Validation of robust radiobiological optimization algorithms based on the mixed beam model for intensity-modulated carbon-ion therapy.

Currently, treatment planning systems (TPSs) that can compute the intensities of intensity-modulated carbon-ion therapy (IMCT) using scanned carbon-ion beams are limited. In the present study, the computational efficacy of the newly designed IMCT algorithms was analyzed for the first time based on the mixed beam model with respect to the physical and biological doses; moreover, the validity and effectiveness of the robust radiobiological optimization were verified. A dose calculation engine was independently generated to validate a clinical dose determined in the TPS. A biological assay was performed using the HSGc-C5 cell line to validate the calculated surviving fraction (SF). Both spot control (SC) and voxel-wise worst-case scenario (WC) algorithms were employed for robust radiobiological optimization followed by their application in a Radiation Therapy Oncology Group benchmark phantom under homogeneous and heterogeneous conditions and a clinical case for range and position errors. Importantly, for the first time, both SC and WC algorithms were implemented in the integrated TPS platform that can compute the intensities of IMCT using scanned carbon-ion beams for robust radiobiological optimization. For assessing the robustness, the difference between the maximum and minimum values of a dose-volume histogram index in the examined error scenarios was considered as a robustness index. The relative biological effectiveness (RBE) determined by the independent dose calculation engine exhibited a -0.6% difference compared with the RBE defined by the TPS at the isocenter, whereas the measured and the calculated SF were similar. Regardless of the objects, compared with the conventional IMCT, the robust radiobiological optimization enhanced the sensitivity of the examined error scenarios by up to 19% for the robustness index. The computational efficacy of the novel IMCT algorithms was verified according to the mixed beam model with respect to the physical and biological doses. The robust radiobiological optimizations lowered the impact of range and position uncertainties considerably in the examined scenarios. The robustness of the WC algorithm was more enhanced compared with that of the SC algorithm. Nevertheless, the SC algorithm can be used as an alternative to the WC IMCT algorithm with respect to the computational cost.

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.

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 simplified Monte Carlo algorithm considering large-angle scattering for fast and accurate calculation of proton dose.

PURPOSE: The purpose of this study is to improve dose calculation accuracy of the simplified Monte Carlo (SMC) algorithm in the low-dose region. Because conventional SMC algorithms calculate particle scattering in consideration of multiple Coulomb scattering (MCS) only, they approximate lateral dose profiles by a single Gaussian function. However, it is well known that the low-dose region spreads away from the beam axis, and it has been pointed out that modeling of the low-dose region is important to calculated dose accurately. METHODS: A SMC algorithm, which is named modified SMC and considers not only MCS but also large angle scattering resembling hadron elastic scattering, was developed. In the modified SMC algorithm, the particle fluence varies in the longitudinal direction because the large-angle scattering decreases residual range of particles in accordance with their scattering angle and tracking of the particles with large scattering angle is terminated at a short distance downstream from the scattering. Therefore, modified integrated depth dose (m-IDD) tables, which are converted from measured IDD in consideration of the fluence loss, are used to calculate dose. RESULTS: In the case of a 1-liter cubic target, the calculation accuracy was improved in comparison with that of a conventional algorithm, and the modified algorithm results agreed well with Geant4-based simulation results; namely, 98.8% of the points satisfied the 2% dose/2 mm distance-to-agreement (DTA) criterion. The calculation time of the modified SMC algorithm was 1972 s in the case of 4.4 × 108 particles and 16-threading operation of an Intel Xeon E5-2643 (3.3-GHz clock). CONCLUSIONS: An SMC algorithm that can reproduce a laterally widespread low-dose region was developed. According to the comparison with a Geant4-based simulation, it was concluded that the modified SMC algorithm is useful for calculating dose of proton radiotherapy.

Dual ring multilayer ionization chamber and theory-based correction technique for scanning proton therapy.

