title: Analytic considerations and axiomatic approaches to the concept cell death and cell survival functions in biology and cancer treatment.
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.
authors.affiliation: Departments of Mathematics and Biomedical Physics, East Carolina University, 124 Austin Building, East Fifth Street, Greenville, NC, 27858-4353, USA, gkigkitzisi@ecu.edu.
authors.forename: Ioannis
authors.initials: I
authors.lastname: Gkigkitzis
authors.forename: Ioannis
authors.initials: I
authors.lastname: Haranas
authors.forename: Carlos
authors.initials: C
authors.lastname: Austerlitz
mesh_terms: D000465:Algorithms; D016923:Cell Death / Q000502:physiology; D002455:Cell Division / Q000502:physiology*; D002468:Cell Physiological Phenomena / Q000502:physiology*; D002470:Cell Survival / Q000502:physiology; D006801:Humans; D007700:Kinetics; D008954:Models, Biological; D009369:Neoplasms / Q000503:physiopathology*