Design of ridge filters for spread-out Bragg peaks with Monte Carlo simulation in carbon ion therapy

Treatment planning of carbon ion radiotherapy for prostate cancer based on cellular experiments with PC3 human prostate cancer cells

[Purpose] Treatment plans for carbon ion radiotherapy (CIRT) in Japan are designed to uniformly deliver the prescribed clinical dose based on the radiosensitivity of human salivary gland (HSG) cells to the planning target volume (PTV). However, sensitivity to carbon beams varies between cell lines, that is, it should be checked that the clinical dose distribution based on the cell radiosensitivity of the treatment site is uniform within the PTV. [Methods] We modeled the linear energy transfer (LET) dependence of the linear-quadratic (LQ) coefficients specific to prostate cancer, which accounts for the majority of CIRT. This was achieved by irradiating prostate cancer cells (PC3) with X-rays from a 4 MV-Linac and carbon beams with different LETs of 11.1-214.3 keV/μm. By using the radiosensitivity of PC3 cells derived from cellular experiments, we reconstructed prostate-cancer-specific clinical dose distributions on patient computed tomography (CT). [Results] The LQ coefficient, α, of PC3 cells was larger than that of HSG cells at low (<50 keV/μm) LET and smaller at high (>50 keV/μm) LET, which was validated by cellular experiments performed on rectangular SOBPs. The reconstructed dose distribution on patient CT was sloped when 1 fraction incident from the one side of the patient was considered, but remained uniform from the sum of 12 fractions of the left-right opposing beams (as is used in clinical practice). [Conclusion] Our study reveals the inhomogeneity of clinical doses in single-field plans calculated using the PC3 radiosensitivity data. However, this inhomogeneity is compensated by using the combination of left-right opposing beams.

Evaluation of a therapeutic carbon beam using a G2000 glass scintillator

A G2000 glass scintillator (G2000-SC) was used to determine the carbon profile and range of a 290-MeV/n carbon beam used in heavy-ion therapy because it was sensitive enough to detect single-ion hits at hundreds of mega electron Volts. An electron-multiplying charge-coupled device camera was used to detect the ion luminescence generated during the irradiation of G2000-SC with the beam. The resulting image showed that the position of the Bragg peak can be determined. The beam passes through the 112-mm-thick water phantom and stops 5.73 ± 0.03 mm from the incident side to the G2000-SC. Additionally, the location of the Bragg peak was simulated when irradiating G2000-SC with the beam using the Monte Carlo code particle and heavy ion transport system (PHITS). Simulation results show that the incident beam stops at 5.60 mm after entering G2000-SC. The beam stop location obtained from images and the PHITS code is defined at 80% distal fall-off from the Bragg peak position. Consequently, G2000-SC provided effective profile measurements of therapeutic carbon beams.

Clinical dose assessment for scanned carbon-ion radiotherapy using linear energy transfer measurements and Monte Carlo simulations

Objective. Dosimetric commissioning of treatment planning systems (TPS) focuses on validating the agreement of the physical dose with experimental data. For carbon-ion radiotherapy, the commissioning of the relative biological effectiveness (RBE) is necessary to predict the clinical outcome based on the radiation quality of the mixed radiation field. In this study, we proposed a approach for RBE commissioning using Monte Carlo (MC) simulations, which was further strengthen by RBE validation based on linear energy transfer (LET) measurements.Approach. First, we tuned the MC simulation based on the results of dosimetric experiments including the beam ranges, beam sizes, and MU calibrations. Furthermore, we compared simulated results to measured depth- and radial-LET distributions of the 430 MeV u^-1carbon-ion spot beam with a 1.5 mm², 36μm thick silicon detector. The measured dose-averaged LET (LET_d) and RBE were compared with the simulated results. The RBE was calculated based on the mixed beam model with linear-quadratic parameters depending on the LET. Finally, TPS-calculated clinical dose profiles were validated through the tuned MC-based calculations.Main results. A 10 keVμm^-1and 0.15 agreement for LET_dand RBE, respectively, were found between simulation and measurement results obtained for a 2σlateral size of 430 MeV u^-1carbon-ion spot beam in water. These results suggested that the tuned MC simulation can be used with acceptable precision for the RBE and LET calculations of carbon-ion spot beam within the clinical energy range. For physical and clinical doses, the TPS- and MC-based calculations showed good agreements within 1.0% at the centre of the spread-out Bragg peaks.Significance. The tuned MC simulation can accurately reproduce the actual carbon-ion beams, and it can be used to validate the physical and clinical dose distributions calculated by TPS. Moreover, the MC simulation can be used for dosimetric commissioning, including clinical doses, without LET measurements.

