Modelling small block aperture in an in-house developed GPU-accelerated Monte Carlo-based dose engine for pencil beam scanning proton therapy.

Purpose. To enhance an in-house graphic-processing-unit accelerated virtual particle (VP)-based Monte Carlo (MC) proton dose engine (VPMC) to model aperture blocks in both dose calculation and optimization for pencil beam scanning proton therapy (PBSPT)-based stereotactic radiosurgery (SRS).Methods and materials. A module to simulate VPs passing through patient-specific aperture blocks was developed and integrated in VPMC based on simulation results of realistic particles (primary protons and their secondaries). To validate the aperture block module, VPMC was first validated by an opensource MC code, MCsquare, in eight water phantom simulations with 3 cm thick brass apertures: four were with aperture openings of 1, 2, 3, and 4 cm without a range shifter, while the other four were with same aperture opening configurations with a range shifter of 45 mm water equivalent thickness. Then, VPMC was benchmarked with MCsquare and RayStation MC for 10 patients with small targets (average volume 8.4 c.c. with range of 0.4-43.3 c.c.). Finally, 3 typical patients were selected for robust optimization with aperture blocks using VPMC.Results. In the water phantoms, 3D gamma passing rate (2%/2 mm/10%) between VPMC and MCsquare was 99.71 ± 0.23%. In the patient geometries, 3D gamma passing rates (3%/2 mm/10%) between VPMC/MCsquare and RayStation MC were 97.79 ± 2.21%/97.78 ± 1.97%, respectively. Meanwhile, the calculation time was drastically decreased from 112.45 ± 114.08 s (MCsquare) to 8.20 ± 6.42 s (VPMC) with the same statistical uncertainties of ~0.5%. The robustly optimized plans met all the dose-volume-constraints (DVCs) for the targets and OARs per our institutional protocols. The mean calculation time for 13 influence matrices in robust optimization by VPMC was 41.6 s and the subsequent on-the-fly 'trial-and-error' optimization procedure took only 71.4 s on average for the selected three patients.Conclusion. VPMC has been successfully enhanced to model aperture blocks in dose calculation and optimization for the PBSPT-based SRS.

Modelling small block aperture in an in-house developed GPU-accelerated Monte Carlo-based dose engine for pencil beam scanning proton therapy.

Purpose: To enhance an in-house graphic-processing-unit (GPU) accelerated virtual particle (VP)-based Monte Carlo (MC) proton dose engine (VPMC) to model aperture blocks in both dose calculation and optimization for pencil beam scanning proton therapy (PBSPT)-based stereotactic radiosurgery (SRS). Methods and Materials: A module to simulate VPs passing through patient-specific aperture blocks was developed and integrated in VPMC based on simulation results of realistic particles (primary protons and their secondaries). To validate the aperture block module, VPMC was first validated by an opensource MC code, MCsquare, in eight water phantom simulations with 3cm thick brass apertures: four were with aperture openings of 1, 2, 3, and 4cm without a range shifter, while the other four were with same aperture opening configurations with a range shifter of 45mm water equivalent thickness. Then, VPMC was benchmarked with MCsquare and RayStation MC for 10 patients with small targets (average volume 8.4 cc with range of 0.4 - 43.3 cc). Finally, 3 typical patients were selected for robust optimization with aperture blocks using VPMC. Results: In the water phantoms, 3D gamma passing rate (2%/2mm/10%) between VPMC and MCsquare was 99.71±0.23%. In the patient geometries, 3D gamma passing rates (3%/2mm/10%) between VPMC/MCsquare and RayStation MC were 97.79±2.21%/97.78±1.97%, respectively. Meanwhile, the calculation time was drastically decreased from 112.45±114.08 seconds (MCsquare) to 8.20±6.42 seconds (VPMC) with the same statistical uncertainties of ~0.5%. The robustly optimized plans met all the dose-volume-constraints (DVCs) for the targets and OARs per our institutional protocols. The mean calculation time for 13 influence matrices in robust optimization by VPMC was 41.6 seconds and the subsequent on-the-fly "trial-and-error" optimization procedure took only 71.4 seconds on average for the selected three patients. Conclusion: VPMC has been successfully enhanced to model aperture blocks in dose calculation and optimization for the PBSPT-based SRS.

