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IndLin accuracy and speed without and with the stopping rule compared with the reference solution ode45

Journal: Journal of Pharmacokinetics and Pharmacodynamics

Article Title: Exploring Inductive Linearization for simulation and estimation with an application to the Michaelis–Menten model

doi: 10.1007/s10928-022-09813-z

Figure Lengend Snippet: IndLin accuracy and speed without and with the stopping rule compared with the reference solution ode45

Article Snippet: This will be compared with a reference numerical ODE solver ( ode45 , MATLAB, with Absolute Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-6$$\end{document} 1 e - 6 and Relative Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-3$$\end{document} 1 e - 3 for all examples in this work).

Techniques:

Comparison of the IndLin accuracy ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{ss}=0.1$$\end{document} ss = 0.1 , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{ss}=0.01$$\end{document} ss = 0.01 , and adaptive ss using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{\alpha }=0.01$$\end{document} α = 0.01 ) with ode45 for simulation

Journal: Journal of Pharmacokinetics and Pharmacodynamics

Article Title: Exploring Inductive Linearization for simulation and estimation with an application to the Michaelis–Menten model

doi: 10.1007/s10928-022-09813-z

Figure Lengend Snippet: Comparison of the IndLin accuracy ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{ss}=0.1$$\end{document} ss = 0.1 , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{ss}=0.01$$\end{document} ss = 0.01 , and adaptive ss using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{\alpha }=0.01$$\end{document} α = 0.01 ) with ode45 for simulation

Article Snippet: This will be compared with a reference numerical ODE solver ( ode45 , MATLAB, with Absolute Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-6$$\end{document} 1 e - 6 and Relative Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-3$$\end{document} 1 e - 3 for all examples in this work).

Techniques: Comparison

Concentration–time profile for simulated data by typical profile from MATLAB ode45 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma =0.1$$\end{document} σ = 0.1

Journal: Journal of Pharmacokinetics and Pharmacodynamics

Article Title: Exploring Inductive Linearization for simulation and estimation with an application to the Michaelis–Menten model

doi: 10.1007/s10928-022-09813-z

Figure Lengend Snippet: Concentration–time profile for simulated data by typical profile from MATLAB ode45 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma =0.1$$\end{document} σ = 0.1

Article Snippet: This will be compared with a reference numerical ODE solver ( ode45 , MATLAB, with Absolute Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-6$$\end{document} 1 e - 6 and Relative Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-3$$\end{document} 1 e - 3 for all examples in this work).

Techniques: Concentration Assay

Comparison of parameter estimates and speed for IndLin and ode45

Journal: Journal of Pharmacokinetics and Pharmacodynamics

Article Title: Exploring Inductive Linearization for simulation and estimation with an application to the Michaelis–Menten model

doi: 10.1007/s10928-022-09813-z

Figure Lengend Snippet: Comparison of parameter estimates and speed for IndLin and ode45

Article Snippet: This will be compared with a reference numerical ODE solver ( ode45 , MATLAB, with Absolute Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-6$$\end{document} 1 e - 6 and Relative Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-3$$\end{document} 1 e - 3 for all examples in this work).

Techniques: Comparison

Comparison of relative difference of estimated parameters from their nominal simulation values (%) for a ode45, b IndLin (ss = 0.1), c IndLin (ss = 0.01) and d IndLin (adaptive step size, α = 0.01)

Journal: Journal of Pharmacokinetics and Pharmacodynamics

Article Title: Exploring Inductive Linearization for simulation and estimation with an application to the Michaelis–Menten model

doi: 10.1007/s10928-022-09813-z

Figure Lengend Snippet: Comparison of relative difference of estimated parameters from their nominal simulation values (%) for a ode45, b IndLin (ss = 0.1), c IndLin (ss = 0.01) and d IndLin (adaptive step size, α = 0.01)

Article Snippet: This will be compared with a reference numerical ODE solver ( ode45 , MATLAB, with Absolute Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-6$$\end{document} 1 e - 6 and Relative Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-3$$\end{document} 1 e - 3 for all examples in this work).

Techniques: Comparison

Comparison of speed (seconds) among ode45, IndLin ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ss=0.1$$\end{document} s s = 0.1 ), IndLin ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ss=0.01$$\end{document} s s = 0.01 ) and IndLin (adaptive step size, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0.01$$\end{document} α = 0.01 ) ( a in linear scale and b in log scale)

Journal: Journal of Pharmacokinetics and Pharmacodynamics

Article Title: Exploring Inductive Linearization for simulation and estimation with an application to the Michaelis–Menten model

doi: 10.1007/s10928-022-09813-z

Figure Lengend Snippet: Comparison of speed (seconds) among ode45, IndLin ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ss=0.1$$\end{document} s s = 0.1 ), IndLin ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ss=0.01$$\end{document} s s = 0.01 ) and IndLin (adaptive step size, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0.01$$\end{document} α = 0.01 ) ( a in linear scale and b in log scale)

Article Snippet: This will be compared with a reference numerical ODE solver ( ode45 , MATLAB, with Absolute Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-6$$\end{document} 1 e - 6 and Relative Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-3$$\end{document} 1 e - 3 for all examples in this work).

Techniques: Comparison

Comparison of the objective function value (OFV) among ode45, IndLin (ss = 0.1), IndLin (ss = 0.01) and IndLin (adaptive step size, α = 0.01) ( a in linear scale and b in log scale)

Journal: Journal of Pharmacokinetics and Pharmacodynamics

Article Title: Exploring Inductive Linearization for simulation and estimation with an application to the Michaelis–Menten model

doi: 10.1007/s10928-022-09813-z

Figure Lengend Snippet: Comparison of the objective function value (OFV) among ode45, IndLin (ss = 0.1), IndLin (ss = 0.01) and IndLin (adaptive step size, α = 0.01) ( a in linear scale and b in log scale)

Article Snippet: This will be compared with a reference numerical ODE solver ( ode45 , MATLAB, with Absolute Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-6$$\end{document} 1 e - 6 and Relative Tol = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1e-3$$\end{document} 1 e - 3 for all examples in this work).

Techniques: Comparison