Track structure in radiation biology: theory and applications

Purpose: A brief review is presented of the basic concepts in track structure and the relative merit of various theoretical approaches adopted in Monte-Carlo track-structure codes are examined. In the second part of the paper, a formal cluster analysis is introduced to calculate cluster-distance distributions. Method: Total experimental ionization cross-sections were least-square fitted and compared with the calculation by various theoretical methods. Monte-Carlo track-structure code Kurbuc was used to examine and compare the spectrum of the secondary electrons generated by using functions given by Born-Bethe, Jain-Khare, Gryzinsky, Kim-Rudd, Mott and Vriens' theories. The cluster analysis in track structure was carried out using the k-means method and Hartigan algorithm. Results: Data are presented on experimental and calculated total ionization cross-sections: inverse mean free path (IMFP) as a function of electron energy used in Monte-Carlo track-structure codes; the spectrum of secondary electrons generated by different functions for 500 eV primary electrons; cluster analysis for 4 MeV and 20 MeV alpha-particles in terms of the frequency of total cluster energy to the root-mean-square (rms) radius of the cluster and differential distance distributions for a pair of clusters; and finally relative frequency distribution for energy deposited in DNA, single-strand break and double-strand breaks for 10 MeV/u protons, alpha-particles and carbon ions. Conclusions: There are a number of Monte-Carlo track-structure codes that have been developed independently and the benchmarking presented in this paper allows a better choice of the theoretical method adopted in a track-structure code to be made. A systematic bench-marking of cross-sections and spectra of the secondary electrons shows differences between the codes at atomic level, but such differences are not significant in biophysical modelling at the macromolecular level. Clustered-damage evaluation shows: that a substantial proportion of dose (similar to 30%) is deposited by low-energy electrons; the majority of DNA damage lesions are of simple type; the complexity of damage increases with increased LET, while the total yield of strand breaks remains constant; and at high LET values nearly 70% of all double-strand breaks are of complex type.