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PREDICTION OF ONE REPETITION MAXIMUM LOAD

BY TOTAL AND LEAN BODY MASS IN TRAINED AND

UNTRAINED MEN

Eduardo Lusa Cadore(A,B,C,D,E,F), Ronei Silveira Pinto(C,D,E,F), Michel Arias Brentano(A,B,C,D,E,F), Rodrigo Fer-

rari Silva(A,B,C,F), Eduardo Marczwski da Silva(A,B,C,F), Rafael Spinelli(A,B,C,F), Cleiton Silva Correa(C,D,E,F), Luiz

Fernando Martins Kruel(A,B,C,D,E,F)

Exercise Research Laboratory, Physical Education School, Federal University of Rio Grande do Sul, Porto

Alegre, Brazil

Abstract

Introduction: One repetition maximum test (1RM) is often used to evaluate muscle strength and to prescribe the in-

tensity of strength training. However, the determination of the initial test load, and duration of the test make difficult to use

the same in non-individualised environments.

Objective: To determine coefficients to estimate the maximum strength (1RM), based on the relationship between

muscular strength, lean body mass and total body mass.

Methods: Twenty-eight strength-trained and non-strength-trained men participated in this study. Muscle strength was

determined using the 1 RM test in the bench press, supported barbell row, 45° leg press and squat exercise, while body

composition was measured using the skinfolds method. After verifying the correlations between muscular strength and body

mass and composition, the coefficients to predict the maximal strength were calculated by dividing the value of the 1 RM

by the total body mass and lean body mass (kg) and by linear regression equation based in these parameters.

Results: Significant correlations were found between body mass and lean body mass with muscular strength in all the

exercises (r = 0.47 - 0.76, P < 0.05). The greatest correlations were observed between the muscular strength values and

lean body mass. There was a significant difference between the coefficients obtained from trained and non-trained subjects

in all the tested exercises (P < 0.05).

Conclusions: The results suggest that the coefficients of prediction of the 1RM should take into account the body

composition and the training status of the individuals.

Key words: strength training, fat-free mass, force development, body composition

Introduction

Strength training promotes neuromuscular adap-

tations which are dependent of the intensity relative

to maximum load (% of 1-RM) at which the training

is performed. Low to moderate intensity of training

(40-60% of 1-RM) result in an increase in the local

muscular endurance, while moderate to high intensity

training (65 to 90% of 1-RM) result in greater increases

in the maximum strength and of the cross-sectional

area – CSA [1]. The prescription of the overload in

each exercise in the training routine can be determined

using apercentage relative to the 1-RM (i.e. 50, 70,

80%) [2], using arange of maximum repetitions –

RMs (i.e. 8-10 RMs, 12-15 RMs) [3], or using scales

of perceived exertion (i.e. Borg, OMNI) [4]. Different

overloads result in distinct physiological responses,

and it may be modulated accordingly with the aims

of the training program [5,6].

The 1-RM test is amethod widely used for the

determination of the intensity of strength training.

Nevertheless, the 1-RM test is difficult to apply in

health gyms, physical training centres and rehabilita-

tion clinics. Among the factors that limit its utilisation

in these environments are the lack of valid criteria

for establishing the initial overload (i.e., first trial),

and the total time spent in its performance [7]. Given

this situation, some investigators have proposed the

prediction of the 1-RM values in strength exercises

using linear regression equations, based on the inverse

relationship observed between the overload lifted with

the number of maximum repetitions performed with

this overload (RMs) [8-16]. With the same purpose,

some investigators have proposed the use of coef-

ficients to predict the maximum strength, calculated

using the total body mass (TBM) values [17-18]. In

study of Baechle and Groves [18], specific coefficients

calculated from the quotient between 1RM and the

TBM values were proposed for each exercise, based

on the relationship between TBM and the strength

development. Hence, these authors suggested that

each exercise presents aspecific coefficient, and the

1RM value in each exercise may be obtained by the

product between these generic coefficient calculated

and the TBM. However, in this purpose, the investiga- However, in this purpose, the investiga-However, in this purpose, the investiga-

