Modeling Long-Term Facilitation of Respiration During Interval Exercise in Humans

Figures

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  Fig. 1. Block diagram of phrenic nerve activity model. Note that the denominator of equation (Bruce et al.) [3] corresponds to a second-order differential equation. The curvilinear shape of the slow gradual increase during long-term facilitation suggests second-order dynamics as will be shown later. First-order or exponential dynamics have a close to linear initial shape

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  Fig. 2. Long-term facilitation model predictions compared to peak integrated phrenic data (wn = 0.075 rad/s, ζ = 0.7, step = 18.5). Time zero is when stimulation ended

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  Fig. 3. Chemoreceptor model predictions compared to group data during air breathing. Subjects carried out three intermittent level change exercises: rest to 40 W, 40 W to 45% maximal oxygen uptake (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{{{\text{O}}_{2} \max }}$$\end{document}VO2max), and 45% \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{{{\text{O}}_{2} \max }}$$\end{document}VO2max to 40 W. VE minute ventilation, Gp peripheral gain in (L/min)/mmHg, Gc central gain in (L/min)/mmHg

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  Fig. 4. Chemoreceptor model predictions compared to group data during 3% CO2 inhalation. Subjects carried out three intermittent level change exercises: rest to 40 W, 40 W to 45% maximal oxygen uptake (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{{{\text{O}}_{2} \max }}$$\end{document}VO2max), and 45% \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{{{\text{O}}_{2} \max }}$$\end{document}VO2max to 40 W. VE minute ventilation, Gp peripheral gain in (L/min)/mmHg, Gc central gain in (L/min)/mmHg. The standard deviation (SD) for the CO2 fit for 40 W exercise + CO2 = 1.73 L/min, standard error (SE) = 1.73/sqrt (7) = 0.654. The SD of the final ventilation = 6.32 L/min. By adding the variance of the CO2 fit, total combined variance = 6.322 + 1.732, total combined SD = 6.55 L/min, SE = 6.55/sqrt (7) = 2.48 L/min for the final…

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  Fig. 5. Estimated neurally mediated ventilation augmentation after removal of chemoreceptor-mediated contribution. VE minute ventilation. Maximum augmentation estimated was 17.0 ± 2.48 L/min over control level. p < 0.001 (see caption for Fig. 4)

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  Fig. 6. Neural model predictions compared to estimated ventilation from Fig. 4 (wn = 0.375, ζ = 0.7, B = 9, A = 0, baseline = 7.6 L/min, start τ = 2). VE minute ventilation

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  Fig. 7. Predicted neural augmentation past observation period. VE minute ventilation