A theoretical model for the microdosimetry of discontinuous distributions of heavy particle tracks

A novel approach to solving microdosimetry problems using conditional probabilities and geometric concepts has been developed. This approach is valid for cases where a convex site is immersed in uniform or discontinuous distributions of heavy charged particle tracks and assumes no restrictions in site geometry or the kind of randomness. These conditions are relevant to the study of microdosimetry in applications such as neutron capture therapy (NCT), irradiation experiments using heavy ion particle beams, environmental radon, or occupational exposure to radioactive materials. Expressions applicable to the case of surface-distributed sources of tracks are presented that may represent situations such as NCT, where boron compounds are bound to the membranes of cellular nuclei. Microdosimetric spectra, specific energy averages, and mean number of 10B capture reactions for cell inactivation are calculated, showing their dependence on 10B localisation.