Deep learning-based synthetic dose-weighted LET map generation for intensity modulated proton therapy

The advantage of proton therapy as compared to photon therapy stems from the Bragg peak effect, which allows protons to deposit most of their energy directly at the tumor while sparing healthy tissue. However, even with such benefits, proton therapy does present certain challenges. The biological effectiveness differences between protons and photons are not fully incorporated into clinical treatment planning processes. In current clinical practice, the relative biological effectiveness (RBE) between protons and photons is set as constant 1.1. Numerous studies have suggested that the RBE of protons can exhibit significant variability. Given these findings, there is a substantial interest in refining proton therapy treatment planning to better account for the variable RBE. Dose-average linear energy transfer (LETd) is a key physical parameter for evaluating the RBE of proton therapy and aids in optimizing proton treatment plans. Calculating precise LETddistributions necessitates the use of intricate physical models and the execution of specialized Monte-Carlo simulation software, which is a computationally intensive and time-consuming progress. In response to these challenges, we propose a deep learning based framework designed to predict the LETddistribution map using the dose distribution map. This approach aims to simplify the process and increase the speed of LETdmap generation in clinical settings. The proposed CycleGAN model has demonstrated superior performance over other GAN-based models. The mean absolute error (MAE), peak signal-to-noise ratio and normalized cross correlation of the LETdmaps generated by the proposed method are 0.096 ± 0.019 keVμm-1, 24.203 ± 2.683 dB, and 0.997 ± 0.002, respectively. The MAE of the proposed method in the clinical target volume, bladder, and rectum are 0.193 ± 0.103, 0.277 ± 0.112, and 0.211 ± 0.086 keVμm-1, respectively. The proposed framework has demonstrated the feasibility of generating synthetic LETdmaps from dose maps and has the potential to improve proton therapy planning by providing accurate LETdinformation.

A systematic analysis of the particle irradiation data ensemble in the key of the microdosimetric kinetic model: Should clonogenic data be used for clinical relative biological effectiveness?

PURPOSE

To perform a systematic analysis of the Particle Irradiation Data Ensemble (PIDE) database for clonogenic survival assays in the context of the Microdosimetric Kinetic Model (MKM).

METHODS AND MATERIAL

Our study used data from the PIDE database containing data on various cell lines and radiation types. Two main parameters of the MKM were determined experiment-wise: the domain radius, which accounts for the increase of the linear parameter as a function of LET or lineal energy, and the nucleus radius, which accounts for the overkilling effect at LET high enough. We used experiments with LET less and more than 75 keV/μm to determine domain and nucleus radius, respectively. Experiments with cells in asynchronous phase of the cell cycle and monoenergetic beams were considered, and data from 294 out of 461 available experiments with protons, alpha, and carbon beams were used.

RESULTS

Domain and nucleus radii were determined for 32 cell lines as the median among cell-specific experiments after filtering experiments using protons, α-particles, and carbon ions, including 28 human cells and 12 rodent cells. The median values found for domain radii were 380 nm for normal human cells, 390 nm for tumor human cells, 295 nm for normal rodent cells, and 525 nm for tumor rodent cells (only one experiment with rodent tumor cells) with large variability across cell lines and across experiments on each cell line.

CONCLUSIONS

Large inter-experiment variabilities were found for the same cell lines, based on enormous experimental uncertainties and different experimental conditions. Our analysis raises questions about how convenient is to use clonogenic data to feed RBE models to be utilized in the clinical practice in particle therapy.

Hyperfractionated intensity-modulated proton therapy for pharyngeal cancer with variable relative biological effectiveness: A simulation study

BACKGROUND

The relative biological effectiveness (RBE) of proton is considered to be dependent on biological parameters and fractional dose. While hyperfractionated photon therapy was effective in the treatment of patients with head and neck cancers, its effect in intensity-modulated proton therapy (IMPT) under the variable RBE has not been investigated in detail.

PURPOSE

To study the effect of variable RBE on hyperfractionated IMPT for the treatment of pharyngeal cancer. We investigated the biologically effective dose (BED) to determine the theoretical effective hyperfractionated schedule.

