doi:10.3900/fpj.3.2.108.e
EISSN 1676-5133
Comparative study of equations of
estimate of the maximum heart rate
Original Article
Fernando Policarpo Barbosa
Universidade Católica de Brasília UCB, Brasília – DF Brasil.
[email protected]
Paula Roquetti Fernandes
Universidade Castelo Branco UCB, Rio de Janeiro – RJ Brasil.
[email protected]
Hildeamo Bonifácio Oliveira
Universidade Católica de Brasília UCB, Brasília – DF Brasil
José Fernandes Filho
Universidade Castelo Branco UCB, Rio de Janeiro – RJ Brasil.
[email protected]
BARBOSA, F.P., OLIVEIRA, H.B., FERNANDES, P.R., FERNANDES FILHO, J. Comparative study of equations of estimate of the maximum heart rate. Fitness & Performance Journal, v.3, n.2, p.108-114, 2004.
Abstract: Recently, researches have developed a new equation to estimate maximum heart rate (HRmax) for individuals from both
male and female sexes and they also have demonstrated that equation (220-age), usually utilized, tends to overestimate HRmax.
The objective of this work was to evaluate the precision and applicability of HRmax equation among male and female sexes, both of
them healthy, 17 up to 33 years-old. In order to determine the reference of HRmax, called as HRref, it was taken in turn maximum
effort test utilizing electrical treadmill machine with incremental progressive weights. Results showed that studied equations (220 –
age) (198.40±3.70), Jones et al. (196.00±2.30) and Tanaka et al. (192.90±2.50), have low correlation with observed HRref and
variation of (0.07; 0.02; and 0.02), respectively, showing no significance (p > 0.05). It was also verified that excluding those equations proposed by Tanaka et al. all the others showed tendency to overestimate Wilk’s Ë HRref = 0.001 F (3.119) = 29265.85; p =
0.01. It is concluded that among analysed equations, those of Tanaka et al. have best relationship with young individual’s reference
values. It is suggested more studies with older individuals.
Keywords - Equations; maximum heart rate; prescription; health.
Correspondence to:
Av. Central, bloco 1025, casa 09 – Núcleo Bandeirante – Brasília – DF – CEP 71710-019
Submitted: November / 2003
Accepted: December / 2003
Copyright© 2004 por Colégio Brasileiro de Atividade Física, Saúde e Esporte
108
Fit Perf J
Rio de Janeiro
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2
108-114
Mar/Apr 2004
RESUMO
RESUMEN
Estudo comparativo de equações de estimativa da freqüência cardíaca
máxima
Estudio comparativo de ecuaciones de estimación de la frecuencia de
corazón de máximo
Recentemente, pesquisadores desenvolveram uma nova equação para estimativa da Freqüência Cardíaca Máxima (FCmáx) em indivíduos de ambos os
sexos, demonstrando que a equação (220 - idade), usualmente utilizada tende
a superestimar a FCmáx. O objetivo deste estudo foi avaliar a precisão e aplicabilidade de equações de estimativa da FCmáx em homens e mulheres jovens
aparentemente saudáveis (n = 122) com idade entre 17 e 33 anos (21,48±3,67).
Para a determinação da FCmáx de referência (FCref), foi realizado teste de esforço
máximo em esteira rolante com incremento de cargas progressivas. Os resultados demonstram que as equações (220 – idade) (198,40±3,70); Jones et al.
(196,00±2,30) e Tanaka et al. (192,90±2,50), estudadas apresentam uma
baixa correlação com a FCref observada, sendo que a variação foi entre (0,07;
0,02; e 0,02), respectivamente, demonstrando não haver significância (p >
0,05). Verificou-se também que, com exceção da equação proposta por Tanaka
et al. (2001), as demais apresentaram tendência significativa em superestimar
a FCref Wilk’s Ë = 0,001 F (3,119) = 29265,85; p = 0,001. Conclui-se assim
que, dentre as equações analisadas, a que apresenta melhor relação com os
valores de referência em indivíduos jovens foi a de Tanaka et al. (2001), sendo
necessários outros estudos que envolvam indivíduos em diferentes faixas etárias.
