Confidence intervals for the parameters estimated from simulated O2 uptake kinetics: effects of different data treatments

Baroreflex dynamics during the rest to exercise transient in acute normobaric hypoxia in humans

PURPOSE

We hypothesised that during a rest-to-exercise transient in hypoxia (H), compared to normoxia (N), (i) the initial baroreflex sensitivity (BRS) decrease would be slower and (ii) the fast heart rate (HR) and cardiac output (CO) response would have smaller amplitude (A1) due to lower vagal activity in H than N.

METHODS

Ten participants performed three rest-to-50 W exercise transients on a cycle-ergometer in N (ambient air) and three in H (inspired fraction of O2 = 0.11). R-to-R interval (RRi, by electrocardiography) and blood pressure profile (by photo-plethysmography) were recorded non-invasively. Analysis of the latter provided mean arterial pressure (MAP) and stroke volume (SV). CO = HR·SV. BRS was calculated by modified sequence method.

RESULTS

Upon exercise onset in N, MAP fell to a minimum (MAPmin) then recovered. BRS decreased immediately from 14.7 ± 3.6 at rest to 7.0 ± 3.0 ms mmHg-1 at 50 W (p < 0.01). The first BRS sequence detected at 50 W was 8.9 ± 4.8 ms mmHg-1 (p < 0.05 vs. rest). In H, MAP showed several oscillations until reaching a new steady state. BRS decreased rapidly from 10.6 ± 2.8 at rest to 2.9 ± 1.5 ms mmHg-1 at 50 W (p < 0.01), as the first BRS sequence at 50 W was 5.8 ± 2.6 ms mmHg-1 (p < 0.01 vs. rest). CO-A1 was 2.96 ± 1.51 and 2.31 ± 0.94 l min-1 in N and H, respectively (p = 0.06). HR-A1 was 7.7 ± 4.6 and 7.1 ± 5.9 min-1 in N and H, respectively (p = 0.81).

CONCLUSION

The immediate BRS decrease in H, coupled with similar rapid HR and CO responses, is compatible with a withdrawal of residual vagal activity in H associated with increased sympathetic drive.

The algorithm used for the calculation of gas exchange affects the estimation of O2 uptake kinetics at the onset of moderate-intensity exercise

At the start of a moderate-intensity square-wave exercise, after a short delay, breath-by-breath O2 uptake at the mouth is approximated to a mono-exponential function, whose time constant is considered matched to that of the O2 uptake of the working muscles. We compared the kinetic parameters obtained from the breath-by-breath gas exchange data yielded by the 'Independent-breath' algorithm (IND), which accounts for the changes in lung gas stores, with those obtained with the classical 'Expiration-only' algorithm (EXP). The two algorithms were applied on the same flow and gas fraction traces acquired on 10 healthy volunteers, performing 10 times the same moderate-intensity exercise transition. Repeated O2 uptake responses were stacked together and the kinetic parameters of a mono-exponential function were estimated by non-linear regression, removing the data pertaining to 1-s progressively longer initial periods (ΔTr ). Independently of ΔTr , the mean response time (time constant + time delay) obtained for the IND data was faster compared to the EXP data (∼43 s vs. ∼47 s, P < 0.001), essentially because of shorter time delays. Between ΔTr  = 16 s and ΔTr  = 29s, the time constants of the IND data decreased (30.7 s vs. 28.0 s, P < 0.05; drop = 10%), but less than those of the EXP data (32.2 s vs. 26.2 s, P < 0.001; drop = 23%); with the same ΔTr , the time constants of the two algorithms' data were not different (P > 0.07). The different decrease in the time constant, together with the different mean response time, suggests that the data yielded by the two algorithms provide a different picture of the phenomena occurring at the beginning of the exercise.

Influence of the fitting window on the O2 uptake kinetics at the onset of moderate intensity exercise

