a training intensity for competitivecyclists.
K
EY
W
ORDS
heart rate, fatigue threshold, ventilatory threshold,respiratory compensation point, exercise intensity domain,endurance exercise
I
NTRODUCTION
V
arious fatigue thresholds have been used todetermine the onset of metabolic acidosis (10),prescribe exercise training intensity (2,8,18), predict endurance exercise performance (2,8,12), andexamine the mechanisms associated with neuromuscularfatigue (16). For example, the lactate threshold has been usedto determine the workload at which the net blood lactateconcentration increases from the onset of exercise (10).In addition, Casaburi et al. (8) suggested that the lactatethreshold be used as a training intensity. The respiratorycompensation point (RCP) (18) and maximal lactate steadystate (12) have also been prescribed as training intensities forcyclists. Furthermore, Rhodes and McKenzie (31) reporteda correlation of
r
= 0.94 between actual marathon time andpredicted marathon time estimated from the ventilatorythreshold (VT). Amann et al. (2) also reported that theVT was a better predictor of a 40km cycling time trial thanthe onset of blood lactate accumulation or individualanaerobic threshold.Fatiguethresholdssuchasthelactatethreshold,VT,criticalpower (CP), maximal lactate steady state, and RCP have alsobeen used to estimate the exercise intensity that demarcatesfatiguing from nonfatiguing work (2,8,12,26,28). The demarcation between fatiguing and nonfatiguing work isusually based on the boundaries of the 3 exercise intensitydomains (moderate, heavy, and severe) as described byGaesser and Poole (13). These boundaries are based on
_
V
O
2
and blood lactate responses during constantintensityexercise. The moderate exercise domain includes intensitiesthat can be maintained without an increase in
_
V
O
2
or bloodlactate levels; therefore, it has been suggested that the lactatethreshold and/or VT demarcates the moderate from heavyexercise domains. The lower boundary of the heavy exercisedomain is the lowest work intensity that elicits an increase in
Address correspondence to Michelle Mielke, mmielke@paciﬁc.edu.
25(2)/504–510 Journal of Strength and Conditioning Research
2011 National Strength and Conditioning Association
504
Journal of Strength and Conditioning Research
the
TM
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blood lactate, whereas the upper boundary is the highestwork intensity at which blood lactate eventually stabilizes.Within the heavy exercise domain,
_
V
O
2
increases buteventually stabilizes without reaching
_
V
O
2
max. Gaesserand Poole (13) have suggested that the CP or the maximallactate steady state demarcates the heavy from severeexercise domains. The RCP has been deﬁned as the exerciseintensity at which
_
V
E
increases disproportionately to
_
V
CO
2
(Figure 1) and has been used to noninvasively demarcate theheavy from severe exercise intensity domains (4,34).The CP concept, of Monod and Scherer (25) for individualand synergistic muscle groups, relates the amount of work accomplished at exhaustion or work limit (W
lim
) and thetime to exhaustion or time limit (T
lim
) (Figure 2A) and alsoprovides estimates of 2 independent parameters called theCP and anaerobic work capacity (AWC). The CP is the slopeand AWC is the yintercept of the W
lim
vs. T
lim
relationshipand they have been deﬁned, theoretically, as the maximumpower output (P) that can be maintained for an extendedperiod without fatigue (i.e., the asymptote of the P vs. T
lim
relationship [Figure 2B]) and the total amount of work that canbe performed using only stored energy reserves (i.e., independent of oxygen supply), respectively (25). Moritani et al.(26) extended the CP concept to cycle ergometry, and CP wasdetermined from a series of 4 continuous, fatiguing workboutsat varying
P
values. The W
lim
(P
3
T
lim
) was then plotted as a function of the T
lim
for each
P
value. The relationship betweenW
lim
and T
lim
was highly linear (
r
.
