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

Implementation of simplified stochastic microdosimetric kinetic models into PHITS for application to radiation treatment planning

PURPOSE

The stochastic microdosimetric kinetic (SMK) model is one of the most sophisticated and precise models used in the estimation of the relative biological effectiveness of carbon-ion radiotherapy (CRT) and boron neutron capture therapy (BNCT). However, because of its complicated and time-consuming calculation procedures, it is nearly impractical to directly incorporate this model into a radiation treatment-planning system.

MATERIALS AND METHODS

Through the introduction of Taylor expansion (TE) or fast Fourier transform (FFT), we developed two simplified SMK models and implemented them into the Particle and Heavy Ion Transport code System (PHITS). To verify the implementation, we calculated the photon isoeffective doses in a cylindrical phantom placed in the radiation fields of passive CRT and accelerator-based BNCT.

RESULTS AND DISCUSSION

Our calculation suggested that both TE-based and FFT-based SMK models can reproduce the data obtained from the original SMK model very well for absorbed doses approximately below 5 Gy, whereas the TE-based SMK model overestimates the original data at higher doses. In terms of computational efficiency, the TE-based SMK model is much faster than the FFT-based SMK model.

CONCLUSION

This study enables the instantaneous calculation of the photo isoeffective dose for CRT and BNCT, considering their cellular-scale dose heterogeneities. Treatment-planning systems that use the improved PHITS as a dose-calculation engine are under development.

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. I: Uniform distribution of heavy ion tracks

In this work we describe a novel approach to solving microdosimetry problems using conditional probabilities and geometric concepts. The intersection of a convex site with a field of randomly oriented straight track segments is formulated in terms of the relative overlap between the chord associated with the action line of the track and the track itself. This results in a general formulation that predicts the contribution of crossers, stoppers, starters, and insiders in terms of two separate functions: the chord length distribution (characteristic of the site geometry and the type of randomness) and an independent set of conditional probabilities. A Monte Carlo code was written in order to validate the proposed approach. The code can represent the intersection between an isotropic field of charged particle tracks and a general ellipsoid of unrestricted geometry. This code was used to calculate the event distribution for a sphere as well as the expected mean value and variance of the track length distribution and to compare these against the deterministic calculations. The observed agreement was shown to be very good, within the precision of the Monte Carlo approach. The formulation is used to calculate the event frequency, lineal energy, and frequency mean specific energy for several monoenergetic and isotropic proton fields in a spherical site, as a function of the site diameter, proton energy, and the event type.