tors did not take into consideration the subjects’ body

composition, particularly the lean body mass (LBM),

Medicina Sportiva

Med Sport 16 (3): 111-117, 2012

DOI: 10.5604/17342260.1011391

ICID: 1011391

Copyright © 2012 Medicina Sportiva

ORIGINAL RESEARCH

111

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Cadore E.L., Pinto R.S., Brentano M.A., Silva R.F., Marczwski da Silva E., Spinelli R., Correa C.S., Kruel L.F.M./ Medicina

Sportiva 16 (3): 111-117, 2012

which is adeterminant variable in the force produc-

tion. Another unconsidered factor in this method was

the physical fitness status of the subjects (i.e. trained,

untrained), which could change the relationship be-

tween TBM and LBM with maximum strength, due to

the possible neural adaptations resulting from strength

training in trained individuals [19]. Therefore, this

methodological approach may have conditioned the

results, since the strength development appears to be

greatly affected by the body composition or the quality

of the neuromuscular function of the subjects.

Due to the greater relationship between the LBM,

even assessed using indirect methods, with the mus-

cle strength, when compared with the relationship

between TBM with muscular strength [8,20-22], the

determination of specific coefficients for each exercise,

based on the LBM, may improve the 1RM prediction.

Furthermore, to take into consideration the subjects’

training status (i.e. strength-trained and untrained)

could better explain the relationship between maxi-

mum strength with the LBM, and consequently pro-

vide more accurate coefficients of strength prediction.

Therefore, the aim of this study was to calculate

coefficients to predict the maximum strength (1RM)

of strength-trained and untrained men, based on the

relationships between the muscle strength with the

LBM, as well as the relationship between the mus-

cle strength with the TBM. Our hypothesis is that

the LBM, even when measured indirectly, will have

agreater correlation with the maximal strength than

the TBM. In addition, our second hypothesis is that

the coefficients of 1RM prediction will be different

between strength-trained and untrained subjects.

Methods

Experimental Design

The subjects attended the laboratory on two differ-

ent days. Firstly, their anthropometric characteristics

were measured. On asecond test day, the subjects per- On asecond test day, the subjects per-On asecond test day, the subjects per-

formed the maximum dynamic strength tests (1RM) in

four free-weight exercises. After that, the relationship

between maximum strength (1RM values) with total

body mass and lean body mass were evaluated in both

groups (i.e. trained and untrained). Based on these

relationships, the coefficients were calculated using

the quotient between the individual maximal strength

values and the corresponding total body mass and lean

body mass. After that, the coefficients obtained from

the different groups were compared.

Participants

Twenty-eight healthy (40 ± 4 years) strength-

trained and untrained men volunteered for this study

after completing an ethical consent form. Subjects were

carefully informed about the design of the study with

special information given regarding the possible risks

and discomfort related to the procedures. The study

was conducted according to Declaration of Helsinki

and was approved by Ethics Committee of Federal

University of Rio Grande do Sul, Brazil. According

with their characteristics, subjects were divided into

two groups: the strength-trained group (TG, n = 13)

and the untrained group (UG n = 15). Those subjects

that were able to perform asquat exercise with 130%

of their body weight and the bench press with 100% of

their body weight were considered trained. The sub- The sub-he sub-

jects of TG used to practiced non-competitive strength

training composed by multiple sets of 6-12 maximum

repetitions (RM), 4 to 6 weekly training sessions with

the aim of hypertrophy for at least three years. The UG

included sedentary individuals who had not engaged

in any regular or systematic training program during

the year prior to the study. None of the subjects were

using anabolic steroids or any medication that might

have influenced the muscle-skeletal metabolism.