The O₂ uptake (V̇o₂) data at the onset of an exercise are usually fitted with a mono-exponential function, after removal of the data pertaining to a conventional initial time period (ΔTr) lasting ∼20 s. We performed a thorough quantitative analysis on the effects of removing data pertaining to different ΔTr, aiming at identifying an objective method to establish the appropriate ΔTr. Breath-by-breath O₂ uptake responses, acquired from 25 healthy adults performing a step moderate-intensity exercise, and 10⁴ simulated biexponential responses, were analyzed. For all the responses, the kinetic parameters of a mono-exponential function and the corresponding asymptotic standard errors (ASEs) were estimated by nonlinear regression, removing the data pertaining to progressively longer initial periods (1 s each) up to 60 s. Four methods to establish objectively ΔTr were compared. The minimum estimated τ was obtained for ΔTr ≅ 35 s in both the V̇o₂ and simulated data, that was about 30% lower compared with that obtained for ΔTr ≅ 0s. The average ASE values remained quite constant up to ΔTr ≅ 35 s, thereafter they increased remarkably. The τ used to generate the simulated response fell within the confidence intervals of the estimated τ in ∼85% of cases for ΔTr = 20 s ("20 s-w" method); this percentage increased to ∼92% of cases when ΔTr was established according to both the minimum τ and its narrowest confidence interval ("Mixed" method). In conclusion, the effects of removing V̇o₂ data pertaining to different ΔTr are remarkable. The "Mixed" method provided estimated parameters close to those used to generate the simulated responses and is thus endorsed.NEW & NOTEWORTHY We propose a method to objectively establish the initial time period to be removed from the fitting window when, using a mono-exponential model, the kinetics of the fundamental component is determined on breath-by-breath O₂ uptake data collected at the onset of a moderate-intensity exercise. Innovative statistical parameters ("Coverage" and "Concordance_5%," applicable on simulated responses) were used to compare its performance with that of other three methods. The proposed method yielded the best "Coverage" and "Concordance_5%."

Training status affects between-protocols differences in the assessment of maximal aerobic velocity

Purpose

Continuous incremental protocols (CP) may misestimate the maximum aerobic velocity (V_max) due to increases in running speed faster than cardiorespiratory/metabolic adjustments. A higher aerobic capacity may mitigate this issue due to faster pulmonary oxygen uptake (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O₂) kinetics. Therefore, this study aimed to compare three different protocols to assess V_max in athletes with higher or lower training status.

Methods

Sixteen well-trained runners were classified according to higher (HI) or lower (LO) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O_2max\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O₂-kinetics was calculated across four 5-min running bouts at 10 km·h⁻¹. Two CPs [1 km·h⁻¹ per min (CP1) and 1 km·h⁻¹ every 2-min (CP2)] were performed to determine V_max\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O_2max, lactate-threshold and submaximal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O₂/velocity relationship. Results were compared to the discontinuous incremental protocol (DP).

Results

V_max, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O_2max, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙CO₂ and VE were higher [(P < 0.05,(ES:0.22/2.59)] in HI than in LO. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O₂-kinetics was faster [P < 0.05,(ES:-2.74/ − 1.76)] in HI than in LO. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O₂/velocity slope was lower in HI than in LO [(P < 0.05,(ES:-1.63/ − 0.18)]. V_max and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O₂/velocity slope were CP1 > CP2 = DP for HI and CP1 > CP2 > DP for LO. A lower [P < 0.05,(ES:0.53/0.75)] V_max-difference for both CP1 and CP2 vs DP was found in HI than in LO. V_max-differences in CP1 vs DP showed a large inverse correlation with V_max, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O_2max and lactate-threshold and a very large correlation with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O₂-kinetics.

Conclusions

Higher aerobic training status witnessed by faster \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{V}$$\end{document}V˙O₂ kinetics led to lower between-protocol V_max differences, particularly between CP2 vs DP. Faster kinetics may minimize the mismatch issues between metabolic and mechanical power that may occur in CP. This should be considered for exercise prescription at different percentages of V_max.

Relationship between maximal aerobic power with aerobic fitness as a function of signal-to-noise ratio

Efforts to better understand cardiorespiratory health are relevant for the future development of optimized physical activity programs. We aimed to explore the impact of the signal quality on the expected associations between the ability of the aerobic system in supplying energy as fast as possible during moderate exercise transitions with its maximum capacity to supply energy during maximal exertion. It was hypothesized that a slower aerobic system response during moderate exercise transitions is associated with a lower maximal aerobic power; however, this relationship relies on the quality of the oxygen uptake data set. Forty-three apparently healthy participants performed a moderate constant work rate (CWR) followed by a pseudorandom binary sequence (PRBS) exercise protocol on a cycle ergometer. Participants also performed a maximum incremental cardiopulmonary exercise testing (CPET). The maximal aerobic power was evaluated by the peak oxygen uptake during the CPET, and the aerobic fitness was estimated from different approaches for oxygen uptake dynamics analysis during the CWR and PRBS protocols at different levels of signal-to-noise ratio. The product moment correlation coefficient was used to evaluate the correlation level between variables. Aerobic fitness was correlated with maximum aerobic power, but this correlation increased as a function of the signal-to-noise ratio. Aerobic fitness is related to maximal aerobic power; however, this association appeared to be highly dependent on the data quality and analysis for aerobic fitness evaluation. Our results show that simpler moderate exercise protocols might be as good as maximal exertion exercise protocols to obtain indexes related to cardiorespiratory health.NEW & NOTEWORTHY Optimized methods for cardiorespiratory health evaluation are of great interest for public health. Moderate exercise protocols might be as good as maximum exertion exercise protocols to evaluate cardiorespiratory health. Pseudorandom or constant workload moderate exercise can be used to evaluate cardiorespiratory health.

