Reconstruction of the respiratory signal through ECG and wrist accelerometer data

Figures

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  Figure 1. Boxplot of the average synchronization between proxies and measured respiration. Phase synchronization indices \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}γ according to Eq. (5) between all respiration proxies (see Table 1) and the recorded flow signal have been averaged over the complete sleeping period and all 223 subjects (see Table 2). The orange part of each box represents the values between the lower quartile and the median, and the blue part represents the values between the median and the upper quartile. The ends of the whiskers mark the 2.5% quantile and the 97.5% quantile, respectively. The total average values appear as black crosses in the boxplot along with the averages for male (yellow dots) and female (red dots) subjects. According to t-tests, the results for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

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  Figure 2. Synchronization matrix. Phase synchronization indices \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}γ according to Eq. (5) between all pairs of respiration proxies (see Table 1) and the flow have been averaged over the complete sleeping period and all 223 subjects. They are presented in a symmetrical color-coded matrix with brown indicating full synchronization and white indicating no synchronization—see color bar on the right.

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  Figure 3. Best synchronization with flow during nocturnal hours. For each respiration proxy (see Table 1), this matrix shows the average phase synchronization index \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}γ with respect to the flow signal (see color bar on the bottom) during the considered nocturnal hour.

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  Figure 4. Histogram of best achievable proxy synchronization. The histograms show the numbers of 30 s segments of the total data (all 223 subjects) for which a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}γ value in the particular interval (0.0 to 0.1, 0.1 to 0.2, etc.) could be achieved taking into account all proxies (green), only acceleration-derived proxies (orange), and only ECG-derived proxies (blue).

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  Figure 5. Boxplot of average difference of respiratory rate. The differences of respiratory rates calculated from each respiration proxy and the measured flow signal has been averaged over all 30 s segments and all 223 subjects. The boxes and markers correspond to those in Fig. 1. Note that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}φ yielded a slightly lower respiratory rate (negative difference) than the other acceleration-derived proxies. The results regarding the ECG-derived proxies B1, B2, and B5 were also lower. Differences between males and females were not significant.

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  Figure 6. Acceleration recording at the wrist. The photo shows the placement of the SOMNOwatch plus device (Somnomedics GmbH, Randersacker, Germany) at the wrist with the coordinate axes (x, y, and z; yellow) according to the device’s orientation as well as the gravity acceleration vector (red) pointing vertically upwards from the center of the earth. The device measures the three components of the gravity acceleration with respect to its coordinate axes. From this data the two orientational angles, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vartheta $$\end{document}ϑ = angle between x axis and gravity acceleration and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}φ = angle between y axis and projection of the gravity acceleration into the \documentclass[12pt]{minimal} \usepackage{amsmath}…

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  Figure 7. Proxy data and reconstructed respiratory phases. (a) Respiration proxies determined from the averages of maximum and minimum of each QRS complex (proxy B1, green) and smoothened lateral y axis acceleration \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {Acc}}_y$$\end{document}Accy (red) recorded at the subjects wrist during sleep. For comparison, the respiratory flow recorded by a separate sensor placed at the subject’s nose is also shown (blue). The vertical line at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=30 \hbox {s}$$\end{document}t=30s marks the window size we have used for our comparisons. (b) Corresponding respiratory phases \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…