_{2}max estimation in healthy adults

^{1}Department of Sports Medicine, Kyunghee University, 17104 Yongin, Republic of Korea

^{2}Physical Acitvity and Performance Institute, Konkuk University, 05029 Seoul, Republic of Korea

^{3}Department of Sports Medicine and Science, Graduate School of Konkuk University, 05029 Seoul, Republic of Korea

^{4}Taekwondo Research Institute, Kukkiwon, 06130 Seoul, Republic of Korea

**Submitted: 24 March 2021 | Accepted: 23 April 2021 | Published: 17 January 2022**

**Background and objective**: The disadvantage of the traditional 20-m
multistage shuttle run test (MST) is that it requires a long space for
measurements and does not include various age groups to develop the test.
Therefore, we developed a new MST to improve the spatial limitation by reducing
the measurement to a 10-m distance and to resolve the bias via uniform
distributions of gender and age.
**Material and methods**: Study subjects included 120 healthy adults (60
males and 60 females) aged 20 to 50 years. All subjects performed a graded
maximal exercise test (GXT) and a 10-m MST at five-day intervals. We developed a
regression model using 70% of the subject’s data and performed a
cross-validation test using 30% of the data.
**Results**: The male
regression model’s coefficient of determination (R*SEE*) was 4.17 mL/kg/min. The female
regression model’s R*SEE* was 3.39 mL/kg/min.
The 10-m MST showed a high correlation with GXT on the VO*SEE* was 4.38 mL/kg/min, and the female’s *SEE*
was 4.56 mL/kg/min.
**Conclusion**: Thus, the 10-m MST is an accurate and valid method for
estimating the VO

_{2}max estimation

Cardiopulmonary endurance is the most important physical factor for human
health, daily life, occupational activity, leisure, and sports [1]. The
VO

We can measure the VO

Researchers have developed a variety of field tests to address the limitations
of the maximal exercise test and to measure multiple individuals simultaneously.
Brouha *et al*. [13] estimated the VO

Balke [14] and Cooper [15] estimated the VO*r* = 0.84) with the
maximal exercise load test.

The researchers were also interested in developing a method for the estimation
of VO*et al*.
[17] estimated the VO*et al*. [18] developed an equation for estimating the
VO*et al*. [19] estimated the VO*et al*. [20] estimated the Japanese’s VO*et al*. [21]
estimated the VO

Among the various methods used for VO*et al*. [25] reported that the 20-m MST was excellent for predicting
maximal exercise capacity in a study that compared a 6-min endurance running test
and a 20-m MST in Dutch children. Leger and Gadoury [24] also reported that the
20-m MST was a highly effective measure of endurance in healthy adults.
Therefore, in Korea, we use the 20-m MST for physical training and evaluation of
professional athletes, in the Physical Activity Promotion System (PAPS), and in
physical fitness testing for the selection of fire service personnel.

However, the traditional estimation formula developed by Leger and Lambert [16] has the following disadvantages. First, there is no gender distinction in estimating results [27]. Second, the subjects’ age in the estimation formula is concentrated in the twenties. Third, a relatively large distance of 25 m (straight line distance of 20 m, and a safety distance of 5 m) or more is required for indoor measurement. Therefore, studies to improve the shuttle run test have been tried as follows.

Matsuzaka *et al*. [22] developed a new VO*et al*. [28] developed a new VO*r* = 0.84) for children, athletic college students, and soccer
players using a modified 20-m MST (Anderson test). Mikawa and Senjyu [29]
reported that the results of the 15-m shuttle run test developed for 68
middle-aged men in their 40s and 50s showed a strong correlation with the
measured values (*r* = 0.86). These studies have partially addressed the
limitations of the shuttle run test, but efforts to overcome the spatial
limitations of bias such as gender and age and to target traits were relatively
inadequate.

