Adaptation of stochastic microdosimetric kinetic model for charged-particle therapy treatment planning

Incorporating boron distribution variations in microdosimetric kinetic model-based relative biological effectiveness calculations for boron neutron capture therapy

This study introduces the MKM_B model, an approach derived from the MKM model, designed to evaluate the biological effectiveness of Boron Neutron Capture Therapy (BNCT) in the face of challenges from varying microscopic boron distributions. The model introduces a boron compensation factor, allowing for the assessment of compound Biological Effectiveness (CBE) values for different boron distributions. Utilizing the TOPAS simulation platform, the lineal energy spectrum of particles in BNCT was simulated, and the sensitivity of the MKM_B model to parameter variations and the influence of cell size on the model were thoroughly investigated. The CBE values for 10B-boronphenylalanine (BPA) and 10B-sodium (BSH) were determined to be 3.70 and 1.75, respectively. These calculations were based on using the nucleus radius of 2.5 μm and the cell radius of 5 μm while considering a 50% surviving fraction. It was observed that as cell size decreased, the CBE values for both BPA and BSH increased. Additionally, the model parameter rd was identified as having the most significant impact on CBE, with other parameters showing moderate effects. The development of the MKM_B model enables the accurate prediction of CBE under different boron distributions in BNCT. This model offers a promising approach to optimize treatment planning by providing increased accuracy in biological effectiveness.

Dosimetric analysis of six whole-breast irradiation techniques in supine and prone positions

In breast cancer radiation therapy, minimizing radiation-related risks and toxicity is vital for improving life expectancy. Tailoring radiotherapy techniques and treatment positions can reduce radiation doses to normal organs and mitigate treatment-related toxicity. This study entailed a dosimetric comparison of six different external beam whole-breast irradiation techniques in both supine and prone positions. We selected fourteen breast cancer patients, generating six treatment plans in both positions per patient. We assessed target coverage and organs at risk (OAR) doses to evaluate the impact of treatment techniques and positions. Excess absolute risk was calculated to estimate potential secondary cancer risk in the contralateral breast, ipsilateral lung, and contralateral lung. Additionally, we analyzed the distance between the target volume and OARs (heart and ipsilateral lung) while considering the treatment position. The results indicate that prone positioning lowers lung exposure in X-ray radiotherapy. However, particle beam therapies (PBTs) significantly reduce the dose to the heart and ipsilateral lung regardless of the patient's position. Notably, negligible differences were observed between arc-delivery and static-delivery PBTs in terms of target conformity and OAR sparing. This study provides critical dosimetric evidence to facilitate informed decision-making regarding treatment techniques and positions.

Biological dose optimization incorporating intra-tumoural cellular radiosensitivity heterogeneity in ion-beam therapy treatment planning

Objective.Treatment plans of ion-beam therapy have been made under an assumption that all cancer cells within a tumour equally respond to a given radiation dose. However, an intra-tumoural cellular radiosensitivity heterogeneity clearly exists, and it may lead to an overestimation of therapeutic effects of the radiation. The purpose of this study is to develop a biological model that can incorporate the radiosensitivity heterogeneity into biological optimization for ion-beam therapy treatment planning.Approach.The radiosensitivity heterogeneity was modeled as the variability of a cell-line specific parameter in the microdosimetric kinetic model following the gamma distribution. To validate the developed intra-tumoural-radiosensitivity-heterogeneity-incorporated microdosimetric kinetic (HMK) model, a treatment plan with H-ion beams was made for a chordoma case, assuming a radiosensitivity heterogeneous region within the tumour. To investigate the effects of the radiosensitivity heterogeneity on the biological effectiveness of H-, He-, C-, O-, and Ne-ion beams, the relative biological effectiveness (RBE)-weighted dose distributions were planned for a cuboid target with the stated ion beams without considering the heterogeneity. The planned dose distributions were then recalculated by taking the heterogeneity into account.Main results. The cell survival fraction and corresponding RBE-weighted dose were formulated based on the HMK model. The first derivative of the RBE-weighted dose distribution was also derived, which is needed for fast biological optimization. For the patient plan, the biological optimization increased the dose to the radiosensitivity heterogeneous region to compensate for the heterogeneity-induced reduction in biological effectiveness of the H-ion beams. The reduction in biological effectiveness due to the heterogeneity was pronounced for low linear energy transfer (LET) beams but moderate for high-LET beams. The RBE-weighted dose in the cuboid target decreased by 7.6% for the H-ion beam, while it decreased by just 1.4% for the Ne-ion beam.Significance.Optimal treatment plans that consider intra-tumoural cellular radiosensitivity heterogeneity can be devised using the HMK model.

Effects of cellular radioresponse on therapeutic helium-, carbon-, oxygen-, and neon-ion beams: a simulation study

Objective. Helium, oxygen, and neon ions in addition to carbon ions will be used for hypofractionated multi-ion therapy to maximize the therapeutic effectiveness of charged-particle therapy. To use new ions in cancer treatments based on the dose-fractionation protocols established in carbon-ion therapy, this study examined the cell-line-specific radioresponse to therapeutic helium-, oxygen-, and neon-ion beams within wide dose ranges.Approach. Response of cells to ions was described by the stochastic microdosimetric kinetic model. First, simulations were made for the irradiation of one-field spread-out Bragg peak beams in water with helium, carbon, oxygen, and neon ions to achieve uniform survival fractions at 37%, 10%, and 1% for human salivary gland tumor (HSG) cells, the reference cell line for the Japanese relative biological effectiveness weighted dose system, within the target region defined at depths from 90 to 150 mm. The HSG cells were then replaced by other cell lines with different radioresponses to evaluate differences in the biological dose distributions of each ion beam with respect to those of carbon-ion beams.Main results. For oxygen- and neon-ion beams, the biological dose distributions within the target region were almost equivalent to those of carbon-ion beams, differing by less than 5% in most cases. In contrast, for helium-ion beams, the biological dose distributions within the target region were largely different from those of carbon-ion beams, more than 10% in several cases.Significance.From the standpoint of tumor control evaluated by the clonogenic cell survival, this study suggests that the dose-fractionation protocols established in carbon-ion therapy could be reasonably applied to oxygen- and neon-ion beams while some modifications in dose prescription would be needed when the protocols are applied to helium-ion beams. This study bridges the gap between carbon-ion therapy and hypofractionated multi-ion therapy.