Recientemente, las investigaciones han desarrollado una nueva ecuación para
estimar frecuencia de corazón de máximo (FCmax) para los individuos del varón y
“ los géneros hembras y ellos también han demostrado esa ecuación (220-edad),
normalmente utilizó, tiende a sobrestimar FCmax. El objetivo de este trabajo era
evaluar la precisión y pertinencia de ecuación de FCmax entre el varón y los gansos
hembras, los dos de ellos saludable, 17 a 33 año-de-edad. Para determinar
la referencia de FCmax, llamó como FCref, se utilización tomó máximo esfuerzo
prueba a su vez la máquina de la rueda de molino eléctrica con pesos progresivos
incrementales. Los resultados mostraron eso estudió ecuaciones (220 - edad)
(198,40±3,70), Jones el al. (196,00±2,30) y Tanaka et al. (192,90±2,50),
tiene correlación baja con FCref observado y variación de (0,07; 0,02 y 0,02)
respectivamente, no mostrando importancia (p> 0,05). También fue verificado
que excluyendo esas ecuaciones propuestas por Tanaka et al. todos los otros
mostraron tendencia a sobrestimar Wilk Ë FCref = 0,001 F (3.119) = 29265,85;
p = 0,01. Se concluye que entre las ecuaciones analizadas, aquéllos de Tanaka
et al. tenga relación mejor con los valores de la referencia de individuo joven.
Se hace pensar en más estudios con individuo más viejo.
Palavras-chave - Equações; Freqüência Cardíaca Máxima; prescrição; saúde.
Palabras clave - Ecuaciones; máximo de frecuencia de corazón; prescripción;
salud.
INTRODUCTION
The key points to the success of a program of physical exercise
are focused on determining the functional parameters obtained
by a careful physical evaluation and the principles that will guide
the orientation of physical exercises, such as: frequency, duration
and intensity (AMCS, 2003; FERNANDES FILHO, 2003).
The technological advances provided a better quality equipment
that enable the obtaining data, such as the maximum oxygen
intake (VO2máx); ventilating threshold (LV), the lactate threshold
(LT); maximum cardiac frequency(FCmax) among others DENADAI
et al ., 2000 (WASSERMAN et al., 1994;).
a reflection on methodologies for assessing aerobic fitness and
the prescription of physical training that are substantiated in the
equation (220-age).
Methodology
This study had a correlation act of accosting, to assess the applicability of different equations to estimate the FCmáx in apparently
healthy individuals, using as a reference the test of maximum effort
(THOMAS; NELSON, 2002).
There was the relation between the values obtained by different
According Dantas (1995), Marins and Giannichi (1998), Milk
(2000), Fernandes Filho (2003) and AMCS (2003), the equations
for estimating the FCmáx are a methodology of low cost and
easier to apply.
equations to estimate the maximum cardiac frequency: Tanaka et
Despite the existence of a great variety of equations for estimate
of the FCmáx, one notices that the equation (220 - age) continues
being widely used as base for such determination (LANDWEHR;
ROBERGS, 2002).
Sample
A point that calls attention on the equation 220-age, is attributed
authorship to Karvonen et al. (1957). Meanwhile, the mentioned
study does not refer to the equation 220-age, and therefore, aimed
to the development of the equation [FCt-FCrest/FCmáx - FCrest)
x 100] in a group of six students. Policarpo and Bottaro (2000),
Tanaka et al. (2001), Oliveira, Policarpo and Bottaro (2001) and
Cardoso and Forjaz (2001) demonstrated that the equation (220age) tends to overestimate the values gotten with FCmáx obtained
both in rolling mat as a cycle ergometer. Such a finding requires
Fit Perf J, Rio de Janeiro, 3, 2, 109, Mar/Apr 2004
al. (2001) [208 - (0.7 x age]), Jones et al. (1975) [210 - (0.65
x age)], and [220 - age] and the values of maximum cardiac
frequency measured in effort test.
The sample was a special selection at the university students at
the first semester of the course of Physical Education, apparently
healthy, volunteers of both sex, aged between 17 and 33 years.
This study was approved by the Ethics Committee at the Catholic
University of Brasilia (UCB), Brasilia DF.
Local
All tests were performed in the Laboratory of Physical Evaluation
and Training (LAFIT) of the Catholic University of Brasilia (UCB),
according to the criteria of safety recommended by the National
Consensus Ergometer(2000).
109
Procedure
Participants were selected in the classroom and informed of the
objectives, procedures, possible discomfort, risks and benefits
involved in participating on this research.
