Assessment of Fractional-Order Arterial Windkessel as a Model of Aortic Input Impedance

Fig. 1.. Distribution and summary statistic (mean and standard deviation values) of: (a) mean blood pressure (MBP) in (mmHg), (b) pulse pressure (PP) in (mmHg), (c) diastolic pressure (DP) in (mmHg) and systolic pressure (SP) in (mmHg) at the level of of ascending aorta for the in-silico database.

Fig. 2.. A flowchart outlining the framework of the proposed FWK2 model calibration and comparison with the standard Windkessel models (WK2, WK3, and VWK).

Fig. 3.. Distribution, mean value and standard deviation of the FWK2 parameter estimates: (a) the fractional differentiation order parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\alpha$\end{document}, (b) the pseudo-compliance \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\tau _\alpha$\end{document}, and (c) the peripheral resistance (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$R_p$\end{document}).

Fig. 4.. Examples of the validation of the in-silico impedance modulus and phases using the proposed model (FWK2) along with the standard Windkessel models (WK2, WK3, and VWK). The first and second rows represents, respectively, the blood flow (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$Q_a$\end{document}) and pressure (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$P_a$\end{document}) at the level of the ascending aorta for three different virtual subjects. The approximated impedance modulus and phase angles, along with the in-silico one, are depicted in the below figures.

Fig. 5.. Scatter plots of the arterial compliance modulus’ estimates, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\mathrm{|C_F(\omega _h)|}$\end{document}, obtained at the heart pulsation, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\mathrm{\omega _h}$\end{document}, versus the corresponding estimates of: (a) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\mathrm{C_{W2}}$\end{document} the arterial compliance based WK2 model. Linear regression yielded the line: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs}…