Computational Pharmacokinetics
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Summary
Being that pharmacokinetics (PK) is the study of how the body handles various substances, it is not surprising that PK plays an important role in the early development of new drugs. However, the clinical research community widely believes that mathematics in some way blurs the true meaning of PK. Demonstrating that quite the opposite is true, Computational Pharmacokinetics outlines the fundamental concepts and models of PK from a mathematical perspective based on clinically relevant parameters.
After an introductory chapter, the book presents a noncompartmental approach to PK and discusses the numerical analysis of PK data, including a description of an absorption process through numerical deconvolution. The author then builds a simple physiological model to better understand PK volumes and compares this model to other methods. The book also introduces compartmental models, discusses their limitations, and creates a general-purpose type of model. The final chapter looks at the relationship between drug concentration and effect, known as PK/pharmacodynamics (PD) modeling.
With both a solid discussion of theory and the use of practical examples, this book will enable readers to thoroughly grasp the computational factors of PK modeling.
Table of Contents
INTRODUCTION
Goal with this book
A short course in pharmacokinetics
Overview of book disposition
Integrals and convolution
Linear kinetics and compartments
Markov processes and compartmental models
EMPIRICAL PHARMACOKINETICS
Problem specification and some notations
Distribution and elimination
Absorption
Multiple dosing
One compartment drugs with capacity limited elimination
A recirculation model
NUMERICAL METHODS FOR PK PARAMETER ESTIMATION
Introduction
Estimating the terminal elimination rate
Integral estimation
Numerical deconvolution
Population average vs. subject-specific approach
A real example
Pharmacokinetics in drug development
PHYSIOLOGICAL ASPECTS ON PHARMACOKINETICS
Some physiological preliminaries
Distribution volume
Events within an organ
Building a physiological PK model
Absorption from the intestines
An alternative liver model
MODELING THE DISTRIBUTION PROCESS
The peripheral space
Two-compartment models
Three-compartment models
A general model for distribution and elimination
Example: Distribution analysis of budesonide and fluticasone
The distribution model and the recirculation model
PK/PD MODELING
Therapeutic response
Modeling a simple agonist
Modeling an antagonist
Hysteresis and approaches to PD/PK modeling
Four types of turn-over models
Modeling considerations
REFERENCES
APPENDIX A: LINEAR ORDINARY DIFFERENTIAL EQUATIONS
Linear differential equations
Explicit formulas for 2-by-2 systems
APPENDIX B: KEY NOTATIONS
INDEX
Editorial Reviews
"I was not disappointed . . . I highly recommend this book to anyone who wants to learn about mathematical models for characterizing pharmacokinetics and pharmacodynamics."
– Gary L. Rosner, University of Texas M.D. Anderson Cancer Center, in JASA, March 2009
"Overall, the book provides a good introduction to some of the problems in the area of PK modelling to which statistical methods are now being routinely applied."
– David Woods, University of Southampton, in Journal of the Royal Statistical Society