Integrating microdosimetricin vitroRBE models for particle therapy into TOPAS MC using the MicrOdosimetry-based modeliNg for RBE ASsessment (MONAS) tool

Objective.In this paper, we present MONAS (MicrOdosimetry-based modelliNg for relative biological effectiveness (RBE) ASsessment) toolkit. MONAS is a TOPAS Monte Carlo extension, that combines simulations of microdosimetric distributions with radiobiological microdosimetry-based models for predicting cell survival curves and dose-dependent RBE.Approach.MONAS expands TOPAS microdosimetric extension, by including novel specific energy scorers to calculate the single- and multi-event specific energy microdosimetric distributions at different micrometer scales. These spectra are used as physical input to three different formulations of themicrodosimetric kinetic model, and to thegeneralized stochastic microdosimetric model(GSM2), to predict dose-dependent cell survival fraction and RBE. MONAS predictions are then validated against experimental microdosimetric spectra andin vitrosurvival fraction data. To show the MONAS features, we present two different applications of the code: (i) the depth-RBE curve calculation from a passively scattered proton SOBP and monoenergetic12C-ion beam by using experimentally validated spectra as physical input, and (ii) the calculation of the 3D RBE distribution on a real head and neck patient geometry treated with protons.Main results.MONAS can estimate dose-dependent RBE and cell survival curves from experimentally validated microdosimetric spectra with four clinically relevant radiobiological models. From the radiobiological characterization of a proton SOBP and12C fields, we observe the well-known trend of increasing RBE values at the distal edge of the radiation field. The 3D RBE map calculated confirmed the trend observed in the analysis of the SOBP, with the highest RBE values found in the distal edge of the target.Significance.MONAS extension offers a comprehensive microdosimetry-based framework for assessing the biological effects of particle radiation in both research and clinical environments, pushing closer the experimental physics-based description to the biological damage assessment, contributing to bridging the gap between a microdosimetric description of the radiation field and its application in proton therapy treatment with variable RBE.

Cell Survival Computation via the Generalized Stochastic Microdosimetric Model (GSM2); Part II: Numerical Results

In the present paper we numerically investigate, using Monte Carlo simulation, the theoretical results predicted by the Generalized Stochastic Microdosimetric Model (GSM2), as shown in the published companion paper. Taking advantage of the particle irradiation data ensemble (PIDE) dataset, we calculated GSM2 biological parameters of human salivary gland (HSG) and V79 cell lines. Further, exploiting the TOPAS-microdosimetric extension, we simulated the microdosimetric spectra of different radiation fields of therapeutic interest generated by four different ions (protons, helium-4, carbon-12 and oxygen-16) each at three different residual ranges. We investigated the properties of the initial damage distributions as well as the cell survival curve predicted by GSM2, focusing especially on the non-Poissonian effects naturally included in the model. GSM2 successfully computed cell survival curves, accurately describing experimental behavior even under challenging LET and dose conditions.

GPU-accelerated calculation of proton microdosimetric spectra as a function of target size, proton energy, and bounding volume size

Objective.Shortcomings of dose-averaged linear energy transfer (LETD), the quantity which is most commonly used to quantify proton relative biological effectiveness, have long been recognized. Microdosimetric spectra may overcome the limitations of LETDbut are extremely computationally demanding to calculate. A systematic library of lineal energy spectra for monoenergetic protons could enable rapid determination of microdosimetric spectra in a clinical environment. The objective of this work was to calculate and validate such a library of lineal energy spectra.Approach. SuperTrack, a GPU-accelerated CUDA/C++ based application, was developed to superimpose tracks calculated using Geant4 onto targets of interest and to compute microdosimetric spectra. Lineal energy spectra of protons with energies from 0.1 to 100 MeV were determined in spherical targets of diameters from 1 nm to 10μm and in bounding voxels with side lengths of 5μm and 3 mm.Main results.Compared to an analogous Geant4-based application, SuperTrack is up to 3500 times more computationally efficient if each track is resampled 1000 times. Dose spectra of lineal energy and dose-mean lineal energy calculated with SuperTrack were consistent with values published in the literature and with comparison to a Geant4 simulation. Using SuperTrack, we developed the largest known library of proton microdosimetric spectra as a function of primary proton energy, target size, and bounding volume size.Significance. SuperTrack greatly increases the computational efficiency of the calculation of microdosimetric spectra. The elevated lineal energy observed in a 3 mm side length bounding volume suggests that lineal energy spectra determined experimentally or computed in small bounding volumes may not be representative of the lineal energy spectra in voxels of a dose calculation grid. The library of lineal energy spectra calculated in this work could be integrated with a treatment planning system for rapid determination of lineal energy spectra in patient geometries.

Event-by-event approach to the oxygen-effect-incorporated stochastic microdosimetric kinetic model for hypofractionated multi-ion therapy

An oxygen-effect-incorporated stochastic microdosimetric kinetic (OSMK) model was previously developed to estimate the survival fraction of cells exposed to charged-particle beams with wide dose and linear energy transfer (LET) ranges under various oxygen conditions. In the model, hypoxia-induced radioresistance was formulated based on the dose-averaged radiation quality. This approximation may cause inaccuracy in the estimation of the biological effectiveness of the radiation with wide variation in energy deposited to a sensitive volume per event, such as spread-out Bragg peak (SOBP) beams. The purpose of this study was to apply an alternative approach so as to consider the energy depositions on an event-by-event basis. The production probability of radiation-induced lesions per energy was formulated with oxygen partial pressure to account for the hypoxia-induced radioresistance. The reduction in the oxygen enhancement ratio for high-LET radiations was modeled by reducing the sensitive-volume size and increasing the saturation energy in microdosimetry. The modified OSMK model was tested against the reported survival data of three cell lines exposed to six species of ions with wide dose and LET ranges under aerobic and hypoxic conditions. The model reasonably reproduced the reported cell survival data. To evaluate the event-by-event approach, survival distributions of Chinese hamster ovary cells exposed to SOBP beams were estimated using the original and modified OSMK models. The differences in the estimated survival distributions between the models were marginal even under extreme hypoxia. The event-by-event approach improved the theoretical validity of the OSMK model. However, the original OSMK model can still provide an accurate estimation of the biological effectiveness of therapeutic radiations.