Moreover, none of the subjects were on acontrolled

diet or any other kind of dietary restriction. The an- The an-The an-

thropometric characteristics and the strength values

(1 RM) of both groups are shown in table 1. There

were no significant differences between the groups

Table 1. Physical characteristics and muscular strength

Trained Untrained

Age (years) 40.3 ± 4.7 39.9 ± 3.7

Height (cm) 173.2 ± 5.3 173.7 ± 7.3

Body mass (kg) 79.3 ± 9.7 79.7 ± 10.9

% Fat mass 19.4 ± 5.6 25 ± 4.8†

% Lean mass 80.6 ± 5.6 74.9 ± 4.8†

Bench Press (kg) 87.2 ± 19.2 56.6 ± 11.9†

Supported Row (kg) 84.7 ± 18.4 61.5 ± 9.7†

Squat (kg) 139 ± 50.2 90.3 ± 15.4†

Leg Press (kg) 385.8 ± 84.8 231.2 ± 37.3†

Values are mean ± SD; Strength-trained group (n = 13); and untrained group (n = 15), respectively. Significant difference between groups: †P < 0.01

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Sportiva 16 (3): 111-117, 2012

in relation to age, total body mass and height. The

subjects in the TG had significantly greater 1RM

values (P<0.001) in all the assessed exercises, as well

as greater lean body mass (P<0.001).

Anthropometric measurements

Body mass and height were measured using an

Asimed analog scale (resolution of 0.1 kg) and an

Asimed stadiometer (resolution of 1 mm), respec-

tively.. Body density was estimated using the skinfold

protocols proposed by Jackson and Pollock [23]. In

order to measure the skinfolds, aplicometer (CES-

CORF) with aresolution of 0.1 mm was used. Body

composition was assessed using the skinfold tech-

nique. Aseven-site skinfold equation was used to esti-

mate body density [23] and body fat was subsequently

calculated using the Siri equation [24].

Dynamic muscular strength

The 1RM test was performed in the bench press,

supported barbel row, 45° leg press and squat exer-45° leg press and squat exer-

cises, using free weights with 0.5 kg of resolution. One

week prior to the test day, subjects were familiarized

with all procedures in two sessions. On the test day,

the subjects warmed up for five minutes on acycle

ergometer, stretched all major muscle groups, and

performed specific movements for the exercise test.

To avoid the influence of fatigue in the 1RM values,

each subject’s maximal load was determined with no

more than five attempts with afour-minute recovery

between attempts and 5 minutes between exercises.

Performance time for each contraction (concentric

and eccentric) was two seconds, controlled by an

electronic metronome (Quartz, CA, USA). The test-

retest reliability coefficients (ICC) were over 0.95 in

all strength tests.

Calculation of the coefficients

In order to calculate the coefficients, the data from

the 1 RM in each exercise were normalized by the body

mass (formula 1) and by the lean body mass (formula

2), individually for each exercise, and then the mean

for each group was calculated. Basically, the formulas

used were:

Coefficientbody mass = 1 RM/TBM

Coefficientlean body mass= 1 RM/LBM

Which 1 RM is the dynamic maximum strength

(kg), TBM is the body mass (kg) and LBM is the lean

body mass (kg).

Statistical analysis

The data are expressed as means ± standard devia-

tion. After determining normality and homogeneity,

by means of the Shapiro-Wilk and Levene tests respec-

tively, the differences in the muscle strength between

groups was tested using independent t tests. Pe a r s on’s

product-moment correlation tests were employed to

investigate the possible correlations between the mus-

cle strength in the different exercises with the lean body

mass and the body mass values in the different groups.

To establish equations to estimate maximal strength

based on total and lean body mass, linear regression

equation was employed. Because of the differences

between the muscle strength values between groups,

different coefficients to estimate maximal strength

were determined in each group. Differences between

coefficients obtained in each groups were tested using

independent t tests. Furthermore, ANOVA one-way

was used to compare the muscle strength tested and

those predicted by the coefficients and linear regres-

sion equations. The level of significance adopted was

P < 0.05, the statistical power was over 0.90 and all the

tests were done in SPSS 15.0 software.