Therefore, we hypothesized that “10-m MST will be able to predict VO

We hoped that the statistical power of the study results would be over 90%. So, we set the rho square (regression coefficient) to 0.7 [16], the statistical significance level to less than 0.05, and the number of predictors to be 5. As a result of the calculation using G*Power, the sample size was 18. However, to further increase the statistical power, we decided each male and females sample size to be 60 persons. Also, since the sample size is more than 30, citing the central limit theorem, we judged the sampling distribution is a normal distribution.

By the Institutional Review Board’s approval, we recruited applicants to participate in the experiment by attaching a poster for participation in the experiment in the residential area around the institute. The study subjects included a total of 120 males and females with equal sex ratios. Their ages ranged between 20 and 50 years. We selected Korean subjects who had no history of musculoskeletal, cardiovascular, or metabolic disease during the previous six months. We hoped that the level of physical activity of the participants would not be biased. So we took people with different levels of physical activity into the experiment. Also, we instructed the test participants to maintain their physical activity as usual during the end of the two tests. Subjects’ physical characteristics are as Table 1.

**Participant characteristics.**

Gender | Ages | N | Height (cm) | Weight (kg) | BMI (kg/m |
Body fat (%) |

Male | 20 | 15 | 173.9 |
69.5 |
23.0 |
16.4 |

30 | 15 | 174.9 |
78.5 |
25.6 |
22.4 | |

40 | 15 | 171.4 |
74.4 |
25.3 |
23.29 | |

50 | 15 | 170.5 |
69.3 |
23.8 |
21.80 | |

Female | 20 | 15 | 161.6 |
56.8 |
21.7 |
25.7 |

30 | 15 | 161.9 |
57.6 |
22.0 |
27.2 | |

40 | 15 | 160.7 |
58.6 |
22.7 |
28.5 | |

50 | 15 | 158.6 |
58.0 |
23.0 |
29.9 | |

BMI, Body Mass Index. |

We divided the subjects of both genders according to a 7 : 3 ratio using Bernoulli’s trials. We developed the regression model by using 70% of the subjects, and we used the remaining 30% of the subjects for cross-validation [30, 31]. The actual sample size distribution according to Bernoulli’s trials is shown in Table 2.

**Divided sample size according to Bernoulli’s trials.**

Gender | Total sample size | For develop | For validity test | Separating rate (%) |

Male | 60 | 42 | 18 | 7 : 3 |

Female | 60 | 42 | 18 | 7 : 3 |

We used questionnaires and blood pressure tests to select healthy persons among the 150 volunteers. We used the questionnaire for physical activity preparation (PAR-Q & YOU) and the AHA/ACSM Health/Fitness Facilities Screening questionnaires. Based on the results of the tests above, we included 120 subjects without any risk factors in this study. We randomly assigned the test order of the subjects using Microsoft Excel’s “RANDBETWEEN” function. Therefore, 120 subjects performed the treadmill GXT test and the 10-m MST test according to the order in which they were randomly assigned. We kept the interval between the two tests at least 5 days.

The subjects fasted for at least 10 hours before the test and were only lightly dressed during the test. We used a body composition analyzer (Karada Scan, Omron, Kyoto, Japan) to measure the body weight, body fat, and skeletal muscle [32]. Also, we measured the subject’s height, weight, waist circumference, and hip circumference and calculated BMI and waist-hip ratio (WHR) using these measured values.

We measured respiratory gas during rest and exercise using an automatic
breathing gas analyzer (K4B2, COSMED, Rome, Italy) for the treadmill test and the
10-m shuttle run test. We warmed up the gas analyzer for more than 30 minutes before
testing to improve the reliability of the measurements. We also adjusted the gas
analyzer to zero using a calibration gas (16% O

Like the shuttle run test, we did not apply the gradient in the treadmill test. Also, to observe the subjects’ physiological responses (heart rate, respiratory gas, etc.) during exercise in more detail, we created a protocol with a small increase in exercise load between the examination stages. This protocol’s initial starting speed was 3.6 km/h and increased by 1.2 km/h every 2 minutes. The slope was at 0% at all stages [31]. We measured respiratory gas and heart rate continuously during the maximal exercise testing. We stopped the exercise test when the oxygen uptake stopped increasing despite the increase in exercise intensity [34, 35] and when the respiratory exchange rate exceeded 1.15 [36].