The Mayo Clinic Florida Microdosimetric Kinetic Model of Clonogenic Survival: Application to Various Repair-Competent Rodent and Human Cell Lines

The relative biological effectiveness (RBE) calculations used during the planning of ion therapy treatments are generally based on the microdosimetric kinetic model (MKM) and the local effect model (LEM). The Mayo Clinic Florida MKM (MCF MKM) was recently developed to overcome the limitations of previous MKMs in reproducing the biological data and to eliminate the need for ion-exposed in vitro data as input for the model calculations. Since we are considering to implement the MCF MKM in clinic, this article presents (a) an extensive benchmark of the MCF MKM predictions against corresponding in vitro clonogenic survival data for 4 rodent and 10 cell lines exposed to ions from ¹H to ²³⁸U, and (b) a systematic comparison with published results of the latest version of the LEM (LEM IV). Additionally, we introduce a novel approach to derive an approximate value of the MCF MKM model parameters by knowing only the animal species and the mean number of chromosomes. The overall good agreement between MCF MKM predictions and in vitro data suggests the MCF MKM can be reliably used for the RBE calculations. In most cases, a reasonable agreement was found between the MCF MKM and the LEM IV.

Linear energy transfer-independent calibration of radiochromic film for carbon-ion beams

For carbon-ion beams, radiochromic film response depends on the dose and linear energy transfer (LET). For film dosimetry, we developed an LET-independent simple calibration method for a radiochromic film for specific therapeutic carbon-ion beams. The measured film doses were calibrated with a linear function within 5% error. The penumbra positions of the films were consistent with the differences from the planned ones within ~0.4 mm. The results indicated sufficient accuracy for use as a tool for the confirmation of the penumbra position of the fields.

Commissioning a newly developed treatment planning system, VQA Plan, for fast-raster scanning of carbon-ion beams

In this study, we report our experience in commissioning a commercial treatment planning system (TPS) for fast-raster scanning of carbon-ion beams. This TPS uses an analytical dose calculation algorithm, a pencil-beam model with a triple Gaussian form for the lateral-dose distribution, and a beam splitting algorithm to consider lateral heterogeneity in a medium. We adopted the mixed beam model as the relative biological effectiveness (RBE) model for calculating the RBE values of the scanned carbon-ion beam. To validate the modeled physical dose, we compared the calculations with measurements of various relevant quantities as functions of the field size, range and width of the spread-out Bragg peak (SOBP), and depth–dose and lateral-dose profiles for a 6-mm SOBP in water. To model the biological dose, we compared the RBE calculated with the newly developed TPS to the RBE calculated with a previously validated TPS that is in clinical use and uses the same RBE model concept. We also performed patient-specific measurements to validate the dose model in clinical situations. The physical beam model reproduces the measured absolute dose at the center of the SOBP as a function of field size, range, and SOBP width and reproduces the dose profiles for a 6-mm SOBP in water. However, the profiles calculated for a heterogeneous phantom have some limitations in predicting the carbon-ion-beam dose, although the biological doses agreed well with the values calculated by the validated TPS. Using this dose model for fast-raster scanning, we successfully treated more than 900 patients from October 2018 to October 2020, with an acceptable agreement between the TPS-calculated and measured dose distributions. We conclude that the newly developed TPS can be used clinically with the understanding that it has limited accuracies for heterogeneous media.

A Mathematical Method to Adjust MLC Leaf End Position for Accurate Dose Calculation in Carbon Ion Beam Radiation Therapy Treatment Planning System

Introduction

We present a mathematical method to adjust the leaf end position for dose calculation correction in the carbon ion radiation therapy treatment planning system.

Methods and Materials

A straggling range algorism of 400 MeV/n carbon ion beam in nine different multileaf collimator (MLC) materials was conducted to calculate the dose 50% point to derive the offset corrections in the carbon ion treatment planning system (ciPlan). The visualized light field edge position in the treatment planning system is denoted as X _tang.p, and MLC position (X _mlc.p) is defined as the source to leaf end midpoint projection on axis for monitor unit calculation. The virtual source position of energy at 400 MeV/n and straggling range in MLC at different field sizes were used to calculate the dose 50% position on axis. On-axis MLC offset (correction) could then be obtained from the position corresponding to 50% of the central axis dose minus the X _mlc.p.

