Modeling Considerations for Improving Accuracy of a Proton Therapy Beam with GEANT4 Samuel R. S. Barnes, Grant A. McAuley, James M. Slater, and Andrew J. Wroe Abstract–Simulations of a clinical proton treatment nozzle with GEANT4 were performed and compared against measured data to assess simulation accuracy. Various parameters were then adjusted to examine their effect of accuracy and determine optimal values. This analysis included GEANT version (9.3 and 9.5), range cuts, step max, and initial beam model. GEANT4 version 9.5 was found to give better range accuracy than version 9.3. Simulation accuracy was found to not be very sensitive to range cuts and step max parameters, but recommended values for high accuracy simulations are 250 µm for range cuts and 0.1 mm for step max. Finally, the initial beam model was shown to change the lateral profile in the phantom, however, lateral profiles still show significantly higher error rates than depth profiles.
I. INTRODUCTION are becoming the standard for MaccurateCarloprotonsimulations therapy simulations [1, 2]. Many recent ONTE
publications have focused on proper choice of physics models [3] and simulation settings [4] to achieve accurate simulations. Following these guidelines we have implemented a GEANT4 Monte Carlo simulation of our clinical proton treatment nozzle. With this software we have been able to accurately reproduce a standard set of commissioning data that spans all energies, multiple aperture sizes, and multiple range modulations used clinically. The focus of this paper will be on recent efforts to improve the accuracy and execution time of these simulations with an emphasis on verifying simulation results with measured data. All simulations results were compared with measured data using automated tools, and the accuracy of all modifications was evaluated on this basis. A number of factors were looked at including GEANT4 version, secondary particle range cuts, maximum allowed particle step size, and various beam models. II. MATERIALS AND METHODS Simulations were performed using our in-house developed Monte Carlo program called mbeam. This is built using GEANT4 and outputs results to a standard XML file format Manuscript received November 15, 2012. This work was supported in part by the U.S. Department of Defense under Grant No. W81XWH-BAA-10-1. S. R. S. Barnes is with the Radiation Medicine Department, Loma Linda University, Loma Linda, CA 92350 USA (telephone: 909-558-4000, e-mail:
[email protected]). G. A. McAuley is with the Radiation Medicine Department, Loma Linda University, Loma Linda, CA 92350 USA (e-mail:
[email protected]). J. M. Slater is with the Radiation Medicine Department, Loma Linda University, Loma Linda, CA 92350 USA. A. J. Wroe is with the Radiation Medicine Department, Loma Linda University Medical Center, Loma Linda, CA 92350 USA (e-mail:
[email protected]).
used by the open source Visualization Tool Kit (VTK). Analysis was performed with custom developed python scripts and open source tools such as ParaView (Kitware Inc., NY). All geometry in the treatment nozzle was accurately represented in the simulation from the exit window of the vacuum pipe to the phantom located at isocenter. This includes: two scattering elements, four dose monitoring detectors, four fixed apertures, a range modulator wheel, and a patient aperture. Simulation results were dose deposited by a circular field to a voxelized water phantom. Dose from all primary and secondary particles was considered. A voxel size of 1 mm x 1 mm x 1 mm was used in all simulations. A. GEANT4 Settings GEANT4 physics were selected based on what is recommended in the literature for proton therapy applications [3, 4]. Two different versions of GEANT4 were analyzed. For version 9.3 the same physics packages were used as those recommended by Jarlskog and Paganetti [3] with the exception of using the Livermore EM package. For version 9.5 similar physics packages were chosen and the following classes were used the with default constructors: EmLivermorePhysics, HadronHElasticPhysics, HadronInelasticQBBC, and IonBinaryCascadePhysics. The Livermore EM physics uses the same models for Hadron interactions as the EmStandardPhysics_option3 and only uses separate models for low energy elections and gammas. To parallelize our GEANT4 simulations a distributed run manager developed by Brain Harrawood from Duke University was used. This open source extension of GEANT4 is simply a subclass of the G4RunManager and uses a client and master design. A single master process starts a simulation and breaks it up into a number of smaller “tickets”. As clients are brought online they request jobs from the master and are issued a “ticket” for a job to complete (this includes all geometry information that is necessary). The master monitors client status and ticket completion so job execution will continue as clients are added and removed from a given job. When all tickets are completed the master collates all results and exits. This design allows a collection of unspecialized workstations to be combined together to create an effective cluster. No specialized software is required and clients can even run different operating systems. The only requirement is that all clients have IP access to the master. This software is made available to all researchers and is simple to add into an existing GEANT4 software project.
