The oxygen uptake (VO₂) is considered an important metric in assessing cardiorespiratory fitness, health status, or endurance performance potential (Guazzi et al., 2012). With the application of standardised procedures and interpretation protocols, during graded exercise tests (GXT), the (maximal oxygen uptake) VO_2max can be established (Bentley et al., 2007). GXT is the most widely used assessment to examine the dynamic relationship between exercise and integrated physiological systems (Albouaini et al., 2007; Bentley et al., 2007). The information from GXT during cardiopulmonary exercise testing (CPET) can be applied across the spectrum of sport performance, occupational safety screening, research, and clinical diagnostics (Guazzi et al., 2017).

VO_{2 max} is often used as a boundary between severe and extreme intensity domains and by definition requires maximal effort from the tested subject (Gaesser and Poole, 1996). However, it is not always recommended or possible to undertake a test to exhaustion (Guazzi et al., 2012). For the athletes, the proximity of competition or injury history can allow submaximal testing, but not testing to exhaustion (Sassi et al., 2006). Testing that requires maximal effort may be disruptive to the training process or interfere with race performance (Coutts et al., 2007; Lamberts et al., 2011). Due to practical constraints, tests to exhaustion or peak-power-output tests are often performed only two or three times a year (Coutts et al., 2007).

However, VO₂ values are widely used in sport science and the decision-making process (Mann et al., 2013). VO₂ is widely considered one of the major endurance performance determinants (Joyner and Coyle, 2008). Using VO_2max to guide the selection process, prescribing training intensity, assessing training adaptations, or predicting race times is a common practice in high-performance sports (Bassett and Howley, 2000; Bentley et al., 2007; Hawley and Noakes, 1992; Noakes et al., 1990).

VO_2max is also one of the critical vital signs coordinating the function of the cardiovascular, respiratory, and muscular systems, it is an indicator of overall body health status (Kaminsky et al., 2017). Quantifying VO_2max provides additional input regarding clinical decision-making, risk stratification, evaluation of therapy, and physical activity guidelines (Guazzi et al., 2012). For patients undertaking a test to exhaustion is rarely needed or possible due to health restraints or cardiac risk (Guazzi et al., 2016).

For many years researchers have studied indirect methods of estimating VO_2max(Sartor et al., 2013). Protocols such as the Astrand-Ryhming Test, Six-Minute Walk Test, or YMCA Step Test have been established and validated (Astrand and Ryhming, 1954; Beutner et al., 2015; Carey, 2022; Jalili et al., 2018). Moreover, estimation of the VO₂ and heart rate (HR) values below the ventilatory threshold can be based on cardiorespiratory kinetics assessment using randomised changes in the work rate known as a pseudo-random binary sequences testing (Hoffmann et al., 2022). However, with the development of technology, the accessibility of laboratory testing and mobile testing improved (Montoye et al., 2020; Pritchard et al., 2021). Therefore, new opportunities to develop more precise yet simple and accessible methods and models to assess VO_2max occur (Jurov et al., 2023). This appears to be especially important considering the low prediction accuracy of most of the VO_2max formulae that were validated in our previous study (Wiecha et al., 2023).

Recently, we have been observing the development of prediction methods with the usage of machine learning (ML) and artificial intelligence (AI) (Ashfaq et al., 2022). Both ML and AI are used in sport science as forecasting and decision-making support tools (Abut and Akay, 2015; Bobowik and Wiszomirska, 2022; Chmait and Westerbeek, 2021; Hammes et al., 2022; Rossi et al., 2021). There is growing evidence that VO_2max prediction based on ML models, especially support vector ML and artificial neural network models, exhibits more robust and accurate results compared to MLR only (Abut and Akay, 2015; Ashfaq et al., 2022).

Therefore, in this research, with the support of ML, we look for algorithms and prediction patterns that allow us to use values obtained during submaximal CPET and somatic measurements to estimate maximal VO_2max values in male runners and cyclists. We stipulate that prediction models allow for accurate calculation of VO_2max based on somatic or submaximal CPET variables.

