Application of ACP Nonlinear Math in Analyzing Toxicokinetic and Pharmacokinetic Data (Application 5 and 6)

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Application of ACP Nonlinear Math in Analyzing Toxicokinetic and Pharmacokinetic Data (Application 5 and 6)

Journal Title: Advances in Clinical Toxicology - Year 2024, Vol 9, Issue 2

Abstract

Analyses of toxicokinetic and pharmacokinetic are demonstrated using the ACP (asymptotic curve based and proportionality oriented) Alpha Beta (αβ) Nonlinear Math. In the new nonlinear concepts, various skewed-bell elementary “y” data are collected, followed by analyzing the asymptotic cumulative Y curves. In using the concise data, the asymptotic cumulativenumbers are emphasized and shun the use of unrelated elementary-numbers. The kinetic results are expressed as equations and straight lines in the proportionality graphs, where the change of the response β (Y, Yu, Yb) is proportional to the change of the time or dose α(X, Xu, Xb) and assuming the mathematical form dα = Kdβ. The K is the proportionality constant or the kinetic constant. The baseline asymptote Yb is mostly a nonlinear zero thus no need of calculation, but the upper asymptote Yu can be resolved through guided estimation using the coefficient of determination (COD) and graphical resolution.

Authors and Affiliations

Lai RW and Lai-Becker MW

Keywords

Asymptotic Concave and Convex Curve; Upper and Baseline Asymptote; Demulative Numbers (Opposite to Cumulative Numbers); Coefficient of Determination (COD); Proportionality and Position Constant; Skewed Bell; Sigmoid Curve; Symbols: q = Log (Nonlinear Logarithmic); αβ (Extension of XY); ϕ = (0) (Nonlinear Zero); x = Elementary Independent Variable; y or (y) = Elementary Dependent Variable or y = Equation y (inside the graph); X = Cumulative of x Y = Cumulative of y or (y).

EP ID EP754556
DOI 10.23880/act-16000304
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