Interchangeability between two breath-by-breath O2 uptake calculation algorithms in asthmatic and healthy volunteers

INTRODUCTION

The interchangeability analysis has been recently proposed to objectively assess whether a newly developed measurement tool can substitute the older ones; this analysis assumes that the measures yielded by the compared tools should differ less than a maximum acceptable value. We aimed to assess the interchangeability rate (IR) of the breath-by-breath O₂ uptake data calculated with the "Independent breath" (IND) and the "Expiration-only" (EXP) algorithms.

METHODS

Oxygen, carbon dioxide fractions, and ventilatory flow were recorded continuously over 26 min in 18 asthmatic and 20 well-matched healthy volunteers at rest, during cycling, and recovery; oxygen uptake (V'O₂) was calculated with the two algorithms under comparison. Coefficients of variation (CVs) of all the steady-state condition were modeled as a function of the average V'O₂ values and IR was calculated accordingly.

RESULTS

CVs were significantly greater in the asthmatic volunteers (F = 5.97, p < 0.05), being lower for IND compared to EXP (F > 7.04, p < 0.02). CVs decreased as a function of the reciprocal of the square root of the average V'O₂. The IR, calculated on the basis of this relationship, was not significantly different in the two groups of volunteers (F = 0.77, p = 0.385); taking as reference method the IND, or EXP algorithms, the IR values were significantly different (F = 58.6, p < 0.001), amounting to 97.4 ± 2.2% or to 98.2 ± 1.7%, respectively.

CONCLUSION

The relative noise of V'O₂ was greater in the asthmatic volunteers compared to the healthy ones and was lower for IND compared to EXP. The interchangeability analysis suggested that IND might be a better substitute for EXP than the opposite.

VO₂FITTING: A Free and Open-Source Software for Modelling Oxygen Uptake Kinetics in Swimming and other Exercise Modalities

The assessment of oxygen uptake (VO₂) kinetics is a valuable non-invasive way to evaluate cardiorespiratory and metabolic response to exercise. The aim of the study was to develop, describe and evaluate an online VO₂ fitting tool (VO₂FITTING) for dynamically editing, processing, filtering and modelling VO₂ responses to exercise. VO₂FITTING was developed in Shiny, a web application framework for R language. Validation VO₂ datasets with both noisy and non-noisy data were developed and applied to widely-used models (n = 7) for describing different intensity transitions to verify concurrent validity. Subsequently, we then conducted an experiment with age-group swimmers as an example, illustrating how VO₂FITTING can be used to model VO₂ kinetics. Perfect fits were observed, and parameter estimates perfectly matched the known inputted values for all available models (standard error = 0; p < 0.001). The VO₂FITTING is a valid, free and open-source software for characterizing VO₂ kinetics in exercise, which was developed to help the research and performance analysis communities.

The "independent breath" algorithm: assessment of oxygen uptake during exercise

PURPOSE

Reduction of noise of breath-by-breath gas-exchange data is crucial to improve measurements. A recently described algorithm ("independent breath"), that neglects the contiguity in time of breaths, was tested.

METHODS

Oxygen, carbon dioxide fractions, and ventilatory flow were recorded continuously over 26 min in 20 healthy volunteers at rest, during unloaded and moderate intensity cycling and subsequent recovery; oxygen uptake ([Formula: see text]) was calculated with the "independent breath" algorithm (IND) and, for comparison, with three other "classical" algorithms. Average [Formula: see text] and standard deviations were calculated for steady-state conditions; non-linear regression was run throughout the [Formula: see text] data of the transient phases (ON and OFF), using a mono-exponential function.

RESULTS

Comparisons of the different algorithms showed that they yielded similar average [Formula: see text] at steady state (p = NS). The standard deviations were significantly lower for IND (post hoc contrasts, p < 0.001), with the slope of the relationship with the corresponding data obtained from "classical" algorithms being < 0.69. For both transients, the overall kinetics (evaluated as time delay + time constant) was significantly faster for IND (post hoc contrasts, p < 0.001). For the ON transient, the asymptotic standard errors of the kinetic parameters were significantly lower for IND, with the slope of the regression line with the corresponding values obtained from the "classical" algorithms being < 0.60.