METHODS

The treatment plans of three pharyngeal cancer patients were used to define the ΔBED for the clinical target volume (CTV) and soft tissue (acute and late reaction) as the difference between the BED for the altered schedule with variable RBE and conventional schedule with constant RBE. The ΔBED with several combinations of parameters (treatment days, number of fractions, and prescribed dose) was comprehensively calculated. Of the candidate schedules, the one that commonly gave a higher ΔBED for CTV was selected as the resultant schedule. The BED volume histogram was used to compare the influence of variable RBE and fractionation.

RESULTS

In the conventional schedule, compared with the constant RBE, the variable RBE resulted in a mean 2.6 and 2.7 Gy reduction of BED_mean for the CTV and soft tissue (acute reaction) of the three plans, respectively. Moreover, the BED_mean for soft tissue (late reaction) increased by 7.4 Gy, indicating a potential risk of increased RBE. Comprehensive calculation of the ΔBED resulted in the hyperfractionated schedule of 80.52 Gy (RBE = 1.1)/66 fractions in 6.5 weeks. When variable RBE was used, compared with the conventional schedule, the hyperfractionated schedule increased the BED_mean for CTV by 7.6 Gy; however, this was associated with a 7.8 Gy increase for soft tissue (acute reaction). The BED_mean for soft tissue (late reaction) decreased by 2.4 Gy.

CONCLUSION

The results indicated a potential effect of the variable RBE on IMPT for pharyngeal cancer but with the possibility that hyperfractionation could outweigh this effect. Although biological uncertainties require conservative use of the resultant schedule, hyperfractionation is expected to be an effective strategy in IMPT for pharyngeal cancer.

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 D_99% 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.

Evaluation of radiophotoluminescent glass dosimeter response for therapeutic spot scanning proton beam: suggestion of linear energy transfer-based correction

A radiophotoluminescent glass dosimeter (RGD) is used for a postal audit of a photon beam because of its various excellent characteristics. However, it has not been used for scanning proton beams because its response characteristics have not been verified. In this study, the response of RGD to scanning protons was investigated to develop a dosimetry protocol using the linear energy transfer (LET)‐based correction factor. The responses of RGD to four maximum‐range‐energy‐pattern proton beams were verified by comparing it with ionization chamber (IC) dosimetry. The LET at each measurement depth was calculated via Monte Carlo (MC) simulation. The LET correction factor (kLETRGD) was the ratio between the uncorrected RGD dose (DrawRGD) and the IC dose at each measurement depth. kLETRGD can be represented as a function of LET using the following equation: kLETRGDLET=‐0.035LET+1.090. DrawRGD showed a linear under‐response with increasing LET, and the maximum dose difference between the IC dose and DrawRGD was 15.2% at an LET of 6.07 keV/μm. The LET‐based correction dose (DLETRGD) conformed within 3.6% of the IC dose. The mean dose difference (±SD) of DrawRGD and DLETRGD was –2.5 ± 6.9% and 0.0 ± 1.6%, respectively. To achieve accurate dose verification for scanning proton beams using RGD, we derived a linear regression equation based on LET. The results show that with appropriate LET correction, RGD can be used for dose verification of scanning proton beams.

Normal Tissue Injury Induced by Photon and Proton Therapies: Gaps and Opportunities

Despite technological advances in radiation therapy (RT) and cancer treatment, patients still experience adverse effects. Proton therapy (PT) has emerged as a valuable RT modality that can improve treatment outcomes. Normal tissue injury is an important determinant of the outcome; therefore, for this review, we analyzed 2 databases: (1) clinical trials registered with ClinicalTrials.gov and (2) the literature on PT in PubMed, which shows a steady increase in the number of publications. Most studies in PT registered with ClinicalTrials.gov with results available are nonrandomized early phase studies with a relatively small number of patients enrolled. From the larger database of nonrandomized trials, we listed adverse events in specific organs/sites among patients with cancer who are treated with photons and protons to identify critical issues. The present data demonstrate dosimetric advantages of PT with favorable toxicity profiles and form the basis for comparative randomized prospective trials. A comparative analysis of 3 recently completed randomized trials for normal tissue toxicities suggests that for early stage non-small cell lung cancer, no meaningful comparison could be made between stereotactic body RT and stereotactic body PT due to low accrual (NCT01511081). In addition, for locally advanced non-small cell lung cancer, a comparison of intensity modulated RTwith passive scattering PT (now largely replaced by spot-scanned intensity modulated PT), PT did not provide any benefit in normal tissue toxicity or locoregional failure over photon therapy. Finally, for locally advanced esophageal cancer, proton beam therapy provided a lower total toxicity burden but did not improve progression-free survival and quality of life (NCT01512589). The purpose of this review is to inform the limitations of current trials looking at protons and photons, considering that advances in technology, physics, and biology are a continuum, and to advocate for future trials geared toward accurate precision RT that need to be viewed as an iterative process in a defined path toward delivering optimal radiation treatment. A foundational understanding of the radiobiologic differences between protons and photons in tumor and normal tissue responses is fundamental to, and necessary for, determining the suitability of a given type of biologically optimized RT to a patient or cohort.

