A new model for evaluating pressure-induced vascular tone in small cerebral arteries

Figures

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  Fig. 1. Chemical sub-model represented as signalling network. The symbols \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\leftarrow }$$\end{document}← and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vdash$$\end{document}⊢ represent activation and inhibition processes, respectively. The symbol \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\star$$\end{document}⋆ indicates that the dynamics of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi _5$$\end{document}ξ5 is…

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  Fig. 2. Logistic functions of the signalling network depicted in Fig. 1. The associated coefficients (obtained through optimization of the chemical sub-model parameters) are reported in Table 1

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  Fig. 3. Chemical model fitting - pMLCP and pLC20. The experimental data are reported as mean value ± standard deviation. The reported pMLCP values are normalized with respect to their control case at 10 mmHg. The experimental measurements of pMLCP and pLC20 under 3.0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μM GF in Johnson et al. (2009) were reported with respect to the 100 mmHg control case. Here, these values were re-scaled with respect to the reference control values. The standard deviations were re-calculated accordingly (by assuming that the quantities are independent variables)

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  Fig. 4. Chemical model fitting - pHSP27, pCofilin and G-actin. The experimental data are reported as mean value ± standard deviation. All the reported values are normalized with respect to their control case at 10 mmHg. In the 3.0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μM GF case, pHSP27 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi _2$$\end{document}ξ2) was set equal to 0.1 across the whole pressure range to simulate the drug effect

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  Fig. 5. Mechanical model fitting for vessels group 1 under control, extracellular Ca2+ removal and 0.3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μM H1152 conditions. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_o$$\end{document}Do is the outer diameter in the deformed configuration. The experimental data are reported as mean value ± standard deviation

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  Fig. 6. Mechanical model validation for vessels group 2 under control, extracellular Ca2+ removal and 3.0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μM GF conditions. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_o$$\end{document}Do is the outer diameter in the deformed configuration. The experimental data are reported as mean value ± standard deviation

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  Fig. 7. Simulation results - role of luminal pressure on normalized relative filament sliding for vessels group 1 and group 2

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  Fig. 8. Simulation results—role of luminal pressure on total CU stiffness and actin cortex stiffness. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{k}_{\text {tCU}}$$\end{document}k¯tCU is the total CU stiffness normalized with respect to the corresponding control value. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{k}_{\text {AC}}$$\end{document}k¯AC is the actin cortex stiffness normalized with respect to the corresponding control value

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  Fig. 9. Dependency of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{\text {d}}\bar{u}_{\text {fs}}}{{\text {d}}t}$$\end{document}du¯fsdt on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{u}_{\text {fs}}$$\end{document}u¯fs across the pressure range 10–120 mmHg. For each pressure level, intersection of the associated curve with the horizontal dashed line indicates a steady-state solution