Biomaterial Database

Nonlinear least-squares regression analysis by a simplex method using differential equations containing Michaelis-Menten type rate constants. 1989

K Murata, and K Kohno

Products Formulation Research Laboratory, Tanabe Seiyaku Co., Ltd, Osaka, Japan.

Computer curve fittings were carried out to observed data as well as theoretically generated plasma concentrations of several drugs, using differential equations which contained nonlinear Michaelis-Menten type rate constants to discuss problems of initial parameter estimation in pharmacokinetic analysis. Calculation based on two different algorithms, each carried out by using SIMP (simplex method) and NONLIN (modified Gauss-Newton method) produced similar results. However, occasional divergence or unreasonable solutions occurred in a later case, when assumed values of Km and Vmax were used as initial parameters. A combined use of SIMP and NONLIN in which calculated values by SIMP were used as initial values for NONLIN, was shown to be effective to analyse plasma concentration data of indocyanine green bearing difficulty in estimating initial values. It is suggested that the successive method is useful for the curve fitting of plasma concentration with nonlinear pharmacokinetic rate processes.

UI	MeSH Term	Description	Entries
D010599	Pharmacokinetics	Dynamic and kinetic mechanisms of exogenous chemical DRUG LIBERATION; ABSORPTION; BIOLOGICAL TRANSPORT; TISSUE DISTRIBUTION; BIOTRANSFORMATION; elimination; and DRUG TOXICITY as a function of dosage, and rate of METABOLISM. LADMER, ADME and ADMET are abbreviations for liberation, absorption, distribution, metabolism, elimination, and toxicology.	ADME,ADME-Tox,ADMET,Absorption, Distribution, Metabolism, Elimination, and Toxicology,Absorption, Distribution, Metabolism, and Elimination,Drug Kinetics,Kinetics, Drug,LADMER,Liberation, Absorption, Distribution, Metabolism, Elimination, and Response
D012044	Regression Analysis	Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see LINEAR MODELS) the relationship is constrained to be a straight line and LEAST-SQUARES ANALYSIS is used to determine the best fit. In logistic regression (see LOGISTIC MODELS) the dependent variable is qualitative rather than continuously variable and LIKELIHOOD FUNCTIONS are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable.	Regression Diagnostics,Statistical Regression,Analysis, Regression,Analyses, Regression,Diagnostics, Regression,Regression Analyses,Regression, Statistical,Regressions, Statistical,Statistical Regressions
D015233	Models, Statistical	Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.	Probabilistic Models,Statistical Models,Two-Parameter Models,Model, Statistical,Models, Binomial,Models, Polynomial,Statistical Model,Binomial Model,Binomial Models,Model, Binomial,Model, Polynomial,Model, Probabilistic,Model, Two-Parameter,Models, Probabilistic,Models, Two-Parameter,Polynomial Model,Polynomial Models,Probabilistic Model,Two Parameter Models,Two-Parameter Model