PURPOSE: To develop a multilayer ionization chamber (MLIC) and a correction technique that suppresses differences between the MLIC and water phantom measurements in order to achieve fast and accurate depth dose measurements in pencil beam scanning proton therapy. METHODS: The authors distinguish between a calibration procedure and an additional correction: 1-the calibration for variations in the air gap thickness and the electrometer gains is addressed without involving measurements in water; 2-the correction is addressed to suppress the difference between depth dose profiles in water and in the MLIC materials due to the nuclear interaction cross sections by a semiempirical model tuned by using measurements in water. In the correction technique, raw MLIC data are obtained for each energy layer and integrated after multiplying them by the correction factor because the correction factor depends on incident energy. The MLIC described here has been designed especially for pencil beam scanning proton therapy. This MLIC is called a dual ring multilayer ionization chamber (DRMLIC). The shape of the electrodes allows the DRMLIC to measure both the percentage depth dose (PDD) and integrated depth dose (IDD) because ionization electrons are collected from inner and outer air gaps independently. RESULTS: IDDs for which the beam energies were 71.6, 120.6, 159, 180.6, and 221.4 MeV were measured and compared with water phantom results. Furthermore, the measured PDDs along the central axis of the proton field with a nominal field size of 10 × 10 cm(2) were compared. The spread out Bragg peak was 20 cm for fields with a range of 30.6 and 3 cm for fields with a range of 6.9 cm. The IDDs measured with the DRMLIC using the correction technique were consistent with those that of the water phantom; except for the beam energy of 71.6 MeV, all of the points satisfied the 1% dose/1 mm distance to agreement criterion of the gamma index. The 71.6 MeV depth dose profile showed slight differences in the shallow region, but 94.5% of the points satisfied the 1%/1 mm criterion. The 90% ranges, defined at the 90% dose position in distal fall off, were in good agreement with those in the water phantom, and the range differences from the water phantom were less than ±0.3 mm. The PDDs measured with the DRMLIC were also consistent with those that of the water phantom; 97% of the points passed the 1%/1 mm criterion. CONCLUSIONS: It was demonstrated that the new correction technique suppresses the difference between the depth dose profiles obtained with the MLIC and those obtained from a water phantom, and a DRMLIC enabling fast measurements of both IDD and PDD was developed. The IDDs and PDDs measured with the DRMLIC and using the correction technique were in good agreement with those that of the water phantom, and it was concluded that the correction technique and DRMLIC are useful for depth dose profile measurements in pencil beam scanning proton therapy.

Evaluation of the influence of double and triple Gaussian proton kernel models on accuracy of dose calculations for spot scanning technique.

PURPOSE: The main purpose in this study was to present the results of beam modeling and how the authors systematically investigated the influence of double and triple Gaussian proton kernel models on the accuracy of dose calculations for spot scanning technique. METHODS: The accuracy of calculations was important for treatment planning software (TPS) because the energy, spot position, and absolute dose had to be determined by TPS for the spot scanning technique. The dose distribution was calculated by convolving in-air fluence with the dose kernel. The dose kernel was the in-water 3D dose distribution of an infinitesimal pencil beam and consisted of an integral depth dose (IDD) and a lateral distribution. Accurate modeling of the low-dose region was important for spot scanning technique because the dose distribution was formed by cumulating hundreds or thousands of delivered beams. The authors employed a double Gaussian function as the in-air fluence model of an individual beam. Double and triple Gaussian kernel models were also prepared for comparison. The parameters of the kernel lateral model were derived by fitting a simulated in-water lateral dose profile induced by an infinitesimal proton beam, whose emittance was zero, at various depths using Monte Carlo (MC) simulation. The fitted parameters were interpolated as a function of depth in water and stored as a separate look-up table. These stored parameters for each energy and depth in water were acquired from the look-up table when incorporating them into the TPS. The modeling process for the in-air fluence and IDD was based on the method proposed in the literature. These were derived using MC simulation and measured data. The authors compared the measured and calculated absolute doses at the center of the spread-out Bragg peak (SOBP) under various volumetric irradiation conditions to systematically investigate the influence of the two types of kernel models on the dose calculations. RESULTS: The authors investigated the difference between double and triple Gaussian kernel models. The authors found that the difference between the two studied kernel models appeared at mid-depths and the accuracy of predicting the double Gaussian model deteriorated at the low-dose bump that appeared at mid-depths. When the authors employed the double Gaussian kernel model, the accuracy of calculations for the absolute dose at the center of the SOBP varied with irradiation conditions and the maximum difference was 3.4%. In contrast, the results obtained from calculations with the triple Gaussian kernel model indicated good agreement with the measurements within ±1.1%, regardless of the irradiation conditions. CONCLUSIONS: The difference between the results obtained with the two types of studied kernel models was distinct in the high energy region. The accuracy of calculations with the double Gaussian kernel model varied with the field size and SOBP width because the accuracy of prediction with the double Gaussian model was insufficient at the low-dose bump. The evaluation was only qualitative under limited volumetric irradiation conditions. Further accumulation of measured data would be needed to quantitatively comprehend what influence the double and triple Gaussian kernel models had on the accuracy of dose calculations.