Results

The correlations between individual values of

1RM in the different exercises with the correspond-

ing values of TBM and LBM are shown in the figures

1 to 8. There were significant correlations between

the individual 1RM values and the corresponding

values of TBM and LBM in the bench press and r

= 0.78; P = 0.0001, respectively); squat (r = 0.4; P =

0.035 and r = 0.65; P = 0.0001, respectively), and only

between the between the 1 RM values and the LBM

in the supported barbel row (r = 0.64, P = 0.001) and

Fig. 1. Relationship between bench press 1 RM values (kg) and total body mass (kg)

Fig. 2. Relationship between supported barbell row 1 RM values (kg) and

total body mass (kg)

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Sportiva 16 (3): 111-117, 2012

Fig. 3. Relationship between squat 1 RM values (kg) and total body mass (kg)

Fig. 4. Relationship between leg press 1 RM values (kg) and total body

mass (kg)

Fig. 5. Relationship between bench press (kg) 1 RM values and lean body

mass (kg)

Fig. 6. Relationship between supported row 1 RM values (kg) and lean body

mass (kg)

Fig. 7. Relationship between squat 1 RM values (kg) and lean body mass (kg)

Fig. 8. Relationship between leg press 1 RM values (kg) and lean body mass (kg)

Table 2. Coefficients to prediction 1 repetition maximum (1 RM) values by total body mass and lean body mass

Trained subjects

TBM

Untrained subjects

TBM

Trained subjects LBM Untrained subjects

LBM

Bench press 1.1 ± 0.7* 0.7 ± 0.12 1.4 ± 0.17* 1.0 ± 0.13

Squat 1.7 ± 0.5* 1.2 ± 0.2 1.3 ± 0.6* 1.1 ± 0.2

Supported row 1.1 ± 0.2* 0.8 ± 0.12 2.1 ± 0.2* 1.6 ± 0.13

Leg press 4.9 ± 0.8* 3.0 ± 0.5 6.0 ± 0.9* 4.0 ± 0.7

TBM, total body mass; LBM, lean body mass. *P < 0.0001, significant differences between groups. Strength-trained subjects (n=13) and untrained

subjects (n=15).

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Sportiva 16 (3): 111-117, 2012

leg press exercises (r = 0.59; P = 0.001). There were

no significant correlations between the 1 RM and the

TBM in the 1RM values of supported barbel row (r =

0.35; P = 0.071) and 45° leg press exercises (r = 0.33;

P = 0.083).

The coefficients determined by the relationship

between 1 RM and TBM and 1 RM and LBM in the

different exercises are shown in table 2; and, those pre-

dicted by linear regression equations are shown in table

3. There were significant differences between trained

and untrained subjects in all coefficients calculated (P

< 0.01). There were no significant differences between

the assessed strength values and the strength values

predicted by the total and lean body mass (Table 4).

Discussion

The primary findings of the present study were

the greater correlation values found between 1RM

values with LBM, even when determined indirectly

(skinfolds measures), when compared with the correla-

tions between 1RM values with TBM in the different

strength exercises tested. Moreover, the present study

has shown that the coefficients to estimate the 1 RM,

based in the TBM and LBM were different between

groups with different training status (i.e. strength

trained, untrained). Thus, our results suggest that

the quality of the neuromuscular function interferes

in the estimation of the maximum strength by these

coefficients. Our results confirm our hypotheses that

LBM would obtain greater correlation values with

muscle strength than TBM, and the coefficients would

be different between strength-trained and untrained

subjects.