0.98) and described by theequation W
lim
= AWC + CP(T
lim
) (Figure 2B) (26).The CP model is estimated from the linear relationshipbetween W
lim
and T
lim
(Figure 2A) and has been successfullyapplied to other modes of exercise such as running (17),kayaking (9), rowing (20), and swimming (33). This modelhas not, however, been applied to a physiological parametersuch as heart rate (HR). Heart rate is a simple, easilymeasured, and practical method of determining exerciseintensity. Theoretically, the CP model can be applied to HRto develop a HRbased analog of the CP test called thecritical heart rate (CHR) test (Figure 3). The slope of the totalnumber of heart beats (HB
lim
) vs. T
lim
relationship from theCHR test would provide a physiological measure (i.e., HR)which represents a threshold exercise intensity that, theoretically, could be maintained for an extended period.Therefore, the purposes of this study were to (a) determineif the mathematical model that has previously been used toestimate the CP (25,26) was applicable to HR to estimate theCHR, and (b) compare the CHR to the HRvalues at the CP(CP
HR
), VT (VT
HR
), and RCP (RCP
HR
). Based on previousstudies, it was hypothesized that (a) the mathematical modelused for the estimation of CP would be applicable to HRmeasurements to derive the CHR (25,26), and (b) the meanCHR, CP
HR
, and RCP
HR
would not be signiﬁcantly differentbut would be greater than the VT
HR
(26).
M
ETHODS
Experimental Approach to the Problem
In this study,
_
V
O
2
and HR values were measured during anincremental test to exhaustion on a cycle ergometer todetermine peak oxygen consumption (
_
V
O
2
peak), HR
max
,VT
HR
, and RCP
HR
. In addition, HR was measured during 4 continuous workbouts to exhaustion at different poweroutputs to determine the CHR and CP
HR
. The mathematicalmodel that has previously been used to estimate CP (25,26)was applied to the heart rate data to derive the CHR (a heartrate analog of the CP test). The mean CHR was thenstatistically compared to VT
HR
, RCP
HR
, and CP
HR
.
Subjects
Fifteen women volunteered for the study. Their mean (
6
SD
)age, body weight, height, and
_
V
O
2
peak were 21.7
6
2.1 years,65.7
6
9.9 kg, 168.1
6
5.7 cm, and 2.7
6
0.4 L
min
2
1
(40.7
6
4.6 mL
kg
2
1
min
2
1
), respectively. The physical activity levelsof the subjects’ ranged fromsedentary (
n
= 4) to moderatelyactive (
n
= 11). Sedentary wasdeﬁned as not currently participating in aerobic and/or resistance training, whereasmoderately active was deﬁnedas participating in aerobic and/or resistance training for 4 to5 hours per week. All subjectswere instructed to avoid exercising the day prior to the testand to not eat for approximately 4 hours prior to testing.The subjects had no knowncardiovascular, pulmonary,metabolic, muscular, and/orcoronary heart disease and didnot regularly use prescription
Figure 1.
The method used for determining the RCP.
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medication. The study was approved by the UniversityInstitutional Review Board for Human Subjects, and allsubjects completed a health history questionnaire (3) andsigned a written informed consent prior to any testing.
Determination of
_
V
O
2
peak
Each subject performed an incremental test to exhaustion onaCalibrated Quinton(Corval400)electronically brakedcycleergometer (Quinton Instruments Inc., Seattle, Washington,U.S.A.) at a pedal cadence of 70 rev
min
2
1
. Seat height wasadjusted so that the subject’s legs were at near full extensionduring each pedal revolution. The subjects wore a nose clipand breathed through a mouthpiece (2700; Hans Rudolph,Kansas City, Missouri, U.S.A). Expired gas samples werecollected (20second average) and analyzed using a calibrated TrueMax 2400 metabolic measurement system(Parvo Medics, Sandy, Utah, U.S.A.). Prior to all testing sessions the gas analyzers were calibrated with room air andgases of known concentration. The subjects were ﬁtted witha Polar Heart Watch system (Polar Electro Inc., LakeSuccess, New York, U.S.A.) to monitor HR throughout thetest. The test began with a 3minute warmup at a poweroutput of 50 watts and a pedaling rate of 70 rev
min
2
1
. Thepower output was increased by 30 watts every 2 minutesuntil voluntary exhaustion or the subject could no longermaintain a pedal cadence of 70 rev
min
2
1
despite strong verbal encouragement.
_
V
O
2
peak was deﬁned as the highest
_
V
O
2
value during the last 30 seconds of the exercise test. Asubject’s
_
V
O
2
peak data were used if they met at least 2 of thefollowing 3 criteria (1,11): (a) 90% of agepredicted heartrate, (b) respiratory exchange ratio
.