Modelling the HPRT-gene mutation induction of particle beams: systematic in vitro data collection, analysis and microdosimetric kinetic model implementation

Objective. Since the early years, particle therapy treatments have been associated with concerns for late toxicities, especially secondary cancer risk (SCR). Nowadays, this concern is related to patients for whom long-term survival is expected (e.g. breast cancer, lymphoma, paediatrics). In the aim to contribute to this research, we present a dedicated statistical and modelling analysis aiming at improving our understanding of the RBE for mutation induction ( RBE M ˜ ) for different particle species. Approach. We built a new database based on a systematic collection of RBE data for mutation assays of the gene encoding for the purine salvage enzyme hypoxanthine-guanine phosphoribosyltransferase from literature (105 entries, distributed among 3 cell lines and 16 particle species). The data were employed to perform statistical and modelling analysis. For the latter, we adapted the microdosimetric kinetic model (MKM) to describe the mutagenesis in analogy to lethal lesion induction. Main results. Correlation analysis between RBE for survival (RBES) and RBE M ˜ reveals significant correlation between these two quantities (ρ = 0.86, p < 0.05). The correlation gets stronger when looking at subsets of data based on cell line and particle species. We also show that the MKM can be successfully employed to describe RBE M ˜ , obtaining comparably good agreement with the experimental data. Remarkably, to improve the agreement with experimental data the MKM requires, consistently in all the analysed cases, a reduced domain size for the description of mutation induction compared to that adopted for survival. Significance. We were able to show that RBES and RBE M ˜ are strongly related quantities. We also showed for the first time that the MKM could be successfully applied to the description of mutation induction, representing an endpoint different from the more traditional cell killing. In analogy to the RBES, RBE M ˜ can be implemented into treatment planning system evaluations.

The Mayo Clinic Florida microdosimetric kinetic model of clonogenic survival: formalism and first benchmark against in vitro and in silico data

Objective. To develop a new model (Mayo Clinic Florida microdosimetric kinetic model, MCF MKM) capable of accurately describing the in vitro clonogenic survival at low and high linear energy transfer (LET) using single-event microdosimetric spectra in a single target. Methodology. The MCF MKM is based on the ‘post-processing average’ implementation of the non-Poisson microdosimetric kinetic model and includes a novel expression to compute the particle-specific quadratic-dependence of the cell survival with respect to dose (β of the linear-quadratic model). A new methodology to a priori calculate the mean radius of the MCF MKM subnuclear domains is also introduced. Lineal energy spectra were simulated with the Particle and Heavy Ion Transport code System (PHITS) for 1H, 4He, 12C, 20Ne, 40Ar, 56Fe, and 132Xe ions and used in combination with the MCF MKM to calculate the ion-specific LET-dependence of the relative biological effectiveness (RBE) for Chinese hamster lung fibroblasts (V79 cell line) and human salivary gland tumor cells (HSG cell line). The results were compared with in vitro data from the Particle Irradiation Data Ensemble (PIDE) and in silico results of different models. The possibility of performing experiment-specific predictions to explain the scatter in the in vitro RBE data was also investigated. Finally, a sensitivity analysis on the model parameters is also included. Main results. The RBE values predicted with the MCF MKM were found to be in good agreement with the in vitro data for all tested conditions. Though all MCF MKM model parameters were determined a priori, the accuracy of the MCF MKM was found to be comparable or superior to that of other models. The model parameters determined a priori were in good agreement with the ones obtained by fitting all available in vitro data. Significance. The MCF MKM will be considered for implementation in cancer radiotherapy treatment planning with accelerated ions.

Roadmap: helium ion therapy

Helium ion beam therapy for the treatment of cancer was one of several developed and studied particle treatments in the 1950s, leading to clinical trials beginning in 1975 at the Lawrence Berkeley National Laboratory. The trial shutdown was followed by decades of research and clinical silence on the topic while proton and carbon ion therapy made debuts at research facilities and academic hospitals worldwide. The lack of progression in understanding the principle facets of helium ion beam therapy in terms of physics, biological and clinical findings persists today, mainly attributable to its highly limited availability. Despite this major setback, there is an increasing focus on evaluating and establishing clinical and research programs using helium ion beams, with both therapy and imaging initiatives to supplement the clinical palette of radiotherapy in the treatment of aggressive disease and sensitive clinical cases. Moreover, due its intermediate physical and radio-biological properties between proton and carbon ion beams, helium ions may provide a streamlined economic steppingstone towards an era of widespread use of different particle species in light and heavy ion therapy. With respect to the clinical proton beams, helium ions exhibit superior physical properties such as reduced lateral scattering and range straggling with higher relative biological effectiveness (RBE) and dose-weighted linear energy transfer (LET_d) ranging from ∼4 keVμm^-1to ∼40 keVμm^-1. In the frame of heavy ion therapy using carbon, oxygen or neon ions, where LET_dincreases beyond 100 keVμm^-1, helium ions exhibit similar physical attributes such as a sharp lateral penumbra, however, with reduced radio-biological uncertainties and without potentially spoiling dose distributions due to excess fragmentation of heavier ion beams, particularly for higher penetration depths. This roadmap presents an overview of the current state-of-the-art and future directions of helium ion therapy: understanding physics and improving modeling, understanding biology and improving modeling, imaging techniques using helium ions and refining and establishing clinical approaches and aims from learned experience with protons. These topics are organized and presented into three main sections, outlining current and future tasks in establishing clinical and research programs using helium ion beams-A. Physics B. Biological and C. Clinical Perspectives.

Development of ripple filter composed of metal mesh for charged-particle therapy

Objective. In charged-particle therapy, a ripple filter (RiFi) is used for broadening the Bragg peak in the beam direction. A conventional RiFi consists of plates with a fine ridge and groove structure. The construction of the RiFi has been a time-consuming and costly task. In this study, we developed a simple RiFi made of multi-layered metal mesh (mRiFi), with which the Bragg peak is broadened due to structural randomness, similar to what occurs for the already proposed RiFi with porous material. Approach. The mRiFi was constructed by stacking commercially available metal meshes at random positions and angles. The mRiFi was inexpensive to fabricate due to its high availability and low machining accuracy. The Bragg peak width modulated by the mRiFi can be uniquely determined by the wire material, wire diameter, wire-to-wire spacing of the metal mesh, and the number of mesh sheets. We fabricated four mRiFis consisting of 10, 20, 30, and 40 layers of stainless steel meshes with a wire diameter of 0.1 mm and a wire-to-wire spacing of 0.508 mm. Main results. Using the mRiFis consisting of 10, 20, 30, and 40 mesh sheets, we succeeded in broadening the Bragg peak following the normal distribution with the respective standard deviation σ values of 0.83, 1.15, 1.41, and 1.56 mm in water in experimental planar-integrated depth dose measurements with 140.3 MeV u−1 carbon-ion beams. The effect of range broadening with the mRiFi was independent of its lateral position, and the measurement of the surface dose using radiochromic films showed no severe inhomogeneity with a homogeneity index greater than 0.3 caused by the mRiFis. Significance. The developed mRiFi can be used as a RiFi in charged-particle therapy. The mRiFi has three advantages: high supply stability of the material for manufacturing it, easy fabrication, and low cost.