We used nine sound sources as Do, Re, Mi, Fa, So, La, Ti, Do, and a buzzer sound in the 10-m MST. We reproduced the speed of the sound sources to be similar to the speed increase between the stages of the graded exercise test. Thus, we converted the speed of each stage of the graded exercise test to beats per minute (bpm) and adjusted the playback speed of sound accordingly. The subjects had a rest time of 5 min before the test. A researcher demonstrated the test method. We stopped the test when the subject either requested that we stop or when the subject was unable to follow the playback speed on more than one occasion. We also considered breath gas data in deciding when to stop such tests as the treadmill test. The detailed protocol of the 10-m MST is shown in Table 3.

**Table 3. Protocol of multistage 10-m shuttle run test (converting from speed to beats).**

Start time | Finish time | Speed (km/h) | Moving time per 10-m (s) | (Moving time per 10-m)/9 (s) | Beats per min | Number of shuttles |

0:00:00 | 0:01:00 | 3.6 | 10.00 | 1.11 | 54 | 6 |

0:01:00 | 0:02:00 | 4.8 | 7.50 | 0.83 | 72 | 8 |

0:02:00 | 0:03:00 | 6.0 | 6.00 | 0.67 | 90 | 10 |

0:03:00 | 0:04:00 | 6.0 | 6.00 | 0.67 | 90 | 10 |

0:04:00 | 0:05:00 | 7.2 | 5.00 | 0.56 | 108 | 12 |

0:05:00 | 0:06:00 | 7.2 | 5.00 | 0.56 | 108 | 12 |

0:06:00 | 0:07:00 | 8.4 | 4.29 | 0.48 | 126 | 14 |

0:07:00 | 0:08:00 | 8.4 | 4.29 | 0.48 | 126 | 14 |

0:08:00 | 0:09:00 | 9.6 | 3.75 | 0.42 | 144 | 16 |

0:09:00 | 0:10:00 | 9.6 | 3.75 | 0.42 | 144 | 16 |

0:10:00 | 0:11:00 | 10.8 | 3.33 | 0.37 | 162 | 18 |

0:11:00 | 0:12:00 | 10.8 | 3.33 | 0.37 | 162 | 18 |

0:12:00 | 0:13:00 | 12.0 | 3.00 | 0.33 | 180 | 20 |

0:13:00 | 0:14:00 | 12.0 | 3.00 | 0.33 | 180 | 20 |

0:14:00 | 0:15:00 | 13.2 | 2.73 | 0.30 | 198 | 22 |

0:15:00 | 0:16:00 | 13.2 | 2.73 | 0.30 | 198 | 22 |

0:16:00 | 0:17:00 | 14.4 | 2.50 | 0.28 | 216 | 24 |

0:17:00 | 0:18:00 | 14.4 | 2.50 | 0.28 | 216 | 24 |

0:18:00 | 0:19:00 | 15.6 | 2.31 | 0.26 | 234 | 26 |

0:19:00 | 0:20:00 | 15.6 | 2.31 | 0.26 | 234 | 26 |

0:20:00 | 0:21:00 | 16.8 | 2.14 | 0.24 | 252 | 28 |

0:21:00 | 0:22:00 | 16.8 | 2.14 | 0.24 | 252 | 28 |

The reason for dividing the 10-m moving time by nine is that we split the shuttle-run section into nine sections (Do, Re, Mi, Pa, Sol, La, Si, Do, turn). And we calculated the beats per minute using this section-time (the moving time per 10-m divide nine). |

For data analysis, we used the IBM SPSS 26.0 software for Windows and the Excel
2016 spreadsheet. We calculated the descriptive statistics for all measured data
and performed multiple regression analyses to develop an equation to estimate
VO

We used 70% of the data to develop regression models and 30% of the data for validity testing. We used Pearson’s correlation analysis to correlate the actual and the predicted values. Using the residuals of the predicted values, we calculated the standard error of the estimation, as shown in Eqn. 1 [31]. We set the statistical significance level to be less than 5% for all tests.