A Critical Review of LET-Based Intensity-Modulated Proton Therapy Plan Evaluation and Optimization for Head and Neck Cancer Management

In this review article, we review the 3 important aspects of linear-energy-transfer (LET) in intensity-modulated proton therapy (IMPT) for head and neck (H&N) cancer management. Accurate LET calculation methods are essential for LET-guided plan evaluation and optimization, which can be calculated either by analytical methods or by Monte Carlo (MC) simulations. Recently, some new 3D analytical approaches to calculate LET accurately and efficiently have been proposed. On the other hand, several fast MC codes have also been developed to speed up the MC simulation by simplifying nonessential physics models and/or using the graphics processor unit (GPU)–acceleration approach. Some concepts related to LET are also briefly summarized including (1) dose-weighted versus fluence-weighted LET; (2) restricted versus unrestricted LET; and (3) microdosimetry versus macrodosimetry. LET-guided plan evaluation has been clinically done in some proton centers. Recently, more and more studies using patient outcomes as the biological endpoint have shown a positive correlation between high LET and adverse events sites, indicating the importance of LET-guided plan evaluation in proton clinics. Various LET-guided plan optimization methods have been proposed to generate proton plans to achieve biologically optimized IMPT plans. Different optimization frameworks were used, including 2-step optimization, 1-step optimization, and worst-case robust optimization. They either indirectly or directly optimize the LET distribution in patients while trying to maintain the same dose distribution and plan robustness. It is important to consider the impact of uncertainties in LET-guided optimization (ie, LET-guided robust optimization) in IMPT, since IMPT is sensitive to uncertainties including both the dose and LET distributions. We believe that the advancement of the LET-guided plan evaluation and optimization will help us exploit the unique biological characteristics of proton beams to improve the therapeutic ratio of IMPT to treat H&N and other cancers.

A systematic review on the usage of averaged LET in radiation biology for particle therapy

Linear Energy Transfer (LET) is widely used to express the radiation quality of ion beams, when characterizing the biological effectiveness. However, averaged LET may be defined in multiple ways, and the chosen definition may impact the resulting reported value. We review averaged LET definitions found in the literature, and quantify which impact using these various definitions have for different reference setups. We recorded the averaged LET definitions used in 354 publications quantifying the relative biological effectiveness (RBE) of hadronic beams, and investigated how these various definitions impact the reported averaged LET using a Monte Carlo particle transport code. We find that the kind of averaged LET being applied is, generally, poorly defined. Some definitions of averaged LET may influence the reported averaged LET values up to an order of magnitude. For publications involving protons, most applied dose averaged LET when reporting RBE. The absence of what target medium is used and what secondary particles are included further contributes to an ill-defined averaged LET. We also found evidence of inconsistent usage of averaged LET definitions when deriving LET-based RBE models. To conclude, due to commonly ill-defined averaged LET and to the inherent problems of LET-based RBE models, averaged LET may only be used as a coarse indicator of radiation quality. We propose a more rigorous way of reporting LET values, and suggest that ideally the entire particle fluence spectra should be recorded and provided for future RBE studies, from which any type of averaged LET (or other quantities) may be inferred.