B. Parameters Examined Four different options were examined for their effect on simulation accuracy and execution time. First, two versions of GEANT4 were compared. Version 9.3, which had been verified in previous publications [3], was compared with version 9.5, which was the latest version as of this writing. Similar physics packages were chosen for both versions as described above. For the version comparison, range cuts and step max were set to the very conservative values of 3 µm and 0.01 mm, respectively. Second, range cuts in the phantom, which control the generation of secondary particles, were varied. Range cuts specify that only secondary particles that will travel further than a specified range in the current medium will be generated. If their range would be less than the cut value their energy is deposited locally. Lower range cut values should generate more secondary particles, which will increase execution time, but might result in more accurate simulations. Range cuts were varied from 3 µm to 1 mm. For this comparison step max was set to 0.01 mm and GEANT version 9.5 was used. Third, maximum particle step size in the phantom was varied. This specifies the maximum step size that a particle is allowed to take as is propagates through the phantom material. Again lower values will increase execution time, as more steps are required, but might increase simulation accuracy. Step max was varied from 10 µm to 5 mm. For this comparison range cuts were set to 250 µm and GEANT version 9.5 was used. Finally, two different proton beam models used to generate the initial proton beam were compared. These were a point source in the vacuum pipe and a 2D Gaussian source located at the exit window of the vacuum pipe. The angular spread was the same between the two models, and the point source was positioned in the vacuum pipe to give the same spatial distribution at the exit window as the 2D Gaussian. In this way the only difference between the two models was the phase space, or correlation between a protons position and its direction of travel. In the Gaussian source the position and initial direction are chosen individually and randomly so they are completely uncorrelated. In the point source the position at the exit window is determined by its initial direction as it travels down the vacuum pipe, so as it reaches the exit window its direction of travel and position are perfectly correlated. GEANT version 9.3 was used for the initial model comparison, later experiments with customized beam profiles for each energy was performed on version 9.5. C. Data Analysis Simulation results were compared to measured results from ion chamber (PTW Markus) for depth dose profiles and film measurements (Kodak X-OMAT V) for lateral profiles. For depth dose comparison the range error of the simulation was calculated by shifting the simulation dose profile in 0.1 mm increments until the maximum difference between the two was minimized. The amount of shift was recorded as the range
error of the simulation. Once the data was shifted a percent error was calculated for every simulation voxel (every 1 mm). Since the measured data was not collected at regular 1 mm intervals the two nearest measurement points were linearly interpolated to get an estimated measurement value at each simulation voxel.
Fig. 1. Example depth dose profile (top) and lateral profile (bottom) simulation results compared with measured data. Note the higher noise levels in the center of the lateral profile due to the averaging of multiple radial projections.
To reduce the noise in lateral profiles and take advantage of the circular symmetry of the simulation results, 80 lateral profile projections at equally spaced angular intervals around the circular cross section are calculated. These 80 projections are then averaged together to generate a single cross profile. This has the effect of dramatically reducing the simulation statistical noise around periphery of the profile. Unfortunately the noise at the center of the profile is largely unaffected, as the very small number of voxels in the center of the cross section does not allow for much noise reduction from averaging. A percent error compared to measured data was calculated for every voxel similar to that described above. However, since the film data the simulations are compared against are at a much higher resolution than the simulations all
III. RESULTS
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Fig. 2. The error rates between two different versions of GEANT4. There are no significant differences except of the range error were G4.9.5 shows over a 1 mm reduction in error.
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A. GEANT4 Version The standard simulation set was run with both versions of GEANT4 and the amount of error seen in each version was compared. No significant differences were seen except for the range error where version 9.5 showed over 1 mm less range error (Fig. 2).
B. Step Max The maximum particle step size allowed in the phantom was varied from 0.01 mm (or 1/100th of the voxel size) to 5 mm. All types of simulation error were seen to decrease with smaller step max (Fig. 3) while execution time was seen to increase especially once the step max was reduced below 0.1 mm (Fig. 4).
film measurement points that lay inside a simulation voxel were averaged together for the comparison. Analysis was restricted to the central points that are >80% of the nominal dose. Analysis was done at two depths one close to the surface and the other at the center of the spread out Brag peak (center of modulation). A standard commissioning set of simulations was developed that spanned all clinical energies in a wide variety of configurations. This set of simulations was used to test every change to the simulation settings. This set included all six clinical energies used, two stereotactic (127 and 157 MeV) and four large field energies (150, 186, 225, and 250 MeV). The stereotactic energies are distinct from the large field energies as they are run with a different scattering system that consists of a single uniform lead foil (S1). The large fields, in addition to S1, have a second scatterer (S2) that is a contoured foil of high and low z material that is designed to give a broad flat profile [5]. The stereotactic energies were run using a small (2 cm) field with 15 and 60 mm of range modulation. The large field energies were run with two field diameters (8.6 and 13.2 cm) and three range modulations (15, 60, and 100 mm). Results from all of these settings were compared to physical measurements to evaluate different simulation settings. To analyze any change in the error across all simulations in our standard set five measures of error were examined. For each lateral and depth profile the maximum error and the average of the entire profile was recorded. For depth profiles the range error was also recorded. These values were then averaged across all simulations performed.