Virtual particle Monte Carlo: A new concept to avoid simulating secondary particles in proton therapy dose calculation.

BACKGROUND: In proton therapy dose calculation, Monte Carlo (MC) simulations are superior in accuracy but more time consuming, compared to analytical calculations. Graphic processing units (GPUs) are effective in accelerating MC simulations but may suffer thread divergence and racing condition in GPU threads that degrades the computing performance due to the generation of secondary particles during nuclear reactions. PURPOSE: A novel concept of virtual particle (VP) MC (VPMC) is proposed to avoid simulating secondary particles in GPU-accelerated proton MC dose calculation and take full advantage of the computing power of GPU. METHODS: Neutrons and gamma rays were ignored as escaping from the human body; doses of electrons, heavy ions, and nuclear fragments were locally deposited; the tracks of deuterons were converted into tracks of protons. These particles, together with primary and secondary protons, are considered to be the realistic particles. Histories of primary and secondary protons were replaced by histories of multiple VPs. Each VP corresponded to one proton (either primary or secondary). A continuous-slowing-down-approximation model, an ionization model, and a large angle scattering event model corresponding to nuclear interactions were developed for VPs by generating probability distribution functions (PDFs) based on simulation results of realistic particles using MCsquare. For efficient calculations, these PDFs were stored in the Compute Unified Device Architecture textures. VPMC was benchmarked with TOPAS and MCsquare in phantoms and with MCsquare in 13 representative patient geometries. Comparisons between the VPMC calculated dose and dose measured in water during patient-specific quality assurance (PSQA) of the selected 13 patients were also carried out. Gamma analysis was used to compare the doses derived from different methods and calculation efficiencies were also compared. RESULTS: Integrated depth dose and lateral dose profiles in both homogeneous and inhomogeneous phantoms all matched well among VPMC, TOPAS, and MCsquare calculations. The 3D-3D gamma passing rates with a criterion of 2%/2 mm and a threshold of 10% was 98.49% between MCsquare and TOPAS and 98.31% between VPMC and TOPAS in homogeneous phantoms, and 99.18% between MCsquare and TOPAS and 98.49% between VPMC and TOPAS in inhomogeneous phantoms, respectively. In patient geometries, the 3D-3D gamma passing rates with 2%/2 mm/10% between dose distributions from VPMC and MCsquare were 98.56 ± 1.09% in patient geometries. The 2D-3D gamma analysis with 3%/2 mm/10% between the VPMC calculated dose distributions and the 2D measured planar dose distributions during PSQA was 98.91 ± 0.88%. VPMC calculation was highly efficient and took 2.84 ± 2.44 s to finish for the selected 13 patients running on four NVIDIA Ampere GPUs in patient geometries. CONCLUSION: VPMC was found to achieve high accuracy and efficiency in proton therapy dose calculation.

GPU-accelerated Monte Carlo-based online adaptive proton therapy: A feasibility study.