Spot-scanning hadron arc (SHArc) therapy: A proof of concept using single and multi-ion strategies with helium, carbon, oxygen and neon ions

PURPOSE

To present particle arc therapy treatments using single and multi-ion therapy optimization strategies with helium (⁴ He), carbon (¹² C), oxygen (¹⁶ O) and neon (²⁰ Ne) ion beams.

METHODS AND MATERIALS

An optimization procedure and workflow were devised for spot-scanning hadron arc therapy (SHArc) treatment planning in the PRECISE (PaRticle thErapy using single and Combined Ion optimization StratEgies) treatment planning system (TPS). Physical and biological beam models were developed for helium, carbon, oxygen and neon ions via FLUKA MC simulation. SHArc treatments were optimized using both single ion (¹² C, ¹⁶ O, or ²⁰ Ne) and multi-ion therapy (¹⁶ O+⁴ He or ²⁰ Ne+⁴ He) applying variable relative biological effectiveness (RBE) modeling using a modified microdosimetric kinetic model (mMKM) with (α/β)_x values of 2Gy, 5Gy and 3.1Gy respectively, for glioblastoma, pancreatic adenocarcinoma, and prostate adenocarcinoma patient cases. Dose, effective dose, linear energy transfer (LET) and RBE were computed with the GPU-accelerated dose engine FRoG and dosimetric/biophysical attributes were evaluated in the context of conventional particle and photon-based therapies (e.g., volumetric modulated arc therapy [VMAT]).

RESULTS

All SHArc plans met the target optimization goals (3GyRBE) and demonstrated increased target conformity and substantially lower low-dose bath to surrounding normal tissues than VMAT. SHArc plans using a single ion species (¹² C, ¹⁶ O, or ²⁰ Ne) exhibited favorable LET distributions with the highest-LET components centralized in the target volume, with values ranging from ∼80-170keV/μm, ∼130-220keV/μm and ∼180-350keV/μm, for ¹² C, ¹⁶ O, or ²⁰ Ne, respectively, exceeding mean target LET of conventional particle therapy (¹² C:∼60, ¹⁶ O:∼78 ²⁰ Ne:∼100 keV/μm). Multi-ion therapy with SHArc delivery (SHArc_MIT ) provided a similar level of target LET enhancement as SHArc compared to conventional planning, however, with additional benefits of homogenous physical dose and RBE distributions.

CONCLUSION

Here, we demonstrate that arc delivery of light and heavy ion beams, using either a single ion species (¹² C, ¹⁶ O, or ²⁰ Ne) or combining two ions in a single fraction (¹⁶ O+⁴ He or ²⁰ Ne+⁴ He), affords enhanced physical and biological distributions (e.g., LET) compared with conventional delivery with photons or particle beams. SHArc marks the first single and multi-ion arc therapy treatment optimization approach using light and heavy ions. This article is protected by copyright. All rights reserved.

Predicting the Biological Effects of Human Salivary Gland Tumour Cells for Scanned 4He-, 12C-, 16O-, and 20Ne-Ion Beams Using an SOI Microdosimeter

Experimental microdosimetry along with the microdosimetric kinetic (MK) model can be utilized to predict the biological effects of ions. To predict the relative biological effectiveness (RBE) of ions and the survival fraction (SF) of human salivary gland tumour (HSGc-C5) cells, microdosimetric quantities measured by a silicon-on-insulator (SOI) MicroPlus-mushroom microdosimeter along the spread-out Bragg peak (SOBP) delivered by pencil beam scanning of 4He, 12C, 16O, and 20Ne ions were used. The MK model parameters of HSGc-C5 cells were obtained from the best fit of the calculated SF for the different linear energy transfer (LET) of these ions and the formerly reported in vitro SF for the same LET and ions used for calculations. For a cube-shaped target of 10 × 10 × 6 cm3, treatment plans for 4He, 12C, 16O, and 20Ne ions were produced with proprietary treatment planning software (TPS) aiming for 10% SF of HSGc-C5 cells over the target volume and were delivered to a polymethyl methacrylate (PMMA) phantom. Afterwards, the saturation-corrected dose-mean lineal energy derived based on the measured microdosimetry spectra, along with the physical dose at various depths in PMMA phantoms, was used for the estimation of the SF, RBE, and RBE-weighted dose using the MK model. The predicted SF, RBE, and the RBE-weighted dose agreed with what was planned by the TPS within 3% at most depths for these ions.

On the calculation of the relative biological effectiveness of ion radiation therapy using a biological weighting function, the microdosimetric kinetic model (MKM) and subsequent corrections (non-Poisson MKM and modified MKM)

Objective. To investigate similarities and differences in the formalism, processing, and the results of relative biological effectiveness (RBE) calculations with a biological weighting function (BWF), the microdosimetric kinetic model (MKM) and subsequent modifications (non-Poisson MKM, modified MKM). This includes: (a) the extension of the V79-RBE10% BWF to model the RBE for other clonogenic survival levels; (b) a novel implementation of MKMs as weighting functions; (c) a benchmark against Chinese Hamster lung fibroblast (V79) in vitro data; (d) a study on the effect of pre- or post- processing the average biophysical quantities used for the RBE calculations; (e) a possible modification of the modified MKM parameters to improve the model accuracy at high linear energy transfer (LET). Methodology. Lineal energy spectra were simulated for two spherical targets (diameter = 0.464 or 1.0 μm) using PHITS for 1H, 4He, 12C, 20Ne, 40Ar, 56Fe and 132Xe ions. The results of the in silico calculations were compared with published in vitro data. Main results. All models appear to underestimate the RBE α of hydrogen ions. All MKMs generally overestimate the RBE50%, RBE10% and RBE1% for ions with an LET greater than ∼200 keV μm−1. This overestimation is greater for small surviving fractions and is likely due to the assumption of a radiation-independent quadratic term of clonogenic survival (ß). The overall RBE trends seem to be best described by the novel ‘post-processing average’ implementation of the non-Poisson MKM. In case of calculations with the non-Poisson MKM, pre- or post- processing the average biophysical quantities affects the computed RBE values significantly. Significance. This study presents a systematic analysis of the formalism and results of widely used microdosimetric models of clonogenic survival for ions relevant for cancer particle therapy and space radiation protection. Points for improvements were highlighted and will contribute to the development of upgraded biophysical models.

