Monitoring blood potassium concentration in hemodialysis patients by quantifying T-wave morphology dynamics

Figures

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  Figure 1. Diagram of the study protocol: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_0$$\end{document}h0 to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_5$$\end{document}h5 are the time points (in minutes) for blood sample extraction. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_4$$\end{document}h4 is taken at the end of the HD (minute 215-th or 245-th, depending on the HD duration).

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  Figure 2. Analysis stages performed in this study. In panel (a) is the flow chart showing the ECG processing steps for T-wave time-warping markers extraction. The analysis starts with the original ECG, followed by a filtering step before spatial PCA analysis, to conclude with markers computation. Panel (b) shows an example of the linear and nonlinear time-warping markers for the same patient as in Fig. 5a. In particular, subpanel (i) shows both the reference (blue) and the i-th MWTW (red) while subpanel (ii) shows the warping function (red dotted line) that optimally relates the reference and studied MWTWs. Subpanel (iii) shows the MWTWs after warping and subpanel (iv) are the normalized reference and warped MWTWs.

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  Figure 3. Scatterplot showing the values of both \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_w$$\end{document}dw panel (a) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{d}}_{w,c}$$\end{document}d^w,c panel (b) with respect to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta RR$$\end{document}ΔRR for a given patient in PCA approach. Spearman’s correlation coefficients (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho$$\end{document}ρ) and p-values…

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  Figure 4. Boxplots showing the distribution of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta [K^{+}]$$\end{document}Δ[K+] (blue) and all the described PCA-based time-warping biomarkers (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{w}^{u}$$\end{document}dwu, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_a$$\end{document}da, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_w^{\mathrm{NL}}$$\end{document}dwNL, \documentclass[12pt]{minimal}…

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  Figure 5. PCA-based time-warping markers and RR interval time trends. An example for a given patient undergoing 4h-long HD therapy, is depicted in panel (a) with the evolution of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{w}$$\end{document}dw (filled green squares), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{d}}_{w,c}$$\end{document}d^w,c (filled orange squares), both referring to the left vertical scale, and the average RR intervals (unfilled dark red squares, referring to the right vertical scale). \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta [K^{+}]$$\end{document}Δ[K+] relative variations with respect to the concentration…