289+xxvii pp. $18.50 George W. Swan, ,Some Current Mathematical Topics in Cancer Research (1977) .
✍ Scribed by Robert Rosen
- Book ID
- 104272320
- Publisher
- Springer
- Year
- 1979
- Tongue
- English
- Weight
- 69 KB
- Volume
- 41
- Category
- Article
- ISSN
- 1522-9602
No coin nor oath required. For personal study only.
✦ Synopsis
The volume under review represents a heroic eflort to organize and evaluate the chaotic literature bearing on modelling approaches to the origins, growth, diagnosis, and control of malignancy, primarily in man. The book has 15 chapters, together with an introduction, a chapter on conclusions and discussion, and a most valuable 50-page bibliography.
More than half the book (8 chapters) is devoted to models of kinetics of tumor cell populations, either in themselves, or in relation to other cell populations (particularly those of the immune system). Various approaches are reviewed: continuous time, discrete-time, deterministic and stochastic, in various permutations and combinations. There is necessarily a heavy overlap between these approaches and similar procedures which have been developed in mathematical ecology; indeed, the models of Bell and his co-workers, treated in Chapter 12, are variants of the Lotka-Volterra predator-prey models. The age structure of tumor cell populations treated in earlier chapters derives m large part from the Leslie. matrix approach of the ecologist.
Somewhat surprisingly, only three chapters are devoted to the analysis of individual cells. Chapter 6 is concerned with mathematical models of the cell cycle in normal and neoplastic cells. Chapter 8 is mainly concerned with stimulation studies of linked systems of catalyzed reactions as found in cells, and their response to various kinds of perturbations. Somewhat surprisingly, there is no credit given here to the pioneering studies of Heinmets, on whose work the models which are discussed are based. In Chapter 13, this kind of analysis is pursued from a more qualitative point of view; bifurcation studies and their implications are briefly developed, as exemplified by a series of papers by Okan Gurel.
The remaining chapters are devoted to diagnosis and therapy. Chapter 7 is concerned with chemotherapy and radiation therapy of cancer as problems in optimal control, including dynamic programming approaches. A rather poignant chapter (Chapter 11) contains less than 100 words; it deals with endocrine therapy, and points out that although endocrine therapy is one of the most widely used therapies for malignancy, and oilers numerous advantages over other procedures, there is apparently no mathematical analysis available anywhere in the literature. This is a clear challenge to all those interested in medical applications of mathematical biology. The final chapters contain discussions of thermal aspects of tumors and thermography, and of chronobiological aspects.
The text is eminently readable, and the level of the presentation is quite high. Indeed, it is .somewhat disconcerting to see the pith of a model lucidly presented in a few hundred words in this book, when the original author's paper runs to a score of pages or more. In all, Dr. Swan has done the biomedical community a'n extraordinary service in preparing his book, and it is warmly recommended to all those interested in the analysis of malignancy.