The individuals previously selected had been instructed not to feed
three hours before the test and not ingesting alcoholic beverage
48 hours before the test, as well as not exercising 12 hours before
they be presenting at the laboratory. As arriving at the laboratory,
they read and signed the term of agreement assent as the law
196/96, after that they had answered to anamnesis, ending with
the acquisition of the following data:
Body Mass (MC), height (EST) and Skin Folds (DC)
The body mass (MC) was evaluated by means of electronic balance
TOLEDO DIGITAL with accuracy of 50g; the height was measured
through a (estadiômetro ) indispensable tool for the practice of
a complete physical evaluation (COUNTRY TECNOLOGY INC,
Gays Mills, Wl. Model 67031) with scale in millimeters. Estimates
of the percentage of fat (% G) and lean body mass (MCM) were
obtained by the equation of three skin folds both for men as for
women (POLLOCK; WILMORE, â1993). For the collection of skin
folds, used up the compass mark Lange (CAMBRIDGE SCIENTIFIC
INDUTRIES, Cambridge, MD). The data were calculated using
the Galileo of physical evaluation, version 2.0 (MICROMED ©,
Brasilia, DF).
Electrocardiogram (ECG) and Blood Pressure
(BP) of Sleep
After anthropometric assessment, the candidates were accommodated in a bed, where he remained in dorsal position
for 10 minutes. Soon after, gauged to blood pressure at rest
through a sphygmomanemeter (BECTON DICKINSON ®),
then took the ECG at rest through the equipment (MARQUETTE HELLIGE ©, Medical Systems, model: Cardio smart,
version 3.0 CS-MI).
Testing Maximum Effort with metabolic analysis of Gases Test
of maximum effort was made in rolling mat model Super ATL
(INBRAMED, Porto Alegre, Brazil). The metabolic analysis of
gas was done by VO2000 ® attached to the computerized
system ERGOPC Elite ®, version 2.0 (MICROMED ©, Brasilia, DF).
This analyzer can assess the following parameters: volume of air
expired per minute (VE), volume of oxygen consumed per minute
(VO2), volume of carbon dioxide produced per minute (VCO2),
and respiratory exchange ratio of (R). Before the start of each test,
the metabolic gas analyzer was calibrated, as the manufacturer’s
specifications, with a gas known and attested by the Center for
Quality Assurance of Special Gases, composed of 17% O2, 5%
CO2, and with nitrogen balance. Heart rate (HR) was monitored
through derivation (CM5). Therefore, we used the electrocardiogram system ERGOPC Elite ®, version 2.0 (MICROMED ©,
Brasilia, DF).
Testing Maximum Effort with metabolic analysis
of Gases
The register used in the tests was the maximum effort of progressive
intensity with increasing the burden (of 1km/h) to each minute
and one percent of the tilt (0% initial and final of 6%) every two
Figure 2 - Distribution of FCmáx measure and FCmáx estimated in
relation to age.
Figure 1 - Histogram distribution of FCmáx extent test effort
110
Fit Perf J, Rio de Janeiro, 3, 2, 110, Mar/Apr 2004
Table 1 - Characterization of the sample (N = 122)
N
Min.
Max.
Average
Standard Deviation
Year
122
17
33
21.48
3.67
stature
122
148
189
172
8.47
corporea mass
122
40.30
96.60
66.63
10.24
IMC =
122
16.00
31.10
22.50
2.42
fat mass
122
1.73
25.42
9.02
4.76
lean mass
122
35.55
77.46
57.62
9.60
percentage of fat
122
2.85
31.66
13.52
6.47
FC rest
122
39
92
63.67
10.44
Systolic pressure
122
90
140
115
9.20
Diastolic pressure
122
60
90
71.84
8.31
Table - 2: Values of FCmáx measure and FCmáx estimated by different equations in individuals of both sexes (n = 122).
FCmáx measure
(220 – year)
Jones et al.
Tanaka et al.
N
12
12
12
12
Mínimo
16
18
18
18
Máximo
20
20
19
19
Average
190.4
190.4*
196.0*
192.9*
Standard Deviation
706
3.7
2.3
2.5
*p > 0.05
minutes, until the participant reaches the exhaust. The initial speed
was 4km / end of 16km/h.
tive analysis, b) analysis of co-variance corrected by the method
We excluded those who had borderline hypertension, diabetes,
cardiovascular disease and diseases of the respiratory system
ACSM, 2003 (SOCIEDADES BRASILEIRAS DE CARDIOLOGIA,
2002).
standard error of estimate (SEE), and e) analysis of the scores
Statistical Treatment
analysis was performed using the Statistical Package for the Social
The statistical criteria used in determining the applicability and
accuracy of equations for estimating the FCmáx were: a) descrip-
Sciences for Windows (SPSS 10.0). The significance level was p
Figure 3 - Scores for residual equation (220 - age) and to test
FCmáx extent of effort in terms of age.
Figure 4 - Scores for residual equation proposed by Jones et al.
(1975) and to test FCmáx extent of effort in terms of age.