Regarding the correlations between the 1 RM

values with the anthropometric variables, the greater

r values obtained between the 1 RM and the LBM are

in accordance with observations reported in previ-

ous studies [8,15,27-29], in which higher correlation

indices were noted between the 1 RM and the LBM

(predicted by the skinfolds method), than between

the 1 RM and the TBM. In study assessing the bench

press exercise in agroup of male strength-trained

students, Mayhew et al. [28], found asignificant

correlation between the 1 RM and the TBM (r =

0.68, P < 0.01), and a greater correlation between

the 1 RM and the LBM (r = 0.73, P < 0.01). Similarly,

in another investigation by Mayhew et al. [15], in

which school-aged strength-trained soccer players

were evaluated, greater correlations were reported

between the 1 RM with the LBM, when compared

with those observed between the 1 RM with the TBM

in several strength exercises: bench press (r = 0.68 vs.

r = 0.53; both P < 0.05), squat (r = 0.60 vs. r = 0.50;

both P < 0.05) and dead lift (r = 0.64 vs. r = 0.50;

both P < 0.05). Similar results were found in astudy

by Bale et al. [9] in which correlations were found

Table 3. Linear regression equations based on total and lean body mass in trained and untrained subjects

Trained subjects by

body mass

Untrained subjects by

body mass

Trained subjects by

Lean body mass

Untrained subjects by

lean body mass

Bench press y=1,243x – 11,4 y=0,628x – 6,49 y=2,22x – 54,3 y=1,152x – 12,05

Squat y=2,825x – 84,6 y=1,6938x – 37,6 y=5,036x – 181,6 y=2,3953x – 45,2

Supported row y=0,705x – 28,7 y=0,6923x – 7,9 y=1,563x – 14,93 y=0,9874x – 4,3

Leg press y=4,586x – 22,1 y=3,2224x – 12,7 y=7,878x – 116,4 y=3,9978x – 6,12

Table 4. Dynamic strength values (1 RM) based on test, calculated TBM and LBM coefficients, and calculated by linear

regression equation based on TBM and LBM in strength-trained and untrained subjects

1 RM

(kg)

1 RMTBM

(kg)

1 RMLBM

(kg)

1 RMTBMEQ

(kg)

1RMLBMEQ

(kg)

Bench pressTG 87 ± 19† 87 ± 10† 86 ± 10† 87 ± 12† 87 ± 16†

SquatTG 139 ± 50† 138 ± 17† 137 ± 15† 139 ± 27† 139 ± 37†

Supported rowTG 84 ± 18† 84 ± 10† 84 ± 9† 84 ± 6† 84 ± 11†

Leg pressTG 385 ± 84† 386 ± 47† 384 ± 44† 385 ± 44† 385 ± 57†

Bench pressUG 56 ± 11 56 ± 7 56 ± 7 56 ± 6 56 ± 8

SquatUG 97 ± 31 97 ± 13 97 ± 12 97 ± 18 97 ± 18

Supported rowUG 63 ± 11 63 ± 8 63 ± 8 63 ± 7 63 ± 7

Leg pressUG 244 ± 62 244 ± 33 244 ± 31 244 ± 35 244 ± 30

TG, Strength-trained subjects (n = 13); UG, untrained subjects (n = 15); TBM, total body mass; LBM, lean body mass; TBMEQ, linear regression equ-

ation based on TBM; LBMEQ, linear regression equation based on LBM. †Significant differences between groups: P<0.001

116

Sportiva 16 (3): 111-117, 2012

between the 1 RM value in the bench press with the

TBM (r = 0.54; P < 0.05), and with the LBM (r = 0.68;

P < 0.05), as well as between 1 RM in the dead lift

with the TBM (r = 0.50) and with LBM (r = 0.54) in

college-aged players. The greater correlation values

between 1 RM with the LBM, though predicted by

indirect methods (i.e. skinfolds measurements), such

as in the abovementioned studies, as well as in the

present investigation, could be explained by the fact

that LBM is amore representative value of the muscle

mass, and consequently, of the tissue responsible to

the strength development. Indeed, it has been shown

that the fat mass was related with lower strength

performance in the bench press [15,28] and dead lift

exercises [15], as well as in the isometric strength of

the knee extensors muscles [27]. Moreover, athletes

with alow percentage of fat mass used to have greater

strength values [30].

