A factor VII-based method for the prediction of anticoagulant response to warfarin

Figures

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  Figure 1. The 4-step workflow to predict tSS,INR and INRSS. Dref is the typical dose that would yield this value of INR (i.e. sensitivity of the patient to warfarin), INRSS the steady-state INR, SIVII the sensitivity index of INR to factor VII, and tSS,INR the time to reach steady-state INR.

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  Figure 2. The left hand panels show the time course of INR, factors II, VII, and X, and SIVII following initiation of 4 mg warfarin daily predicted from the QSP model. The right-hand panels show the corresponding derivative plots with respect to time for INR, and factors II, VII and X, and SIVII. SIVII refers to the sensitivity index of INR to factor VII. Note the units of the factor concentrations are % of change from baseline.

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  Figure 3. Approximating SIVII using the ratio of INR-to-factor VII. The solid line is the model prediction from a one-parameter linear model (Equation 8) with slope, q = 0.233 and the filled circles are the data vectors for SIVII and INR-to-factor VII ratio that were simulated from the coagulation network model. SIVII is the sensitivity index of INR to factor VII. The units of factor VII here are % of change from baseline and INR is dimensionless.

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  Figure 4. Model fits of the dose-dependent general logistic function for the time course of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{dS{I}_{VII}}{dt}$$\end{document}dSIVIIdt. The solid lines are the predictions from the empirical logistic function (Equation 11) and the filled circles are the data vectors for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{dS{I}_{VII}}{dt}$$\end{document}dSIVIIdt that were simulated from the QSP coagulation network model. Data beyond the model predictions are omitted from the figure. SIVII is the sensitivity index of INR to factor VII.

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  Figure 5. Model fits of the general quadratic function for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{dINR}{dt}$$\end{document}dINRdt versus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{dS{I}_{VII}}{dt}$$\end{document}dSIVIIdt data. The solid lines are the prediction from the empirical quadratic model (Equation 14) and the filled circles are the data that were simulated from the QSP coagulation network model. Data beyond the model predictions are omitted from the figure. SIVII is the sensitivity index of INR to factor VII.

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  Figure 6. Prediction algorithm of tSS,INR, INRSS, and D. ai defines the dose-dependency of h, bi the dose-dependency of g, ci the dose-dependency of k, D is the warfarin daily dose, Dref the typical dose that would yield this value of INR (sensitivity of the patient to warfarin), g the horizontal shift of the logistic function modelling the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{dS{I}_{VII}}{dt}$$\end{document}dSIVIIdt time course, h the upper horizontal asymptote of the logistic function modelling the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{dS{I}_{VII}}{dt}$$\end{document}dSIVIIdt time course, INRSS the steady-state INR, INR0 the INR at baseline, si defines the dose-dependency of m, k and m are the coefficient of the quadratic function modelling \documentclass[12pt]{minimal} \usepackage{amsmath}…

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  Figure 7. tSS,INR is dose-dependent based on simulations from the QSP coagulation network model27. tSS,INR is the time to reach steady-state INR. The vertical lines represent the minimum value of time where the change in INR over time is within a predefined tolerance.