Biological Dose Optimization for Particle Arc Therapy using Helium and Carbon Ions

PURPOSE

To present biological dose optimization for particle arc therapy using helium and carbon ions.

METHODS

Treatment plan planning and optimization procedures were developed for spot-scanning hadron arc (SHArc) delivery using the RayStation TPS and a GPU-accelerated dose engine (^†TPS-XXX). The SHArc optimization algorithm is applicable for charged particle beams and determines angle-dependencies for spot/energy selection with three main initiatives: i) achieve standard clinical optimization goals and constraints for target and OARs, ii) target dose robustness and iii) increasing LET in the target volume. Three patient cases previously treated at the ^†INSTITUTION-XXX were selected for evaluation of conventional versus arc delivery for the two clinical particle beams (helium [⁴He] and carbon [¹²C] ions): glioblastoma, prostate-adenocarcinoma and skull-base chordoma. Biological dose and dose-averaged linear energy transfer (LET_d) distributions for SHArc were evaluated against conventional planning techniques (VMAT and IMPT_2F) applying the modified microdosimetric kinetic model (mMKM) for considering bio-effect with (α/β)_x=2Gy. Clinical viability and deliverability were assessed via evaluation of plan quality, robustness and irradiation time.

RESULTS

For all investigated patient cases, SHArc treatment optimizations met planning goals and constraints for target coverage and OARs, exhibiting acceptable target coverage and reduced normal tissue volumes with effective dose >10GyRBE compared to conventional 2F planning. For carbon ions, LET_d was increased in the target volume from ∼40-60keV/µm to ∼80-140keV/µm for SHArc compared to conventional treatments. Favorable LET_d distributions were possible with the SHArc approach, with maximum LET_d in CTV/GTV and potential reductions of high-LET regions in normal tissues and OARs. Compared to VMAT, SHArc affords substantial reductions in normal tissue dose (40-70%).

CONCLUSION

SHArc therapy offers potential treatment benefits such as increased normal tissue sparing from higher doses >10GyRBE, enhanced target LET_d, and potential reduction in high-LET components in OARs. Findings justify further development of robust SHArc treatment planning towards potential clinical translation.

Applications of nanodosimetry in particle therapy planning and beyond

This topical review summarizes underlying concepts of nanodosimetry. It describes the development and current status of nanodosimetric detector technology. It also gives an overview of Monte Carlo track structure simulations that can provide nanodosimetric parameters for treatment planning of proton and ion therapy. Classical and modern radiobiological assays that can be used to demonstrate the relationship between the frequency and complexity of DNA lesion clusters and nanodosimetric parameters are reviewed. At the end of the review, existing approaches of treatment planning based on relative biological effectiveness (RBE) models or dose-averaged linear energy transfer are contrasted with an RBE-independent approach based on nandosimetric parameters. Beyond treatment planning, nanodosimetry is also expected to have applications and give new insights into radiation protection dosimetry.

In vitro modified microdosimetric kinetic model-based predictions for B14-150 cells survival in 450 MeV/u carbon ion beam with aluminum ridge filter for biologically optimized spread-out Bragg peak

The relative biological efficiency of particle irradiation could be predicted with a wide variety of radiobiological models for various end-points. We validate the forecast of modified Microdosimetric Kinetic Model in vitro using combined data of reference Co-60 radiation and carbon ion plateau data for specific cell line to optimize the survival function in spread-out Bragg Peak obtained with an especially designed ridge filter. We used Geant4 Monte-Carlo software to simulate the fragment contribution along Bragg curve inside water phantom, open-source toolkit Survival to predict the expected linear-quadratic model parameters for each fragment, and in-house software to form the total survival curve in spread-out Bragg Peak. The irradiation was performed at U-70 synchrotron with an especially designed Aluminum ridge filter under the control of PTW and in-house ionization chambers. The cell clonogenic assay was conducted with the B14-150 cell line. The data analysis was accomplished using scipy and CERN ROOT. The clonogenic assay represents the survival in spread-out Bragg Peak at different points and qualitatively follows the modeled survival curve very well. The quantitative difference is within 3σ, and the deviation might be explained by the uncertainties of physical modeling using Monte-Carlo methods. Overall, the obtained results are promising for further usage in radiobiological studies or carbon ion radiotherapy. Shaping the survival curve in the region of interest (i.e., spread-out Bragg Peak) is a comprehensive task that requires high-performance computing approaches. Nevertheless, the method's potential application is related to the development of next-generation treatment planning systems for ion beams. This can open a wide range of improvements in patient treatment outcome, provide new optimized fractionation regimes or optimized dose delivery schemes, and serve as an entrance point to the translational science approach.

Adaptation of stochastic microdosimetric kinetic model to hypoxia for hypo-fractionated multi-ion therapy treatment planning

For hypo-fractionated multi-ion therapy (HFMIT), the stochastic microdosimetric kinetic (SMK) model had been developed to estimate the biological effectiveness of radiation beams with wide linear energy transfer (LET) and dose ranges. The HFMIT will be applied to radioresistant tumors with oxygen-deficient regions. The response of cells to radiation is strongly dependent on the oxygen condition in addition to radiation type, LET and absorbed dose. This study presents an adaptation of the SMK model to account for oxygen-pressure dependent cell responses, and develops the oxygen-effect-incorporated stochastic microdosimetric kinetic (OSMK) model. In the model, following assumptions were made: the numbers of radiation-induced sublethal lesions (double-strand breaks) are reduced due to lack of oxygen, and the numbers of oxygen-mediated lesions are reduced for radiation with high LET. The model parameters were determined by fitting survival data under aerobic and anoxic conditions for human salivary gland tumor cells and V79 cells exposed to helium-, carbon-, and neon-ion beams over the LET range of 18.5-654.0 keVμm^-1. The OSMK model provided good agreement with the experimental survival data of the cells with determination coefficients >0.9. In terms of oxygen enhancement ratio, the OSMK model reproduced the experimental data behavior, including slight dependence on particle type at the same LET. The OSMK model was then implemented into the in-house treatment planning software for the HFMIT to validate its applicability in clinical practice. A treatment plan with helium- and neon-ion beams was made for a pancreatic cancer case assuming an oxygen-deficient region within the tumor. The biological optimization based on the OSMK model preferentially placed the neon-ion beam to the hypoxic region, while it placed both helium- and neon-ion beams to the surrounding normoxic region. The OSMK model offered the accuracy and usability required for hypoxia-based biological optimization in HFMIT treatment planning.

