Beyond Gaussians: a study of single-spot modeling for scanning proton dose calculation

Study on induced radioactivity and individual dose evaluation in Gantry room for Varian ProBeam Proton Therapy System

Proton therapy has emerged as an advantageous modality for tumor radiotherapy due to its favorable physical and biological properties. However, this therapy generates induced radioactivity through nuclear reactions between the primary beam, secondary particles, and surrounding materials. This study focuses on systematically investigating the induced radioactivity in the gantry room during pencil beam scanning, utilizing both experimental measurements and Monte Carlo simulations. Results indicate that patients are the primary source of induced radioactivity, predominantly producing radionuclides such as 11C, 13N, and 15O. Long-term irradiation primarily generates radionuclides like 22Na, 24Na, and 54Mn etc. Additionally, this study estimates the individual doses received by medical workers in the gantry room, the irradiation dose for patient escorts, and the additional dose to patients from residual radiation. Finally, the study offers recommendations to minimize unnecessary irradiation doses to medical workers, patient escorts, and patients.

Validating a double Gaussian source model for small proton fields in a commercial Monte-Carlo dose calculation engine

PURPOSE

The primary fluence of a proton pencil beam exiting the accelerator is enveloped by a region of secondaries, commonly called "spray". Although small in magnitude, this spray may affect dose distributions in pencil beam scanning mode e.g., in the calculation of the small field output, if not modelled properly in a treatment planning system (TPS). The purpose of this study was to dosimetrically benchmark the Monte Carlo (MC) dose engine of the RayStation TPS (v.10A) in small proton fields and systematically compare single Gaussian (SG) and double Gaussian (DG) modeling of initial proton fluence providing a more accurate representation of the nozzle spray.

METHODS

The initial proton fluence distribution for SG/DG beam modeling was deduced from two-dimensional measurements in air with a scintillation screen with electronic readout. The DG model was either based on direct fits of the two Gaussians to the measured profiles, or by an iterative optimization procedure, which uses the measured profiles to mimic in-air scan-field factor (SF) measurements. To validate the DG beam models SFs, i.e. relative doses to a 10 × 10 cm2 field, were measured in water for three different initial proton energies (100MeV, 160MeV, 226.7MeV) and square field sizes from 1×1cm2 to 10×10cm2 using a small field ionization chamber (IBA CC01) and an IBA ProteusPlus system (universal nozzle). Furthermore, the dose to the center of spherical target volumes (diameters: 1cm to 10cm) was determined using the same small volume ionization chamber (IC). A comprehensive uncertainty analysis was performed, including estimates of influence factors typical for small field dosimetry deduced from a simple two-dimensional analytical model of the relative fluence distribution. Measurements were compared to the predictions of the RayStation TPS.

RESULTS

SFs deviated by more than 2% from TPS predictions in all fields <4×4cm2 with a maximum deviation of 5.8% for SG modeling. In contrast, deviations were smaller than 2% for all field-sizes and proton energies when using the directly fitted DG model. The optimized DG model performed similarly except for slightly larger deviations in the 1×1cm2 scan-fields. The uncertainty estimates showed a significant impact of pencil beam size variations (±5%) resulting in up to 5.0% standard uncertainty. The point doses within spherical irradiation volumes deviated from calculations by up to 3.3% for the SG model and 2.0% for the DG model.

CONCLUSION

Properly representing nozzle spray in RayStation's MC-based dose engine using a DG beam model was found to reduce the deviation to measurements in small spherical targets to below 2%. A thorough uncertainty analysis shows a similar magnitude for the combined standard uncertainty of such measurements.

Intensity modulated proton arc therapy via geometry-based energy selection for ependymoma

PURPOSE

We developed and tested a novel method of creating intensity modulated proton arc therapy (IMPAT) plans that uses computing resources similar to those for regular intensity-modulated proton therapy (IMPT) plans and may offer a dosimetric benefit for patients with ependymoma or similar tumor geometries.

METHODS

Our IMPAT planning method consists of a geometry-based energy selection step with major scanning spot contributions as inputs computed using ray-tracing and single-Gaussian approximation of lateral spot profiles. Based on the geometric relation of scanning spots and dose voxels, our energy selection module selects a minimum set of energy layers at each gantry angle such that each target voxel is covered by sufficient scanning spots as specified by the planner, with dose contributions above the specified threshold. Finally, IMPAT plans are generated by robustly optimizing scanning spots of the selected energy layers using a commercial proton treatment planning system (TPS). The IMPAT plan quality was assessed for four ependymoma patients. Reference three-field IMPT plans were created with similar planning objective functions and compared with the IMPAT plans.

RESULTS

In all plans, the prescribed dose covered 95% of the clinical target volume (CTV) while maintaining similar maximum doses for the brainstem. While IMPAT and IMPT achieved comparable plan robustness, the IMPAT plans achieved better homogeneity and conformity than the IMPT plans. The IMPAT plans also exhibited higher relative biological effectiveness (RBE) enhancement than did the corresponding reference IMPT plans for the CTV in all four patients and brainstem in three of them.

CONCLUSIONS

The proposed method demonstrated potential as an efficient technique for IMPAT planning and may offer a dosimetric benefit for patients with ependymoma or tumors in close proximity to critical organs. IMPAT plans created using this method had elevated RBE enhancement associated with increased linear energy transfer (LET) in both targets and abutting critical organs.

Collimating individual beamlets in pencil beam scanning proton therapy, a dosimetric investigation

The purpose of this work is to investigate collimating individual proton beamlets from a dosimetric perspective and to introduce a new device concept, the spot scanning aperture (SSA). The SSA consists of a thin aperture with a small cylindrical opening attached to a robotics system, which allows the aperture to follow and align with individual beamlets during spot delivery. Additionally, a range shifter is incorporated (source-side) for treating shallow depths. Since the SSA trims beamlets spot by spot, the patient-facing portion of the device only needs to be large enough to trim a single proton beamlet. The SSA has been modelled in an open-source Monte-Carlo-based dose engine (MCsquare) to characterize its dosimetric properties in water at depths between 0 and 10 cm while varying the following parameters: the aperture material, thickness, distance to the water phantom, distance between the aperture and attached range shifter, and the aperture opening radius. Overall, the SSA greatly reduced spot sizes for all the aperture opening radii that were tested (1 - 4 mm), especially in comparison with the extended range shifter (ranger shifter placed at 30 cm from patient); greater than 50% when placed less than 10 cm away from the patient at depths in water less than 50 mm. The peak to entrance dose ratio and linear energy transfer was found to depend on the thickness of the aperture and therefore the aperture material. Neutron production rates were also investigated and discussed.