In the present study, free weight exercises were used

to calculate the prediction coefficients of the maxi-

mum strength (1 RM), based on anthropometric vari-

ables (TBM and LBM). The utilisation of free-weight

exercises have an important practical application since

these coefficients may have great reproducibility in any

other location when the same free-weight exercises are

employed. The 1 RM values may be greatly affected by

the mechanical characteristics of the external load of

the apparatus used in strength training (i.e. variable-

radius pulleys – CAMS and invariables, position of

the pulleys, different external moment).

The results of the present study demonstrated that

the LBM, calculated indirectly using a2-component

model, presented greater correlation coefficients than

those obtained between muscle strength and TBM.

Therefore, the LBM should be considered when elab-

orating maximum strength prediction coefficients.

Nevertheless, the 1 RM values predicted by coef-

ficients based on TBM, as well as by linear equation

regression calculated by the TBM were not different

from the real 1RM values. Thus, given the impos-

sibility of measuring the lean body mass, the use of

coefficients derived from the TBM may represent

apractical and easy way to estimate the 1 RM, or at

least the first test load during the 1RM test. Likewise,

differences were observed in the coefficients between

strength-trained and untrained subjects, with the

strength-trained participants having greater strength

values in all exercises. These differences appear to be

associated with the neural adaptations resulting from

strength training [2,19], such as the greater number

of motor units recruited and the greater firing rate

in this recruitment [2,19].

Based on the results reported here, it can be in-

ferred that strength-trained would present greater

coefficients of strength prediction. In the present

investigation, the 1 RM prediction coefficients elabo-

rated from the LBM, together with the consideration

of the subjects’ physical fitness levels, made possible

to define the predicted 1 RM values, which did not

differ significantly from the evaluated 1 RM values

(Table 4). This methodological strategy for predicting

the 1 RM based on specific coefficients in strength

exercises appears to be both efficient and appropri-

ate and its use reduces the time spent in maximum

strength evaluation tests (1 RM). The coefficients

calculated in the present study can be applied in any

place, since the exercises used were performed with

free weights.

In summary, the present study showed greater

correlation values between maximum muscle strength

(1 RM) with LBM, when compared with TBM. Fur-

thermore, the coefficients to predict 1RM values were

different between strength-trained and untrained

subjects. The present results have aimportant practi-

cal application, since the 1RM test is widely used to

investigate the neuromuscular adaptations to strength

training, as well as to prescribe this type of physical

training. Thus the coefficients calculated in the present

study may be an useful method to reduce the time

spent during this test, as well as to facilitate the same

by providing the initial test overload, which can be

very much closer of the real strength value. Further

studies are required in order to establish coefficients

of strength prediction in others populations, such as

children and the elderly.

Acknowledgements

This study was partially supported by the National

Council of Technological and Scientific Development

(CNPq), Coordination of Improvement of Higher

Education Personnel (CAPES).

Declaration of interest

The authors report no conflicts of interest.

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Accepted: September 15, 2012

Published: September 25., 2012

Address for correspondence:

Eduardo Lusa Cadore

LAPEX, Escola de Educação Física, UFRGS

Felizardo St, 750

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Ronei Silveira Pinto: ronei.pinto@ufrgs.br

Rodrigo Ferrari Silva: rod.ferrari@terra.com.br

Cleiton Silva Correa: cleitonesef@yahoo.com.br

Michel Arias Brentano: michel.brentano@bol.com.br

Eduardo Marczwski da Silva: eduardomarczwski@yahoo.com.br

Rafael Spinell: larrys@terra.com.br

Luiz Fernando Martins Kruel: kruel@esef.ufrgs.br