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Register a new userBiological dose representation for carbon-ion radiotherapy of unconventional fractionation
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Added by
Nobuyuki Kanematsu Ph.D.
Publication date
2016
fields
Physics
and research's language is
English
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In carbon-ion radiotherapy, single-beam delivery each day in alternate directions has been commonly practiced for operational efficiency, taking advantage of the Bragg peak and the relative biological effectiveness (RBE) for uniform dose conformation to a tumor. The treatment plans are usually evaluated with total RBE-weighted dose, which is however deficient in relevance to the biological effect in the linear-quadratic model due to its quadratic-dose term, or the dose-fractionation effect. In this study, we reformulate the extrapolated response dose (ERD), or synonymously BED, which normalizes the dose-fractionation and cell-repopulation effects as well as the RBE of treating radiation, based on inactivation of a single model cell system and a typical treating radiation in carbon-ion RT. The ERD distribution virtually represents the biological effect of the treatment regardless of radiation modality or fractionation scheme. We applied the ERD formulation to simplistic model treatments and to a preclinical survey for hypofractionation based on an actual prostate-cancer treatment of carbon-ion radiotherapy. The proposed formulation was demonstrated to be practical and to offer theoretical implications. In the prostate-cancer case, the ERD distribution was very similar to the RBE-weighted-dose distribution of the actual treatment in 12 fractions. With hypofractionation, while the RBE-weighted-dose distribution varied significantly, the ERD distribution was nearly invariant, implying that the carbon-ion radiotherapy would be insensitive to fractionation. However, treatment evaluation with simplistic biological dose is intrinsically limited and must be complemented in practice somehow by clinical experiences and biology experiments.
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item[Purpose] A recent study revealed that polyethylene (PE) would cause extra carbon-ion attenuation per range shift by 0.45%/cm due to compositional differences in nuclear interactions. The present study aims to assess the influence of PE range compensators on tumor dose in carbon-ion radiotherapy. item[Methods] Carbon-ion radiation was modeled to be composed of primary carbon ions and secondary particles, for each of which the dose and the relative biological effectiveness (RBE) were estimated at a tumor depth in the middle of spread-out Bragg peak. Assuming exponential behavior for attenuation and yield of these components with depth, the PE effect on dose was calculated for clinical carbon-ion beams and was partly tested by experiment. The two-component model was integrated into a treatment-planning system and the PE effect was estimated in two clinical cases. item[Results] The attenuation per range shift by PE was 0.1%--0.3%/cm in dose and 0.2%--0.4%/cm in RBE-weighted dose, depending on energy and range-modulation width. This translates into reduction of RBE-weighted dose by up to 3% in extreme cases. In the treatment-planning study, however, the effect on RBE-weighted dose to tumor was typically within 1% reduction. item[Conclusions] The extra attenuation of primary carbon ions in PE was partly compensated by increased secondary particles for tumor dose. In practical situations, the PE range compensators would normally cause only marginal errors as compared to intrinsic uncertainties in treatment planning, patient setup, beam delivery, and clinical response.
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.
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.
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 proton pencil 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.
Purpose: Beam range control is the essence of radiotherapy with heavy charged particles. In conventional broad-beam delivery, fine range adjustment is achieved by insertion of range shifting and compensating materials. In dosimetry, solid phantoms are often used for convenience. These materials should ideally be equivalent to water. In this study, we evaluated dosimetric water equivalence of four common plastics, HDPE, PMMA, PET, and POM. Methods: Using the Bethe formula for energy loss, the Gottschalk formula for multiple scattering, and the Sihver formula for nuclear interactions, we calculated the effective densities of the plastics for these interactions. We experimentally measured variation of the Bragg peak of carbon-ion beams by insertion of HDPE, PMMA, and POM, which were compared with analytical model calculations. Results: The theoretical calculation resulted in slightly reduced multiple scattering and severely increased nuclear interactions for HDPE, compared to water and the other plastics. The increase in attenuation of carbon ions for 20-cm range shift was experimentally measured to be 8.9% for HDPE, 2.5% for PMMA, and 0.0% for POM while PET was theoretically estimated to be in between PMMA and POM. The agreement between the measurements and the calculations was about 1% or better. Conclusions: For carbon-ion beams, POM was dosimetrically indistinguishable from water and the best of the plastics examined in this study. The poorest was HDPE, which would reduce the Bragg peak by 0.45% per 1-cm range shift, although with marginal superiority for reduced multiple scattering. Between the two clear plastics, PET would be superior to PMMA in dosimetric water equivalence.
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