Validation and testing of a novel pencil-beam model derived from Monte Carlo simulations in carbon-ion treatment planning for different scenarios

PURPOSE

The calculation ability of the newly-proposed accurate beam model, the double Gaussian-logistic (DG-L) model, was validated in both homogeneous and heterogeneous phantoms to provide helpful information for its future application in clinical carbon-ion treatment planning system (TPS).

METHODS

MatRad was used as the new algorithm test platform. Based on Monte Carlo (MC) method, the basic database in matRad was generated, then comparative dosimetric analyses between the single Gaussian (SG), double Gaussian (DG) and DG-L models against the MC recalculations were performed on the treatment plans of a cubic water phantom, a TG119 phantom and a liver patient scenario. Absolute dose differences, dose-volume histograms (DVHs) and global γ-index analyses derived from the treatment plans were evaluated.

RESULTS

Calculated with the DG-L model, the deviations of the target dose coverage (D₉₅) for the cubic water phantom, the TG119 phantom and the liver patient case against the MC recalculations could be reduced from -2.5%, -4.6% and -6.4% to -0.3%, -2.0% and -4.5% respectively compared to the SG model, while the γ pass rates (3%/3mm) could be enhanced from 98.0%, 90.6% and 90.1% to 99.8%, 95.7% and 91.6%, respectively. The novel beam model also shows improved performance compared with the DG model, without substantially increasing the computation time.

CONCLUSIONS

The DG-L model could effectively improve the dose calculation accuracy and mitigate the delivered dose deficiency in target volumes compared to the SG and DG models. The lateral heterogeneities should be considered for its future implementation in a clinical TPS.

Whole Three-Dimensional Dosimetry of Carbon Ion Beams with an MRI-Based Nanocomposite Fricke Gel Dosimeter Using Rapid T1 Mapping Method

MRI-based gel dosimeters are attractive systems for the evaluation of complex dose distributions in radiotherapy. In particular, the nanocomposite Fricke gel dosimeter is one among a few dosimeters capable of accurately evaluating the dose distribution of heavy ion beams. In contrast, reduction of the scanning time is a challenging issue for the acquisition of three-dimensional volume data. In this study, we investigated a three-dimensional dose distribution measurement method for heavy ion beams using variable flip angle (VFA), which is expected to significantly reduce the MRI scanning time. Our findings clarified that the whole three-dimensional dose distribution could be evaluated within the conventional imaging time (20 min) and quality of one cross-section.

Three-dimensional dose-distribution measurement of therapeutic carbon-ion beams using a ZnS scintillator sheet

The accurate measurement of the 3D dose distribution of carbon-ion beams is essential for safe carbon-ion therapy. Although ionization chambers scanned in a water tank or air are conventionally used for this purpose, these measurement methods are time-consuming. We thus developed a rapid 3D dose-measurement tool that employs a silver-activated zinc sulfide (ZnS) scintillator with lower linear energy transfer (LET) dependence than gadolinium-based (Gd) scintillators; this tool enables the measurement of carbon-ion beams with small corrections. A ZnS scintillator sheet was placed vertical to the beam axis and installed in a shaded box. Scintillation images produced by incident carbon-ions were reflected with a mirror and captured with a charge-coupled device (CCD) camera. A 290 MeV/nucleon mono-energetic beam and spread-out Bragg peak (SOBP) carbon-ion passive beams were delivered at the Gunma University Heavy Ion Medical Center. A water tank was installed above the scintillator with the water level remotely adjusted to the measurement depth. Images were recorded at various water depths and stacked in the depth direction to create 3D scintillation images. Depth and lateral profiles were analyzed from the images. The ZnS-scintillator-measured depth profile agreed with the depth dose measured using an ionization chamber, outperforming the conventional Gd-based scintillator. Measurements were realized with smaller corrections for a carbon-ion beam with a higher LET than a proton. Lateral profiles at the entrance and the Bragg peak depths could be measured with this tool. The proposed method would make it possible to rapidly perform 3D dose-distribution measurements of carbon-ion beams with smaller quenching corrections.

A Review of the Robust Optimization Process and Advances with Monte Carlo in the Proton Therapy Management of Head and Neck Tumors

In intensity-modulated proton therapy, robust optimization processes have been developed to manage uncertainties associated with (1) range, (2) setup, (3) anatomic changes, (4) dose calculation, and (5) biological effects. Here we review our experience using a robust optimization technique that directly incorporates range and setup uncertainties into the optimization process to manage those sources of uncertainty. We also review procedures for implementing adaptive planning to manage the anatomic uncertainties. Finally, we share some early experiences regarding the impact of uncertainties in dose calculation and biological effects, along with techniques to manage and potentially reduce these uncertainties.

Fast spot-scanning proton dose calculation method with uncertainty quantification using a three-dimensional convolutional neural network

This study proposes a near-real-time spot-scanning proton dose calculation method with probabilistic uncertainty estimation using a three-dimensional convolutional neural network (3D-CNN). CT images and clinical target volume contours of 215 head and neck cancer patients were collected from a public database. 1484 and 488 plans were extracted for training and testing the 3D-CNN model, respectively. Spot beam data and single-field uniform dose (SFUD) labels were calculated for each plan using an open-source dose calculation toolkit. Variable spot data were converted into a fixed-size volume hereby called a 'peak map' (PM). 300 epochs of end-to-end training was implemented using sets of stopping power ratio and PM as input. Moreover, transfer learning techniques were used to adjust the trained model to SFUD doses calculated with different beam parameters and calculation algorithm using only 7.95% of training data used for the base model. Finally, accuracy of the 3D-CNN-calculated doses and model uncertainty was reviewed with several evaluation metrics. The 3D-CNN model calculates 3D proton dose distributions accurately with a mean absolute error of 0.778 cGyE. The predicted uncertainty is correlated with dose errors at high contrast edges. Averaged Sørensen-Dice similarity coefficients between binarized outputs and ground truths are mostly above 80%. Once the 3D-CNN model was well-trained, it can be efficiently fine-tuned for different proton doses by transfer learning techniques. Inference time for calculating one dose distribution is around 0.8 s for a plan using 1500 spot beams with a consumer grade GPU. A novel spot-scanning proton dose calculation method using 3D-CNN was developed. The 3D-CNN model is able to calculate 3D doses and uncertainty with any SFUD spot data and beam irradiation angles. Our proposed method should be readily extendable to other setups and plans and be useful for dose verification, image-guided proton therapy, or other applications.

