Analysis of heart rate and oxygen uptake kinetics studied by two different pseudo-random binary sequence work rate amplitudes

The Fuzzy Kinetics Index: an indicator conflating cardiorespiratory kinetics during dynamic exercise

Purpose

The aim of the present study was to develop a novel index using fuzzy logic procedures conflating cardiorespiratory and pulmonary kinetics during dynamic exercise as a representative indicator for exercise tolerance.

Methods

Overall 69 data sets were re-analyzed: (age: 29 ± 1.2 y [mean ± SEM], height: 179 ± 1.0 cm; body mass: 78 ± 1.4 kg; peak oxygen uptake (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{V}}$$\end{document}V˙˙O_2peak): 48 ± 1.1 ml·min⁻¹·kg⁻¹), that comprised pseudo random binary sequence work rate (WR) changes between 30 and 80 W on a cycle ergometer, with additional voluntary exhaustion to estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{V}}$$\end{document}V˙O_2peak. Heart rate (HR), stroke volume (SV) and gas exchange (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}$$\dot {\text{V}}$$\end{document}V˙O_2pulm)) were measured beat-to-beat and breath-by-breath, respectively. For estimation of muscle oxygen uptake (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{V}}$$\end{document}V˙O_2musc) kinetics and for the analysis of kinetic responses of the parameters of interest (perfusion (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{Q}}$$\end{document}Q˙ = HR·SV), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{V}}$$\end{document}V˙O_2pulm, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{V}}$$\end{document}V˙O_2musc) the approach of Hoffmann et al. (2013) was applied. For calculation of the Fuzzy Kinetics Index \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{Q}}$$\end{document}Q˙, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{V}}$$\end{document}V˙O_2pulm, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{V}}$$\end{document}V˙O_2musc were used as input variables for the subsequent fuzzy- and defuzzyfication procedures.

Results

For both absolute and relative \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{V}}$$\end{document}V˙O_2peak a significant correlation has been observed with FKI, whereas the correlation coefficient is higher for relative (r = 0.430; p < 0.001; n = 69) compared to absolute \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{V}}$$\end{document}V˙O_2peak (r = 0.358; p < 0.01; n = 69). No significant correlations have been found between FKI and age, height or body mass (p > 0.05 each).

Conclusions

The significant correlations between FKI and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot {\text{V}}$$\end{document}V˙O_2peak represent a physiological connection between the regulatory and the capacitive system and its exercise performance. In turn, the application of FKI can serve as an indicator for healthy participants to assess exercise tolerance and sport performance.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00421-021-04611-w.

Frequency domain analysis to extract dynamic response characteristics for oxygen uptake during transitions to moderate- and heavy-intensity exercises

At the onset of an exercise transition, exponential modeling to calculate a time constant (τ) is the conventional method to analyze pulmonary oxygen uptake (V̇O_2p) kinetics for moderate and heavy exercises. A new frequency domain analysis technique, mean normalized gain (MNG), has been used to analyze V̇O_2p kinetics during moderate exercise, but has not been evaluated for its ability to detect differences in kinetics between moderate and heavy exercises. This study tested the hypothesis that MNG would detect smaller amplitude V̇O_2p responses in the heavy-exercise domain compared with moderate-exercise domain. Eight young healthy adults (3 female; age: 27 ± 6 yr; peak V̇O_2p: 43 ± 6 mL·min^-1·kg^-1; means ± SD) performed three bouts of pseudorandom binary sequence (PRBS) exercise for frequency analysis, with the work rate (WR) changing between 25 W and 90% ventilatory threshold (VT; L → M_PRBS), 25 W and 50% of the difference between VT and peak V̇O_2p (Δ50%; L → H_PRBS), and VT to Δ50% (VT → H_PRBS). Step exercise tests with equivalent changes in WR to the PRBS tests were performed to facilitate the comparison between MNG and τ. MNG was the highest for L → M_PRBS (59 ± 7%), then L → H_PRBS (52 ± 6%), and the lowest for VT → H_PRBS (38 ± 7%, F_(2,14) = 129.755, P < 0.001) exercise conditions indicating slower kinetics with increasing exercise intensity that correlated strongly in repeated measures with τ from step transitions (r_rm = -0.893). These results indicate that frequency domain analysis and MNG reliably detect differences in V̇O_2p kinetics observed across exercise intensity domains.NEW & NOTEWORTHY Mean normalized gain is able to detect differences in V̇O_2p kinetics between moderate-, heavy-, and heavy-intensity exercises from a raised WR within the same individuals. This new method of kinetic analysis may be advantageous compared with conventional V̇O_2p curve fitting, as it is less sensitive to breath-by-breath noise, it can provide useful information from a single exercise testing session, and it can be applied to nonconstant work rate exercise situations.

