Aspects of linear energy transfer (LET) and relative biological effectiveness (RBE) in radiation therapy with positively charged particles and the role of electron capture

Abstract

In radiotherapy, dose-effect relations induced by Co60 serve as a reference of the LET and RBE in normal and tumor tissue, which are usually handled by the linear-quadratic model S (LQ) with the parameters α and β, i.e. S = exp (-α·D-β·D2), working excellently up to the shoulder domain. In particle therapy, we have strictly to 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. Protons are also dense ionizing in the Bragg peak region, but their magnitude is rather smaller compared to carbon ions. A generalization of the LQ-model based on the nonlinear reaction-diffusion model is proposed to include LET and RBE of dense ionizing particles, which accounts for intra-cellular properties, too. The linear term of the reaction diffusion formula describes destroy of cells, the nonlinear term is related to repair. 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. However, a rigorously theoretical access starting with neglect of energy straggling and lateral scatter must account for electron capture of positively charged particles. By mathematical descriptions local dense of radiation effects and their consequences in dose-effect curves are interpreted providing a key to understanding modern therapy planning with different modalities and properties of intracellular processes.