Detection and categorization of severe cardiac disorders based solely on heart period measurements

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  Figure 1. Cardiac disorders plotted against Hr, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Cv$$\end{document}log10Cv, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Lv$$\end{document}log10Lv. Each dot represents the average of 10-minute statistics for a single subject over 18 hours. Vertical axes are the logarithm of (a) premature ventricular contraction (PVC); (b) premature atrial contraction (PAC); and (c) atrial fibrillation (AF). Values of the Pearson correlation r are indicated above. Yellow zones represent regions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$>0.1$$\end{document}>0.1.

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  Figure 2. The true positive rate (TPR), true negative rate (TNR), and the Matthews correlation coefficient (MCC) measuring the ability of two individual metrics, thresholds of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Cv$$\end{document}log10Cv and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Lv$$\end{document}log10Lv, to detect cardiac disorders: (a) PVC, (b) PAC, and (c) AF. For each cardiac disorder, each subject was categorized into positive or negative, according to whether the ratio of anomalous states identified by an automatic detection algorithm of ECG was higher or lower than 10%. TPR and TNR indicate the probability of each person being positive and negative according to whether the metric Cv or Lv is higher and lower than a given value, respectively. MCC measures a balance between true and…

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  Figure 3. Different cardiac disorders plotted on a plane spanned by the new and old metrics \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Lv$$\end{document}log10Lv and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Cv$$\end{document}log10Cv. (a) Dots represent 1,017 subjects, who were diagnosed as atrial fibrillation (AF), premature ventricular contraction (PVC), premature atrial contraction (PAC), and negative, respectively colored in magenta, blue, and green, and black. The prediction zone for each cardiac disorders, given by the set of constraints \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Lv >…

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  Figure 4. The MCCs for Cv and Lv, and the combination method based on datasets with various recording durations: 1 minute, 10 minutes, 1 hour, and 18 hours. (a) PVC, (b) PAC, and (c) AF. The MCCs for the shorter recording durations are represented with the mean and standard deviation.

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  Figure 5. Two metrics \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Lv$$\end{document}log10Lv and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Cv$$\end{document}log10Cv computed from shorter recording periods. (a), (b), and (c) Datasets of 1 minute, 10 minutes, and 1 hour, plotted on a plane spanned by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Lv$$\end{document}log10Lv and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10}…

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  Figure 6. The MCCs for the combination method applied to recording duration of 1 minute and 18 hours. (a) PVC, (b) PAC, and (c) AF. Original pulse times were jittered with Gaussian noises of the standard deviation of 10, 50, 100, 200, and 500 ms.

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  Figure 7. Noisy datasets of different cardiac disorders plotted on a plane spanned by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Lv$$\end{document}log10Lv and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Cv$$\end{document}log10Cv. (a), (b), and (c): Datasets were obtained by jittering original pulse times with Gaussian noises of the standard deviation of 10 ms, 50 ms, and 100 ms. The parameters a and b of each prediction zone were adapted to respective noisy datasets.

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  Figure 8. Two metrics \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Lv$$\end{document}log10Lv and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} Cv$$\end{document}log10Cv computed for three kinds of MIT-BIH databases. (a), (b), (c), and (d): Datasets of 1 minute, 10 minutes, 1 hour, and 18 hours plotted on a plane spanned by the two metrics. The parameters a and b of the prediction zone (magenta) for the AF cases were adapted to respective datasets.

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  Figure 9. Synthetic pulse sequences and the computed values of the coefficient of variation Cv, the local variation Lv, and the local-global variation ratio Lg. (a) Pulsation is locally regular while the rate is slowly modulated from low to high and then back to low. (b) Pulsation is irregular, although the average rate is nearly constant. (c) Long and short RR intervals alternate with each other. Cv has the same value for (a) and (b), which are composed of identical sets of RR intervals, whereas Lv is small for (a), in which the RR intervals are well organized, and is large for (b), in which RR intervals are arranged randomly. Lg is very small for (a), in which the rate is slowly modulated. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Lg \approx 3/2$$\end{document}Lg≈3/2 for (b), in which RR intervals are randomly arranged. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…