1.1, and (c) a plateauing of oxygen uptake (less than 150mL
min
2
1
in
_
V
O
2
over thelast 30 seconds of the test). At the completion of the test, thesubjects performed a cooldown period on the cycle ergometerat a lower power output for as long as they wished. Assessmentof
_
V
O
2
peak has been shown to be highly reliable in a similarpopulation, with an intraclass correlation
.
0.80 (27) and SEM
,
5% of the means.
Determination of the Ventilatory Threshold (VT) and VT
HR
The VT was determined by noninvasive gas exchange measurements using the Vslope method of Beaver et al. (4). TheVTwas deﬁned as the
_
V
O
2
value corresponding to the intersection of 2 linear regression lines derived separately from thedata points below and above the breakpoint in the
_
V
CO
2
vs.
_
V
O
2
relationship (Figure 4). Heart rate values from the incremental test were plotted against
_
V
O
2
values, and the regression equation derived was usedto determine the VT
HR
.
Determination of theRespiratory CompensationPoint (RCP) and RCP
HR
The RCP was determined bynoninvasive gas exchangemeasurements using the
_
V
E

_
V
CO
2
plot as described byBeaver et al. (4). The RCPwas deﬁned as the
_
V
O
2
valuecorresponding to the point of departure from linearity of
_
V
E
and
_
V
CO
2
(Figure 1). Heart ratevalues from the incrementaltest were plotted against
_
V
O
2
values, and the regression equation derived was used to determine the RCP
HR
.
Figure2.
(A). Schematic diagram of the relationships for work limit (W
lim
)versus time limit T
lim
for the estimation of the critical power (CP) andanaerobic work capacity (AWC). (B). Schematic diagram of therelationships for power output (P) versus T
lim
.
Figure 3.
Relationship for HB
lim
versus T
lim
for 1 subject.
506
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Critical Heart Rate Test
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Determination of CHR, CP, and CP
HR
Onseparatedays,atleast48hoursfollowingthe
_
V
O
2
peak test,the subjects performed 4 randomly ordered rides (1 ride oneach day) to exhaustion at 70 rev
min
2
1
at 4 different poweroutputs. The seat height, toe clips, and warmup procedureswere the same as for the incremental test. The power outputswere selected by experienced investigators and were basedon the ﬁtness level of the subject (23,24). The power outputswere selected so that the subjects could complete approximately 8 to 20 minutes before exhaustion (23,24). Heart ratevalues were continuously monitored and recorded every 5seconds. For each power output, the HB
lim
was calculated asthe product of the average 5second HR (bpm) and totalT
lim
(minutes). The HB
lim
for each of the 4 power outputswere plotted as a function of the T
lim
at each power output(Figure 2). The CHR was deﬁned as the slope coefﬁcient of the regression line between HB
lim
and T
lim
.To determine CP, the total work (W
lim
in kilogrammeters)performed at each power output was calculated asthe productof the power output (kg
min
2
1
)and time to exhaustion (minutes). The W
lim
for each of the4 power outputs was plotted asa function of T
lim
at each poweroutput (Figure 2A). The CPwas deﬁned as the slope coefﬁcient of the regression linebetween W
lim
and T
lim
. Heartrate values from the incremental test were plotted againstpower output values, and theregression equation derived wasused to determine the CP
HR
.
Statistical Analyses
Means and standard deviationswere calculated for CHR,CP
HR
, VT
HR
, and RCP
HR
. A1way repeatedmeasures analysis of variance (ANOVA) was used to determine if therewere signiﬁcant differences among the thresholds. An alpha level of
p
#
0.05 was selected for all statistical comparisons. Azeroorder correlation matrix was used to determine therelationships among the thresholds. The analyses wereconducted using the Statistical Package for the SocialSciences software (v.17.0, SPSS Inc., Chicago, Illinois, USA).
R
ESULTS
Table 1 includes the mean (
6
SD
) and range values for CHR,CP
HR
, VT
HR
, and RCP
HR
. The mean CHR (172
6
11 bpm,92.9
6
2.7%HR
max
) was not signiﬁcantly different fromRCP
HR
(172
6
9 bpm, 92.9
6
2.2%HR
max
) but was higher(
p
,
0.05) than the CP
HR
(154
6
10 bpm, 83.2
6
3.7%HR
max
)and VT
HR
(152
6
12 bpm, 82.1
6
4.3%HR
max
). The
r
2
valuesfor HB
lim
vs. T
lim
relationships ranged from 0.985 to 1.0
.
