Modelling and regulating of cardio-respiratory response for the enhancement of interval training

Dose variability of supplemental oxygen therapy with open patient interfaces based on in vitro measurements using a physiologically realistic upper airway model

BACKGROUND

Supplemental oxygen therapy is widely used in hospitals and in the home for chronic care. However, there are several fundamental problems with the application of this therapy such that patients are often exposed to arterial oxygen concentrations outside of the intended target range. This paper reports volume-averaged tracheal oxygen concentration measurements (FtO2) from in vitro experiments conducted using a physiologically realistic upper airway model. The goal is to provide data to inform a detailed discussion of the delivered oxygen dose.

METHODS

A baseline FtO2 dataset using a standard, straight adult nasal cannula was established by varying tidal volume (Vt), breathing frequency (f), and continuous oxygen flow rate (QO2) between the following levels to create a factorial design: Vt = 500, 640, or 800 ml; f = 12, 17, or 22 min- 1; QO2 = 2, 4, or 6 l/min. Further experiments were performed to investigate the influence on FtO2 of variation in inspiratory/expiratory ratio, inclusion of an inspiratory or expiratory pause, patient interface selection (e.g. nasal cannula versus a facemask), and rapid breathing patterns in comparison with the baseline measurements.

RESULTS

Oxygen concentration measured at the trachea varied by as much as 60% (i.e. from 30.2 to 48.0% of absolute oxygen concentration) for the same oxygen supply flow rate due to variation in simulated breathing pattern. Among the baseline cases, the chief reasons for variation were 1) the influence of variation in tidal volume leading to variable FiO2 and 2) variation in breathing frequency affecting volume of supplemental oxygen delivered through the breath.

CONCLUSION

For oxygen administration using open patient interfaces there was variability in the concentration and quantity of oxygen delivered to the trachea over the large range of scenarios studied. Of primary importance in evaluating the oxygen dose is knowledge of the breathing parameters that determine the average inhalation flow rate relative to the oxygen flow rate. Otherwise, the oxygen dose cannot be determined.

Dynamic characteristics of oxygen consumption

Background

Previous studies have indicated that oxygen uptake (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$VO_2$$\end{document}VO2) is one of the most accurate indices for assessing the cardiorespiratory response to exercise. In most existing studies, the response of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$VO_2$$\end{document}VO2 is often roughly modelled as a first-order system due to the inadequate stimulation and low signal to noise ratio. To overcome this difficulty, this paper proposes a novel nonparametric kernel-based method for the dynamic modelling of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$VO_2$$\end{document}VO2 response to provide a more robust estimation.

Methods

Twenty healthy non-athlete participants conducted treadmill exercises with monotonous stimulation (e.g., single step function as input). During the exercise, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$VO_2$$\end{document}VO2 was measured and recorded by a popular portable gas analyser (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K4b^2$$\end{document}K4b2, COSMED). Based on the recorded data, a kernel-based estimation method was proposed to perform the nonparametric modelling of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$VO_2$$\end{document}VO2. For the proposed method, a properly selected kernel can represent the prior modelling information to reduce the dependence of comprehensive stimulations. Furthermore, due to the special elastic net formed by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}_1$$\end{document}L1 norm and kernelised \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}_2$$\end{document}L2 norm, the estimations are smooth and concise. Additionally, the finite impulse response based nonparametric model which estimated by the proposed method can optimally select the order and fit better in terms of goodness-of-fit comparing to classical methods.

Results

Several kernels were introduced for the kernel-based \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$VO_2$$\end{document}VO2 modelling method. The results clearly indicated that the stable spline (SS) kernel has the best performance for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$VO_2$$\end{document}VO2 modelling. Particularly, based on the experimental data from 20 participants, the estimated response from the proposed method with SS kernel was significantly better than the results from the benchmark method [i.e., prediction error method (PEM)] (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$76.0\pm 5.72$$\end{document}76.0±5.72 vs \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$71.4\pm 7.24\%$$\end{document}71.4±7.24%).

Conclusions

The proposed nonparametric modelling method is an effective method for the estimation of the impulse response of VO₂—Speed system. Furthermore, the identified average nonparametric model method can dynamically predict \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$VO_2$$\end{document}VO2 response with acceptable accuracy during treadmill exercise.

An equivalent circuit model for onset and offset exercise response

Background

The switching exercise (e.g., Interval Training) has been a commonly used exercise protocol nowadays for the enhancement of exerciser’s cardiovascular fitness. The current difficulty for simulating human onset and offset exercise responses regarding the switching exercise is to ensure the continuity of the outputs during onset-offset switching, as well as to accommodate the exercise intensities at both onset and offset of exercise.

Methods

Twenty-one untrained healthy subjects performed treadmill trials following both single switching exercise (e.g., single-cycle square wave protocol) and repetitive switching exercise (e.g., interval training protocol). During exercise, heart rate (HR) and oxygen uptake (VO ₂) were monitored and recorded by a portable gas analyzer (K4b ², Cosmed). An equivalent single-supply switching resistance-capacitor (RC) circuit model was proposed to accommodate the observed variations of the onset and offset dynamics. The single-cycle square wave protocol was utilized to investigate the respective dynamics at onset and offset of exercise with the aerobic zone of approximate 70% - 77% of HR _max, and verify the adaption feature for the accommodation of different exercise strengths. The design of the interval training protocol was to verify the transient properties during onset-offset switching. A verification method including Root-mean-square-error (RMSE) and correlation coefficient, was introduced for comparisons between the measured data and model outputs.

Results

The experimental results from single-cycle square wave exercises clearly confirm that the onset and offset characteristics for both HR and VO ₂ are distinctly different. Based on the experimental data for both single and repetitive square wave exercise protocols, the proposed model was then presented to simulate the onset and offset exercise responses, which were well correlated indicating good agreement with observations.

Conclusions

Compared with existing works, this model can accommodate the different exercise strengths at both onset and offset of exercise, while also depicting human onset and offset exercise responses, and guarantee the continuity of outputs during onset-offset switching. A unique adaption feature by allowing the time constant

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and steady state gain to re-shift back to their original states, more closely mimics the different exercise strengths during normal daily exercise activities.