Clinical Validation of a Ray-Casting Analytical Dose Engine for Spot Scanning Proton Delivery Systems

Purpose:

To describe and validate the dose calculation algorithm of an independent second-dose check software for spot scanning proton delivery systems with full width at half maximum between 5 and 14 mm and with a negligible spray component.

Methods:

The analytical dose engine of our independent second-dose check software employs an altered pencil beam algorithm with 3 lateral Gaussian components. It was commissioned using Geant4 and validated by comparison to point dose measurements at several depths within spread-out Bragg peaks of varying ranges, modulations, and field sizes. Water equivalent distance was used to compensate for inhomogeneous geometry. Twelve patients representing different disease sites were selected for validation. Dose calculation results in water were compared to a fast Monte Carlo code and ionization chamber array measurements using dose planes and dose profiles as well as 2-dimensional–3-dimensional and 3-dimensional–3-dimensional γ-index analysis. Results in patient geometry were compared to Monte Carlo simulation using dose–volume histogram indices, 3-dimensional–3-dimensional γ-index analysis, and inpatient dose profiles.

Results:

Dose engine model parameters were tuned to achieve 1.5% agreement with measured point doses. The in-water γ-index passing rates for the 12 patients using 3%/2 mm criteria were 99.5% ± 0.5% compared to Monte Carlo. The average inpatient γ-index analysis passing rate compared to Monte Carlo was 95.8% ± 2.9%. The average difference in mean dose to the clinical target volume between the dose engine and Monte Carlo was −0.4% ± 1.0%. For a typical plan, dose calculation time was 2 minutes on an inexpensive workstation.

Conclusions:

Following our commissioning process, the analytical dose engine was validated for all treatment sites except for the lung or for calculating dose–volume histogram indices involving point doses or critical structures immediately distal to target volumes. Monte Carlo simulations are recommended for these scenarios.

Transitioning from measurement-based to combined patient-specific quality assurance for intensity-modulated proton therapy

OBJECTIVE

This study is part of ongoing efforts aiming to transit from measurement-based to combined patient-specific quality assurance (PSQA) in intensity-modulated proton therapy (IMPT). A Monte Carlo (MC) dose-calculation algorithm is used to improve the independent dose calculation and to reveal the beam modeling deficiency of the analytical pencil beam (PB) algorithm.

METHODS

A set of representative clinical IMPT plans with suboptimal PSQA results were reviewed. Verification plans were recalculated using an MC algorithm developed in-house. Agreements of PB and MC calculations with measurements that quantified by the γ passing rate were compared.

RESULTS

The percentage of dose planes that met the clinical criteria for PSQA (>90% γ passing rate using 3%/3 mm criteria) increased from 71.40% in the original PB calculation to 95.14% in the MC recalculation. For fields without beam modifiers, nearly 100% of the dose planes exceeded the 95% γ passing rate threshold using the MC algorithm. The model deficiencies of the PB algorithm were found in the proximal and distal regions of the SOBP, where MC recalculation improved the γ passing rate by 11.27% (p < 0.001) and 16.80% (p < 0.001), respectively.

CONCLUSIONS

The MC algorithm substantially improved the γ passing rate for IMPT PSQA. Improved modeling of beam modifiers would enable the use of the MC algorithm for independent dose calculation, completely replacing additional depth measurements in IMPT PSQA program. For current users of the PB algorithm, further improving the long-tail modeling or using MC simulation to generate the dose correction factor is necessary.

ADVANCES IN KNOWLEDGE

We justified a change in clinical practice to achieve efficient combined PSQA in IMPT by using the MC algorithm that was experimentally validated in almost all the clinical scenarios in our center. Deficiencies in beam modeling of the current PB algorithm were identified and solutions to improve its dose-calculation accuracy were provided.

Nuclear halo measurements for accurate prediction of field size factor in a Varian ProBeam proton PBS system

Purpose

For pencil‐beam scanning proton therapy systems, in‐air non‐Gaussian halo can significantly impact output at small field sizes and low energies. Since the low‐intensity tail of spot profile (halo) is not necessarily modeled in treatment planning systems (TPSs), this can potentially lead to significant differences in patient dose distribution. In this work, we report such impact for a Varian ProBeam system.

Methods

We use a pair magnification technique to measure two‐dimensional (2D) spot profiles of protons from 70 to 242 MeV at the treatment isocenter and 30 cm upstream of the isocenter. Measurements are made with both Gafchromic film and a scintillator detector coupled to a CCD camera (IBA Lynx). Spot profiles are measured down to 0.01% of their maximum intensity. Field size factors (FSFs) are compared among calculation using measured 2D profiles, calculation using a clinical treatment planning algorithm (Raystation 8A clinical Monte Carlo), and a CC04 small‐volume ion chamber. FSFs were measured for square fields of proton energies ranging from 70 to 242 MeV.

Results

All film and Lynx measurements agree within 1 mm for full width at half maximum beam intensity. The measured radial spot profiles disagree with simple Gaussian approximations, which are used for modeling in the TPS. FSF measurements show the magnitude of disagreements between beam output in reality and in the TPS without modeling halo. We found that the clinical TPS overestimated output by as much as 6% for small field sizes of 2 cm at the lowest energy of 70 MeV while the film and Lynx measurements agreed within 4% and 1%, respectively, for this FSF.

Conclusions

If the in‐air halo for low‐energy proton beams is not fully modeled by the TPS, this could potentially lead to under‐dosing small, shallow treatment volumes in PBS treatment plans.

