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.

Impact of a spatially dependent dose delivery time structure on the biological effectiveness of scanning proton therapy.

PURPOSE: In the scanning beam delivery of protons, different portions of the target are irradiated with different linear energy transfer protons with various time intervals and irradiation times. This research aimed to evaluate the spatially dependent biological effectiveness of protracted irradiation in scanning proton therapy. METHODS: One and two parallel opposed fields plans were created in water phantom with the prescribed dose of 2 Gy. Three scenarios (instantaneous, continuous, and layered scans) were used with the corresponding beam delivery models. The biological dose (physical dose × relative biological effectiveness) was calculated using the linear quadratic model and the theory of dual radiation action to quantitatively evaluate the dose delivery time effect. In addition, simulations using clinical plans (postoperative seminoma and prostate tumor cases) were conducted to assess the impact of the effects on the dose volume histogram parameters and homogeneity coefficient (HC) in targets. RESULTS: In a single-field plan of water phantom, when the treatment time was 19 min, the layered-scan scenario showed a decrease of <0.2% (almost 3.3%) in the biological dose from the plan on the distal (proximal) side because of the high (low) dose rate. This is in contrast to the continuous scenario, where the biological dose was almost uniformly decreased over the target by approximately 3.3%. The simulation with clinical geometry showed that the decrease rates in D99% were 0.9% and 1.5% for every 10 min of treatment time prolongation for postoperative seminoma and prostate tumor cases, respectively, whereas the increase rates in HC were 0.7% and 0.2%. CONCLUSIONS: In protracted irradiation in scanning proton therapy, the spatially dependent dose delivery time structure in scanning beam delivery can be an important factor for accurate evaluation of biological effectiveness.

Validation of dose distribution for liver tumors treated with real-time-image gated spot-scanning proton therapy by log data based dose reconstruction.

In spot scanning proton therapy (SSPT), the spot position relative to the target may fluctuate through tumor motion even when gating the radiation by utilizing a fiducial marker. We have established a procedure that evaluates the delivered dose distribution by utilizing log data on tumor motion and spot information. The purpose of this study is to show the reliability of the dose distributions for liver tumors treated with real-time-image gated SSPT (RGPT). In the evaluation procedure, the delivered spot information and the marker position are synchronized on the basis of log data on the timing of the spot irradiation and fluoroscopic X-ray irradiation. Then a treatment planning system reconstructs the delivered dose distribution. Dose distributions accumulated for all fractions were reconstructed for eight liver cases. The log data were acquired in all 168 fractions for all eight cases. The evaluation was performed for the values of maximum dose, minimum dose, D99, and D5-D95 for the clinical target volumes (CTVs) and mean liver dose (MLD) scaled by the prescribed dose. These dosimetric parameters were statistically compared between the planned dose distribution and the reconstructed dose distribution. The mean difference of the maximum dose was 1.3% (95% confidence interval [CI]: 0.6%-2.1%). Regarding the minimum dose, the mean difference was 0.1% (95% CI: -0.5%-0.7%). The mean differences of D99, D5-D95 and MLD were below 1%. The reliability of dose distributions for liver tumors treated with RGPT-SSPT was shown by the evaluation of the accumulated dose distributions.

Difference in LET-based biological doses between IMPT optimization techniques: Robust and PTV-based optimizations.

PURPOSE: While a large amount of experimental data suggest that the proton relative biological effectiveness (RBE) varies with both physical and biological parameters, current commercial treatment planning systems (TPS) use the constant RBE instead of variable RBE models, neglecting the dependence of RBE on the linear energy transfer (LET). To conduct as accurate a clinical evaluation as possible in this circumstance, it is desirable that the dosimetric parameters derived by TPS ( D RBE = 1.1 ) are close to the "true" values derived with the variable RBE models ( D v RBE ). As such, in this study, the closeness of D RBE = 1.1 to D v RBE was compared between planning target volume (PTV)-based and robust plans. METHODS: Intensity-modulated proton therapy (IMPT) treatment plans for two Radiation Therapy Oncology Group (RTOG) phantom cases and four nasopharyngeal cases were created using the PTV-based and robust optimizations, under the assumption of a constant RBE of 1.1. First, the physical dose and dose-averaged LET (LETd ) distributions were obtained using the analytical calculation method, based on the pencil beam algorithm. Next, D v RBE was calculated using three different RBE models. The deviation of D v RBE from D RBE = 1.1 was evaluated with D99 and Dmax , which have been used as the evaluation indices for clinical target volume (CTV) and organs at risk (OARs), respectively. The influence of the distance between the OAR and CTV on the results was also investigated. As a measure of distance, the closest distance and the overlapped volume histogram were used for the RTOG phantom and nasopharyngeal cases, respectively. RESULTS: As for the OAR, the deviations of D max v RBE from D max RBE = 1.1 were always smaller in robust plans than in PTV-based plans in all RBE models. The deviation would tend to increase as the OAR was located closer to the CTV in both optimization techniques. As for the CTV, the deviations of D 99 v RBE from D 99 RBE = 1.1 were comparable between the two optimization techniques, regardless of the distance between the CTV and the OAR. CONCLUSION: Robust optimization was found to be more favorable than PTV-based optimization in that the results presented by TPS were closer to the "true" values and that the clinical evaluation based on TPS was more reliable.

