Ebook: Transient Processes in Cell Proliferation Kinetics

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.

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This research monograph on the theory of unsteady cell kinetics based on stochastic and semi-stochastic models sets out to fill a gap in the literature. Specifically, considering the effect of transient processes in cell proliferation kinetics reveals new possible applications of the mathematical methods and also new regularity features of systems with induced cell proliferation. Thus for instance, a comprehensive analysis of the transition of hepatocytes to DNA synthesis and mitosis in regenerating rat liver is presented. Addressed primarily to researchers concerned with cell/tissue kinetics, the book can also be used by students knowing basic probability, as an introduction to the mathematics of cell proliferation kinetics.

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This research monograph on the theory of unsteady cell kinetics based on stochastic and semi-stochastic models sets out to fill a gap in the literature. Specifically, considering the effect of transient processes in cell proliferation kinetics reveals new possible applications of the mathematical methods and also new regularity features of systems with induced cell proliferation. Thus for instance, a comprehensive analysis of the transition of hepatocytes to DNA synthesis and mitosis in regenerating rat liver is presented. Addressed primarily to researchers concerned with cell/tissue kinetics, the book can also be used by students knowing basic probability, as an introduction to the mathematics of cell proliferation kinetics.
Content:
Front Matter....Pages I-VI
Introduction....Pages 1-12
Some Points of the Theory of Branching Stochastic Processes....Pages 13-36
Induced Cell Proliferation Kinetics within the Framework of a Branching Process Model....Pages 37-83
Semistochastic Models of Cell Population Kinetics....Pages 84-136
The Fraction Labelled Mitoses Curve in Different States of Cell Proliferation Kinetics....Pages 137-175
Applications of Kinetic Analysis. Rat Liver Regeneration....Pages 176-207
Conclusion....Pages 208-212
Back Matter....Pages 213-220

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This research monograph on the theory of unsteady cell kinetics based on stochastic and semi-stochastic models sets out to fill a gap in the literature. Specifically, considering the effect of transient processes in cell proliferation kinetics reveals new possible applications of the mathematical methods and also new regularity features of systems with induced cell proliferation. Thus for instance, a comprehensive analysis of the transition of hepatocytes to DNA synthesis and mitosis in regenerating rat liver is presented. Addressed primarily to researchers concerned with cell/tissue kinetics, the book can also be used by students knowing basic probability, as an introduction to the mathematics of cell proliferation kinetics.
Content:
Front Matter....Pages I-VI
Introduction....Pages 1-12
Some Points of the Theory of Branching Stochastic Processes....Pages 13-36
Induced Cell Proliferation Kinetics within the Framework of a Branching Process Model....Pages 37-83
Semistochastic Models of Cell Population Kinetics....Pages 84-136
The Fraction Labelled Mitoses Curve in Different States of Cell Proliferation Kinetics....Pages 137-175
Applications of Kinetic Analysis. Rat Liver Regeneration....Pages 176-207
Conclusion....Pages 208-212
Back Matter....Pages 213-220
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