Faster oxygen uptake, heart rate, and ventilatory kinetics in stepping compared with cycle ergometry in patients with COPD during moderate-intensity exercise

Step tests are a stressful and feasible cost-effective modality to evaluate aerobic performance. However, the eccentric in addition to concentric muscle contractions of the legs on stepping emerge as a potential speeding factor for cardioventilatory and metabolic adjustments towards a steady-state, since eccentric contractions would prompt an earlier and stronger mechanoreceptor activation, as well as higher heart rate/cardiac output adjustments to the same metabolic demand. Moreover, shorter tests are ideal for exercise-limited subjects. Nine subjects with chronic obstructive pulmonary disease were invited to participate in comprehensive lung function tests and constant work tests performed on different days at a 90% gas exchange threshold for 6 min, in single-step tests or cycle ergometry. After careful monoexponential regression modelling, statistically relevant faster phase II time constants for oxygen uptake (45 ± 18 s vs 53 ± 17 s, p = 0.017) and minute ventilation (61 ± 13 s vs 74 ± 17 s, p = 0.027) were observed in the 6-min step tests compared with cycle ergometry, respectively. Despite an absence of heart rate time constant difference (43 ± 20 s vs 69 ± 46 s, p = 0.167), there was a significantly faster rate constant toward a steady state for heart rate (p = 0.02). In addition, 4-min compared with 6-min analysis presented similar results (p > 0.05), providing an appropriate steady-state. We conclude that step tests might elicit faster time constants compared with cycle ergometry, at the same average metabolic level, and 4-min analysis has similar mean errors compared with 6-min analysis within an acceptable range. New studies, comprising mechanisms and detailed physiological backgrounds, are necessary.

Impact of venous return on pulmonary oxygen uptake kinetics during dynamic exercise: in silico time series analyses from muscles to lungs

The aim of the present study was to investigate whether a single-compartment (SCM) and a multi-compartment (MCM) venous return model will produce significantly different time-delaying and distortive effects on pulmonary oxygen uptake (V̇o2pulm) responses with equal cardiac outputs (Q̇) and muscle oxygen uptake (V̇o2musc) inputs. For each model, 64 data sets were simulated with alternating Q̇ and V̇o2musc kinetics—time constants (τ) ranging from 10 to 80 s—as responses to pseudorandom binary sequence work rate (WR) changes. Kinetic analyses were performed by using cross-correlation functions (CCFs) between WR with V̇o2pulm and V̇o2musc. Higher maxima of the CCF courses indicate faster system responses—equal to smaller τ values of the variables of interest (e.g., τV̇o2musc). The models demonstrated a highly significant relationship for the resulting V̇o2pulm responses ( r = 0.976, P < 0.001, n = 64). Both models showed significant differences between V̇o2pulm and V̇o2musc kinetics for τV̇o2musc ranging from 10 to 30 s ( P < 0.05 each). In addition, a significant difference in V̇o2pulm kinetics ( P < 0.05) between the models was observed for very fast V̇o2musc kinetics (τ = 10 s). The combinations of fast Q̇ dynamics and slow V̇o2musc kinetics yield distinct deviations in the resultant V̇o2pulm responses compared with V̇o2musc kinetics. Therefore, the venous return models should be used with care and caution if the aim is to infer V̇o2musc by means of V̇o2pulm kinetics. Finally, the resultant V̇o2pulm responses seem to be complex and most likely unpredictable if no cardiodynamic measurements are available in vivo.

NEW & NOTEWORTHY A single-compartment and a multi-compartment venous return model were tested to see whether they result in different pulmonary oxygen uptake (V̇o2pulm) kinetics from equal cardiac output and muscle oxygen uptake (V̇o2musc) kinetics. To infer V̇o2musc kinetics by means of V̇o2pulm kinetics, both models should only be used for V̇o2musc time constants ranging from 40 to 80 s. The resultant V̇o2pulm responses seem to be complex and most likely unpredictable if no cardiodynamic measurements are available.

