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Purpose: This is a theoretical simulation study for proof of concept of radiochromic film dosimetry to measure physical and biological doses without plan-based quenching correction for patient-specific quality assurance of carbon-ion radiotherapy. Methods: We took a layer-stacking carbon-ion beam comprised of range-shifted beamlets. The dosimeter response was simulated according to an experimental quenching model. The beam model followed a treatment planning system. The beam was decomposed into finely arranged beamlets with weights estimated by deconvolution of longitudinal dosimeter responses. The distributions of physical and biological doses were reconstructed from the estimated weights, and were compared with the plan. We also evaluated the sensitivity to measurement errors and to erratic delivery with an undelivered beamlet. Results: The reconstructed physical and biological doses accurately reproduced the simulated delivery with errors approximately corresponding to the measurement errors. The erratic beam delivery was easily detectable by comparison of biological dose distribution to the plan. Conclusions: We have developed a method to measure physical and biological doses by longitudinal dosimetry of quenched response without using plan data. The method only involves a general optimization algorithm, a radiobiology model, and experimental beamlet data, and requires no extra corrections. Theoretically, this approach is applicable to various dosimeters and to proton and ion beams of any delivery method, regardless of quenching or biological effectiveness.

The pencil-beam model is valid only when elementary Gaussian beams are small enough with respect to lateral heterogeneity of a medium, which is not always the case in heavy charged particle radiotherapy. This work addresses a solution for this problem by applying our discovery of self-similar nature of Gaussian distributions. In this method, Gaussian beams split into narrower and deflecting daughter beams when their size has exceeded the lateral heterogeneity limit. They will be automatically arranged with modulated areal density for accurate and efficient dose calculations. The effectiveness was assessed in an carbon-ion beam experiment in presence of steep range compensation, where the splitting calculation reproduced the detour effect of imperfect compensation amounting up to about 10% or as large as the lateral particle disequilibrium effect. The efficiency was analyzed in calculations for carbon-ion and proton radiations with a heterogeneous phantom model, where the splitting calculations took about a minute and were factor of 5 slower than the non-splitting ones. The beam-splitting method is reasonably accurate, efficient, and general so that it can be potentially used in various pencil-beam algorithms., Comment: 13 pages, 8 figures, 3 tables

A model for beam customization with collimators and a range-compensating filter based on the phase-space theory for beam transport is presented for dose distribution calculation in treatment planning of radiotherapy with protons and heavier ions. Independent handling of pencil beams in conventional pencil-beam algorithms causes unphysical collimator-height dependence in the middle of large fields, which is resolved by the framework comprised of generation, transport, collimation, regeneration, range-compensation, and edge-sharpening processes with a matrix of pencil beams. The model was verified to be consistent with measurement and analytic estimation at a submillimeter level in penumbra of individual collimators with a combinational-collimated carbon-ion beam. The model computation is fast, accurate, and readily applicable to pencil-beam algorithms in treatment planning with capability of combinational collimation to make best use of the beam-customization devices., Comment: 16 pages, 5 figures

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 figures