An analytical model for the upper bound estimation of respiratory motion-induced dose uncertainty in spot-scanning proton beam therapy

PURPOSE

We developed an analytical model of a spot-scanning beam delivery system to estimate the upper bound of respiratory motion-induced dose uncertainty for a given treatment plan.

METHODS

The effective delivery time for each spot position in the treatment plan was calculated on the basis of the parameters of the delivery system. The upper bound of the dose uncertainty was then calculated as a function of the effective delivery time. Two-dimensional (2D) measurements with a detector array on a one-dimensional moving platform were obtained to validate the model.

RESULTS

We performed 351 two-dimensional measurements on a moving platform for different delivery sequences of a single-layer uniform pattern and patient treatment field. The measured dose uncertainty was a strong function of the effective delivery time: The shortest effective delivery time resulted in a maximum absolute dose error of >90%, while the longest ones resulted in a maximum absolute dose error of 4.9% for a single layer and 9.7% for a patient field with heterogeneity. The relationship of the effective delivery time and the measured dose uncertainty followed the analytical formula.

CONCLUSIONS

With our analytical model, the upper bound of the dose uncertainty due to motion can be estimated in spot-scanning proton therapy without four-dimensional dynamic dose calculation.

Technical Note: Treatment planning system (TPS) approximations matter - comparing intensity-modulated proton therapy (IMPT) plan quality and robustness between a commercial and an in-house developed TPS for nonsmall cell lung cancer (NSCLC)

PURPOSE

Approximate dose calculation methods were used in the nominal dose distribution and the perturbed dose distributions due to uncertainties in a commercial treatment planning system (CTPS) for robust optimization in intensity-modulated proton therapy (IMPT). We aimed to investigate whether the approximations influence plan quality, robustness, and interplay effect of the resulting IMPT plans for the treatment of locally advanced lung cancer patients.

MATERIALS AND METHODS

Ten consecutively treated locally advanced nonsmall cell lung cancer (NSCLC) patients were selected. Two IMPT plans were created for each patient using our in-house developed TPS, named "Solo," and also the CTPS, Eclipse^TM (Varian Medical Systems, Palo Alto, CA, USA), respectively. The plans were designed to deliver prescription doses to internal target volumes (ITV) drawn by a physician on averaged four-dimensional computed tomography (4D-CT). Solo plans were imported back to CTPS, and recalculated in CTPS for fair comparison. Both plans were further verified for each patient by recalculating doses in the inhalation and exhalation phases to ensure that all plans met clinical requirements. Plan robustness was quantified on all phases using dose-volume-histograms (DVH) indices in the worst-case scenario. The interplay effect was evaluated for every plan using an in-house developed software, which randomized starting phases of each field per fraction and accumulated dose in the exhalation phase based on the patient's breathing motion pattern and the proton spot delivery in a time-dependent fashion. DVH indices were compared using Wilcoxon rank-sum test.

RESULTS

Compared to the plans generated using CTPS on the averaged CT, Solo plans had significantly better target dose coverage and homogeneity (normalized by the prescription dose) in the worst-case scenario [ITV D_95% : 98.04% vs 96.28%, Solo vs CTPS, P = 0.020; ITV D_5% -D_95% : 7.20% vs 9.03%, P = 0.049] while all DVH indices were comparable in the nominal scenario. On the inhalation phase, Solo plans had better target dose coverage and cord D_max in the nominal scenario [ITV D_95% : 99.36% vs 98.45%, Solo vs CTPS, P = 0.014; cord D_max : 20.07 vs 23.71 Gy(RBE), P = 0.027] with better target coverage and cord D_max in the worst-case scenario [ITV D_95% : 97.89% vs 96.47%, Solo vs CTPS, P = 0.037; cord D_max : 24.57 vs 28.14 Gy(RBE), P = 0.037]. On the exhalation phase, similar phenomena were observed in the nominal scenario [ITV D_95% : 99.63% vs 98.87%, Solo vs CTPS, P = 0.037; cord D_max : 19.67 vs 23.66 Gy(RBE), P = 0.039] and in the worst-case scenario [ITV D_95% : 98.20% vs 96.74%, Solo vs CTPS, P = 0.027; cord D_max : 23.47 vs 27.93 Gy(RBE), P = 0.027]. In terms of interplay effect, plans generated by Solo had significantly better target dose coverage and homogeneity, less hot spots, and lower esophageal D_mean , and cord D_max [ITV D_95% : 101.81% vs 98.68%, Solo vs CTPS, P = 0.002; ITV D_5% -D_95% : 2.94% vs 7.51%, P = 0.002; cord D_max : 18.87 vs 22.29 Gy(RBE), P = 0.014].

CONCLUSIONS

Solo-generated IMPT plans provide improved cord sparing, better target robustness in all considered phases, and reduced interplay effect compared with CTPS. Consequently, the approximation methods currently used in commercial TPS programs may have space for improvement in generating optimal IMPT plans for patient cases with locally advanced lung cancer.

Potential for Improvements in Robustness and Optimality of Intensity-Modulated Proton Therapy for Lung Cancer with 4-Dimensional Robust Optimization

BACKGROUND

Major challenges in the application of intensity-modulated proton therapy (IMPT) for lung cancer patients include the uncertainties associated with breathing motion, its mitigation and its consideration in IMPT optimization. The primary objective of this research was to evaluate the potential of four-dimensional robust optimization (4DRO) methodology to make IMPT dose distributions resilient to respiratory motion as well as to setup and range uncertainties; Methods: The effect of respiratory motion, characterized by different phases of 4D computed tomography (4DCT), was incorporated into an in-house 4DRO system. Dose distributions from multiple setup and range uncertainty scenarios were calculated for each of the ten phases of CT datasets. The 4DRO algorithm optimizes dose distributions to achieve target dose coverage and normal tissue sparing for multiple setup and range uncertainty scenarios as well as for all ten respiratory phases simultaneously. IMPT dose distributions of ten lung cancer patients with different tumor sizes and motion magnitudes were optimized to illustrate our approach and its potential; Results: Compared with treatment plans generated using the conventional planning target volume (PTV)-based optimization and 3D robust optimization (3DRO), plans generated by 4DRO were found to have superior clinical target volume coverage and dose robustness in the face of setup and range uncertainties as well as for respiratory motion. In most of the cases we studied, 4DRO also resulted in more homogeneous target dose distributions. Interestingly, such improvements were found even for cases in which moving diaphragms intruded into the proton beam paths; Conclusion: The incorporation of respiratory motion, along with setup and range uncertainties, into robust optimization, has the potential to improve the resilience of target and normal tissue dose distributions in IMPT plans in the face of the uncertainties considered. Moreover, it improves the optimality of plans compared to PTV-based optimization as well as 3DRO.