PURPOSE: To develop an online graphic processing unit (GPU)-accelerated Monte Carlo-based adaptive radiation therapy (ART) workflow for pencil beam scanning (PBS) proton therapy to address interfraction anatomical changes in patients treated with PBS. METHODS AND MATERIALS: A four-step workflow was developed using our in-house developed GPU-accelerated Monte Carlo-based treatment planning system to implement online Monte Carlo-based ART for PBS. The first step conducts diffeomorphic demon-based deformable image registration (DIR) to propagate contours on the initial planning CT (pCT) to the verification CT (vCT) to form a new structure set. The second step performs forward dose calculation of the initial plan on the vCT with the propagated contours after manual approval (possible modifications involved). The third step triggers a reoptimization of the plan depending on whether the verification dose meets the clinical requirements or not. A robust evaluation will be done for both the verification plan in the second step and the reopotimized plan in the third step. The fourth step involves a two-stage (before and after delivery) patient-specific quality assurance (PSQA) of the reoptimized plan. The before-delivery PSQA is to compare the plan dose to the dose calculated using an independent fast open-source Monte Carlo code, MCsquare. The after-delivery PSQA is to compare the plan dose to the dose recalculated using the log file (spot MU, spot position, and spot energy) collected during the delivery. Jaccard index (JI), dice similarity coefficients (DSCs), and Hausdorff distance (HD) were used to assess the quality of the propagated contours in the first step. A commercial plan evaluation software, ClearCheck™, was integrated into the workflow to carry out efficient plan evaluation. 3D Gamma analysis was used during the fourth step to ensure the accuracy of the plan dose from reoptimization. Three patients with three different disease sites were chosen to evaluate the feasibility of the online ART workflow for PBS. RESULTS: For all three patients, the propagated contours were found to have good volume conformance [JI (lowest-highest: 0.833-0.983) and DSC (0.909-0.992)] but suboptimal boundary coincidence [HD (2.37-20.76 mm)] for organs-at-risk. The verification dose evaluated by ClearCheck™ showed significant degradation of the target coverage due to the interfractional anatomical changes. Reoptimization on the vCT resulted in great improvement of the plan quality to a clinically acceptable level. 3D Gamma analyses of PSQA confirmed the accuracy of the plan dose before delivery (mean Gamma index = 98.74% with a threshold of 2%/2 mm/10%), and after delivery based on the log files (mean Gamma index = 99.05% with a threshold of 2%/2 mm/10%). The average time cost for the complete execution of the workflow was around 858 s, excluding the time for manual intervention. CONCLUSION: The proposed online ART workflow for PBS was demonstrated to be efficient and effective by generating a reoptimized plan that significantly improved the plan quality.

Technical note: Evaluation and second check of a commercial Monte Carlo dose engine for small-field apertures in pencil beam scanning proton therapy.

PURPOSE: To evaluate the accuracy of the RayStation Monte Carlo dose engine (RayStation MC) in modeling small-field block apertures in proton pencil beam scanning. Furthermore, we evaluate the suitability of MCsquare as a second check for RayStation MC. METHODS: We have enhanced MCsquare to model block apertures. To test the accuracy of both RayStation MC and the newly enhanced MCsquare, we compare the dose predictions of each to in-water dose measurements obtained using diode detectors and radiochromic film. Nine brass apertures with openings of 1, 2, 3, 4, and 5 cm and either 2 cm or 4 cm thickness were used in the irradiation of a water phantom. Two measurement setups were used, one with a range shifter and 119.7 MeV proton beam energy and the other with no range shifter and 147 MeV proton beam energy. To further test the validity of RayStation MC and MCsquare in modeling block apertures and to evaluate MCsquare as a second check tool, 10 small-field (average target volume 8.3 cm3 ) patient treatment plans were calculated by each dose engine followed by a statistical comparison. RESULTS: Comparing to the absolute dose measurements in water, RayStation MC differed by 1.2% ± 1.0% while MCsquare differed by -1.8% ± 3.7% in the plateau region of a pristine Bragg peak. Compared to the in-water film measurements, RayStation MC and MCsquare both performed well with an average 2D-3D gamma passing rate of 99.4% and 99.7% (3%/3 mm), respectively. A t-test comparing the agreement with the film measurements between RayStation MC and MCsquare suggested that the relative spatial dose distributions calculated by MCsquare and RayStation MC were statistically indistinguishable. Directly comparing the dose calculations between MCsquare and RayStation MC over 10 patients resulted in an average 3D-3D gamma passing rates of 98.5% (3%/3 mm) and 94.1% (2%/2 mm), respectively. CONCLUSION: The validity of RayStation MC algorithm for use with patient-specific apertures has been expanded to include small apertures. MCsquare has been enhanced to model apertures and was found to be an adequate second check of RayStation MC in this scenario.

Technical Note: Clinical modeling and validation of breast tissue expander metallic ports in a commercial treatment planning system for proton therapy.

