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Compartmental Modeling and Tracer Kinetics

  • Book
  • © 1983

Overview

Authors:
  1. David H. Anderson

    1. Department of Mathematics, Southern Methodist University, Dallas, USA

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Part of the book series: Lecture Notes in Biomathematics (LNBM, volume 50)

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Table of contents (27 chapters)

  1. Front Matter

    Pages I-VII
    Download chapter PDF

  2. Compartmental Systems

    • David H. Anderson
    Pages 1-6

  3. Elementary Compartmental Models

    • David H. Anderson
    Pages 7-12

  4. First-order Chemical Reactions

    • David H. Anderson
    Pages 13-14

  5. Environmental Studies

    • David H. Anderson
    Pages 15-21

  6. Nonlinear Compartmental Models

    • David H. Anderson
    Pages 22-29

  7. The General Compartmental Model

    • David H. Anderson
    Pages 30-32

  8. Tracer Kinetics in Steady State Systems

    • David H. Anderson
    Pages 33-38

  9. Uptake of Potassium by Red Blood Cells

    • David H. Anderson
    Pages 39-42

  10. Standard Types of Tracer Experiments

    • David H. Anderson
    Pages 43-44

  11. Analytical Solution of the Tracer Model

    • David H. Anderson
    Pages 45-49

  12. System Structure and Connectivity

    • David H. Anderson
    Pages 50-54

  13. System Eigenvalues and Stability

    • David H. Anderson
    Pages 55-68

  14. The Inverse of a Compartmental Matrix

    • David H. Anderson
    Pages 69-78

  15. Mean Times and the Inverse Matrix

    • David H. Anderson
    Pages 79-89

  16. Solution of the Steady State Problem for SEC Systems

    • David H. Anderson
    Pages 90-98

  17. Structural Identification of the Model

    • David H. Anderson
    Pages 99-119

  18. Necessary and Sufficient Conditions for Identifiability

    • David H. Anderson
    Pages 120-125

  19. A Simple Test for Nonidentifiability

    • David H. Anderson
    Pages 126-145

  20. Computation of the Model Parameters

    • David H. Anderson
    Pages 146-156
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Keywords

About this book

This monograph is concerned with mathematical aspects of compartmental an­ alysis. In particular, linear models are closely analyzed since they are fully justifiable as an investigative tool in tracer experiments. The objective of the monograph is to bring the reader up to date on some of the current mathematical prob­ lems of interest in compartmental analysis. This is accomplished by reviewing mathematical developments in the literature, especially over the last 10-15 years, and by presenting some new thoughts and directions for future mathematical research. These notes started as a series of lectures that I gave while visiting with the Division of Applied ~1athematics, Brown University, 1979, and have developed in­ to this collection of articles aimed at the reader with a beginning graduate level background in mathematics. The text can be used as a self-paced reading course. With this in mind, exercises have been appropriately placed throughout the notes. As an aid in reading the material, the e~d of a proof is indicated by ~. Sub­ section titles are utilized to make it easier for the reader to skim over detailed material on a first reading and make the entire manuscript somewhat more accessible, especially to nonmathematicians in the biosciences. The preparation of this monograph has been a long task that would not have been completed without the influence of a number of individuals. I am especially indebted to H. T. Banks, J. W. Drane, J. Eisenfe1d, J. A. Jacquez, D. J.

Authors and Affiliations

  • Department of Mathematics, Southern Methodist University, Dallas, USA

    David H. Anderson

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