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This work is dedicated to Wassiliy Leontief's concepts of
Input-Output Analysis and to the algebraic properties of Piero
Sraffa's seminal models described consequently by matrix algebra
and the Perron-Frobenius Theorem. Detailed examples and visualizing
graphs are presented for applications of various mathematical
methods.
During the last 30 years, many chemical compounds that are active
against tumors have been discovered or developed. At the same time,
new methods of testing drugs for cancer therapy have evolved.
nefore 1964, drug testing on animal tumors was directed to
observation of the incfease in life span of the host after a single
dose. A new approach, in which the effects of multiple doses on the
proliferation kinetics of the tumor in vivo as well as of cell
lines in vitro are investigated, has been outlined by Skipper and
his co-workers in a series of papers beginning in 1964 (Skipper,
Schabel and Wilcox, 1964 and 1965). They also investigated the
influence of the time schedule in the treatment of experimental
tumors. Since the publication of those studies, cell population
kinetics cannot be left out of any discussion of the rational basis
of chemotherapy. When clinical oncologists began to apply cell
kinetic concepts in practice about 15 years ago, the theoretical
basis was still very poor, in spite of Skipper's progress, and the
lack of re levant cytokinetic and pharmacologic data was apparent.
Subsequently, much theoretical work has been done and many cell
kinetic models have been elaborated (for a review see Eisen,
1977)."
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