Finally, we selected the model introduced by Whyte et al. 25 for HRmax estimation (δ̅ = 5.73%):
The maximal oxygen uptake (VO2max) estimation has been a subject of research for many years. Cardiorespiratory measurements during incremental tests until exhaustion are considered the golden yard stick to assess VO2max. However, precise VO2max determination based on submaximal tests is attractive for athlete as well for clinical populations. Here, we propose and verify such a method based on experimental data. Using a recently developed model of heart rate (HR) and VO2 kinetics in graded exercise tests, we applied a protocol, which is terminated at 80% of the estimated maximal HR during ergometer cycling. In our approach, initially, formula for maximal HR is selected by retrospective study of a reference population (17 males, 23.5 ± 2.0 years, BMI: 23.9 ± 3.2 kg/m 2 ). Next, the subjects for experimental group were invited (nine subjects of both sexes: 25.1 ± 2.1 years, BMI 23.2 ± 2.2 kg/m 2 ). After calculation of maximal HR using cardiorespiratory recordings from the submaximal test, VO2max is predicted. Finally, we compared the prediction with the values from the maximal exercise test. The differences were quantified by relative errors, which vary from 1.2% up to 13.4%. Some future improvements for the procedure of VO2max prediction are discussed. The experimental protocol may be useful for application in rehabilitation assessment and in certain training monitoring settings, since physical exertion is not a prerequisite and the approach provides an acceptable VO2max estimation accuracy.
Maximal oxygen uptake (VO2max) is one of the parameters used to to assess the performance potential of endurance athletes 1,2,3 . VO2max is determined during incremental cardiopulmonary exercise testing (CPET) simultaneously with ventilatory thresholds allowing for the estimation of fixed and physiological training zones, respectively 4 . Additionally, VO2max determination is recommended during the training cycle to monitor the quality and to quantity the training progress 5 or before the return to regular training regimens after a break 6 . Submaximal testing is sufficient for assessing functional limitations (equivalent to impairment observed in daily activities), verifying the outcome of interventions and evaluating the effects of pharmacological treatment in some patients 7 . However, VO2max remains the “gold standard” to assess functional capacity and cardiorespiratory responses to cardiovascular rehabilitation programs 8 . Direct VO2max determination requires laboratory conditions, appropriate equipment, sensor calibration and adherence to the guidelines for performing cardiorespiratory exercise testing 9 . Beyond the costs, laboratory CPET raises many organizational problems due to the standardization of experimental protocols and the need for an experienced and well trained staff. Further, in case of athletes, tests until exhaustion may interfere with their actual training plans, ambitions and may raise motivational issues during intense training periods. Since VO2max assessment requires high motivation and tolerance to exhaustive exercise, the probability of invalid tests and the risk of adverse events, especially in patient population, is increased.
Therefore, valid VO2max determination based on submaximal test can be a valuable alternative in clinical and sport applications. Lots of indirect methods have been developed, also taking into account the specificity of the sports discipline 3, 10 or certain populations 2 . These indirect methods can be divided into two groups, i.e. those that require maximal effort (without monitoring VO2 kinetics) and those that rely on submaximal trials or resting parameters.
VO2max, or maximal oxygen consumption, represents the highest rate at which an individual's body can consume oxygen during intense exercise. To determine true VO2max, the traditional criterion has been introduced - the observation of a plateau in oxygen consumption despite an increase in exercise intensity. This plateau indicates that the individual has reached his physiological limit or maximal aerobic capacity. However, it's important to note that achieving this plateau can be subjective and challenging to define precisely. In clinical settings, when assessing patients with cardiovascular or pulmonary disease, it is often difficult to observe a clear plateau in oxygen consumption due to physiological limitations. Therefore, the term “VO2peak” is commonly used instead 11 . VO2peak represents the highest VO2 value achieved during an exercise test, even if a clear plateau is not observed. This term allows clinicians to express the patient's exercise capacity in a more practical and measurable way. On the other hand, in apparently healthy individuals without underlying cardiovascular or pulmonary conditions, it is more likely to observe a true VO2max response during exercise testing. Thus, the term “VO2max” is often used to describe their maximal physiological response 12 .
Incremental tests performed until the subject terminates the effort due to perceived exhaustion are the most common for the VO2max determination. Since both, a lack of experience in the experimental protocol and low motivation can distort its proper calculation: additional criteria were introduced for accuracy improvement and standardization of VO2max determination. Attaining of VO2 plateau was one of the main factors, but it met a lot of criticism 13, 14 . Further, the support by other markers was proposed and widely discussed as secondary criteria: respiratory exchange ratio, percentage age-adjusted estimates of HR, values of lactate concentration (usually > 7.9 mM 13 ) and ratings of perceived exertion.
For the indirect exercise based methods, maximal power, covered distance, time to exhaustion or similar parameters are used to predict VO2max 15, 16 .
Similarly to the lab-based assessments, specific testing protocols and termination criteria are defined for indirect methods 2, 17 . Many aspects characterize the advantages of the field tests, but there are also limitations: poor control of the experimental conditions (which cause difficulties in repeatability of the test), bias due to the subjective assessments of physical activity or fitness in questionnaires 18 , sport specific approaches that may not only reflect the cardiorespiratory capacity but also technical factors, motivation or experience. Considering such limitations, one should expect an imperfection of indirect techniques, which is confirmed by validation procedures in relation to the measured VO2max 19, 20 . However, the usefulness of such field tests is wide: usually, many subjects can perform the experiment simultaneously, the cost of equipment is low and there is no need to use sophisticated calculation techniques. Further, many tests appear to be valid and safe for assessing group-level mean changes in VO2max. In result, the number of the indirect methods of VO2max estimation remains high in wide ranges of applications.