Computational models and tools

In this chapter, we describe two different methods, analytical (pencil beam) algorithms and Monte Carlo simulations, used to obtain the intended dose distributions in patients and evaluate their strengths and shortcomings. We discuss the difference between the prescribed physical dose and the biologically effective dose, the relative biological effectiveness (RBE) between ions and photons and the dependence of RBE on the linear energy transfer (LET). Lastly, we show how LET- or RBE-based optimization can be used to improve treatment plans and explore how the availability of multimodality ion beam facilities can be used to design a tumor-specific optimal treatment.

A novel pencil beam model for carbon-ion dose calculation derived from Monte Carlo simulations

An accurate kernel model is of vital importance for pencil-beam dose algorithm in charged particle therapy using precise spot-scanning beam delivery, in which an accurate depiction of the low dose envelope is especially crucial. Based on the Monte Carlo method, we investigated the dose contribution of secondary particles to the total dose and proposed a novel beam model to depict the lateral dose distribution of carbon-ion pencil beam in water. We demonstrated that the low dose envelope in single-spot profiles in water could be adequately modelled with the addition of a logistic distribution to a double Gaussian one, which was verified in both single carbon-ion pencil beam and superposed fields of different sizes with multiple pencil beams. Its superiority was mainly manifested at medium depths especially for high-energy beams with small fields compared with single, double and triple Gaussian models, where the secondary particles influenced the total dose considerably. The double Gaussian-logistic model could reduce the deviations from 4.1%, 1.7% to 0.3% in the plateau and peak regions, and from 19.2%, 4.9% to 1.2% in the tail region compared for the field size factor (FSF) calculations of 344 MeV/u carbon-ion pencil beam with the single and double Gaussian models. Compared with the triple Gaussian one, our newly-proposed model was on a par with it, even better than it in the plateau and peak regions. Thus our work will be helpful for improving the dose calculation accuracy for carbon-ion therapy.

RADIOTHERAPY PROTON BEAM PROFILOMETRY WITH scCVD DIAMOND DETECTOR IN SINGLE PARTICLE MODE

Proton radiotherapy requires precise knowledge of the volumetric dose distribution. In proton beam delivery systems, based on narrow pencil beams, a contribution from small doses in low-intensity regions, consisting mainly of scattered protons, may have not negligible influence on total dose delivered to patient. Insufficient information about dose profile can cause underestimation of dose and potential delivery of inflated dose during hadrontherapy treatment. Presented work aims to verify applicability of diamond detectors, produced by Chemical Vapor Deposition method, for therapeutic proton beam profilometry at large fields. This requires the capability of measuring the core of the beam intensity profile (wide dynamic range) as well as its lateral spread (very high sensitivity) with a single device.

Power-law relationship in the long-tailed sections of proton dose distributions

The halo portion of a proton therapy dose creates a long tail in proton dose distributions, but so far study of this phenomenon has been limited. We used statistical methods and mathematical models to confirm that the long-tailed portion of proton dose distributions exhibits a power-law relationship. By analyzing 299 measured dose profiles, we found that all proton lateral dose distributions had a significant power-law scaling correlation with a high correlation coefficient in the tail. We set up a dual-mechanism model, containing both direct and indirect impact mechanisms. In the direct impact mechanism, the proximal dose deposition is mainly due to the direct impact of a proton on a particle. In the indirect mechanism, the impact of a proton on a given particle is considered in terms of the proton’s impact on a neighboring particle that then impacts the given particle. We found that the indirect impact mechanism led to a tail in the distribution exhibiting a power-law relationship because the probability of the indirect impacts was proportional to the distance; i.e., the longer the distance, the larger the indirect impact probability. Upon analyzing the experimental data, we observed that the power-law exponent increased with proton energy.

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.

Robust intensity-modulated proton therapy to reduce high linear energy transfer in organs at risk

PURPOSE

We propose a robust treatment planning model that simultaneously considers proton range and patient setup uncertainties and reduces high linear energy transfer (LET) exposure in organs at risk (OARs) to minimize the relative biological effectiveness (RBE) dose in OARs for intensity-modulated proton therapy (IMPT). Our method could potentially reduce the unwanted damage to OARs.

METHODS

We retrospectively generated plans for 10 patients including two prostate, four head and neck, and four lung cancer patients. The "worst-case robust optimization" model was applied. One additional term as a "biological surrogate (BS)" of OARs due to the high LET-related biological effects was added in the objective function. The biological surrogate was defined as the sum of the physical dose and extra biological effects caused by the dose-averaged LET. We generated nine uncertainty scenarios that considered proton range and patient setup uncertainty. Corresponding to each uncertainty scenario, LET was obtained by a fast LET calculation method developed in-house and based on Monte Carlo simulations. In each optimization iteration, the model used the worst-case BS among all scenarios and then penalized overly high BS to organs. The model was solved by an efficient algorithm (limited-memory Broyden-Fletcher-Goldfarb-Shanno) in a parallel computing environment. Our new model was benchmarked with the conventional robust planning model without considering BS. Dose-volume histograms (DVHs) of the dose assuming a fixed RBE of 1.1 and BS for tumor and organs under nominal and uncertainty scenarios were compared to assess the plan quality between the two methods.

RESULTS

For the 10 cases, our model outperformed the conventional robust model in avoidance of high LET in OARs. At the same time, our method could achieve dose distributions and plan robustness of tumors assuming a fixed RBE of 1.1 almost the same as those of the conventional robust model.

CONCLUSIONS

Explicitly considering LET in IMPT robust treatment planning can reduce the high LET to OARs and minimize the possible toxicity of high RBE dose to OARs without sacrificing plan quality. We believe this will allow one to design and deliver safer proton therapy.