We have applied the development and validation of the prediction TRIPOD guidelines to conduct the study (see Supplementary Material 1TRIPOD Checklist for Prediction Model Development and Validation) (Collins et al., 2015). The study is based on retrospective data analysis from the CPET registry collected from 2013 to 2021 at the medical clinic (Sportslab, Warsaw, Poland). All CPET have been performed at the individual request of participants, as a part of regular training monitoring or performance assessment.

Derivation cohort

Request a detailed protocol

We selected the cohort with the use of rigorous exclusion/inclusion criteria. Due to the insufficient number of women in our database and the number of potential variables in the regression models for adequate power, we had to limit ourselves to conduct analysis in the male population only (Martens and Logan, 2021). Out of 6439 healthy, adult male cyclists and long-distance runners that undergone CPET, 4423 met the criteria as further: (1) age ≥18 years, (2) declared regular cycling or running training for ≥3 months, (3) had no extreme outliers ≤ or ≥±3 standard deviations (SD) from mean for all of the testing variables (beyond ≥±3 SD in VO_2max), (4) lack of any injury, medical condition, or addiction in medical history that may affect exercise capacity, (5) not taking any medications with a modifying effect on exercise capacity, (6) maximum exertion achieved during CPET. We defined the maximum exertion in CPET as the fulfilment of the minimum six of the following criteria: (1) respiratory exchange ratio (RER) ≥1.10, (2) present VO₂ plateau (growth <100 mL·min^–1 in VO₂ despite increased running speed or cycling power), (3) respiratory frequency (fR) ≥45 breaths·min^–1, (4) declared subjective exertion intensity during CPET ≥18 in the Borg scale (Borg, 1970), (5) blood lactate concentration [La^-]_b ≥8 mmol·L^–1, (6) growth in speed/power ≥10% of respiratory compensation point (RCP) values after exceeding the RCP, (7) peak heart rate (HRpeak) ≥15 beats·min^–1 below predicted maximal heart rate (HR_max) (Lach et al., 2021).

Participants’ selection procedure has been shown in Figure 1.

Figure 1

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In the present study, we derived and internally validated novel advanced and accurate prediction models for VO_2max. The main findings are as follows: (1) we can precisely predict VO_2max based on submaximal CPET parameters, (2) inclusion of cardiopulmonary and BC variables enriches their prediction performance, (3) based only on somatic parameters, weak-to-low VO_2max assessment is currently possible, (4) derived equations showed high transferability abilities during validation. Our findings indicate that prediction models based on AT and RCP variables allow for accurate VO_2max calculation. Equations based on somatic variables allow for limited precision.

The main advantage of our research is the unified CPET protocol conducted on a wide cohort of endurance athletes with different levels of fitness. This approach enables the comprehensive evaluation of the most important predictors which were further applied to build prediction equations. In the current literature, prediction models for sports and performance diagnostics are mostly derived from narrow and specified athletic cohorts which limit their applicability to broader populations (Paap and Takken, 2014). Moreover, the advantage of the presented research was the fact that regression equations for the treadmill and cycle ergometer were derived based on the most commonly used machines and forms of activity or movement in the laboratory stress exercise tests.

An important issue addressed in publications on various attempts to estimate VO_2max is the question of their usefulness in assessing changes in endurance over a training cycle (Klusiewicz et al., 2016). As reported by Klusiewicz et al., the suitability of the two indirect methods of assessing VO_2max was statistically confirmed, their usefulness for estimating changes in the endurance of the trained individuals during the training cycle was rather low (Klusiewicz et al., 2016). The standard estimation error of these methods (ranged between 4.2% and 7.7% in the female and 5.1% and 7.4% in the male) was higher than the real differences in the VO_2max values determined in the direct measurements (between the first and the second examination the VO_2max rose by 3.0% in the female athletes and dropped by 4.3% in the male athletes) (Klusiewicz et al., 2016). Popularly used wearables provided substantial accuracy on population level when considered devices with exercise-based algorithms (Molina-Garcia et al., 2022). However, VO_2max predictions on the individual’s level still need improvement in the context of both sports and clinical settings (Molina-Garcia et al., 2022).

