### Abstract

VO_{2}max is an invaluable measure for the assessment of aerobic fitness; however, to yield accurate results direct assessment requires costly equipment, trained investigators, and that the participant produce a maximal effort to volitional fatigue. The majority of VO_{2}max prediction equations have attempted to predict aerobic capacity without considering physiological variables other than age and body composition. As a result, a majority of VO_{2}max prediction equations have been found to be invalid. A recent study proposed an equation accounting for additional physiological variables known to influence aerobic capacity, including blood volume, fat-free mass, urinary creatine excretion, and total body potassium. Therefore, this investigation sought to evaluate the validity of novel non-exercise prediction equations, which utilize bioelectrical impedance analysis (BIA) to obtain an estimate of blood volume and skeletal muscle mass as predictor variables in an attempt to increase the accuracy of non-exercise VO_{2}max prediction equations. VO_{2}max was assessed using indirect calorimetry. Healthy male (30.9 ± 6.0 y, 179.0 ± 4.3 cm, 94.1 ± 19.5 kg; n = 23) and female (32.0 ± 6.1 y, 167.8 ± 7.9 cm, 72.0 ± 9.6 kg; n = 25) participants completed a VO_{2}max test and a physical activity survey (PA-R) and were analyzed using bioelectrical impedance. Results indicated that each equation resulted in a significant (p ≤ 0.025) underestimation of VO_{2}max. These outcomes suggest that the use of BIA to estimate blood volume and skeletal muscle mass does not improve the accuracy of VO_{2}max prediction equations. Coaches and trainers will not benefit from the inclusion of BIA in an equation to predict aerobic fitness. Currently, the best methods to estimate aerobic fitness require submaximal and maximal exercise testing. Predicting aerobic fitness using non-exercise equations does not appear to be practical or valid.

**Keywords:** maximal, aerobic capacity, prediction, gender-specific

### Introduction

The rate of maximal oxygen consumption (VO_{2}max) has practicality in research and field settings as a measure of aerobic fitness, in order to prescribe exercise intensities and to assess exercise training responses following an intervention (19). An acceptable standard for VO_{2}max determination is the direct measure of expired gas samples obtained while an individual is performing maximal exertion exercise (2). From a research perspective reliable non-exercise VO_{2}max prediction equations could prove to be beneficial, as experimenters could obtain an immediate, valid measure of the aerobic fitness of an individual without maximal exercise testing. Additional advantages of non-exercise VO_{2}max prediction equations include the ease and cost associated with test administration and use in participants who are unable to perform a treadmill test, as VO_{2}max tends to be underestimated with other modes of exercise (19). However, the greatest advantage of an accurate VO_{2}max prediction equation is the practicality of use in research laboratories that do not possess the necessary equipment to access VO_{2}max and for coaches and trainers looking to evaluate several athletes and/or an entire team. Due to the disadvantages associated with VO_{2}max testing numerous submaximal (1,8,18,23) and non-exercise prediction equations (4,5,10,17,21,24,25) have been developed to reduce the necessity of direct VO_{2}max assessment.

Previous non-exercise prediction equations have been developed but the need to improve the accuracy of these equations has been suggested in previous literature (4,16,17,21). However, due to known deviations in VO_{2}max values determined from varying modes of exercise (bike, treadmill walking, treadmill running, and arm ergometry), the use of VO_{2}max prediction equations are dependent on the task. For example, a prediction equation for VO_{2}max during a treadmill run may not be accurate for predicting VO_{2}max during cycle ergometry. In addition, another primary shortcoming of non-exercise VO_{2}max prediction equations is the limited ability to account for genetic variability in VO_{2}max (21). According to Stahn et al. (21), the primary physiological determinants measured at rest to predict VO_{2}max are blood volume, which has been found to account for up to 80% of the variance in VO_{2}max, and a group of variables including fat-free mass, urinary creatine excretion, and total body potassium, which have been proposed to be related to skeletal muscle mass. Additional evidence supporting this claim was provided by Sananda et al. (20) who found total skeletal muscle mass to be highly correlated (r = 0.92, p < 0.001) with VO_{2}max (20).