Results

The exact MLC position in the carbon ion treatment planning system can be used as an offset to do the correction. The offset correction of pure tungsten is the smallest among the others due to its shortest straggling range of carbon ion beam in MLC. The positions of 50% dose of all MLC materials are always located in between X _tang.p and X _mlc.p under the largest field of 12 cm by 12 cm.

Conclusions

MLC offset should be adjusted carefully at different field sizes in the treatment planning systems especially of its small penumbra characteristic in the carbon ion beam. It is necessary to find out the dose 50% position for adjusting MLC leaf edge on-axis location in the treatment planning system to reduce dose calculation error.

Physical and biological beam modeling for carbon beam scanning at Osaka Heavy Ion Therapy Center

We have developed physical and biological beam modeling for carbon scanning therapy at the Osaka Heavy Ion Therapy Center (Osaka HIMAK). Carbon beam scanning irradiation is based on continuous carbon beam scanning, which adopts hybrid energy changes using both accelerator energy changes and binary range shifters in the nozzles. The physical dose calculation is based on a triple Gaussian pencil-beam algorithm, and we thus developed a beam modeling method using dose measurements and Monte Carlo simulation for the triple Gaussian. We exploited a biological model based on a conventional linear-quadratic (LQ) model and the photon equivalent dose, without considering the dose dependency of the relative biological effectiveness (RBE), to fully comply with the carbon passive dose distribution using a ridge filter. We extended a passive ridge-filter design method, in which carbon and helium LQ parameters are applied to carbon and fragment isotopes, respectively, to carbon scanning treatment. We then obtained radiation quality data, such as the linear energy transfer (LET) and LQ parameters, by Monte Carlo simulation. The physical dose was verified to agree with measurements to within ±2% for various patterns of volume irradiation. Furthermore, the RBE in the middle of a spread-out Bragg peak (SOBP) reproduced that from passive dose distribution results to within ±1.5%. The developed carbon beam modeling and dose calculation program was successfully applied in clinical use at Osaka HIMAK.

A mechanistic relative biological effectiveness model-based biological dose optimization for charged particle radiobiology studies

In charged particle therapy, the objective is to exploit both the physical and radiobiological advantages of charged particles to improve the therapeutic index. Use of the beam scanning technique provides the flexibility to implement biological dose optimized intensity-modulated ion therapy (IMIT). An easy-to-implement algorithm was developed in the current study to rapidly generate a uniform biological dose distribution, namely the product of physical dose and the relative biological effectiveness (RBE), within the target volume using scanned ion beams for charged particle radiobiological studies. Protons, helium ions and carbon ions were selected to demonstrate the feasibility and flexibility of our method. The general-purpose Monte Carlo simulation toolkit Geant4 was used for particle tracking and generation of physical and radiobiological data needed for later dose optimizations. The dose optimization algorithm was developed using the Python (version 3) programming language. A constant RBE-weighted dose (RWD) spread-out Bragg peak (SOBP) in a water phantom was selected as the desired target dose distribution to demonstrate the applicability of the optimization algorithm. The mechanistic repair-misrepair-fixation (RMF) model was incorporated into the Monte Carlo particle tracking to generate radiobiological parameters and was used to predict the RBE of cell survival in the iterative process of the biological dose optimization for the three selected ions. The post-optimization generated beam delivery strategy can be used in radiation biology experiments to obtain radiobiological data to further validate and improve the accuracy of the RBE model. This biological dose optimization algorithm developed for radiobiology studies could potentially be extended to implement biologically optimized IMIT plans for patients.

Design of spread-out Bragg peaks in hadron therapy with oxygen ions

Aim

Design of a numerical method for creating spread-out Bragg peak (SOBP) and evaluation of the best parameter in Bortfeld Model to this aim in oxygen ion therapy.

Background

In radiotherapy, oxygen ions have more biological benefits than light beams. Oxygen ions have a higher linear energy transfer (LET) and larger relative biological effectiveness (RBE) than lighter ones.

Materials and methods

For the design of the spread-out Bragg peak (SOBP) for oxygen beam, we designed a numerical method using the Geant4 Monte Carlo simulation code, along with matrix computations.