In general, the indirect methods do not consider the kinetics of physiological responses to progressive exercise in estimating VO2max, but focus on the parameters obtained at exercise cessation and/or on markers characterizing the subject (body mass, age, sex, etc.), only. These parameters are then used to feed regression models, that are constructed from population studies 15 . An optimal approach should guarantee not only the accurate estimation of VO2max but also a protocol that does not require complete exhaustion of the subject, i. e. submaximal testing. Such models are still rare because they require both monitoring of certain variables and dedicated computational tools 21 . However, they are attractive due to the elements of individualization, precision and submaximal effort 7 . Submaximal exercise testing often relies on the linear relationships between oxygen uptake and HR. Due to deflection at higher intensities such linearity may be not observed causing large error (about 15%) between extrapolated and true VO2max values 22 . Focusing on the submaximal tests requiring the cycle ergometer two are well known in the literature (and recommended for athletes): the Åstrand-Ryhming (A-R) 23 and the YMCA protocol 2, 24 . Both tests are based on HR and thus has limited application to patients (especially these with pharmacological treatment affecting the HR) 22 . A-R is a 6 min test on a cycle ergometer with VO2max depending on both workload and HR. The modification contains an age correction factor. The second protocol is constructed from extrapolation of HR responses relative to power output increases. VO2max depends on age predicted maximal HR, from which maximal power output is found. Our proposal for VO2max prediction goes beyond these limitations. Here, the kinetics of VO2 and HR as a response to incremental workload are considered and modeled without the assumption of a linear relation between both variables. The maximal HR was also validated on the reference group resulting in the application of Whyte’s formula. Final extrapolation for VO2 is performed and the time series are obtained (not only final values, which is typical in other submaximal models). VO2max is found at the time point equivalent to the moment of attaining maximal HR in the model. This approach can be used for other populations with respect to successive steps described in the “Results” section. In the method not only the final values are determined, but the time evolution of both markers is presented in extrapolation.
Subjects: Data from incremental cycling tests recorded at the Institute of Sport Science of the University of Rostock (Germany) was selected for a retrospective study. In the analysis, time series from 17 healthy and young males (23.5 ± 2.0 years, BMI: 23.9 ± 3.2 kg/m 2 ) were used. Participants considered for the study were classified as physically active (> 180 min of moderate to vigorous physical activity per week). All subjects were free of medication and resigned from intensive exercise and alcohol consumption for > 48 h prior to the test. Caffeine and nicotine were not allowed during the night and on the morning of the experiment. The volunteers performed an incremental cycling test on an SRP 3000 bicycle ergometer (Sportplus, Germany) until volitional exhaustion (VO2max test). Respiratory gas and volume analysis were carried out breath-by-beath using the MetaMax 3B system (Cortex Biophysics Inc., Germany). HR was monitored by the RS800 heart rate monitor (Polar Inc., Finland). The VO2max test included an adaptation (without cycling) lasting no more than 6 min, then 3 min warm-up at 50 W, incremental phase with step 25 W/min and at least 3 min cool-down at 50 W after effort termination. The study adhered to the ethical standards for research involving human subjects set in the declaration of Helsinki and was approved by the local ethics committee at the University of Rostock (A 2017-0034). All particpants gave their written informed consent.
Ten subjects of both sexes (5/5) were recruited among physical education students of the University of Rostock. One female participant had to be excluded due to medications before the beginning of the study. Thus, time series from 9 subjects (five males: 24.6 ± 1.3 years, BMI 23.0 ± 1.1 kg/m 2 and four females: 25.7 ± 3.1 years, BMI 23.4 ± 3.2 kg/m 2 ) were included in the final validation analysis. The volunteers performed two incremental cycling tests on an SRM Ergometer (Schoberer Messtechnik GmbH, Germany) in the validation protocol: until volitional exhaustion (VO2max test) and until reaching 80% of their estimated HRmax, respectively, in a randomized order. Respiratory gas and volume analysis were carried out breath-by-beath using the MetaMax 3B system. HR was monitored by the RS800 heart rate monitor. The maximal protocol included 3 min of familarization, at least 5 min warm-up and a 5 min cool-down cycling phase, both at 50 W. The increments during the ramp phase were 25 W/min. Participants were verbally encouraged during the test until exhausion. The submaximal protocol was terminated during the ramp phase and afterwards 5 min recovery at 50 W workload started. The termination point (80% of estimated HRmax) was estimated from retrospective analysis (details are given in Sect. “A method for determination of the termination point in a step incremental tests”).
The proposed method of VO2max determination relies on the HRmax estimation. For comparison purposes, the estimation of the VO2max was also required. Note, that in both markers, only equations which consider resting parameters were taken into consideration. For clarification, the concepts used in the text: estimation is dedicated to determination of maximal parameters from equations using resting markers, while prediction is obtained from differential models.
We verified the agreement of the retrospective data with the results estimated from linear equations with resting parameters. For the analysis, five methods for HRmax estimation were selected 25,26,27,28,29 and three for VO2max 30,31,32 . The quality of agreement between estimated and experimental values was assessed by the mean δ̅ calculated from all relative errors δ (Eq. 1):
$$\delta = \frac <<\left|Finally, we selected the model introduced by Whyte et al. 25 for HRmax estimation (δ̅ = 5.73%):