Fig. 4. Execution time as a function of step max is shown. As expected execution time increases with a smaller step max value.
C. Range Cuts The secondary particle range cuts value was varied from 3 µm to 1 mm. No significant change in the accuracy of the simulations was seen with change in the range cuts value. ! " #$ ! " #$
D. Beam Model The analysis across all simulation results (Fig. 7) between the Gaussian and the point source model showed no difference between the two (Fig. 7). However, a more detailed analysis broken down by energy and nozzle configuration showed that the beam model affects the lateral profile, but not the depth profile. In the lateral profiles, the point source shows lower error at the high energies and the Gaussian model shows lower error at the medium energies (Fig. 8). The stereotactic energies, which use a different single foil scattering system, showed no change at all between the two models. *#
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Fig. 9. The amount of error for the generic beam parameters (spot size and divergence) and for unique beam parameters measured at each energy. Using more specific accurate initial beam parameters failed to improve simulation accuracy.
IV. DISCUSSION GEANT4 version 9.5 showed significantly better range agreement in our simulations compared to the earlier release 9.3. This was the most significant change noted between the two versions. No other significant changes were noted across all simulations, however on one of the stereotactic setups (157 MeV with 2 cm collimator) a small scrapping interaction that was not present in the measured data did appear in version 9.5. This caused an approximate 1.5% increase in error over a 10 mm region in this single simulation. It appears to be caused by enhanced energy loss from a scrapping interaction of the protons with the small brass collimator. Further investigation into this is warranted but was outside the scope of the current work. Our data for decreasing the phantom step max showed a small but consistent decrease in error for depth profiles, lateral profiles, and range, with the largest decrease in error for range.
These small but significant gains are balanced against the large increase in computation time seen at small values of step max. In our opinion a good trade off between these two would be a value of about 0.1 mm or 1/10th of our voxel size. This gives most of the accuracy gains with a relatively small increase in computation time. Our data for decreasing the range cuts showed no significant effect on any of our measures for simulation accuracy. Since no change in simulation accuracy was observed we would recommend a value of 250 µm of 1/4th the voxel size. While this didn’t show more accurate results than a larger value, it showed almost not increase in simulation time compared to larger values and we feel it is prudent to keep the range cuts value smaller than the voxel size. The range results seen for step max is qualitative the same as the range results seen by Grevillot et al. [4] although the magnitude of changes reported here are markedly less, while the range cuts data shown here appear to be at odds with the changes Grevillot observed. This is most likely due to the fact that the very large step max and range cuts changes shown by Grevillot et al. (with range changes of 3-5 mm) were driven by the very low number of bins/decade used in the EM tables. We used the default value for electromagnetic standard option 3, which is 20 bins/decade. This appears to dramatically lessen the influence of both step max and range cuts values. While some effect can still be seen, the choice of parameters is much less sensitive. The lateral error seen in the simulations is significantly greater than the depth error. Both the beam model modification and unique beam profiles for each energy failed to significantly decrease this lateral error (although a small effect on lateral profile was seen by modifying the beam model). The source of this increased error currently remains unknown although there are a number of possibilities. First, since some changes to the lateral profile were seen with the modification of the beam source model, perhaps further improvements in modeling of the beam in the vacuum pipe could improve simulation results. All models attempted so far have been significant over simplifications of the actual beam so perhaps a more sophisticated model could improve accuracy. Second, due primarily to beam steering the beam profile is not a static value. Our experiments have shown that beam profile, shape, size, and divergence all have an effect on the lateral profile observed in the phantom. Since these values will all be affected and change to some degree due to beam steering this makes precise matching of the lateral profile more difficult as it is a moving target in some respects. The magnitude of this effect should be looked at more closely as it may limit the achievable accuracy for lateral profiles. Third, the lateral profiles are measured with film due to its high spatial resolution; however, film has a significantly higher uncertainty (approximately 4.6-5% [6, 7] depending of film and scanner used) compared to ion chambers. The higher uncertainty in the reference measurements may limit achievable uncertainty. Fourth, other studies have reported problems with the multiple coulomb scattering algorithms in
GEANT4 [4], which will decrease accuracy of the lateral profile. This is consistent with our observations and warrants further investigation. V. CONCLUSION In conclusion we have shown that for our application of modeling a clinical proton treatment nozzle GEANT4 version 9.5 gives significantly better range accuracy than version 9.3. We have also shown by comparing simulation results to measured data that the simulations are not very sensitive to range cuts and step max parameters, but recommended values for high accuracy simulations are 250 µm for range cuts and 0.1 mm for step max. Finally, the initial beam model was shown to change the lateral profile in the phantom, however, lateral profiles still show significantly higher error rates than depth profiles. ACKNOWLEDGMENT We would like to thank Brian Harrawood from Duke University for contributing the distributed run manager code. REFERENCES [1] [2]
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