*SEE* is standard error of the estimate (mL/kg/min).
VO*n*’ is sample size.

The males’ 10-m MST reached the VO*p **r* = 0.816; HRmax: *r* = 0.954).

**Oxygen uptake and heart rates comparison of GXT and 10-m MST in
males.** GXT means gradually maximal exercise test and MST means multistage
shuttle-run test. The X-axis is exercise duration time by the minute, and the
Y-axis of (A) is oxygen consumption during exercise, and the Y-axis of (B) is
heart rate per minute during exercise.

The females’ 10-m MST reached the VO*p **r* = 0.821; HRmax: *r* =
0.823).

**Oxygen uptake and heart rates comparison of GXT and 10-m MST in
females.** GXT means gradually maximal exercise test and MST means multistage
shuttle-run test. The X-axis is exercise duration time by the minute, and the
Y-axis of (A) is oxygen consumption during exercise, and the Y-axis of (B) is
heart rate per minute during exercise.

We selected independent variables for multiple regression analysis to estimate
the VO

**Correlation of each independent variable vs. measured VO**${}_{\mathrm{2}}$ max by 10-m MST.

Independent variables | Gender | r | p-value |
n |

Shuttle count | Male | 0.738 | 42 | |

Female | 0.795 | 42 | ||

Final speed | Male | 0.614 | 42 | |

Female | 0.648 | 42 | ||

% Body fat | Male | −0.531 | 42 | |

Female | −0.585 | 42 | ||

% Skeletal muscle | Male | 0.383 | 0.012 | 42 |

Female | 0.518 | 42 | ||

BMI | Male | −0.352 | 0.022 | 42 |

Female | −0.393 | 0.010 | 42 | |

WHR | Male | −0.490 | 0.001 | 42 |

Female | −0.311 | 0.045 | 42 | |

Age | Male | −0.247 | 0.115 | 42 |

Female | −0.469 | 0.002 | 42 | |

Dependent variable: Measured VO |

We conducted an *F*-test to confirm the developed regression models’
statistical validity to predict VO

**Results of**

*F*-test for each regression model.Regression model | F-value |
p-value |

Males’ regression model | 13.212 | |

Females’ regression model | 16.140 |

*t*-test for regression coefficient of each independent variable

We performed a *t*-test to confirm the statistical significance of the
regression coefficients of each independent variable. The shuttle count was a
statistically significant independent variable in the case of males. Both the
shuttle count and the BMI were statistically significant independent variables in
the females (Table 6).

**Results of**

*t*-test for regression coefficients of each independent variable.Regression model | Variation | t-value |
p-value |

Regression model for males | Shuttle count | 3.803 | 0.001 |

Final speed | −1.218 | 0.231 | |

BMI | −0.216 | 0.830 | |

WHR | −1.500 | 0.142 | |

Regression model for females | Shuttle count | 4.117 | |

Final speed | −0.934 | 0.357 | |

BMI | −2.084 | 0.044 | |

WHR | 0.965 | 0.341 | |

Age | −0.488 | 0.629 | |

BMI, Body Mass Index; WHR, the waist to hip ratio. |

We calculated the coefficient of determination and the standard error of
estimate (*SEE*) to confirm the goodness-of-fit for regression models. As
a result, the regression model explained about 54% of the value of VO*SEE* values of the regression model for both
males and females were 4.17 mL/kg/min and 3.39 mL/kg/min (Table 7).

