Compartmental Analysis in Biology and Medicine, 3rd Edition

by John A. Jacquez

“The strengths of Jacquez’s classic books on compartmental analysis are the clear, accessible exposition of the theoretical fundamentals, and his emphasis on matters of practical importance, including experimental design, parameter identifiability, and parameter estimation….With this update, Compartmental Analysis in Biology and Medicine remains the single best reference for both students and researchers.”

Leon C. Moore, The Quarterly Review of Biology June 1998, 73:2; 255

The mathematical theory of compartmental systems is of major importance: it is the bread-and-butter of analysis for medical researchers, pharmacokineticists, physiologists, ecologists as well as other researchers. The second edition of this standard reference, published in 1985, greatly expanded the basic material in the first, 1972, edition. This third edition is a thoroughly up-to-date and comprehensive development of the theory and its application. No other book currently available presents such a broad and exhaustive coverage of compartmental analysis.

There are extensive changes from the second edition. The basic theory of linear and nonlinear deterministic compartmental systems has been greatly extended, as has the material on tracer kinetics. The theory of compartmental systems with lags is much more advanced. The book includes a new and relatively complete theory of stochastic compartmental systems with linear and nonlinear rate laws, which are the stochastic analogs of linear and nonlinear deterministic compartmental systems.

The chapters on identifiability and optimal sampling theory have been expanded and, for pharmacokinetictists, there is now a complete chapter on population distributions of parameters.

New applications to analysis of channel kinetics, epidemiological models, fluorescence depolarization, models for calculation of evolutionary distance and control of gene expression are included.

Finally, appendices provide catalogs of solutions of 1-3 compartment systems and identifiability of parameters for many types of experiments on 1-3 compartment systems.

Table of Contents

Chapters

1. Compartmental Systems
2. Compartmental Systems: General Theory
3. Linear Compartmental Systems with Constant Coefficients
4. Linear Compartmental Systems with Periodic Coefficients
5. Nonlinear Compartmental Systems
6. Isotopes and Tracer Kinetics
7. Residence Times: Exit and Transit Times
8. Systems with Time Lags
9. Flow Systems: Aging
10. Flow Systems: Exchange in Capillary Beds
11. Modeling and Modeling systems
12. Stochastic Compartmental Systems: Linear Rate Laws
13. Stochastic Compartmental Systems: Nonlinear Rate Laws
14. Stochastic Process in Basically Deterministic Compartmental Systems
15. Identifiability and Model Distinguishability
16. Parameter Estimation and Optimal Sampling Times
17. Population Distribution of Parameters
18. New Applications

Appendices

1. Catalog of Solutions of Some One to Three Compartment Systems
2. Catalog of Identifiability of Parameters to One to Three Compartment Systems
3. Answers to Exercises