Uncertainty in tissue equivalent proportional counter assessments of microdosimetry and RBE estimates in carbon radiotherapy

Microdosimetry is an important tool for assessing energy deposition distributions from ionizing radiation at cellular and cellular nucleus scales. It has served as an input parameter for multiple common mathematical models, including evaluation of relative biological effectiveness (RBE) of carbon ion therapy. The most common detector used for microdosimetry is the tissue-equivalent proportional counter (TEPC). Although it is widely applied, TEPC has various inherent uncertainties. Therefore, this work quantified the magnitude of TEPC measurement uncertainties and their impact on RBE estimates for therapeutic carbon beams. Microdosimetric spectra and frequency-, dose-, and saturation-corrected dose-mean lineal energy (****) were calculated using the Monte Carlo toolkit Geant4 for five monoenergetic and three spread-out Bragg peak carbon beams in water at every millimeter along the central beam axis. We simulated the following influences on these spectra from eight sources of uncertainty: wall effects, pulse pile-up, electronics, gas pressure, W-value, gain instability, low energy cut-off, and counting statistics. Statistic uncertainty was quantified as the standard deviation of perturbed values for each source. Bias was quantified as the difference between default lineal energy values and the mean of perturbed values for each systematic source. Uncertainties were propagated to RBE using the modified microdosimetric kinetic model (MKM). Variance introduced by statistic sources iny¯Fandy¯Daveraged 3.8% and 3.4%, respectively, and 1.5% iny*across beam depths and energies. Bias averaged 6.2% and 7.3% iny¯Fandy¯D,and 4.8% iny*.These uncertainties corresponded to 1.2 ± 0.9% on average in RBE_MKM. The largest contributors to variance and bias were pulse pile-up and wall effects. This study established an error budget for microdosimetric carbon measurements by quantifying uncertainty inherent to TEPC measurements. It is necessary to understand how robust the measurement of RBE model input parameters are against this uncertainty in order to verify clinical model implementation.

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.

Dose Calculation Algorithms for External Radiation Therapy: An Overview for Practitioners

Radiation therapy (RT) is a constantly evolving therapeutic technique; improvements are continuously being introduced for both methodological and practical aspects. Among the features that have undergone a huge evolution in recent decades, dose calculation algorithms are still rapidly changing. This process is propelled by the awareness that the agreement between the delivered and calculated doses is of paramount relevance in RT, since it could largely affect clinical outcomes. The aim of this work is to provide an overall picture of the main dose calculation algorithms currently used in RT, summarizing their underlying physical models and mathematical bases, and highlighting their strengths and weaknesses, referring to the most recent studies on algorithm comparisons. This handy guide is meant to provide a clear and concise overview of the topic, which will prove useful in helping clinical medical physicists to perform their responsibilities more effectively and efficiently, increasing patient benefits and improving the overall quality of the management of radiation treatment.

Microdosimetric investigation of the radiation quality of low-medium energy electrons using Geant4-DNA

The increasing clinical use of low-energy photon and electron sources (below few tens of keV) has raised concerns on the adequacy of the existing approximation of an energy-independent radiobiological effectiveness. In this work, the variation of the quality factor (Q) and relative biological effectiveness (RBE) of electrons over the low-medium energy range (0.1 keV-1 MeV) is examined using several microdosimetry-based Monte Carlo methodologies with input data obtained from Geant4-DNA track-structure simulations. The sensitivity of the results to the different methodologies, Geant4-DNA physics models, and target sizes is examined. Calculations of Q and RBE are based on the ICRU Report 40 recommendations, the Kellerer-Hahn approximation, the site version of the theory of dual radiation action (TDRA), the microdosimetric kinetic model (MKM) of cell survival, and the calculated yield of DNA double strand breaks (DSB). The stochastic energy deposition spectra needed as input in the above approaches have been calculated for nanometer spherical volumes using the different electron physics models of Geant4-DNA. Results are normalized at 100 keV electrons which is here considered the reference radiation. It is shown that in the energy range ~50 keV-1 MeV, the calculated Q and RBE are approximately unity (to within 1-2%) irrespective of the methodology, Geant4-DNA physics model, and target size. At lower energies, Q and RBE become energy-dependent reaching a maximum value of ~1.5-2.5 between ~200 and 700 eV. The detailed variation of Q and RBE at low energies depends mostly upon the adopted methodology and target size, and less so upon the Geant4-DNA physics model. Overall, the DSB yield predicts the highest RBE values (with RBE_max≈2.5) whereas the MKM the lowest RBE values (with RBE_max≈1.5). The ICRU Report 40, Kellerer-Hahn, and TDRA methods are in excellent agreement (to within 1-2%) over the whole energy range predicting a Q_max≈2. In conclusion, the approximation Q=RBE=1 was found to be valid only above ~50 keV whereas at lower energies both Q and RBE become strongly energy-dependent. It is envisioned that the present work will contribute towards establishing robust methodologies to determine theoretically the energy-dependence of radiation quality of individual electrons which may then be used in subsequent calculations involving practical electron and photon radiation sources.

Estimating the biological effects of helium, carbon, oxygen, and neon ion beams using 3D silicon microdosimeters

In this study, the survival fraction (SF) and relative biological effectiveness (RBE) of pancreatic cancer cells exposed to spread-out Bragg peak helium, carbon, oxygen, and neon ion beams are estimated from the measured microdosimetric spectra using a microdosimeter and the application of the microdosimetric kinetic (MK) model. To measure the microdosimetric spectra, a 3D mushroom silicon-on-insulator microdosimeter connected to low noise readout electronics (MicroPlus probe) was used. The parameters of the MK model were determined for pancreatic cancer cells such that the calculated SFs reproduced previously reported in vitro SF data. For a cuboid target of 10 × 10 × 6 cm³, treatment plans of helium, carbon, oxygen, and neon ion beams were designed using in-house treatment planning software (TPS) to achieve a 10% SF of pancreatic cancer cells throughout the target. The physical doses and microdosimetric spectra of the planned fields were measured at different depths in polymethyl methacrylate phantoms. The biological effects, such as SF, RBE, and RBE-weighted dose at different depths along the fields were predicted from the measurements. The predicted SFs at the target region were generally in good agreement with the planned SF from the TPS in most cases.