Stahn et al. (21) sought to obtain an estimate of blood volume and skeletal muscle mass using bioelectrical impedance analysis (BIA). Previous work has suggested BIA to have a strong correlation with blood volume (r = 0.89, SEE = 9.0%) using the impedance index of height squared divided by impedance (22) and skeletal muscle mass, as compared to magnetic resonance imaging (r = 0.927, SEE = 9.0%) (11). As a result Stahn et al. (21) developed a non-exercise VO_{2}max prediction equation, which utilizes BIA to estimate resting levels of blood volume and skeletal muscle mass as predictor variables. However, the equation by Stahn et al. (21) has yet to be validated by an independent laboratory, and the benefits of utilizing BIA for predicting VO_{2}max have not been established. Therefore, the purpose of this study was to validate treadmill VO_{2}max predictions using the recently published BIA equation of Stahn et al. (21). It was hypothesized that the BIA equations would produce accurate VO_{2}max predictions due to the relationship between VO_{2}max, BIA, skeletal muscle mass, and blood volume.

### Methods

#### Subjects

Sixty participants chose to participate in this study, but 12 were eliminated for not reaching VO_{2}max (n = 48; Table 1). All testing was conducted after the participant signed the IRB-approved informed consent and completed comprehensive medical history questionnaires. Participants were excluded if they: 1) had a history of metabolic, hepatorenal, musculoskeletal, autoimmune, or neurological disease; 2) were currently taking androgenic medications; or 3) had consumed nutritional supplements that may affect metabolism [i.e., over 100 mg•d-1 of caffeine, ephedrine alkaloids, etc.] and/or muscle mass [i.e. creatine, protein/amino acids, androstenedione, dihydroepiandrosterone (DHEA), etc.] within three months of starting the study; 4) were unable to reach at least two of the three stated criteria for reaching VO_{2}max.

Table 1. Participant characteristics of validated equations

Stahn et al. (21) | Current Validation Participants | |||||
---|---|---|---|---|---|---|

N | Males | Females | N | Males | Females | |

N | 66 | 33 | 33 | 48 | 23 | 25 |

Age (yr) | 24.0 (4.0) | 25.0 (4.0) | 23.0 (4.0) | 31.5 (6.0) | 30.9 (6.1) | 32.1 (6.1) |

Height (cm) | 174 (6) | 180 (5) | 168 (6) | 173 (9) | 179.0 (4) | 169 (8) |

Weight (kg) | 68.4 (7.6) | 74.9 (8.3) | 61.8 (6.8) | 82.6 (18.7) | 94.1 (19.5) | 72.0 (9.6) |

PA-R | 6.6 (1.1) | 6.6 (0.9) | 6.3 (1.3) | 2.9 (1.9) | 3.4 (2.3) | 2.4 (1.5) |

VO_{2}max (ml*kg*min^{-1}) |
53.6 (5.0) | 59.6 (5.5) | 47.6 (4.4) | 43.9 (13.4) | 42.4 (14.4) | 45.2 (12.6) |

#### Non-Exercise VO_{2}max Prediction Equations

The equations selected for validation were developed by Stahn et al. (21) and are presented in Table 2.

Table 2. Submaximal VO_{2}max prediction equations

2MF | Stahn et al. (21) | VO_{2}max (DF50) = 14.29 · H^{2}/Z + 104.14 · PA-R – 440.79 • Gender (M = 1, F = 0) + 489.47 |

2M | Stahn et al. (21) | VO_{2}max (DF50) = 14.29 • Height/Z + 104.14 • PA-R– 440.79 • Gender (M = 1) + 489.47 |

2F | Stahn et al. (21) | VO_{2}max (DF50) = 14.29 • Height2/Z + 104.14 • PA-R – 440.79 • Gender (F = 0) + 489.47 |

∗ All values from prediction equations were converted to ml•kg•min-1

H = Height (cm)

Z = Impedance (Ohm)

PA-R = Physical activity rating scale

M = Male

F = Female

#### Experimental Design

Testing was performed between 9:00 a.m. and 3:00 p.m. in a temperature-controlled laboratory maintained at 21.6 ± 0.7oC and 28.2 ± 5.5% relative humidity. Prior to testing, each subject was instructed to avoid the consumption of alcohol, refrain from heavy exertion for 48 hours, and avoid smoking and caffeine consumption the day of testing. Subjects were also instructed to consume 2 liters of water the day before testing in an effort to promote normohydration.