The
r
2
values for the W
lim
versus T
lim
relationships for theestimation of CP ranged from 0.866 to 0.999
.
The
r
2
values for
T
ABLE
1.
Mean (
6
SD
) and range values for CHR,RCP, CP
HR
, and VT
HR
.Mean
6
SD
Range (bpm) %HR
max
CHR 172
6
11 153–193 92.9
6
2.7RCP
HR
172
6
9 162–195 92.9
6
2.2CP
HR
154
6
10* 135–177 83.2
6
3.7*VT
HR
152
6
12* 129–178 82.1
6
4.3*
%HR
max
= percentage of maximum heart rate; CHR =critical heart rate; RCP = respiratory compensation point;CP
HR
= heart rate at critical power; VT
HR
= heart rate atventilatory threshold.*Signiﬁcantly different from CHR and RCP
HR
.
T
ABLE
2.
Correlational matrix for the fatiguethresholds.CHR RCP
HR
CP
HR
VT
HR
CHR 1.00 — — —RCP
HR
0.83* 1.00 — —CP
HR
0.63* 0.58* 1.00 —VT
HR
0.76* 0.80* 0.60* 1.00
CHR = critical heart rate; RCP = respiratorycompensation point; CP
HR
= heart rate at critical power;VT
HR
= heart rate at ventilatory threshold.*
p
,
0.05
Figure 4.
The method used for determining VT.
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the HR vs. power output, from the incremental test, rangedfrom 0.966 to 0.999. Table 2 is a zeroorder correlation matrixamong CHR, CP
HR
, VT
HR
, and RCP
HR
. All the fatiguethresholds were signiﬁcantly intercorrelated at
r
= 0.58 to0.83 (Table 2).
D
ISCUSSION
One purpose of this study was to determine if the mathematicalmodelthathasbeenusedtoestimateCP(25,26)couldbe applied to HR measurements to derive a new fatiguethreshold called the critical heart rate (CHR). The HB
lim
during each exhaustive workbout was substituted for W
lim
inthe W
lim
vs. T
lim
relationship used to estimate CP. For eachsubject, the relationship between HB
lim
and T
lim
wasdescribed by the equation HB
lim
= a + CHR(T
lim
), whichindicated that the total number of heart beats accumulatedduring each exhaustive workbout increased linearly with T
lim
(
r
2
= 0.985–1.0). These
r
2
values were similar to those for theW
lim
vs. T
lim
relationship for the estimation of CP in thepresent study (
r
2
= 0.866–0.999) and to those from previousstudies (
r
2
= 0.982–1.0) (6,7,19,26)
.
The high correlations(
r
2
= 0.985–1.0) for the HB
lim
vs. T
lim
relationships found inthe present study indicated that the mathematical modelused for the determination of CP could be applied to HRmeasurements to estimate the CHR. Thus, theoretically,both the CP and CHR tests provide estimates of the maximalintensity of exercise that can be maintained for an extendedperiod without fatigue. The tests differ, however, in that theCP test estimates the maximal nonfatiguing power output,whereas the CHR test estimates the maximal nonfatiguing HR. Thus, the physiological responses during a continuousworkbout at a constant power output differ from those ata constant HR. For example, previous studies (6,7,14,15,29)have shown that during continuous exercise at the CP,
_
V
O
2
and HR increased and did not reach steady state. Maintenance of a constant HR during a continuous workbout,however, requires a reduction in power output (5). Therefore,it is unclear if the threshold associated with the maximalnonfatiguing intensity of exercise should be based on a speciﬁc power output or a physiological variable such as HR.Future studies should examine this issue by comparing theT
lim
values for continuous cycle ergometer workbouts at theCP vs. those at the CHR.The ﬁndings of the present study indicated that there wasno mean difference between CHR (172
6
11 bpm, 92.9
6
2.7%HR
max
, 85.5
6
8.8%
_
V
O
2
peak) and RCP
HR
(172
6
9 bpm,92.9
6
2.2%HR
max
, 84.3
6
6.4%
_
V
O
2
peak), but both weregreater (
p
,
0.05) than CP
HR
(154
6
10 bpm, 83.2
6
4.0%HR
max
) and VT
HR
(152
6
12 bpm, 82.1
6
4.3%HR
max
