Journal: Journal of Pharmacokinetics and Pharmacodynamics

Article Title: Exact solutions and equi-dosing regimen regions for multi-dose pharmacokinetics models with transit compartments

doi: 10.1007/s10928-020-09719-8

Figure Lengend Snippet: Run time (desktop PC, Intel(R) Core(TM) i5-9400, 2.9GHz) and value for different implementations of the lower incomplete gamma function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma (n,t)$$\end{document} γ ( n , t ) in MATLAB. The methods include (i) use of built-in function gammainc, (ii) numerical evaluation of the integral in using integral command, (iii) hard-coding the sum in the final term of for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1, \ldots , 10$$\end{document} n = 1 , … , 10 , (iv) use of MATLAB’s Symbolic Toolbox to expand the sum, (v) use of built-in functions gammaln and gamcdf for log-gamma and cumulative distribution functions for the calculation in . A typical result is shown, taking \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=2$$\end{document} t = 2 . Similar results are seen for a range of t values. The average evaluation time in seconds is found using MATLAB’s timeit command. a Evaluation times for different methods, for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1, \ldots , 10$$\end{document} n = 1 , … , 10 . b Evaluation times for different methods, for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1, \ldots , 40$$\end{document} n = 1 , … , 40 . c Computed values for different methods, for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1, \ldots , 10$$\end{document} n = 1 , … , 10 . d Computed values for different methods, for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1, \ldots , 40$$\end{document} n = 1 , … , 40

Article Snippet: Our preferred method for evaluating the lower incomplete gamma function is using the built-in function gammainc in MATLAB, which computes the normalised function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\displaystyle {P(n,t)=\frac{\gamma (n,t)}{\varGamma (n)}}$$\end{document} P ( n , t ) = γ ( n , t ) Γ ( n ) .

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