A Mathematical Approach to Aspects of Linear Energy Transfer (LET), Micro-and Nano-dosimetry in Radiation Therapy with Photons and Protons

Select Volume / Issue:

• Volume 6,Issue 5, Sept. 2018

Year:

2018

Type of Publication:

Article

Keywords:

LET, Micro-and Nano-Dosimetry, Nonlinear Reaction and Diffusion, Repair, Survival Functions

Authors:

W. Ulmer

Journal:

IJISM

Volume:

6

Number:

5

Pages:

150-159

Month:

September

ISSN:

2347-9051

Abstract:

The radiation effects induced by Co60 serve as a reference system for the consideration of LET and RBE (relative biological activity) in normal and tumor tissue dose-effect relations are usually handled by the linear-quadratic model (LQ) of the survival fraction S with the parameters α and β, i.e. S = exp(-α•D-β•D2). This approximation excellently works up to the shoulder domain. In particle therapy we have strictly differ between RBE in the initial plateau and environment of the Bragg peak. Thus for protons LET and RBE of the initial plateau agree with Co60, whereas in the Bragg peak domain both properties are increased, but RBE of SOBP (spread out Bragg peak) only varies between 1.1 and 1.17. The RBE of carbon ions is increased once again. Their dose-effect curves are much steeper with a rather small shoulder domain due to dense ionizing radiation effect. Thus protons are also dense ionizing in the Bragg peak region, but their magnitude is rather smaller compare to carbon ions. A generalization of the LQ-model based on the nonlinear reaction-diffusion model is proposed to describe LET and RBE of dense ionizing particles, which accounts for properties of micro- and nano-dosimettry. A linear term of a reaction diffusion formula describes the destroy of cells, the nonlinear term is related to repair, and the diffusion term accounts for the density of the radiation damages. Based on dose-effect properties of Co60 the parameters of dense ionizing particles can be determined and compared with measurement data. The local dense of radiation effects and their consequences in RBE and dose effect curves provide a key of understanding modern therapy planning with different modalities and properties of nano-dosimetry are interpreted by mathematical descriptions. The irradiation of spheroids is a feature of micro-dosimetry, whereas intracellular exposure refers to nano-dosimetry.

Full text: IJISM_776_FINAL.pdf [Bibtex]