Lineal energy and radiation quality in radiation therapy: model calculations and comparison with experiment

Microdosimetry is a recommended method for characterizing radiation quality in situations when the biological effectiveness under test is not well known. In such situations, the radiation beams are described by their lineal energy probability distributions. Results from radiobiological investigations in the beams are then used to establish response functions that relate the lineal energy to the relative biological effectiveness (RBE). In this paper we present the influence of the size of the simulated volume on the relation to the clinical RBE values (or weighting factors). A single event probability distribution of the lineal energy is approximated by its dose average lineal energy ((y) over bar (D)) which can be measured or calculated for volumes from a few micrometres down to a few nanometres. The clinical RBE values were approximated as the ratio of the alpha-values derived from the LQ-relation. Model calculations are presented and discussed for the SOBP of a C-12 ion (290 MeV u(-1)) and the reference Co-60 gamma therapy beam. Results were compared with those for a conventional x-ray therapy beam, a 290 MeV proton beam and a neutron therapy beam. It is concluded that for a simulated volume of about 10 nm, the alpha-ratio increases approximately linearly with the (y) over bar (D)-ratio for all the investigated beams. The correlation between y and alpha provides the evidence to characterize a radiation therapy beam by the lineal energy when, for instance, weighting factors are to be estimated.