#### Anthropometry and Physical Activity Assessment

After voiding their bladders, subjects changed into minimal clothing and removed footwear for measurement of body mass and height, conducted on a calibrated scale and stadiometer (Detecto, Webb City, MO). Body mass was measured to the nearest 0.2 kg and height was assessed to the nearest 0.5 cm. The PA-R was used to assess the average weekly physical activity patterns of each participant in the 6 months prior to testing (7).

### Bioelectric Impedance Measurement

Whole-body impedance measurements were performed using a single frequency (50 kHz) bioelectrical impedance analyzer (IMPTM DF50, ImpediMed Inc, Queensland, Australia). Each morning prior to testing, the bioelectrical impedance device was calibrated following the manufacturer’s guidelines. Measurements were taken from the right side of the body using a tetrapolar electrode arrangement following the standard procedures used by Stahn et al. (21). Prior to testing each subject was asked remove jewelry and excess clothing before being instructed to lie in a supine position for 10 minutes with arms and legs abducted from the body at 10˚ and 20˚ respectively, allowing body fluids to stabilize. Following identification of electrode placement, body hair was removed with a razor before the skin was cleaned with alcohol and allowed to dry. Current-inducing electrodes (575 mm2: 25 mm x 23 mm) (ImpediMed Electrodes, Queensland, Australia) were placed 1 cm below the phalangeal-metacarpal joint in the middle posterior surface of the hand and 1 cm below the transverse (metatarsal) arch on the dorsum of the foot. Detector electrodes of the same type were placed on the lateral epicondyle of the humerus and the lateral condyle of the femur according to the guidelines of Stahn et al. (21). Interclass and intraclass correlation coefficients for within and between days using this technology vary between 0.960 and 0.997 (6,21), while interindividual within-day reliability measures are commonly 1.3-2.0% (13,15,21).

#### VO_{2}max Assessment

VO_{2}max testing was performed on a calibrated Quinton treadmill (Q65 Series 90, Bothell, WA) according to Stahn et al. (21). Participants began the test with a 4-minute warm-up at 1.5 m·s-1 at a 1% gradient. Following warm-up, 3-minute testing periods began at speeds of 2.0 m·s-1 for women and 2.5 m·s-1 for men. Completion of each stage resulted in a speed increase of 0.5 m·s -1 until volitional fatigue despite verbal encouragement.

Maximal heart rate, respiratory exchange ratio (RER), and VO_{2}max were measured with a calibrated metabolic cart (ParvoMedics TrueOne® 2400 metabolic measuring system, Sandy, UT). The system was calibrated 15 minutes prior to testing according to manufacturer specifications. Mean oxygen uptake (VO2), carbon dioxide output (VCO2), and pulmonary ventilation (VE) were computed for each breath and averaged over 15-second intervals. Heart rate was monitored during testing using a heart rate monitor (Polar F6, Lake Success, NY). The test was considered maximal if two of the following criteria were obtained: 1) a plateau of VO2 occurred, defined as an increase of less than 150 ml·min-1 despite increasing speed, 2) Respiratory exchange ratio (RER) was ≥ 1.15, and 3) maximal heart rate was within 10 beats of age-predicted maximal heart rate (21).

#### Data analysis

Validity of VO_{2}max estimates were based on an evaluation of predicted values versus the criterion value from direct treadmill VO_{2}max assessment by calculating the constant error (CE = actual VO_{2}max – predicted VO_{2}max), r value (Pearson product moment correlation coefficient), standard error of estimate and total error (9,14). The mean difference (CE) between the VO_{2}max prediction equations and the direct measure of VO_{2}max was analyzed using dependent t-tests with the Bonferroni alpha adjustment (12). The method of Bland and Altman (3) was used to identify the 95% limits of agreement between actual VO_{2}max values and predicted VO_{2}max values.

### Results

Demographic information of participants in the Stahn et al. (21) study and the current investigation are presented in Table 1. To optimize the accuracy of the prediction equations, results of the validation analysis are presented in two groups: male- and female-specific equations (Table 3). Each sex-specific equation produced a significantly different VO_{2}max value from the direct measure (p<0.05). TE values were greater than 13.2 ml•kg•min-1, SEE values were greater than 9.1 ml•kg•min-1 and r values were less than 0.75.

