Abstract
To show that some deficiencies arisen can occur as result of owing to the stochastic processes/effects (SP/Es) in areas of ionizing radiations have not been probabilistically treated nor modeled, because they use exponential functions (EFs) derived from unnecessary differential equations (DEs) or unnecessary definition; and 2) to discuss some statistical models project (SMp) proposals of new probabilistic functions (PFs) that have probabilistic foundations, and will overcome the quoted problems.The following results were obtained: 1) Determination of deficiencies due to use of EFs in evaluations of the following SP/Es: cell survival attenuation of radiation, radioactive decay and radioactivity; and 2) The SMp formulations for these SP/Es.The previous SP/Es have not been probabilistically treated nor modelled, since they use EFs that are non-PFs, and some of them are derived from unnecessary solutions of DEs or unnecessary definition. These differential equations used in the derivations do not represent physic properties of the SP/Es, but are simply a mathematic property of the EFs modelling their respective SP/Es. The SMp proposes PFs that will be able to model SP/Es with simple and homogeneous functions using the three types of SP/Es. The SMp models will represent new PFs, where the probability of a random variable X is expressed as PX = p(y), instead of x; and the stochastic region is limited by two 0% and/or 100%-deterministic regions. The SMp treats the radioactivity as a SP/E SMp type P2, and considers there is no need of its current definition.
Highlights
It is very important to understand that, far, except the probabilistic treatments of the tumor control probability and normal tissue complication probability, many stochastic processes/effects (SP/Es) in the areas of ionizing radiations have neither been probabilistically treated nor modeled by other researchers, which has led to the following deficiencies: a) Use of a heterogeneous group of complex-deficient or improper models and complex-mathematic parameters; and b) some SP/Es have not been called with probabilistic names
Despite cell survival (S), radioactive decay, attenuation of radiation, and radioactivity being recognized as SP/Es, these have not been appropriately modeled with probabilistic functions (PFs)
The cell kill probability (CKP) will represent the mean quantity of cells that will be killed divided by total number of cells when same volumes of tissues are independently irradiated with a dose d in various experiments, while cell sub-lethal damage probability (CSLDP) and undamaged cells probability (UCP) will be associated respectively to sub-lethal damaged and undamaged cells
Summary
It is very important to understand that, far, except the probabilistic treatments of the tumor control probability and normal tissue complication probability (respectively TCP and NTCP), many stochastic processes/effects (SP/Es) in the areas of ionizing radiations have neither been probabilistically treated nor modeled by other researchers, which has led to the following deficiencies: a) Use of a heterogeneous group of complex-deficient or improper models and complex-mathematic parameters; and b) some SP/Es have not been called with probabilistic names. Despite cell survival (S), radioactive decay, attenuation of radiation, and radioactivity being recognized as SP/Es, these have not been appropriately modeled with probabilistic functions (PFs). Nowadays, these SP/Es have been modeled with non-PFs that have some similarities with PFs. Exponential functions are used for modeling these SP/Es. Except the S, the others were derived from unnecessary-mathematic procedures; while the derivation of the radioactivity required an unnecessary definition. P1: For values of the independent variable < a threshold value (TV) the process is 0%-deterministic, i.e. it will never occur. The SMp models are PFs capable of describing many SP/Es, which allows simplifying, being more accurate, unifying the treatments and models, and avoiding the current heterogeneous groups of metrics and models based on non-PFs
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