).The mean CHR and RCP
HR
values in the current studywere also highly correlated (
r
= 0.834) and similar to therelative exercise intensities for CP (85.4
6
4.8%
_
V
O
2
max),RCP (85.3
6
5.6%
_
V
O
2
max), and HR at RCP (174
6
10 bpm,90 %HR
max
) reported by Dekerle et al. (12), and the meanRCP (91.8%HR
max
, 87.5%
_
V
O
2
max) reported by Impellizzeriet al. (18). Furthermore, in the present study, there was nomean difference between CP
HR
and VT
HR
, and they weremoderately correlated (
r
= 0.598). These ﬁndings were consistent with those of Moritani et al. (26), who reported a highcorrelation (
r
= 0.927) and no mean difference betweenthe
_
V
O
2
at CP (2.48
6
0.54 L
min
2
1
) and VT (2.30
6
0.44 L
min
2
1
). In addition, Le Chevalier et al. (21) andVautier et al. (32) have reported that CP corresponded to theVTand lactate threshold, respectively. In contrast, Pooleet al.(29) reported that CP (197
6
12 W, 79
6
8.1%
_
V
O
2
max) was64% higher than VT (120
6
8 W, 46
6
4.6 %
_
V
O
2
max) andrepresented an ‘‘upper limit for sustainable power’’ (p. 421).In addition, Dekerle et al. (12) reported that CP (278
6
22 W,85.4
6
4.8%
_
V
O
2
max) coincided with RCP (286
6
28 W,85.3
6
5.6%
_
V
O
2
max). Thus, previous studies (12,18,21,26,29,32) have provided conﬂicting results regarding the associations among the VT, RCP, CP, and lactate threshold,whereas the present study indicated that CHR and RCP
HR
were greater than CP
HR
and VT
HR
. The differences betweenstudies may have been a result of the training status of thesubjects, the durations and intensities of the workbouts usedto estimate CP, and/or the procedures used to determine theVTand RCP. For example, the subjects in the present studywere sedentary to moderately active, whereas those of Dekerle et al. (12) were well trained (
_
V
O
2
max = 50.8
6
2.7mL
kg
2
1
min
2
1
) and those of Impellizzeri et al. (18) wereinternationally competitive mountain bikers. In addition, thedurations of the workbouts (63.3–95.7%
_
V
O
2
peak) used toestimate CP in the current study ranged from approximately8 to 20 minutes, whereas other studies used workbouts (90.0–110.0%
_
V
O
2
max) that led to exhaustion in 2 to 15 (12) or 4 to8 minutes (29). Furthermore, in the present study, VT andRCP were determined using the procedures of Beaver et al.(4). In contrast, Moritani et al. (26) determined the VT byvisual inspection of the changes in
_
V
E
,
_
V
CO
2
, and
_
V
E
/
_
V
CO
2
across time, whereas Poole et al. (29) used the changes inventilatory equivalents along with the end tidal partialpressures of O
2
and CO
2
.The close similarity between the CHR and RCP
HR
in thepresent study suggests that (a) the RCP can be estimatedfrom the CHR test without measuring expired gas samples,and (b) the CHR can be used for the same purposes as theRCP such as demarcating the heavy from severe exerciseintensity domains (4,35), predicting endurance exerciseperformance (30), and prescribing training intensity forcompetitive cyclists (22). For example, Yamamoto et al.(35) demonstrated that the RCP coincided with thedemarcation of the heavy and severe exercise intensitydomains and that exercise above, but not at, the RCPelicited an increase in lactate from the 15th to the 30thminute of exercise. In addition, Reybrouck et al. (30)reported that the RCP was a better predictor (
r
= 0.82) of performance in a 12minute run than the VT (
r
= 0.73) (30)and that the RCP accounted for 67% of the variance inendurance exercise performance. Furthermore, Lucia et al.
508
Journal of Strength and Conditioning Research
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TM
Critical Heart Rate Test
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