Dosimetric response of a glass dosimeter in proton beams: LET-dependence and correction factor

A radiophotoluminescent glass dosimeter (RGD) is widely used in postal audit system for photon beams in Japan. However, proton dosimetry in RGDs is scarcely used owing to a lack of clarity in their response to beam quality. In this study, we investigated RGD response to beam quality for establishing a suitable linear energy transfer (LET)-corrected dosimetry protocol in a therapeutic proton beam. The RGD response was compared with ionization chamber measurement for a 100-225 MeV passive proton beam. LET of the measurement points was calculated by the Monte Carlo method. An LET-correction factor, defined as a ratio between the non-corrected RGD dose and ionization chamber dose, of 1.226×(LET)^-0.171 was derived for the RGD response. The magnitude of the LET-dependence of RGD increased with LET; for an LET of 8.2 keV/μm, the RGD under-response was up to 16%. The coefficient of determination, mean difference ± SD of non-corrected RGD dose, residual range-corrected RGD dose, and LET-corrected RGD dose to the ionization chamber are 0.923, 3.7 ± 4.2%, -2.4 ± 7.5%, and 0.04 ± 2.1%, respectively. The LET-corrected RGD dose was within 5% of the corresponding ionization chamber dose at all energies until 200 MeV, where it was 5.3% lower than the ionization chamber dose. A corrected LET-dependence of RGD using a correction factor based on a power function of LET and precise dosimetric verification close to the maximum LET were realized here. We further confirmed establishment of an accurate postal audit under various irradiation conditions.

Microdosimetry of a therapeutic proton beam with a mini-TEPC and a MicroPlus-Bridge detector for RBE assessment

Proton beams are widely used worldwide to treat localized tumours, the lower entrance dose and no exit dose, thus sparing surrounding normal tissues, being the main advantage of this treatment modality compared to conventional photon techniques. Clinical proton beam therapy treatment planning is based on the use of a general relative biological effectiveness (RBE) of 1.1 along the whole beam penetration depth, without taking into account the documented increase in RBE at the end of the depth dose profile, in the Bragg peak and beyond. However, an inaccurate estimation of the RBE can cause both underdose or overdose, in particular it can cause the unfavourable situation of underdosing the tumour and overdosing the normal tissue just beyond the tumour, which limits the treatment success and increases the risk of complications. In view of a more precise dose delivery that takes into account the variation of RBE, experimental microdosimetry offers valuable tools for the quality assurance of LET or RBE-based treatment planning systems. The purpose of this work is to compare the response of two different microdosimetry systems: the mini-TEPC and the MicroPlus-Bridge detector. Microdosimetric spectra were measured across the 62 MeV spread out Bragg peak of CATANA with the mini-TEPC and with the Bridge microdosimeter. The frequency and dose distributions of lineal energy were compared and the different contributions to the spectra were analysed, discussing the effects of different site sizes and chord length distributions. The shape of the lineal energy distributions measured with the two detectors are markedly different, due to the different water-equivalent sizes of the sensitive volumes: 0.85 μm for the TEPC and 17.3 μm for the silicon detector. When the Loncol's biological weighting function is applied to calculate the microdosimetric assessment of the RBE, both detectors lead to results that are consistent with biological survival data for glioma U87 cells. Both the mini-TEPC and the MicroPlus-Bridge detector can be used to assess the RBE variation of a 62 MeV modulated proton beam along its penetration depth. The microdosimetric assessment of the RBE based on the Loncol's weighting function is in good agreement with radiobiological results when the 10% biological uncertainty is taken into account.

Linear energy transfer weighted beam orientation optimization for intensity-modulated proton therapy

PURPOSE

In intensity-modulated proton therapy (IMPT), unaccounted-for variation in biological effectiveness contributes to the discrepancy between the constant relative biological effectiveness (RBE) model prediction and experimental observation. It is desirable to incorporate biological doses in treatment planning to improve modeling accuracy and consequently achieve a higher therapeutic ratio. This study addresses this demand by developing a method to incorporate linear energy transfer (LET) into beam orientation optimization (BOO).

METHODS

Instead of RBE-weighted dose, this LET weighted BOO (LETwBOO) framework uses the dose and LET product (LET  ×  D) as the biological surrogate. The problem is formulated with a physical dose fidelity term, a LET  ×  D constraint term, and a group sparsity term. The LET  ×  D of organs at risks is penalized for minimizing the biological effect while maintaining the physical dose objectives. Group sparsity is used to reduce the number of active beams from 600-800 non-coplanar candidate beams to between 2 and 4. This LETwBOO method was tested on three skull base tumor (SBT) patients and three bilateral head-and-neck (H&N) patients. The LETwBOO plans were compared with IMPT plans using manually selected beams with only physical dose constraint (MAN) and the initial MAN plan reoptimized with additional LET  ×  D constraint (LETwMAN).

