A theoretical model for event statistics in microdosimetry. I: Uniform distribution of heavy ion tracks

The microdosimetry of boron neutron capture therapy in a randomised ellipsoidal cell geometry

Two reactions deliver the majority of local dose in boron neutron capture therapy. The ionised particles (protons, alpha particles and lithium nuclei) produced in the two reactions, 10B(n,alpha,gamma)7Li and 14N(n,p)14O, have short ranges that are less than -14 microm (which is on the order of the diameter of a typical human cell). The ionised particles are heavy and are in the 2+ charge state in the case of the boron reactions. These heavy 2+ ions will do significant damage to molecules near their tracks. Thus, the distribution of nitrogen and, in particular, of boron determines the spatial characteristics of the radiation field. Since the distribution of nitrogen is nearly homogeneous in the brain and is not easily altered for the purpose of radiotherapy, the spatial variation in the radiation dose is due mainly to the spatial distribution of boron. This implies that the spatial distribution of boron determines the microscopic energy deposition and therefore the spatial characteristics of the microscopic dose. The microscopic dose from the (n,alpha) and (n,p) reactions has been examined in detail and, as averred, the proton dose is relatively homogeneous except for statistical variability. The statistical variability in essence adds a false spatial variability that would not be seen if a large number of histories were performed. Since the majority of spatial variability occurs in the boron distribution, the (n,p) reaction can be suppressed to better understand the spatial distribution effects on the microscopic dose. Programs have been written in FORTRAN using Monte Carlo techniques to model ellipsoidal cells that are either randomly sized and located in the region of interest or are arranged in a face centred cubic array and are identical except for the location of the nuclei, which may be random. It is shown that closely packed prolate ellipsoidal cells with a large eccentricity in one dimension will receive a larger nuclear dose than cells that are more sparsely packed. This demonstrates that the boron content of a cell and its nucleus can have a significant impact upon the dose to neighbouring cells. The local boron distribution in a region of interest can be shown to affect the macrodosimetric dose, with possible implications for clinical outcomes.

The Microdosimetry of the10B Reaction in Boron Neutron Capture Therapy: A New Generalized Theory

The microdosimetry of (10)B thermal neutron capture reactions should be considered as an essential step to be followed before studying the radiobiological aspects of boron neutron capture therapy. The boron dose itself is insufficient as the only quantity used to describe the biological effectiveness of the (10)B reaction for two important reasons: the specific microdistribution that the (10)B carrier compound exhibits at the cellular level and the primarily stochastic nature of the energy deposition process, which influences the biological response to the particulate radiation. In this work, these two aspects are analyzed in detail and an innovative rigorous analytical framework is developed in the microdosimetry domain. This formalism provides the necessary microdosimetric tools for more precisely describing the (10)B dose distribution deposited in sensitive microscopic structures and offers improved approaches for analyzing the biological dose--effect relationship of (10)B reactions.

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 surface-distributed).