Application of lung substitute material as ripple filter for multi-ion therapy with helium-, carbon-, oxygen-, and neon-ion beams

A development project for hypo-fractionated multi-ion therapy has been initiated at the National Institute of Radiological Sciences in Japan. In the treatment, helium, carbon, oxygen, and neon ions will be used as primary beams with pencil beam scanning. A ripple filter (RiFi), consisting of a thin plastic or aluminum plate with a fine periodic ridge and groove structure, has been used to broaden the Bragg peak of heavy-ion beams in the beam direction. To sufficiently broaden the Bragg peak of helium-, carbon-, oxygen-, and neon-ion beams with suppressed lateral scattering and surface dose inhomogeneity, in this study, we tested a plate made of a lung substitute material, Gammex LN300, as the RiFi. The planar integrated dose distribution of a 183.5-MeV/u neon-ion beam was measured behind a 3-cm-thick LN300 plate in water. The Bragg peak of the pristine beam was broadened following the normal distribution with the standard deviation value of 1.29 mm, while the range of the beam was reduced by 8.8 mm by the plate. To verify the LN300 performance as the RiFi in multi-ion therapy, we measured the pencil beam data of helium-, carbon-, oxygen, and neon-ion beams penetrating the 3-cm-thick LN300 plate. The data were then modeled and used in a treatment planning system to achieve a uniform 10% survival of human undifferentiated carcinoma cells within a cuboid target by the beam for each of the different ion species. The measured survival fractions were reasonably reproduced by the planned ones for all the ion species. No surface dose inhomogeneity was observed for any ion species even when the plate was placed close to the phantom surface. The plate made of lung substitute material, Gammex LN300, is applicable as the RiFi in multi-ion therapy with helium-, carbon-, oxygen, and neon-ion beams.

Development of a new microdosimetric biological weighting function for the RBE10 assessment in case of the V79 cell line exposed to ions from 1H to 238U

An improved biological weighting function (IBWF) is proposed to phenomenologically relate microdosimetric lineal energy probability density distributions with the relative biological effectiveness (RBE) for the in vitro clonogenic cell survival (surviving fraction = 10%) of the most commonly used mammalian cell line, i.e. the Chinese hamster lung fibroblasts (V79). The IBWF, intended as a simple and robust tool for a fast RBE assessment to compare different exposure conditions in particle therapy beams, was determined through an iterative global-fitting process aimed to minimize the average relative deviation between RBE calculations and literature in vitro data in case of exposure to various types of ions from ¹H to ²³⁸U. By using a single particle- and energy- independent function, it was possible to establish an univocal correlation between lineal energy and clonogenic cell survival for particles spanning over an unrestricted linear energy transfer range of almost five orders of magnitude (0.2 keV µm^-1 to 15 000 keV µm^-1 in liquid water). The average deviation between IBWF-derived RBE values and the published in vitro data was ∼14%. The IBWF results were also compared with corresponding calculations (in vitro RBE₁₀ for the V79 cell line) performed using the modified microdosimetric kinetic model (modified MKM). Furthermore, RBE values computed with the reference biological weighting function (BWF) for the in vivo early intestine tolerance in mice were included for comparison and to further explore potential correlations between the BWF results and the in vitro RBE as reported in previous studies. The results suggest that the modified MKM possess limitations in reproducing the experimental in vitro RBE₁₀ for the V79 cell line in case of ions heavier than ²⁰Ne. Furthermore, due to the different modelled endpoint, marked deviations were found between the RBE values assessed using the reference BWF and the IBWF for ions heavier than ²H. Finally, the IBWF was unchangingly applied to calculate RBE values by processing lineal energy density distributions experimentally measured with eight different microdosimeters in 19 ¹H and ¹²C beams at ten different facilities (eight clinical and two research ones). Despite the differences between the detectors, irradiation facilities, beam profiles (pristine or spread out Bragg peak), maximum beam energy, beam delivery (passive or active scanning), energy degradation system (water, PMMA, polyamide or low-density polyethylene), the obtained IBWF-based RBE trends were found to be in good agreement with the corresponding ones in case of computer-simulated microdosimetric spectra (average relative deviation equal to 0.8% and 5.7% for ¹H and ¹²C ions respectively).

Modelling Dose Effects from Space Irradiations: Combination of High-LET and Low-LET Radiations with a Modified Microdosimetric Kinetic Model

The Microdosimetric Kinetic Model (MKM) to predict the effects of ionizing radiation on cell colonies is studied and reformulated for the case of high-linear energy transfer (LET) radiations with a low dose. When the number of radiation events happening in a subnuclear domain follows a Poisson distribution, the MKM predicts a linear-quadratic (LQ) survival curve. We show that when few events occur, as for high-LET radiations at doses lower than the mean specific energy imparted to the nucleus, zF,n, a Poisson distribution can no longer be assumed and an initial pure linear relationship between dose and survival fraction should be observed. Predictions of survival curves for combinations of high-LET and low-LET radiations are produced under two assumptions for their comparison: independent and combined action. Survival curves from previously published articles of V79 cell colonies exposed to X-rays, α particles, Ar-ions, Fe-ions, Ne-ions and mixtures of X-rays and each one of the ions are predicted according to the modified MKM. We conclude that mixtures of high-LET and low-LET radiations may enhance the effect of individual actions due to the increase of events in domains provided by the low-LET radiation. This hypothesis is only partially validated by the analyzed experiments.

Assessment of RBE-Weighted Dose Models for Carbon Ion Therapy Toward Modernization of Clinical Practice at HIT: In Vitro, in Vivo, and in Patients

PURPOSE

Present-day treatment planning in carbon ion therapy is conducted with assumptions for a limited number of tissue types and models for effective dose. Here, we comprehensively assess relative biological effectiveness (RBE) in carbon ion therapy and associated models toward the modernization of current clinical practice in effective dose calculation.

METHODS

Using 2 human (A549, H460) and 2 mouse (B16, Renca) tumor cell lines, clonogenic cell survival assay was performed for examination of changes in RBE along the full range of clinical-like spread-out Bragg peak (SOBP) fields. Prediction power of the local effect model (LEM1 and LEM4) and the modified microdosimetric kinetic model (mMKM) was assessed. Experimentation and analysis were carried out in the frame of a multidimensional end point study for clinically relevant ranges of physical dose (D), dose-averaged linear energy transfer (LET_d), and base-line photon radio-sensitivity (α/β)_x. Additionally, predictions were compared against previously reported RBE measurements in vivo and surveyed in patient cases.