Fit Perf J, Rio de Janeiro, 3, 2, 111, Mar/Apr 2004
of Bonferone c) test the Pearson correlation (r) d) analysis of the
by residual method of Bland and Altman (1986). The cases
were extreme outliers defined by 3.0 standard deviations of the
average±individual scores of exclusion (STEVENS, 1996). Data
<0.05.
111
RESULTS
The analysis was based originally 144 individuals, and 17 individuals was excluded, due the criterion. The sample was composed of
n = 122 individuals of both sex, with 69% men and 31% women.
We observed the following descriptive to the anthropometric variables and for the rest of functional parameters (Table 1).
The correlation was not significant (p> 0.05) between the equations and data obtained in testing for the equations of Fox et al.
(1971), Jones et al. (1975), and Tanaka et al. (2001), for values
of (r = 0071, 0022 and 0023), respectively.
The results showed significant differences between mean values
of measured HRmax and estimated HRmax. Obtained the following
data for the scores of co-variance: Wilk’s Ë = 0.001. F (3.119)
= 29265.85, p = 0.001. As the null hypothesis (H0) rejected, it
was accepted the alternative hypothesis (H1) that the equations
have significant differences (p > 0.05) in determining HRmax with a
tendency to overestimate the reference values, as shown in Table
2 and in the Graphs 1 to 6.
The results for the scores showed the residual values of 45.08%,
31.15% and 19.67%, respectively, for the equations of (220 - age),
Jones et al. (1975) and Tanaka et al. (2001). The error constant
was considered significant for all equations.
DISCUSSION
The development of equations for the estimation of FCmáx definition has been subject of several studies (ARAÚJO; BASTO, 1980;
CAMPILLO, 2003). LONDEREE; and MOESCHBERGER,1982.
Figure 5 - Scores residual equation for Tanaka et al. (2001) and
to test FCmáx extent of effort in terms of age.
112
These equations are used to specify the intensities and to control
physical exercises. Other important aspects are related to its ease
of handling and low cost (ACMS, 2003).
In the present study, it was verified the effectiveness of three
equations in determining FCmáx in young individuals, healthy
university students, all active, observing a tendency to overestimate the FCmáx measured in effort’s test. According to Tanaka
et al. (2001), the equation (220 - age) tended to overestimate
FCmáx in young individuals. The same results were observed
by Polycarpo and Bottaro (2000), when comparing the values
obtained in effort’s test with the equations of Jones et al. (1975)
and (220 - age).
In research conducted by Araújo and Basto (1980), in young individuals, they verified that the equation proposed by Jones et al. had
better parity between the obtained and estimated values. Mesquita
et al. (1996) compared if there would be better relation between
the equation (220 - age) and table of Sheffield in determining
FCmáx in sedentary individuals, by means of maximum ergometric
test, noting that the equation showed better relation with the data
obtained in testing. In the present study, no significance was observed (p> 0.05) between the studied equations and the obtained
data. The equation (220 - age) was the one that presented the
highest tendency to overestimate the reference values.
It can be as a possible explanation for this trend the characteristics of the studied population. Both in the study performed by Araujo and Basto (1980) as the one from Polycarpo
and Bottaro (2000), the samples were composed of active
individuals who had different hemodynamic responses to the
effort (EVANGELISTA, BRUM, 1999; FPRJAZ et al., 1998;
Figure 6 - Scores waste for different equations to estimate the
FCmáx and FCmáx extent test effort in relation with age.
Fit Perf J, Rio de Janeiro, 3, 2, 112, Mar/Apr 2004
NEGRÃO et al., 1996). Evangelita and Brum (1999) in review
on the effects of detraining in the endurance athletes, in a
period of four weeks, on the heart rate, observed changes
in responses to submaximal and maximum exercise. Rivera
(1981) reports that this type of training would influence the
response of the achievement of FCmáx in young individuals
aged 21 to 23 years.
Other important aspects that could be influencing the response
in obtaining FCmáx, according to Londeree and Moeschberger
(1982), would be: age, sex, training, and ethnicity. The conclusion
was that age would be the variable with the greatest influence.
Thus, an important point to be observed in defining the equation
for the estimation of FCmáx would be the correction factor for age.
equations in determining the point of interruption of the assessment
cardio respiratory sub maxima held in the academies, and for the
prescription of the intensity of aerobic exercises so individualized.
Recommend is to other studies that meet the influence of factors
that may interfere in the responses of CF in trial of effort, such
as: level of fitness, body mass, age, in the Brazilian population,
because the equations of reference were advocated in other
ethnic groups.
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