RESULTS

The LETwBOO plans show superior physical dose and LET  ×  D sparing. On average, the [mean, maximal] doses of organs at risks (OARs) in LETwBOO are reduced by [2.85, 4.6] GyRBE from the MAN plans in the SBT cases and reduced by [0.9, 2.5] GyRBE in the H&N cases, while LETwMAN is comparable to MAN. cLET × Ds of PTVs are comparable in LETwBOO and LETwMAN, where c is a scaling factor of 0.04 μm/keV. On average, in the SBT cases, LETwBOO reduces the OAR [mean, maximal] cLET × D by [1.1, 2.9] Gy from the MAN plans, compared to the reduction by LETwMAN from MAN of [0.7, 1.7] Gy. In the H&N cases, LETwBOO reduces the OAR [mean, maximal] cLET × D by [0.8, 2.6] Gy from the MAN plans, compared to the reduction by LETwMAN from MAN of [0.3, 1.2] Gy.

CONCLUSION

We developed a novel LET weighted BOO method for IMPT to generate plans with improved physical and biological OAR sparing compared with the plans unaccounted for biological effects from BOO.

The impact of dose delivery time on biological effectiveness in proton irradiation with various biological parameters

PURPOSE

The purpose of this study is to evaluate the sublethal damage (SLD) repair effect in prolonged proton irradiation using the biophysical model with various cell-specific parameters of (α/β)_x and T_1/2 (repair half time). At present, most of the model-based studies on protons have focused on acute radiation, neglecting the reduction in biological effectiveness due to SLD repair during the delivery of radiation. Nevertheless, the dose-rate dependency of biological effectiveness may become more important as advanced treatment techniques, such as hypofractionation and respiratory gating, come into clinical practice, as these techniques sometimes require long treatment times. Also, while previous research using the biophysical model revealed a large repair effect with a high physical dose, the dependence of the repair effect on cell-specific parameters has not been evaluated systematically.

METHODS

Biological dose [relative biological effectiveness (RBE) × physical dose] calculation with repair included was carried out using the linear energy transfer (LET)-dependent linear-quadratic (LQ) model combined with the theory of dual radiation action (TDRA). First, we extended the dose protraction factor in the LQ model for the arbitrary number of different LET proton irradiations delivered sequentially with arbitrary time lags, referring to the TDRA. Using the LQ model, the decrease in biological dose due to SLD repair was systematically evaluated for spread-out Bragg peak (SOBP) irradiation in a water phantom with the possible ranges of both (α/β)_x and repair parameters ((α/β)_x  = 1-15 Gy, T_1/2  = 0-90 min). Then, to consider more realistic irradiation conditions, clinical cases of prostate, liver, and lung tumors were examined with the cell-specific parameters for each tumor obtained from the literature. Biological D_99% and biological dose homogeneity coefficient (HC) were calculated for the clinical target volumes (CTVs), assuming dose-rate structures with a total irradiation time of 0-60 min.

RESULTS

The differences in the cell-specific parameters resulted in considerable variation in the repair effect. The biological dose reduction found at the center of the SOBP with 30 min of continuous irradiation varied from 1.13% to 14.4% with a T_1/2 range of 1-90 min when (α/β)_x is fixed as 10 Gy. It varied from 2.3% to 6.8% with an (α/β)_x range of 1-15 Gy for a fixed value of T_1/2  = 30 min. The decrease in biological D_99% per 10 min was 2.6, 1.2, and 3.0% for the prostate, liver, and lung tumor cases, respectively. The value of the biological D_99% reduction was neither in the order of (α/β)_x nor prescribed dose, but both comparably contributed to the repair effect. The variation of HC was within the range of 0.5% for all cases; therefore, the dose distribution was not distorted.

CONCLUSION

The reduction in biological dose caused by the SLD repair largely depends on the cell-specific parameters in addition to the physical dose. The parameters should be considered carefully in the evaluation of the repair effect in prolonged proton irradiation.