RESULTS

RBE model prediction performance varied among the investigated perspectives, with mMKM prediction exhibiting superior agreement with measurements both in vitro and in vivo across the 3 investigated end points. LEM1 and LEM4 performed their best in the highest LET conditions but yielded overestimations and underestimations in low/midrange LET conditions, respectively, as demonstrated by comparison with measurements. Additionally, the analysis of patient treatment plans revealed substantial variability across the investigated models (±20%-30% uncertainty), largely dependent on the selected model and absolute values for input tissue parameters α_x and β_x.

CONCLUSION

RBE dependencies in vitro, in vivo, and in silico were investigated with respect to various clinically relevant end points in the context of tumor-specific tissue radio-sensitivity assignment and accurate RBE modeling. Discovered model trends and performances advocate upgrading current treatment planning schemes in carbon ion therapy and call for verification via clinical outcome analysis with large patient cohorts.

On the concepts of dose-mean lineal energy, unrestricted and restricted dose-averaged LET in proton therapy

To calculate 3D distributions of microdosimetric-based restricted dose-averaged LET (LETd) and dose-mean lineal energy ([Formula: see text]) in order to explore their similarities and differences between each other and with the traditional unrestricted LETd. Additionally, a new expression for optimum restricted LETd calculation is derived, allowing for disregarding straggling-associated functions in the classical microdosimetric theory. Restricted LETd and [Formula: see text] for polyenergetic beams can be obtained by integrating previously developed energy-dependent microdosimetric functions over the energetic spectrum of these beams. This calculation is extended to the entire calculation volume using an algorithm to determine spectral fluence. Equivalently, unrestricted LETd can be obtained integrating the stopping power curve on the spectrum. A new expression to calculate restricted LETd is also derived. Results for traditional and new formulas are compared for a clinical 100 MeV proton beam. Distributions of unrestricted LETd, restricted LETd and [Formula: see text] are analyzed for a prostate case, for microscopic spherical sites of 1 µm and 10 µm in diameter. Traditional and new expressions for restricted LETd remarkably agree, being the mean differences 0.05  ±  0.04 keV µm^-1 for the 1 µm site and 0.05  ±  0.02 keV µm^-1 for the 10 µm site. In the prostate case, the ratio between the maximum and the central value for central axis (CAX) profiles is around 2 for all the quantities, being the highest for restricted LETd for 1 µm (2.17) and the lowest for [Formula: see text] for 1 µm (1.78). Unrestricted LETd, restricted LETd and [Formula: see text] can be analytically computed and compared for clinical plans. Two important consequences of the calculation of [Formula: see text] are: (1) its distribution can be verified by directly measuring it in clinical beams; and (2), optimization of proton treatments based on these quantities is enabled as well as future developments of RBE models based on them.

Nuclear-interaction correction for patient dose calculations in treatment planning of helium-, carbon-, oxygen-, and neon-ion beams

In charged-particle therapy treatment planning, the patient is conventionally modeled as variable-density water, i.e. stopping effective density ρ _S, and the planar integrated dose distribution measured in water (PID) is applied for patient dose calculation based on path length scaling with the ρ _S. This approximation assures the range accuracy of charged-particle beams. However, it causes dose calculation errors due to water nonequivalence of body tissues in nuclear interactions originating from compositional differences. We had previously proposed and validated a PID correction method for the errors in carbon-ion radiotherapy. In the present study, we verify the PID correction method for helium-, oxygen-, and neon-ion beams. The one-to-one relationships between ρ _S and the nuclear effective density ρ _N of body tissues were constructed for helium-, carbon-, oxygen-, and neon-ion beams, and were used to correct the PIDs to account for the dose calculation errors in patient. The correction method was tested for non-water materials with un-scanned and scanned ion beams. In un-scanned beams penetrating the materials, the dose calculation errors of up to 5.9% were observed at the Bragg peak region, while they were reduced to  ⩽0.9% by the PID correction method. In scanned beams penetrating olive oil, the dose calculation errors of up to 2.7% averaged over the spread-out Bragg peak were observed, while they were reduced to  ⩽0.4% by the correction method. To investigate the influence of water nonequivalence of body tissues on tumor dose, we carried out a treatment planning study for prostate and uterine cases. The tumor over-doses of 0.9%, 1.8%, 2.0%, and 2.2% were observed in the uterine case for the helium-, carbon-, oxygen-, and neon-ion beams, respectively. These dose errors could be diminished by the PID correction method. The present results verify that the PID correction method is simple, practical, and accurate for treatment planning of these four ion species.

Sensitivity study of the microdosimetric kinetic model parameters for carbon ion radiotherapy

In carbon ion therapy treatment planning, the relative biological effectiveness (RBE) is accounted for by optimization of the RBE-weighted dose (biological dose). The RBE calculation methods currently applied clinically in carbon ion therapy are derived from the microdosimetric kinetic model (MKM) in Japan and the local effect model (LEM) in Europe. The input parameters of these models are based on fit to experimental data subjected to uncertainties. We therefore performed a sensitivity study of the MKM input parameters, i.e. the domain radius (r _d ), the nucleus radius (R _n ) and the parameters of the linear quadratic (LQ) model (α _x and β). The study was performed with the FLUKA Monte Carlo code, using spread out Bragg peak (SOBP) scenarios in water and a biological dose distribution in a clinical patient case. Comparisons were done between biological doses estimated applying the MKM with parameters based on HSG cells, and with HSG parameters varied separately by  ±{5, 25, 50}%. Comparisons were also done between parameter sets from different cell lines (HSG, V79, CHO and T1), as well as versions of the LEM. Of the parameters, r _d had the largest impact on the biological dose distribution, especially on the absolute dose values. Increasing this parameter by 25% decreased the biological dose level at the center of a 3 Gy(RBE) SOBP by 14%. Variations in R _n only influenced the biological dose distribution towards the particle range, and variations in α _x resulted in minor changes in the biological dose, with an increasing impact towards the particle range. β had the overall smallest influence on the SOBPs, but the impact could become more pronounced if alternative (LET dependent) implementations are used. The resulting percentage change in the SOBPs was generally less than the percentage change in the parameters. The patient case showed similar effects as with the SOBPs in water, and parameter variations had similar impact on the biological dose when using the clinical MKM and the general MKM. The clinical LEM calculated the highest biological doses to both tumor and surrounding healthy tissues, with a median target dose (D _50%) of 40.5 Gy(RBE), while the MKM with HSG and V79 parameters resulted in a D _50% of 34.2 and 36.9 Gy(RBE), respectively. In all, the observed change in biological dose distribution due to parameter variations demonstrates the importance of accurate input parameters when applying the MKM in treatment planning.