Evaluating the accuracy of a three-term pencil beam algorithm in heterogeneous media

The goal of this work was to evaluate the accuracy of our in-house analytical dose calculation code against MCNPX data in heterogeneous phantoms. The analytical model utilizes a pencil beam model based on Fermi-Eyges theory to account for multiple Coulomb scattering and a least-squares fit to Monte Carlo data to account for nonelastic nuclear interactions as well as any remaining, uncharacterized scatter (the 'nuclear halo'). The model characterized dose accurately (up to 1% of maximum dose in broad fields (4  ×  4 cm² and 10  ×  10 cm²) and up to 0.01% in a narrow field (0.1  ×  0.1 cm²) fit to MCNPX data). The accuracy of the model was benchmarked in three types of stylized phantoms: (1) homogeneous, (2) laterally infinite slab heterogeneities, and (3) laterally finite slab heterogeneities. Results from homogeneous phantoms and laterally infinite slab heterogeneities showed high levels of accuracy (>98% of points within 2% or 0.1 cm distance-to-agreement (DTA)). However, because range straggling and secondary particle production were not included in our model, central-axis dose differences of 2-4% were observed in laterally infinite slab heterogeneities when compared to Monte Carlo dose. In the presence of laterally finite slab heterogeneities, the analytical model resulted in lower pass rates (>96% of points within 2% or 0.1 cm DTA), which was attributed to the use of the central-axis approximation.

Mixed integer programming with dose-volume constraints in intensity-modulated proton therapy

Background

In treatment planning for intensity‐modulated proton therapy (IMPT), we aim to deliver the prescribed dose to the target yet minimize the dose to adjacent healthy tissue. Mixed‐integer programming (MIP) has been applied in radiation therapy to generate treatment plans. However, MIP has not been used effectively for IMPT treatment planning with dose‐volume constraints. In this study, we incorporated dose‐volume constraints in an MIP model to generate treatment plans for IMPT.

Methods

We created a new MIP model for IMPT with dose volume constraints. Two groups of IMPT treatment plans were generated for each of three patients by using MIP models for a total of six plans: one plan was derived with the Limited‐memory Broyden–Fletcher–Goldfarb–Shanno (L‐BFGS) method while the other plan was derived with our MIP model with dose‐volume constraints. We then compared these two plans by dose‐volume histogram (DVH) indices to evaluate the performance of the new MIP model with dose‐volume constraints. In addition, we developed a model to more efficiently find the best balance between tumor coverage and normal tissue protection.

Results

The MIP model with dose‐volume constraints generates IMPT treatment plans with comparable target dose coverage, target dose homogeneity, and the maximum dose to organs at risk (OARs) compared to treatment plans from the conventional quadratic programming method without any tedious trial‐and‐error process. Some notable reduction in the mean doses of OARs is observed.

Conclusions

The treatment plans from our MIP model with dose‐volume constraints can meet all dose‐volume constraints for OARs and targets without any tedious trial‐and‐error process. This model has the potential to automatically generate IMPT plans with consistent plan quality among different treatment planners and across institutions and better protection for important parallel OARs in an effective way.

Factors influencing the performance of patient specific quality assurance for pencil beam scanning IMPT fields

PURPOSE

A detailed analysis of 2728 intensity modulated proton therapy (IMPT) fields that were clinically delivered to patients between 2007 and 2013 at Paul Scherrer Institute (PSI) was performed. The aim of this study was to analyze the results of patient specific dosimetric verifications and to assess possible correlation between the quality assurance (QA) results and specific field metrics.

METHODS

Dosimetric verifications were performed for every IMPT field prior to patient treatment. For every field, a steering file was generated containing all the treatment unit information necessary for treatment delivery: beam energy, beam angle, dose, size of air gap, nuclear interaction (NI) correction factor, number of range shifter plates, number of Bragg peaks (BPs) with their position and weight. This information was extracted and correlated to the results of dosimetric verification of each field which was a measurement of two orthogonal profiles using an orthogonal ionization chamber array in a movable water column.

RESULTS

The data analysis has shown more than 94% of all verified plans were within defined clinical tolerances. The differences between measured and calculated dose depend critically on the number of BPs, total thickness of all range shifter plates inserted in the beam path, and maximal range. An increase of the dose difference was observed with smaller number of BPs (i.e., smaller tumor) and smaller ranges (i.e., superficial tumors). The results of the verification do not depend, however, on the prescribed dose, NI correction, or the size of the air gap. There is no dependency of the transversal and longitudinal spot position precision on the beam angle. The value of NI correction depends on the number of spots and number of range shifter plates.

CONCLUSIONS

The presented study has shown that the verification method used at Centre for Proton Therapy at Paul Scherrer Institute is accurate and reproducible for performing patient specific QA. The results confirmed that the dose discrepancy is dependent on the size and location of the tumor.

An efficient method to determine double Gaussian fluence parameters in the eclipse™ proton pencil beam model

PURPOSE

To find an efficient method to configure the proton fluence for a commercial proton pencil beam scanning (PBS) treatment planning system (TPS).

METHODS

An in-water dose kernel was developed to mimic the dose kernel of the pencil beam convolution superposition algorithm, which is part of the commercial proton beam therapy planning software, eclipse™ (Varian Medical Systems, Palo Alto, CA). The field size factor (FSF) was calculated based on the spot profile reconstructed by the in-house dose kernel. The workflow of using FSFs to find the desirable proton fluence is presented. The in-house derived spot profile and FSF were validated by a direct comparison with those calculated by the eclipse TPS. The validation included 420 comparisons of the FSFs from 14 proton energies, various field sizes from 2 to 20 cm and various depths from 20% to 80% of proton range.

RESULTS

The relative in-water lateral profiles between the in-house calculation and the eclipse TPS agree very well even at the level of 10^-4. The FSFs between the in-house calculation and the eclipse TPS also agree well. The maximum deviation is within 0.5%, and the standard deviation is less than 0.1%.

CONCLUSIONS

The authors' method significantly reduced the time to find the desirable proton fluences of the clinical energies. The method is extensively validated and can be applied to any proton centers using PBS and the eclipse TPS.