Development and evaluation of a short-range applicator for treating superficial moving tumors with respiratory-gated spot-scanning proton therapy using real-time image guidance.

Treatment of superficial tumors that move with respiration (e.g. lung tumors) using spot-scanning proton therapy (SSPT) is a high-priority research area. The recently developed real-time image-gated proton beam therapy (RGPT) system has proven to be useful for treating moving tumors deep inside the liver. However, when treating superficial tumors, the proton's range is small and so is the sizes of range straggling, making the Bragg-peaks extremely sharp compared to those located in deep-seated tumors. The extreme sharpness of Bragg-peaks is not always beneficial because it necessitates a large number of energy layers to make a spread-out Bragg-peak, resulting in long treatment times, and is vulnerable to motion-induced dose deterioration. We have investigated a method to treat superficial moving tumors in the lung by the development of an applicator compatible with the RGPT system. A mini-ridge filter (MRF) was developed to broaden the pristine Bragg-peak and, accordingly, decrease the number of required energy layers to obtain homogeneous irradiation. The applicator position was designed so that the fiducial marker's trajectory can be monitored by fluoroscopy during proton beam-delivery. The treatment plans for three lung cancer patients were made using the applicator, and four-dimensional (4D) dose calculations for the RGPT were performed using patient respiratory motion data. The effect of the MRF on the dose distributions and treatment time was evaluated. With the MRF, the number of energy layers was decreased to less than half of that needed without it, whereas the target volume coverage values (D99%, D95%, D50%, D2%) changed by less than 1% of the prescribed dose. Almost no dose distortion was observed after the 4D dose calculation, whereas the treatment time decreased by 26%-37%. Therefore, we conclude that the developed applicator compatible with RGPT is useful to solve the issue in the treatment of superficial moving tumors with SSPT.

Design of a ridge filter structure based on the analysis of dose distributions.

Dose distributions distorted by a periodic structure, such as a ridge filter, are analytically investigated. Based on the beam optics, the fluence distributions of scanned beams passing through the ridge filter are traced. It is shown that the periodic lateral dose distribution blurred by multiple Coulomb scattering can be expressed by a sum of cosine functions through Fourier transform. The result shows that the dose homogeneity decreases exponentially as the period of the structure becomes longer. This analysis is applied to the example case of a mini-ridge filter. The mini-ridge filter is designed to broaden sharp Bragg peaks for an energy-stacking irradiation method. The dose distributions depend on the period of the ridge filter structure and the angular straggling at the ridge filter position. Several cases are prepared where the period and angular straggling are supposed to be probable values. In these cases, the lateral distributions obtained by the analytical method are compared to Monte Carlo simulation results. Both distributions show good agreement with each other within 1%, which means that this analysis allows estimation of the dose distribution downstream of the ridge filter quantitatively. The appropriate period of grooves and scatterer width can be determined which ensures sufficient homogeneity.

Reduction of the number of stacking layers in proton uniform scanning.

Uniform scanning with a relatively large beam size can improve beam utilization efficiency more than conventional irradiation methods using scatterers and can achieve a large-field, long-range and large spread-out Bragg peak (SOBP). The SOBP is obtained by energy stacking in uniform scanning, but its disadvantage is that the number of stacking layers is large, especially in the low-energy region, because the Bragg peak of the pristine beam is very sharp. We applied a mini-ridge filter to broaden the pristine Bragg peak up to a stacked layer thickness of 1 or 2 cm in order to decrease the number of stacking layers. The number of stacking layers can be reduced to 20% or less than that in the case of pristine beam stacking. Although the distal falloff of the SOBP is deteriorated by applying the mini-ridge filter, we can improve the distal falloff to that of pristine beam stacking by introducing the distal filter to the irradiation of the most distal layer. Uniform scanning in combination with mini-ridge filter use can more than double the beam utilization efficiency over that of passive irradiation techniques.