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Objective. The fact that ramp incremental exercise yields quasi-linear responses for pulmonary oxygen uptake ( V ˙ O 2 ) and heart rate (HR) seems contradictory to the well-known non-linear behavior of underlying physiological processes. Prior research highlights this issue and demonstrates how a balancing of system gain and response time parameters causes linear V ˙ O 2 responses during ramp tests. This study builds upon this knowledge and extracts the time-varying dynamics directly from HR and V ˙ O 2 data of single ramp incremental running tests. Approach. A large-scale open access dataset of 735 ramp incremental running tests is analyzed. The dynamics are obtained by means of 1st order autoregressive and exogenous models with time-variant parameters. This allows for the estimates of time constant (τ) and steady state gain (SSG) to vary with work rate. Main results. As the work rate increases, τ-values increase on average from 38 to 132 s for HR, and from 27 to 35 s for V ˙ O 2 . Both increases are statistically significant (p < 0.01). Further, SSG-values decrease on average from 14 to 9 bpm (km·h−1)−1 for HR, and from 218 to 144 ml·min−1 for V ˙ O 2 (p < 0.01 for decrease parameters of HR and V ˙ O 2 ). The results of this modeling approach are line with literature reporting on cardiorespiratory dynamics obtained using standard procedures. Significance. We show that time-variant modeling is able to determine the time-varying dynamics HR and V ˙ O 2 responses to ramp incremental running directly from individual tests. The proposed method allows for gaining insights into the cardiorespiratory response characteristics when no repeated measurements are available.
Objective. The fact that ramp incremental exercise yields quasi-linear responses for pulmonary oxygen uptake ( V ˙ O 2 ) and heart rate (HR) seems contradictory to the well-known non-linear behavior of underlying physiological processes. Prior research highlights this issue and demonstrates how a balancing of system gain and response time parameters causes linear V ˙ O 2 responses during ramp tests. This study builds upon this knowledge and extracts the time-varying dynamics directly from HR and V ˙ O 2 data of single ramp incremental running tests. Approach. A large-scale open access dataset of 735 ramp incremental running tests is analyzed. The dynamics are obtained by means of 1st order autoregressive and exogenous models with time-variant parameters. This allows for the estimates of time constant (τ) and steady state gain (SSG) to vary with work rate. Main results. As the work rate increases, τ-values increase on average from 38 to 132 s for HR, and from 27 to 35 s for V ˙ O 2 . Both increases are statistically significant (p < 0.01). Further, SSG-values decrease on average from 14 to 9 bpm (km·h−1)−1 for HR, and from 218 to 144 ml·min−1 for V ˙ O 2 (p < 0.01 for decrease parameters of HR and V ˙ O 2 ). The results of this modeling approach are line with literature reporting on cardiorespiratory dynamics obtained using standard procedures. Significance. We show that time-variant modeling is able to determine the time-varying dynamics HR and V ˙ O 2 responses to ramp incremental running directly from individual tests. The proposed method allows for gaining insights into the cardiorespiratory response characteristics when no repeated measurements are available.
Oxygen uptake plays a vital role in evaluating endurance performance during exercise and is widely used for metabolic assessment. In this study, the oxygen uptake during the exercise phase (i.e. ascending or descending) of the stairs exercise are recorded and the experimental dataset features ten participants and a range of different exercise periods. Based on the designed experiment protocol, a non-parametric modeling method with kernel-based regularization is generally applied to estimate the oxygen uptake changes during the switching stairs exercise that is close to the daily life status. Compared with the fixed-order models on accuracy, stability and compatibility, the modeling results demonstrate the effectiveness of the non-parametric modeling approach. The influence of exercise duration on estimated fitness reveals that the model of the phase-oxygen uptake system is not time-invariant related to respiratory metabolism regulation and muscle fatigue. Accordingly, it allows us to study the humans' conversion mechanism at different metabolic rates and facilitates the standardization and development of exercise prescriptions.
Backround: Oxygen uptake (VO2) is one of the most important measures of fitness and critical vital sign. Cardiopulmonary exercise testing (CPET) is a valuable method of assessing fitness in sport and clinical settings. There is a lack of large studies on athletic populations to predict VO2max using somatic or submaximal CPET variables. Thus, this study aimed to: (1) derive prediction models for maximal VO2 (VO2max) based on submaximal exercise variables at anaerobic threshold (AT) or respiratory compensation point (RCP) or only somatic and (2) internally validate provided equations.Methods: 4424 male endurance athletes (EA) underwent maximal symptom-limited CPET on a treadmill (n=3330) or cycle ergometer (n=1094). The cohort was randomly divided between: variables selection (nrunners=1998; ncyclist=656), model building (nrunners=666; ncyclist=219) and validation (nrunners=666; ncyclist=219). Random Forest was used to select the most significant variables. Models were derived and internally validated with Multiple Linear Regression.Results: Runners were 36.24±8.45 yrs.; BMI=23.94±2.43 kg·m−2; VO2max=53.81±6.67 mL·min−1·kg−1. Cyclists were 37.33±9.13 yr.; BMI=24.34±2.63 kg·m−2; VO2max=51.74±7.99 mL·min−1·kg−1. VO2 at AT and RCP were the most contributing variables to exercise equations. Body mass and body fat had the highest impact on the somatic equation. Model performance for VO2max based on variables at AT was R2=0.81, at RCP was R2=0.91, at AT&RCP was R2=0.91 and for somatic-only was R2=0.43.Conclusions: Derived prediction models were highly accurate and fairly replicable. Formulae allow for precise estimation of VO2max based on submaximal exercise performance or somatic variables. Presented models are applicable for sport and clinical settling. They are a valuable supplementary method for fitness practitioners to adjust individualised training recommendations.Funding: No external funding was received for this work.
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