Using field size factors to characterize the in-air fluence of a proton machine with a range shifter

INTRODUCTION

The range shifter (RS) is used to treat shallow tumors for a proton pencil beam scanning system (PBS). Adding RS certainly complicates the commissioning of the treatment planning system (TPS) because the spot sizes are significantly enlarged with RS. In this work, we present an efficient method to configure a commercial TPS for a PBS system with a fixed RS.

METHODS

By combining a spiral delivery with customized control points, we were able to significantly improve measurement efficiency and obtain 250 field size factors (FSF) within three hours. The measured FSFs were used to characterize the proton fluence and fit the parameters for the double-Gaussian fluence model used in the TPS. Extensive validation was performed using FSFs measured in air and in water, absolute doses of spread-out Bragg peak (SOBP) fields, and the dose measurements carried out for patient-specific quality assurance (QA).

RESULTS

The measured in-air FSFs agreed with the model's prediction within 3% for all 250 FSFs, and within 2 for 94% of the FSFs. The agreement between model's prediction and measurement was within 2% for the in-air and in-water FSFs and the absolute doses for SOBP beams. The patient-specific QA of 113 fields showed an excellent gamma passing rates (96.95 ± 2.51%) for the absolute dose comparisons with gamma criteria of 2 mm and 2%.

CONCLUSION

The excellent agreement between the model's prediction and measurements proved the efficiency and accuracy of the proposed method of using FSFs to characterize the proton fluence and configure the TPS for a PBS system with fixed RS.

Robust treatment planning with conditional value at risk chance constraints in intensity-modulated proton therapy

BACKGROUND AND PURPOSE

Intensity-modulated proton therapy (IMPT) is highly sensitive to range uncertainties and uncertainties caused by setup variation. The conventional inverse treatment planning of IMPT based on the planning target volume (PTV) is not often sufficient to ensure robustness of treatment plans. We applied a probabilistic framework (chance-constrained optimization) in IMPT planning to hedge against the influence of uncertainties.

MATERIAL AND METHODS

We retrospectively selected one patient with lung cancer, one patient with head and neck (H&N) cancer, and one with prostate cancer for this analysis. Using their original images and prescriptions, we created new IMPT plans using two methods: (1) a robust chance-constrained treatment planning method with the clinical target volume (CTV) as the target; (2) the margin-based method with PTV as the target, which was solved by commercial software, CPLEX, using linear programming. For the first method, we reformulated the model into a tractable mixed-integer programming problem and sped up the calculation using Benders decomposition. The dose-volume histograms (DVHs) from the nominal and perturbed dose distributions were used to assess and compare plan quality. DVHs for all uncertain scenarios along with the nominal DVH were plotted. The width of the "bands" of DVHs was used to quantify the plan sensitivity to uncertainty. The newly developed Benders decomposition method was compared with a commercial solution to demonstrate its computational efficiency. The trade-off between nominal plan quality and plan robustness was investigated.

RESULTS

Our chance-constrained model outperformed the PTV method in terms of tumor coverage, tumor dose homogeneity, and plan robustness. Our model was shown to produce IMPT plans to meet the dose-volume constraints of organs at risk (OARs) and had better sparing of OARs than the PTV method in the three clinical cases included in this study. The chance-constrained model provided a flexible tool for users to balance between plan robustness and plan quality. In addition, our in-house developed method was found to be much faster than the commercial solution.

CONCLUSION

With explicit control of plan robustness, the chance-constrained robust optimization model generated superior IMPT plans compared to the PTV-based method.

Clinical Commissioning of a Pencil Beam Scanning Treatment Planning System for Proton Therapy

Purpose

In this report, we present the commissioning and validation results for a commercial proton pencil beam scanning RayStation treatment planning system.

Materials and Methods

The commissioning data requirements are (1) integrated depth dose curves, (2) spot profiles, (3) absolute dose/monitor unit calibration, and (4) virtual source position. An 8-cm parallel plate chamber was used to measure the integrated depth dose curves by scanning a beam composed of a single spot in a water phantom. The spot profiles were measured at 5 different planes using a 2-dimensional scintillation detector. The absolute dose/monitor unit calibration was based on dose measurements in single-layer fields of size 10 × 10 cm². The virtual-source position was calculated from the change in spot spacing with the distance from the isocenter. The beam model validation consisted of a comparison against commissioning data as well as a new set of verification measurements. For end-to-end testing, a series of phantom plans were created. These plans were measured at 1 to 3 depths using a 2-dimensional ion chamber array and evaluated for gamma index using the 3% and 3 mm criteria.

Results

The maximum deviation for spot sigma measured versus calculated was -0.2 mm. The point-dose measurements for single-layer beams were within ± 3%, except for the largest field size (29 × 29 cm²) and the highest energy (226 MeV). The point doses in the spread-out Bragg peak plans showed a trend in which differences > 3% were seen for ranges > 30 cm, field sizes > 15 × 15 cm², and depths > 25 cm. For end-to-end testing, 34 planes corresponding to 13 beams were analyzed for gamma index with a minimum pass rate of 92.8%.

Conclusion

The acceptable verification results and successful end-to-end testing ensured that all components of the treatment planning system were functional and the system was ready for clinical use.

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.

Fast Pencil Beam Dose Calculation for Proton Therapy Using a Double-Gaussian Beam Model

The highly conformal dose distributions produced by scanned proton pencil beams (PBs) are more sensitive to motion and anatomical changes than those produced by conventional radiotherapy. The ability to calculate the dose in real-time as it is being delivered would enable, for example, online dose monitoring, and is therefore highly desirable. We have previously described an implementation of a PB algorithm running on graphics processing units (GPUs) intended specifically for online dose calculation. Here, we present an extension to the dose calculation engine employing a double-Gaussian beam model to better account for the low-dose halo. To the best of our knowledge, it is the first such PB algorithm for proton therapy running on a GPU. We employ two different parameterizations for the halo dose, one describing the distribution of secondary particles from nuclear interactions found in the literature and one relying on directly fitting the model to Monte Carlo simulations of PBs in water. Despite the large width of the halo contribution, we show how in either case the second Gaussian can be included while prolonging the calculation of the investigated plans by no more than 16%, or the calculation of the most time-consuming energy layers by about 25%. Furthermore, the calculation time is relatively unaffected by the parameterization used, which suggests that these results should hold also for different systems. Finally, since the implementation is based on an algorithm employed by a commercial treatment planning system, it is expected that with adequate tuning, it should be able to reproduce the halo dose from a general beam line with sufficient accuracy.

