American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2017, 5(4), 119-124
DOI: 10.12691/ajams-5-4-2
Open AccessArticle

The Statistical Models Project (SMp) for Evaluations of Biological Radiation Effects

Terman Frometa-Castillo1,

1Oncology Hospital of Santiago of Cuba, 6134 N Oakley Ave Unit 2, Chicago, 60659, IL, USA

Pub. Date: November 10, 2017

Cite this paper:
Terman Frometa-Castillo. The Statistical Models Project (SMp) for Evaluations of Biological Radiation Effects. American Journal of Applied Mathematics and Statistics. 2017; 5(4):119-124. doi: 10.12691/ajams-5-4-2

Abstract

This document provides probabilistic-mechanistic models for describing the cell kill (K) and cell sub-lethal damage (SL) for one fraction with a dose of radiation that is absorbed by a living tissue; also this provides the K and SL formalisms for fractioned irradiation regimens. These models and formalisms are based on real mean behavior of cell survival (S) - a complement of K- and strong probabilistic-radiobiological foundations. The K and SL formalisms include all possible factors affecting the biological radiation effects: dose (d), fractionations (n), SL, and the temporal factors: cell repair and cell repopulation. It is discussed some aspects about the widely used linear-quadratic (LQ) S(d) model and LQ S(n,d) formalism, and one of its derivations, the BED (biologically effective dose). The SMp K(d) parameters can be obtained from S data, or using graphical/analytical tools developed by this study. These new formalisms will be useful for simulations of treatments, and together regional damage distribution for optimizations of the treatment planning.

Keywords:
BED LQ model stochastic effects cell survival

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