CONCLUSION

The "independent breath" algorithm provided consistent average O₂ uptake values while reducing the overall noise of about 30%, which might result in the halving of the required number of repeated trials needed to assess the kinetic parameters of the ON transient.

Open-circuit respirometry: real-time, laboratory-based systems

This review explores the conceptual and technological factors integral to the development of laboratory-based, automated real-time open-circuit mixing-chamber and breath-by-breath (B × B) gas-exchange systems, together with considerations of assumptions and limitations. Advances in sensor technology, signal analysis, and digital computation led to the emergence of these technologies in the mid-20th century, at a time when investigators were beginning to recognise the interpretational advantages of nonsteady-state physiological-system interrogation in understanding the aetiology of exercise (in)tolerance in health, sport, and disease. Key milestones include the 'Auchincloss' description of an off-line system to estimate alveolar O₂ uptake B × B during exercise. This was followed by the first descriptions of real-time automated O₂ uptake and CO₂ output B × B measurement by Beaver and colleagues and by Linnarsson and Lindborg, and mixing-chamber measurement by Wilmore and colleagues. Challenges to both approaches soon emerged: e.g., the influence of mixing-chamber washout kinetics on mixed-expired gas concentration determination, and B × B alignment of gas-concentration signals with respired flow. The challenging algorithmic and technical refinements required for gas-exchange estimation at the alveolar level have also been extensively explored. In conclusion, while the technology (both hardware and software) underpinning real-time automated gas-exchange measurement has progressively advanced, there are still concerns regarding accuracy especially under the challenging conditions of changing metabolic rate.

Data collection, handling, and fitting strategies to optimize accuracy and precision of oxygen uptake kinetics estimation from breath-by-breath measurements

Phase 2 pulmonary oxygen uptake kinetics (ϕ2 τV̇o_2P) reflect muscle oxygen consumption dynamics and are sensitive to changes in state of training or health. This study identified an unbiased method for data collection, handling, and fitting to optimize V̇o_2P kinetics estimation. A validated computational model of V̇o_2P kinetics and a Monte Carlo approach simulated 2 × 10⁵ moderate-intensity transitions using a distribution of metabolic and circulatory parameters spanning normal health. Effects of averaging (interpolation, binning, stacking, or separate fitting of up to 10 transitions) and fitting procedures (biexponential fitting, or ϕ2 isolation by time removal, statistical, or derivative methods followed by monoexponential fitting) on accuracy and precision of V̇o_2P kinetics estimation were assessed. The optimal strategy to maximize accuracy and precision of τV̇o_2P estimation was 1-s interpolation of 4 bouts, ensemble averaged, with the first 20 s of exercise data removed. Contradictory to previous advice, we found optimal fitting procedures removed no more than 20 s of ϕ1 data. Averaging method was less critical: interpolation, binning, and stacking gave similar results, each with greater accuracy compared with analyzing repeated bouts separately. The optimal procedure resulted in ϕ2 τV̇o_2P estimates for transitions from an unloaded or loaded baseline that averaged 1.97 ± 2.08 and 1.04 ± 2.30 s from true, but were within 2 s of true in only 47-62% of simulations. Optimized 95% confidence intervals for τV̇o_2P ranged from 4.08 to 4.51 s, suggesting a minimally important difference of ~5 s to determine significant changes in τV̇o_2P during interventional and comparative studies.NEW & NOTEWORTHY We identified an unbiased method to maximize accuracy and precision of oxygen uptake kinetics (τV̇o_2P) estimation. The optimum number of bouts to average was four; interpolation, bin, and stacking averaging methods gave similar results. Contradictory to previous advice, we found that optimal fitting procedures removed no more than 20 s of phase 1 data. Our data suggest a minimally important difference of ~5 s to determine significant changes in τV̇o_2P during interventional and comparative studies.

Pulmonary oxygen uptake and muscle deoxygenation kinetics during heavy intensity cycling exercise in patients with emphysema and idiopathic pulmonary fibrosis

BACKGROUND

Little is known about the mechanistic basis for the exercise intolerance characteristic of patients with respiratory disease; a lack of clearly defined, distinct patient groups limits interpretation of many studies. The purpose of this pilot study was to investigate the pulmonary oxygen uptake ([Formula: see text] O₂) response, and its potential determinants, in patients with emphysema and idiopathic pulmonary fibrosis (IPF).

