Abstract
This study contains a discussion on the connection between current mathematical and biological modeling systems in response to the main research need for the development of a new mathematical theory for study of cell survival after medical treatment and cell biological behavior in general. This is a discussion of suggested future research directions and relations with interdisciplinary science. In an effort to establish the foundations for a possible framework that may be adopted to study and analyze the process of cell survival during treatment, we investigate the organic connection among an axiomatic system foundation, a predator-prey rate equation, and information theoretic signal processing. A new set theoretic approach is also introduced through the definition of cell survival units or cell survival units indicating the use of "proper classes" according to the Zermelo-Fraenkel set theory and the axiom of choice, as the mathematics appropriate for the development of biological theory of cell survival.
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