In the Astrand-Ryhming method, a widely used VO_2max prediction method for almost 70 years, in several papers published so far, the correlation coefficients of the measured values to the predicted values ranged from 0.63 to 0.85. Standard estimated error values (in L·min^–1) generally exceeded 0.5 (Grant et al., 1995; Legge and Banister, 1986). In our study, the highest R² was 0.913 and the lowest was 0.775. As an additional advantage, we propose an equation based only on somatic variables, which showed a low R² - 0.35 for runners and 0.43 for cyclists. Although, it still presents that our models are more accurate than those widely described in the literature so far (Paap and Takken, 2014; Wiecha et al., 2023).

As VO₂ is an exercise parameter that combines the function of the respiratory, circulatory, and muscular systems, the use of only somatic variables such as body fat, weight, or age was not sufficient for optimal prediction (Bassett and Howley, 2000). It is worth underlining that the main factors contributing to VO_2max were submaximal variables VO_2AT and VO_2RCP, as well as running speed for runners and pedalling power for cyclists (Billat and Koralsztein, 1996). Thus, VO₂ is a universal and interchangeable measurement of endurance (Albouaini et al., 2007). Our results suggest that VO₂ is an indicator of both endurance and critical vital signs (Blair et al., 1989; Kaminsky et al., 2015). It is also in line with current standings as Kaminsky et al. and Blair et al. postulate that the higher the VO_2max, the fitter the individual is (Kaminsky et al., 2015), and the lower its all-cause mortality (Blair et al., 1989).

In sports medicine and exercise physiology, evaluation of the body’s functional performance remains crucial (Sartor et al., 2013). Our results indicate that VO_2max was possible to accurately predict based only on submaximal parameters (without the inclusion of maximal ones), which is reflected in R² (Wiecha et al., 2022). This confirms that submaximal CPET is a valuable tool in assessing fitness levels. Thus, submaximal exercise testing appears to be more applicable by physicians and fitness professionals in their role as clinical exercise specialists (Noonan and Dean, 2000). For individuals who have a moderate to high possibility of cardiovascular diseases, exerting themselves up to their maximum abilities increases risk of adverse outcomes (Guazzi et al., 2012; Noonan and Dean, 2000). There are numerous possibilities to use results of submaximal CPET. Currently, pseudo-random binary sequencing appears as one of the feasible approaches. Its enables assessment of cardiorespiratory kinetics within the selected workload ranges (Hoffmann et al., 2022; Koschate et al., 2016). This is important as CPET until refusal is often impossible to conduct or highly dangerous (Guazzi et al., 2016). Such situations appear mainly in clinical cardiovascular conditions, such as heart failure, dyspnea of unknown aetiology, or risk evaluation for providing treatment protocol (Guazzi et al., 2016). Furthermore, previous studies have described that submaximal variables are significant predictors for performance measurements, as pointed out by Snowden et al., 2010, and Albouaini et al., 2007. In conclusion, ensuring high repeatability through submaximal prediction methods is crucial for monitoring endurance changes in both sports and medical diagnostics (Mann et al., 2013; Noonan and Dean, 2000).

It is worth mentioning the effect of body fat percentage on VO_2max. This variable has been included in the majority of our models. With the increase in body fat percentage, VO₂ decreased, and this relationship was particularly important in the somatic equation and is previously described in the literature (Shete et al., 2014). This is due to the fact that a higher level of adipose tissue and general body mass have both a negative impact on the results during long-term endurance sports (i.e. running and cycling) and with increasing fitness levels, the level of participant fatness decreases (Schwartz et al., 1991).

Results of internal validation show that our prediction models allow for an accurate assessment of VO_2max. The observed RMSE and MAE values are significantly lower than in the validation of other prediction models on endurance athletes’ cohorts. Petek et al., 2022, and Malek et al., 2004, while validating the majority of widely used prediction models, observed MAE and RMSE on the level of 7–9 mL·kg^–1·min^–1. Our highest value of error for the somatic equation was in the cycling model (MAE; 4.74 mL·kg^–1·min^–1). Moreover, as we mentioned above, the somatic equation showed the lowest accuracy, and the remaining equations have RMSE between 1.94 and 6.11 and MAE in the range of 1.46–4.74 mL·kg^–1·min^–1.