METHODS

Following a ramp incremental test for the determination of peak [Formula: see text] O₂ and the gas exchange threshold, six emphysema (66 ± 7 years; FEV_1, 36 ± 16%), five IPF (65 ± 12 years; FEV₁, 82 ± 11%) and ten healthy control participants (63 ± 6 years) completed three repeat, heavy-intensity exercise transitions on a cycle ergometer. Throughout each transition, pulmonary gas exchange, heart rate and muscle deoxygenation ([HHb], patients only) were assessed continuously and subsequently modelled using a mono-exponential with ([Formula: see text] O₂, [HHb]) or without (HR) a time delay.

RESULTS

The [Formula: see text] O₂ phase II time-constant (τ) did not differ between IPF and emphysema, with both groups significantly slower than healthy controls (Emphysema, 65 ± 11; IPF, 69 ± 7; Control, 31 ± 7 s; P < 0.05). The HR τ was slower in emphysema relative to IPF, with both groups significantly slower than controls (Emphysema, 87 ± 19; IPF, 119 ± 20; Control, 58 ± 11 s; P < 0.05). In contrast, neither the [HHb] τ nor [HHb]:O₂ ratio differed between patient groups.

CONCLUSIONS

The slower [Formula: see text] O₂ kinetics in emphysema and IPF may reflect poorer matching of O₂ delivery-to-utilisation. Our findings extend our understanding of the exercise dysfunction in patients with respiratory disease and may help to inform the development of appropriately targeted rehabilitation strategies.

Breath-by-breath pulmonary O2 uptake kinetics: effect of data processing on confidence in estimating model parameters

To improve the signal-to-noise ratio of breath-by-breath pulmonary O2 uptake (V̇O2p) data, it is common practice to perform multiple step transitions, which are subsequently processed to yield an ensemble-averaged profile. The effect of different data-processing techniques on phase II V̇O2p kinetic parameter estimates (V̇O2p amplitude, time delay and phase II time constant (τV̇O2p)] and model confidence [95% confidence interval (CI95)] was examined. Young (n = 9) and older men (n = 9) performed four step transitions from a 20 W baseline to a work rate corresponding to 90% of their estimated lactate threshold on a cycle ergometer. Breath-by-breath V̇O2p was measured using mass spectrometry and volume turbine. Mono-exponential kinetic modelling of phase II V̇O2p data was performed on data processed using the following techniques: (A) raw data (trials time aligned, breaths of all trials combined and sorted in time); (B) raw data plus interpolation (trials time aligned, combined, sorted and linearly interpolated to second by second); (C) raw data plus interpolation plus 5 s bin averaged; (D) individual trial interpolation plus ensemble averaged [trials time aligned, linearly interpolated to second by second (technique 1; points joined by straight-line segments), ensemble averaged]; (E) 'D' plus 5 s bin averaged; (F) individual trial interpolation plus ensemble averaged [trials time aligned, linearly interpolated to second by second (technique 2; points copied until subsequent point appears), ensemble averaged]; and (G) 'F' plus 5 s bin averaged. All of the model parameters were unaffected by data-processing technique; however, the CI95 for τV̇O2p in condition 'D' (4 s) was lower (P < 0.05) than the CI95 reported for all other conditions (5-10 s). Data-processing technique had no effect on parameter estimates of the phase II V̇O2p response. However, the narrowest interval for CI95 occurred when individual trials were linearly interpolated and ensemble averaged.

Assembling more O₂ uptake responses: is it possible to merely stack the repeated transitions?

Kinetic parameters for pulmonary O2 uptake at exercise onset are estimated by non-linear regression on repeated responses assembled together. The native data contain the information, thus the "stacking" of the responses should provide correct values and uncertainties. Kinetic parameters and corresponding uncertainties (computed from the asymptotic standard errors; ASE) were estimated on 10(4) simulated noisy responses (with time constant τ=25s), repeated 10 times and assembled over an increasing number of repetitions (Nr) by "stacking" or ensemble averaging the responses processed to obtain 1s bins ("1-s-bins"). Independent of the assembling method, the average estimated τ amounted to ∼25.05 s. Independent of Nr, the "1-s-bins" and the "stacking" yielded an ASE/SD ratio for τ amounting to ∼0.52 and ∼0.98, respectively, resulting in a probability of including τ=25s within the estimated uncertainty from an individual kinetics amounting to ∼70% and >94% for the "1-s-bins" and the "stacking", respectively. In conclusion, the "stacking" allowed obtaining, also for individual kinetics, coherent estimated parameters and associated uncertainties.