Transient Processes in Cell Proliferation Kinetics

  • Andrej Yu. Yakovlev
  • Nikolaj M. Yanev

Part of the Lecture Notes in Biomathematics book series (LNBM, volume 82)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Andrej Yu. Yakovlev, Nikolaj M. Yanev
    Pages 1-12
  3. Andrej Yu. Yakovlev, Nikolaj M. Yanev
    Pages 13-36
  4. Andrej Yu. Yakovlev, Nikolaj M. Yanev
    Pages 84-136
  5. Andrej Yu. Yakovlev, Nikolaj M. Yanev
    Pages 176-207
  6. Andrej Yu. Yakovlev, Nikolaj M. Yanev
    Pages 208-212
  7. Back Matter
    Pages 213-220

About this book

Introduction

A mathematician who has taken the romantic decision to devote himself to biology will doubtlessly look upon cell kinetics as the most simple and natural field of application for his knowledge and skills. Indeed, the thesaurus he is to master is not so complicated as, say, in molecular biology, the structural elements of the system, i. e. ceils, have been segregated by Nature itself, simple considerations of balance may be used for deducing basic equations, and numerous analogies in other areas of science also superficial add to one"s confidence. Generally speaking, this number of impression is correct, as evidenced by the very great theoretical studies on population kinetics, unmatched in other branches of mathematical biology. This, however, does not mean that mathematical theory of cell systems has traversed in its development a pathway free of difficulties or errors. The seeming ease of formalizing the phenomena of cell kinetics not infrequently led to the appearance of mathematical models lacking in adequacy or effectiveness from the viewpoint of applications. As in any other domain of science, mathematical theory of cell systems has its own intrinsic logic of development which, however, depends in large measure on the progress in experimental biology. Thus, during a fairly long period running into decades activities in that sphere were centered on devising its own specific approaches necessitated by new objectives in the experimental in vivo and in vitro investigation of cell population kinetics in different tissues.

Keywords

Branching process Galton-Watson process dynamics kinetics mathematics stochastic processes

Authors and affiliations

  • Andrej Yu. Yakovlev
    • 1
  • Nikolaj M. Yanev
    • 2
  1. 1.Leningrad Polytechnical InstituteLeningradUSSR
  2. 2.Institute of MathematicsBulgarian Academy of SciencesSofiaBulgaria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-48702-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-51831-0
  • Online ISBN 978-3-642-48702-6
  • Series Print ISSN 0341-633X
  • About this book