Modeling of beam customization devices in the pencil-beam splitting algorithm for heavy charged particle radiotherapy

A broad-beam-delivery system for radiotherapy with protons or ions often employs multiple collimators and a range-compensating filter, which offer complex and potentially useful beam customization. It is however difficult for conventional pencil-beam algorithms to deal with fine structures of these devices due to beam-size growth during transport. This study aims to avoid the difficulty with a novel computational model. The pencil beams are initially defined at the range-compensating filter with angular-acceptance correction for upstream collimation followed by stopping and scattering. They are individually transported with possible splitting near the aperture edge of a downstream collimator to form a sharp field edge. The dose distribution for a carbon-ion beam was calculated and compared with existing experimental data. The penumbra sizes of various collimator edges agreed between them to a submillimeter level. This beam-customization model will be used in the greater framework of the pencil-beam-splitting algorithm for accurate and efficient patient dose calculation

Dose calculation algorithm of fast fine-heterogeneity correction for heavy charged particle radiotherapy

This work addresses computing techniques for dose calculations in treatment planning with proton and ion beams, based on an efficient kernel-convolution method referred to as grid-dose spreading (GDS) and accurate heterogeneity correction method referred to as Gaussian beam splitting. The original GDS algorithm suffered from distortion of dose distribution for beams tilted with respect to the dose-grid axes. Use of intermediate grids normal to the beam field has solved the beam-tilting distortion. Interplay of arrangement between beams and grids was found as another intrinsic source of artifact. Inclusion of rectangular-kernel convolution in beam transport, to share the beam contribution among the nearest grids in a regulatory manner, has solved the interplay problem. This algorithmic framework was applied to a tilted protonpencil beam and a broad carbon-ion beam. In these cases, while the elementary pencil beams individually split into several tens, the calculation time increased only by several times with the GDS algorithm. The GDS and beam-splitting methods will complementarily enable accurate and efficient dose calculations for radiotherapy with protons and ions

Semi-empirical formulation of multiple scattering for Gaussian beam model of heavy charged particles stopping in tissue-like matter

Dose calculation for radiotherapy with protons and heavier ions deals with a large volume of path integrals involving a scattering power of body tissue. This work provides a simple model for such demanding applications. There is an approximate linearity between RMS end-point displacement and range of incident particles in water, empirically found in measurements and detailed calculations. This fact was translated into a simple linear formula, from which the scattering power that is only inversely proportional to residual range was derived. The simplicity enabled analytical formulation for ions stopping in water, which was designed to be equivalent with the extended Highland model and agreed with measurements within 2% or 0.02 cm in RMS displacement. The simplicity will also improve the efficiency of numerical path integrals in the presence of heterogeneity.Comment: 6 pages, 3 figures, submitted to Physics in Medicine and Biolog

Biological dose representation for carbon-ion radiotherapy of unconventional fractionation

In carbon-ion radiotherapy, single-beam delivery each day in alternate directions has been common practice for effcient operation, taking advantage of the Bragg peak and the relative biological effectiveness (RBE) for uniform dose conformation to a tumor. Treatments are usually fractionated and treatment plans are evaluated with the total RBE-weighted dose; however, this is of limited relevance to the biological effect. In this study, we reformulate the biologically effective dose (BED) to normalize the dose-fractionation and cell-repopulation effects as well as the RBE of treating radiation, based on inactivation of a reference cell line by a reference carbon-ion radiation. The BED distribution virtually represents the biological effect of a treatment regardless of radiation modality or fractionation scheme. We applied the BED formulation to simplistic model treatments and to a preclinical survey for hypofractionation based on an actual prostate cancer treatment with carbon ions. The proposed formulation was demonstrated to be practical and to give theoretical implications. For a prostate cancer treatment in 12 fractions, the distributions of BED and of RBE-weighted dose were very similar. With hypofractionation, while the RBE-weighted dose distribution varied signifcantly, the BED distribution was nearly invariant, implying that carbon-ion radiotherapy would be effectively insensitive to fractionation. However, treatment evaluation with such a simplistic biological dose is intrinsically limited and must be complemented in practice by clinical experience and biological experiments

The grid-dose-spreading algorithm for dose distribution calculation in heavy charged particle radiotherapy

A new variant of the pencil-beam (PB) algorithm for dose distribution calculation for radiotherapy with protons and heavier ions, the grid-dose spreading (GDS) algorithm, is proposed. The GDS algorithm is intrinsically faster than conventional PB algorithms due to approximations in convolution integral, where physical calculations are decoupled from simple grid-to-grid energy transfer. It was effortlessly implemented to a carbon-ion radiotherapy treatment planning system to enable realistic beam blurring in the field, which was absent with the broad-beam (BB) algorithm. For a typical prostate treatment, the slowing factor of the GDS algorithm relative to the BB algorithm was 1.4, which is a great improvement over the conventional PB algorithms with a typical slowing factor of several tens. The GDS algorithm is mathematically equivalent to the PB algorithm for horizontal and vertical coplanar beams commonly used in carbon-ion radiotherapy while dose deformation within the size of the pristine spread occurs for angled beams, which was within 3 mm for a single proton pencil beam of $30^\circ$ incidence, and needs to be assessed against the clinical requirements and tolerances in practical situations.Comment: 7 pages, 3 figure

Modeling of body tissues for Monte Carlo simulation of radiotherapy treatments planned with conventional x-ray CT systems

In the conventional procedure for accurate Monte Carlo simulation of radiotherapy, a CT number given to each pixel of a patient image is directly converted to mass density and elemental composition using their respective functions that have been calibrated speci cally for the relevant x-ray CT system. We propose an alternative approach that is a conversion in two steps: the rst from CT number to density and the second from density to composition. Based on the latest compilation of standard tissues for reference adult male and female phantoms, we sorted the standard tissues into groups by mass density and de ned the representative tissues by averaging the material properties per group. With these representative tissues, we formulated polyline relations between mass density and each of the following; electron density, stopping-power ratio and elemental densities. We also revised a procedure of stoichiometric calibration for CT-number conversion and demonstrated the two-step conversion method for a theoretically emulated CT system with hypothetical 80 keV photons. For the standard tissues, high correlation was generally observed between mass density and the other densities excluding those of C and O for the light spongiosa tissues between 1.0 g cm−3 and 1.1 g cm−3 occupying 1% of the human body mass. The polylines tted to the dominant tissues were generally consistent with similar formulations in the literature. The two-step conversion procedure was demonstrated to be practical and will potentially facilitate Monte Carlo simulation for treatment planning and for retrospective analysis of treatment plans with little impact on the management of planning CT systems