Results

The profiles of the Bragg Peak have been calculated for each section in the target area by the Geant4 tool. Then, in order to produce SOBP smoothly, a set of weighting factors for the intensity of oxygen ion radiation in each energy was extracted through a numerically designed method. This method was tested for producing SOBP at various widths and at different depths of a phantom. Also, weighting factors of intensity for producing a flat SOBP with oxygen ions were also obtained using the Bortfeld model in order to determine the best parameters. Then, the results of the Bortfeld model were compared with the outcomes of the method that was developed in this study.

Conclusions

The results showed that while the SOBP designed by the Bortfeld model has a homogeneity of 92-97%, the SOBP designed by the numerical method in the present study is above 99%, which in some cases even closed to 100%.

Estimation of linear energy transfer distribution for broad-beam carbon-ion radiotherapy at the National Institute of Radiological Sciences, Japan

A treatment of carbon-ion radiotherapy (CIRT) is generally evaluated using the dose weighted by relative biological effectiveness (RBE) while ignoring the radiation quality varying in the patient. In this study, we have developed a method of estimating linear energy transfer (LET) from the RBE in an archived treatment plan to represent the radiation quality of the treatment. The LET in a beam database was associated with the RBE by two fitting functions per energy, one for the spread-out Bragg peak (SOBP) and the other for shallower depths, to be differentiated by RBE per energy per modulation. The estimated LET was generally consistent with the original calculation within a few keV/μm, except for the overkill region near the distal end of SOBP. The knowledge of experimental radiobiology can thereby be associated with CIRT treatments through LET, which will potentially contribute to deeper understanding of clinical radiobiology and further optimization of CIRT.

RBE and related modeling in carbon-ion therapy

Carbon ion therapy is a promising evolving modality in radiotherapy to treat tumors that are radioresistant against photon treatments. As carbon ions are more effective in normal and tumor tissue, the relative biological effectiveness (RBE) has to be calculated by bio-mathematical models and has to be considered in the dose prescription. This review (i) introduces the concept of the RBE and its most important determinants, (ii) describes the physical and biological causes of the increased RBE for carbon ions, (iii) summarizes available RBE measurements in vitro and in vivo, and (iv) describes the concepts of the clinically applied RBE models (mixed beam model, local effect model, and microdosimetric-kinetic model), and (v) the way they are introduced into clinical application as well as (vi) their status of experimental and clinical validation, and finally (vii) summarizes the current status of the use of the RBE concept in carbon ion therapy and points out clinically relevant conclusions as well as open questions. The RBE concept has proven to be a valuable concept for dose prescription in carbon ion radiotherapy, however, different centers use different RBE models and therefore care has to be taken when transferring results from one center to another. Experimental studies significantly improve the understanding of the dependencies and limitations of RBE models in clinical application. For the future, further studies investigating quantitatively the differential effects between normal tissues and tumors are needed accompanied by clinical studies on effectiveness and toxicity.

Analysis of Neutron Production in Passively Scattered Ion-Beam Therapy

A new treatment facility for heavy ion therapy since 2010 was constructed. In the broad beam, a range shifter, ridge filter and multi leaf collimator (MLC) for the generation of the spread-out Bragg peak is used. In this case, secondary neutrons produced by the interactions of the ion field with beam-modifying devices (e.g. double-scattering system, beam shaping collimators and range compensators) are very important for patient safety. Therefore, these components must be carefully examined in the context of secondary neutron yield and associated secondary cancer risk. In this article, Monte Carlo simulation has been carried out with the FLUktuierende KAskade particle transport code, the fluence and distribution of neutron generation and the neutron dose equivalent from the broad beam components are compared using carbon and proton beams. As a result, it is confirmed that the yield of neutron production using a carbon beam from all components of the broad beam was higher than using a proton beam. The ambient dose by neutrons per heavy ion and proton ion from the MLC surface was 0.12-0.18 and 0.0067-0.0087 pSv, respectively, which shows that heavy ions generate more neutrons than protons. However, ambient dose per treatment 2 Gy, which means physical dose during treatment by ion beam, is higher than carbon beam because proton therapy needs more beam flux to make 2-Gy prescription dose. Therefore, the neutron production from the MLC, which is closed to the patient, is a very important parameter for patient safety.

Influence of nuclear interactions in polyethylene range compensators for carbon-ion radiotherapy

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.

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.

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.

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.