Physical and biological impacts of collimator-scattered protons in spot-scanning proton therapy.

To improve the penumbra of low-energy beams used in spot-scanning proton therapy, various collimation systems have been proposed and used in clinics. In this paper, focused on patient-specific brass collimators, the collimator-scattered protons' physical and biological effects were investigated. The Geant4 Monte Carlo code was used to model the collimators mounted on the scanning nozzle of the Hokkaido University Hospital. A systematic survey was performed in water phantom with various-sized rectangular targets; range (5-20 cm), spread-out Bragg peak (SOBP) (5-10 cm), and field size (2 × 2-16 × 16 cm2 ). It revealed that both the range and SOBP dependences of the physical dose increase had similar trends to passive scattering methods, that is, it increased largely with the range and slightly with the SOBP. The physical impact was maximized at the surface (3%-22% for the tested geometries) and decreased with depth. In contrast, the field size (FS) dependence differed from that observed in passive scattering: the increase was high for both small and large FSs. This may be attributed to the different phase-space shapes at the target boundary between the two dose delivery methods. Next, the biological impact was estimated based on the increase in dose-averaged linear energy transfer (LETd ) and relative biological effectiveness (RBE). The LETd of the collimator-scattered protons were several keV/µm higher than that of unscattered ones; however, since this large increase was observed only at the positions receiving a small scattered dose, the overall LETd increase was negligible. As a consequence, the RBE increase did not exceed 0.05. Finally, the effects on patient geometries were estimated by testing two patient plans, and a negligible RBE increase (0.9% at most in the critical organs at surface) was observed in both cases. Therefore, the impact of collimator-scattered protons is almost entirely attributed to the physical dose increase, while the RBE increase is negligible.

An analytical dose-averaged LET calculation algorithm considering the off-axis LET enhancement by secondary protons for spot-scanning proton therapy.

PURPOSE: To evaluate the biological effects of proton beams as part of daily clinical routine, fast and accurate calculation of dose-averaged linear energy transfer (LETd ) is required. In this study, we have developed the analytical LETd calculation method based on the pencil-beam algorithm (PBA) considering the off-axis enhancement by secondary protons. This algorithm (PBA-dLET) was then validated using Monte Carlo simulation (MCS) results. METHODS: In PBA-dLET, LET values were assigned separately for each individual dose kernel based on the PBA. For the dose kernel, we employed a triple Gaussian model which consists of the primary component (protons that undergo the multiple Coulomb scattering) and the halo component (protons that undergo inelastic, nonelastic and elastic nuclear reaction); the primary and halo components were represented by a single Gaussian and the sum of two Gaussian distributions, respectively. Although the previous analytical approaches assumed a constant LETd value for the lateral distribution of a pencil beam, the actual LETd increases away from the beam axis, because there are more scattered and therefore lower energy protons with higher stopping powers. To reflect this LETd behavior, we have assumed that the LETs of primary and halo components can take different values (LETp and LEThalo ), which vary only along the depth direction. The values of dual-LET kernels were determined such that the PBA-dLET reproduced the MCS-generated LETd distribution in both small and large fields. These values were generated at intervals of 1 mm in depth for 96 energies from 70.2 to 220 MeV and collected in the look-up table. Finally, we compared the LETd distributions and mean LETd (LETd,mean ) values of targets and organs at risk between PBA-dLET and MCS. Both homogeneous phantom and patient geometries (prostate, liver, and lung cases) were used to validate the present method. RESULTS: In the homogeneous phantom, the LETd profiles obtained by the dual-LET kernels agree well with the MCS results except for the low-dose region in the lateral penumbra, where the actual dose was below 10% of the maximum dose. In the patient geometry, the LETd profiles calculated with the developed method reproduces MCS with the similar accuracy as in the homogeneous phantom. The maximum differences in LETd,mean for each structure between the PBA-dLET and the MCS were 0.06 keV/µm in homogeneous phantoms and 0.08 keV/µm in patient geometries under all tested conditions, respectively. CONCLUSIONS: We confirmed that the dual-LET-kernel model well reproduced the MCS, not only in the homogeneous phantom but also in complex patient geometries. The accuracy of the LETd was largely improved from the single-LET-kernel model, especially at the lateral penumbra. The model is expected to be useful, especially for proper recognition of the risk of side effects when the target is next to critical organs.