PURPOSE: To validate breast tissue expander metallic port (MP) models in a commercial treatment planning system (TPS) in proton pencil beam scanning (PBS) treatments for breast cancer patients with breast tissue expanders. METHODS AND MATERIALS: Three types of MPs taken out of a Mentor CPX4, a Natrelle 133, and a PMT Integra breast tissue expanders and a 650 cc saline filled Mentor CPX4 expander were placed on top of acrylic slabs, and scanned using a Siemens Somatom Definition AS Open RT CT scanner. Structure templates for each of the MPs were designed within Eclipse TPS. The CT numbers for the metallic parts were overridden to reflect measured or calculated relative proton stopping powers (RPSPs). Mock targets were contoured in acrylic to represent postmastectomy chest-wall radiation therapy (PMRT) targets. Plans with different beam incident angles were optimized using the Eclipse TPS to deliver uniform prescription dose to the target using Hitachi Probeat-V PBS beams. Eclipse calculated doses and an in-house Monte Carlo (MC) code calculated doses were compared to the measured Gafchromic EBT3 film doses in acrylic. RESULTS: TPS/MC and film dose comparison results showed that (1) 3%/2 mm/10% threshold Gamma pass rates were better than 90.8% in the acrylic target region for all plans; (2) comparing TPS and film doses for the individual beam plans in the MP dose shadow areas, the area with dose difference above 5% ([ΔA] 5%) ranged from 1.1 to 5.0 cm2 , and the maximum dose difference ([ΔD] 0.01 cm2 ) ranged from 12.5% to 25.0%; (3) comparing MC and film doses for the individual beam plans in the MP dose shadow areas, the (ΔA) 5% varied from 1.1 to 2.9 cm2 and (ΔD) 0.01 cm2 varied from 8.5% to 24.2%; (4) for a plan composed of three individual beams treating through the Mentor CPX4 expander, the TPS (ΔA) 5% was less than 0.13 cm2 , and the (ΔD) 0.01 cm2 was less than 6% in the MP dose shadow areas. CONCLUSIONS: It is feasible to treat patients with tissue expanders using multiple PBS beams using a structure template with CT number overridden to represent the measured/calculated RPSP for MPs for PBS treatment planning. MC dose was more accurate than analytical dose in the areas with high dose gradient caused by the density heterogeneity of the breast tissue expander MPs.

Technical Note: Integrating an open source Monte Carlo code "MCsquare" for clinical use in intensity-modulated proton therapy.

PURPOSE: To commission an open source Monte Carlo (MC) dose engine, "MCsquare" for a synchrotron-based proton machine, integrate it into our in-house C++-based I/O user interface and our web-based software platform, expand its functionalities, and improve calculation efficiency for intensity-modulated proton therapy (IMPT). METHODS: We commissioned MCsquare using a double Gaussian beam model based on in-air lateral profiles, integrated depth dose of 97 beam energies, and measurements of various spread-out Bragg peaks (SOBPs). Then we integrated MCsquare into our C++-based dose calculation code and web-based second check platform "DOSeCHECK." We validated the commissioned MCsquare based on 12 different patient geometries and compared the dose calculation with a well-benchmarked GPU-accelerated MC (gMC) dose engine. We further improved the MCsquare efficiency by employing the computed tomography (CT) resampling approach. We also expanded its functionality by adding a linear energy transfer (LET)-related model-dependent biological dose calculation. RESULTS: Differences between MCsquare calculations and SOBP measurements were <2.5% (<1.5% for ~85% of measurements) in water. The dose distributions calculated using MCsquare agreed well with the results calculated using gMC in patient geometries. The average 3D gamma analysis (2%/2 mm) passing rates comparing MCsquare and gMC calculations in the 12 patient geometries were 98.0 ± 1.0%. The computation time to calculate one IMPT plan in patients' geometries using an inexpensive CPU workstation (Intel Xeon E5-2680 2.50 GHz) was 2.3 ± 1.8 min after the variable resolution technique was adopted. All calculations except for one craniospinal patient were finished within 3.5 min. CONCLUSIONS: MCsquare was successfully commissioned for a synchrotron-based proton beam therapy delivery system and integrated into our web-based second check platform. After adopting CT resampling and implementing LET model-dependent biological dose calculation capabilities, MCsquare will be sufficiently efficient and powerful to achieve Monte Carlo-based and LET-guided robust optimization in IMPT, which will be done in the future studies.