Table 3. Validity of non-exercise prediction equations for estimating VO_{2}max ml•kg•min-1

Method | VO_{2}max ± (x SD) |
CE | r | Slope | Y-intercept | SEE | TE |
---|---|---|---|---|---|---|---|

Direct VO_{2}M |
42.4 (14.4) | ||||||

Male | 33.3 (8.3) | 9.1* | 0.74 | 1.2 | -0.5 | 9.9 | 13.3 |

Direct VO_{2}F |
45.2 (12.6) | ||||||

Female | 34.0 (6.5) | 11.2* | 0.70 | 1.3 | -0.78 | 9.2 | 14.5 |

### Discussion

The sex-specific equations analyzed in this investigation produced predicted VO_{2}max values that were significantly below the actual VO_{2}max (p<0.05). Using the predicted VO_{2}max values to produce exercise prescriptions would yield exercise intensities underestimated by an equivalent amount.

The aim of the Stahn et al. (21) study was to demonstrate the viability of using BIA for the non-exercise prediction of VO_{2}max. The authors attempted to account for the influence of physiological variables on aerobic performance by indirectly accounting for blood volume, fat-free mass, urinary creatine excretion and total body potassium with a time efficient assessment of blood volume and skeletal muscle mass using a BIA device. Results from the Stahn et al. (21) study appeared promising as their equation was reported to account for 88.7% of the variance in VO_{2}max in an athletic population, and the authors postulated the equation would be more effective in a more diverse population. However, in the current investigation the equations developed by Stahn et al. (21) were found to be invalid in a population of healthy men and women. Errors in the equations were most likely introduced by using predicted values of blood volume and skeletal muscle mass (via BIA). In essence, predicted variables were used to predict another predictor, VO_{2}max. The validity of the equations developed by Stahn et al. (21) may be improved by using a more accepted and still cost-effective measure of skeletal muscle mass, such as a multiple-site skinfold, as was used in VO_{2}max prediction equations developed by Jackson et al. (10).

### Conclusions

The equation developed by Stahn et al. (21) may have been effective at predicting VO_{2}max in the athletic population used in the original investigation but appears to significantly underestimate VO_{2}max in a representative sample of healthy young men and women. Future prediction equations should include percent body fat and physical activity rating scales, as these variables appear to have the greatest predictive power in the estimation of non-exercise VO_{2}max prediction equations. Although the prediction equations developed by Stahn et al. (21) were not found to be valid in this investigation, non-exercise VO_{2}max prediction equations should attempt to increase their predictive power by accounting for physiological factors that are known to influence VO_{2}max, namely skeletal muscle mass. Furthermore, future research should examine the accuracy of the equations developed by Stahn et al. (21) in an athletic population and determine the viability of using a BIA device in the prediction of VO_{2}max.

### Applications in Sport

An athlete’s aerobic fitness is a crucial component of performance regardless of the sporting event. Aerobic athletes and coaches/trainers can benefit from accurate measurements of aerobic fitness through VO_{2}max testing. However, direct VO_{2}max testing requires expensive equipment and is not practical in the field. Many prediction equations have been developed in an attempt to find an easy way to predict VO_{2}max in the field. However, results from this investigation suggest that using BIA in a non-exercise VO_{2}max equation may not be appropriate or valid in healthy men and women. Specifically, the Stahn et al. (21) BIA VO_{2}max equations underpredicted VO_{2}max, resulting in significantly lower VO_{2}max values, giving the impression of an individual who is less aerobically fit. Therefore, it is suggested that coaches and trainers utilize either submaximal or maximal VO_{2}max prediction equations for their athletes and clients, as non-exercise prediction equations may not provide valid information.

### Acknowledgements

The authors would like to thank all the participants for their willingness to participate in this investigation.

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### Corresponding Author

Jordan R. Moon, PhD

Department Head

Department of Sports Fitness and Health

United States Sports Academy

One Academy Drive

Daphne, AL 36526

### Author Affiliations

Jordan R. Moon, PhD

Department of Sports Fitness and Health

United States Sports Academy

One Academy Drive

Daphne, AL 36526

Chad M. Kerksick, PhD and Jeffrey R. Stout, PhD

Department of Health and Exercise Science

University of Oklahoma

1401 Asp Ave.

Norman, OK 73019

Vincent J. Dalbo, PhD

School of Medical and Applied Sciences

Institute of Health and Social Science Research

Central Queensland University

Rockhampton, Australia

Michael D. Roberts, PhD

University of Missouri-Columbia

Department of Biomedical Science

Veterinary Medicine Building

Columbia, MO 65211