Mathematical Modeling of Pharmacokinetic Data

by David W.A. Bourne, Ph.D.

Technomic Publishing Company
851 New Holland Avenue, Box 3535
Lancaster, PA 17604
(717) 291-5609
(800) 233-9936

Technomic Publishing AG
Missionsstrasse 44
CH-4055 Basel, Switzerland

Library of Congress Catalog Card No. 94-61269
ISBN No. 1-56676-204-9

Table of Contents (139 pages)

1 Why Model the Data

1.1 Condense the Data 1.2 Exploring Mechanisms 1.3 Making Predictions

2 General Approach

2.1 General Method 2.2 Error in Y Alone 2.3 Parameter Adjustments

3 Pharmacokinetic Models

3.1 Compartmental Models 3.2 Physiologically Based Models 3.3 Pharmacodynamic Models

4 Simulation of Data

4.1 Explicit Equations 4.2 Implicit Equations 4.3 Differential Equations 4.4 Integration using Laplace Transforms 4.5 Numerical Integration of Differential Equations

5 Initial Estimates

5.1 Graphical Methods 5.2 Linear Regression 5.3 Curve Stripping 5.4 Area Under the Curve Estimation 5.5 Deconvolution

6 Nonlinear Regression

6.1 Grid Search Method 6.2 Steepest Descent Method 6.3 Gauss-Newton Methods 6.4 Simplex Method 6.5 Local Minima

7 Weighting Schemes

7.1 Equal Weight 7.2 Variance Model 7.3 Iteratively Reweighted Least Squares 7.4 Extended Least Squares 7.5 Bayesian Methods 7.6 Analysis of Population Data

8 Evaluation of Program Output

8.1 Tabular Output 8.2 Graphical Output 8.3 Statistical Output

9 Experimental Design

9.1 Pilot Study 9.2 Identifiability - Sampling Sites 9.3 Optimal Sampling - Sampling Times 9.4 Model Testing