A theoretical model for event statistics in microdosimetry. II: Nonuniform distribution of heavy ion tracks

A microdosimetry model, described in Part I, applies to the case of a convex site immersed in a uniform distribution of heavy particle tracks, and assumes no restrictions in site geometry or the kind of randomness. In Part II, this model is extended to include nonuniform distributions of particle tracks. This situation is relevant to the study of microdosimetry, for example, in boron neutron capture, in irradiation experiments using heavy ion particle beams, where the sources of particle tracks are external to the cell, or in irradiation from internally incorporated particle-emitting radionuclides, such as environmental radon or occupational exposure to radioactive materials. The formalism developed permits the calculation of statistical properties, track length distributions, and microdosimetric spectra for convex sites where the "inner" and "outer" concentrations of sources may be different, or for tracks originating on the surface of a convex site. Expressions applicable to the case of surface-distributed sources of tracks are presented that may represent situations such as boron compounds bound to the membrane of a cellular nucleus in boron neutron capture. A series of Monte Carlo calculations and analytical solutions, illustrating the case of spherical site geometry, are presented and compared. Finally, microdosimetric spectra and specific energy averages are calculated for alpha and lithium particles originating from thermal neutron capture in 10B, showing their dependence on 10B localization (extra-site, uniform, intra-site, or surfacedistributed).