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

PURPOSE: The dose-averaged linear energy transfer (LETd ) 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 LETd calculation that is more accurate than 1D analytical model. METHODS: We used the Geant4 MC code to generate 3D LETd distributions of monoenergetic proton beams in water for all energies and used a customized error function to fit the LETd lateral profiles at various depths to the MC simulation. The 3D LETd calculation kernel was a lookup table of these fitted coefficients, and LETd was determined directly from spot energies and voxel coordinates during analytical dose calculations. We validated our new method by comparing the calculated LETd 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 LETd 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 LETd simultaneously using an Intel Xeon E5-2680 2.50 GHz workstation was approximately 2.5 min. CONCLUSIONS: Our new method significantly improved the LETd calculation accuracy compared to the 1D method while maintaining significantly shorter calculation time even comparing with the GPU-based fast MC code.

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.

Use of a radial projection to reduce the statistical uncertainty of spot lateral profiles generated by Monte Carlo simulation.

Monte Carlo (MC) simulation has been used to generate commissioning data for the beam modeling of treatment planning system (TPS). We have developed a method called radial projection (RP) for postprocessing of MC-simulation-generated data. We used the RP method to reduce the statistical uncertainty of the lateral profile of proton pencil beams with axial symmetry. The RP method takes advantage of the axial symmetry of dose distribution to use the mean value of multiple independent scores as the representative score. Using the mean as the representative value rather than any individual score results in substantial reduction in statistical uncertainty. Herein, we present the concept and step-by-step implementation of the RP method, as well as show the advantage of the RP method over conventional measurement methods for generating lateral profile. Lateral profiles generated by both methods were compared to demonstrate the uncertainty reduction qualitatively, and standard error comparison was performed to demonstrate the reduction quantitatively. The comparisons showed that statistical uncertainty was reduced substantially by the RP method. Using the RP method to postprocess MC data, the corresponding MC simulation time was reduced by a factor of 10 without quality reduction in the generated result from the MC data. We concluded that the RP method is an effective technique to increase MC simulation efficiency for generating lateral profiles for axially symmetric pencil beams.

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.

Clinical Implementation of a Proton Dose Verification System Utilizing a GPU Accelerated Monte Carlo Engine.

PURPOSE: To develop a clinical infrastructure that allows for routine Monte Carlo dose calculation verification of spot scanning proton treatment plans and includes a simple biological model to aid in normal tissue protection. MATERIALS AND METHODS: A graphical processing unit accelerated Monte Carlo dose engine was used as the calculation engine for dose verification on spot scanning proton plans. An infrastructure was built around this engine that allows for seamless exporting of treatment plans from the treatment planning system and importing of dose distribution from the Monte Carlo calculation via DICOM (digital imaging and communications in medicine). An easy-to-use Web-based interface was developed so that the application could be run from any computer. In addition to the standard relative biological effectiveness = 1.1 for proton therapy, a simple linear equation dependent on dose-weighted linear energy transfer was included. This was used to help detect possible high biological dose in critical structures. RESULTS: More than 270 patients were treated at our proton center in the first year of operation. Because most plans underwent multiple iterations before final approval, more than 1000 plans have been run through the system from multiple users with minimal downtime. The average time from plan export to importing of the Monte Carlo doses was less than 15 minutes. Treatment plans have been modified based on the nominal Monte Carlo dose or the biological dose. CONCLUSION: Monte Carlo dose calculation verification of spot scanning proton treatment plans is feasible in a clinical environment. The 3-dimensional dose verification, particularly near heterogeneities, has resulted in plan modifications. The biological dose data provides actionable feedback for end of range effects, especially in pediatric patients.

Variations in proton scanned beam dose delivery due to uncertainties in magnetic beam steering.