**Coefficient of determination (R**${}^{\mathrm{2}}$ ) and standard error of
estimate (

*SEE*) in each regression model.Regression model | R |
adj R |
SEE (mL/kg/min) |

Regression model for males | 0.588 | 0.544 | 4.17 |

Regression model for female | 0.692 | 0.649 | 3.39 |

Average | 0.640 | 0.597 | 3.78 |

We developed the regression equations for the estimation of VO

**The regression equation for prediction of VO**${}_{\mathrm{2}}$ max using
10-m MST.

Regression model | Regression equation |

Regression model for males | VO |

Regression model for females | VO |

BMI, Body Mass Index; WHR, the waist to hip ratio. |

We used the 30% of the total data that had not been included in developing the
regression models (males: 42, females: 42). We calculated the *SEE* using
Equation 1. As a result, the *SEE*s of regression models for males and
females were 4.38 mL/kg/min and 4.56 mL/kg/min. These values were like the
*SEE* of the developed regression models (Table 9).

**Results of the validity test.**

Regression model | SEE (mL/kg/min) |

Regression model for males | 4.38 |

Regression model for females | 4.56 |

In this study, we performed GXT and 10-m MST in 120 healthy volunteers, between
20 and 50 years of age. The VO*r* = 0.84) [16] and the revised 20-m MST versions, for example, the
Anderson test (*r* = 0.84). This study can be used at various ages (20–50
years) and genders. It can be utilized to overcome the disadvantages of previous
studies [16, 23, 26, 28, 37]. Also, the VO

In the present study, we used 70% of the data pertaining to 120 adult males and
females based on Bernoulli’s trials. We performed multiple regression analyses by
selecting variables that were highly correlated without autocorrelation. Several
studies validated and developed the formula for the evaluation of adults using
the 20-m MST [16]. Leger *et al*. [23] studied 77 adults subjected to
tests with a speed increase of 0.5 km/h/min (start speed of 8.5 km/h). As a
result, we estimated the VO*r*
= 0.90) with the actual VO

In addition, Ramsbottom *et al*. [26] reported that the 20-m MST [23]
strongly correlated with the maximal exercise test (*r* = 0.92) and the
5-km running record (*r* = 0.94) in 74 male adults (19–36 years). In
addition, several researchers have developed a VO

The validation of the estimating equation developed in this study of 120 adult
males and females utilized 30% the data divided by Bernoulli’s trials. As a
result of the validity test, the estimated standard error (*SEE*,
mL/kg/min) ratio was within 2% (male 4.38, female 4.56). Based on these results,
we confirmed that the regression model was highly valid. Thus, we have developed
a new 10-m MST as an alternative to the existing 20-m MST by overcoming its
limitations (gender classification, application across various ages, and short
measurement distance).

Lastly, our made 10-m MST has the advantage of being able to estimate
VO

Additionally, when considering this study’s results, there was no evidence that the 10-m MST made by reducing the measurement distance overestimated the maximum exercise capacity. However, even to address these concerns, we hope that this test method will be modified-developed as it is widely used.

In this study, we developed a 10-m MST for VO

Towards this end, we collected 120 data measurements and divided them according
to a 7 : 3 ratio based on Bernoulli’s trials. We used the data for 70% of males
and females for VO*SEE* of 4.47 mL/kg/min also confirmed the high validity of the
regression model. However, since the study included general population subjects,
additional studies are needed before the results can be applied to athletes and
other individuals.

In summary, the 10-m MST developed by us can be used when the existing 20-m MST cannot be used due to spatial limitations and can be applied to both men and women in their 20s and 50s.

SSN conceived and designed this study; SSN, HYP, and HLC performed the experiment and measurement; SSN conducted the data analysis; HLC and HYP wrote the original draft preparation; SSN discussed of result and concluded. All authors have read and agreed to the published version of the manuscript.

This study was conducted according to the Helsinki Declaration’s guidelines and approved by the local ethics committee of Kyunghee University (KHU IRB 2014-G01). Also, informed consent was obtained from all subjects involved in the study.

Thanks to all the peer reviewers for their opinions and suggestions.

The Samsung Advanced Institute of Technology funded this research.

The authors declare no conflict of interest.

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