Impact of 60 days of 6° head down tilt bed rest on muscular oxygen uptake and heart rate kinetics: efficacy of a reactive sledge jump countermeasure

PURPOSE

The effects of 60 days of head down tilt bed rest (HDBR) with and without the application of a reactive jump countermeasure were investigated, using a method which enables to discriminate between pulmonary ([Formula: see text]O₂pulm) and muscular ([Formula: see text]O₂musc) oxygen uptake kinetics to control for hemodynamic influences.

METHODS

22 subjects were randomly allocated to either a group performing a reactive jumps countermeasure (JUMP; n = 11, male, 29 ± 7 years, 23.9 ± 1.3 kg m^- 2) or a control group (CTRL; n = 11, male, 29 ± 6 years, 23.3 ± 2.0 kg m^- 2). Heart rate (HR) and [Formula: see text]O₂pulm were measured in response to repeated changes in work rate between 30 and 80 W before (BDC-9) and two times after HDBR (R+ 2, R+ 13). Kinetic responses of HR, [Formula: see text]O₂pulm, and [Formula: see text]O₂musc were assessed applying time series analysis. Higher maxima in cross-correlation functions (CCF_max(x)) between work rate and the respective parameter indicate faster kinetics responses. Statistical analysis was performed applying multifactorial analysis of variance.

RESULTS

CCF_max([Formula: see text]O₂musc) and CCF_max([Formula: see text]O₂pulm) were not significantly different before and after HDBR (P > 0.05). CCF_max(HR) decreased following bed rest (JUMP: BDC-9: 0.30 ± 0.09 vs. R+ 2: 0.28 ± 0.06 vs. R+13: 0.28 ± 0.07; CTRL: 0.35 ± 0.09 vs. 0.27 ± 0.06 vs. 0.33 ± 0.07 P = 0.025). No significant differences between the groups were observed (P > 0.05). Significant alterations were found for CCF_max of mean arterial blood pressure (mBP) after HDBR (JUMP: BDC-9: 0.21 ± 0.07 vs. R+ 2: 0.30 ± 0.13 vs. R+ 13: 0.28 ± 0.08; CTRL: 0.25 ± 0.07 vs. 0.38 ± 0.13 vs. 0.28 ± 0.08; P = 0.008).

CONCLUSIONS

Despite hemodynamic changes, [Formula: see text]O₂ kinetics seem to be preserved for a longer period of HDBR, even without the application of a countermeasure.

Temporal dissociation between muscle and pulmonary oxygen uptake kinetics: influences of perfusion dynamics and arteriovenous oxygen concentration differences in muscles and lungs

PURPOSE

The aim of the study was to test whether or not the arteriovenous oxygen concentration difference (avDO₂) kinetics at the pulmonary (avDO₂pulm) and muscle (avDO₂musc) levels is significantly different during dynamic exercise.

METHODS

A re-analysis involving six publications dealing with kinetic analysis was utilized with an overall sample size of 69 participants. All studies comprised an identical pseudorandom binary sequence work rate (WR) protocol-WR changes between 30 and 80 W-to analyze the kinetic responses of pulmonary ([Formula: see text]) and muscle ([Formula: see text]) oxygen uptake kinetics as well as those of avDO₂pulm and avDO₂musc.

RESULTS

A significant difference between [Formula: see text] (0.395 ± 0.079) and [Formula: see text] kinetics (0.330 ± 0.078) was observed (p < 0.001), where the variables showed a significant relationship (r_SP = 0.744, p < 0.001). There were no significant differences between avDO₂musc (0.446 ± 0.077) and avDO₂pulm kinetics (0.451 ± 0.075), which are highly correlated (r = 0.929, p < 0.001).

CONCLUSION

It is suggested that neither avDO₂pulm nor avDO₂musc kinetic responses seem to be responsible for the differences between estimated [Formula: see text] and measured [Formula: see text] kinetics. Obviously, the conflation of avDO₂ and perfusion ([Formula: see text] ) at different points in time and at different physiological levels drive potential differences in [Formula: see text] and [Formula: see text] kinetics. Therefore, [Formula: see text] should, in general, be considered whenever oxygen uptake kinetics are analyzed or discussed.