A kernel-based algorithm for the spectral fluence of clinical proton beams to calculate dose-averaged LET and other dosimetric quantities of interest

PURPOSE

To introduce a new analytical methodology to calculate quantities of interest in particle radiotherapy inside the treatment planning system. Models are proposed to calculate dose-averaged LET (LETd) in proton radiotherapy.

MATERIAL AND METHODS

A kernel-based approach for the spectral fluence of particles is developed by means of analytical functions depending on depth and lateral position. These functions are obtained by fitting them to data calculated with Monte Carlo (MC) simulations using Geant4 in liquid water for energies from 50 to 250 MeV. Contributions of primary, secondary protons and alpha particles are modeled separately. Lateral profiles and spectra are modeled as Gaussian functions to be convolved with the fluence coming from the nozzle. LETd is obtained by integrating the stopping power curves from the PSTAR and ASTAR databases weighted by the spectrum at each position. The fast MC code MCsquare is employed to benchmark the results.

RESULTS

Considering the nine energies simulated, fits for the functions modeling the fluence in-depth provide an average R 2 equal to 0.998, 0.995 and 0.986 for each one of the particles considered. Fits for the Gaussian lateral functions yield average R 2 of 0.997, 0.982 and 0.993, respectively. Similarly, the Gaussian functions fitted to the computed spectra lead to average R 2 of 0.995, 0.938 and 0.902. LETd calculation in water shows mean differences of -0.007 ± 0.008 keV/μm with respect to MCsquare if only protons are considered and 0.022 ± 0.007 keV/μm including alpha particles. In a prostate case, mean difference for all voxels with dose >5% of prescribed dose is 0.28 ± 0.23 keV/μm.

CONCLUSION

This new spectral fluence-based methodology allows for simultaneous calculations of quantities of interest in proton radiotherapy such as dose, LETd or microdosimetric quantities. The method also enables the inclusion of more particles by following an analogous process.

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 (DRBE=1.1) are close to the “true” values derived with the variable RBE models (DvRBE). As such, in this study, the closeness of DRBE=1.1 to DvRBE 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 (LET_d) distributions were obtained using the analytical calculation method, based on the pencil beam algorithm. Next, DvRBE was calculated using three different RBE models. The deviation of DvRBE from DRBE=1.1 was evaluated with D₉₉ and D_max, 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 DmaxvRBE from DmaxRBE=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 D99vRBE from D99RBE=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.

Hybrid 3D analytical linear energy transfer calculation algorithm based on precalculated data from Monte Carlo simulations

PURPOSE

The dose-averaged linear energy transfer (LET_d ) for intensity-modulated proton therapy (IMPT) calculated by one-dimensional (1D) analytical models deviates from more accurate but time-consuming Monte Carlo (MC) simulations. We developed a fast hybrid three-dimensional (3D) analytical LET_d calculation that is more accurate than 1D analytical model.

METHODS

We used the Geant4 MC code to generate 3D LET_d distributions of monoenergetic proton beams in water for all energies and used a customized error function to fit the LET_d lateral profiles at various depths to the MC simulation. The 3D LET_d calculation kernel was a lookup table of these fitted coefficients, and LET_d was determined directly from spot energies and voxel coordinates during analytical dose calculations. We validated our new method by comparing the calculated LET_d distributions to MC results using 3D Gamma index analysis with 3%/2 mm criteria in 12 patient geometries. The significance of the improvement in Gamma index analysis passing rates over the 1D analytical model was determined using the Wilcoxon rank-sum test.

RESULTS

The passing rate of 3D Gamma analysis comparing LET_d distributions from the hybrid 3D method and the 1D method to MC simulations was significantly improved from 94.0% ± 2.5% to 98.0% ± 1.0% (P = 0.0003). The typical time to calculate dose and LET_d simultaneously using an Intel Xeon E5-2680 2.50 GHz workstation was approximately 2.5 min.

CONCLUSIONS

Our new method significantly improved the LET_d calculation accuracy compared to the 1D method while maintaining significantly shorter calculation time even comparing with the GPU-based fast MC code.

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 (LET_d) and relative biological effectiveness (RBE). The LET_d 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 LET_d 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.