Our study has some limitations. The applied exercise protocol may affect CPET results. There may be differences in performance measured in 2 min steps comparing to longer steps, but this should not significantly impact the participants’ exercise results. Additionally, longer constant intervals may increase accuracy in determining AT and RCP level, but have negligible impact on VO_2max values (Muscat et al., 2015). The study, due to the insufficient number of women in the database to obtain reliable results, was restricted to men only. Therefore, the equations should be applied with more caution in women.

To summarise, our study has vast practical applications in the comprehensive assessment of an athlete’s training and is a valuable tool for coaches in the preparation of individualised training prescriptions (Mann et al., 2013). Targeting training regimens and diet to optimise the most important parameters contributing to the VO_2max (i.e. VO_2AT, VO_2RCP, RER, body fat, etc.) will allow for achieving better results during the competition and they provide a useful indirect method for assessing changes in endurance during the training cycle (Mann et al., 2013). Various areas of application of prediction models have also been postulated in the literature so far, for example in submaximal and maximal efforts, or simulating the overcoming of the starting distance, or even at rest (Zhou et al., 1997). It is also worth mentioning their clinical implications in cardiology for the diagnosis of heart disease in athletes (where a reduction in VO_2max may occur despite maintaining other parameters, e.g. RER) (Guazzi et al., 2016; Löllgen and Leyk, 2018).

All data generated or analysed during this study are included in the manuscript.

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Author details

1. Szczepan Wiecha

   Department of Physical Education and Health in Biala Podlaska, Faculty in Biala Podlaska, Jozef Pilsudski University of Physical Education, Warsaw, Poland

   Contribution

   Conceptualization, Resources, Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing – original draft, Project administration, Writing – review and editing

   For correspondence

   szczepan.wiecha@awf.edu.pl

   Competing interests

   received payment for leading CPET workshops at IX Małopolskich Warsztatach Niewydolności Serca. The author has no other competing interest to declare

   "This ORCID iD identifies the author of this article:" 0000-0001-9458-557X

2. Przemysław Seweryn Kasiak

   Students' Scientific Group of Lifestyle Medicine, 3rd Department of Internal Medicine and Cardiology, Medical University of Warsaw, Warsaw, Poland

   Contribution

   Data curation, Writing – original draft

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-0303-6135

3. Piotr Szwed

   Department of Experimental and Clinical Pharmacology, Center for Preclinical Research and Technology CEPT, Medical University of Warsaw, Warsaw, Poland

   Contribution

   Data curation, Writing – original draft

   Competing interests

   No competing interests declared

4. Tomasz Kowalski

   Institute of Sport-National Research Institute, Warsaw, Poland

   Contribution

   Data curation, Methodology, Writing – original draft

   Competing interests

   has received funding from the Institute of Sport - National Research Institute. The author has received consulting fees for regular coaching and consulting work with private clients, Polish Triathlon Federation and The Triathlon Squad professional triathlon team. The author has no other competing interests to declare

5. Igor Cieśliński

   Department of Physical Education and Health in Biala Podlaska, Faculty in Biala Podlaska, Jozef Pilsudski University of Physical Education, Warsaw, Poland

   Contribution

   Data curation, Software, Formal analysis, Validation

   Competing interests

   No competing interests declared

6. Marek Postuła

   Department of Experimental and Clinical Pharmacology, Center for Preclinical Research and Technology CEPT, Medical University of Warsaw, Warsaw, Poland

   Contribution

   Supervision, Writing – review and editing

   Competing interests

   No competing interests declared

7. Andrzej Klusiewicz

   Department of Physical Education and Health in Biala Podlaska, Faculty in Biala Podlaska, Jozef Pilsudski University of Physical Education, Warsaw, Poland

   Contribution

   Supervision, Writing – review and editing

   Competing interests

   No competing interests declared

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