The purpose of this work was to develop a method to calculate and study the impact of fluctuations in the magnetic field strengths within the steering magnets in a proton scanning beam treatment nozzle on the dose delivered to the patient during a proton therapy treatment. First, an analytical relationship between magnetic field uncertainties in the steering magnets and the resulting lateral displacements in the position of the delivered scanned beam "dose spot" was established. Next, using a simple 3D dose calculation code and data from a validated Monte Carlo model of the proton scanning beam treatment nozzle, the uniform dose delivery to a 3D treatment volume was calculated. The dose distribution was then recalculated using the calculated lateral displacements due to magnetic field fluctuations to the proton pencil beam position. Using these two calculated dose distributions, the clinical effects of the magnetic field fluctuations were determined. A deliberate displacement of four adjacent spots either toward or away from each other was used to determine the "maximum" dose impact, while a random displacement of all spots was used to establish a more realistic clinical dose impact. Changes in the dose volume histogram (DVH) and the presence of hot and cold spots in the treatment volume were used to quantify the impact of dose-spot displacement. A general analytical relationship between magnetic field uncertainty and final dose-spot position is presented. This analytical relationship was developed such that it can be applied to study magnetic beam steering for any scanned beam nozzle design. Using this relationship the authors found for the example beam steering nozzle used in this study that deliberate lateral displacements of 0.5 mm or random lateral displacements of up to 1.0 mm produced a noticeable dose impact (5% hot spot) in the treatment volume. A noticeable impact (3% decrease in treatment volume coverage) on the DVH was observed for random displacements of up to 1.5 mm. For the scanning nozzle studied in this work, these displacement values correlated with an uncertainty value of 2.04% in the magnetic field values of the nozzle steering magnets. The authors conclude that fluctuations in the dose-spot delivery caused by uncertainty in the magnet fields used for beam steering could have clinically significant effects on the delivered dose distribution. Due to differences in the design and implementation of proton beam scanning nozzles at different treatment facilities, the effects of magnetic field fluctuations of dose delivery should be evaluated and understood for each specific nozzle design during clinical commissioning of the treatment nozzle.

Benchmarking analytical calculations of proton doses in heterogeneous matter.

A proton dose computational algorithm, performing an analytical superposition of infinitely narrow proton beamlets (ASPB) is introduced. The algorithm uses the standard pencil beam technique of laterally distributing the central axis broad beam doses according to the Moliere scattering theory extended to slablike varying density media. The purpose of this study was to determine the accuracy of our computational tool by comparing it with experimental and Monte Carlo (MC) simulation data as benchmarks. In the tests, parallel wide beams of protons were scattered in water phantoms containing embedded air and bone materials with simple geometrical forms and spatial dimensions of a few centimeters. For homogeneous water and bone phantoms, the proton doses we calculated with the ASPB algorithm were found very comparable to experimental and MC data. For layered bone slab inhomogeneity in water, the comparison between our analytical calculation and the MC simulation showed reasonable agreement, even when the inhomogeneity was placed at the Bragg peak depth. There also was reasonable agreement for the parallelepiped bone block inhomogeneity placed at various depths, except for cases in which the bone was located in the region of the Bragg peak, when discrepancies were as large as more than 10%. When the inhomogeneity was in the form of abutting air-bone slabs, discrepancies of as much as 8% occurred in the lateral dose profiles on the air cavity side of the phantom. Additionally, the analytical depth-dose calculations disagreed with the MC calculations within 3% of the Bragg peak dose, at the entry and midway depths in the phantom. The distal depth-dose 20%-80% fall-off widths and ranges calculated with our algorithm and the MC simulation were generally within 0.1 cm of agreement. The analytical lateral-dose profile calculations showed smaller (by less than 0.1 cm) 20%-80% penumbra widths and shorter fall-off tails than did those calculated by the MC simulations. Overall, this work validates the usefulness of our ASPB algorithm as a reasonably fast and accurate tool for quality assurance in planning wide beam proton therapy treatment of clinical sites either composed of homogeneous materials or containing laterally extended inhomogeneities that are comparable in density and located away from the Bragg peak depths.