eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2017-11-10 5 4 119 124 10.12691/ajams-5-4-2 AJAMS2017542 article Terman Frometa-Castillo terman.frometa@gmail.com 1 Oncology Hospital of Santiago of Cuba, 6134 N Oakley Ave Unit 2, Chicago, 60659, IL, USA 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. http://pubs.sciepub.com/ajams/5/4/2/ajams-5-4-2.pdf BED LQ model stochastic effects cell survival