Theoretical analysis of angular distribution of scattering in nozzle components using a response-function method for proton spot-scanning therapy.

In spot-scanning proton therapy, highly precise beam control is required in the treatment nozzle such that the proton beam does not spread out during transportation by restraining the divergence of the beam angle and spot size, simultaneously. In order to evaluate the beam-broadening behaviour induced by passing through the various nozzle components, we have developed a new method to calculate the angular divergence profile of a proton beam in the nozzle. The angular divergence of the proton beam for each nozzle component is calculated by the Monte Carlo simulation code, Geant4, assuming that the initial beam has no divergence. The angular divergence profiles generated in the various nozzle components are then fitted by the analytic function formula with triple Gaussian distributions. The fitted profiles can be treated like analytic response functions and the angular divergence profile in the nozzle can be easily and systematically calculated by using a convolution theorem. The beam-broadening behaviour during transportation in the nozzle is carefully evaluated. The beam profiles are well-characterized by the proposed angular divergence analysis, i.e. triple Gaussian profile analysis. The primary Gaussian part of the beam profile is mainly generated by air and dose monitors with plate electrode components. The secondary and tertiary Gaussian parts are so-called wide-angle scattering and generated mainly by spot-position and profile monitors with metal window and wire components. The scattering of the nozzle component can be analysed using the proposed response function method for the angular distribution. Multiple convolved angular scattering can be determined from the response function of the individual nozzle components. The angular distribution from small to large angle regions can then be quantitatively evaluated by the proposed method. The method is quite simple and generalized, and is a straightforward way to understand the nozzle and component characteristics related to the beam-broadening behaviour.

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.

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.

A patient-specific aperture system with an energy absorber for spot scanning proton beams: Verification for clinical application.

PURPOSE: In the authors' proton therapy system, the patient-specific aperture can be attached to the nozzle of spot scanning beams to shape an irradiation field and reduce lateral fall-off. The authors herein verified this system for clinical application. METHODS: The authors prepared four types of patient-specific aperture systems equipped with an energy absorber to irradiate shallow regions less than 4 g/cm(2). The aperture was made of 3-cm-thick brass and the maximum water equivalent penetration to be used with this system was estimated to be 15 g/cm(2). The authors measured in-air lateral profiles at the isocenter plane and integral depth doses with the energy absorber. All input data were obtained by the Monte Carlo calculation, and its parameters were tuned to reproduce measurements. The fluence of single spots in water was modeled as a triple Gaussian function and the dose distribution was calculated using a fluence dose model. The authors compared in-air and in-water lateral profiles and depth doses between calculations and measurements for various apertures of square, half, and U-shaped fields. The absolute doses and dose distributions with the aperture were then validated by patient-specific quality assurance. Measured data were obtained by various chambers and a 2D ion chamber detector array. RESULTS: The patient-specific aperture reduced the penumbra from 30% to 70%, for example, from 34.0 to 23.6 mm and 18.8 to 5.6 mm. The calculated field width for square-shaped apertures agreed with measurements within 1 mm. Regarding patient-specific aperture plans, calculated and measured doses agreed within -0.06% ± 0.63% (mean ± SD) and 97.1% points passed the 2%-dose/2 mm-distance criteria of the γ-index on average. CONCLUSIONS: The patient-specific aperture system improved dose distributions, particularly in shallow-region plans.