Validation of nuclear models in Geant4 using the dose distribution of a 177 MeV proton pencil beam

A proton pencil beam is associated with a surrounding low-dose envelope, originating from nuclear interactions. It is important for treatment planning systems to accurately model this envelope when performing dose calculations for pencil beam scanning treatments, and Monte Carlo (MC) codes are commonly used for this purpose. This work aims to validate the nuclear models employed by the Geant4 MC code, by comparing the simulated absolute dose distribution to a recent experiment of a 177 MeV proton pencil beam stopping in water. Striking agreement is observed over five orders of magnitude, with both the shape and normalisation well modelled. The normalisations of two depth dose curves are lower than experiment, though this could be explained by an experimental positioning error. The Geant4 neutron production model is also verified in the distal region. The entrance dose is poorly modelled, suggesting an unaccounted upstream source of low-energy protons. Recommendations are given for a follow-up experiment which could resolve these issues.

Exploratory Study of 4D versus 3D Robust Optimization in Intensity Modulated Proton Therapy for Lung Cancer

PURPOSE

The purpose of this study was to compare the impact of uncertainties and interplay on 3-dimensional (3D) and 4D robustly optimized intensity modulated proton therapy (IMPT) plans for lung cancer in an exploratory methodology study.

METHODS AND MATERIALS

IMPT plans were created for 11 nonrandomly selected non-small cell lung cancer (NSCLC) cases: 3D robustly optimized plans on average CTs with internal gross tumor volume density overridden to irradiate internal target volume, and 4D robustly optimized plans on 4D computed tomography (CT) to irradiate clinical target volume (CTV). Regular fractionation (66 Gy [relative biological effectiveness; RBE] in 33 fractions) was considered. In 4D optimization, the CTV of individual phases received nonuniform doses to achieve a uniform cumulative dose. The root-mean-square dose-volume histograms (RVH) measured the sensitivity of the dose to uncertainties, and the areas under the RVH curve (AUCs) were used to evaluate plan robustness. Dose evaluation software modeled time-dependent spot delivery to incorporate interplay effect with randomized starting phases of each field per fraction. Dose-volume histogram (DVH) indices comparing CTV coverage, homogeneity, and normal tissue sparing were evaluated using Wilcoxon signed rank test.

RESULTS

4D robust optimization plans led to smaller AUC for CTV (14.26 vs 18.61, respectively; P=.001), better CTV coverage (Gy [RBE]) (D95% CTV: 60.6 vs 55.2, respectively; P=.001), and better CTV homogeneity (D5%-D95% CTV: 10.3 vs 17.7, respectively; P=.002) in the face of uncertainties. With interplay effect considered, 4D robust optimization produced plans with better target coverage (D95% CTV: 64.5 vs 63.8, respectively; P=.0068), comparable target homogeneity, and comparable normal tissue protection. The benefits from 4D robust optimization were most obvious for the 2 typical stage III lung cancer patients.

CONCLUSIONS

Our exploratory methodology study showed that, compared to 3D robust optimization, 4D robust optimization produced significantly more robust and interplay-effect-resistant plans for targets with comparable dose distributions for normal tissues. A further study with a larger and more realistic patient population is warranted to generalize the conclusions.

Reducing Dose Uncertainty for Spot-Scanning Proton Beam Therapy of Moving Tumors by Optimizing the Spot Delivery Sequence

PURPOSE

To develop and validate a novel delivery strategy for reducing the respiratory motion-induced dose uncertainty of spot-scanning proton therapy.

METHODS AND MATERIALS

The spot delivery sequence was optimized to reduce dose uncertainty. The effectiveness of the delivery sequence optimization was evaluated using measurements and patient simulation. One hundred ninety-one 2-dimensional measurements using different delivery sequences of a single-layer uniform pattern were obtained with a detector array on a 1-dimensional moving platform. Intensity modulated proton therapy plans were generated for 10 lung cancer patients, and dose uncertainties for different delivery sequences were evaluated by simulation.

RESULTS

Without delivery sequence optimization, the maximum absolute dose error can be up to 97.2% in a single measurement, whereas the optimized delivery sequence results in a maximum absolute dose error of ≤11.8%. In patient simulation, the optimized delivery sequence reduces the mean of fractional maximum absolute dose error compared with the regular delivery sequence by 3.3% to 10.6% (32.5-68.0% relative reduction) for different patients.

CONCLUSIONS

Optimizing the delivery sequence can reduce dose uncertainty due to respiratory motion in spot-scanning proton therapy, assuming the 4-dimensional CT is a true representation of the patients' breathing patterns.

On the parametrization of lateral dose profiles in proton radiation therapy

PURPOSE

The accurate evaluation of the lateral dose profile is an important issue in the field of proton radiation therapy. The beam spread, due to Multiple Coulomb Scattering (MCS), is described by the Molière's theory. To take into account also the contribution of nuclear interactions, modern Treatment Planning Systems (TPSs) generally approximate the dose profiles by a sum of Gaussian functions. In this paper we have compared different parametrizations for the lateral dose profile of protons in water for therapeutical energies: the goal is to improve the performances of the actual treatment planning.

METHODS

We have simulated typical dose profiles at the CNAO (Centro Nazionale di Adroterapia Oncologica) beamline with the FLUKA code and validated them with data taken at CNAO considering different energies and depths. We then performed best fits of the lateral dose profiles for different functions using ROOT and MINUIT.

RESULTS

The accuracy of the best fits was analyzed by evaluating the reduced χ(2), the number of free parameters of the functions and the calculation time. The best results were obtained with the triple Gaussian and double Gaussian Lorentz-Cauchy functions which have 6 parameters, but good results were also obtained with the so called Gauss-Rutherford function which has only 4 parameters.

CONCLUSIONS

The comparison of the studied functions with accurate and validated Monte Carlo calculations and with experimental data from CNAO lead us to propose an original parametrization, the Gauss-Rutherford function, to describe the lateral dose profiles of proton beams.